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and p is a chain-bending modulus. Within the limits of the simplifying assumptions made in the development of this diffusion model (45) the numerical factor 0 was found to be equal with 9.1 x lo4. One can assume that for a given penetrant polymer system E * , m* and p* are known or can be determined from appropriate experimental data reported in the literature. Further one can assume that AE has been estimated theoretically using this diffussion model. Then, by substituting these parameters into Eq. 5-4 one could in principle calculate a diffusion coefficient D. The problem is that both Eqs. (5-3 and 5-4) contain one parameter, namely the mean-square “jump” distance, h, which is generally not known or very difficult to determine experimentally. Thus, in order to calculate a D a “shrewd guess” is needed for h, based on similitudes with other penetrant polymer systems. In other words is not possible to use the formula for D given in the framework of this model to effectivelly predict the magnitude of D from “first principles”, i.e. thermodynamic, molecular and structural data on the penetrant polymer system. Moreover it was discussed in (50) that a correct solution of a key problem in the derivation of the statistical mechanical approach used in the Pace and Datyner model is possible only at 0 K. Adding this fact to the “shroud guessing” of h in order to produce (estimate) a diffusion coefficient largely impairs the usefulness of this model for the type of migration estimations which might be envisaged by a process engineer from the packaging sector, see Chapter 15.
c,
Modelsfor diffirsion in polymers
133
Free-volume models Among the popular methods for interpreting the diffusion of small penetrants in polymers are the so called “free-volume’’ models (6,11,13,51-54). The basic assumption of these models is that the mobility of both polymer segments and penetrant molecules is primarly determined by the available free-volume in the penetrant polymer system. The free-volume of the polymer is regarded as an “empty” volume between the chains of the polymer. Similarly the free-volume of the penetrant can be regarded as the volume not occupied between the molecules of the penetrant. Most free-volume models for diffusion in polymers follow the phenomenological basis set in (55) where the self-diffusion of an ideal liquid of hard spheres (“molecules”) has been analysed. These molecules are confined - for most of the time - in a “cage” formed by their immediate neighbours. A local fluctuation in density may open a “hole” within a cage, large enough to permit a considerable displacement of the sphere contained by it. This displacement gives rise to diffusion only if another sphere jumps into the “hole” before the first sphere returns to its initial position. Diffusion occurs not as a result of an activation process in the ordinary sense but rather as a result of the redistribution of the free-volume within the liquid of hard spheres. The model of diffusion of hard spheres is applicable to interpret self-diffusion in liquids which behave according to the van der Waals physical interaction model (56). This might be the case for simple dense fluids at high temperature, T >> T,, but it is an oversimplified model for the real diffusion of small organic penetrants in polymers. The functional relationships derived in the model of hard-spheres have been reinterpreted over course of the time, leading to a series of more sophisticated free-volume diffusion models. Some of these models are presented briefly below. An attempt to correlate experimental diffusion data with free-volume, for the system of organic vapors with polyvinyl acetate, has been made in (57). The experiments showed that in this system, for T > T,, the diffusion is Fickian and that the measured average diffusion coefficient steeply increases with the concentration, c,, of penetrant in the polymer. To quantify such a finding, an empirical relation has been proposed earlier (58): D+
= D,,,exp
(w c,)
(5-5)
where w is a parameter. To refine this approach it was proposed that the diffusion coefficient might be proportional to the frequency with which segments of polymer chains were able to undergo rotational jumps (57). The relationship between the diffusion coefficient and penetrant concentration, expressed as solvent volume fraction, v,, was derived in terms of a theory for polymer segmental mobility (59). Eventually a relation was obtained which allowed examination of the relationship between the intrinsic diffusion coefficient, D’, and v, (57). To calculate with this formula D’, some thermodynamic and free-volume parameters for the penetrant polymer system must be calculated from data given in the literature and two adjustable parameters must be determined by fitting the theoretical curves to experimental diffusion data (57). Once these data were known the formula for D’ showed an excellent fit over the concentration range which covered a 1000-fold increase of D+ (5357). Despite this positive result one can conlcude that the model has only a semi-predictive and correlative character and it would be quiet unpractical to use it for the type of diffusion coeffi-
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cient estimations currently of interest in the field of substance migration through and from polymeric packaging materials. One of the simplest early free-volume diffusion models was formulated in (51,52,60). The concept of this model was considered an advance, because some of the parameters required to describe the concentration dependence of the diffusion coefficient could be obtained from the physico-chemical properties of the polymer and penetrant. The relation proposed for the calculation of the thermodynamic diffusion coefficient, DT, was (51,60):
where Vf is the average fractional free-volume. The proportionality coefficient Ad is considered to be dependent primarily upon the size and shape of the penetrant, while Bd is a parameter which is independent of temperature and penetrant concentration. To work effectively with Eq. 5-6 the magnitude of its parameters must be determined. For this the free-volume of the penetrant poylmer system must be evaluated from viscosity data. Eventually the two adjustable parameters Ad and Bd must be calculated by fitting appropriate experimental diffusion data. For the diffusion of organic vapors in rubbery polymers, the correlation between theoretical curves and experimental data is often acceptable. In such cases the model can be used in a semi-predictive manner in order to estimate diffusion coefficients DT. beyond the penetrant concentration and/or temperature range where experimental results were collected. As already mentioned, the model includes in its formulae the adjustable coefficients Ad and Bd which cannot be determined from “first principles”. Hence, one cannot ascertain true predictive capabilities from the model and thus it is of little efective help for the practical diffusion coefficient estimations envisaged in this work. The free-volume model of Vrentas and Duda
In the last two decades Vrentas, Duda and their co-workers have published a substantial number of papers (61-67) on the free-volume model of diffusion in polymersolvent systems they developed in the late 70’s (68-72). This model, which is often cited and used in the literature, underwent a number of modifications over the years and appears to apply well to the diffusion of organic solvents in rubbery and glassy polymers. In order to develop a consistent free-volume diffusion model, there are some issues which must be addressed, namely: i) how the currently available free-volume for the diffusion process is defined, ii) how this free-volume is distributed among the polymer segments and the penetrant molecules and iii) how much energy is required for the redistribution of the free-volume. Any valid free-volume diffusion model addresses these issues both from the phenomenologic and quantitative points of view such that the diffusion process is described adequately down to the “microscopic” level. Vrentas and Duda stated that their free-volume model addresses these three issues in a more detailed form than previous diffusion models of the same type. Moreover, it was stated that the model allows the calculation of the absolute value of the diffusion coefficient and the activation energy of diffusion mainly from parameters which have physical significance, i.e. so-called “first principles”. In the framework of this model the derivation of the relation for the calculation of the self-diffusion coefficient of the sol-
vent Dls is not a trivial task. A relation can obtained which gives the dependence of Dls on the nature of the penetrant and its concentration in the polymer-solvent system, the temperature and on the molecular weight of the polymer. For a rubery polymer a condensed form of this relation, valid also for low penetrant concentration levels, can be cited from (63):
D,,
=Do
(
exp {-y
exp -RTE')
("'
w 5-+ v i s ) }
"FIi
(5-7)
For the definition of all parameters involved in the above relation see (62,63). The explicit form of Eq. (5-7) contains fifteen parameters of which thirteen can be determined from thermodynamic and molecular data of the penetrant and polymer. These parameters include: two specific hole-free volumes for the components, free-volume parameters for the penetrant and polymer, the thermal expansion coefficient of the polymer, free-volume overlap factors, glass transition temperatures, the fractional composition of the system, etc. For a non initiated reader, the procedures followed to determine these thirteen parameters are not quite simple, although the authors of the model state that the data needed for this purpose are generally available in the literature. In the scheme for the estimation of these parameters presented in (63) one can see that in order to perform calculations with the model, two parameters must be calculated by fitting the theoretical curves to experimental results obtained in the socalled "zero-penetrant" concentration limit. Thus, it is stated that using a non-linear regression analysis "...all of the parameters of the theory can be determined in general with as few as two diffusivity data points" (63). The results obtained with this complex but straightforward procedure have shown that the model provides excellent correlations for diffusivity data in several polymer-solvent systems Fig. 5-3. Having mentioned the correlative capabilities of this model, one can consider its semi-predictive abilities. It was mentioned that a number of diffusion data taken from a limited range of penetrant concentrations are required to calculate two of the parameters of the model. Once these parameters have been determined, one can make theoretical predictions for diffusion coefficients over a wider range of penetrant concentration or temperature variation. This is a critical test for any theoretical model,
0
0.2
0.4 W S
0.6
O8
Figure 5-3: Test of predictive capabilities of proposed free-volume model using data for the toluene polystyrene system. Only data points represented by solid symbols were used to obtain free-volume parameters (73).
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since an useful model should have at least an established semi-predictive capability. These results are encouraging evidence that the proposed model is a suitable tool for a more accurate description of the diffusion process in rubbery polymers. The model was most often tested by its authors for polymer-solvents systems like: polystyrene, polymethylacrylate, polyethylmethacrylate and polyvinylacetate; and for toluene, benzene, ethylbenzene as solvents. The experimental test conditions reported in (6170), especially for high concentration of solvent in the polymers, often differ considerably from what is generally of interest when these polymers are used in the packaging sector. Therefore, to assess the potential use of this free-volume diffusion model in the field of small substance migration in polymeric food packagings, the model must be tested for penetrant polymer systems which are specific for this field (see Chapter 9). Moreover it is to mention that, because the model contains two parameters which cannot be determined from “first principles” but only by fitting a limited amount of experimental data, one cannot ascribe true predictive capabilities to the model. To conclude this section, it may be interesting to mention what was concluded recently in (17) on the future of the free-volume diffusion models: ...“However, phenomenological transport models based on free-volume concepts are likely to become obsolete during the coming decade, due to the development of computational techniques of simulating polymer microstructures” .... The development of such techniques and their results are discussed in Section 5.2.
5.1.2 Diffusion in glassy polymers As already mentioned at the beginning of this section, the diffusion of small penetrants in glassy polymers is a much more complex process than that in rubbery polymers. This is due, at least in part, to the fact that free rotation of the polymer chains is restricted below T,. Thus, it was assumed that fixed microcavities or “holes” of various sizes result throughout the matrix of the polymer below T,. These “holes” are “frozen” into the polymer as it is quenched from the rubbery state (74). The concept that two mechanisms of sorption may be implicated in the diffusion and behaviour of small penetrants in amorphous glassy polymers was first suggested in (75). Here, and later in (76) it was speculated that below T, the “holes” may act to immobilize a portion of the penetrant molecules by binding them at high energy sites at the periphery of the “holes” or by entrapment in the “holes”. Based on this concept it has been suggested (77) that the sorption of organic vapors in a glassy polymer is due to two concurrent mechanisms: (i) ordinary dissolution in the matrix of the polymer (so called Henry’s law sorption) and (ii) a ‘‘hole’’-filling process obeying Langmuir’s law. This phenomenological model was accompanied, for the sorption of simple gases and organic vapors, by the equation (77): C=k,p+
a1 P
1
+
bp
(5-8)
where a], b and kD are adjustable coefficients and p is t h e pressure of the gaseous penetrant. It has been reasoned that al and b are given approximately by the statistical thermodynamic treatment of Langmuir’s isotherm (78) and kD by the lattice theory of penetrant polymer solutions (79). Later it was postulated that in Eq. (5-8) one
Models for difiiision in polymers
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may equate a l = c‘Hb and designate b and c ’ ~as “hole affinity” and “hole saturation” constants respectively (80). This quantitative description of the solution of a simple penetrant in a glassy polymer is known today as the Dual Sorption Theory (with total immobilization), (DST). The problem is that the basic assumptions of DST cannot be justified “a priori” (9). The possibility that penetrant molecules adsorbed in “holes” may not be completely immobilized is one of these problems and has been addressed (81,82). If that is the case, both the normally dissolved penetrant molecules (according to Henry’s law) and the partialy immobilized ones could diffuse through the matrix of the polymer and contribute to the diffusional flux. Moreover, in order to better describe real systems, another key postulate from the initial DST should be relaxed, namely that the normally dissolved species and those adsorbed into the “holes” are always in local equlibrium (82). That means the diffusion model should incorporate some kinetics for the immobilzation process. There will be cases where the diffusion and immobilization proceed at comparable rates; and limiting cases, where one of the two processes predominates. The phenomenological sorption theory which resulted from taking account of these assumptions is known as Dual Sorption (with partial immobilization) Theory. Because of the assumed dual sorption mechanism present in glassy polymers, the explicit form of the time dependent diffusion equation in these polymers is much more complex than that for rubbery polymers (82-86). As a result exact analytical solutions for this equation can be found only in limiting cases (84,85,87). In all other cases numerical methods must be used to correlate the experimental results with theoretical estimates. Often the numerical procedures require a set of starting values for the parameters of the model. Usually these values are “shroud guessed” in a range where they are expected to lie for the particular penetrant polymer system. Starting from this set of arbitrary parameters, the numerical procedure adjusts the values until the best fit with the experimental data is obtained. The problem which may arise in such a procedure (88), is that the numerical procedures may lead to excellent fits with the experimental data for quite different starting sets of parameters. Of course the physical interpretation of such a result is difficult. However, the mathematical formulae of DST satisfactorily present the dependence of the solubility and diffusion coefficients for simple gases and organic vapors on the concentration of the penetrant in the glassy polymer (9,11,13,15,17,33,34,89). From the point of view of earlier discussions, namely the true prediction of diffusion coefficients for volatile and nonvolatile organic penetrants in glassy polymers, the diffusion equations derived in the framework of the DST have only a limited usefulness. That means that, because the parameters of the DST models are not directly related to “first principles”, the equations can be used with success to correlate experimental results, but not to truly predict diffusion coefficients. One possible solution to this problem is to develop “microscopic” diffusion models for glassy polymers, similar to those already presented for rubbery polymers. Ref. (90) combines some of the results obtained with the statistical model of penetrant diffusion in rubbery polymers, presented in the first part of Section 5.1.1, with simple statistical mechanical arguments to devise a model for sorption of simple penetrants into glassy polymers. This new statistical model is claimed to be applicable at temperatures both above and below T,. The model encompasses dual sorption modes for the glassy polymer and it has been assumed that “hole”-filling is an important sorption mode above as well as below T,. The sites of the “holes” are assumed to be fixed within the matrix
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of the polymer. Starting from these assumptions and using elementary statistical mechanical arguments, the authors of the model estimated the values of parameters approximately, which were then included in relation to the solubility coefficient (90). For a series of simple gases diffusing in some glassy polymers, solubilty data calculated with the model were compared with experimental sorption data. Semiquantitative to qualitative agreements between theory and experiment were found. Unfortunately, for the scope of the present book, the model was not developed for estimating of diffusion coefficients in glassy polymers. Local density fluctuations occur in penetrant polymer systems both above and below T,. It is then reasonable to expect that a free-volume diffusion model should also provide an adequate description of the diffusion of small penetrants in glassy polymers. To reach this goal the free-volume model for diffusion of small penetrants in rubbery polymers, second part of Section 5.1.1, was modified to include transport below T, (64,65,72,91-93). In principle the diffusion process in a penetrant polymer system can be characterized by determining the mutual diffusion coefficient and its dependence on temperature, penetrant concentration, pressure and polymer molecular weight. When molecular relaxation in the polymer-solvent system is much faster than the diffusive transport, the conformational changes in the polymer structures appear to take place instantaneously. The diffusional transport is comparable in such cases to the transport observed in simple liquids. This type of transport mechanism is considered to characterize quite well polymer solvent systems for T > T,. As the temperature decreases towards T, the probability that a local fluctuation in density will produce a “hole” of sufficient size so that a polymer jumping unit or a penetrant molecule can move in decreases. When T < T, the “hole-free’’ volume which can be rebistributed with no energy change in the penetrant-polymer system becomes very small. Below T, the motions of the polymer are so hindered that, for a given penetrant concentration, significant movements do not occur at the time scale of the diffusion experiment. Moreover at a very low penetrant mass fraction, the structure of the glassy polymer is essentially unaffected by the presence of the penetrant and the diffusion process is Fickian (61,72,92). The diffusion process under such conditions has been denoted as an elastic diffusion process (61,71) which can be analysed using the classical theory of diffusion. In the limit of zero penetrant mass fraction these phenomenological assumptions were included into the relations of a mathematical formalism which led eventually to an expression for the dependence of the mutual diffusivity on temperature (72):
where the parameter 9+ describes the character of the change of the volume contraction which can be attributed to the glass transition. For glassy polymers, T < Tg2,the temperature dependence of D at zero penetrant concentration can be described by an apparent activation energy for diffusion, Ed, (72,93): (5-10)
Modelsfor diffiisron in pol.yniers
139
The temperature dependence of D for the n-pentane-polystyrene system both above and below Tg2 has been calculated using the formulae of this free-volume model (64). The results obtained are shown in Fig. 5-4 along with a few experimental data (94) for the same system at three temperatures below Tg2. Similarly to Fig. 5-4 for other glassy polymer-solvent systems also the predictions of this free-volume theory are in general agreement with experimental data on t h e temperature dependence of D in the vicinity of Tg2.,In particular, the theory predicts a step change in Ed at TR2,and this is consistent with most experimental investigations of polymer-solvent diffusion at temperatures just above and below the glass transition temperature (6,11J5). Vrentas, Duda and their co-workers refined in recent years their free-volume model for diffusion in glassy polymers to address also the problem of Fickian diffusion at finite solvent concentrations (64,65,92). For this the free-volume and thermodynamical parameters involved in Eq. (5-7).which gives the solvent self-diffusion coeffcient D,, in a rubbery polymer, were adapted to describe adequately the phenomenology of diffusion below the glass transition temperature,T,,,, of the polymer-solvent mixture at a particular solvent mass fraction. A series of assumptions on the structure, properties and sample history and the introduction of an additional expansion coefficient were necessary (65) to express the behavior of the free-volume parameters below Tgm.Eventually a set of equations was obtained and it was stated that using them "... calculation of D,, for glassy polymers is no more difficult that computing D,, for rubbery polymer-solvent systems" (65). However it was emphasized that the predictions of the model are sensitive to the sample preparation history. that means reasonably good agreement between theory and experiment will be obtained only for sample preparation histories which are similar to the one used in the model. Anyway one can see that up to nineteen parameters are needed to express, with this free-volume model, the concentration and temperature dependence of D1, in a glassy polymer (65,92). It is stated in these publications that all these parameters except two can de estimated from physico-chemical data generally available in the literature. To determine the remaining parameters a small amount of experimental diffusion data is needed.
-7
A
v)
\
N
E
-9
0
n
-D -11 -12
2.0
2.5
I/T . 1 0 3
3.0 ( ~ - 1 )
FigureS-4: Comparison of predictions with experiment for the n-pentane-polystyrene system (64.94).
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The reasonably good agreement between theory and experiment shown by this free-volume model (65) recommends it as an interesting tool to model the diffusion in glassy polymers used in the packaging sector. However, the problem is that the correlative, semi-predictive and predictive capabilities of this model do not address exactly the type of diffusion coefficient prediction which is of interest for the estimation of many migration processes in polymeric packagings. When we state this we are thinking not only on how difficult it would be to specify all the parameters of the model for a complex penetrant like an antioxidant or stabilizer but even more if the model is still valid for this type of polymer penetrant systems. The above sections have presented models that link the process of diffusion of small penetrants in polymers to “microscopic” features of the penetrant polymer system. Strictly speaking the type of diffusion models presented above are not truly “microscopic” because they actually describe average and not truly local - “microscopic” - properties of the penetrant polymer system. Sometimes even excellent correlations of experimental data offered by these models are due to the fact that the experimental methods used to determine the diffusion coefficients are in turn probing the penetrant polymer system over %on-microscopic” distances and comparatively long times. Somewhat closer to the designation of a “microscopic” model are those diffusion theories which model the transport processes by stochastic rate equations. In the most simple of these models an unique transition rate of penetrant molecules between smaller “cells” of the same energy is determined as function of gross thermodynamic properties and molecular structure characteristics of the penetrant polymer system. Unfortunately, until now the diffusion models developed on this basis also require a number of adjustable parameters without precise physical meaning. Moreover, the problem of these later models is that in order to predict the absolute value of the diffusion coefficient at least a most probable “average length” of the elementary diffusion jump must be known. But in the framework of this type of “microscopic” model, it is not possible to determine this parameter from “first principles”. To conclude one can state that in the framework of the “classical” diffusion models more or less complex mathematical formulae have been developed with the aim of interpreting experimental data and even offering an insight on the mechanics of diffusion. The mathematical relations for the diffusion coefficient rely on parameters which must be determined from given physico-chemical and structural data about the penetrant polymer system. But, almost without exception, these models also include a number of adjustable parameters which can be determined only by fitting experimental data to theoretical curves. In some models the physical meaning of these adjustable parameters is quite unsubstantiated. Moreover, among the earlier “classical” diffusion models some “shrewd guessing” of some model parameters is needed. Therefore one can state that the main limitation of all these phenomenological models is that they cannot truly predict diffusion coefficients only from “first principles”.
Models for rliffiision in polymers
141
5.2 Diffusion in polymers - The computational approach It was shown in the above section that as a rule, at the base of the “classical” or “microscopic” diffusion models, there are ad hoc (heuristic) assumptions on a certain molecular behaviour of the polymer penetrant system. The fact that the mathematical formulae developed on such bases often lead to excellent correlations and even semipredictions of diffusion coefficients must be aknowledged. It is true that the “classical” models are not capable to predict diffusion coefficients only from “first principles” but this is often not an obstacle to hinder their use in certain types of investigations. Therefore we are quiet sure that this type of diffusion models will certainly be used in the future too for the interpretation of diffusion experiments. The problem of diffusion modeling in polymers changes to some degree when one envisages to develop a really atomistic model, with trully predictive capabilities and without making any ad hoc assumption on the molecular behaviour and/or motions in the polymer penetrant system. In principle, a possibility to develop such diffusion modelings, is to simulate theoretically the process of penetrant diffusion in a polymer matrix by computer calculations. For this one starts by considering only an appropriate set of “first principles” which describe at a trully atomistic level the polymer and the penetrant. Then, these data about the atoms and molecules of the polymer are used to generate, by some means, a polymeric structure that has the “microscopic” and “macroscopic” properties of the true polymer, i.e. a low energetic state, an appropriate distribution of torsional angles, a physically acceptable distribution of unoccupied volume, density, and so on (95-99). Once this structure is generated a number of penetrant molecules are randomly “inserted” in it (where enough unoccupied volume is available). Then, the sytem is left to pursue its “molecular dynamics”, i.e. the atoms and molecules of the system are allowed to move in the force fields and under the interactions acting inside the system over a certain time interval. During this process there is no interference from the outside and, in particular, no heuristic assumptions are made about the molecular motions. If the process is simulated consistently enough time, by observing for example the average displacement of the penetrant species, one can eventually calculate their diffusion coefficient (98). Though, this scheme sounds very elegant and attractive its practical achievement is a complex and demanding task. Because of that computer simulation, as a method for the estimation of the diffusion coefficients in polymers, has only lately become a practicable approach. The prerequisites which make possible the development of “atomistic” simulations of diffusion in polymers are the development of powerful methods for the simulation of polymer microstructures and dynamics and also great computation capabilities of supercomputers. The first attempts in the direction of simulating theoretically at an atomistic level the diffusion of simple gas molecules in a polymer matrix were made more than two decades ago (100). But, the systematic development of “ab initio” computer simulations of penetrant diffusion in polymeric systems dates only from the late 80’s (101104). At the beginning of the 90’s it was achieved to simulate some qualitative aspects such as the diffusion mechanism, temperature, and pressure dependence of diffusion coefficients (105-109). The polymers chosen for investigation mainly fell into two categories: either they were easily described (model elastomers or polyethylene) or they were known to have, for simple permanent gases like H2, 02,N2, H20 or CH4,
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large diffusion coefficients (polydimethylsiloxane (PDMS) (11CL112) and atactic polypropylene (aPP) (113) ). The advantage of simulating at room temperature. for example the diffusive motion of H2 in aPP (D about lo4 cm2/s), is that the diffusive motion of the hydrogen molecules can already be sampled in relatively short simulations (about 0,5 ns (113) ). Based on these encouraging achievements, in the last five or six years, the interest of the researchers shifted from easy-to-compute polymer penetrant systems to those which have interesting technological potentials in such fields as: gas barriers (114117), gas or liquid separation processes (1 18-121), molded objects (packagings for example) (122) or swelling of polymers by solvents (123-126). Trying to model, theoretically, the transport of small penetrants in polymer matrices, one realizes that the characteristic length and time scales vary greatly and depend on the polymer morphology (98). Most of the polymers used technologically are either amorphous or partially crystalline. From experimental results obtained over the past four decades it is commonly assumed that both diffusion and sorption in crystalline polymers are orders of magnitude smaller than in amorphous ones (11,13,16,17,29,30). These facts determine that different theoretical and computational techniques will be appropriate for modeling the diffusion in different polymer penetrant systems (98). For the diffusion of small penetrants, i.e. simple gases and vapors of water and/or simple organic substances, in purely amorphous polymers the computational techniques of choice will be molecular dynamics, MD, (97-99, 127129) or the transition-state approach, TSA, (115,130-132). In a semicrystalline polymer a similar task can be approached for example by a Monte-Carlo 2-phase model (133). So far, the “atomistic” modeling of diffusion of small penetrants in polymers was predominantly done for amorphous polymers and using the MD or TSA techniques, which will be presented briefly in the next sections.
5.2.1 Molecular dynamics Because time is explicitly present in the formulations of MD, this technique is the most straightforward way of computer simulating the motion of penetrant molecules in amorphous polymer matrices (97-99). The MD method allows one to look at a truly “atomistic” level within the system as it evolves in time. Recently, excellent reviews on the use of MD for simulating penetrant diffusion in polymers have been published (96-99). A summary of the basic concepts and some relevant results obtained so far with MD will be presented bellow. To start a MD simulation of a diffusional process an amorphous polymer structure of the host material must first be theoretically generated. This structure must be low in energy and have the known physical properties of the polymer; chain length and distribution of torsional angles of polymer chains, density, distribution of free volume, etc. The origins of the MD approach to the problem of generating polymer structures lies in works done in the late 70’s to investigate theoretically amorphous bulk polymers (134-138). A MD approach to the problem of modeling the structure of amorphous polymers was introduced in (139) and a few years later developed in (140,141) to allow a detailed description of such systems. An overview of the various MD methods used to generate amorphous polymer structures can be found in (142). The principal methods are: (i) structural generation methods which in an ideal case are used to
Models for diffiision in polymers
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generate a structure which needs no further refinement, (ii) structural refinement methods that ideally are so efficient that the starting structure can be arbitrary and (iii) coarse-graining methods in which the atomistic model of a polymer is mapped into a coarse representation of several atoms or even monomers. To generate a polymer structure theoretically its matrix is presented as an ensemble of microscopic structures which satisfy the requirements of detailed mechanical equilibria (140). For every atom its initial position and velocity have to be specified. Chain bond lengths and bond angles are fixed. Molecular movements are allowed to occur exclusively through rotations around the skeletal bonds of macromolecules. A polymer chain meeting these assumptions is built in vacuum by an iterative process that is started from an initially guessed “parent” structure which is then relaxed to a state of minimum potential energy (140). The density of the structure obtained must eventually equal that of the simulated polymer. The free-volume in the polymer can be estimated from the generated structure. To obtain a statistical average of this free-volume, a number of structures are generated starting from different “parent” chain configurations. Once the host structure was generated the next step in the MD simulation of diffusion is to “place” (insert) the diffusant molecules into the computed structure. The condition for inserting the penetrant molecules into the structure is to find “freevolumes” where the energy is below a certain threshold and that any two of the penetrant molecules are separated by some minimum distance. Then the penetrant and polymer molecules are allowed to interact with each other and move within the limits of the constrains they are subjected to. The straightforward technique is now to follow by computer simulation the displacement of the penetrants into the potential field of the system and eventually to estimate the mean-square displacement (MSD) of the penetrant species. Among the first remarcable results of MD simulations was the finding that diffusion of small molecules in amorphous polymeric structures proceeds by “hopping” (jumping) motions (106). From a phenomenologic point of view this is not a new result if one takes into account that such a mechanism was intuitively assumed in some “microscopic” diffusion models long before the development of computer simulation techniques, see the preceeding section. The new aspect is that the computational approach has led to this picture of the diffusion mechanism starting from true “first principles” of the penetrant polymer system and not on the basis of “shrewd guesses”. To illustrate this type of motion in Figure 5-5 a typical trajectory of a water molecule through an amorphous elastomer (PDMS) is presented (119,120). From Fig. 5-5 one can clearly discern that the voids forming the free volume of the rubbery polymer are clearly separated from each other and that there are two types of motion of the penetrant molecule: - for a relatively long period of time (typically a few 100 ps) the penetrant molecule stays confined in certain small regions of space, the “cavities” of the polymer matrix. The molecule explores the cavity thoroughly without being able to move beyond the confines of the volume it resides in. Thereby the penetrant is reflected by the polymer matrix about every few picoseconds (98,119,120); - the quasi-stationary period is interrupted by quick leaps from one such cavity to another close by. The jump between the two neighboring cavities is preceeded by the formation of a channel between them. Under favourable circumstances (right momentum) the penetrant then slips through this opening, essentially without activation energy or more exactly surpassing a small energy barrier, due to the fact that
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Mercea Jump between cavities
I
Movements in
ca76
Figure5-5: A typical trace of the center of mass of one representative water molecule in a PDMS matrix (120).
the channels are on average narrow (98). The jump duration is short compared to the residence time in the cavities. A “hopping” event in a polymer matrix, as found typically in MD simulations is presented in Fig. 5-6 (106). As announced above these findings are in astonishing agreement with the “heuristic” pictures of the diffusion mechanism discussed in the framework of some “microscopic” diffusion models. But, besides being free of the conceptual drawbacks (the ad hoc assumptions) of the “classical” diffusion models, the MD method of computer simulation of diffusion in polymers makes it possible to get an even closer look at the diffusion mechanism and explain from a true atomistic level well known experimental findings. For example the results reported in (119,120) on the “hopping” mechanism reveal the following additional features. In a rubbery polymer with flexible macromolecular chains (PDMS for example) the cavities forming the free-volume are clearly separated from each other. The detailed evaluation of the movement of a penetrant particle from cavity (1) to the neighboring (2), did not show any immediate back jumps (2) + (1). This is mainly do to the fact that the channel between (1) and (2) closes quiet quickly. In a polymer with stiff chains (glassy polyimide (PI) for example) the individual cavities are closer to each other and a rather large number of immediate back jumps ocurred during the time interval simulated (120). This indicates that once a channel between two adjacent cavities in a stiff chain polymer is formed it will stay open for some 100 ps. This makes the back jump (2) -+ (1) of the penetrant more probable than a jump to any other adjacent hole (3). This process seems to be one cause for the general tendency that the diffusion coefficient of small penetrants in stiff chain glassy polymers is smaller than in flexible chain rubbery polymers. The results of MD simulations will be useful if they are able to reproduce with sufficient accuracy diffusion coefficients measured experimentally. Given the scatter between the results of different experiments reported in the literature, a computational method can be considered accurate enough if, for absolute diffusion coefficients, it reproduces the experimental values within one order of magnitude. Such results are presented in Table 5-1.
145
Models for difliision in po1ymer.s
t=6.0 PS
t=11.1 ps
k10.1 ps
(9
-
-
5A
t=12.1 ps
-
5A
t=l2.9PS
t=12.5ps
5A
t=13.3PS
I
\
t=13.7PS
t=14.1 ps
\
Penetrant molecule 5A )-------I
t=l6.1 PS Figure 5-6: Molecular dynamics simulation of a "jump" of an 0
2
molecule (106)
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Table 5-1: Diffusion coefficients calculated by molecular dynamic simulation and from experiment,
Polymer Polydimethylsiloxane
He
180.0 (300)
144
100.0 (300)
145
144
20.6 (300)
146
Pol ydimethylsiloxane
CH4
21.0 (300)
Polydimethylsiloxane Polydimethylsiloxane
H2O
15.3 (300)
112
14.5 (298)
147
EtOH
2.0 (300)
112
4.5 (298)
147
Polydimethylsiloxane Polydimethylsiloxane
H2O EtOH
20.0 (300)
1 I9
14.5 (298)
147
4.4 (300)
119
4.5 (298)
147
Polyisobutylene
He
30.0 (300)
148
5.96 (300)
151
Polyisobutylene
Hz
9.0 (300)
148
1.52 (300)
151
Polyisobutylcne
0 2
0.169 (300)
149
0.081 (300)
151
Polyisobutylene
CH4
0.63 (350)
150
1.7 (375)
152
Polyethylene
CH4
1.12 (300)
150
0.54 (296)
155
Polyethylene
CH4
1.6 (300)
112
0.54 (296)
155
Polyethylene Polyethylene
H20
7.8 (300)
150
4.4 (296)
155
0.7 ( 3 0 )
112
0.15 (296)
155
atactic Polypropylene
H2
44.0 (300)
154
-4.9'** (296)
155
atactic Polypropylene
0 2
4.0 (300)
154
-0.95'** (296) 155
atacticPolypropylene
CHJ
0.48 (300)
154
-0.24'** (296)
Pol yamidimide
HZ
0.97 (300)
143
1.3 (300)
156
Polyimide
N2
0.28 (300)
143
0.52 (300)
156
0.74 (300)
150
2.69 (300)
156
EtOH
Polyimide 0 2 Poly[ 1-(trimethylsily1)-I-Propyne] He
465 (300)
155
121
316 ( 3 0 K )
157
121
30.0 (303)
147
Poly[1-(trimethylsilyl)-1-Propyne] Oz
23.8 (300)
Poly[1-(trimethy1silyl)-1-Propyne] N2
20.5 (300)
121
36.0 (298)
158
Poly[ 1-(trimethy1silyl)-1-Propyne] CH4
16.7 (300)
121
22.0 (303)
147
Poly[l-(trimethylsilyl)-1-Propyne] CO'
4.0 (300)
121
19.5 (303)
147
Polyethylenetherephthalate Polvstvrene
CH4 CHI
-0.0063"
(333)
-0.056" (3251
117
0.0031 (333)
80
116
0.0338 (323)
159
(* diffusion coefficient extrapolated from higher temperatures) (** diffusion coefficient estimated from data for semicrystalline PP)
The results given in Table 5-1 show that the agreement between the diffusion coefficients predicted from MD simulations and experimental ones ranges from reasonable to excellent. At temperatures around 300 K this is found both for polymers which are above their glass transition temperature, T,, (PDMS, PIB, PE and aPP) and for polymers which are below T, (PET, PS, PTMSP, PI and PAI). As a trend one can notice, and this not only from Tab. 5-1 but also from other works published in the last six or seven years, that the agreement between MD simulations of diffusion and solvation of small penetrants in polymers and experiment steadily improved. These are encouraging developments, showing that modern softwares (some of them available for
example from the Molecular Simulations Inc./San Diego. CA, USA) and powerful computers (for example IBM RS 6000 workstations or Cray C916 supercomputers) are capable today to model and predict diffusional processes for a certain range of polymer penetrant systems. The spread of this range is given by the general conditions tied to the ability of the MD procedure to simulate a polymer penetrant system large enough to sample the configurational statistics of the polymer sufficiently well. For a simple polymer like linear polyethylene with flexible chains one may need a few hundred [-CH2-] repeat units or a few hundred to a few thousand atoms (98). To generate a bulk PDMS structure in which 3 water molecules are “inserted” 220 monomer units [-Si(CH3)2-O-], i.e. 2238 atoms, were for example used in (119). One might expect that many more repeat units are needed if the polymer has stiff chains (98). However, it should be noted that it is the number of flexible bonds in a chain and not just the number of repeat units that is a decisive parameter for the achievable quality of the amorphous polymeric structure generated from a chain (143). Other factors determining the range of application of the MD method arise from the mobility of the penetrant itself. To be sufficiently precise with the computer simulation one needs to observe, say, 10 jump events for every single penetrant (which is probably the bare minimum). At equilibrium and assuming hopping motion the diffusion coefficient can be given by Eq. (5-3), where h is now the mean-square “jump” distance and v-’ the average residence time between jumps. Hence for a D of about 5 x lo-‘ cm2/s (a comparatively high diffusion coefficient for packaging applications) and a “jump distance” of about 0,5 nm (see (117) for example) one finds that in an 1 ns simulation one will encounter about 12 jumps on average. It is interesting to notice that if the MD simulation is done in steps of 1 fs (121) 10‘ time steps must be computed to complete a 1 ns simulation. To simulate with MD slower diffusion processes, i.e. smaller D, one must either extend the duration of the simulation (and hence the computing time and costs) or to “insert” several penetrants at the same time in the generated polymer structure and thereby improve the quality of the sampling (98,117,119,120). However, the later option is valid only if the diffusion coefficient is not very sensitive to the penetrant concentration. With nowadays softwares and computers MD simulations can be extended to about 10 ns which brings the D of about 5 . cm2/swithin reach of the method. Diffusion processes which evolve at a rate of 5 . 10-’cm2/s or faster are typical for: - the diffusion, at very low concentrations, of small penetrants (simple gases or vapors) in low barrier polymers: i.e. polyethylenes (112,1.51), polypropylenes (160), polybutadienes (149-151) and siloxanes (112,119,144) at room temperature or polystyrene (116), polyethylenetherephthalate ( I 17) well above room temperature, - the diffusion, at room temperature, of simple gases and vapors through glassy polymers with large interchain regions: i.e. Poly[ 1-(trimethylsily1)-1-propyne](1 17) and cis-poly(tert-butylacetylene) (161). However in the packaging sector the large majority of the diffusion processes in polymers imply penetrants with a relative molecular weight ranging between 100 and 1200 daltons and have often quite complex structures. From experiments one knows that these diffusion processes are characterized by D ranging from lo-’ to 10-’2cm2/s or even lower levels (see Appendix I). In (98) it was stated that, to study with MD techniques polymer penetrant systems in which the D are that small, is certainly out of reach for several generations of supercomputers to come.
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The posibility of extending MD to slower diffusion processes has been discussed (98). But applying such algorithms has a tradeoff on the overall quality of the computational approach. To perform calculations at time scales beyond those accessible to MD is possible nowadays only by using the transition state approach (TSA) proposed in (97,115,132). This method will be presented briefly below.
5.2.2 The transition-state approach As already mentioned in Section 5.1.1 one of the early theoretical models of gas diffusion in solid polymers (3,37,162) was based on the Transition-State Theory (TST) (40). More than fifty years ago it was assumed ad hoc that gas molecules move through a dense polymer in a series of activated “jumps” between “holes” which exist in the polymer matrix. Fortunately, results of “ab initio” MD simulations, Section 5.2.1, demonstrate that the computed trajectories of small penetrants in atomistic structures of dense polymers are consistent with the “heuristic” picture of this early “classical’’ model. In its framework it was estimated, from solubility data, that at room temperature the vibrational frequency v,, of the gas molecule trapped by the surrounding chains is of about 10l2 ssl (163). This finding is also in reasonable agreement with the bouncing frequency of a small gas molecule inside a “cavity” of the polymer matrix, as found in MD simulations. These results indicate that the “jumps” of a penetrant in a dense polymer could be treated as an elementary process, thus justifying the use of TST for developing a computer simulation technique to evaluate the rate of the penetrant’s jumps and out of this the diffusion coefficients. The development of a Transition-State Approach (TSA), based on a simplified description of thermal motions in the host matrix and stochastic methods in treating the penetrant dynamics, promises to allow much longer simulation intervals than MD can practically achieve nowadays (about 10 ns). This feature is important because: (i) the occurence, in some polymer penetrant systems, of anomalous diffusion (115,130) leads to the necessity of carrying out very long MD simulation runs for penetrants to enter the Einstein diffusive regime (97,98) and (ii) unpracticably long MD simulations would be needed to simulate and predict slower diffusion processes, Section 5.2.1 and Appendix I. In the development of the TSA besides the “jumping” mechanism already mentioned another fundamental mechanistic feature assumed is that the penetrant dynamics is coupled to the elastic motion of the polymer chains, but, to a first approximation, is independent from the structural relaxations of the matrix (973 15,130,132). The thermal motion causes the polymer matrix to move in its configurational space. At short times the vibrational modes of motion dominate: vibration of chemical bonds or bond-anlges, small-amplitude rotations of side groups or wiggling of torsion angles. As time goes by, the system tends to perform structural relaxation for example through torsional transitions in the main chain or in side groups. Using MD to simulate an appropriate penetrant trajectory one can specify an upper bond for times at which the system at hand can be treated as essentially executing elastic motions (97). Elastic motion implies that the atoms of the matrix fluctuate about their equilibrium positions. Allow now a small dissolved molecule to reside in the system and suppose that one can neglect the correlation between the structural relaxation of the matrix and the dynamics of the penetrant. In this case one can write a penetrant distribution
Models for diffiision in polymers
149
function p(r) which is obtained by integrating over all possible values of the deviations of the host atoms the result of the potential energy of interaction between the dissolved molecule and the host atoms and a normalized probability density, W((A)), describing the elastic fluctuations (132). The function p(r) is related to the Helmholtz energy, A(r), of the dissolved molecule at location r according to a general equation given in (164). The TST can be used then for describing the spatial movement of a dissolved molecule as a series of activated jumps between adjacent local minima of A(r) (132). The rate constants Ri.j for the penetrant’s transition from site i to site j can be written as (40): (5-11)
where Q,,, and Q, denote partition functions of penetrant on the crest surface between sites i and j and in site i , respectively. In Eq. 5-1 1 k* is a transmission factor taken to be about 0.5 (132). It was shown that in the quasi-classical case one can link Q,,, and Q, to the function p(r) (164). Hence, specification of the elastic fluctuations of the atoms of the host matrix through the probability density W((A))yields p(r) which, in turn, yield the transition rates R,,, (130). If the network of local minima of A(r) with the associated R,.,’s are known, one can use stochastic methods to evaluate the correlation function describing the penetrant dynamics (130,132). The procedures of simulating the dynamics of guest molecules on the network of sites and of evaluating W( (A)) were described in (1 30) and (132), respectively. An important parameter in these procedures is the mean-square deviation, (Am2), of host atom o! from its average position. The values of (A$) are expected to depend on the time scale of averaging: for very short times (Aa’) increases with time approaching then, by definition of elastic motion, an asymptotic value. Using atomistic short-scale trajectories calculated with MD and specifying an averaging time one can calculate for (Am2) a “smearing” factor (A2) and use it in the TSA simulations (97,132). Another possible way to evaluate (A2) is to match the short-time region of the meansquare displacement, (r2), of the penetrant versus time curves obtained from TSA with those from MD calulations (97). To follow to actually carry out a TSA simulation a three-dimensional grid, with grid interval of about 0.2 A ( 5 . lo6 equispaced points in (132)) is built and the Helmholtz energies at all grid points are computed. Before this can be done in practice, a value for (A2)must be found. Then, local minima and the crest surfaces must be found, using the procedures given in (130,132,165). To study the dynamics of the penetrant molecules on the network of sites a Monte-Carlo procedure is employed, which is presented is some detail in (97). Eventually the stochastic trajectory of a dissolved molecule is obtained and subsequently by averaging a large number of such trajectories, about lo3 in (132), the diffusion coefficient D of the penetrant in the polymer can be calculated from the plot of (r2) versus the time t (using for the linear portions (Einstein diffusion) of the curves a simple equation similar to Eq. 5-3). In Figure 5-7 the (r2)’s of He and Ar in glassy polycarbonate, PC, at 300 K , as calculated with TSA, are shown. The results plotted in this figure represent averages over 500 independent simulation paths. The simulations presented in Fig. 5-7 show a region of “anomalous diffusion” of the penetrant He for (r2)’ssmaller than =lo3A2(simulation interval of ~ 0 . ns) 5 . This is similar those reported in (98,166) on the MD simulation of H e diffusion in rubbery polyisobutylene, where the transition to normal diffusion was captured at around (r2)=10A2 and a sim-
150
Mercen
-14
-12
-10
-8
lg t (s)
-6
’
Figures-7: Computed dynamics of He and Ar in polycarbonate at 300 K (132).
ulation interval of 4 . 1 ns. It is believed that this anomalous behavior is caused by a separation of time scales consistent with the jumping pattern (98). The very fast motions of the penetrant molecules inside the cavities (timescales of several 100 ps) is determined by the shape of these cavities. Therefore these motions don’t have a random-walk-like behavior and consequently it is not appropriate to use the Einstein equation, i.e. D = (r2)/6t (which similar to Eq. 5-3), to calculate D. In fact the Einstein equation holds true if the slope of the log (r2)versus log t plot is equal to one. A direct consequence of this fact is that, in order to predict diffusion coefficients, a MD or TSA computation must simulate a time interval long enough to get fulfiled the above requirement. For some polymer penetrant systems this means already the need to carry out simulations over time intervals that are out of reach of the MD method ( t > 10 ns) (120,130,132). In these cases the method of choice will be the TSA. In Table 5-2 a comparison between diffusivities obtained with the TSA method and experimental D is presented. From this table one can see that, in all cases computed D agree with experimental data to within an order of magnitude. Moreover most of these D are considerably smaller than the 5 . lo-’ cm2/s lower threshold assumed to be in reach of nowadays MD simulations Section 5.2.1. This is an encouraging sign that computer simulations of diffusional processes are already able to predict, with a reasonable accuracy and for small and simple penetrants, diffusion coefficients around cm2/s. From the point of view the packaging sector it would be interesting to learn if and when further theoretical developments of the TSA method will be able to simulate (predict) such slow diffusional processes for organic penetrants with a much more complex structure, see Chapter 3 and Appendix I. Two “atomistic” approaches have been presented briefly above: molecular dynamics and the transition-state approach. They are still not ideal tools for the prediction of diffusion constants because: (i) in order to obtain a reliable chain packing with a MD simulation one still needs the experimental density of the polymer and (ii) though TSA does not require classical dynamics it involves a number of simplifying assumptions, i.e. duration of jump mechanism, elastic polymer matrix, size of smearing factor, that impair to a certain degree the “ab initio” character of the method. However MD and TSA are valuable achievements, they are complementary in several
151
Models f o r diffiisinn in polyniers
Table 5-2: Diffusion coefficients calculated with the transition-state approach and from experiment. Polymer
Diffusant
D"dC (cm'is) lo7 Cnl ( K )
Ref.
Dex7 (cm2/s)10 @I ( K )
35.0 (300)
132
64.6 (308)
Ref
Pol ycarbonate
He
Pol ycarbonate
0 2
0.10 (300)
132
0.56 (308)
167
Polycarhonate
N2
0.(19 (300)
112
0.18 (308)
167
Pol yamidimide
H2
120
9.4 (300)
I20
Polyamidimide
0 2
0.40 (300)
120
0.30 (300)
120
Polyamidimide
NZ
0.20 (300)
120
0.10 (300)
120
Polyimide
0 2
15.3 (300)
120
7.40 (300)
120
15.9 (300)
Polyimide
N7
2.6 (300)
120
Polyvinylchloride
He
17.0 (318)
97
40.0 (318)
2.80 (300)
167
I20
147.168,169
Polyvinylchloride
Ne
2.0 (318)
97
4.0 (318)
147,168,169
Polyvinylchloride
Ar
0.04 (318)
97
0.05 (318)
147.168.169
Pol yvinylchloride
Kr
0.003 (318)
97
0.01 (318)
147,168,169
ways and can be used to predict the diffusion coefficients of small penetrants (so far simple gases and simple organic vapors) in both rubbery and glassy amorphous polymers. These computational methods can be used to understand the behavior of small penetrants in the matrix of a polymer starting from an "atomistic level" and without ad hoc assumptions on the movements of the polymer chains. In this respect M D is the less coarse-grained of the two methods. The main drawback of M D is the computational cost that nowadays prohibits simulations beyond 10 ns, which are still being far from routine. The TSA is well suited to extend the time-scale of simulations, bringing new phenomena within reach. In this respect it is important to use M D and TSA in conjunction. The limitations of the TSA. as developed so far, are evident when one intends to simulate' penetrant polymer systems where there is strong interaction between the penetrant and the host atoms, or where larger penetrant molecules require a deformation of the polymer structure for their passage. In such systems, as well as in systems where the penetrant induces a swelling of the polymer matrix, MD seems to be the method of choice to properly simulate the diffusion mechanism (125,126,170).
5.3 Conclusions A process or manufacturing engineer is often confronted with the difficult and expensive task of measuring experimentally the migration (diffusion) of rather complex organic molecules in rubbery o r glassy semicrystalline polymer matrices. For such systems the knowledge/prediction of diffusion coefficients would he crucial for the theoretical estimation of substance transfer for example from a polymeric packaging into the wrapped good (foodstuff, medicine, etc.). Therefore a theoretical method/model for performing the true prediction of diffusion coefficients for small organic penetrants in rubbery and glassy polymers would be of great help to reduce
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the costs and worktime nowadays spent in the field of polymer packaging research and law enforcement. The problem is that ideally such a theoretical method/model should be as simple as possible, rely on parameters, which for the penetrant polymer systems specific in the packaging sector, are well known and easily available and, at last but not at least, the use of the method to predict diffusion processes should not consume more time and resources than the direct migration/diffusion experiments. If a given diffusion model cannot meet the one or the other of these requirements, from a purely pragmatic point of view, a process engineer or law enforcer may not see incentives to use the theoretical approach instead of a well established experimental one. Unfortunately, it seems that none of the diffusion models presented in the above sections meets completely these practical goals. It is beyond any question that the type of “classical” diffusion models presented in Section 5.1 were, at the time of their conceivement, important steps for the qualitative understanding of the phenomenology of penetrant diffusion in polymers. Moreover some of these models are very successful in rationalizing average experimental diffusion coefficients with macroscopic parameters as temperature and penetrant concentration. Trying to use these models for predicting diffusion coefficients for penetrant polymer systems which are specific in the packaging sector one is confronted with several problems. First, with no exception, in all “classical” diffusion models one or more adjustable parameters enter in the formula of D. To calculate the magnitude of thislthese parameter/s a number of diffusion experiments must be performed with the very penetrant polymer system which one intends to simulate theoretically. In practice such experiments most often require quite sophisticated equipment to obtain the experimental data, and often non-trivial theoretical schemes to evaluate them. The attempt to save experimental work by using the adjustable parameters determined for a certain penetrant polymer system in order to estimate/predict Ds in a related system is generally not recomendable. Hence, in a first step, in order to use one or other of the “classical” diffusion models, one is forced to replace migration experiments with diffusion ones. Then, as already mentioned, once all adjustable parameters in the formula of D are known semi-predictions and predictions of D can be made most often only if the physico-chemical parameters of the system (temperature, concentration, pressure, degree of swelling, etc.) do not vary beyond a relatively limited range. Finally, in some of the most widely used “classical” models - the free-volume models of Fujita, Vrentas and Duda and their alternatives (171-175) - more than a dozen structural and physical parameters are needed to calculate the free-volume in the penetrant polymer system and subsequently the D. This might prove to be a relatively simple task for simple gases and some organic vapors, but not for the non-volatile organic substances (rest-monomers, additives, stabilizers, fillers, plasticizers) which are typical for polymers used in the packaging sector. As suggested indirectly in (17) sometimes in the future it will maybe possible to calculate all the free-volume parameters of a “classical” model by using MD computer simulations of the penetrant polymer system. On the other hand, based on the rapid progress which was recorded in the last decade in the “atomistic” simulation of diffusion processes in polymers one may be confident that these computational methods will be one day able to cope with the prob-
Models for diffiision in polyniers
153
lem of a true prediction of D for the type o f migration estimations envisaged with polymeric packagings. In our oppinion this will be not an easy target to reach. As is well known todays MD simulations are better suited to describe at a true atomistic level the host matrix and the dynamics of the penetrants. However, most of the MD performed so far are dealing with purely amorphous polymers and with very simple penetrants. In the packaging practice however most of the polymers are partly crystalline and the penetrants are often complex organic molecules. In (98) it was mentioned that a straightforward atomistic MD simulation of a semicrystalline material is not yet achievable, since crystallite dimensions may range from several 10 nm to several microns and crystallites often aggregate to form larger domains of macroscopic dimensions (3536). In contrast, typical MD simulations use, for completely amorphous structures, cells with a length of a few nm. Therefore to simulate a semicrystalline cell several orders of magnitude larger seems to be completely out of question for nowadays computers. The possibility to adopt a less atomistic viewpoint and use a Monte-Carlo 2-phase simulation technique for semicrystalline polymers was analysed in (98). One should also not forget that the typical organic molecule migratingldiffusing from a polymeric packaging has usually a geometry differing strongly from that of the penetrants investigated so far with M D simulations. Moreover, at an atomic level, the interaction of most such organic molecules with the host matrix is much stronger and difficult to quantify that the interaction of simple permanent gases with the same matrix. If further developments of the MD and/or Monte-Carlo 2-phase techniques will be able to simulate at an atomistic level the dynamics of a semicrystalline polymer and of a complex organic penetrant the question remains: how long will be the time interval simulated? According to those mentioned above in Section 5.2.1 simulations of a few 100 ns to a few ps are needed to predict D in the range of 10-"' to 10-"cm2/s, which is often found in technical applications of polymers. From todays perspective the computer time (and costs) needed for a MD simulation of such duration are out of reach in the near future. With the TSA developed in (115,130,132,165) it was possible to almost reach simulation intervals of 1 milisecond. This makes in principle possible to predict D as small as a few cm2/s. Therefore the TSA seems to be a good choice to predict D for the type of diffusion processes encountered in packaging applications. But for this, the actual TSA algorithms must be developed to take also into account strong interactions between the penetrant and the host atoms, and the deformation of the polymer structure at the passage of complex penetrant molecules. We are confident that sometimes in the future suitable computational approaches and powerful hardwares will be available to predict D of additives, stabilizers, monomers, dyes and/or plasticizers in polymeric materials used in packaging applications. To evaluate, if such an endeavour may help to reduce the considerable volume and costs of experimental migration testings peformed nowadays, it is necessary to consider also the following aspects. How much software development and computing time will be needed to predict the D for a penetrant polymer system not yet investigated? In (120) it was stated that even the rather fast TSA simulation technique will presumably not lead to a fast predictability of transport paramaters for large numbers of hypotetical polymers in the near future. This was mainly atributed to the fact, that the construction of well equili-
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brated polymer packing models is still demanding large amounts of computer time (not to mention the much longer time needed to effectively develop the appropriate algorithms). Then an important aspect is how precise the predicted D will be? So far an agreement within one order of magnitude between an experiment and an atomistic simulation is considered to be a good achievement. For completely amorphous polymer structures and simple penetrants even better agreements have been reported in Tables 5-1 and 5-2. From the point of view of estimating the migration from polymeric materials used in the technical sector a prediction of D within the order of magnitude of the experimental one would be a result of certain practical use, see Chapter 15. The question is: to what sophistication must be developed the computer simulation approach to meet this requirement also for the type of penetrant polymer systems which are usual in the named sector? In the end it is legitimate to mention that for a considerable number of process engineers and law enforcement personnel the material costs of using an atomistic computational approach to predict a D and subsequently use it in a migration estimations will also play an important role. Pragmatically speaking one can expect that somebody interested to reduce its expenses for migration testings from polymeric packagings, will not have to much interest to replace these tests with much more expensive and less precise theoretical simulations! Therefore, from the point of view of the practical value of migration estimations in the technological sector, it will be maybe worthwhile to compare the trade-off between the cost and precision of estimating a D with the “upper bond” concept presented in Chapter 15 with the cost and precision of predicting the same D with an atomistic computer simulation (when this will be achievable). References I . Mitchell, J.K., Philadelphia J.Med.Sci., 13 (1831) 36.
2. Graham, T., Phil.Mag., 32 (1866) 401. 3. Barrer. R.M.. “Diffusion in and through Solids”. Cambridge University Press. Cambridge, 1951.
4. Tuwiner. S.B.. “Diffusion and Membrane Technology” ACS Monographies. Reinhold. New York,1962. 5. Rogers, C.E., “Solubility and Diffusivity” in “Physics and Chemistry of the Organic Solid State”, Fox. D., Labes. M.M.. Weissberger. A.. (Eds.),Intescience, New York, 1965, p. 509. 6. Crank, J., Park, G.S., “Diffusion in Polymers”. Academic Press, London, 1968. 7. Stannett, V.T., Hopfenberg, H.B., Petropoulos, J.H., “MTV 1nt.Rev.Sci.. Macromol. Sci.. 8 (1972) 329. 8. Hwang, S.-T.. Kammermeyer, K., “Membranes in Separations”, Wiley Interscience. New York. 1975. 9. Vieth, W.R., Howell, J.H.. Hsieh, J.H.. J. Membrane Sci., l(1976) 177. 10. Meares, P., “Membrane Separation Processes”, Elsevier Scientific, New York, 1976. 11. Stannett,V.T.. Koros, W.J., Paul, D.R., Lonsdale, H.K., Baker, R.W., Adv.Polyrn.Sci., 32 (1979) 71. 12. Mason, E.A.. Lonsdale, H.K., J. Membrane Sci.. 51 (1990) 1. 13. Frisch. H.L., Stern, S.A., “Diffusion of Small Molecules in Polymers”. CRC Crit.Rev. Solid State and Materials Sci. 11 (1983) 123. 14. Rogers, C.E., Machin. D., CRC Crit.Rev. Macrornol. Sci. (1972) 245. 15. Vieth. W.R.. “Diffusion in and through Polymers”. Hanser, Munchen, 1991. 16. Koros. W.J., (Ed.), “Barrier Polymers and Structures”, ACS SyrnpSer. 423, Arn.Chern. Soc., Washington, 1990. 17. Stern. S.A., J. Mcmbrane Sci., 94 (1994) 1.
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Reactivity in Molecular Crystals Edited by Yuli Ohashi Copyright @ K d a o r h a Ltd .Tokyo. 1999
6 Prediction of diffusion coefficients in gases, liquids, amorphous solids and plastic materials using an uniform model Otto Piringer
6.1 Introduction Diffusion is a mass transport process resulting from random molecular motions. Such molecular motions occur in gases and condensed phases and can be described in principle as using the commonly held theoretical picture of “random walk”. This means the particles (molecules, atoms) move in a series of small random steps and gradually migrate from their original positions. Each particle can jump through a distance h in a time 7. But the direction o f each step may be different, and the net distance traveled must take the changing directions into account. The coefficient of diffusion D is related to h and z in the Einstein-Smoluchowski equation: 2
D = h
2r
If A/T = C, and h are interpreted as the mean speed of the particle and the mean free path, then Eq. (6-1) has the same structure as the following equation obtained from the kinetic theory of gases:
where k is the Boltzmann constant,
where M A H= 2((1/MA)+(1/Mfi)]-’, with molecular weights M A , and MB. oASis a characteristic length, n is the number density of molecules in the mixture, Q, is the diffusion collision integral a n d f n a correction term with the order of unity.
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The collision integral for diffusion depends upon the choice of the intermolecular force law between colliding molecules and is a function of temperature. The characteristic length also depends upon the intermolecular force law selected. In comparison with the simple Eq. (6-2) for perfect gases, Eq. (6-3) takes into account the interactive forces between real molecules. But, while in the first case only two specific parameters are needed, the diffusion collision integral, Q,, is a complicated function of several parameters. Whereas h and T are characteristic parameters of microscopic particle motion, the diffusion coefficient D is a specific macroscopic parameter. A main difficulty in predicting D for condensed systems lies in the derivation of correct expressions for the microscopic parameters. The most common basis for estimating diffusion coefficients in liquids is the Stokes-Einstein equation:
in which D L is related to another macroscopic parameter, the viscosity q of the medium. The solute radius is denoted by a. It must not be forgotten, however, that Eq. (6-4) was derived for a very special situation in which the solute is much larger than the solvent molecule. Nevertheless, many authors have used the form of Eq. (6-4) as a starting point in developing empirical predictions. A significant difference in Eq. (6-4) compared to Eqs. (6-2) and (6-3) for gases lies in the effect of temperature on the diffusion coefficient in liquids. This can be assumed via the viscosity q to be an exponential function of the form Aexp(-BIT). Diffusion coefficients in solids are commonly expressed as exponential functions: Ds
= Do
exp
( )::
--
(6-51
where the pre-exponential athermal factor Do and the molar enthalpy AH are estimated empirically. As shown in the previous chapter, the diffusion behavior in polymers lies between that of liquids and solids. As a consequence, the models for diffusion coefficient estimation are based on ideas drawn from diffusion in both liquids and solids. In general, diffusion coefficients in gases can be often be predicted accurately. Predictions of diffusion coefficients in liquids are also possible using the Stokes-Einstein equation or its empirical parallels. On the contrary in solids and polymers, models allow coefficients to be correlated but predictions are rarely possible. The aim of this Chapter is the development of an uniform model for predicting diffusion coefficients in gases and condensed phases, including plastic materials. The starting point is a macroscopic system of identical particles (molecules or atoms) in the critical state. At and above the critical temperature, T,, the system has a single phase which is, by definition, a gas or supercritical fluid. The critical temperature is a measure of the intensity of interactions between the particles of the system and consequently is a function of the mass and structure of a particle. The derivation of equations for self-diffusion coefficients begins with the gaseous state at pressures p below the critical pressure p p A reference state of a hypothetical gas will be defined, for which the unit value D,, = 1 m2/sis obtained at p = 1 Pa and a reference temperature, T,. Only two specific parameters, Tc, and the critical molar volume, Vc,of the mono-
Prediction of dcffiision co~ffi:cir17ts it7 gnse.~,Iiqiiids, anzory/ioris soIids ._.
161
atomic system particles are needed and, for the reference state, their corresponding values are defined by the equation of the diffusion coefficient, DG. The equation for the diffusion coefficient in a gaseous state, DG, is the starting point for the derivation of an equation for diffusion coefficients in an amorphous solid state (S). The homologous series of n-alkanes is used as a reference class of chemical compounds which asymptotically reach an unlimited molecular chain in the form of polymethylene. The diffusion coefficient, Ds,ji, is derived theoretically for a member of t h e series with j carbon atoms at infinite dilution in a matrix of a n-alkane with i carbon atoms in the molecule. In addition, the diffusion in polymethylene, which is considered as the reference structure for all polymers is also derived theoretically. The corresponding diffusion coefficient in the liquid state (L), DL,ji,is derived from D,5.jiand DG. Starting from the reference class of n-alkanes, diffusion coefficients can be estimated for any solute and matrix with corresponding specific values for the critical temperature and critical pressure of the matrix and the critical molar volume of the solute. For any polymer a value is needed for a specific structure parameter instead of the critical temperature and pressure. Due to the very complex structure of most plastic materials, this value must be determined experimentally using a reference solute in a diffusion measurement. In order to facilitate the theoretical treatment, the above mentioned homologous series of n-alkane chemical compounds is used as a reference compound class. The structures of the individual members of this series do not deviate significantly from one another. Out of all known classes of chemical compounds the saturated open-chain and non-branched (normal) hydrocarbons, the n-alkanes, or n-paraffins, represent the most frequently studied homologous series with the largest number of available members in pure form. The number of carbon atoms of a n-alkane, i, or more exactly, the i structural methylene groups including the two methyl end groups, can be interpreted in such comparisons as playing the role of i identical sub-units which compose the molecule. The properties of a macroscopic n-alkane sample can then be described as a function of i sub-units making up every molecule of the macroscopic system. The homologous series of n-alkanes is used as the reference backbone. Each member of the series represents a macroscopic system of identical particles (the n-alkane molecules) and the particles of the system themselves represent sub-systems of i uniform structural units. At room temperature systems in all physical states occur among the series of n-alkanes.
6.2 Interaction model As mentioned in the introduction, the discussion starts from a macroscopic system composed of n>>l identical particles. Among the particles there exists an attractive interaction that is responsible for the formation of condensed phases. The particles on the other hand possess a certain degree of freedom of motion in any direction within the system, as required by the liquid state. Because no preferred distribution of particles can be assumed, the system seems on average to be totally homogeneous and isotropic. This leads to an essential simplification of the problem. The background process in all interactions is an energy exchange between the n particles of the system, which is related to a change in position of the particles by oscillation and/or translation.
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6.2.1 Model assumptions The following assumptions apply to systems of n identical particles (molecules, atoms) that leave their chemical identities essentially unchanged. Above a certain number of particles in the system, the sum of all interactions on a single particle by the other particles of the system becomes independent of the number of particles. This allows identification of a macroscopic system by its specific properties. 1. The interactions between the n particles are based on an exchange of discrete values E, = d~,, of energies E relative to an unit amount E ~ , .The consequence of this exchange is a relative density of interaction energy qGn= ( l + ~ $ n ) "in form of a n-fold product with the limit value q, = exp(e,) for n+w. The exponential expression is assumed because (i) the exponential function represents a mathematical order of magnitude which is higher than that of any other power of E,, this means exp(E,)IEra +ffi for a > 1 and E, +ffi;
($it reaches a constant value, independent of the number of particles in a macroscopic system with n>>l. The relative density q, is again considered a starting point for additional dynamic processes occurring in the system. Self-diffusion of the particles is an example of such a process. Based on the same mathematical assumption (i), the magnitude of the diffusion coefficient D = D,,exp(q,) is derived as an exponential function of q, with an unit amount D,,. This assumption is further supported by many empirically established equations describing dynamic properties of macroscopic systems. 2. A common characteristic of all particles is their extension in space, which means they possess a finite volume surrounded by a surface with area A . This area is equivalent to A for a surface of revolution which equals the product of the length of a meridian y and the length of the path of the center of gravity of y when y is rotated through the angle 211 (the theorem of GuldinIPappus):
The common function of all particles, independent of their specific structure is the ratio AIY = 2 7 ~The amount of energy transferred from one particle during an interaction step (see assumption 1 ) can now be written as E, = E: + a = 211 + a, where a is a specific parameter of the system and E: = 211 is defined as the relative reference exchange energy. 3. Mathematically, the interaction process is assumed to be an exchange of energy between n particles and can be treated as a permutation. Both the n particles and their n starting positions are labeled with the natural numbers 1, 2, ..., n. The whole process of energy exchange can now be understood as a result of n! consecutively occurring individual interaction steps. Each individual step represents a transport of one energy quantum from one partide to another and is interpreted mathematically as one change of places between the two particles. The total number of such place exchanges equals n!. The relative number, pI1,of exchanges related to n! in which n o particle remains in its starting position is then: Pn
=
I
1
-3!
+ .... + (-1) n 2l
;
lini pn = pc = 1 e
n--x
(6-7)
Prediction o,f diffiision coefficients in gases, liquids, amorphous Jolids .__
163
The limit value p e = l/e for n>>l is designated as the maximal probability of a place exchange in a macroscopic system. With these assumptions a common characteristic of all macroscopic particle systems can be expressed as qr = exp(e,) = exp(2n + a) (assumptions 1 and 2). However, taking into consideration a diminution of E, which is proportional to the maximum probability p e of place exchange (assumption 3), the value qr = exp(e,p,) = exp[(a + 2x)/e] = ea/ee2n/r= C 1 ’ e becomes ~ the specific relative density of interaction energy for a system where w = grde and C1le= e(d‘’. A special case occurs whenever the II particles are molecules from a homologous series of chemical compounds, e.g. n-alkanes. In such a case the specific parameter C can be enlarged into C = C0(l+2x/i)’, where i represents the number of carbon atoms in an unbranched alkane chain and C1Ir= C0”c’(1+2x/i)de = Kwi.
If a specific property f(i) of the macroscopic system can be correlated with qCiin form of a direct proportionality, than a simple dimensionless relationship between the values of this property for two members i and k of the homologous series results from Eq. (6-8):
The number w = eZde derived from the three assumptions of the model is the common limit value of the two power sequences:
These power sequences, designated as interaction functions, represent the mathematical backbone of the model described in this chapter.
164
Piringer
6.3 Prerequisites for diffusion coefficients 6.3.1 Critical temperatures of n-alkanes The critical temperature may be considered to be a measure of the intensity of interaction between the n particles of a system, as produced by van der Waals forces. Although the critical temperature for n>>l is practically independent of the number of particles, there exists a possibility for estimating the influence of the number of i structural subunits composing a particle based on the value of the critical temperature of a macroscopic system. Critical temperatures are especially suitable for the comparison of numerical values within a homologous sequence because at these temperatures the systems are in corresponding states. If Tc,iand Tc,kare designated the critical temperatures of two different n-alkanes containing i and k carbon atoms, we may tentatively let the dimensionless ratio Tc,i/Tc,kbe equal to the ratio of the two corresponding interaction functions w ~ and , ~ Wk,e in Eq. (6-9): (6-11)
Experimental values for the critical temperatures of n-alkanes are known up to eicosane (i=20) (Reid et al., 1987). For longer molecular chains the experimental determination of the critical temperature is not possible with sufficient accuracy due to the onset of thermal decomposition. By means of Eq. (6-11) it is possible to calculate, starting from each experimental value corresponding to i carbon atoms, a limit value T , , , (for k +co) (Table 6-1). Due to the fact that the terminal methyl groups in the initial members of the n-alkane represent an important deviation from a system containing only methylene groups, it is more convenient to use alkanes having chains as long as possible for the determination of Tc,m.As seen in Table 6-1 these deviations become unimportant after i=9. This is because the individual Tc,mvalues are irregularly distributed for the 12 longest
800 -Y
.-
2
600 --
I
04 1
3
5
7
9
11
13
15
17
19
i
Figure 6-1: Critical temperatures of n-alkanes as a function of the number i of carbon atoms. Calculated values using Eq. (6-11) (-), measured values ( + ) and limit value, T, (- - -).
Prediction of diffusion coe,fficients in gases, liquids, amorphous solids ...
165
Table 6-1: Critical temperatures of n-alkanes. Number i of carbon atoms
TJK
T,,,/K
T,-T,,,
9
594.6
1039.1
-2.0
10
617.7
1036.8
4.6
11
638.8
1035.5
+0.7
12
658.2
1034.9
+1.3
13
676.0
1034.8
+1.4
14
693.0
1036.0
+0.2
15
707
1034.7
s1.5
16
722
1036.7
-0.5
17
733
1034.4
+1.8
18
748
1039.2
-3.0
19
756
1035.4
+0.8
20
767
1036.8
4.6
chains (i=9-20). The mean limit value obtained from Table 6-1 is Tc,x = T, = 1036.2 K. Figure 6-1 shows the estimated curve for TC,*from Eq. (6-11) using Tc,k = T, = 1036.2 K as well as the experimental values of T,,, for 15 i520. The remarkable coincidence between the ratios of the critical temperatures, T,,,/T, within the homologous series and the ratios of the corresponding values of the interaction function w,.,Iw supports the interpretation that this function is a measure of the energy density of interaction. Due to the translation and rotation of particles in the liquid state of a macroscopic system, the value of the interaction function may be assumed to be independent of the configuration of the particles within the system. Therefore, there is no need for data related to orientation. This is also valid for the i chainlike subunits of an alkane molecule. Due to the possibility of a free rotation of any of the i subunits around the bond axis with the neighboring subunits, a relative motion of segments of several subunits is also possible.
6.3.2 Critical compression factor The first term w l = (1+27t)'/' of the power series w, defined in Eq. (6-10) plays a special role within the interaction model in that it represents a perfect gas phase. If V,, p,, T , and R represent the molar volume of a compound, the critical pressure and critical temperature of the system and the gas constant, then the product prVn is reduced to l i w of the product RT, due to the interaction between the particles in the system. Taking into account an empty (free) volume fraction in the critical state, the critical molar volume is written as V , = wlVo. Consequently, a dimensionless critical compression factor, Z,, is defined using the following equation: (6-12)
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Piringer
From a data collection with 349 experimental values for the critical compression factor (Reid et al., 1987) obtained with organic and inorganic compounds and elements, a mean value of Z , = 0.2655 is obtained with a standard deviation of o = 0.0346.
6.3.3 The entropy of evaporation Systems with comparable amounts of disorder are especially important for developing a common basis for relationships between diffusion coefficients. Such a comparable amount of disorder is generated when any liquid evaporates and becomes a gas. According to Trouton's Rule the entropy of evaporation has values around 85 JK-'rnol-l for many liquids at their boiling point Th at a standard pressure of 1bar. This rule was modified by Hildebrand (1915; Hildebrand et al., 1970).According to Hildebrand, the value of the molar entropy of evaporation, ASv, for many substances is nearly the same at temperatures where their molar vapor volumes are equal to the standard value of 24.8 dm3 mol-' at 25 "C.The validity of this rule extends over boiling points ranging over three orders of magnitude and for classes of substances as different as monoatomic noble gases, high boiling metals and compounds with polyatomic molecules with complex structures. The deviation from the mean value of 84.9 JK-'mol-' does not exceed 1.5 JK-'mol-' with few exceptions when using the Hildebrand correction. As a conclusion from the Hildebrand/Trouton Rule, the definition of a standard vapor phase in a standard state with a well known amount of disorder can be made. This definition can be used as a starting point for modeling diffusion coefficients of gases and liquids. The change in entropy AS for a reversible isothermal expansion of an ideal gas and therefore V2W1= from its initial volume Vl to a volume Vzis AS = R In(Vz/VI) exp(AS/R). By setting V2/VIequal to the ratio between the molar volume V; = 24.8 dm3 mol-' of an ideal gas under standard conditions ( T = 298.15 K , p = 1 bar) and assigning a volume V i to one mole of a liquid at Th. then VE/V: = exp(AS,/R) = exp(AHv/RTh).Where A H v stands for the molar enthalpy of evaporation at the Hildebrand temperature, Th,and AS, is the molar entropy of evaporation. By using ASv = 84.9 JK-'mol-' the value V ; = 0.91 cm'mol-' is obtained. An interpretation of the Hildebrand/Trouton Rule is that this "free" volume, VL,allows for the freedom of movement of molecules (particles) necessary for the liquid state at the temperature Th.The explanation of the constant entropy of evaporation is that it takes into account only the translational entropy of the vapor and the liquid. It has to be pointed out that VE does not represent the real molar volume of a liquid, but designates only a fraction of the corresponding molar volume of an ideal gas V& derived from the entropy of evaporation. The real molar volume VLof the liquid contains in addition the molar volume occupied by the molecules Vo. As a result the following relations are valid: V L= V i + V ,and V , = V&+ V,. However, while V;*< V , and V Lis practically independent of the pressure, V , << VE in the gaseous phase. Only in the critical phase does V,/V, = 1 and the entropy difference between the two phases vanishes.
Prediction of diffiision coqfFcieritsit7 gases, liquids, amorphous solids ...
167
6.3.4 The reference temperature The first term, w ~ ,of~ the , power series w ~represents , ~ a macroscopic system of interacting monoatomic particles in the model. In the gaseous state even polyatomic molecules are considered to behave like monoatomic particles. In gases the difference w I - w ~ , ~ is interpreted to be a pure translational contribution to the energy of the system and can therefore be related to its temperature. In order to establish a connection between the difference wI-wl,, and Sl units let us start with n = 1000 mol of hypothekg in a volume V=l m'. tical particles with the atomic mass unit u = 1.66054 x This system with N = nNA = 1000(m01)~6.0221410~~ (mol-') particles defines the mass unit of Nu = 1 kg. The total energy of the system is E = Cniejwhere nj particles are in the state with energy E ~ Using . the Boltzmann distribution and E = (N/q)CEiexp(-Pq) with p=I/kT, the following relationship between the internal energy of the system and is postulated to be: the two terms wI and wl,, (6-13) With the translational partition function 9 = VIA3and h3= h3/(2nrckT)3'2a value for the temperature T = 2.98058 K results, when using the values for N,V,u, the Planck constant h = 6.62608 x Js and the Boltzmann constant k = 1.38066x JK-I. The self diffusion of particles and the entropy of the system are both a result of random particle motions. With the Sackur-Tetrode equation the molar entropy, S,,, of the above system can be calculated at temperature Tand pressure p : (6-14) As shown in the previous section a common feature of all systems in the liquid state is their molar entropy of evaporation at similar particle densities at pressures with an order of magnitude of one bar. Taking this into account a reference temperature, T,, will be selected for systems at a standard pressure, p o = lo5 Pa = 1 bar, having the same molar entropy as for the pressure unit, p,, = 1 Pa at T = 2.98058 K. As can easily be verified, the same value of molar entropy and consequently the same degree of disorder results at p if a one hundred-fold value of the above T-value is used in Eq. (614). This value denoted as T,, = 298.058 K = T, is used as the temperature reference value for the following model for diffusion coefficients. The coincidence of T, with the standard temperature T = 298.15 K is pure chance. With Tv a reference molar volume of gas, Vg = RT,,/po = 24.782 dm'mol-' is defined, which by chance is very close to the value of the standard volume VG = RT"/p" = 24.79 dm'mol-'. Assuming that the molar volume VL discussed in the previous section is a result of interaction between the particles in a condensed macroscopic system, a reference molar volume, V,W,is defined using the reference volume Vg and the limit value w of the interaction function w, for a macroscopic system (n-m):
svll -
exp(%)
= e x p ( F ) = ew = 24078.88
(6-15)
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Piringer
VW , = Vg/ew= 1.029 cm3mol-'. The product w R = 10.0891 . 8.31451 = 83.8858 JK-' mol-' defines a reference entropy of evaporation and lies within the limits of deviation from the values of the Hildebrand entropy of evaporation.
6.4 The diffusion coefficient The following discussion starts with macroscopic systems in the gaseous state. However, its main distinction from the kinetic theory of perfect gases lies in taking interactions between particles into consideration from the start. The difference from the treatment of perfect gases is accounted for by two parameters, the critical temperature, T,, and the critical molar volume, V,. All particles in the gaseous phase are treated as monoatomic particles. Liquid systems occupy a special place between gaseous and solid phases. The high mobility of particles in a liquid and the values of diffusion coefficients falling in a narrow range supports the assumption of a free volume of about 1 cm"mo1-' (see Section 6.3.3) as a prerequisite for the manifestation of the typical properties of a liquid phase. The solid phase is considered to be an amorphous pile having a maximum disorder amongst the particles. Such a close-packed assemblage has some similarity with a liquid. But an essential difference from liquids lies in the absence of the supplementary free volume. An amorphous solid phase with interacting particles having a certain degree of mobility is considered to be essential for the diffusion process in plastic materials. In all aggregate states in this model, diffusion is considered to be a consequence of interactions between the particles that are in conformity with the first assumption of the model. This means the diffusion coefficient can be described as an exponential function of a relative density of interaction energy 4,.
6.4.1 Diffusion in gases At constant temperature the ratio D G , 2 / D ~ of, the ~ diffusion coefficients in a gas at two states 1 and 2 equals the ratio V2/Vl of the system volumes at the two states. Then together with the first assumption a starting point for modeling diffusion coefficients will be the relation DG,Z= (V2/VI)D,exp(q,) with the unit value D,, = lm2/s and q, = wI for a perfect gas. By selecting Vl= lo5 VE at p u = 1 Pa as a reference volume the following equation results for a self-diffusion coefficient, DG in a perfect gas: (6-16) This equation is typical for ideal gases in which neither an interaction term in form of activation energy nor the volume of the diffusing particles are considered. At p = 1 bar and T=O"C for example, DG = 1.36 cm2/s is obtained using Eq. (6-16) compared with 1.4 cm2/smeasured in He (Landolt-Bornstein, 1969). For real gases two additional terms in the exponent of Eq. (6-16) must be introduced:
Prediction of diffusion cocfficients iri gases, liquids,aniorphous solids ...
169
1. A molar activation energy EA of diffusion is defined as the product EA = wl,,RTc, with the critical temperature, T,, of the system. This definition takes into account the connection between the interaction terms of the model, w, and w,,, and IS units, as shown in section 6.3.4. At the critical temperature, T,, a pure translational amount, wI-w/,e,of the relative energy density is responsible for the magnitude of DG. 2. The second term takes into account the size magnitude of the diffusing particle. Let A , = V0213 m2mol-' be the molar cross-sectional area of the diffusing particle. When moving through the system a particle with this cross sectional area must overcome the force exerted on it by the other particles in the system while they are moving about in a disordered fashion. The magnitude of this force F divided by the unit area A,, = 1 m2 to which the force is being applied defines a pressure, p = F/A,. The product pA,,,d = (A,/A,,)Fd = Enl,AJ mol-' represents the necessary molar work to overcome the resistance of the matrix by moving A,,, along the distance d in a direction perpendicular to it. Referred to the corresponding work for moving A , along the same distance, E u , A = Fd J, we get E , n , A / E , , = ,~ = A,/A,, = A,n mol-'. On the other hand, the pressure p can be expressed as p = m(N/V)
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Piringer
first approximation. Examples of such molecules are N2 and 0 2 . In Table 6-2 the selfdiffusion coefficients of noble gases at 1 bar, calculated with Eq. (6-17) are compared with experimental values (Kestin et al., 1984). Helium behaves at T >> T, like a perfect gas (Eq. 6-16) without interaction ( T , = 0) and atomic size (Vc= 0). Molecular hydrogen has the same behavior. Table 6-2: Self-diffusion coefficients of noble gases at 1 bar.
TJK He
Ne
Ar
Kr
Xe
5.19
44.44
150.8
209.4
289.7
Vc/(10-' m3mol-') T/K 5.74
4.16
DG/(cm* s-')
50
0.093
0.089
100
0.21
0.29
200
0.44 (1.00)"
0.92
300
0.67 (1 SO)'
1.82
0.021
0.021
50
7.49
9.12
11.84
*) Values obtained for a perfect gas with T,
DG/(cm2s-I) calc.
=0
exp.
100
0.11
0.08
200
0.34
0.27
300
0.59
0.53
200
0.083
0.087
300
0.21
0.19
373
0.32
0.28 0.045
200
0.040
300
0.12
0.10
373
0.20
0.15
300
0.058
0.058
373
0.1 1
0.09
and V, = 0.
The mutual diffusion coefficient, DG,AB= DG,BAfor a binary mixture of A and B is and V , A B defined by Eq. (6-18), using the critical temperature T c , A=~ XAT,,A+XBT~,B = (VC,,+V,,8)/2,where X A and XB are the corresponding mole fractions:
(6-18) Examples of diffusion coefficients calculated with Eq. (6-18) are summarized in Table 6-3 where they are compared with corresponding experimental values (Reid et al., 1987). Diffusion coefficients of water and hydrocarbons in air are especially important parameters in mass transfer processes between plastic materials and the atmospheric environment.
Prediction of diffiision coeffiicirrirsin gases, liquids, anzorphoirs solids ...
171
Table 6-3: Diffusion coefficients of water and n-alkanes in air at 1 bar. Compound Water
T/K
DG,BA/(cm2 SKI) calc.
DG.BA/(cm2 s8) exp.
273
0.21
0.22
288
0.23
0.24
298
0.25
0.25
308
0.26
0.26
318
0.28
0.28
Pentane
298
0.106
0.084
Hexane
298
0.089
0.080
313
0.098
0.085
333
0.109
0.096
293
0.073
0.067
313
0.083
0.077
293
0.062
0.064
313
0.071
0.071
333
0.079
0.078
293
0.053
0.060
313
0.061
0.062
333
0.068
0.071
313
0.052
0.060
333
0.059
0.064
Hcptane Octane
Nonane
Decane
The following example illustrates the mode of calculation for obtaining the diffusion coefficient DC;,AB of water (B) at low concentrations in a gas phase which is mainly composed of air (A). Air as the gaseous matrix is considered a homogeneous mixture for which
T c ,= ~ xo2 . Tc,02+ X
+
N .~T c , ~= 20.2 . 154.6
Vc.= ~ (Vc,02 V C , ~ /2 2 ) = (73.4E-6
+
+ 0.8. 126.2 = 131.88K and
89.8E-6)/2
= 81.6E-6
m3mol-'.
The critical molar volume of water is V c , R= 57.1E-6 m3 mol-I. With these values V,~,, = (81.6E3-6+57.1B-6)/2= 69.35E4 m3mol-'. Together with T c . and ~ Eq. (6-18) the calculated values in Table 6-3 for the diffusion coefficients of water in air were obtained. The diffusion coefficients DG,ABof small amounts of n-alkanes in a matrix of air are calculated in the same manner as shown above for water. But in the case of the homologous series of n-alkanes a simplification is possible because the critical molar volume, V,,,, for a member of the homologous series can be obtained with good approximation from the corresponding molecular weight, M,.,,using the relation V , , = 4.238E-6. M,,,, as shown later in Eq. (6-25).As an example, for n-octane V , , = 114.4.238E4 = 4.83E4 m3 mol-'. With V L , A = 81.6E4 for air and V<,AB = 2.824E-4 m3 mol-' together with Tc.A and Eq. (6-18) the value D G , J A = 0.062 cm2s-' at 20 "C and 1 bar is obtained.
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Piringer
The tracer diffusion or intradiffusion coefficient, DL,BA,for the compound B in a mixture of A and B can be a function of composition, like the mutual diffusion coefficient. But instead of V,,,, for mutual diffusion, Vc.Bis introduced in Eq. (6-18).
6.4.2 Diffusion coefficients in the critical state Equation (6-17) can be easily adapted for the critical state, if p is substituted with the critical pressure, p c , obtained with Eq. (6-12) and if w I in the exponent is substituted with wI,e This takes into account the absence of a pure translational energy contribution in the critical state. On the contrary, an additional negative term, the critical compression factor Z , = -w,/w, is introduced in the exponent, taking into account the decrease in diffusion velocity caused by attraction between the particles. As a result the following equation gives the coefficient of self-diffusion in the critical state:
6.4.3 Diffusion coefficients in amorphous solids A reference equation Let us now consider a macroscopic system in an amorphous state above its glass temperature. The particles of the system are n-alkanes with i >> 1 carbon atoms in the molecular chain. Let us first consider the theoretical case with one single macromolecule of infinite length that forms a polymethylene chain in the shape of a disordered coil. Due to the possibility of free rotation of any of the methylene subunits around the bond axis relative to the neighboring subunits, a relative motion of segments of more subunits is also possible. In the following a reference equation for the diffusion coefficient of a n-alkane with a number i of carbon atoms in a hypothetical infinite chain will be derived in manner analogous to that for gases. If in the first approximation we neglect the existence of activation energy, EA, for the diffusion process and the volume and mass of the diffusing solute, a ratio of diffusion coefficients D2/D1= exp(q,) = exp(w) = exp(wR/R) = exp(AS,/R) in two states of the system is the starting point. This conforms to the first assumption of the model where the amount 0 2 is related to a value D I for an initial state. This ratio is a measure of the disordered motion of the methylene groups, with a corresponding increase of the molar entropy ASw = wR, resulting from the interaction between these groups in the polymer matrix with the relative density of interaction energy, qr =w. One mole of polymethylene is defined as one mole of methylene groups, -CH2-. The disordered motion of the methylene groups providing the value D2 related to D I is assumed to be analogous to the reversible expansion in a gas with the same change in entropy ASw In comparison with the behavior of a gas, the expansion of this system is neglected and the ratio V2/Vl z 1.For the reference equation D1 = D, = 1m2s-I. In a second step, a molar activation energy, EA, of the motion of the methylene groups in the polymethylene chain is introduced. This activation energy EA = wRT, = 10.089 . 8.31451 . 1036.2 = 86.923 kJ mol-I is defined as a magnitude proportional to
Prediction of diffusion coefficients in gases, liquids, amorphous solids ...
173
w (analogous to wI for gases) and to the limit value of the critical temperature T, = T,,, = 1036.2 K in the homologous series of n-alkanes. In this way D2 = D,, exp(wE,/RT). The next step takes into account the diffusing solute as described for the gaseous state. Due to the practically immobilized matrix composed of macromolecules, the solute is considered to be a tracer for which only its critical molar volume, Vc,i,must be considered. In the special situation of a n-alkane with repeating -CH2- groups in the molecular chain, a constant value of the ratio VJM,.; can be expected for the homologous series excepting the first few members. The first few members deviate from this substructure because of the presence of the two -CH3- endgroups. For the n-alkanes with i = 5-17 a mean value V J M , ; = 4.2385 x lo4 m'mol-' is obtained (Reid et al., 1987). With this value ~ O O O ( V , , ; / W = ~lOOO(4.2385 )~~~ x l0-h M , ; / w , ) ~ /= ~ 0.1351 Mf,i3results. Finally, analogous to the gas phase an equation for the diffusion coefficient, D,,,of a n-alkane with i carbon atoms in an amorphous polymethylene is obtained (Brandsch et al., 1998): Dp,i
= D,
[
exp w - 1000($)
213 -
F] D, exp (w =
-
213 0.1351M,,i
-
(6-20)
Equation (6-20) can be used as a reference equation for all polymers. It represents a theoretical construction resulting from an asymptotic correlation and the assumption of an infinite chain composed of methylene groups representing the amorphous polymer matrix. Diffusion coefficients of n-alkanes in polyethylene While w = Ap stands for the theoretical structure of polymethylene, other characteristic Ap-values can be obtained for other polymers or solids depending on their specific structure. Nevertheless, the remaining two terms in the exponent of Eq. (6-20) can be held unchanged for polyolefins and alkanes. For other diffusing compounds the corresponding critical molar volumes would be more appropriate than the molecular weights. Taking A P to be a characteristic parameter of the polymer which must be determined experimentally, the following more general equation for the diffusion coefficient Dp,ican be used (Brandsch et al., 1998): Ap
-
0.1351M,.i 213
-
(6-21)
The factor 0.1351 in the exponent of Eq. (6-21) can be used as an acceptable approximation for most hydrocarbons and other solutes with low polarity. Comparison of calculated and experimental data The diffusion coefficients of n-paraffins with 12 to 22 carbon atoms in high density (HDPE) and low density polyethylene (LDPE) have been measured by a permeation method (Koszinowski, 1986). Methanol (MeOH) and ethanol (EtOH) were used as contacting liquid phases which minimized interaction between these polar solvents and the nonpolar polymers. No interaction was observed over the investigated temperature range of 6 to 40 "C for both solvents.
4,
0
-
-10.0 --
... p
.
- -Ap=8,8 -
Ap=lo.o89
-10,4 T
Figure 6-2: Logarithm of diffusion coefficients of n-alkanes in polyolefins at 23°C as a function of the relative molecular mass.
Figure 6-2 contains the measured values of the diffusion coefficients from HDPE and LDPE at 23 "C and the calculated curves obtained with Eqs. (6-20) and (6-21) for the corresponding range of masses. The measured diffusion coefficients are in good agreement with the calculated values obtained with Eq. (6-21) using A P =8.8 for HDPE and AP = 10.6 for LDPE, respectively. The most important finding is the close agreement of experimental values with the M:,y-dependence in the exponent of Eq. (6-21) and the reference Eq. (6-20) with the theoretical value Ap = w = 10.089. Figure 6-3 shows the temperature dependence of the diffusion coefficients obtained with i = 12 to i = 22 in LDPE. Comparison of experimental data with the corresponding curves obtained with Eq. (6-21) and AP = 10.6 for i = 12 and i = 22 shows again a reasonable agreement. This result is used as a proof for the activation energy ( E A ) order of magnitude used in reference Eq. (6-20). The value of 86.923 kJ mo1-l is of the same order of magnitude as that for bimolecular reactions in solution.
I -8 --
-. 6
3.1
u)
v
0
-9
--
-
--- ---
A
x
0
c12 C14 C16 C18 c20 c22 cak C12 calc C22
a
O cn
2 -10 --
-1 1
4
3,15
3.35
335
l/r (10001K)
Figure 6-3: Logarithm of diffusion coefficients of n-alkanes in LDPE as a function of temperature.
Prediction o f rfiffiisioncoefficienls in gases, liquids, amorphous solids ...
175
A general equation for plastics In the general case of a solute B in a plastic matrix P the parameter AP is a function of temperature and produces a more or less significant deviation from the activation energy, E A = 86.923 kJ mol-' in reference Eq. (6-20). Consequently we can write: A p = Ap'--Zp/T,with the athermal, dimensionless number Ap' and the parameter z p with the dimension of a temperature, respectively. Both values, Ap' and - z can ~ be obtained from two diffusion measurements at different temperatures, using a reference solute B in matrix P (see Chapter 15). The specific contribution of B in the DcB-value can be taken into account by two supplementary dimensionless parameters. While ps,B stands for a structural difference of B in comparison to a hypothetical n-alkane with the same relative molecular mass Mr.B, the number p ~ =p p:f + &/T represents an interaction increment between B and P, due to the different polarities of the solute and plastic. This interaction is generand p s p can be considered as ally a function of temperature. The two parameters, vs~B relative mass increments (positive or negative) which vanish in the reference system of n-alkanes in polymethylene. If the diffusion coefficient, DKB, is obtained by measuring the mass transfer of B from P into a liquid phase L in contact with the plastic material, more or less strong interactions can occur between the two phases. If the polarities of the plastic material and the liquid phase are similar, swelling of the plastic occurs and the direct consequence of this interaction is an increase of the DRB-values.This process is also a function of temperature and, taking it into account, two supplementary increments, AL for interaction between P and L and p B L for the interaction between B and L are introduced, respectively. Collecting all these parameters, the following general equation can be written: D P ~ B = DU
2/3- 10454 (6-22) ( + AL - 0.1351 ( M ~ . B+ L.B + pBp + pBL) 7)
~ X PAP
with Ap = Ap'-TpIT ; AL= AL'--zL/T ;
p ~= p p:p
+ pgp/T ;
+ piL/T.
~(B= L P ~ L
Due to the temperature dependence of the parameters A A A L , P E P and P E L , an apparent activation energy, E A , results which deviates more or less from the reference value of 86.923 kJ mol-'. An open question remains over the influence of solutes with high molecular masses on the DpB-values. Measurements were performed using bilayers of polyethylene and polypropylene, consisting of a thin (0.1 pm) film of deuterated polymer atop a thicker (1-2 pm) film of the corresponding hydrogenated polymer (Gel1 et al., 1997). The bilayers were then annealed for appropriate times and temperatures, permitting diffusion to develop a concentration depth profile of the deuterium nuclei. The deuterium depth profile was determined by the forward recoil spectrometry (FRES) technique. The entangled polymer coils show a remarkable diffusion rate, which is orders of magnitude higher than predicted with Eq. (6-21). For diffusion in amorphous polymers at temperatures above their glass point, Tg, one can assume a behavior with some analogy to a liquid. On the other hand the Stokes-Einstein Eq. (6-4) for liquids was derived under the assumption that the diffusing particle is much larger in size than the matrix particles. If we let the matrix be a
176
Piringer
macroscopic system of identical particles composed of -CHZ- groups and the diffusing solute is the whole entangled macromolecule, then the system fulfills the assumption of Eq. (6-4). The decrease of DeB with increasing M,.Bin this equation is much slower than in Eq. (6-21). In order to cover the whole range of molecular weights for solutes in a polymer matrix we can start with Eq. (6-21) and introduce a supplementary positive term, aM,B: Ap - 0.1351MfjB3
+ aMr,B - 10454/T)
(6-23)
A comparison of predicted and measured values of diffusion coefficients for solutes with a large range of molecular weights in polyolefins is shown in Chapter 15 and allows an empirical selection of the U-value.
Diffusion ofparafins in paraffin
Reference Eq. (6-20) for an infinite chain of covalently bonded methylene groups can be considered to be an asymptotic limit for the homologous series of n-alkanes. By substitution of w into the exponent of Eq. (6-20) by the corresponding term, w ~ , ~ , which represents a matrix composed of a paraffin with i carbon atoms, an equation for the diffusion coefficient Ds,ki for trace amounts of a paraffin with k carbon atoms results:
= D,
exp(wi,e - 0.1351M;,f
-
~
%).
i
~
(6-24)
from using the limit value T, = 1036.2 K and the molecular weight, k f r , k , of solute k or its critical molar volume, v , , k . For self-diffusion i = k and for solutes with structures significantly different compared to paraffins, the critical molar volume instead of the molecular weight is preferred. Diffusion coefficients in liquids
With the exception of the super cooled region below the melting point, the liquid state of a substance occurs between its melting point and its critical state. Correspondingly, an equation of diffusion coefficients for liquids is based on Eqs. (6-19) and (6-24) representing these limits. Starting with the homologous series of n-alkanes as a reference structure series and the entropy of evaporation discussed in section 6.3.3, the development of an equation for the liquid state is possible with the following steps: With Eq. (6-17) a value of the self-diffusion coefficient, D T l for the first member of the reference series is calculated using the critical temperature TC,,= ( W ~ , ~ / W ) T , (Eq. 6-11) and the relation: (6-25)
Prediction of diffusion coefficients in gases, liquids, amorphoits solids ...
177
This relation is used for the reference series in Eq. (6-20), with the value 0.1351 Mf,? = 0.1351 . 162'3for the first member of the series. At the reference temperature T, and the standard pressure of 1 bar, the value D P l = 1.42735 x m2s-' is obtained with Eq. (6-17) for the gas phase. This value is a reference number and not the experimental value found for methane. Taking into account that the same disorder occurs for liquids in equilibrium with their vapor phases having the same molar gas volume, a reference diffusion coefficient, D!,l = D z l / e w = 5.9278 x lo-"' m2s-l is obtained from the reference diffusion coefficient in the gas phase. In the next step, Eq. (6-24) with i = k is used to calculate a temperature, TIo,for which the self-diffusion coefficient, D,,, is equal to the reference value DO,.,: (6-26)
Df,, is a first approximation and is obtained only if T? = T,. Consequently, a correction must be introduced which accounts for the deviation of TP from T, This corrected value, denoted D f , , = (T,/T?)Df.,defines the lower limit of self-diffusion coefficients for a paraffin i at T?. The upper limit of the self-diffusion coefficient in the liquid phase is obtained with Eq. ) T , the critical pressure, p,;=(RT,I (6-19) at the critical temperature, TC,;= ( W ~ , ~ / Wusing VC,;). ( w J w ) from Eq. (6-12) in combination with the Eq. (6-25) for the n-alkane series: & 4 . 2 3 8R 5 . 1 0 - 6 ~ ~ w, r,i.D
D C J. - T~
= 6.3939.
10-9exp(-$
-
exp(-?
0.1351M:%i3)
-
0.1351M:,f) (6.27)
It can be assumed that the self-diffusion coefficient DL,; at a temperature T between T? and Tc,;follows the exponential function D = ae-"'. Collecting all results from the above steps and writing Dt,l = a exp(-h/Tp) and D , ; = a exp(-blT,,J, the following equation is obtained for the diffusion coefficient DL,;:
~
~= a , exp( i -
+)
(6-28)
with
Taking into account that, for the reference homologous series of n-alkanes the relative molecular masses of the member i in the series is M,,= 2 + 14 i, the self-diffusion ~ be calculated with Eqs. (6-27) and (6-28). This can be done using coefficient D L , can only two values based on experimental results, the limit value of the critical temperature, T,, and the mean value for the ratio, Vc,,/Mc,. Table 6-4 shows a comparison between experimental (Landolt-Bornstein, 1969) self-diffusion coefficients and calculated values obtained with Eq. (6-28). A mutual diffusion coefficient, DL,,k,can be defined in the same manner as for gases + vc,k)/2 and P c , i k = x i ' p c , ~-k x k Pc.k. with Tc.rk = X I TC,If X k Tc.k and Vc.rk (vc,~ '
'
178
Piringer
Table 6-4 Self-diffusion coefficientsof n-alkanes. Alkane with i carbon atoms
T/K
D ~ , ~ / ( Icm2 o - ~s-') calc.
Heptane
298
3.23
3.10
Octane
298
2.28
2.75
333
3.8
3.6
298
1.67
1.70
333
2.8
3.0
Nonane
t1~,~/(10-'cm2 s?) exu.
298
1.28
1.31
333
2.2
2.5
Dodecane
333
1.4
1.5
Octadecane
323
0.52
0.46
Dotriakontane
373
0.42
0.30
Decane
In Table 6-5 the mutual diffusion coefficients of a binary mixture of n-heptane and n-hexadecane at 25 "C are calculated for different molar fractions of the solutes and compared with experimental values (Landolt-Bornstein, 1969). Table 6-5: Mutual diffusion coefficients of a binary mixture of n-heptane and n-hexadecane at 25 "C and different molar fractions x. XI6
0.0056
0.1064
0.2024
0.3934
0.5821
0.7920
0.9761
x7
0.9944
0.8936
0.7976
0.6066
0.4179
0.2080
0.0231)
DL.ij talc./( 10-'cm2s-')
1.72
1.59
1.45
1.18
0.95
0.74
0.58
DL-,, exp./(I0-'cm2s-')
1.78
1.59
1.45
1.24
1.07
0.895
0.76
Tc,7= 534.58 K, Tc,,6= 721.68 K, pC,,= 27.4 bar, pC.l6= 14.1 bar, Vc,7= 4.2378E-4 m3 mol-'. Vc,lb= 9.577E-4 m3 mol-'
The tracer or intradiffusion coefficient, DtTkiof an n-alkane k in a solution of n-alkanes i and k at temperature T can be calculated with Eq. (6-28) in two steps: first, the ratio D,?k,/Dzi, for mutual diffusion at T and T,, is calculated. In the next step the tracer dif usion coefficient D$, at the reference temperature T,, is calculated using M , . k instead of M,; in Eq. (6-26) and in the exponent of Eq. (6-27). The corresponding values for TZj and Dc,kiare then used for bki and ak; in Eq. (6-28), respectively. Finally we obtain: (6-29) In order to generalize Eq. (6-28) for any organic solutes, the self-diffusion coefficient DL.Aof a compound A can be calculated in the following manner: (6-30)
with
Prediction ofdiffiaion coqfficierits in gases, liquids, aniorphoirs soli~ls__.
179
and 1
I n D t , l + 1O3
1
(%)
2'3).
The product w . T c , A in the above relation results from Tc.,= T,(wj,,/w) if the critical temperature, T L . , A ,of liquid A, which is not a member of the homologous series, is used instead TC.;.In this case wj,, in Eq. (6-24) is substituted by (TC.,A/TC)w. If no value for the critical molar volume Vc.,Ais available the use of the relative molecular mass, MKA, is an acceptable approximation. In this case Eq. (6-25) has to be used for substitution of Vc,Aby MGAin Eq. (6-30). The mutual diffusion coefficient, D/,,,,R, in a mixture of A and B is defined in the ~ X A . Tc.A + x B . T C ,and ~ V,:, = (Vc.~ + same manner as for n-alkanes, with T c , A = vc,B)/2 and P c , A B = X A ' p c . A + X B 'Pc.B. As shown above for the homologous series for n-alkanes the tracer-diffusion coefficient, Df7BA,of a compound B in the solvent A at temperature Tis obtained within two steps: first the ratio of mutual diffusion coefficients D:,,,/DT". L , A B i ~calculated using Eq. (6-30).Then D;TBAis calculated at the reference temperature T,, using Vc.Binstead of Vc..Ain Eq. (6-30). Finally the value of D;,7jjAresultsas: (6-31) For B = A, the tracer diffusion coefficient equals the self-diffusion coefficient, D:TBA= Dl,A. In Table 6-6 the self-diffusion coefficient of water and some diffusion coefficients of organic solutes in water at infinite dilution calculated with Eq. (6-31) are compared with experimental values (Reid et al., 1987). The experimental value for sucrose is from Cussler (1997). If no value for Vc,B is available, again M Kcan ~ be used as a reasonable approximation, using the substitution 103(Vc,~Iw~)2'3 = 0.1351 . M:,$ (relation 6-25) in Eq. (6-30). With water as the liquid phase A, an upper limit for the mass M G Bof a diffusing solute B at infinite dilution is reached at M G B= 212, because above this value bHA in Eq. (6-30) changes its sign. As mentioned before, for solutes with significantly higher sizes than the sizes of the matrix particles, the Stokes-Einstein equation (6-4) can be used. In this equation the solute radius a is used which can be correlated with V,,,li3 and MKBIi3. Taking this into account in the case of aqueous solutions, the diffusion coefficient D / . , B A for solutes with Mr,B> 212 can be estimated with the following equation:
(z) I /3
'L.l3A
= DL.212A
, with
> 212
(6-32)
D[,2,,A is calculated with Eq. (6-31) using Mr., = 212. In Table 6-7 diffusion coefficients of high molecular solutes in water calculated with Eq. (6-32) are compared with experimental values (Tanford, 1961). With the homologous series of n-alkanes, such an upper limit, Mr.,nn.rk, for the relative molecular mass of a trace paraffin k in a solution of paraffin i is obtained for each member of the series. Consequently, an analogous equation to 6-32 can be written for the series:
180
Piringer
Table 6-6: Diffusion coefficients in water at infinite dilution.
TIK
Solute
DITBA calc. cm2 s-'
Water
D&
exp.
% error
lo-' cm2 SC'
298
2.24
2.13
+ 5.4
273
1.41
0.97
+45
- 28
373
6.24
8.65
275
1.27
0.85
+49
333
3.20
3.55
-
Carbon dioxide
298
1.95
2.00
- 2.7
Propylene
298
1.50
1.44
+
Methanol
288
1,52
1.26
+20
Ethanol
288
1.32
1.00
+32
Acetic acid
293
1.42
1.19
+20
Ethyl acetate
293
1.10
1.oo
+10
Aniline
293
1.13
0.92
+23
Diethylamine
293
1.07
0.97
+10
Pyridine
288
I .09
0.58
+88
Ethylbenzene
293
0.94
0.81
+I7
Methylcyclopentane
275
0.79
0.48
+64
293
1.04
0.85
+22
333
1.72
1.92
- 10
298
1.55
1.34
+16
348
3.02
3.67
-18
298
0.5247
0.5228
+ 0.4
Methane
Vinyl chloride Sucrose
Table 6-7: Diffusion coefficients of macromolecules in water at 20°C. Solute B exp. Sucrose
342
5.03
4.59
Ribonuclease
13700
1.47
1.19
Lysozyme
14100
1.46
1.04
Serum albumin
65000
0.88
0.59
Haemoglobin
68000
0.86
0.69
Urease
480000
0.45
0.346
Collagen
345000
0.50
0.069
Myosin
493000
0.45
0.116
9.7 4.2
Prediction of diffiision coefficients in gases, liquids, nmorphous solids ... DL.ni T --D TL.imxki (Mr.'llaxk)
'I3, with Mr." > Mr,maxk
181 (6-33)
DI,~~,~~~
where is calculated with Eq. (6-29) using M r , k = for which bk reaches a minimum positive value. With increasing values of the relative molecular masses of the solvent, M,;, the corresponding maximum value Mr,,,taxk is approximately M , = (~~,,/0.1351)"~, a value which results from Eq. (6-24) for w ; , ~= 0.1351M,.k2'3. For i +M, w ; , ~+ w and M K m n x k = 645. Above this molecular weight a significant slower decrease of the DeB-values in plastic materials occurs and this is taken into account in Eq. (6-23). References Brandsch J, Mercea P, Piringer 0. 1998: in Risch S (ed). New developments in the chemistry of packaging materials, ACS Symposium Series, Washington. to be published. Cussler E L, 1997: Diffusion. Mass transfer in fluid systems, 2 nd. ed., Cambridge University Press. Cell C B. Graessley W W, Fetters L J, 1997: J. Polymer Science: Part B: Polymer Physics 35 1933. Hildebrand J H. 191.5:J. Am. Chem. SOC.37.970. Hildebrand J H, Prausnitz J M, Scott R L, 1970: Regular and related solutions, van Nostrand Reinhold Company, New York. Kestin J, Knierim K, Mason E A, Najafi B. R o S T. Waldnian M. 1984: J. Phys. Chem. Ref. Data 13 229. Koszinowski J, 1986: J. Applied Polymer Science 31. 1805. Landolt-Bornstein, 1969: Zahlenwerte und Funktionen. 11. Band, 5. Teil. Bandteil a Transportphanomene. Springer-Verlag,Berlin, New York. Reid R C, Prausnitz J M, Poling B E. 1987: The properties of gases and liquids, 4 th ed.. Mc.Graw-Hill Book Company, New York. Tanford C, 1961: Physical chemistry of macromolecules, Wiley. New York.
Reactivity in Molecular Crystals Edited by Yuli Ohashi Copyright @ K d a o r h a Ltd .Tokyo. 1999
7 Transport equations and their solutions Otto Piringer
7.1 The transport equations Interactions between packaging and product are always connected with transport processes occurring within the packaging system. A transport process is understood to be a general movement of mass, energy or other quantity from one location to another. An example of mass transport in packed liquid products is the convection that occurs during the heating or shaking of the package. Macroscopic regions of the liquid move with different speeds relative to one another and cause mixing to occur. With heating, a simultaneous transport of heat takes place along with mass transport. The convection of mass and energy takes place in liquid products during distribution of the packaging from the manufacturer to its final storage destination and during heating and cooling of the package. Mixing by convection in viscous and solid packed products has very little or no practical significance. A special case is the mixing of particulate products by shaking, which gives results similar to convection. The most important transport processes in solid, viscous and liquid filled products during the storage period are diffusion and thermal conductance. Mass transport by diffusion and energy transport by conductance have a common molecular basis. They are both affected by the unordered movement of molecules in the medium in which transport takes place. It is the vibration of atoms and groups of atoms, transmitted to neighboring atoms which is responsible for conductance in solids. Unordered collisions between the mobile molecules of a liquid or gas are also a source of mass transport by diffusion (Chapters 5 and 6). A further example of energy transport through packaging into the filled product is electromagnetic radiation. This radiation in the form of light can start chemical reactions or, in the case of microwaves be transformed into heat and then further distributed through the packaging system by conduction or convection. In addition to mass and energy, other quantities can also experience transfer. Flowing layers with different flow rates in a convection stream can influence one another. The slower flowing layer acts as a brake on the faster layer, while at the same time the faster layer acts to accelerate the slower one. The cause of this behavior is the inner friction of the liquid appearing as a viscosity difference, which is a consequence of the attractive forces between the molecules. Viscosity can be explained as the transport of momentum. The viscosity of different media can be very different and thus plays an important role in transport processes.
184
Piringer
7.1.1 The terminology of flow For the mathematical description and understanding of transport processes, it is advantageous for their descriptions to have several common characteristics, regardless of the nature of the transport quantity, to allow them to be treated in a similar manner. Without knowledge of their fundamental causes at the molecular level, which corresponds to their historical development, transport processes can be described with help from quantities that can be quantitatively measured on a macroscopic level. One such quantity is that of flux. The flux J is understood to be the amount of a quantity transported per unit time through a unit surface area. Flux is a vector for which a direction must be specified in addition to the quantity or contribution J. This is accomplished with the help of the unit vector e giving:
J = Je = Jx
+ J, + Jz = Jxi + J y j + Jzk
(7-1)
J,, J,, J, are the vector components in the x, y and z axis directions of the coordinate system, J,, J,, J, are their contributions and i, j and k are the corresponding unit vectors. Given a mass quantity rn that is transported during time t through an area A, then let J represent the contribution of the mass flux. For energy transport, then J is the contribution of the energy flux with the dimensions J/m2s(where J = Joule). In a very general sense, the flux of a quantity G is proportional at a given location to the gradient of the scalar field produced by the flux, a(x, y, z ) . Mathematically, one obtains the contributions of the three components with the gradient of a, grad a, from the partial derivative of a at the coordinates x, y, z which for the flux G results in:
-b
(& @i
a)
J,(mass,convection)
= p
b)
Jz(momentum in x - direction) = -q
c)
J,(mass,diffusion)
d)
J,(energy,conduction)
J(G)=-bgrada
=
+ “j (b + “k az
(7-2) The location independent proportionality factor is designated b. The minus sign in Eq. (7-2) shows that the flux goes in the direction of decreasing a-values. This means the quantity G “flows” down the gradient. The usefulness of the flow terms as common characteristics for transport processes allows them to illustrate such seemingly diverse processes as convection, momentum transport (viscosity), diffusion and heat conductance. To simplify the written expression, the flux components of the four processes are expressed in Eq. (7-3) in the direction of one axis of the coordinate system whereby, instead of the partial derivative for the function, a variable and useful form of the derivative expression is used:
=
i &x dz
k (7-3)
-D a dx i =
-n dx i
In Eq. (7-3a) p and dxldt are the contributions of the density and the velocity of the liquid in the x-direction. The material specific constants q, D and n are for the viscosity, diffusion and thermal conductivity coefficients. The derivatives in the z and x
Trrirrsport equations and their solutions
185
directions, dv,/dz, dc/dx and dT/dx are for the velocity components (in the x-direction), the concentration and temperature. A comparison of the four equations in Eq. (7-3) shows the similarities between the expressions. With respect to their individual historical development, the four expressions above are quite separate. While the above representation of momentum can be traced back to Newton, the expression for heat conductance was first derived by the mathematician and physicist Joseph Fourier at the beginning of the last century. The physiologist Adolf Fick, who was concerned with measuring the transport of oxygen in blood, recognized the analogy of diffusion to heat conductance and published in 1855 the diffusion equation now known as Fick's first law (Eq. 7-3c). The relationships between the different processes at the molecular level was first recognized by Einstein and other physicists and led to quantitative relationships between material specific constants, in particular between D and q , which are important for calculating their respective contributions (see Chapters 5 and 6).
7.1.2 The differential equations of diffusion During a diffusion process, e.g. the migration of an additive from a plastic into the atmosphere, a change in the concentration of the diffusing substance takes place at every location throughout the plastic. The mass flux caused by diffusion is represented by a vector quantity whereas the concentration c and its derivative of time t is a scalar quantity and is connected by the flux with help of the divergence operator. The following example serves to emphasize this relationship. In a body with any given shape, e.g. a piece of soap, there is an aroma compound which is initially uniformly distributed throughout the entire body. During storage without any packaging a decrease in concentration takes place due to diffusion into the atmosphere particularly in the outer layers of the soap. The resulting scalar concentration field with the levels c1 > c2 > c3 (Fig. 7-1) forms a gradient field that describes the external direction of the aroma compound flux.
Figure 7-1. Diffusion and the divergence operator.
186
Piringer
Figure 7-2. Diffusion through a volume element.
Now consider only a suitably small section of the soap in the form of a cube with side lengths of Ax, Ay, and Az (Fig. 7-2). The aroma compound will diffuse in as well as out of the cube because of its perpendicular side surface areas. Due to the greater decrease in the aroma near the soap’s external surface, the flux out of the side of the cube closer to the surface is greater than the flux into the side of the cube that lies deeper in the soap. The difference between the aroma diffusing in and out will be positive which means one can consider the cube as an aroma source. As a consequence of the flux out of the cube, the concentration in the cube decreases with time. The concentration is also a function of time, c = c(x, y, z, t) and its decrease with time, i.e. the partial derivative -&/at in the cubic volume AV = Ax Ay Az, represents the net flux out of the cube and designated div J the divergence of the flux. Mathematically the divergence is obtained as the sum of the differences between flux components in and out of the cube in the coordinate axis direction with respect to the cube’s volume. Placing the coordinate axis parallel to the corners of the cube as a helpful construction (Fig. 7-2), then one can label the incoming flux component contributions through the side walls Ay Az at the location x with Jx(x) and the outgoing component through the opposite side wall at x + Ax on the x-axis with Jx(x + Ax). When this is done in the same manner for the other components, then one gets:
+
IJZ(Z+AZ)- J ~ ( z )Ax ] Ay Ax Ay Az
(7-4a)
By letting the length of the cube’s sides Ax, Ay and Az become infinitely small, then the differences on the right side of Eq. (7-4a) become the partial derivatives of the flux component contributions at the location P(x, y, z) and one obtains: (7-4b)
Trnrisport equations and their solutions
187
Then the contribution of the diffusion flux in the direction of the three coordinate axis are according to Eqs. (7-2) and (7-3c):
J, = - D &/Ox, J, = - D i)c/dy and J,
=
-
D &/dz
(7-5)
With help from the divergence and gradient, one obtains the same result in the form of the expression: div J = D div grad c
=
(7-6)
The mathematical operator V, called Nabla or del, appearing in Eq. (7-6) has the structure:
When del is applied to concentration c, Vc = grad c, and to the vector of the diffusion flux J = -D grad c, it gives VJ = - div J = D div grad c = DV'c. The application of the del operator twice leads to a scalar, to a vector and once again to a scalar, then i - i = j - j = k - k = 1 and i . j = i - k =j - k = 0 and subsequently:
Eqs. (7-5) and (7-6) are known as Fick's second law for the case where the diffusion has a constant diffusion coefficient. The immediate result of the above discussion is that the diffusion equation can be transformed into the differential equation for heat conduction by substitution of c by T and D by IC. This analogy has the consequence that practically all mathematical solutions of the heat conductance equation are applicable to the diffusion equation. The analogy between diffusion and conductance should be kept in mind in the following discussion although the topic here will be mainly the treatment of the diffusion equation, which represents the most important process of mass transport.
7.1.3 The general transport equations If diffusion and convection currents are similar in magnitude then the total transport is the sum of all the individual contributions. While convection currents caused by mild shaking of low viscosity liquids lead to a much faster mixing than by diffusion processes, the influence of convection decreases with increasing viscosity (e.g. mayonnaise). A decrease in concentration in addition to physical transport effects can also be the consequence of a chemical reaction taking place. The concentration decrease per unit time caused by chemical reaction is defined as the rate of reaction r and is a function of the concentrations present at the reaction site:
The proportionality factor k is the reaction rate constant. The exponent n, usually 1 or 2, specifies the order of the reaction.
188
Piringer
The simultaneous occurrence of reaction and transport processes can be represented by adding the contributions together and, for the total concentration decrease over time at a given point P(x,y,z) in the media considered by the general transport equation one obtains:
II
- _
at total
= div
J (Diffusion)
+ div J (Convection) +
r (reaction)
A typical example of transport and reaction occurring during storage of a package is the spoilage of fat-containing food by oxidation with oxygen transported from the atmosphere through the packaging. Equation (7-10) is a mass balance. At every location a decrease in concentration of substance i takes place by transport and chemical reaction. Thus the total decrease -&/at is equal to the amount of substance leaving the location, which includes the changes due to diffusion and convection plus the loss due to chemical reaction. By this the description of the location where the processes take place is properly described as the source of substance i.
7.2 Solutions of the diffusion equation For interactions between packaging and product the above descriptions of both material transport processes by diffusion and convection as well as the simultaneous chemical reactions come into consideration. The general transport equation (7-10) is the starting point for solutions of all specific cases occurring in practice. Material loss through poorly sealed regions in the package can be considered as convection currents and/or treated as diffusion in the gas phase. A solution of the general equation delivers the concentration contribution at every point in time and at every location throughout the volume considered, thus c = c(x, y, z, t). The general form of the transport equation as a second order partial differential equation has no solution. Analytical solutions are given however for numerous special cases. For solutions involving complicated cases, simplifying approximations are used or numerical solutions are carried out. Since the general equation (7-10) represents a starting point not only for interesting interactions but also for the complete chemical reaction technology, there are numerous solutions described in the literature which can be applied to interaction problems. The usefulness of analogous considerations was already mentioned in the comparison of diffusion and heat conductance. Since Eq. (7-10) is composed of the sum of its members, it is logical to consider next the contribution of each individual component. The fastest step in a group of simultaneous overlapping processes is the most important. If the overall process is the result of a series of processes taking place one after another, for example as a consequence of transport processes through one or more boundary surfaces, then the slowest step of the process determines the rate of the overall process. Mass transport by diffusion is without doubt the most important process throughout the storage of packed products. The discussion of the solution begins then with the diffusion equation Eqs. (7-5) or (7-6). In order to start with the most general case in which the diffusion coefficient D is not constant, one can also write:
Trailsport equations and their solutions
189 (7-11)
While numerical methods come into question for solutions involving variable D, D can be assumed to be constant or practically constant for most cases of practical interest. In addition, simplified solutions for diffusion along the x-axis can be used instead of the general solution, except for some particular cases which will be pointed out later. This greatly simplifies presentation of the problem and the resulting equation for diffusion is:
(7-12)
7.2.1 Steady state The simplest case t o solve is when the concentration stays constant over time in the polymer. If diffusion occurs only along the direction of the x-axis then: (7-13)
D $=O
This particular case exists for example in the diffusion of a substance through a film with thickness d (Fig. 7-3) if the concentrations at the two surfaces C I at x = 0 and c2 at x = d remain constant (stationary case):
0
X
d
Figure 7-3. Diffusion (permeation) through a film at steady state.
A first integration of Eq. (7-13) then gives:
* dx
= constant
(7-14)
A constant concentration gradient exists in the film perpendicular to the film’s surface and consequently there is a constant diffusion flux in the x-axis direction according to Eq. (7-3c) at every location between x = 0 and x = d. Integrating Eq. (7-14) again leads to:
190
Piringer
c-c1 ~2 - ~1
-s
(7-15)
d
and the amount of the flux through the film is:
.D & = D dX
d
(7-16)
7.2.2 Nonsteady state A number of solutions exist by integration of the diffusion equation (7-12) that are dependent on the so-called initial and boundary conditions of special applications. It is not the goal of this section to describe the complete mathematical solution of these applications or to make a list of the most well-known solutions. It is much more useful for the user to gain insight into how the solutions are arrived at, their simplifications and the errors stemming from them. The complicated solutions are usually in the form of infinite series from which only the first or first few members are used. In order to understand the literature on the subject it is necessary to know how the most important solutions are arrived at, so that the different assumptions affecting the derivation of the solutions can be critically evaluated. Most solutions of the diffusion equation (7-12) are taken from analogous solutions of the heat conductance equation that has been known for many years: (7-17) which can be directly applied to diffusion problems. The standard reference work on the mathematics of diffusion is by Crank (1975), from which most of the solutions contained in this chapter have been taken. The solutions themselves have their origins in the older and more comprehensive reference work on heat conductance in solids by Carslaw and Jaeger (1959). The selection of diffusion equation solutions included here are: diffusion from films or sheets (hollow bodies) into liquids and solids as well as diffusion in the reverse direction, diffusion controlled evaporation from a surface, influence of barrier layers and diffusion through laminates, influence of swelling and heterogeneity of packaging materials, coupling of diffusion and chemical reactions in filled products as well as permeation through packaging.
7.2.3 Diffusion in a single phase homogeneous system The diffusion problem is simplest to solve analytically if the diffusing substance is concentrated at the beginning of the process in an infinitely thin sheet (plane) and then diffuses perpendicular to the plane of this sheet into an infinite liquid media found on both sides of the sheet. The flowing away from or diverging from the source is, once more, a graphic example for the expression of the diffusion equation in the form represented in Eq. (7-6): -dc/at = div J. A model corresponding to this situation can be represented by a long cylindrical shape made from a polymeric material, e.g. polyethylene, with a cross section of 1 cm2. In the middle of the material there is a very thin layer of material colored with a pigment which acts as a diffusion source (Fig. 7-4a). The color molecules then diffuse outwards towards both ends of the bar
191
Transport equations and their solutions a
6.
1
I o,8i "'€1 A 1
0
- X t -
Ib
0.6
-+X
0.4
i,
Dt=0.3
0.2
0
--
__.I
-3
-1
-2 -x
0
-._ 2
1
3
x
Figure 7-4: a ) Two sided diffusion from an infinitely thin layer (source). b) Distribution of concentrations for different values of the product Dt.
along the x-axis of the coordinate system without reaching the ends of the bar during the time interval considered. At t h e beginning of diffusion, time t = 0 and the total amount of color having mass m is located at position x = 0. Because of the theoretically infinitely thin layer 6x of the color source, the initial concentration there is infinite and the concentrations at all other positions of the bar are zero. The solution of the diffusion equation (7-12) is immediately given as: c=
A
exp
(-a&)
(7-18)
1 1 -
where A is the integration constant whose formation can be easily checked from the partial derivatives ocli3 and i)2cldx2 from Eq. (7-12). The expression in Eq. (7-18) is symmetric with respect to x = 0 because of x2 and goes to zero if x becomes positively or negatively infinite and t > 0. With help from the substitution:
_ _ = q2;
dx
=
2 (D t)ll2 dq
(7-19)
and because the total amount m is obtained, which means: +x
m = ,[ c dx
(7-20)
--x
one can write: +x
m = 2 A D1/2
exp (- q2) dq = 2 A (n D)'/'
(7-21)
--x
The values for A resulting from Eq. (7-21) are used in Eq. (7-18) and then one obtains the solution: (7-22) for the spreading of the color by diffusion. The increased spreading with time can be seen in Fig. 7-4b.
192
Piringer
In the above case, half of the substance diffuses in the positive direction and the other half in the negative direction of the x-axis. If an absolute barrier is now assumed to exist at position x = 0 so that diffusion can occur only in the direction x > 0 then the half of m diffusing in the x < 0 is reflected by the barrier and overlaps the other half diffusing in the x > 0 direction (Fig. 7-5a). Because the symmetry of the curve (7-22) with respect to the source at the position x = 0, one obtains a solution for diffusion in a half open media that is double the value of Eq. (7-22): c=-
(7-23)
The requirement of a barrier layer at x = 0 is expressed mathematically by the boundary condition of 8c/& = 0 at x = 0. The first complication for the application of the diffusion equation Eq. (7-12) comes when the complete left half of the plastic bar, x < 0, is uniformly and completely colored with coloring agent which can diffuse in the direction of x > 0 (Fig. 7-5b). The concentration of the color is expressed by the finite concentration of co. In order to find a solution to the problem the colored region x < 0 is thought of as being divided into an infinite number of layers perpendicular to the x-axis. In doing this, the problem can be related to an infinite number of diffusion sources and the mathematical solution can be arrived at by overlapping many solutions of the form of Eq. (7-18). Considering the thickness 6s of such a source (Fig. 7-5b), then one gets the amount of substance contained in the cross section of the bar, co 6s, because it has the unit surface area. One obtains the expression for the concentration c, of the color originating from this source at a distance s at time t according to Eq. (7-22): 2
(K
(7-25)
D t)‘
The integration of c, over all layers 6s gives with Eq. (7-25) the concentration c(x, t) at any position x > 0 at time t:
(7-26)
b
a
il 0
-X-
+X
-X-
s
O
-+x
Figure 7-5: a) Single layer diffusion from a source with a bamer on one side. b) Diffusion from an infinite thick layer represented as coming from infinitely many sources.
Trmsport equations and their solutions
193
With c,(x, t), the concentration coming from the source is designated for position x at time t at a distance s from the initial point. In order to make the right side of Eq. (7-26) easier to use, the following relationship can be considered:
1 - erf(z) = erfc
=
(7-28)
(2)
where the error function erf (z) is given by: erf(z) = $Texp(-q2)
dq,erf(-z)
=
-erf(z);erf(O) = O;erf(m) = 1
(7-29)
0
for which complete tables are available (Table 7-1). The complement of erf (z) is designated erfc (z) and is also given in Table 7-1. The solution Eq.(7-26) can now be expressed in a convenient and easily useable form: c (x, t)
= 2:1 c0
erfc
(7-30)
Table 7-1: Table of different error function forms. z
erf z
erfc z
F(Z)
0.00
0.000000
1.000000
0.00000
1.10
0.880205
0.119795
0.59827
0.05
0.056372
0.943628
0.05401
1.20
0.910314
0.089686
0.62146
0.10
0.1 12463
0.887537
0.10354
1.30
0.934008
0.065992
0.64236
0.15
0.167996
0.832004
0.14908
1.40
0.952285
0.047715
0.661 26
0.20
0.222703
0.777297
0.19098
I .so
0.Y66105
0.033895
0.67841
0.25
0.276326
0.723674
0.22965
1.60
0.976348
0.023652
0.69405
0.30
0.328627
0.671373
0.26540
1.70
0.983790
0.016210
0.70834
0.35
0.379382
0.620618
0.29850
1.80
0.989091
0.010909
0.72144
0.40
0.428392
0.571608
0.32921
1.90
0.992790
0.007210
0.73349
0.45
0.475482
0.524518
0.35775
2.00
0.995322
0.004678
0.74460
0.50
0.520500
0.479500
0.3843 I
2.10
0.997021
0.002979
0.75488
0.55
0.563323
0.436677
0.40907
2.20
0.998137
0.001865
0.76441
0.60
0.603856
0.3961 44
0.43220
2.30
0.998857
0.001 143
0.77326
0.65
0.642029
0.357971
0.45382
2.40
0.999311
0.000689
0.78150
0.70
0.677801
0.3221 99
0.47407
2.50
0.999593
0.000407
0.78919
0.75
0.71 1156
0.288844
0.49306
2.60
0.999764
0.000236
0.79640
0.80
0.742101
0.257899
0.51090
2.70
0.999866
0.000134
0.80310
0.85
0.770668
0.229332
0.52767
2.80
0.999925
0.000075
0.80950
0.90
0.796908
0.203092
0.54347
2.90
0.999941
0.000041
0.81540
0.95
0.820891
0.179109
0.55836
3.00
0.999978
0.000022
0.81540
1.00
0.842701
0.157299
0.57242
194
0 1
Piringer
0” 0.5
Figure 7-6: Concentration distribution curve for diffusion from an infinitely thick initial layer.
X __ 2 m
The shape of the concentration curve is shown in Fig. 7-6. At position x = 0, c = 0.5 cg for all values o f t > 0. The amount of substance diffused into the uncolored portion of the bar up to time t (shaded region after x > 0) is equal to the amount of substance diffusing out of the colored portion (shaded region x < 0). Example 7-1. A 10 cm high cylindrical shaped wheel of cheese contains a homogeneously dispersed ingredient with a concentration c,, = 100 mg/kg. A second similar wheel of the same type of cheese without this ingredient is laid on top of the first wheel. Assuming there is intimate contact between the two wheels o f checsc. what is the concentration of this ingredient in the second block of cheese at a depth of 1 mm after 25 hours of contact? D = 3E-7 cm2/s. This problem corresponds to the example in Figure 7-Sb. A 10 cm thick wheel of cheese can be considered to be infinitely thick with respect to the diffusion coefficient provided the contact time is not too long. Eq. (7-30) can be used to solve the problem. For x = 0.1 cm, t = 2Sh 3600s/h = 90000s and D = 3E-7 cm’h on calculates:
Looking up the value for erfc z in Table 7-1. erfc(0.3) = 0.671373, and using this value in Eq. (7-30) the concentration of the ingredient at this time and distance can be calculated to be: c(x, t) = . c0 erfc(z) = 0.5 . 100 0.671373 = 34 mg/kg
f
Example 7-2. What would the distance from the surface of the second wheel for the 34 mg/kg concentration from Example 1 be after a) three months? b) after one year? Assume that the storage conditions remain constant and the properties of the cheese wheels also remain constant during these times. Because the z values from Eqn. (7-30) will always lead to the same concentration (i.e. 34 mg/ kg), one can simply solve z for the distance: After 3 months: (3mo .30d/mo .24h/d 3600s/h = 7776000 s: X X z =- 0.3 x = 0.93 cm 2 ( D ti”’
= 2 (3 09E-7 7776(XXh)’” -
After 1 year: z =
X
2 [D.l)’/’
~
~
-0.3
2 - ( 3 096-7.31 IllJO~Xls)”2 -
x = 1.9 cm
Trrrrisport equations and their solutions
195
Dimensionless parameters and the proportionulity of mass transfer to the square root of time
In order to compare results of studies that are expressed in different quantities, dimensionless representations are always preferred. Examples of dimensionless quantities are the relative concentration c/cOalready mentioned above and the parameter appearing in the error function z = x / 2 (D t)1’2 in Fig. 7-6. Systems described with help from the same model but differing from one another with respect to material constants, e.g. D values, can have the same z and c/co values at different times. As a result, whole series of curves can be represented by a single, easy to read curve. Since the same z values always lead to the same c/co values, the distance xc which is the distance the diffusion front having concentration c has traveled from the surface with a constant initial concentration cg to time t, the definition of z is given as: 2 (D t)lI2 z xc :
(7-31)
Like in the solution given for the diffusion out of a bar colored on one side bar in Eq. (5-30),it can be seen that the same c/co values always result for the same z values. This means that the diffusion front of a given concentration c is proportional to the square root of Dt. The error function used in solving the above diffusion problem occurs as a consequence of the summation of an infinite number of infinitely thin colored layers, which themselves bring about an exponential distribution of the concentration. Because of the error function’s significance for numerous practical cases, this solution will be treated in somewhat more detail. In the same manner, one obtains a solution to the diffusion equation starting with a colored layer having a finite thickness 2d and an initial concentration cg in both directions of the unbounded x-axis (Fig. 7-7): (7-32)
In the next example a short section of length 1 is cut from the plastic bar (Fig. 7-8). The bar is uniformly colored from one end up to a layer thickness of d with a pigment having concentration co. The zero position of the x-axis is assigned to the colored end of the bar. With the mathematical boundary conditions x = 1, ac/ax = 0, one finds that the diffusion of a color molecule in the uncolored section cannot go further than the theoretical barrier existing at x = 1 and is reflected back. For illustration purposes the representation of the concentration profiles of this process are shown by straight lines with different slopes in Fig. 7-8. The reflected path of the curve from a source 6, now overlaps the original curve and the concentration at a given location x of the bar is the
-X
-
0 -+x
Figure7-7: Two sided diffusion from a finitely thick layer.
196
Piringer
Figure 7-8: Single sided diffusion from a finite thick layer into a finite layer of the same material.
sum of the two contributions. A further reflection takes place at the other end of the bar at x = 0 and then again at x = 1 and so forth, whereby every reflected curve section overlaps the previous section. Because the original curve is already represented as the sum of two error functions, the complete system is represented by a series of error functions:
’
i co n = O [erf (d 2+ (D2 n l - x t)l/*
)
+
erf
(
d-2nl+x 2 (D t)’/*
)]
(7-33)
Even though the above method of solution of the diffusion equation (Eq. 7-12) becomes impractical for complicated cases, it illustrates the appearance of the error function in problems where diffusion from an infinite number of sources occurs and the solution is obtained in the form of an infinite series as a result of the overlapping of diffusion streams. The overlapping diffusion streams are due to an infinite number of repeated reflections at the ends of the diffusion path which are spaced finite distances apart. As seen in Fig. 7-8 the decrease in concentration is shown by sloping lines so that after each reflection the corresponding amount relative to the total concentration c becomes smaller. Due to the exponential character of the solution, the decrease is much more rapid than in the simplified representation shown in the figure and the series converge very rapidly, so that after a few terms the total concentration at a given location and time stays practically constant. There are other different methods for solving the diffusion equation in Eq. (7-12) which are described in mathematics books. Older methods, in particular separation of variables x and t are worth mentioning. They also produce infinite series in their solutions in the form of the Fourier trigonometric series. A further, very elegant analytical method uses the Laplace transforms (Kreyszig 1993). In addition to analytical solutions the possibility exists to obtain numerous exact solutions using numerical methods with help from computers. The advantage of numerical methods lies primarily with their application for complicated cases, e.g. for non-constant diffusion coefficients, for which there are no analytical solutions.
Transport equations und their solutions
197
Example 7-3. A 100 pm thick plastic film contains an initial concentration of 100 mg/kg of some additive. This film is brought in direct contact with another 100 pm thick plastic film of the same material initially containing no additive. Assuming ideal contact between the two films (i.e. no boundary conditions exist to hinder the transfer across the interface). The exterior sides of the f i l m are no1 permeable (they are in contact with a glass or metal surface). The diffusion coefficient of the additive is 3E-7 cm2/s for both films. What is the concentration on the outside of the second film after one minute contact time? This example corresponds to Fig. 7-8 in the text. The solution can be obtained using Eqn. (7-33). Putting d = 0.01 cm, 1 = 0.02 cm and x = 0.02 cm one gets a constant sum of c = 14.8 mg/kg after two steps n = 0 and n = 1: c =1 ' C() ' 2
5{
erf(ci
n=O
;, { (" erf
cg
n=O
forn=O: forn=O: forn=1: forn=1: forn=-1: forn=-l: c=
1 '
(+ ( ( ( (+ (
f 2 . n . I - x) 2 . (D . t)'/*
2 . (D . t)'I2
d -2.n . I
+
+
(" ("
erf
erf
)=( + )=( + )=( )=( ) =( + )=( +
2.n ' 1 -x
d
+
- 2 . n .I x) 2 . (D . t)'/'
- 2 , n . 1 +x) 2 . (D . t)'/'
}+ }
0.01 f 2 ' 0 0.02 - 0.02 2 (3E - 7 . 60)1'2
x
2 . (D . t)1/2
0.01 f2 . O -0.02 + 0.02 2 (3E - 7 . 60)'12
d+2 .n . I -x
0.01
2 (D . t)'/' d-2.n.l-t~
2 . (3E - 7 . 60)'12 0.01 2 ' 1 0.02 + 0.02
2 . (D . t)'/'
2 . 1 .0.02 - 0.02
-
= -1.1785
= 3.5355
= 3.5355
'
2 . (3E - 7 . 60)'12
2.n 1-x
0.01 - 2 1 .0.02 - 0.02
2 . (D . t)"2 d - 2 . n .1 x 2 . (D . t)'/'
2 . (3E - 7 .60)'/' 0.01 2 . 1 '0.02 + 0.02 2 . (3E - 7.60)'/'
d
=
-1.1785 =
-5.8926
= 8.2496
+ erf(3.5355) + erf(3.5355) + erf(-1.1785)}+ {erf(-1.1785) + erf(3.5355) + erf(-5.8926) + erf(8.2496)) =
100' {erf(-1.1785)
1 100 2 = 50{-0,9012 -.
+
2 . n , 1 - x) 2 . (D . t)1/2
+ 1 + 1 + -0,9012) + 50{ -0.Y012 + 1 - 1 + l } = 9.88 + 4.94 = 14.8 mg/kg
After terms higher than n = 1 the error function terms start canceling themselves out.
Comparison of different solutions for the same special cases
Various methods can give different expressions for the solution of the same application. Even though these lead to the same result, the solutions of problems in the form of infinite series can converge at varying rates. Consequently some solutions are favored over others, depending on the parameters under consideration. Finally, the considerations of the homogenous plastic bar model will be used as an example to show the differences between different solutions.
198
Piringer
-I
0
+I
-+x
-X
Figure 7-9: Two-sided diffusion into a finitely thick layer.
A plastic bar of “infinite” length (e.g. 1 m or longer) is uniformly colored with an initial color concentration of co (Fig. 7-9) except for a thin layer in the middle with thickness d = 2 1 (approximately 1 cm). As a simplified approximation it is assumed that the concentration of the color at the location x = f 1 remains constant at co. The boundary conditions are expressed mathematically as: c=co,
x=fl,
g=0,
x=0,
t
> o (7.34)
t > 0
The condition of &/ax = 0 at the location x = 0 expresses the requirement that no diffusion can take place through the axis of symmetry at x = 0. This leads to the same result as single sided diffusion in a layer having half the thickness. For the solution of the diffusion equation, Eq. (7-12), two different series expressions can be obtained:
The first series converges very rapidly for not too large values of D t / 12, in other words for relatively short diffusion times. For D t / l2 = 1 the concentration ratio c/co at location x = 0: c/co = 0.9590 - 0.0678 + 0.0008 = 0.8920 and for D t / l2 = 0.25: c/co = 0.3146 - 0.0001 = 0.3145. The trigonometric series in Eq. (7-35) converges rapidly for large t values. For D t / l2 = 1 it is: c/co = 1 - 0.01080 = 0.8920 and for D t / I* = 0.25: c/co = 1 - 0.6872 + 0.0017 = 0.3145.
7.2.4 Diffusion in multi-phase systems In this section the important cases for food packaging are treated. These cases differ from the previous examples in that mass transfer takes place across an interface between two different media with different characteristics, e.g. with different diffusion coefficients. If the value of a quantity is desired, for example the concentration of the substance transported across the interface in one of the two media, then a mass balance must be considered that takes into account the ratio of the contact surface area and the volume of the corresponding medium.
Trnrisport equations and their soiuiions
199
Diffusion in polymer / liquid systems For the sake of conformity, in the following every quantity related to the packaging is designated with the index P; and the quantities related to the food are labeled with the index L. Fig. 7-10a shows a model that describes the mass transfer of a component dissolved in the filled product L, e.g. an aroma compound, into the packaging material P. The model is based on the following assumptions: 1. A component i in the liquid phase with an initial concentration C L . ~is sorbed onto the contact surface area A between the liquid and packaging and subsequently diffuses into the matrix of the packaging. In so doing there is a decrease in concentration in the region of the contact surface which leads to further transport of i from the matrix of the liquid to the contact surface. 2. The mass transfer, controlled mainly by diffusion taking place in the packaging during storage, is several orders of magnitude lower than diffusion in the liquid phase. The difference is even greater when mixing (convection) occurs by shaking, e.g. during transport. It can be assumed that the concentration of component i in L, CL,~, is dependent on time t but not on the distance x from the contact surface. 3. A constant distribution of i between L and P takes place that is independent of concentration of i and time. For relatively small concentrations of i (< 1 YO) this approximate assumption is fulfilled and one defines the partition coefficient K as a constant ratio of the concentration i in the packaging material at time t on the contact surface cp., (dp) to the concentration of i in the liquid independent of location at the same time, c ~ , ~ :
(7-36) Where K is the ratio at t = o(j of the equilibrium concentrations of i in P, cp,, to that in L, this concentration ratio is also sometimes referred to as the relative solubility constant, S,, of i in P (relative to cL.,). 4. The second important quantity influencing the mass transport is the diffusion coefficient DP of i in P. For relatively low concentration ranges assumed for i in L, Dp is assumed to be constant. The diffusion controlled mass transport rate of i in P leads to a decrease in concentration of i with increasing distance from the contact surface (Fig. 7-10a). Particularly in the initial stages of diffusion, the total amount of substance i transferred into the package can be concentrated in a region near to the contact surface next to L while the location dependent concentration of i in P in the matrix of the packaging is equal to zero. 5. The mass transport is assumed to occur in the x direction perpendicular to the contact surface. Even though the geometry of the packaging/product system influences the amount of mass transport occurring, it is of minor significance for most practical cases. 6. All above assumptions are valid for mass transfer in the reverse direction as well. This means the migration of component i from the package into the product is also described (Fig. 7-lob). By considering the corresponding initial conditions the mathematical solution of the problem results in the same form. 7. The contact between packaging and product shown in Fig. 7-10a and b is singlesided. This means the external surface of the packaging at location x = 0 is assumed to
200
Piringer
a
L
P
I
I
C
d
I
x =d,
X=O
P
L
L
L
x =dp+dL
c
d,-
P
L
Figure 7-10. Mass transfer between a packaging material and a liquid product; a) diffusion out of the liquid into the package, b) diffusion out of the package into the liquid, c) cross section of a representative container, d) two-sided contact of a package material with a liquid.
Trmsport equutions and their solutions
201
be impermeable to i. The model also establishes an absolute barrier layer at the location x = dp + dL which simplifies the representation of the problem. A representation closer to conditions in practice is shown in Fig. 7-1Oc for a plastic container with a wall thickness of dp. The single difference to Fig. 7-10a is that the sum of the two contact surfaces A‘ in Fig. 7-1Oc is replaced by A = 2 A’ in Fig. 7-10a and b. In the literature one frequently finds a two sided contact with the packaging using the same model shown by the representation in Fig. 7-10d. Because the axis of symmetry at x = 0 serves as a barrier layer in the mathematical boundary conditions, the expression for the solution is not changed when instead of the half layer thickness dJ2 = 1 for two sided-contact of P, the actual layer thickness dp with single-sided contact is used. This is because in the symmetrical model in Fig. 7-10d the total layer thickness of the liquid dL is taken into consideration. The symmetrical model in Fig. 7-10d also illustrates the common two-sided contact migration measurement practice in which a film or sheet is immersed in a liquid. One obtains the corresponding volumes of the packaging, Vp = dp A, and liquid, VL = dL A, using the layer thicknesses dR dL and the contact surface area A. With the corresponding densities of the liquid, pL, and packaging, pp, the mass of liquid, mL = pLVLand mass of packaging, mp = pp Vp can be calculated. In many practical cases the assumption pL = pp E 1 can be made for simplification without significant error. With dimensionless quantities a and T (7-37) one obtains for the mass transfer by diffusion of i from a well mixed liquid (assumption 2) into a package or the migration in the opposite direction the general expression from Crank:
(7-38) Eq. (7-38) is a solution of the diffusion equation (7-12) for the models shown in Fig. 7-10. Where m, is the mass of i diffusing up to time t from L through the boundary surface A into the package or opposite direction and m, is the amount which has migrated at equilibrium. The parameters qn in the series are the positive roots of the trigonometric identity tan q,, = - a 4., Several values of this parameter for various a and n are given in Table 7-2. The values of q, lie between n n ( for a = 0) and (n - 1/2) n (for a = m). For a << 1 then qn 2 n n/(1 + a ) , and for the remaining a values q, z [n - a/2(1+ a)]n. The solutions of Eq. (7-38) converge rapidly for long diffusion times, while for short times, e.g. at the beginning of diffusion (T z 0.001), approximately 50 terms are needed. Even though this equation is no obstacle for today’s PCs, it is more convenient for short times to use the form of the solution based on the error function: (7-39) with: (7-40)
202
Piringer
Table 7-2: Roots of tan qn = -aq, ~~
a
41
q2
q3
q4
1.5708
4.7124
7.8540
10.9956
4s 14.1372
qh
02
9.0000
1.6385
4.7359
7.8681
11.0057
14.1451
17.2852
4.0000
1.7155
4.7648
7.8857
11.0183
14.1549
17.2933
17.2788
2.3333
1.8040
4.8014
7.9081
11.0344
14.1674
17.3036
1.5000
1.9071
4.8490
7.9378
11.0558
14.1841
17.3173
1.mo
2.0288
4.9132
7.9787
11.0856
14.2075
17.3364
0.6667
2.1746
5.0037
8.0385
11.1296
14.2421
17.3649
0.4286
2.3521
5.1386
8.1334
11.2010
14.2990
17.4119
0.2500
2.5704
5.3540
8.3029
11.3349
14.4080
17.5034
0.1111
2.8363
5.7172
8.6587
11.6532
14.6870
17.7481
0.000
3.1416
6.2832
9.4248
12.5664
15.7080
18.8496
In Table 7-1 the values for the function contained in brackets in Eq. (7-39) are given as: F(z)
=
1
-
exp (z2) erfc (z)
(7-41)
Equation (7-39) is particularly suitable for T < 1 and a < 100. A convenient rational approximation of the error function formula in Eq. (7-39) is: 5
x = ( I +a) 1 m ,
-
C n = l
anr”
I
(7-42)
with r = 1/(1 + 0.3275911 T1’2/a); a l = 0.25482592; a2 = -0.28449636; a3 = 1.42141371; a4 = -1.45315207; a5 = 1.061405429. For T > 1 or a > 100 this approximation must not be used (Chang, 1988). The solutions in Eqs. (7-38), (7-39) and (7-42) are valid for material transfer of a component i from food into the package (Fig. 7-10a) as well as for the migration from packaging into the food (Fig. 7-lob) under the assumptions of the described model. However, because at the beginning of diffusion in the first case the total amount mo of i is in L and in the second case it is in P, the values of m, and mOcrelative to mo must be different for the two cases.
1. Mass transfer from L into R The mass balance for i is given as: VL
CL,m
+
VP
CP>,
= VL CL,0 = mL.0
(7-43)
where cL.0 is the initial concentration of i in L. For the amount m, = mp,nc,the amount of substance i in P after reaching equilibrium is obtained from Eq. (7-43) with the L , ~ Eq. (7-36) when Eq. (7-37) is taken into consideration: definition K = C ~ , ~ / C from (7-44)
Trctnsport equations and their solutions
203
The ratio of mP,= and mL,o labeled Up,, shows the fraction of the total amount of i in the package at equilibrium: (7-45) For a = 1then up t o half of i would diffuse into the package at equilibrium. 2. Migration from P into L.
The total amount mp,o of i is contained in P at time t = 0 and the mass balance is expressed as: VL
CL.X
+
VP CP,,
= VP CP,0 = mp.0
(7-46)
The amount of substance transferred into the food at equilibrium m, = mL,m= V L . C ~ ,is obtained by combining Eqs. (7-36), and (7-37): (7-47) and related to mp.o the fraction of the total amount is given by:
The fraction of i diffused from L into P up to time t, from mL.(] = VL cL.0 and the fraction migrated from P into L up to time t, from mCo= Vp cP,()are: (7-49)
(7-50)
Example 7-4. Ten 4 cm diameter circular 200 pm thick plastic film pieces are mounted on a stainless steel wire and placed in a glass vial containing 100 ml solvent. What percentage of the additives initially contained in the plastic migrate into the liquid over the 24 hour period ( D p = 2.1OE-10 cm2/s)? Note that the plastic additives are readily soluble in the solvent, the solvent has low viscosity and the solvent does not swell the plastic. This case corresponds to Fig. 7-10b with variation 7-10d. Because the additives are readily soluble in the solvent K z 1 can be assumed in Eq. (7-36). The volume of the plastic is: Vp = 10. n:. r2 . h = 10 K 2 cm2 0.02 cm = 2.51 cm3 llsing Eq. (7-37) one gets:
Given the two sided contact of the liquid with the plastic 0.5 d p = 0.5.0.02 cm = 0.01 cm and thus with Eq. (7-37) one gets for T: Dp.1
2 IE-lOcmZ/s (2460.60 s)
(0.01 cm)*
= 0.181
204
Piringer
With a = 39.8 one uses the values for a equal to infinity (00) in Table 7-2 for the roots of tan qn = -CI. q,?.Carrying out calculations with Eq. (7-38) for the fraction of additive migrating at time f to what would migrate at f = co:
1 -
2.3Y.X(l+39.8) I +39.8+3Y.X2I 570S2 exp(-1.570S2
2-39.8(1+39.X)
.0.181) - 1+.3Y.X+39,824,7,242exp(-4.71242 .0.181) =
1 - 0.65544 - 0.001657 = 0.473 Note that for the summation the second term is quite small. Because the mass balance for migration out of plastic into a liquid (Eq. 7-47) shows mL.x, = mp.0: a
mL.r = mp.0,
39.8
= mp.O1+39,
I
..
2 mP.0
Therefore, the percentage of additive that has migrated from the polymer in 24 hours is according to Eq. (7-50) is 46.1 YO:
Example 7-5. What percentage of the additives migrate out of the plastic into the liquid in Example 4 when the partition coefficient K = 133? Starting with Eq. (7-38) one first calculates mt/m,: a = -1 .vL = -1. _100 = 0.300 K
133 2.51
Vp
1 - 0.13368 - 0.00128 = 0.865 Note that the values for q,, are estimated by linear interpolation of Table 7-2 values. Now calculating the fraction migrated from the polymer into the liquid: mL1 a 03 U L ,= ~ 2 - = 0.865 . __ = 0.20 mL.x
]+a
1+03
The percentage remaining in the polymer is 20 YO.Compared with Example 4, this result illustrates the effect of the larger partition coefficient where the migrant is more favorably retained in the polymer as opposed to the liquid. Example 7-6. Solve Example 4 using Eq. (7-39) and compare the two results. Starting with a = 39.8 and T = 0.181 from Example 4 calculate the value for z: T'12
z = - =a
0.181'/z
~- - 0.01069 39.8
Entering this value for z in Eq. (7-39) one can solve for m,/m,: ml -=
my
(1 + a )[l - exp(z2)erfc(z)]= (1 + 39.8) [l - exp(0.010692)erfc(0.01069)]=
(1+ 39.8) [l - e~p(0.01069~) . (0.98795)] = 0.487 Then calculating the fraction migrated using the mass balance equation: mLl a 3Y x U L ,= ~ _ _ . - = 0.487 . __ = 0.475 mLx
l+a
1+3Y.X
Transport equations and their solutions
205
rhus 47.5 % of the additive in the polymer migrates in 24 hours which is very close and within :xperimental error to the result in Example 4 of 46.1 %. Vote the values of erfc(0.01069) are estimated from the Table 7-1 values by linear interpolation.
Example 7-7. Edible oil is stored in a plastic bottle with an external diameter of 10 cm and with a wall thickness of 2 mm. What percent of the antioxidant contained in the plastic bottle nigrates after a) 100 days and b) after 2 years into the oil when the antioxidant has a diffusion :oefficient of D p = 1E-11 cm2/s? I ) This example corresponds to the case shown in Fig. 7-1Oc. Calculating a, Tand z:
, = - I. LV= - AI -d - 1 4 . 8 - 24 K
K dp
Vp
r = -d=i c=-=
1 0.2
IE-llcm2/s (100.24-6l)bOs)
Dp t
= 0.00216
(0.2 cm)2 0.00216'~'
TI/?
~
24
= 0.00194
For small times one can use Eq. (7-39) and performing linear interpolation on the z values between 1 and 0.05 in Table 7-1: mt -=
n,
(1 + a)[l- exp(z2)erfc(z)]= ( I
+ 24)[1 - exp(0.001942)erfc(0.00194)]=
( 1 + 24) [l - e ~ p (0 . 0 0 1 9 4 .~(0.997813)] ) = 0.0546 m~~
UL I = ~.
mLx
a
-=
I+a
24
0.0546 . = 0.0524 1124
Thus 100' mL/mx= 5.24 YO migrates b) Using Eq. (7-39): = Dp' = IE~11cm2/s-(2.3h5.24h0.60s) d; TI,'*
z = - = a-
= 0.01577
(0.2 cm)2
0.01.5771/2
24
= 0.005232
Using the same Eq. (7-39) and performing a linear interpolation on the erfc values for z between 0.05 and 1.0 in Table 7-1: mt
-= n1
(1
( 1 + a ) [l - exp(z2)erfc(z)]= (1 + 24) [ I
-
e~p(0.00523~)erfc(O.00523)] =
+ 24) [l - e ~ p( 0 . 0 0 5 2 3 ~(0.994104)] ) = 0.1467
UL.t
mLI
a
= -..-= Ita niL
24
0.1467. -= 0.141 1+24
Thus 100. mt/m,= 14.1 %
Example 7-8. Plastic film 100 pm thick are placed between 3 mm thick slices of cheese. How many mg of plastic additive are found per kg cheese after being in contact for one day given the initial concentration of additive is cRo = I g/kg and the diffusion coefficient in the plastic is D p = 2E-10 cm2/s? The diffusion coefficient in the cheese is D L= 1E-7 cm2/s and the partition coefficient between the plastic and cheese is K = 1. The densities are pL = pp = lgkm'. This problem corresponds to the example shown in Fig. 7-1Oc. First it is necessary to calculate (Y and 7?
206
Piringer 2E-IOcm2/s.(24.60.60 s)
Dp.t
T = - d;-
(0.01
-
= 0.1728
Using Eq. (7-38) one calculates m,/m,:
1 - 0.53931 - 0.0020026 Given that: K = l = S
CL.r
’ ; , c L.m
0.45869
= CP.,
One can use the mass balance Eq. (7-46) to calculate C L . ~ . : Using the mass balance Eq. (7-46) to calculate the concentration of additive in the cheese: VL . C L . + ~ VP . CP., = VP . cp.n = mP.0 0.3 cm3 . C L +~ 0.02 cm3 C L , ~ = , 0.02 cm3 . lmg/cm3 cL.%= 0.0625 mg/cm3 = 62.5mg/kg.
By definition: CL.1 mL.1 _ =__
mL.r
CL.%
Then solve for CL.~: CL.1
-=
62.5
0.45869, :. c ~=.28.7 ~ mg/kg
In order to take into account the influence of the rate of diffusion in the cheese, Eq.(7-56) is used to calculate p: D p = -I . ( L)= -1 .
K
1
DP
The effect of smaller.
(-)1E-7 2E-10
‘1’
= 22.4
p on Eq. (7-57) versus Eq. (7-54) without p is about ( p / c I + p )
=
0.957 (4.3 %)
With equations (7-38) and (7-50), taking the mass balance into account, the migrated amount mL.,through the contact surface A during time t can be calculated as follows [if the dimension of cp,gis w/w (mg/g), then cp.0 . pp means w/v (mg/cm3)]: (7-51) The following equation (7-52) represents the simplified form of Eq. (7-51) for a >> 1:
-
(7-52)
qn = (2n-l)n/2.
Equation (7-53) is an alternative migration equation for small t-values using the error function:
Trcmsport equations and [heir sollitions
207 (7-53)
mL.tlmL..x. L 0.5
The following equation (7-54) is a simplified migration equation for K 5 1 and relatively small t-values, for which an infinite thickness of P is assumed: = 2 ~ ~ , ~Dpt)1/2= p p ( 1.128cp7opp(Dpt)'/*rcp30pp(Dpt)' I 2
J=
(7-54)
The maximum amount of migration derived from the mass balance is:
(7-55) Two typical examples of food packages with the corresponding values of the needed parameters are shown below, together with the results obtained with Eqs. (7-51) to (7-54): A = 600 cm2, d p = 0.02 em, pp = 1 g/cm', t = 864000 s (10 d), cp,o= 1000 mg/kg, DP = 1.OE-10 cm%, K = 1.
vL= 1000 cm'.
a = 83 mL.,/A (mg/dmz)
VL= 300 cm3, a = 25
(7-51)
1.042
1.030
(7-52)
1.047
1.047
(7-53)
1.049
1.049
(7-54)
1.049
1.049
Calculated with equation
The maximum amounts mL,,/A 1.92 mg/dm2, respectively.
m~.t/A (mddm')
calculated with equation (7-55) are 1.98 and
Example 7-9. Solve example 8 using the approximation equation solution in Eq. (7-54) and compare the two results. Given that: VL= AdL-= 2 cm2 0.3 cm = 0.6 cm' one can then calculate cL., using Eq. (7-54):
-
C L t =--m L ' "L PL
A cp,oK(Dpt)i'2= 1000-2 ( 2 . lo-'()' 2 4 60.60) 112-- 13.9 mg/kg.
06
This is a difference of 6.4 % between the two results which is well within most experimental migration measurement errors.
In order to use the migration equations, especially the generally accepted equation (7-51), values for the partition coefficient K of the migrant between P and L and the diffusion coefficient D P of the migrant in P are needed. For migrants with a high solubility in the foodstuff or simulant, the value K = 1 can be used and a worst case estimation is obtained in this way. For migrants with a low solubility in the foodstuff or simulant water K = 1000 can be used to obtain a worst case estimation (see also Chapters 4 , 9 and 15).
208
Piringer 1 --
I
Figure 7-11: The behavior of mass transfer from a packaging material into food for different a values.
Currently, there exists only a limited number of reliable diffusion coefficients, due to the enormous requirements needed for the experimental determination. However, even for diffusion coefficients useful estimation procedures exist (see Chapters 6 and 15). The diffusion coefficient at a given temperature T depends on the nature of the polymer, the mass and structure of the solute and on the activation energy E, in the diffusion process. The material transport from a liquid assumed to be well mixed, into packaging and the migration from packaging into a liquid both vary proportionally to the square root of time and the square root of the diffusion coefficient. While in the beginning phase (approximation equation is only valid for small z values, meaning short times) the mass transfer of i into the package is proportional to K, the migration of i from the package is independent of K. The partition coefficient plays a deciding role in the sorption (solution) of i in the packaging layer in contact with the liquid. This leads to the total amount of sorbed material being concentrated in a thin layer of packaging material in contact with the liquid and the transport process in the initial stage is independent of the material thickness. In contrast the migration process into the liquid takes place independent of K. Due to good mixing in the initial stages of migration, the total amount of material i is transported away from the contact layer of liquid into the volume of the liquid, so that the concentration in the liquid contact layer goes to zero. The rate of diffusion of i out of the package is the rate determining step and is independent of the layer thickness dp. With longer migration times the partition coefficient also plays a deciding role through the a value because for a << 1 (K >> l), mL..u/mp,m+ a and subsequently only a very small fraction of mp,omigrates into L (Eq. 7-50) (Fig.7-11).
Influence of difision in food The diffusion coefficient in the filled product must be taken into account in liquids that are not well mixed and in viscous and solid foods. This is done through the definition of a further dimensionless parameter p:
Transport rqiintions m r l their solutions
209 (7-56)
which, in addition to the parameters K and DP,contains the diffusion coefficient of i in the food. This dimensionless parameter can be combined with the approximation formula in equation (7-54) in the following way: (7-57) From this expression two limiting cases can be derived: 1. Where DL >> Dp and K 5 1,then p/(l+ p) + 1 and Eq. (7-57) goes to Eq. (7-54). This means that for high diffusion rates in the food, the rate of migration is determined by diffusion into packaging. The same result is obtained for DL DP and K << 1 meaning for approximately equal diffusion coefficients of i in L and P that transport through the packaging determines the rate of the whole process if i dissolves much better in L than in P. The flux of i through the unit surface area for equal diffusion coefficients is directly proportional to its concentration. 2. Where DL < DP and K > 1, then p/(1+ p) + p which in this case gives the following expression instead of Eq. (7-57):
=
(7-58) Here the migration rate of i in the food is determined by the value of the diffusion coefficient in the food as well as by the partition coefficient. The concentration c L , ~of migrants that are poorly dissolved in the food (K > 1) increases more slowly than when they are more easily dissolved. The exact expression for the differential equation (7-12) that takes into consideration the diffusion in food and finite values for Vp and VL is extremely complicated. The extensive calculation required for the exact expression does not justify its use when one compares the accuracy achievable in practice with the errors or deviations resulting from the use of the approximate formula (Reid et al. 1980).
7.2.5 Diffusion through a liquid boundary layer With large K values, that is low solubility of component i in a liquid food, the material transport through A can also be determined from the contribution of diffusion in L under conditions of thorough mixing. Van der Waals attractive forces between the package surface and the molecules of L in intimate contact with P lead to the formation of a thin but immobile layer in which the diffusion coefficient of i in L, DL, controls mass transport (the Nernst diffusion layer). If diffusion through the stagnant boundary layer determines the rate of transport through A for the system, then one can assume a constant, location-independent concentration cp in P. The partition equilibrium is assumed to be reached on the boundary area between P and L at x = 0 and consequently K = cp/cL(0).If one lets the thickness of the diffusion layer in L next to the surface of P be lL and if L assumes a constant concentration of cL, then one can assume a constant material transport flux through the boundary layer for short time intervals that follows Fick's first law and the contribution of the flux to time t is expressed according to Eq. (7-16):
210
Piringer
(7-59) Because up to time t: (7-60)
and CL =!EL “L
one obtains from Eq. (7-59), considering the ratio mp,o/mnc = (1 + a ) / a according to Eq. (7-48) and the definition of a (Eq. 7-37) and because Vp = A . dp: mt (1
+ 41
(7-61)
and after several rearrangements one finally obtains: d(mt/mx) dt
-
D mp.O K d i k m,
(1
- Z.!L
mx)
(7-62)
with the solution: %= mX
1
-
exp
(-0t)
(7-63)
where: (7-64) For short times if mate solution: %c%(T.
mm
(T
.t << 1 the following equation can be used as a good approxi-
t
(7-65)
The determination of (T in Eq. (7-63) is carried out by plotting In (1 - m,/m,) versus t. The slope of the line is then -o (Chang et al. 1988). If diffusion in the packaging determines the rate of migration, there is a deviation from linearity in the plot (Fig.7-12).
7.2.6 Surface evaporation A substance diffusing through the packaging towards the external environment will enter the atmosphere in the absence of a barrier layer. Water or aroma loss through permeation, and drying of a printed film by evaporation of the residual solvent are common examples of this process. In cases where the substance reaching the surface has a very low vapor pressure, e.g. a plasticizer, the rate of evaporation can be slower than the rate of diffusion through the packaging, thus determining the rate of the entire process. At very low evaporation rates the entire process can reach a standstill or lead to “sweating” in the case of low solubility of the plasticizer in the plastic. It is also possible to have the reverse process whereby a substance condenses out of the atmosphere on the package surface, e.g. water, with subsequent diffusion into P. If the packaging surface (or also that of the food) is dry, i.e. the surface has a lower water partial pressure than that in the gas phase G, then water can be absorbed.
Trrinsport equations and their solutions
I
I
21 1
I
In order to mathematically describe the evaporation and condensation processes, the simplifying assumption is used that the rate of material transport through the surface is directly proportional to the difference between the concentration cA,pon the package surface at that time and the concentration c ~in G . in~ equilibrium with the partial pressure of the substance in the atmosphere. Using this assumption one obtains the boundary condition for the surface at the location x = 0: -Dp
2
= k (CA,G
-
CA,~)
(7-66)
with the proportionality constant k. If C A , ~ ; > C A , ~condensation will take place and if CA,G < C A . ~then evaporation will take place.
212
Piringer
The general solution for this problem in the form of the dimensionless ratio mt/mnc according to Crank is:
(7-67) d
k
with L = L. DP
Values of the positive roots of the equation p tan p = L are given in Table 7-3. m, is the amount of material taken up by the packaging or evaporated from the surface up to time t and msc is the corresponding amount at equilibrium. In Fig. 7-13 the ratio of m,/m, is given as a function of the dimensionless quantity (Dp t/d;)li2 for various L values. In the absence of evaporation, the curves show a linear increase at the beginning of diffusion (Fig. 7-11) while the obvious curving shown in Fig. 7-13 for small k values is caused by the slower evaporation process. Table 7-3: Roots of ptanP=L. ~
L
PI
P2
P3
Ps
06
0.00
0.0000
3.1416
6.2832
9.4248
12.5664
15.7080
0.01
0.0998
3.1448
6.2848
9.4258
12.5672
15.7086
0.10
0.31 11
3.1731
6.2991
9.4354
12.5743
15.7143
0.20
0.4328
3.2039
6.3148
9.4459
12.5823
15.7207
0.50
0.6533
3.2923
6.3616
9.4775
12.6060
15.7397
1.00
0.8603
3.4256
6.4373
9.5293
12.6453
15.7713
2.00
1.0769
3.6436
6.5783
9.6296
12.7223
15.8336 16.0107
P4
5.00
1.3138
4.0336
6.9096
9.8928
12.9352
10.00
1.4289
4.3058
7.2281
10.2003
13.2142
16.2594
100.00
1.5552
4.6658
7.7764
10.8871
13.9981
17.1093
1S708
4.71 24
7.8540
10.9956
14.1372
17.2788
cc
0
2
4 u
dP
6
Figure 7-13: Sorption or desorption curves in the valid range of Eq. (7-66) for different L-values
Transport equations and their solutions
213
7.2.7 Permeation through homogeneous materials Steady state permeation which follows Fick’s first law has been previously described in Eq. (7-16). Assuming the concentration of i in P has a constant value cp.1 at the surface (x = 0) and has a constant value C P , ~at the other surface (x = dp) and at the beginning of permeation the concentration in the inside of P has the value cp.0 (t = O), then a nonsteady state of diffusion will take place leading to a change in the concentration cP.[ within P. For simplification one can set cRo= 0 and cr2 = 0. The resulting amount of mass diffusing through the package up to time t is then given as: mt = A dp cp,l
(7
-
5 C [g exp(-Dp XI
-
n2 n2 t/d$)
n = l
This equation becomes asymptotic to the straight line: (7-69) as t
---f
00.
The intersection of this straight line with the t-axis at location 0 is: (7-70)
This is Barrer’s equation for determining of the diffusion coefficient using permeation measurements (Fig. 9-1). The steady state permeation flux is given by the slope of the straight line (7-69): (7-71) This expression is identical to Eq. (7-16) for
= 0.
7.2.8 Permeation through a functional barrier Let us consider a plain sheet of a laminate made of a solute containing core layer (P) and a virgin layer (B) of the same polymer type (Piringer et al. 1998). The thickness of P and B are a and b, respectively, and d = a+b. The virgin layer is in contact with a liquid layer (L). The thickness of the virgin layer (B) is such that it acts as a barrier against the diffusing solute out of the core layer (Fig.7-14). When the liquid L comes in contact with the laminate, the following two extreme situations can occur: ( i ) The solute is homogeneously distributed in the core layer with the concentration C’~,(,(W/V) or cP.(,(w/w)with the density pp of the polymer. The concentration of the solute in B, cg.0, is 0. (ii)The solute is already homogeneously distributed in the whole laminate with cp,,, the equilibrium concentration, that means cp,, = cp = CB = cp.oa/(a+b)= cp,Oa/d. The starting point for modeling permeation (migration) to the liquid is the second case (ii). This is because it represents the well-studied diffusion of a solute from a polymer of limited volume, Vp, into a stirred solution of limited volume, VL. A suitable equation for all of these cases is Eq. (7-51), where cp,o= cp,,.
214
Piringer
Let us consider the laminate system for situation (ii) with a >> 1 and a very short contact time t = ti. This means the initial solute concentration in the vicinity of x=d at t=O is cp=cp, and cL., 2 0 (Fig. 7-14a). This illustration is the case of a system with diffusion between two semi-infinite media (Crank, 1975) for which Eq. (7-51) reduces to Eq. (7-54). A more realistic situation for diffusion in a laminate is illustrated in Fig. 7-14b, which shows the solute concentration profile in the barrier layer after a short contact time t=tl. In this illustration the concentration profile of the solute just reaches the polymer/liquid interface and cL.t 2 0. If we now consider a similar case with a semi-infinite polymer system with the initial solute concentration (cp,,) at the distance x 5 x, = a+b/2 and cp=O at x>xo and t=O (Fig.7-14c), then the possible concentration profiles for the three different times, t d l , t=tl and t>tl can be illustrated in Fig. 7-14d. If we assume a mass transfer through the interface A at X = X I at t=tl in Fig. 7-14d, then mp,,/A = 0.5cp.,pp(d-xl), which corresponds to mp.,/A = cP.epp(xo-a) = cp.,ppb/2 in Fig. 7-14c. If we combine this result with Eq. (7-54) for t=tl, then we obtain the time (7-72)
a)
) c,=
0
A
0
C X - -
a
d
a
d
1-0
:\-A
0
Figure 7-14: Illustration of the mass transfer through a layered package.
I - t,
Trurisporr equations and their solutions
215
If we allow diffusion to continue until t=t2>tl, then under the same assumptions of a semi-infinite system, the mass transfer during At = t2-tl is (7-73)
As mentioned above, the real concentration of the solute in the laminate at the first moment of IaminateAiquid contact lies between the two extremes (i) and (ii). Let us now consider the special case shown in Fig. 7-14b, where the front of the solute just reaches the barrier/liquid layer interface B/L. By comparing Figure 7-14b with Figure 7-14d, we see similar situations are illustrated. Therefore, using Eq. (7-72) and the notations d-xl = b and t l = 0 , a time 0 = (n/16)(b2/Dp) is defined, which is a little greater than the well-known “time lag” = b2/6Dp. If such a system comes into contact with a liquid-phase L, then the mass transfer after the time At=t2-O=t that results from Eq. (7-73) is:
y -fi +,ppjDP( -
dim -
&)
(7-74)
The specific case in Figure 7-14b and Figure 7-15a can be considered as a general reference case for all other practical cases between the extremes (i) and (ii). Depending on the degree of solute diffusion into the barrier layer before it comes in contact with the liquid-phase L, a fictive time, O’, which is shorter (Fig. 7-1%) or longer (Fig. 7-15c) than 0 described in Figure 7-1Sa, can be determined. By relating
a)
:
t A
0
a
d
a
d
t-0
C X - -
0 --X--,
Distance Figure 7-15: Illustration of the relative mass transfer for different amounts of contamination of the barrier layer.
216
Piringer
this 0' to 0, a relative time can be defined which is a measure of the efficiency of the barrier layer B. The value of 0' can be deduced from the relation in Eq. (7-75), were
or
(7-75)
DP is the diffusion coefficient of the solute at some temperature (T*) for time t*, for example, the extrusion temperature of the laminate, where the diffusion of the solute into the barrier layer is most significant. Dp is the diffusion coefficient of the solute in the polymer at the temperature during the contact with liquid L. By using the relative time 0, instead of 8 and the general valid Eq. (7-51) instead of Eq. (7-54), a final equation for the migration of the solute from the core layer P through the barrier layer B after the contact time t can be written similar to the form of Eq. (7-51):
x
2a( 1+a)
(7-76)
n= 1
with
(7-77) and cP.e = CP.O
& = CP,O ad
(7-78)
In the extreme case (ii) of complete diffusion of the solute into the barrier layer B, O,=O, Eq. (7-76) reduces to Eq. (7-51). In the following example an application of the above treatment in an actual case is shown (Piringer et al. 1998). Films of coextruded polyethyleneterephthalate (PET) (pp = 1.4 g/cm3) with a symmetric three-layer structure were produced in which the core layer P (320 pm thick) contained chlorobenzene as a contaminant with the initial concentration, cp,o = 104 pg/g. The PET films which were 400 pm thick, had two barrier layers B (40 pm) of virgin PET. The films were obtained by coextrusion at about 270°C during about 1 second. After cooling the films were stored a few days at room temperature and then the amount of migration was measured into isooctane at 50 "C. The migration of the contaminant into B during the storage period was neglected due to the very low diffusion rate at room temperature. In Table 7-4 the measured migration amounts, mF.,/A, are shown together with the calculated values using Eq. (7-76). The last column contains the calculated migration amounts from a film (d = a+b = 160+40 = 200 pm) in which the contaminant was uniform distributed at the equilibrium concentration, cp,, = 83 yg/g. The symmetric structure allows calculation with only one half of the total film thickness. The measured diffusion coefficient of chlorobenzene in PET at 50 "C is Dp = 2.13E-13 cm2/s and the assumed value at 270 "C (Chapter 15) is DG = 7.1E-7 cm2/s.
Tmnsport equations and their soltrtroi~s
217
Tahle 7-4: Migration (pgidm') of chlorohenzene into isooctane at 50°C. Time (days)
Measured
Calculated
10
< 0.5
0.3
5.6
39
0.8
1.2
11.o
69
2.0
2.2
14.8
2.9
17.0
110
3.0
3.4
18.7
130
4.0
4.0
20.2
91
Calculated for b=O
From the above results one can see that a functional barrier limits the amount of migration of a component from the package to food-simulating liquids. But when using a coextrusion process to create a functional barrier, the assumed virgin layer becomes contaminated from components of the core layer (recycled polymer layer) during manufacturing. These effects must be considered if reliable predictions of migration are to be obtained (Chapter 10). A solution obtained with numerical mathematics is also shown in chapter 8.
7.2.9 Permeation through a laminate Diffusion through a barrier layer is a special case of diffusion through a laminate film composed of several layers with different thicknesses and diffusion coefficients. The mathematical treatment of the non-steady state case is complicated. The steady state permeation case allows the overall transport to be simply treated. Let n films with thicknesses dP1, dP2,..., dp, with corresponding diffusion coefficients Dp1, Dp2, ..., Dp, be bound together in a laminate. Because in steady state, the flux J of the diffusing substance i is the same through every individual component of the laminate, one obtains an expression for the concentration gradient:
+
R2
+
... Rn) J
(7-79)
with the resistance R 1= d,l / Dpl etc. The total resistance related to the diffusion is then the sum of the individual resistances and the total flux is practically determined by the layer with the smallest diffusion coefficient.
7.2.10 Concentration dependence of the diffusion coefficient At dilute concentrations DP is usually constant. When swelling is caused by either fat, water, essential oils or other organic components found in the product then DP can become concentration-dependent in the region of a boundary layer in P. In such cases the diffusion equation (7-12) is no longer valid and the general form of the diffusion equation (7-11) must be used.
218
Piringer
I
lo-'
El
10-4
10-5
1r4
10-3
IO-~
lo-' t Ihl
loo
10'
1 02
Figure 7-16: Migration from a system with swelling under various conditions (Chang 1988). Dp.0 = 1 6 5 1 0 cm2/s,Dp = 10E-10 cm'ls: t,, = 0; vo: E-S cmls in A. E-6 cmis in B, E-7 cmk in C and E-8 cmis in D.
In this case D = D(c) is a function of the concentration c of the substance causing the swelling. The literature holds numerous recommended solutions for treating such cases, none of which are universally applicable. A general way for solving problems of this type is to use numerical integration in combination with a representative model suitable for the specific case. In the initial stages when the food or another product is brought in contact with the package (t = 0), the migration of the substance i from P into L takes place with a constant DP because the swelling processes require a certain amount of time before they affect the migration process of i. After this initial contact phase the swelling front, XQ,moves into P with a certain speed vQ (Fig. 7-16). In the region x > XQ the diffusion of i takes place with DP and in the region x < XQ with D ~ >QDp. The swelling front XQ moves into P with the speed vQ: XQ
= VQ (t
-
to)
(7-80)
whereby to > 0 signifies the initial contact phase before swelling takes place. The result of such a process can be qualitatively seen in Fig. 7-14 (Chang et al. 1988).
7.2.11 Diffusion and chemical reaction When a first order irreversible chemical reaction (e.g. oxygen absorption and oxidation) takes place simultaneously with diffusion in food for example, then one obtains the following expression from the general mass transfer equation (7-10): (7-81)
Trrrnsport equations and their sokitions
219
where k is the reaction rate constant. If the reaction takes place in a relatively thin layer near the surface or boundary layer of L to P then one can consider L as a half open medium (infinitely thick). This leads to a considerable simplification of the mathematical treatment. Furthermore, letting cL.0 be a constant surface concentration one obtains the absorbed amount m, up to time t: mt = A CL.O (DL/k)'l2[(k t
+ i)erf (k t)1/2 +
(k t/Jc)'l2 e-
'1
(7-82)
For large k . t values the erf (k .t)1'2 goes to one and: mt = A
C L . ~(DL/k)'/*(t
+ A)
(7-83)
that means m, increases linearly with t. For very small values of k . t one obtains:
(7-84)
When k + 0 only diffusion without reaction takes place: mt
E A C L , ~(DL t)II2
(7-85)
Because the diffusion process and the reaction occur in the same medium L the ratio of A N L does not come into consideration. References Carslaw H. S.. Jaeger J. C. 1959, Conduclion c!f'Henr in Solids, Clarendon Press, Oxford. Chang S.-S., Guttman C. M., Sanchez I. C.. Smith L. E.. 1988 in: Hotchkiss J. (ed), Food and Packaging Interactions, ACS Symposium Series No. 365. Washington. Crank J. 1975. Mathematics of Diffusion, Znd ed.. Clarendon Press. Oxford University Press, Oxford. Kreyszig E. 1993, Advanced Engineering Mafhernnrics,7'h ed., John Wiley & Sons, Inc. New York. Piringer O., Franz R.. Huber M., Begley T. H., McNeal T. P,1998, .I Agric.& . Food Cheni. 46,15321538. Reid R. C., Sidman K. R., Schwope A. D.. Till D. E., 1980. Ind. Eng. Chem. Prod. Res. Dev. 19,580-587.
Reactivity in Molecular Crystals Edited by Yuli Ohashi Copyright @ K d a o r h a Ltd .Tokyo. 1999
8 Numerical solutions of the diffusion equation Titus A . Beu
8.1 Why numerical solutions? Despite the large number of analytical solutions available for the diffusion equation, their usefulness is restricted to simple geometries and constant diffusion coefficients. The boundary conditions, which can be analytically handled, are equally simple. However, there are many cases of practical interest where the simplifying assumptions introduced when deriving analytical solutions are unacceptable. For example, the diffusion process in polymer systems is sometimes characterized by markedly concentration-dependent diffusion coefficients, which make any analytical result inapplicable. Moreover, the analytical solutions being generally expressed in the form of infinite series, their numerical evaluation is no trivial task. That is, the simplicity of the adopted models is not necessarily reflected by an equivalent simplicity of evaluation. To obtain solutions to the diffusion equation, which more realistically models practical situations (where, for example, the diffusion coefficient or the boundary conditions are non-linear), one must resort to numerical methods. Basically, these imply restricting the solution of the diffusion problem to a set of gridpoints, conveniently distributed within the integration domain, and approximating the involved derivatives by discrete schemes. Such an approach leads to a system of linear equations, having as unknowns the solution values at the gridpoints. The linear system can be solved in principle by any classical method, even though, for the sake of computational efficiency. more specialized methods are recommended. The numerical discretization methods affect the essence of the physical model much less than analytical approximations do, allowing for much more complex diffusion problems to be treated.
8.2 Finite-difference solution by the explicit method We consider for now the one-dimensional diffusion equation, with constant diffusion coefficient D:
Such an equation is useful for describing the time evolution of the concentration profile of some diffusant across a plane sheet of given thickness L and infinite transverse extension. In order to model a particular experimental arrangement, this equation must be solved in conjunction with certain initial and boundary conditions. We will consider that Eq. (8-1) is subject to the initial condition: c(x, to) = c"(x),
x E [O, L]
(8-2)
222
Beu
which means that the concentration profile at the initial moment to is given over the entire sheet thickness. However, the solution of the initial value (or Cauchy) probZem defined by Eqs. (8-1) and (8-2) cannot be uniquely determined unless supplementary boundary conditions for t > to are specified. For simplicity, we will assume that the concentration values at the outer surfaces of the sheet are constant for any t 2 to: c(0, t ) = c;,
c(L, t) = CL 0
(8-3)
Such boundary conditions, specifying the values of the solution, are known as Dirichlet houndury conditions. The so-called Neumann boundary conditions, which define the derivative of the solution on the boundaries, form another important category, considered among others later in this chapter. The method we use to approximate the solution to the problem (8-1) to (8-3) is based on finite difference schemes for the derivatives involved by the diffusion equation (and, in general, by the boundary conditions, too). The straightforward approach is to choose equally spaced points along the x- and t-axes, covering the space-time integration domain by a regular rectangular grid (Fig. 8-1). Denoting by h and At the corresponding mesh constants (with the stipulation that L/h is an integer), the gridpoints are defined by the discrete coordinates: xi = (i - l ) h ,
i
= 1 , 2 , . . . , M:
(8-4)
tn=nAt,
n = 0 , 1 , 2,...
Here M represents the number of spatial gridpoints and the spatial mesh constant is given by: h = L/(M - 1).
(8-5)
We use the notation c: = c(xi, t,). The time derivative of c at point (xi, tn) can be obtained from its Taylor series in t for constant x = xi:
Taking the linear approximation and expressing the first order time derivative, one obtains:
+ O(At).
(8-7)
O(At) signifies that in the above approximation the leading term that was neglected is of the order At (we have divided (8-6) by At to get (8-7)). This is the socalled Euler forward-difference scheme. While it is only first-order accurate in At, it has the advantage that it allows for the quantities at timestep n 1 being calculated only from those known at timestep n. The discrete approximation for the second order spatial derivative ( $ c / & ~ ) ~ , ,at x = xi results in a similar manner, namely by expressing the concentrations at the neighboring gridpoints xi-1 and X ~ + Ifrom the Taylor series in x at constant t = t,:
+
223
Nirtnericol solutions of’the diffiision equation
explicit
CrankNicholson
x,= 0
implicit
x,=L
Figure 8-1: Space-time grid for the one-dimensional diffusion equation. evidencing the explicit forward-difference. implicit backward-difference and Crank-Nicholson discretization schemes.
On adding we find
(2)
i, =
c+ : I -2c: +c;- I hz
+ O(h2)
(8-9)
This second order approximation is a centered-difference scheme, since it expresses the spatial derivative at point i by means of data from symmetrically distributed points. All the implied information is known at timestep n. By substituting relations (8-7) and (8-9) in Eq. (8-1), one obtains the following finite-difference approximation to the diffusion equation at point (xl,tn): ,n+l -cn I
At
’ = D
c;+l -2c;+c;-l h2
(8-10)
Having in view only the way the time derivative was approximated, this is the forwrrrd-difference representation of the diffusion equation and it is of order O(h2 At). Slight rearrangement yields a formula, which expresses the time-propagated solution cy+’ for any interior spatial gridpoint in terms of the other quantities known at timestep n: c!l+l = Ac?,-I (1 -2A)c) +Aclntl. (8-11) i = 2 , 3,..., M - 1 ,
+
+
where: Dt
A = p
(8-12)
224
Beu
The concentration values on the boundaries, c;+' and cL++',generally result from the boundary conditions and, within the simple adopted model, are seen to be constant: (8-13) Since the solution of Equation (8-11) propagated at timestep tn+l is expressed solely in terms of data from timestep t,, not requiring any previous information, the forward-difference scheme is said to be explicit, and its essence can be extracted from Fig. 8-1, too. The explicit nature of the recursive process described by Eqs. (8-11) to (8-13) becomes even more apparent if using matrix notation for the involved linear system: n = 0 , 1 , 2 ,....
cn+l = B . c n ,
(8-14)
The components of the column-vector c" are the values of the solution from all spatial gridpoints at timestep t,: (8-15) and the propagation matrix B has tri-diagonal structure, i.e., except for the main diagonal and the neighboring upper and lower co-diagonals, all elements are equal to 0 1 0 h 1-2h
0-
h
B=
I
h
1-2h 0
0
(8-16)
h 1-
When solving the one-dimensional diffusion equation (8-15) by the explicit forward-difference formulation described above, one is faced under certain conditions with severe numerical instability problems. This means that, instead of yielding a relatively smooth spatial profile, the algorithm develops oscillations, which grow exponentially in time, "unweaving" the solution and making it unusable. This critical behavior occurs when the used timestep exceeds a certain upper limit for a given spatial mesh constant and is caused by the increasing dominance of round-off errors. In order to emphasize the critical relationship between the timestep and the spatial step, we consider the one-dimensional diffusion equation with constant diffusion coefficient D = 1: ac -
8%
at
Q
-
T
x E [0,1], t > 0,
(8-17)
subject to the simple boundary conditions: c(0, t) = c(1, t)
= 0,
and initial condition:
t
>0
(8-18)
Niinierical soliltions of the diffiision eqiicrtiori
0.16
__
225
numerical solution
0.14 0.12 0.10 c,
0.08 0.06
0.04 0.02 0.00 0.0
0.2
0.6
0.4
0.8
1.o
Y
Figure 8-2: Exact and numerical solutions obtained by the explicit method for the Cauchy problem (8-17) to (8-19). by using the spatial step h = 0.05 and the timestep At = 0.00125.
c(x,0) = sin(nx), x E [0,1].
(8-19)
It can be easily verified that the analytical solution to this problem is: c(x, t) = e-x2t sin(7cx)
(8-20)
We investigate the behavior of the numerical solution to problem (8-17) to (8-19) at the moments t = 2.0, t = 2.5 and t = 3.0 for two different timesteps, by using the constant spatial step h = 0.05. Figure 8-2 shows the spatial concentration profiles obtained by using the timestep At = 0.00125, corresponding to h = 0.5 ( h is defined in Eq. (8-12)). As one may notice, apart from the inaccuracies caused by the finite spatial step size, the profiles resulted from the numerical solution (depicted with dotted lines) fairly reproduce the analytical results (continuous lines). Figure 8-3 shows the spatial concentration profiles obtained with the slightly increased timestep At = 0.0013, corresponding to h = 0.52. Even though the solution at t = 2.0 can hardly be distinguished from the one obtained with At = 0.00125, it is apparent that at t = 2.5 instabilities begin to develop and they dominate the solution entirely at t = 3.0. Hence, a seemingly insignificant change in the timestep leads to a dramatic qualitative change of the solution. This indicates that the value h = 1/2 is critical, and that it separates two domains of numerical parameters characterized by different behavior of the solution: for h < 1/2 the propagation of the solution is stable, while for h > 1/2 it turns out to be unstable.
226
Beu
0.16
-- numerical solution 0.14
0.12 0.10 0
0.08 0.06
0.04 0.02 0.00 0.0
0.2
0.6
0.4
0.8
1.O
Y
A
Figure 8-3: Exact and numerical solutions obtained by the explicit method for the Cauchy problem (8-17) to (8-19) , by using the spatial step h = 0.05 and the timestep At = 0.0013.
8.2.1 von Neumann stability analysis An intuitive way of investigating the stability properties of a finite-difference scheme is the von Neumann stability unulysis, which we briefly outline as follows. The von Neumann analysis is b c a l , being based on the assumption that the coefficients of the difference equation are so slowly varying in space and time as to be considered constant. Under such assumptions, the eigenmodes (the independent solutions) of the difference equation may be written in the general form: u: = t"exp[tk(i
-
l)h]
(8-21)
1 stands for the imaginary unit (not to be confused with the spatial index i), k is the spatial wave number, which can take any real value, and 6 = C(k) is the so-called amplification factor, which is a complex function of k. Apart from the spatial details, the essential feature of the eigenmodes is their time dependence through the timestep index n, as integer powers of the amplification factor. The time propagation of the solution is considered to be stable if the amplification factor satisfies the condition:
since no exponentially growing modes of the difference equation can exist under such circumstances.
Nllnzericnl solutioiis of the difficsiori eqtrntion
227
In order to express the amplification factor for the forward-difference representation of the one-dimensional diffusion equation, one has to replace the general form (8-21) of the eigenmodes into the difference equation (8-11):
5 = hexp(-tkh) + (1 - 2h) + hexp(tkh). By combining the exponentials and employing the trigonometric identity 1 - cosx = 2sin2(x/2),one obtains for the amplification factor:
5 = 1 - 4hsin2(kh/2)
(8-23)
Use of the von Neumann stability criterion (8-18) leads to the condition:
O
(8-24)
which, taking into account the definition (8-12) of h, becomes: 1 h2 at < zB
(8-25)
The significance of this result is that the timestep At insuring the stability of the algorithm is limited by an upper bound, which is proportional to the diffusion time across a cell of width h. This makes the explicit scheme, characterized by forward time differencing, conditionally stable and proves that the value h = 112 is indeed critical.
8.2.2 The Crank-Nicholson implicit method To obtain an algorithm that is unconditionally stable. we consider an implicit discretization scheme that results from using backward finite-differences for the time derivative. The corresponding difference equation is most conveniently obtained by approximating the diffusion equation at point (xi, tn+l): (8-26) Analogous to the forward-difference method previously discussed, it is only firstorder accurate in at. The only formal difference with respect to the forward-difference equation (8-10) appears to be the fact that the space derivative is evaluated at time t,+l, not at time t,. By rearranging the terms in (8-26), the following system of linear equations results:
-hc;:;
+ (1 + 2h)c:+'
- hcn+' l+1
-
ci" '
i = 2 . 3 . . . . , M - 1,
(8-27)
where, as before, h = Dt/h2. By contrast with the forward-difference method, the propagated concentrations c:+' cannot be explicitly expressed, but result from solving the above set of simultaneous linear equations at each timestep. For this reason, the discussed backward-difference scheme is said to befidfy inipficit.The implicit nature of this method can also be observed from Figure 8-1,which indicates the data involved.
228
Beu
By using matrix notation, the linear system (8-27) can be written: n = 0 , 1 , 2 ,...,
A.c"+l =c",
I
(8-28)
with matrix A having tri-diagonal structure:
1
0
0 -
-1 1 + 2 h -A
A=
0
(8-29)
-h
1+2h 0
-a 1 -
It is apparent from the first and last rows of this matrix, that again the simple Dirichlet boundary conditions, Eq. (8-3), have been considered. Since h > 0, the matrix A is positive definite and diagonally dominant. For solving system (8-28), the very efficient Crout factorization method for linear systems with tri-diagonal matrix can be applied (see Press et al. 1986, Section 2.4). The implicit backward-difference algorithm does not show the stability problems encountered in the case of the explicit forward-difference method, and this results immediately by analyzing the expression of the amplification factor:
'
1 = l+4hsin2(kh/2)'
(8-30)
which obviously satisfies the von Neumann stability criterion lC(k)l < 1 for any stepsize At. Hence, the backward-difference scheme is unconditionally stable. Provided the solution of the differential equation satisfies the usual differentiability conditions, the local truncation error of the method is of the order O(h2 + At). The weakness of this method is, however, the low order of the truncation error with respect to time, requiring comparatively much smaller time intervals than the spatial stepsize. A second order method with respect to both space and time can be derived by approximating the diffusion equation at timestep tn+l/2= t, + At/2 and employing a centered-difference scheme for the time derivative, too. Considering the Taylor series in t at constant x = xi:
(8-31) on subtracting we find the time derivative sought:
(8-32) The spatial derivative at timestep tn+1/2 can be approximated by taking its average over the timesteps t, and t,+l. Hence, the discretized diffusion equation takes the form: C?+' -c? c;;-2c;++ ' cr:/ +(cy+, -2c:+c:J I = D (8-33) At 2 h2
Niitnericril solutions of the diffrision equation
229
This is the so-called Crank-Nicholson scheme and, formally, it could have been obtained by simply averaging the explicit forward-difference and implicit backwarddifference schemes. By conveniently grouping the terms, the following system of linear equations results: -hcn+l
1-1
+ (1 + 2h)c:+'
hc?1-1
-
1
1+1
+ (1
+
24c; hC,?,l, i = 2 , 3, . . . , M - 1 , -
(8-34)
with: (8-35) The discretized system (8-34) can be represented in matrix form as:
A.c"+' = B . c n , n = 0 , 1 . 2 ....
(8-36)
where matrices A and B have tri-diagonal structure and are given by Eqs. (8-29) and (8-16), respectively. Since A is positive, definite and diagonally dominant, it is nonsingular, thus allowing for Crout factorization method for tri-diagonal linear systems to be applied to obtain c"+' from c" for any n = 0 , 1 , 2 , . . .. It has to be noted that the evaluation of the right-hand-side members of system (8-36) requires a little more work than in the case of the fully implicit scheme, implying the multiplication of the tri-diagonal matrix B with the "old" solution vector c". The amplification factor resulting from equation (8-34) is:
'
1 -4hsin2(kh/2) = l+4hsin2(kh/2)
(8-37)
and, consequently, the Crank-Nicholson method turns out to be unconditionally stable. Due to its stability and satisfactory order of convergence O(h2 + (At)*), the Crank-Nicholson scheme is the recommended approach for any simple diffusion equation. In order to demonstrate the beneficial influence of the higher order accuracy with respect to time of the Crank-Nicholson method, we consider again the initial value problem Eqs. (8-17) to (8-19), which is solved both by the fully implicit and the Crank-Nicholson schemes. We investigate the numerical solution at time t = 3.0 by using the constant spatial step h = 0.05. Figure 8-4 shows the spatial concentration profiles obtained by using the timestep At = 0.025. which is 20 times larger than the largest value to insure the stability of the explicit method (see Fig. 8-2). As one may notice, the profile yielded by the Crank-Nicholson algorithm (depicted with long dash) agrees very well with the analytical result (continuous line) even for the large timestep considered. By contrast, the solution obtained by the fully implicit method (short dash) departs quite substantially from the exact solution. Hence, it should be obvious that the stability of the fully implicit scheme (absence of oscillations) does not automatically also guarantee high accuracy.
230
Beu
0.08
0.06
u 0.04
0.02
0.00
0.0
0.2
0.4
0.6
0.8
1 .o
X
Figure 8-4: Comparison of the numerical solutions obtained by the fully implicit and Crank-Nicholson methods for the Cauchy problem (8-17) t o (8-19).The spatial step h = 0.05 and the timestep At = 0.025 have been used.
8.3 Spatially variable diffusion coefficient If the diffusion coefficient is spatially variable, the one-dimensional diffusion equation has the form: (8-38) The correct way to differentiate this equation relies on the following centereddifference approximation of the spatial derivative at timestep t,:
(8-39)
The midpoints xi+1/2 = (xi + xi+1)/2 and the corresponding values of the diffusion coefficient Di+1/2 = D(xi+l/2) have been introduced to ensure appropriate centering of the implied derivatives. A convenient approximation for Di+]l2 results from considering the average of the values at the neighboring gridpoints: ~ i + 1 / 2= i(Di + D i + l )
(8-40)
In the case of unequal spacing of the spatial gridpoints, Eq. (8-39) can be generalized to give:
Nirniericn/ solutioris of the diffirsion equation
231
Application of the Crank-Nicholson method based on the spatial difference scheme (5.39) results in the following discretized form of the diffusion equation:
(8-41)
Rearrangement of terms leads to the system of linear equations:
(8-42)
A.1 --4 t 2P
(8-43)
The system (8-42) should be completed with appropriate equations resulting from the boundary conditions and it can be solved, in principle, by the same factorization method of Crout for systems with tri-diagonal matrix. When the diffusion coefficient depends not only on the spatial coordinate but also on the local concentration, the discretization of the diffusion equation proceeds in a similar manner, except that one has to solve at each time step not a system of linear equations, but a quite complicated set of coilpled non-linear equations.
8.4 Boundary conditions In the treatment of explicit and implicit difference methods, we have used Dirichlet type boundary conditions, for the sake of simplicity, which specify the values of the solution on the boundaries. A more general type of boundary condition can be defined in the form of a linear combination of the solution and its derivative. Considering in particular the left boundary, such a mixed boundary condition can be written:
[a+.
t)
+ B i)c(x.t)
I
x=O
=Y
(8-44)
For p = 0 this is a Dirichlet type condition, while for a = 0 it is a Neumann type condition. a,@, and y may, eventually, be functions of time. A practical example for a mixed boundary condition is the evaporation condition:
ac(x.t) ax ! L O
= a[c(0,t)
-
c,]
(8-45)
where ce is the equilibrium surface concentration. The simplest finite-difference representation of the mixed boundary condition (8-44) may be readily obtained by considering for the spatial derivative the forward-
232
Beu
difference scheme implying the concentrations on the boundary, cp, and at the neighboring interior gridpoint, c;: acf
cn-cn + py =y
(8-46)
However, this approximation is of the order O(h) and, since the difference equations for all discussed (explicit and implicit) propagation methods are O(h2),it is definitely not the best choice. An improved O(h2) finite-difference representation of the boundary condition (8-44) results by approximating the solution in the vicinity of the boundary by the second order Lagrange interpolating polynomial passing through the points ( X I , c?), ( x ~c;), , and (x3, cz) (equally spaced gridpoints are assumed):
q x ,t") = & [(x - x2)(x - X3)CT
-
2(x - x*)(x- x3)c5
+ (x
-
XI)(X
-
x2)cg (8-47)
The interpolation properties of this uniquely defined parabola can easily be verified by direct evaluation for XI, x2, and x3, respectively. The derivative of polynomial (8-47) is given by:
=4 =
2h
[(2x - x2
-
x3)c;
-
2(2x - X I
-
x3)c5
+ (2x
-
x1
-
X2)C?],
(8-48)
and for x = XI,where we wish to approximate the boundary condition, it takes the particularly simple form: (8-49) By replacing this approximation in the boundary condition (8-44), one is left with the supplementary equation:
ac;
+
-3c7+4c;-c; 2h
=y
(8-50)
Adding this equation to the set of difference equations resulting from the diffusion equation no longer preserves the tri-diagonal structure of the system matrix. Indeed, appearing as the first equation of the system, the coefficient of cs does not lie on the principal diagonal or on one of the two neighboring co-diagonals. In such cases, one has to resort to general methods for solving the linear system, such as Gaussian elimination or the LU factorization method of Crout. An absolutely analogous treatment may be applied to the right boundary, for which the boundary condition reads:
(8-51) A third possibility of approximating the mixed type boundary condition, widely used, implies considering a fictitious external gridpoint xg and the corresponding concentration c;. The centered-difference approximation of the boundary condition becomes: acy
+ p c"-c"v = y
(8-52)
Nirnierical solutions of the diffusion equation
233
The unknown (and in principle "useless") value of c; may be eliminated by using the diffusion equation approximated at the gridpoint X I (see Eq. 8-39): (8-53)
+
with D3/2 = (D1 + D2)/2 and D1/2 = (Do Dl)/2 = D1. On replacing ci from (8-52) in (8-53) and by considering the Crank-Nicholson scheme, the following difference equation results: cn+ 1 1 At-
,n+l_,n+l
c L & [ ( D 1/2 + D3/2)
+& [ ( D l p + D3p)
+
*
h
'
7
+ 2D1/2 (ac;+l
B
(ac? - y)]
-
y,]
+
(8-54)
.
which can be rearranged to become the first equation of the system (8-42). A similar treatment may be applied to approximate t h e right boundary condition, which then becomes the last equation of the system. In t h e particular case of Neumann boundary conditions modeling impermeable surfaces ( a = y = 0), the two equations can be cast in the simple form:
(1
+ 2hl)C7+'
-2hh4CF1,
-
2h1c;f' = (1 - 2hl)CY
+ 2hlC!,
+ ( 1 + 2h&"M++' = 2hh4C&p1+ (1
(8-55) -
2h&&
where hi is given by Eq. (8-43). Obviously, these approximations of the boundary conditions preserve the tri-diagonal structure of the matrix of system (8-42). In certain applications, it is convenient to impose (eventually, instead of one of the local boundary conditions) a global condition upon the total amount of diffusant, in the form of an integral over the entire spatial region: L
c(x, t)dx = Q
(8-56)
b Such a normalization condition can be readily discretized by considering, for example, the simple trapezoidal rule for performing the numerical quadrature:
(8-57) The quantity Q might be related, for example, to the total amount of diffusant at the initial moment, but it could equally be a function of time.
8.5 One-dimensional diffusion in cylindrical and spherical geometry There are certain practical diffusion problems, which can be treated most appropriately in cylindrical or in spherical coordinates. In many cases, choosing the natural coordinate system allows for the coordinates to be separated, and one is left with the simpler problem of dealing with one-dimensional diffusion along the radial coordinate. Basically, the only technical complication which arises as compared to the one-dimensional diffusion in Cartesian coordinates treated so far, concerns the approximation of the spatial derivative of the concentration involved by the diffusion equation.
234
Beu
Assuming constant diffusion coefficient, the equation describing the radial diffusion in cylindrical coordinates may be written: (8-58)
In order to approximate its solution, we establish a grid of equally spaced points in the interval [0,R] of the radial coordinates. Denoting the corresponding mesh constant by h, the gridpoints are defined by the discrete coordinates: ri=(i-l)h,
i = 1 , 2, . . . , M
(8-59)
A second order representation of the right-hand side u l Eq. (8-58) at point obtained by using centered-differences for the spatial derivatives:
(Ti,
tn) is
(8-60) A special treatment has to be applied to the central gridpoint rl = 0. The singularity arising in the second term is overcome by imposing the natural boundary condition that the first order derivative vanishes at rl = 0. By introducing a fictitious gridpoint ro = rl - h, this condition may be approximated by the second order centered-difference scheme:
(8-61) This relation is practically useful only to eliminate further occurrences of c;. Still, the second term of the spatial derivative, (l/r)(b'c/&), implies an indeterminate form of the type O/O. Making use of 1'Hospital's rule results in the following representation:
d2 l a c [$ + ;z]r1
,tn =
[2$1
c"-2c"+c" rl .t,
2-
c"--c" =4
(8-62)
Having established the appropriate finite-difference expressions of the spatial derivatives, the diffusion equation may be approximated as follows: c" - c" =4D11-, i=l, at r1.t" h2 (8-63) (2i - l ) ~ r + 4(i ~ - 1)cI (2i - 3)crPl =Di , i = 2 , 3 ,... M - 1 . 5,tn 2(i - l )h
$1
+
The equation for the central point (i = 1) actually plays the role of "inner" boundary condition. The above system should be completed with one more boundary condition for the outer point r M = R. Irrespective of the type of the used time difference scheme (explicit, fully implicit or Crank-Nicholson), the further treatment of the resulting system of difference equations is absolutely analogous to the one developed for Cartesian coordinates. The radial diffusion equation in spherical coordinates may be written for constant diffusion coefficient as:
Nuniericcil soliltions ofthe diffusion equation
235 (8-64)
Following the pattern employed in the case of the cylindrical coordinates, one obtains the following finite-difference approximations:
The treatment of the various types of outer boundary conditions (for r M = R) and of the complete system of difference equations is again analogous to the case of the Cartesian coordinates.
8.6 Multi-dimensional diffusion The extension of the methods described so far to multi-dimensional diffusion problems is straightforward in principle. However, in such an attempt one is faced with a quite considerable increase in computational effort. Let us consider for simplicity the two-dimensional diffusion equation: (8-66) for which we wish to find the solution in the rectangular domain [0,a] x [0,b]. We assume that c(x,y, t) is known over the whole spatial region at t = to, and that it is prescribed on the boundary for any t > to. Applying the Crank-Nicholson scheme to equation (8-66), relative to a space-time grid characterized by the points: xi = (i - l ) h ,
yj
=
(j - l ) h ,
tn = nAt
(8-67)
results in the following difference equation: (8-68)
: and 6 : Here, h = Dt/(2h2) and the second order centered-difference operators 6 are defined by: (8-69)
Whereas in the case of the spatially one-dimensional diffusion, the set of difference equations features a tri-diagonal matrix, the system in Eq. (8-68) can be shown to have a block tri-diagonal matrix, which requires the use of special solving methods. A very powerful method for the solution of system 8-68, widely in use, is the so-called alternating-direction implicit method, which is based on the idea of splitting each timestep
into two substeps of size At/2. In each substep, the concentration is kept constant in one of the spatial dimensions, while in the other one it is treated implicitly: (8-70)
The first equation treats the x direction implicitly, keeping the y direction unaffected. In the second equation, the role of the two directions is interchanged. Slight rearrangement of the system: (8-71)
+
n+1/2 , (1 - h62)cnk' Y 1 J = (1 h6,)Ci.j 2
evidences the great advantage of this method: at each substep it requires only the solution of a tri-diagonal system. Hence, instead of solving at each timestep a system with block tri-diagonal structure, one has to solve two systems with simple tri-diagonal structure. Example 8-1 In chapter 7, section 7.2.8 an example of permeation through a functional barrier is described. Three-layered coextruded PET films were produced in which the core layer (P) was contaminated with chlorobenzene and the outer barrier layers (B) were made with virgin material. During the coextrusion process a partial contamination of the virgin layer occurred. The symmetrical structure of this film leads to a simplified treatment of it as a two layer laminate with the thickness d = a + b = 160 + 40 = 200 pm. For the modeling of this problem with numerical mathematics all parameters given in Section 7.2.8 are used. Starting with the one-dimensional diffusion equation (8-1) the concentration profile, cp versus x and t is presented in Fig. 8-5 for one half of the laminate.
40 -
20 -
\\'
-t = o t=1sec t = 10 days t = 130 days
'h
\\
',
\\
0 100
120
160
140
x
180
(w)
Figure 8-5: Concentration profile for the migration of chlorobenzene in and from an impurified PET core layer into a virgin PET barrier layer and a food simulating liquid F.
From this figure one can see that even for a very short period of time (t near zero) there is a considerable migration of chlorobenzene from the core layer P into the barrier layer B. This can be attributed only to the high temperature (about 270 "C) migration process during the
Nirtnericnl solutions of the diffusion rqiintion
237
coextrusion. After cooling, the laminate was stored at room temperature (very slow diffusion rate) until the migration experiment at 50°C during 130 days. The further contamination of the barrier layer B during the storage (few days) was neglected.
---
Figure 8-6 Concentration profiles, at fixed migration times. of chlorobenzene from an impurified PET core layer into a virgin PET harrier layer and a food siniiilating liquid.
From Fig. 8-6 one can clearly see that the very short (1 s) high coextrusion has an important impact on the migration of chlorobenzene from the core layer towards B and later into F. The subsequent migration in the laminate for 10 days at 50°C produces only a small transfer of the contaminant into B. The time dependence of the amount migrated from the laminate into F is shown in Fig. 8-7. I
20,
4 0
20
40
60
80
100
120
140
t (days)
Figure 8-7: Amount of chlorobenzene migrated at 50°C from the PET laminate into isooctane.
For a relatively long time, about 10 days. the net amount of chlorobenzene migrated from PET into isooctane is very small (nearly zero). In practice this is equivalent to a “time lag” needed by the impurity to reach the outer surface of B. It is interesting to compare this time lag with the one which would correspond to the situation with no contamination of B. In this case the chlorobenzene needs a time lag, 0 = b2/6Dp= 145 days, where b = 40 pm. Hence one
238
Beu
can see from these results that the coextrusion process has a very important impact on the final usefulness of the manufactured PET structure for food packaging applications. The results obtained with the numerical approach are systematically smaller (about 60 % at 130 days) than both the experimental and analytically calculated results shown in Table 7-4. The fact that the numerical solution of the diffusion equation led to smaller mE,/A than the experimental ones can be the result of assuming a too short coextrusion time. Increasing this time only by 50 % leads to a much higher impurification of the barrier layer and consequently to a much shorter migration time lag and to a higher migration rate into F. It should be also noticed that the analytical approach given in section 7.2.8 leads over 130 days to an almost linear increase of m,,/A from zero to about 4 pg d w 2 . This may be an indication that the assumptions made in order to develop the analytical solution for this example led to an overestimation of mF,,/Aat the beginning of the migration process.
Suggested further reading Burden, R.L., Faires, J.D. 1985, Numerical Analysis (Prindle, Weber & Schmidt. Boston). Crank, J. 1975, The Marhernarics of Diffusion(Oxford Science Publications, Oxford). Koonin, S.E., Meredith, D.C. 1990, Compurarional Physics (Addison-Wesley Publishing Company, Inc., Redwood CA). Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P. 1986, Numerical Recipes in C (Cambridge University Press, Cambridge).
Reactivity in Molecular Crystals Edited by Yuli Ohashi Copyright @ K d a o r h a Ltd .Tokyo. 1999
9 Permeation of gases, water vapor and volatile organic compounds Otto Piringer
The processes of mass transfer taking place in a packaging system and their consequences for maintaining food quality form the main emphasis of this book. In this and the following chapters, the physical and chemical aspects of these processes (known also as packaging/product interactions), as well as their measurement and evaluation are treated from a food regulatory point of view. Only the simplest mathematical expressions describing the permeation and migration of substances from the environment, packaging and product are used here. It must be emphasized however that these formulae are as a rule very simplified approximations representing various transport processes. The exact mathematical treatment of interactions, along with their solutions for the corresponding differential equations, appear at first to be very difficult to interpret and awkward to use. Because of their complexity, exact solutions of the diffusion equation must be carried out using either numerical methods (Chapter 8) with the help of a computer or solved analytically in simpler cases (Chapter 7). The use of exact solutions does not in all cases bring significant advantages to the problem’s solution and the additional effort is not always justified when one considers the observed variability of material properties found in practice. However, it is very important to be able to estimate both the applicability of an equation to a particular problem and the errors that can occur when it is used outside this area of applicability (Chapter 7). The term permeation, as treated in this chapter, is understood to mean the transport of a substance through the packaging. The permeation of substances can occur from the package’s surrounding environment into the food or from the packed product into the surrounding environment. The term migration is understood to mean the transport of a substance from the packaging into the product or from the product into the packaging (Chapter 7). The same underlying physical process controls both permeation and migration. These processes include sorption and/or adsorption of the transported substance in the packaging and product, as well as diffusion in and through the boundary layers between the packaging and filled product and between the packaging and surrounding atmosphere. Because glass and metal are impermeable, and paper and cartons are very highly permeable, practically all permeation and migration studies are related to plastics. The simplest interaction to describe physically and mathematically is steady state permeation. The same material constants required for describing this interaction are also used for the description of non-steady state permeation and migration processes. Given the numerous different substances found in packaging and products and the resulting large number of possible combinations of packaging materials with products, not all the necessary material constants required have been experimentally determined. This leads to the use of estimation methods for substance material constants based on their chemical structures. In addition to the simple estimation methods for
240
Piringer
material constants of gases contained in this Chapter, Chapters 4, 5 and 6 deal with the estimation of constants for organic compounds.
9.1 Permeation of gases The study of the permeation of gases is the simplest case both theoretically and experimentally and is therefore treated first.
9.1.1 Permeability, diffusion and solubility coefficients Thomas Graham described his observations of the permeation of carbon dioxide through a polymeric membrane in 1826. Following this, he postulated in 1866 the correct description of the permeation phenomena as a solution of gases in the membrane followed by their diffusion through the membrane. The steady state permeation of gases through a membrane, film or plate having thickness d is calculated with the help of the following simple equation:
Where the flux J is the flow of gas. The flux is the amount of material transported per unit time through a unit surface area and according to Eq. (9-1) is proportional to the constant partial pressure difference Ap between both sides of the membrane. The proportionality constant P is called the permeability coefficient and is the product of the diffusion coefficient D and the solubility coefficient S (or sorption constant) of the gas in the membrane:
P = D . S
(9-2)
S is the ratio of the concentration c of the gas in the polymer and the partial pressure p of the gas in the gas phase in equilibrium with the membrane: (9-3)
S = CP
This ratio is constant for normal gases (Henry’s law) at the pressures found in packaging applications. Under these conditions, the gases are only sparingly soluble in the packaging materials and thus any structural changes in the polymer (e.g. swelling) can be ignored. For this same reason D is practically independent of the concentration c for gases. The differing permeability of a given gas through various materials is expressed in terms of the gas and material specific parameter P. Its dimension results from Eq. (9-1): a) b)
P
=
amount x material thickness surface area x time x pressure difference
: cm3 ~STP)cm cm s Pa
(9-4)
Permeation ofgnses, water vapor nnd volatile organic conipoimris
c) d)
D:
241
$
: cm3(STP) cm3 Pa
The amount of permeated substance can be expressed in mass, mole or volume units. For gases, volume is preferred, expressed as the amount permeating under conditions of standard temperature and pressure (STP), which corresponds to the standard temperature of 273.15 K and standard pressure of 1.01325 .1@Pa. The corresponding dimensions for D and S are obtained at the same time from Eq. (9-4). The standard ambient temperature and pressure (SATP) are set at po = 1 bar = 105 Pa = 0.9678 atm and T = 298.15 K. The data in handbooks however is still mostly expressed with p = 1 atm as standard pressure. For practical purposes the difference between these two conventions is insignificant compared to the variability of the materials themselves. The value for P is presented in various dimensions in the literature. One can convert from various dimensions to the desired ones with the help of the conversion factors listed in Table 9-1. Table 9-1: Conversion factors for several units of the permeability coefficient
[in'] [mil] [100in2][day] [atm]
1
7.5 ' 104
6.57 10"'
10-1
7.5 ' 10-5
6.57. 10"
1.32 . lo-'
9.87. 10"
8.64. 10'
3.87. 1 0 - 1 ~
2.90.10-~~
2.54. lo-'
9.82 . lo-''
7.37 ' 10-15
6.45 . 10-I
1.52 ' 10-11
1.14.
1.54 10-"
1.16. lo-''
1.33 . 103
1
1
I .01 8.75. 10"
Table 9-2 contains values of P for oxygen, nitrogen, carbon dioxide, and water vapor in some polymers (Brandrup and Immergut, 1989). The values of P cover a range of several orders of magnitude between the highly permeable silicone elastomers and the extremely impermeable EVOH materials. As an example, for O2 at 0 "C P = 3.7E-11 cm*s-'Pa-' in polydimethylsiloxane and P = 7.4E-18 cm2s-'Pa-' in EVOH at 40 YOrelative humidity(rh).
242
Piringer
Table 9-2: Permeability coefficients P (cm'(STP)cm cm-2s8Pa-') of gases and water in polymers. Polymer
Permeant
T "C
0 2
25
C02
25
P
1. POLYOLEFINS
Polyethylene density 0.922g . cm-'.LDPE
density 0.9548 cm-'.HDPE
Nz
25
H2O
25
0 2
25 25 25 25
5.18 21 1.58
93 0.825 3.225 0.248 13.5
Polypropylene density 0.907g.
30
0.33
crystallinity 50 %
30
1.7
Poly-4-methylpentene- 1
30
6.9
30
51.0
25
5.67
25
24.23
25
69.45
2. POLYSTYRENE Polystyrene
25 25
biaxially oriented
1.9 1350
25
2.0
25
0.59
25 25
7.9 840
stretched stretch ratio
1.0
25
6.0
1.8
25
4.35 2.18
3.1
25
4.4
25
1.13
5.0
25
0.75
25
0.075
3. POLYMETHACRYLATES
Polymethylmethacrylate
0 2
34
HzO
23
0.116
480
243
Pernzention ofgnsrs, w(itcr v n p r nnd volatile orgrrnic cotnpoiinds Table 9-2: Continued Polymer
Perineant
T “C
p . lo’.;
4. POLYNITRILS
Pol yacrylonitrilc
0 2
2s
0.000 15
CO,
25
0.00060
HzO
25
X6/14
0 2
25
HZO
25
66/34
0 2
25
0.036
CO:
2s
0.16
230
Poly(acrylonitrile-co-styrene) 0.0032 640
HzO
25
0 2
25
0.14
C02
25
0.27
H2O
25
0 2
25
0.35
COZ
25
1.0
HLO
25
1Y00
Polyvinyl acetate
0 2
10
0.
Polyvinyl alcohol
Nz(O %rh)
14
0.0001
N>(100 Yo)
14
0.248
OZ(0 Yo)
25
0.00665
CO2(0 % )
25
COZ(100% )
25
OL(O%rh)
30
0.0000248
02(20 % )
30
0.0000335
Oz(40 Yo)
30
0,0000743
O2(60 %)
30
0.000298
02(80%)
30
0.00187
O?(100 Yo)
30
0.0181
Polyvinyl chloride
NZ
2s
0.0089
(non-plasticized)
0 2
25
0.034
CO2
25
H2O
2s
57143
39161
1500
1800
5. VINYLPOLYMERS
0.00924 65.0
Vinyl alcohol-ethylene-copolymer EVOH
Polyvinylidene chloride
0.12 206 0.000706
NZ
30
0 2
30
0.0003x3
COZ
30
0.0218
HzO
25
7.0
244
Piringer
Table 9-2 Continued Polymer
Permeant
T T
P ' 10"
Poly(viny1idene-co-vinylchloride) 88/12 plasticized with acetyltributylcitrate (YO)
0.5
H20
30
1.38
2.7 4.9
H2O H2O
30
3.07
30
4.77
1.2
H20
30
7.38
N2
25
1.0
0 2
25
3.2
co2
25
7.5
6. FLUOR POLYMERS
Poiytetrafluorethylene
7. POLYDIENES
Poly(butadiene-co-acrylonitrile) 80/20 (Perbunan 18)
73/27 (Perbunan)
68/32 (Hycar OR 25)
25
1.89
25
6.15
25
47.6
25
0.8
25 25 25 25
2.9
25 25
61/39 (Hycar OR 15)
23.2 0.454 1.76 13.9 0.177
25
0.721
25
5.59
Poly(butadiene-co-styrene) N2
24
3.83
80/20(Hycar 2001)
N2
24
1.28
Polyisoprene. Amorph
0 2
25
(natural rubber)
coz
25
92/8(Ameripol 1502)
17.6 115
8. POLYOXIDES Polyoxymethylene
25 25
1.35 683
245
Permeation ofgmes, writer vapor and volatile organic compounds Table 9-2: Continued Pdymer
Permeant
T "C
P.
In"
9. POLYESTERS Poly(oxybutyleneoxyterephthaloyl) PBT
coz
25
0.217
PET
25
0.0108
amorph
25
0.0444
25
0.227
25
0.005 13
25
0.0257
25
0.118
Poly(oxyethyleneoxyterephthaloyl)
crystallinity 40 %
10. POLYSILOXANES Polydimethylsiloxane
0
170
0
367
25
2430
35
32300
11. POLYAMIDES Poly(iminoadipoy1iminohexamethylene) (Nylon 66) 02(40%rh)
30
0.013
02(60 %)
30 30
0.017 0.026 0.052 0.071 0.007 13
02(
I00 Yo)
non-stretched
co2
stretched
COZ
25 25
N2
30
Poly(imino-1-oxohexamethylene) (Nylon 6 )
0 2
30
0.0285
02(20%rh)
30
0.02 18
02(60 Yo)
30
0.0305
02( 100 %)
30
0.0435
coz
20
0.066
H20
25
0.139
246
Piringer
Table 9-2: Continued Polvmer
P ' 10'3
Permeant
T"C
Cellulose hydrate
Nz(0 %rh)
25
0.0024
(regenerated)
02(0 Yo)
25
0.0016
C02(0 % )
25
0.00353
HzO N2(43 %)
25 25
0.00507
02(43 %)
25
0.00536
C02(43 Yo)
25
0.00974
N2(76 "A)
25
0.00559
02(76 Yo)
25
0.00665
COz(76 %)
25
0.0539
N2(100%)
25
0.0138
100 %)
25
0.0087
C02(100)
25
0.192
N2
25
0.087
0 2
25
1.46
co2
25
H2O
25
~
~
12. CELLULOSE AND DERIVATES
02(
Cellulose nitrate
1x900
1.59 4720
An useful characteristic of the materials used in practice is the relatively constant relationship between the P values of two gases and their independence from polymer type (Table 9-3). Take for example the P values of various gases with respect to nitrogen. When a value for one gas is known, then values for another can be estimated using the corresponding value from the table. These relative values are also valid to a lesser degree for the D and S values. The values listed in Table 9-3 are averages for various different polymers and are therefore somewhat dependent on those included in the average. As a result they are for orientation purposes only and their accuracy should not be overestimated. A comparison of the ratios of the P values for COz and O2 from a selection of polymers different from those used in Table 9-3 gave an average value of 4.6 with a standard deviation of 1.3 (Hennessy et al., 1966). The corresponding maximum and minimum values were 7.1 and 2.5. From Table 9-3 one obtains a ratio of Pco,/P0, = 24/33 = 6.3. In view of the large variations in material properties of the same polymer type, which are dependent on the manufacturing and treatment processes as well as the different permeation measurement methods, the variation between the two ratios is acceptable. When estimating the maximum package permeability for guaranteeing the minimum shelf life of a food for example, a safety factor is used anyway.
Pernieation ofgases, w u t u vapor rind volrztile organic compoiinds
247
Table 9-3. Relative values of permeability parameters (van Krevelen. 1990) Gas
P
D
S
EP
ED
02
NZ(=l)
1
1
1
1
1
1
CO
1.2
1.1
1.1
1
1
0.95
CH4
3.4
0.7
4.9
(1)
(1)
0.9X
O?
3.8
1.7
2.2
0.X6
0.90
0.83
0.2s
0.62
0.45
0.4s
He
1s
60
H?
22.5
30
C02
24
H2O
1 5
0.70
0.65
0.55
24
0.75
0.75
1.03
-
0.75
0.7s
1.o 0.94
Example 9-1. The value for permeation coefficient ( P ) of COz through a LDPE film was measured to be P = 2 x 10-"cm3 . cm/cm2 - s . Pa at STP conditions and 2.5 "C. a) How large is the estimated value of P for oxygen in cm' . cm/rnz . d . bar at the same temperature? b) How large is the variation range for this estimation of P? a) First, the P value for COz needs to be expressed in the desired units. Using Table 9-1 there are two possibilities: a l . The value is multiplied by 8.75813 to convert from cm3 'cm/cm2 ' s . P a to cm3 . cni/m2 d . atm and then the result divided by 1.01 to transform the units into bur: (2E - 12) 8.7SE13j1.01 = 173 cm3 . cm/mz . d . bar. The difference between the old units of atmosphere (utm) and bar SI-units is pratically negligible since 1 utm = 1.01 bur. a2. The value is multiplied by 3.33E3 and then divided by 1.54E-11 which then gives: 2E - 12 cm3 . cm/cm2 . s . Pa = 173 cm3 . cm/m* . d . bar. From Table 9-3 one gets a value for oxygen of PO, = 173 '3.8124 = 27.3 cm' . cm/m2 . d . bar b) Taking into account the standard deviation from average value of the relationship between the permeation values for C 0 2 and O2 given above, one gets a maximum value for Poz in LDPE at 25 "C of PO, = 173/2.5 = 6Y cm3 . cmlm' . d . bar and Po, = 173/7.1 = 24 cm3 . cm/m' . d . bar as a minimum value. By using the maximum value theworst possible case for oxygen permeation is taken into account. After converting the values for oxygen in Table 9-2 to these units one gets: Po, = 44.9 cm'. cmlm'. d . bar. This value is within the above range. Example 9-2. What is the maximum value for oxygen permeation ( J ) through a 50 pm thick LDPE film at 10°C when the exterior of the film is in contact with air and the maximum estimated value for oxygen permeation at 25 "C from example 1 is used? The permeation is calculated using Eq. (9-1). The maximum value is obtained when one uses Po2 = 69 cm' . cm/m2 d . bar and assumes that the partial pressure of oxygen on the interior of the film is zero. Taking into account the proper units (1 bar z 1 atm), one gets a perrneation based on 1 m2 surface area of film to be: J=P~~69~~=2900cm'/m2d
248
Piringer
The temperature dependence of the P, D and S constants can be represented with the help of an exponential function (Arrhenius Equation): a) b) c) d) e)
P = Po exp (-Ep/RT) D = DOexp (-ED/RT) S = So exp (-A Hs/RT) Po=DoSo EpzE~+hHs
(9-5)
EP and ED are the activation energy of permeation and diffusion and Hs is the molar heat of solution of the gas in the polymer. These parameters are expressed in kJ/mol where R = 8.3145 J/(mol K) and T is the absolute temperature in Kelvin. The ratio of the activation energy EP and ED of two gases are relatively independent of the nature of the polymer. Furthermore, the ratio of ED values corresponds almost exactly to the ratio of the squares of the molecular cross sectional diameters (02)of the two gases (Table 9-3). This knowledge allows the estimation of D, S and P values with help of easily obtainable molecular properties (see Section 9.1.3). If the value of P is known or can be estimated for a gas in a certain material, then the calculation of the gas permeability through that material of a certain thickness can be made using Equation (9-1). In practice the agreement between the calculated and actual permeability of a plastic material is set within limits. Deviations from the calculated permeability for the same material can come from different manufacturing processes that cause changes in the properties of the material’s surface, the orientation of the macromolecules and other effects. The permeability of a material can vary widely at different locations in the package. Different material thickness of the walls, bottoms, edges and seals, different materials for lid and container or the presence of pores or other leaks for example can all cause considerable differences between the calculated and total effective permeability of a package. In practice it must not be forgotten that P values give an order of magnitude estimation for the selection of suitable packaging materials and thus allow a closer calculation of the total package permeability with the help of the flux J: n
n
Q=z Q i = CAi Ji i
(9-6)
I
Q is the sum of the permeabilities for individual packaging materials and wall thickness of different packaging components. Using the corresponding P and d values for every component i, the corresponding flux J is calculated using Equation (9-1) and multiplied by the component’s surface Ai. The partial pressure difference Ap is treated as a constant. The total permeability of a package developed in this way must nevertheless be checked experimentally due to the above mentioned uncertainties (see next Section).
Example 9-3. A 20 cm long HDPE tube with an external diameter of 10 cm and a wall thickness of 1 mm is filled with an oxygen absorbing substance. Both ends of the pipe are sealed with a 100 p n thick LDPE film and the tuhc is stored in air. What is the total oxygen pernieation into this tube using the permeability coefficicnt values from Table 9-2 for HDPE and LDPE at 25 "C? The total permeation of this pipe can be calculatcd using Eq. (9-6) along with Eq. (9.1). The permeability through the surface area of the HDPE tube is: First convert the value in Table 9-2 to the dcsired units: cm7 cm
1 3 z (8.75E13 conversion factor). 7.219E 4? ( ) ( Then calculate the total amount of oxygen permeating through the walls of the tube:
P = 0.825E
-
.
~
ioonn cm2 m2
=
-
em' cm
cni- day alni
AP
QHopE= A ; .Ji = Ai . P - - = ( n . 10 cm . 2 0 cm) . d
0.95cm7/day Similarly one gets QLDPE = 14.4cm3/day for both LDPE end caps. Adding the oxygen permeation for the tube and the ends together one gets a total oxygen permeation of Q = 15.3 cm'/day. The magnitude of this amount of oxygen permeation is largely determined by the LDPE end caps.
Example 9-4. What permeability is obtained in Example 3 when a 10 pm thick PVDC film is used instead of LDPE for sealing the ends of the tube? What is the ratio of a) the permeation from the PVDC film from the ends to the permeation from the surface of the HDPE tube and the permeation from the LDPE film from the ends in Example 3 to the permeation from the surface area of the HDPE tube? When the ends of the HDPE tube are sealed with 10 pm PVDC film one gets the permeation, using permeability coefficient value for oxygen through PVDC at 30°C given in Table 9-2, in the following way: First, convert the units of the permeability coefficient to the desired units: em' cm
0.000383E - 13-cm* s Pa . (8.75E13 conversion factor) . em3 cm
3.351E - 7- cm2 day atm Then, calculate the permeation through the two end caps:
0.011 cm'/day Note that using a permeability coefficient at a higher temperature (30 "C) will tend to give an overestimation of the permeation at 25 "C. Finally, sum the permeation through the end caps together with the permeation through the wall of the tube: n Qsy,lcm
=
Q, =QPVDC
+ QHDPE
= 0.011
cm3/day
+
0.95 &/day
= 0.96
cm3,/day
I
a). Ratio of the permeation through the PVDC end caps to the permeation through the HDPE tube is: = (0.011 &/day ) / (0.95 cm'/day) < 0.012 b). The ratio of the permeation through the LDPE end caps to the permeation through the HDPE tube is: QPVDC/QHDPE
QLDPE/QHDPE
=
(14.4 cm3/day
) / (0.95 cm'/day)
=
15.1
250
Piringer
9.1.2 Experimental measurement of gas permeability The measurement of sorption, diffusion and permeability coefficients takes place as a rule using one of three methods: sorption of the gases in the polymer, permeation through a membrane (film or sheet) into a sealed container or permeation through a membrane into a gas stream. As far as possible sorption methods should be used together with permeation methods that are specific for the measured gas/polymer system in order to uncover any possible anomalies or errors in the measurements by comparison of results. I. Sorption: The method allows a direct measurement of S from the equilibrium between gas and polymer. The volume of gas taken up by the polymer can be measured gravimetrically, manometrically or using a gas specific detector. Headspace gas chromatography is an useful technique for this. The S values then come from:
Where me is the amount of gas absorbed in the volume V of the polymer at equilibrium and pc is the corresponding partial pressure of the gas being studied. In order to check if S stays constant, one measures the me value for several pressures pe at the same temperature. S comes then from the slope of the straight line me = f(p,). Deviations from linearity of the line means deviations from Henry’s law. 2. Permeation in a sealed container: The amount of gas m, found in the container’s chamber as a result of permeation through the film is plotted as a function of time t (Fig. 9-1).The partial pressure p1 of the gas permeating into the film is held constant. Normally the chamber volume is so large that even upon reaching steady state permeation the partial pressure p2of the permeated gas remains negligibly small (p2 << PI). A simple method is to measure the increase in pressure (p2) over time in an initially evacuated chamber. Another possibility is the use of sorbents in the chamber so that the partial pressure (p2) is kept practically at zero. The amount of permeating gas can be gravimetrically determined with the help of the sorbent. It is also possible to use
0
e t -
Figure 9-1: Time dependence of permeation.
Pernieririoti ofgases. it~i[i>r v ( i p o r nnd volatile organic c o n z p n i ~ n ~ ~ s
251
specific gas detectors. Gas chromatography (GC) in combination with a thermal conductivity detector (TCD) is particularly well suited. For the measurement of oxygen permeability a coulornetric method or for carbon dioxide an infrared detector is used. A frequently used item of equipment for measuring gas permeability is composed of a two-piece metal cell. The test gas flows through the upper half while at the same time the amount of gas permeating through the film is measured in the lower half. The amount permeating is measured using a mercury column at constant pressure. The method is applicable to a permeation range of 3-20,000 cm'/(m2 day bar). A corresponding international test method is IS0 2S56. One obtains the permeability coefficient with the help of Eq. (9-1) using the slope of the asymptote in Fig. 9-1 which means steady state permeation has been reached: ~
where pl, d and the film surface area A are known. The intersection of the asymptote with the time x-axis, 0,allows the diffusion coefficient to be calculated (time lag method, see Chapter 7):
The sorption coefficient is then calculated from S = P/D. 3. Permeation in a gas sfreurn. The film being investigated separates a cell into two chambers. A stream of gas, e.g. nitrogen at normal pressure, containing the gas being studied, e.g. oxygen or carbon dioxide with the partial pressure pl, flows through the first chamber. Pure nitrogen flows through the second chamber with a known flow rate f cm3/s (STP) and subsequently into a O2 or C 0 2 detector. After reaching steady state permeation the value of the partial pressure in the second chamber p2 is reached. With help of Eq. (9-1) one then gets:
(9-10) where c2 is the concentration of the test gas in the second chamber expressed as the dimensionless ratio of p2 to the total pressure p in this chamber. If the permeability of a tube is studied instead of a film, the permeability coefficient can be calculated using its length L and its outer r I and inner r2 radii:
(9-1 1) Here, pure carrier gas flows through the inside of the tube (chamber 2) while the outside of the tube is surrounded by the partial pressure of the test gas p1. For materials having extremely low permeabilities one can direct the gas stream from the second chamber through a tube containing sorbent which traps the test gas. The amount sorbed during a given time interval (in steady state) can be determined analytically. This method is also recommended when one has several concurrent test runs and does not have a detector connected directly to every cell. The most common sources of error for permeation measurements are leaks in the film between the two test chambers. Measurements at two or more different pressures in the first chamber can help detect leaks. If for example the permeation rate
252
Piringer
increases proportionally to the total pressure difference between the two chambers and not just to the partial pressure difference of the test gas, then there must be leaks present. These leaks can possibly be in the form of micro pores in the film. When measuring permeation into a gas stream the tests should be repeated at several different gas flow rates to detect possible influences of mass transport in the gas phase. Such influences are negligible if the values for P remain constant below a certain gas flow rate. ~
~
-
Example 9-5. When measuring the gas permeation through a film one obtains a time-axis intercept of the steady-state pcrmeation asymptote of 0 = 254 min using the time-lag method. The thickness of the film being studied is 75 pm. The pressure difference (Ap) between the two sides of the film remains constant at 0.2 bar and the flux through the film is 2 cm”/m’ h. Calculate the value of the solubility coefficient S. Using Eq. (9-9) one can calculate the diffusion coefficient using the lag time 0: d2
(0.0075 cm)’
6.0
6.254 iiiiii (60s/niio)
D=-=
= 6.15E - 10 cm2/s
From Eq. (9-1) one can calculate the permeability coefficient, P:
Finally by using the values for P and D in Eq. (9-2) one can calculate the solubility coefficient S: = p = 2 08E-9 cm3 crn/cmz D h.15E-lll c m l / s
5
bar
= 3.4 cm’(STP)/cm’ bar
Example 9-6. A constant 0.5 ml/min stream of nitrogen flows through a 1 m long hose having an outer diameter of 3 cm and 5 mm wall thickness. The hose is in contact with air. After steady state permeation is reached the oxygen concentration in the nitrogen is 0.8 ppm (v/v). What is the permeability coefficient P o f this hose? Using Eq. (9.11) one can calculate the permeability coefficient as follows:
= 2.05E - 11 cm3 cm/cm2 s atm = 2E
-
16 cm3 cm/cm2 s Pa
z 0.018 cm3 cm/m2 day bar
Total permeation measurement
The total permeability, Q = J A, of a C 0 2 containing package can be measured where the package, e.g. a bottle containing carbonated mineral water with volume VR is placed in a sealed container having volume VC with a C02 free atmosphere. The amount of CO;?permeating out of the package at time t is determined by the concentration cc of the carbon dioxide found in the container at this time. Using relatively small measurement intervals, one can observe a linear increase in cc which allows one to calculate Q: (9-12)
Using the known Q (e.g. expressed in volume at STP) allows calculation of the amount of COz t h e package will lose, Vloss(also at STP), by the end of its shelf-life time t:
Perrnecrtion of gnses, wwter vnpor r i t i d volntile organic cornpoiinds
253 (9-13)
Where VL is the volume of the filled product, SL is the solubility of C 0 2 in the product and po is the initial C 0 2 pressure in the package. The solubility of C02 in water at 20 "C is SL= 0.84 cm3 (STP) /cm3 bar. The concentration cc can easily be measured using a C 0 2 specific detector. One can for example remove 0.5 ml from the container using a gas-tight syringe and inject it into an air carrier gas that comes in contact with a stream of water. The increase in the electrolytic conductivity in the water caused by the presence of C02 is proportional to the concentration in this range. With help of such an analytical system the C 0 2 concentration can be measured within 30 seconds with a detection limit of 3 ppm (Leibl et al., 1990). With this setup, non-destructive testing of the total package permeability can also be carried out. Using the results obtained for C02, the total permeability for other gases can be estimated with the help of Table 9-3. Example 9-7. Sensory analysis of a COz containing mineral water showed that a loss of 15 YO or more from the initial quantity of COr led to a significant quality decrease in the form of a flat taste. A 1.5 liter plastic bottle has an initial fill pressure of 3.8 bar. A tightly sealed bottle has a total permeability of Q = 6 mg/day at 20°C. How long can this bottle be stored before a noticeable sensory change takes place in the mineral water? To solve this problem one can use Eq. (9.13). From the given value for the solubility of CO2 in water at 20 "C, S L = 0.84 cm3 (STP)/cm3bar one can calculate the initial C 0 2 content of the bottle:
PI).SL.VL = 3.8 bar 0.84cm'(STP)/cm3 bar. 1500cm3 = 4788 cm'(STP) The molar volume of a gas at 0°C and 1 bar 2 1 atm is 22.4 dm'. Given the molar mass of C 0 2 at 44 gimol, the C 0 2 loss can be calculated to be 6 mg/day at 20 "C: rnol
Q = 22.4 (dm3/mol) . 1000( cm3/dm3) .0.006 g/day. - = 3.05 cm3(STP)/day 44 R
The loss of 15 YO of the intial COz means VI,,,, = 718 cm' (STP). With these values one can calculate the time t before too much COr is lost:
3os
' )] :_ :_ t = 255 days
After more than 8 months storage there is a noticeable loss in product quality. Note that this loss in quality is based only on the loss of C 0 2 and not caused by possible sensory changes due to migration of sensory active substances from the bottle.
The influence of pores and leaks in a package on the total permeation depends primarily on whether or not the package is vacuum packed or at atmospheric pressure (Becker, 1965). For the case of vacuum packaging, the Hagen-Poiseuille equation for laminar gas flow can be used as a first approximation: (9-14)
254
Piringer
where Vs is the volume of gas flowing through a pore with radius r and length 1 up until time t and pl and pz are the pressures at each end of the pore, Po is the pressure related to Vs (1 bar) and q is the dynamic viscosity of air. If the inside of the package has the same total pressure as its surroundings but a difference exists in the partial pressures of a certain gas, e.g. oxygen, then the transport of this gas occurs by diffusion according to an equation analogous to Eq. (9-1) and one obtains: Vd=xr2D
Po 1
t
(9-15)
where Vd is the volume of gas diffusing through the pore during the time t, and D is the diffusion coefficient of the gas in air. The remaining parameters are identical to those used in Eq. (9-14). A precondition for the optimization of a package having a specified minimum shelf life date for a food with a known oxygen and/or water sensitivity is the calculation of the permeability of laminate structures. The total permeability Q, of a laminate film made from n different plastic layers with thicknesses di and having permeability coefficients of Pi can be calculated using the following formula: (9-16) Here the magnitude of Q, is determined by the layer having the largest ratio of di to Pi. A is the surface area of the laminate and Ap is the partial pressure difference between the two sides of the laminate. A manifold variety of packaging exists on the market as a result of the many possible combinations of packaging materials with different properties. ~
~_____
Example 9-8. A pouch is made from 5 dm2 of a heat sealable laminate film material. The film has the following structure: 25 pm PP, 5 pm EVOH and 50 pm LDPE. How much oxygen permeates into this pouch at room temperature'? The total permeation of the pouch is calculated using Eq. (9-16). Using the permeability coefficient values for the different materials from Table 9-2 one gets:
0.W2.5 cm
S00cmZ.0.21bar.I 1 .Ill E+SPa/bar 1
Qv
20164E+14 ~
10M)SE+7
=
0.lX)oS cm
1.7E- 13 cm3cm/crn2sPa + O.~XM024XE-13
+-)
0 00SOcm 5. IXE- 13
=
1.9013E + 7s/cm3
:_ Qv = 5.259E - 8 cm3/s.8.64E + 4 s/day
=
0.00454 cm'(STP)/day
Making the assumption that room temperature is below 30 "Cthis would be a maximum value for the permeability.
9.1.3 Estimation of gas permeability Given the relationship, P = D . S, the permeability can be calculated from knowledge of the solubility of the gas in polymer and its diffusion coefficient.
Permeation o,fgasrs, w i i t i v vapor atid voInriIe organic cornpoiitiris
255
The soliihility coefficient Due to the very low solubility of normal gases in polymers the S values for various polymers do not differ very strongly from one another. The sorption coefficient S (298) at 25°C can be estimated quite well in an amorphous polymer in its rubbery state with help from the following formula (van Krevelen, 1990): logS(298) = -7.0
+
0.01
(9-17)
f0.25
where E is the potential energy constant of the permeating gas and k is the Boltzmann constant. The ratio Elk is described as the Lennard-Jones temperature (Table 9-4). S is expressed in cm3 / (cm3 Pa). Ihblc 9-4. Diameters of simple molecules. Molccule
(5
E/k
(gas)
(nm)
He
25.5
(K) 10.2
HZO
809 60
H2
26.4 28.3
Ne
28.2
33
N €-i7
29.0
558
0 2
34.7
107
Ar
35.4
93
CH10H
36.3
4x2
Kr
36.6
179
co
36.9
92
CH,
37.6
149
N2
38.0
71
c'oz
39.4
19.5
Xc
40.5
23 I
SO2
41.1
335
CIH4
41.6 41.8
22s
CH.qCl C2Hh
44.4
216
-
CHzClz
49.0
356
C.&
51.2
237
ChHh
53.5
412
The heat of solution (molar enthalpy of sorption) of small molecules in elastomers is positive (endothermic effect) while it becomes negative for larger molecules (exothermic effect). The heat of solution becomes exothermic as soon as the sorption energy evolved becomes larger than the energy needed for the formation of a free volume large enough to accept the size of the gas molecule in the polymer. From the S value at 25 "C the heat of solution AHs and So in a polymer above its glass transition temperature T, can be estimated using:
256
Piringer
3 .lo-3 R logso
=
1.0
= -5.5
-
0.01
-
;
0.5
(9-18)
f 0.8
0.005
For amorphous polymers in their glassy states, the following expressions analogous to Eqs. (9-17) and (9-18) are used:
+ 0.01
logS(298) = -7.4 3R. 1 0 - 3
0.5
=
logso = -6.5
-
0.01
-
i0.6
;+ 1.2
(9-19)
i1.8
0.005
Using these expressions the solubility of a gas at a given temperature, S(T), in an amorphous polymer can be estimated: logS(T) = logso
0.435
-
& = logS(298) AH
- 0.435 3 R ($
-
1 298 )
(9-20)
If the degree of crystallinity in the polymer is designated with x, and S, is designated as the solubility of the gas at 25 "C in the amorphous polymer, then Eq. (9-21a) can be used for an approximation of the solubility in a semi-crystalline polymer: Ssc(298) = Sa(298) (1 Dsc
= Da
(1
(9-21a)
- xC)
(9-21b)
- XC)
The diffusion coefficient If one selects the nitrogen molecule as a reference molecule then one can set up the following relationship between the activation energy of diffusion, ED, of a gas i, its molecular diameter oi and the glass temperature T, of the polymer (van Krevelen, 1990): 10-3
R
=( *)2
[7.5
-
2.5.10-4 (298 - T, ) 2
ON2
1
50.6
(9-22a)
for elastomer (T, < 298 K) and 10-3
!?R =
R
( 2 [7.5 ~) - ~ 2.5. lop4 (Tg- 298)3/2 f 1.0 ON2
(9-22b)
for amorphous polymers in their glassy states (Tg > 298 K). The values of molecular diameters for simple molecules are given in Table 9-4. There is a linear ralationship between log Do and ED:
2 lop3 2
logDo = lop3
-
IogDo =
-
4.0 f 0 . 4
elastomers
5.0 f 0 . 8
glassy polymers
(9-23)
Permeation r>fgases, wrr~ert q m r arid volatile o r p n i c conipoiimis
257
The diffusion coefficient D(298) in cm2k at 25 "C and D(T) at temperature T for a given polymer can be estimated with help from the following expression: logD(298)
logDo
-
!$ = -4.0
1.46.
F.lop3 !$
logD(T) = logDo -
0.46.
-
= logD(298)
!b R
-
0.435
9 (+ A)
(9-24)
-
The influence of crystallinity can be estimated for a first approximated using equation (9-21b) which is analogous to that for S. D, is the diffusion coefficient in the amorphous polymer and x, is the degree of crystallinity. D, is calculated with the help of Eq. (9-24).
The permeability coefficient The estimation of P can be made using the formulae for S and D in following empirical expression (van Krevelen, 1900): for elastomers:
+
logPo = -10.1
1 0 - 3 2 fo.25
logP(298) = -10.1 - 0.46 . lop3
% f0.25
(9-25)
for amorphous glassy polymers: logPo = -11.25
+
lop3
logP(298) = -11.25
-
f0.75
% 5~ 0.25
0.46.
(9-26)
for semi-crystalline polymers:
and for any polymer: logP(T) = logP(298)
E p / R = AHs/R
-
0.435
2 (5
-
I
298)
(9-28)
+ ED/R
Example 9-9. Estimate the average values for the solubility coefficients of oxygen and carbon dioxide in polypropylene (PP) having 50 'YO crystallinity at 30 "C. Use the E/K values for both gases and compare the ratios of carbon dioxide solubility coefficients to the oxygen coefficients (SCO,/SO,) with the ratios of Sco2/SoZusing values from Table 9-3. For the solubility and heat of solution of O2 in PP at 30°C one uses Eq. (9-19) and Table 9-4: ~. AH5
= 1.0 - 0.01 . =
logs,) = -5.5
-
0.005 .
=
1.0 - 0.01 . 107 = -0.07 -5.5
-
0.005 . 107 = -6.035
258
Piringer
Using Eq. (9-20) one calculates a value of S for amorphous PP at 30 "C: logS(303) = logs"
- 0.435
AHs/RT = -6.035
-
0.435 (-70.0) . (L) = -5.9355 303
:. SO,(303) = 1.16E - 6 cm3(STP)/cm3 Pa With a crystallinity of 50 YOone gets using Eq. (9-21a): SsC= S,(303). (1 - xc) = 1.16E - 6 . (1 - 0.5) = 5.8E - 7 cm'(STP)/cm3 Pa = 0.058 cm3(STP)/cm3 bar In the same manner one obtains the solubility for C02: SCO,= 3.87E - 6 cm'(STP)/cm3 Pa = 0.39 cm3(STP)/cm3bar The ratio Sco2/So2is equal to 6.7. The ratio for Sco,/So2using values from Table 9-3 is equal to 2412.2 = 10.9. Example 9-10. Estimate the average value for the diffusion coefficient for oxygen and carbon dioxide in polypropylene with 50 % degree of crystallinity at 30 "C. Use the corresponding molecule diameter (J and the average Tg value of 267 K for PP. Calculate the corresponding permeability coefficient value using the solubility coefficient value determined in Example 9. Using Eq. (9-22) for elastomers and Table 9-3 one gets for oxygen: R
=
)('
(g)2 p.5
2
(298 - Tg)*]=
p.5 - 2.5.
ON2
- 2.5. 10-' . (298 - 267)']
=
6.0536 E
The corresponding value for 10-3 C 0 2 is 7.260. Using Eq. (9-23) for elastomers one can calculate the Do values for 0 2 and COr: D - 4.0 = 6.0535 - 4.0 = 2.0535 for O2 logDo = lo--, ER logDo = 7.260 - 4.0 = 3.260 for C02
Now using Eq. (9-24) calculate the diffusion coefficient for O2 and COz at 30 "C:
IogDo, (303) = logD"
135 -
r . lo-' 5 = 2.0535 R
435
'6.0536 = -6.6373,
:. Do, (303) = 2.3E - 7 cm2/s 435
logDc0, (303) = IogD" - -.T
:. Dco,(303) =0.6YE
-7
435
1 V 3 5 = 3.260 - -. 7.260 = -7.1628. R
303
cm2/s
Correcting for the 50 % degree of crystallinity using Eq. (9-21b) leads to the final estimated diffusion coefficient values: Dsc = D, . (1 - x,) = 2.3E - 7 . (1 - 0.5) = 1.15E - 7 cm2/s for 0 2 Dsc = D, . (1 - x,) = 0.69E - 7 . (1 - 0.5) = 0.35E - 7 cm2/s for C02 With the corresponding S value from Example 8 one can calculate P using the product of S and D: Cm2 cmlcm C~~(STPJ PsC(303) = Ssc(303). Da(303) = 5.8E - 7 x . 1.15E - 7- = 0.67E - 13-cm? s pa for 0 2 PsC(303) = Ssc(303) . Dsc(303)= 3.87E - 6
cmZ(STPl
x
7
cm-
. 0.3SE - 7-
=
Cm3CIIl
1.3E - 1 3 a for C 0 2
Pernienrion uf gases, w i t e r vnpor nnd volatile organic cornportnds
259
Example 9-11. Estimate the average value of the diffusion coefficient for water in polyamide 66 (PA or nylon) with a degree of crystallinity of 70 % and water content of 3.6 % at 25 "C. Compare this value with one at 0 % water content. At 0 YO relative humidity for water in PA 66 at 25 "C and using the T, value of 60°C from Table 2-2, one can calculate the value for 10-'ED/R using Eq. (9-22b) for a polymer in a glassy state and Table 9-4: 7.5 - 2.5E - 4(T, 264 (%)
k.5
- 2.5E - 4(333 - 298)'"]
-
298)'"]
=
= 3.59
For hydrophilic polymers Eq. (9-30) is valid and consequently: 3 ED - 7.0 = 3.59 - 7.0 = -3.405 IogDo = lo-Using Eq. (9-24) one calculates a diffusion coefficient for the amorphous state to be: logD(298) = IogDo - 1.46. lo-' D(298) = 2.3E 9 cm2/s
5 = -3.405 R
-
I .46 .3.59 = -8.646
-
Correcting the diffusion coefficient for the degree of crystallinity (Eq. 9-21) one gets: Dsc = D,(l - x,) = 2.3E - 9(l - 0.7) = 6.8E - 10 cm2/s Eq. (9-31) is used to correct for a water content of 3.6 %: logD = logDw,o + 0 . 0 8 ~ = log(6.8E - 10) + 0.08(3.6) = -8.879 .' .
D.16 (298) = 1.3E 0 " ,
9 cm2/s
~
Example 9-12. Estimate the average value for S. D and P of oxygen and water in polystyrene (PS) at 25 "C. The average value of T, = 90 "C for PS is used from Table 2-2. Using Table 9-4 and Eq. (9-19) for glassy polymers one can immediately calculate the solubility coefficients: logSoz(298) = -7.4 + 0.01 = -7.4 + 0.01 107 = -6.33. So, = 4.7E 7 cm3(STP)/cm3Pa K E l o g S ~ ~ o ( 2 9= 8 )-7.4 + 0.01 ;= -7.4 + 0.01 .460 = -2.8, Soz = 1.6E - 3 cm3(STP)/cm3Pa -
The values for the 1 0 - 3 E ~ / Rvalue for an amorphous polymer in the glassy state are calculated using Eq. (9-22b): k . 5 - 2.5E - 4(T, 1 0 - j E ~ / R= cA)2
-
298)'"]
=
ON2
(h)
747 2
c%)'[
p.5 - 2.5E - 4(363 - 298)"2] = 6.14
iO-;E,,/R
=
(:)'[7.5
-
7 5 - 2.5E
- 4(T, -
298)
"'1
=
2.5E - 4(363 - 298)3!2] = 3 56
Eq. (9-23) for Do in the glassy state and Eq. (9-24) for D(298) one gets: for
0 2 :
for H 2 0
logDo = :
E
A - 5.0 = 6.14 - 5.0 = 1.14
IogDo = IO-'
5 - 5.0 = 3.56 K
-
5.0 = - 1.44
260
I
Piringer
logDo,(298) = IogDo - 1.46.
E
= 1.14-
1.46.6.14 = -7.8244.
Do, (298) = 1.5E - 8 cm2/s lOgD~,o(298)= bgD" - 1.46.
ED
=
-1.44 - 1.46 3.56 = -6.6376,
DHlo(298) = 2.3E - 7 cmZ/s By combining the above solubility coefficient value with the diffusion coefficient the permeability coefficient can be calculated using Eq. (9-2): P0,(298) = D . S = 1.5E - 8 cm2/s . 4.7E - 7 cm3(STP)/cm3Pa = 7.044E - 15 cm3cm/cm2sPa P~,0(298)= D . S = 2.3E - 7 cm2/s . 1.6E - 3 cm3(STP)/cm3Pa= 3.68E - 10 cm'cm/cm*sPa These calculated values are comparable to the experimental values given in Table 9-2 for permeation of oxygen and water through PS.
9.2 Permeation of water vapor Experimentally measured data for water vapor permeation are given in Table 9-2. One recognizes immediately the large differences in water permeability compared to the permanent gases, particularly for polar polymers. The cause of these large differences is the high polarity of the small water molecules and their tendency to form hydrogen bonds. Such H bonds exist between the water molecules themselves as well as between them and polar polymer groups. Each of the polar OH groups in hydrophilic polymers like cellulose undergoes strong interactions with a water molecule, whereby the fraction adsorbed on the polymer surface can have the same order of magnitude as the amount of water dissolved in the polymer according to Henry's law. The water sorption isotherms have different forms depending on the structure of the corresponding polymer. Other factors also play a role in the tendency of polymers to sorb water, like the access of the H20 molecule to the polar groups and the degree of polymer crystallinity. These factors make the correlation between structure and sorption much more difficult. The effect of various polar groups is dependent on the degree of moisture present. From the evaluation of empirical data collected the estimation of water content per polymer structural unit can be made at 25 "C using molar ratios at different relative humidities (Table 9-5). With these values one can calculate the solubility constant (sorption coefficient) in cm3 (STP)/cm3polymer by multiplying them with 22.4E3/Vmwhen the molar volume of the polymer structural unit, V,, (cm3/mol)is used. The molar heat of solubility for water is around 25 k.J/mol for nonpolar polymers and 40 kJ/mol for polar polymers. The diffusion coefficient for water is also strongly dependent on interaction with the polymer. Polymers with many H bonds forming groups increase the D value as one of the consequences of the beginning of swelling. A good approximation is: logD
= logDw,o
+0 . 0 8 ~
(9-29)
where w is designated as the percent water content in the polymer. In hydrophilic polymers the diffusivity of water is greatly reduced due to strong interactions. A good approximation for this case is (van Krevelen, 1990):
261
Permeation of gases, water vapor and volatile organic compounds
logD0 =
%
-
7.0
(9-30)
with E D in J/mol. For weakly hydrophilic polymers like polyethers and polyrnethacrylates the same relationship between Do and ED is valid like that between the simple gases. With increasing water content the diffusion coefficient in this case also decreases significantly due to the clustering of the water molecules about the polar groups, leading to relatively immobile water molecules. In contrast to Eq. (9-29), here: logD
= logDw,O
-
0.08~
(9-31)
In completely hydrophobic polymers like the polyolefins, as well as some polyesters, the water vapor acts like a simple gas because of its extremely low solubility as well as its diffusivity. The permeation of simple gases in polar polymers is also dependent on relative humidity because of the water's strong interaction with the polymer. Particularly large is the effect of humidity on the oxygen permeability of barrier layers made from EVOH. At 20°C and 100 % relative humidity the permeability is 300 times higher than at 0 % relative humidity at the same temperature. By orientation and thermal treatments the barrier properties at high relative humidity can be significantly improved (up to a factor of 10). Table 9-5: Molar water content of polymers related to structure groups at several relative humidities at 25 "C. ~
~
~
Group
Relative humidity 0.3
-CH3 -CH2 -CH=
(1.5. lo-')
0.5 (2.5.
0.7
0.9
1.0
(3.3 lo-')
(4.5 . lo-')
(5 ' 10-5)
0.001
0.002
0.003
0.004
0.005
0.025
0.055
(0.11)
(0.20)
(0.3)
0.025
0.05
0.075
0.14
0.2
O=
0.006
0.01
0.02
0.06
0.1
-OH
0.35
0.5
0.75
1.5
2
-NH2
0.35
0.5
0.75 2.8
(1.5) 5.3
(2)
-COOH
0.2
0.3
0.6
1.0
1.3
-coo-
1.1
2.1
4.2
0.35
0.5
0.75
1.s
2
-CI
0.003
0.006
0.015
0.06
(0.1)
-CN
0.015
0.02
0.065
0.22
(0.3)
..
=c=o -C
P \O-
-NH3'
//O
-c
\NH
262
Piringer
A gravimetric method is often used for the measurement of water vapor permeability. The water vapor transmission rate (WVTR) according to this method is the amount of water vapor in g that permeates in 24 hours under standard test conditions (temperature, air relative humidity, water vapor sorbant) through a 1 m2 sample surface area. The method measure a flux and not a permeability coefficient. To carry out the measurement a dish is filled with a water vapor sorbant. The dish is covered with the sample film, sealed with wax and stored in a moist environment. The amount of water vapor that penetrates through the film is calculated from the steady state weight increase of the dish over time. Example 9-13. Estimate the water content in Nylon 6.6 at 25 "C at a relative humidity of 0.7. The crystallinity of the polymer is 70 YO(van Krevelen, 1990). The structural repeat unit of Nylon 6.6 is: [-NH(C0) - (CH;!),-(C0)NH - (CHz),-] Looking at Table 9-5 it is obvious that one can ignore the water sorption capacity of the CH2 groups. Consequently, the two (C0)NH groups have a molar water content, at a relative humidity of 0.7, of 2.0.75 = 1.5mol/unit The relative molecular mass of the repeat unit on Nylon 6.6 is 226.3 g h o l so that 1.5 times 18 g water in 226.3 g polymer is equal to 12 g water can be absorbed per 100 g polymer. Taking into account the effect of crystallinity using Eq. (9-21a) one gets for the semi-crystalline polymer: S,, = S,(1 - x,) = 12. (1 - 0.7) = 3.6 g/100 g polymer This value is compared to an experimental value of 4 YO for water sorption in Nylon 6.6 at a relative humidity of 0.7.
9.3 Permeation of organic vapors Unlike the slightly soluble simple gases, the solubility of organic compounds in polymers plays an important role. Their solubility determines the distribution of a substance between the polymer and its environment; and consequently the degree of interaction and the resulting property changes. Not all packaging materials are suitable for all applications, due to the good solubility of water, fat and other macro components of a filled product in them. Additionally the good solubility of organic compounds in plastics can under certain conditions lead to a reduction in the product's quality, due to the sorption of aromas, flavors and other food components in the packaging material.
9.3.1 Dependence of permeability coefficient on concentration For a first approximation, the simple expressions in Eqs. (9-1), (9-2) and (9-5) can be used for calculating the permeation of a given organic substance. However, the applicability is to some degree considerably reduced, depending on the molecular structures and their related properties. Various deviations from the behavior of simple gases complicate the calculated estimation of an organic substance's permeability. For the same reasons, the published data for S, D and P values can be plagued to some degree by serious measurement errors. In view of the ranges of the three param-
Permeation of gases, ww[t'r vapor and volatile organic cornpounds
263
eters, potentially extending over several orders of magnitude, it is nevertheless unavoidable to use these data for estimating permeability. Table 9-6 gives the permeability coefficients for a series of organic compounds in LDPE at various temperatures (Salame, 1961). A collection of diffusion coefficient values for organic substances in polyolefins are given in Appendix I. Table 9-6: Permeability coefficients P (g mm m-*d-' bar-') of organic compounds in LDPE (Salame. 1961). Compound Acetaldehyde
0°C 1.34
Acetanilide
21.1 "C
54.4 "C
0.008
0.16
Acetic acid
0.14
1.22
25.9
Acetic acid anhydride
0.051
0.32
11.6
Acetone
0.5s
2.67
72.3
Allylalcohol
0.063
0.57
Aniylacetate
0.22
3.42
i- Amylalcohol
3.9
n-Amylpropionate
11.8
Benzaldehyde Benzene
0.098 0.15 17.7
0.67 2.67 173
Benzoic acid
0.028
Benzylalcohol
0.16
n-Butylacetate n-Butylalcohol
9.04 106
23.4 81.0 1770
119 83.7 295 54.2 430
116 417 5400
2.24
14.2
8.02
59
5.9 0.04
0.18
sek-Butylalcohol
0.05
0.24
14.8
t-Butylalcohol
0.02
0.10
10.6
But yraldehyde
0.35
3.93
n-Butyric acid
0.075
1.89
39.3
0.12
8.5
Camphor Carbontetrachloride
1.34
0.078
i- Amylpropionate
Aniline
73.9 "C
2.36
20
240
Chloroacetic acid
0.12
m-Chloraniline
0.63
229
3080 5.0
109 92.8 393 228 63.7 17700 23.6
Chlorobenzene
22.7
179
1730
8300
p-Chlorotoluene
11.8
110
1640
7300
Cyclohexane
12.4
98.7
1470
5900
3.7
28.0
480
1620
5x2
1230
Dekane 1.2-Dibromoethane Dibutylether Dibutvbhthalate
55.0 4.4
33.6
5.7
10.9
264
Piringer
Table 9-6: Continued Comvound
0 "C
o-Dichlorobenzene
21.1 "C
54.4 "C
73.9 "C
3140
11800
60.9
Diethylenegl ycol Diethylether
0.30 18.9
Diethyloxalate
123 0.28
Dipentene
5.9
50.3
798
3190
Ethylacetate
0.75
6.5
149
669
Ethylalcohol
0.28
Ethylenglykol
0.50
Ethyleneglycolmonobutylether
0.26
Ethylformiate
5.9
Ethylmercaptane
10.2
157
E th ylpropionate
9.8
Formaldehyde
0.21
Formamide Formic acid
0.26
15700
4.7
20.0
0.09
Glycerine
0.14 19.1
n-Heptene
106
0.63
1040
3200
3540
11800
106
n-Heptylacetate
7.1
Heptylalcohol
0.39
n-Hexane
3931
70.8
0.20 0.10
Furfurylalcohol n-Heptane
13.8
18.9
138
Hydrochinone
0.02
Methylacetate
0.14
5.5
Methylalcohol
0.1
Methylethylketone
1.45
Methylcyclohexane
0.48 4.95
10.9 128
39.3 550
108
Nitrobenzene
0.15
1.93
39.3
165
Nitroethane
0.37
1.06
25.1
113
Nitromethane
0.83
Octadekane
0.71
Octylalcohol
0.039
0.20
Oxalic acid
10.1 0.08
73.9 0.09
i-Pentane
18.9
106
1970
7860
n-Pentane
38.1
206
5900
23600
Phenol
0.04
0.2
9.4
47.1
n-Propylalcohol
0.03
0.2
8.8
66.0
i-Propylamine
0.90
16.0
275
1260
Perrnecition of gases, writer vapor and volatile organic conipoitnds
265
Table 9-6:Continued Compound Tetradecane
0°C
0.67
Tetradecene Toluene
p-Xylene
5.7 4.7
22.7
1YY
14.2 33.7
101 191
1.1.l-Trichloroethane o-Xylene
21.1"C
54.4"C
73.9"C
159
393
2270
11300
1420 1890
6530 6410
I02
Some measured values, D and K, (Koszinowski 1986, and Koszinowski and Piringer, 1990) are contained in Table 9-7. These data deal mainly with the partition coefficients of hydrocarbons, alcohols, phenols and a series of aromas between polyolefins and a liquid phase (ethanol, methanol) as well as diffusion coefficients of these substances in the polymer. Table 9-7:Diffusion coefficients of organic compounds in LDPE and partition coefficients between LDPE und methanol or ethanol(*) at 23 "C. Compound
Molecular formula
Hydrocarbons Decane Dodecane Tetradecane Hexadecane Octadecane Eicosane Diphenylmethane Limonene a-Pinene P-Pinene p-Cymene Myrcene
K
D . 10"'
calc.
exp.
[cm2/s]
0.50 0.79
0.55*
-
0.97* 1.3* 1.6* 2.5* 4.2* 0.25* 0.42 0.64 0.63 0.34 0.36
34
1.3 1.8 3.1 4.9 0.22 0.24 0.33 0.33 0.19 0.33
0.0040 0.012 0.020 0.031 0.049 0.0028 0.017
0.0047* 0.021* 0.029* 0.033* 0.053* 0.0023 0.014
55
18
14 10 8.3 48 43 14 14 54 70
Alcohols
Heptanol Dodecanol Tetradecanol Hexadecanol Octadecanol Diethylene glycol-monoethylether Borneo1 (1.7.7-trimethyl-bicyclo-2,2,1-heptane-2-ol)C I , , H I ~ 0 3
11
8.2 6.4 4.8 38 4.8
266
Piringer
Table 9-7: Continued Compound
Molecular formula
K
D . 10''
calc.
exp.
Dimethylbenzylcarbinol
0.0095
0.012
7.5
3,7-Dimethyloctanol
0.0078
0.0085
9.2
Dimethylphenyleth ylcarbinol CllH160 Geraniol (2-trans-3,7-dirnethyI-2.6-octadiene-8-ol) CloHlxO
0.012
0.013
0.0053
0.0066
15
Hexenol (cis-3-Hexene-1-01)
Cdi@
0.0022
0.0024
14
Linalool(3.7-dimethyl-l,6-octa-diene-3-ol)
CIOHIRO
0.012
0.0086
19
Menthol (2-Isopropyl-5-methyl-cyclohexanol)
CIOH200
0.011
0.020
12
Nerol(2-cis-3,7-dimethyl-2,6-octadiene-l-ol) Phenylethylalcohol (2-phenylethylalcohol)
CiuH 1 x 0
0.0038
0.0047
21
C8Hw0
0.0019
0.0029
43
Phenylpropylalcohol(3-phenyll-propanol) C~HIZO CloHIRO Terpineol (I-methyl-4-iso-propyl-I-cyclohexene-4-01)
0.0024
0.0031
28
0.0074
0.012
22
Tetrahydrolinalool(3,7-dimethyl-octane-3-01)
0.025
0.01 1
13
Phenol
0.0028
0.0026*
45
p-Cresol
0.0035
0.0056*
23
CinHzzO
Icm2/sl
7.9
Phenols
2,4,6-Trimethylphenol
0.020
0.019*
23
2,3,5.6-Tetramethylphenol
0.026
0.030"
16
2,4-di-tert-Butylphenol
0.017
0.016*
1.2 9.8
2,6-di-tert-Butylphenol
0.14
0.13*
2,6-di-tert-Butyl-4-methylphenol
0.18
0.19*
6.6
Topanol (1,I ,3-tris(2-methyl-4-hydroxi-S-tertbutylphenyl) butane)
0.00060
0.00031*
0.054
CIOHI 2 0 2
0.015
0.012
26
CIffH1202
0.020
0.019
15.5
Aldehyde Cg (n-octanal)
0.021
0.020
23
Aldehyde CS (n-nonanal
0.026
0.026
18
Aldehyde Clo(n-decana1)
0.033
0.034
14
Aldehyde CII(n-undecanal)
0.042
0.043
10
eugenol(4-allyl-2-methoxyphenol) lsoeugenol(2-methoxy-4-propenylphenol) Aldehydes
Aldehyde C1,en(n-undecene-2-a1)
CI1Hzo0
0.042
0.043
9.6
Aldehyde CIlinter(cis-undecene-8-al)
CiiHzoO
0.030
0.024
9.0
Aldehyde Clz (n-dodecanal)
CizHz40
0.052
0.060
1.9
Permeation of gases, uwrt’r vcrpor and volutile organic cornpoiinds
267
Table 9-7 Continued
Compound
Molecular formula
D . 10’”
K calc.
exp. 0.059
Aldehyde CI2MNA(2-methylundecanal)
CI~HZ.~O
0.052
[CRI’k] 1.8
2-Pentyl-3-phenyl-propenal
Ci-tHixO
0.079
0.064
14
Citral (cis-3.7-dirnethyl-2,6-octadienal)
CIlIHlhO
0.022
0.016
36
Citronellal (3,7-dimethyl-6-ociene-l -al)
CIIIHIXO
0.023
0.019
10 16
Jasmonal (2-hexyl-3-phenyl-propenal) Ci d 2 1 1 0 Hydroxycitronellal (3,7-dimethyl-8-hydroxyoctanal)ClllHZ1102
0.10
0.10
0.00052
0.00090
5.5
Heliotropine (3.4-methylenedioxy-benzaldehyde)
CRHh03
0.032
0.019
8.7
Lilial (3-(4-tert.-butylphenyl)-2-methylpropanal)
CI4HZ00
0.032
0.014
0.0022
0.0018
Acetophenone(pheny1me thyl-ketone)
0.021
0.03
110
Benzophenone
0.063
0.046
4’)
Camphor (1,7,7-trimethyl-2,2,1-heptane-Z-on)
0.031
0.062
15
Ionone (4-(2,6.6-trimethyl-2-cyclohexene-l -yl)-3 butene-2-011)
0.070
0.039
12
Methylionone alpha (5-(2,6,6-trimethyl-2cyclohexene- 1-yl)-4-pentene-3-on)
0.0xx
0.060
6.6
(4-(2,6,6-trimethyl-2-cyclohexene-l-yl)-3-methyl-3butene-2-on)
0.088
0.066
8.6
Menthone (2-isopropyl-5-methyl-hexanon)
0.032
0.082
21
Methylheptenon (3-octene-2-on)
0.033
0.019
73
0.2
0. I
0.0009
0.001
25
OA14X
0.050
17
Lyral (4-(4-methyl-4-hydroxyamyl)-3-cyclohexene- CI3HZ2O2 carboxaldehyde)
14 1.2
Kmwze.7
Methylionone gamma
Tonalid (7-acetyl-1,1,3.4.4,6hexamethyltetrahydronaphthalene)
3.8
Acids
Phcnylacetic acid Nirrilrs Citralva(geranylnitri1e) (cis-3.7-dimethyl-2,6-octa-dicne-l -nitrile)
CioH IA’
268
Piringer
Table 9-7: Continued Compound
Molecular formula
D . 10"'
K calc.
cxp.
[cm2/s]
2-tert-Butylcyclohexylacetate
0.066
0.092
Aldehyde C16 (3-methyl-3-phenyl-glycid acid ethyl cstcr)
0.024
0.027
22
Allylcyclohcxancpropionate (allyl-3-cyclohcxylpropionate)
0.10
0.14
24
Benzilacetate (acetic acid-benzilester)
0.034
0.04
70
Benzilbenzoat (bcnzilic acid-benzil ester)
0.10
0.094
32
Cedrylacctatc
0.19
0.29
Citronellylacetatc (3.7-dimethyl-6-octene-l-yl acetate)
0.047
0.071
29
Citronclly Iformiate
0.038
0.086
23
DEP (diethylphthalate)
0.025
0.019
18
Dicthylmalonate
0.008
0.01 1
44
Esters 9.1
4.1
DMBCA (dimethylbenzil-carbinylacetatc)
0.067
0.049
109
DMP (dimethylphthalate)
0.016
0.012
19
Ethylbenzoate
0.034
0.070
11
Gcranylacetate (2,6-dimcthyl-2.6-octadiene-8-yl acetate)
0.075
0.068
16
Hexenylacetate cis 3 (cis-3-hexcne-1-yl-acetate)
0.019
0.041
93
IPM (isopropylmyristate)
0.21
0.33
17
Isoamylacetate
0.021
0.043
77
Isobornylacetate (1,7,7-trimethyl-bicylo-1,2,2heptanyl-2-acetate)
0.063
0.086
23
Linalylacetate (3,7-dimethyl-1,6-octadicne-3-yl acetate)
0.075
0.065*
12
Oryclene extra (p-tert-butylcyclohexylacetate)
0.064
0.1 1
12
Phenylethylacetate (2-phcnylethyl-acetate)
0.017
0.036
51
Phenylcthylphenylacetate Terpinylacetatc (l-methyl-4-iso-propyl-1-
0.052
0.033
30
0.046
0.088
12
Verdylacetate (dihydronordicyclo-pentadienylacetate)
0.058
0.089
21
Styreneacetate (1-phenylethylacetate)
0.043
0.040
29
Aldehyde C14 (undecalactone)
0.052
0.052
Coumarin (benzopyronc)
0.032
0.024
cyclohcxene-4-yl acetate)
Lactones 2.7 54
Permeation of gases, water vapor and volatile organic compounds
269
Table 9-7: Continued ~~
Compound
Molecular formula
D . 10"'
K
calc.
exp.
[cm2/s]
Ethers Anethol
CioHizO
0.23
0.24
50
Diphenyloxide (diphenylether)
Cl2HlOO
0.22
0.14"
37
0.23 C12H120 CI 1H1402
0.25 0.27
0.25
39
0.43
30
CnH 100 CI I Hi00
0.15
0.15
120
0.20
0.29
47
lndole (2.3-benzopyrrole)
CuH7N
0.013
0.0093
55
Methylquinoline (7-methylquinoline)
CICIHPN
0.019
0.027
43
Bromelia (O-naphthylethylether) Eugenolmethylether Cresylmethylether Yara Yara (methylnaphthylether) Heterocyclic compounds
The dimensionless partition coefficient K = cp/cL=S,, also known as a relative solubility coefficient, is defined as the ratio of the concentration of a substance in the polymer cp to that in the liquid (food) cLat equilibrium. While D is practically independent of the liquid phase in contact with the polymer in these measurements, the K values are determined by the nature of the polymer and liquid contact phases. From the definition S, = K, a relative peremeability coefficient can be calculated, P, = S, D, with the dimension D. Here, accordingly t o Eq. (9-2) and the solubility constant in the polymer and in the liquid phases expressed as Sp = cp/p and SL = cL/p, respectively, the following relationship results between the absolute and relative permeability coefficients:
P
= P,SL =
KDSL =
D CL
P
= SpD
(9-32)
The best agreement between the permeation process and the simplest diffusion model, for example Eq. (g-l), forms the foundation for steady state. This is obtained for a permeant above its critical temperature, at low partial pressures, in completely amorphous polymers above their T,, containing no fillers or substances to cause swelling. Deviations are often observed for organic compounds permeating through polymers below their T, as well as up to temperatures 10°C above their T,. Let m, represent the amount of material absorbed or desorbed in a polymer membrane up to time t; and mo and me represent the amount of material found in the membrane at the beginning of the experiment (t = 0) and after reaching equilibrium (t = m where me = mo+ m-). Then one obtains the same curves for m, as a function of the square root of time t for both sorption and desorption within the applicability of the simple law of diffusion (constant D) shown in Fig. 9-2a. It does not matter whether one measures the absorption curve A or the desorption curve D, for both are the same. After a linear increase, the curves converge asymptotically to an equilibrium value. Every deviation or difference (hysteresis) between curves A and D can be explained in terms of deviations from the simple law of diffusion.
Piringer
Figure 9-2: Several sorption (A) and desorption (D) curves. a) normal diffusion with constant D-value; b) increasing D-value with increasing permeant concentration; c) decreasing D-value with increasing permeant concentration: d) sorption with pronounced swelling: e) concentration- and time-dependent diffusion coefficient.
When the diffusion coefficient increases with increasing permeant concentration, then A lies above D (Fig. 9-2b). This deviation is observed for most organic substances at higher concentrations even though no significant polymer swelling yet takes place. However when D decreases with increasing permeant concentration, for example for the diffusion of water vapor through weakly polar polymers (see 9.2), the D curve lies over the A curve (Fig. 9-2c). The sorption process can be coupled with a significant swelling. Then the A curve has a sigmoidal shape and desorption follows the simple law of diffusion with a relatively high initial rate (Fig. 9-2d) (Felder and Huvard, 1980). The sorption coefficient (solubility constant) is obtained using Eq. (9-7) and the equilibrium values of me and pe. Its independence from the concentration or partial pressure of the permeant can be tested as previously described. If one plots the ratio of m,/m, against t”*, the concentration independence or constancy of the diffusion coefficient can be tested. With a constant D, the curve starts out linear as in Fig. 9-2a. For a permeant passing through a polymer sample with any given geometry, having a surface area A and volume V, one obtains a good approximation from the law of diffusion: (9-33) This expression gives an alternative possibility to Eq. (9-9) for calculating D. If the ratio m,/m, varies linearly with t then this is an indication of a deviation from normal behavior. The sorption isotherm for many substances in polymers in the glassy state, as well as water in cellulose, can be described by two processes that are independent of one another (dual sorption model): (9-34)
Permeation of gases, water vapor and voliitile organic compounds
271
where c, is the total concentration of the permeant in polymer at partial pressure p, at equilibrium. According to Henry’s law (Eq. 9-3) the sorption process with the solubility constant S is superimposed by an adsorption process. This adsorption process can be described by a Langmuir isotherm with constants a and b. At very small partial pressures, the adsorption on the surface and/or active sites within the polymer matrix dominates (Demertzis, 1985). However at high pressures the solution in the polymer determines the process. One consequence of such behavior can lead to a permeability coefficient that is dependent of the film thickness. Because this type of deviation from the simple law of diffusion, it is not surprising that P values for the same polymer can vary from one another by an order of magnitude depending on the measurement method and test conditions. Through the uptake of a substance in a polymer matrix, time dependent changes in the polymer matrix can take place, particularly at high concentrations. As a consequence, the diffusion coefficient can be time- as well as concentration-dependent. One observes such behavior for example by the sorption of substances that lead to swelling at temperatures below the T,. After a relatively rapid approach to an apparent state of equilibrium one observes a slow change towards the actual equilibrium (Fig. 9-2e). These two-step processes are caused by a gradual loosening of the cohesive forces between the macromolecules.
9.3.2 Measurement of partition and diffusion coefficients The dimensionless relative solubility constant S, = K in Eq. (9-32) is a measure of the partitioning of a substance between two phases, as is the absolute solubility constant coming from Henry’s law in Eq. (9-3). The absolute solubility constants can be directly determined using one of the methods for gases, but this is limited to only relatively volatile substances. Large experimental errors like adsorption on the polymer surface and cell walls cannot be avoided in these methods for substances with low volatilities. A measurement system where the substance studied goes from a gas phase through the film and into a second gas phase is shown in Fig. 9-3 (Franz, 1992). The permeant is dissolved in a very non-volatile substance, e.g. polyethylene glycol, in the low cell chamber in order to keep the concentration of the permeant as low as possible in the gas phase and therefore avoid the polymer swelling. The amount of permeated substance is carried to a sorption column by stream of gas flowing through the upper cell chamber. After certain time intervals the amount of sorbed material is extracted and measured using a gas chromatograph. After reaching a steady state in the membrane, the evaluation of the data proceeds in the same manner as described for gases. S and D can be calculated either by using the time lag method (Eq. 9-9) or through combination with an equilibrium sorption measurement of the film at the corresponding permeant partial pressure. As a rule several organic substances can be studied simultaneously, as long as there is no influence of one over an other (i.e. they are measured at very low partial pressures) and it is possible to separate them on a gas chromatograph. Even when swelling processes are avoided, particularly for less volatile substances and certain structures, the differences between permeation measurements made over a gas phase and those made in direct contact with a liquid can be anticipated. The
272
Piringer
c
nitrogen (65% ch.)
permeent reservoir Figure 9-3: Device for permeation measuring of organic vapors.
cause of this difference is the behavior of the permeant on the film surface in the presence of a gas compared to a liquid phase. Theoretically the partition between the polymer and a liquid can be divided into two independent partition processes, one for each of the two contact phases with a gas phase having the same partial pressure. But in practice, different results are obtained because of surface boundary effects. Therefore, for all liquid products where there is direct contact between the liquid and packaging, permeation measurements should be made under similar conditions. The following method, known as the pouch method, is very simple to conduct and delivers adequate accuracy for practical purposes (Becker, 1983). One forms a pouch with the plastic film by sealing three sides. The pouch is then filled with a dilute solution containing the permeants in a solvent and the fourth side is then sealed. In addition to the liquid phase, a gas headspace is also often present in the pouch. The pouch is then immersed in 500 to 1000 ml of pure solvent contained in a 1 L wide mouth flask with stopper. The solvent is stirred using a magnetic stirrer for the duration of the test. For films with very low permeabilities, the stirrer is not needed since the diffusion of the permeant in the solvent is much greater than that in the film, such that no significant concentration gradient can exist in the liquid phase. At suitable time intervals 0.5 to 1.0 ml samples are removed from the solvent surrounding the pouch and analysed by gas chromatography. Calculations are carried out using the following equation, which is for a quasi steady state of permeation from a volume Vi of permeant solution in the pouch into a solvent volume Va surrounding the pouch: (9-35)
In the quasi steady state, the very slight concentration changes occuring over time in the two solvents can be taken into account through a simplified permeation calcula-
Permeation of gases, water wpor and volatile organic compounds
273
tion. Here A is the surface area and d the thickness of the pouch material, c, is the concentration at time t in the external phase and c, is the concentration at equilibrium. The apparent uncertainties in Eq. (9-35) result from the value of A used, due to the presence of the gas headspace volume in the pouch. In the first approximation the partition coefficient can be calculated at equilibrium between the inner pouch surface area, the liquid and the gas phase as K = c p / c =~ (cp/p)/(cL/p) = Sp/S=. For this assumption it is the same, whether the permeant goes directly into the plastic or into the gas phase and then into the plastic. In order to recognize possible systematic errors when making permeation measurements with the pouch method, studies are carried out using the sorption technique. This method follows the non-steady permeation state. To do this, plastic disks are brought in contact with a solution of permeants and the uptake of permeants in the plastic is followed over time. The disks are stamped with a hole in the middle out of the plastic being studied, using a punch. They are then placed on a glass rod and separated using glass rings to prevent the disks sticking together during the study. This plastic assembly is then placed in a suitable screw cap glass vial containing the permeant solution (Till et al., 1987). During measurement, the vials are placed on a shaker. After a given time the disks are removed from the solution, quickly dried with absorbant tissue and washed with a suitable solvent to remove residual solution. The disks are then extracted to remove the absorbed permeants using a solvent that swells the polymer. The evaluation of the sorption curve during the initial sorption phase uses the equation: (9-36) where ct is the concentration of the permeant in the plastic at time t (see Chapter 11). The formula has the same form as Eq. (9-33) so that D can be checked for constancy. At small permeant concentrations D can be practically guaranteed to be constant (Fig. 9-2a). This method for measuring the change in sorption over time cannot be used to measure polymers that absorb permeants very quickly like LDPE, since it produces large errors. In any case the sorption method is suitable for determining of the equilibrium concentration c, of permeant in the polymer and consequently for the measurement of K.
9.3.3 The significance of partition coefficients The value of the partition coefficient of a substance between two phases depends mainly on the polarity of the substance and the polarity of the two media. Using the rule of thumb “like dissolves like” one tries, when selecting a plastic packaging material for example that will come in contact with an aqueous product, to select a nonpolar polymer (e.g. polyolefin) so that it will not be attacked by water. In such a system strongly polar substances prefer the product phase and non-polar substances prefer the packaging material. Between the extremely polar substance, water, and the completely unpolar hydrocarbons in this respect one finds the smaller alcohol molecules. Methanol and ethanol are particularly suitable for the determining the relative solubilities of organic compounds in plastics. They are themselves good solvents for
274
Piringer
many substances, they have no significant interactions with non-polar plastics and are practical to work with analytically. Ethanol in particular can be used as a food simulant for fat-containing products as will be shown later. It can also be used as a fat simulant for the study of polar plastics, on the addition of particular amounts of water. In order to determine the most important influences on the partition coming from the structures of the permeant molecules, 12 compounds have been selected from Table 9-7 and studied closer under different aspects. The selection contains compounds with different functional groups and molecular structures. An additional important criterion for the composition of this mixture is they can be easily separated into individual components by gas chromatography. By doing this, four to eight compounds could be measured simultaneously. Comparisons with measurements made using individual compounds showed no difference beyond measurement uncertainty, up to a concentration of 1 to 2 % (mass fraction) in methanol. It can be seen from the data in Table 9-8 that the partition coefficients of the selected compounds show no significant differences with respect to the liquid phase used. The values for the unpolar limonene are slightly higher in the polyolefin/methanol system than in the polyolefin/ethanol system because the methanol has a higher polarity than ethanol. For the polar cis-3-hexenol compound this difference disappears. Table 9-8: Partition coefficients of organic compounds with different polarities between polyolefins and ethanol or methanol. LDPE Compound
Eth.
HDPE
PP
Meth.
Eth.
Meth.
Eth.
Meth.
Limonene
0.42
0.67
0.36
0.74
0.4s
1.0
Diphenylmethane
0.25
0.27
0.24
0.27
0.20
0.33
Diphenyloxide
0.14
0.23
0.16
0.23 0.043
0.22
0.27
0.10
0.11
-
Isoamylacetate
-
0.046
Aldehyde C14
0.017
0.052
0.035
-
0.030
-
Linalylacetate
0.065
0.058
0.067
0.059
0.066
0.055
Camphor
0.064
0.062
0.057
0.07
0.042
0.12
Eugenol
0.013
0.012
0.024
0.02
0.020
0.015
Dirnethylbenzilcarbinol
0.0062
0.012
0.017
0.012
0.013
0.0088
Menthol
0.0087
0.02
0.019
0.014
0.018
0.018
2-Phenylethylalcohol
0.0028
0.0097
0.011
0.007
0.0087
0.0074
cis-3-Hexenol
0.0024
0.0024
0.014
0.003
0.0062
0.0037
An important point for the estimation purposes is that there is only a very small difference between the partition coefficients in the polyolefins LDPE, HDPE and PP. When the partition coefficients are expressed relative to LDPE (the straight line drawn in Fig. 9-4a) then the values for HDPE and PP are grouped around LDPE, whereas the values for PVC are significantly greater (Kozinowski and Piringer, 1986). The differences in the relative permeability coefficient and degree of crystallinity of the corresponding polyolefins in Fig. 9-4b can be traced back principally to the strong dependence of the diffusion coefficient on the characteristics of the polyolefins in Fig. 9-5 (P, = K D).
PVC
HDPE, PP
-c
KLDPE
b
LDPE
10-10 HDPE PP- cop. PP-homop.
-F
g lo-”
I
d
I
PVC
lo-” 1013
-
10-11
pr, LDPE
10’0 [cmZ/sl
Figure 9-4: Partition and permeability coefficients relative to LDPE. a) partition in the systems polyolefinlethanol and PVC/ethanol: b) permeability in polyolefins and PVC. 1: cis-3-hexenol. 2: phenylcthyl alcohol, 3: eugenol, 4: isoamyl acetate. 5: undccalactone. LDPE
108
IPE
10
T
‘-Cop.
% 10
I-homop.
Y
O
t
-11
lo I
1
1
!
! ! ! ! !
I
I
I
I
I I I I I
lo-’*
10-13
I
PVC
1O Q
10-8
DLDPE Icm2/s]
Figure 9-5: Diffusion coefficients in polyolefins and PVC related to LDPE. The numbers corresponds to the compounds in Fig. 9-4.
276
Piringer
Since the measurement of the partition coefficients for LDPE goes much more rapidly than for the other polyolefins, it is practical to apply the K values obtained for LDPE to other polyolefins. This can be done without any large errors. Table 9-9 lists the partition coefficientsfor the 12 selected compounds between LDPE and PVC polymer phases and ethanol and aqueous ethanol mixtures as liquid phases. Here one can see the enormous influence of water, particularly on the slightly polar substances in contact with the unpolar LDPE. The cause of this is the increasing permeant partial pressure over the solution with increasing water content where according to Henry’s law (Eq. 9-3) the concentration of the permeant in the polymer is proportional to the partial pressure. The non-polar permeant molecules have much less affinity for aqueous solutions than other more polar permeants. The results appear to be a regular “expulsion” of these molecules from the solution and an “attraction” by the plastic. This effect is not as strong for polar substances like cis-3-hexenol and phenyl-ethyl-alcohol.The effect is also much smaller for PVC, which has a greater polarity relative to LDPE, and whose affinity for unpolar molecules is also less. The relationship between permeant and solution is described with help of the generalized Raoult’s Law: (9-37)
P = YXPO
where x is the mole fraction of permeant in the solution, po is the vapor pressure of pure permeant at the same temperature and y is the activity coefficient. With Eq. (93) then one obtains: cp = Syxp”
(9-38)
For an ideal solution y = 1, and the equilibrium concentration of the permeant varies proportionally to the mole fraction over the complete mole fraction range. A practically ideal system is for example a solution of heptanol in methanol (Fig. 9-6). Table 9-9: Partition coefficients of organic compounds between polymers (LDPE, PVC) and several ethanol/water-mixtures at 23 “C. Compound
LDPE Eth.% 100
LDPE 80
LDPE 60
LDPE 40
LDPE 20
PVC 100
PVC 40
PVC 20
30.0 15.0
110.0 -
~
275.0
Limonene
0.42
1.99
6.5
9.7
Camphor
0.064
0.089
0.15
0.44
5.0
0.6 0.4
0.86
-
0.2
~
Linalylacetate
0.065
0.15
0.59
0.46
Diphenylmet hane
0.25
0.82
3.7
6.6
560.0
2.3
69.0
Isoamylacetate
0.046
0.069
0.16
0.99
4.1
3.3
5.2
Citronellol
0.026
0.011
0.052
0.27
3.1
1.2
180.0
17.0
2.1 150.0
0.93 -
11.0 9.1
Diphenyloxide
0.14
0.51
1.7
Eugenol
0.013
0.023
0.047
0.26
1.5
3.6
4.9
Aldehyde C14
0.017
0.030
0.073
0.72
10.0
11.0
31.0
cis-3-Hexenol
0.0024
0.0034
0.0058
0.025
0.077
0.07
0.16
0.33
Menthol
0.0087
0.020
0.053
0.45
5.4
0.05
0.43
0.32
Dimethylbenzylcarbinol
0.0062
0.0096
0.017
0.075
0.32
0.15
0.23
0.15
Phenvlethvlalcohol
0.0028
0.0045
0.0059
0.019
0.098
0.21
0.37
1.5
20.0
-
9.8 -
Permeation of gases, water vapor and volatile organic compounds
-
277
x Heptanol
Figure 9-6: Dependence of the equilibrium concentration of heptanol in LDPE from the mole fraction in methanol ( 0 ) and water (m).
On the other hand a solution of heptanol in water is not ideal and y>> 1. According to Eq. (9-38) the cp of heptanol in LDPE in contact with a dilute aqueous solution is much larger than that for the same concentration of heptanol in methanol (Fig. 9-6). Table 9-10 shows how different the K values can be for a given permeant with different solvent liquid phases. Upon going from methanol to an organic solvent having less polarity, the K values increase due to the increasing deviation from the ideal (y > 1). A closer relationship exists between heptanol and both alcohols and ketones than with the non-polar hydrocarbons because of their polar OH groups. Nevertheless, even with this polarity the difference with water, which is even more polar, is much larger. As a result, after partitioning between LDPE and water, the water contains no residual hydrocarbons. Table 9-10: Solvent dependence of the relative permeability and solubility exemplified with heptanol in LDPE at 23 "C. ~
Solvent Water
P, ' 10'" (crn'/s) 95
K . 10' 155
Methanol
0.24
0.44
Ethanol
0.25
0.47
1.7
2.5
Acetone Benzene
430
n-Hexane
975
6.8 16
The K values increase rapidly for completely unpolar n-alkanes with increasing water content (Table 9-11). Because of the very low solubility of hydrocarbons and most organic compounds in pure water, the partition coefficients for LDPE/water are either obtained by extrapolating the K values from Table 9-10 to 100 % water, or calculated from two independent measurements of the partition coefficients between
278
Piringer
LDPEloctanol (KpIO)and octanol/water ( K ~ I WThe ) . partition coefficient for LDPE/ water (KpN) results then from KP/W= K p ~ o. Ko/w (Table 9-12). Table 9-11: Increase of K-values of n-alkanes with increasing water concentration in ethanollwater mixtures. 60 % Eth.
40 Yo Eth.
20 Yo Eth.
3.5
160
4200
20000
6.5
370
27000
80000
900
120000
280000
7600
1100000 -
-
Compound
100'Yo Eth.
Decane
0.55
Dodecane
0.97
Tetradecane
1.3
11
Hexadecane
1.6
20
80 % Eth.
Octadecane
2.5
35
34000
780000 330000
Eicosane
4.2
59
160000
830000
Table 9-12: Partition coefficients of some aroma compounds between LDPE and octanol and between octanol and water at 23 "C. Compound
LDPElOctanol
Octanol/Water
LDPE/Water calc.values
LDPE/Water extrapol.values
Limonene
0.15
35000
5300
loo00
Camphor
0.062
180
21 1
60
Diphenylmet hane
0.15
19000
2850
4000
Isoamylacetate
0.05
Citronellol
0.0093
Diphenyloxide
0.13
Eugenol
0.021
243
Aldehyde C14
0.022
1600
cis-3-Hexenol
0.0006
175
9.0
19
2600
21
30
11000
1430
1150
34
5.0 35 0.33
21
7.5 115 0.22
Menthol
0.013
1600
Dimethylbenzene-carbinol
0.014
73
1.o
1.14
Phenvlethvl-alcohol
0.013
29
0.38
0.5
70
The consequences of the above results on the partition of aromas and aroma compounds between products and a plastic package can be seen in the values in Table 9-13. It can be seen from the partition coefficients that the values for medium polarity to non-polar substances partitioned between the two wine samples and LDPE are one to two orders of magnitude greater than the partitioning of the same substances between milk and LDPE (limonene, diphenylmethane, diphenyloxide, linalylacetate). The coefficients for the polar substances (cis-3-hexeno1, phenyl ethyl alcohol) show comparatively no difference. The K values for non-polar substances partitioned between milk and LDPE are comparable with values obtained for partitioning into 50% ethanol. Despite the relatively low fat content of whole milk (3.5 %), milk behaves quite differently from wine (Kozinowski, 1989). While wine represents a real aqueous solution whose behavior is determined by its water content, milk is not only aqueous but also a fat containing food which, because of its aqueous
Permeation of gasess water vapor and volatile organic compounds
279
external phase does not swell the polyolefin. The reason for this ambivalent behavior lies with the fat in water emulsion structure of milk. This explains why polar as well as non-polar substances are so well dissolved in milk. In both cases this leads to a decrease in their partial vapor pressure over milk, thus leading to the observed partition coefficients. Table 9-13: Partition coefficients of several aromas in the system polyolefineiaqueous food at 23 "C.
Compound Limonene
Skim milk (1.5 % fat)
Whole milk (3,s % fat)
LDPE
HDPE
LDPE
HDPE
10
12
4.8
7.2
3.5
-
Camphor
6.8
Linalylacetate
5.7
-
2.4
Diphenylmethane
5.7
6.0
2.5
Isoamylacetate
2.3
3.1
I .8
1.s
Citronellol
2.3
2.0
1.x
5.9
Diphenyloxide
7.6
9.6
2.3
2. I
Eugenol
1.3
1.s
1.1
0.96
Aldehyde C 14
2.0
3.5
1.3
1.1
cis-3-Hexenol
0.18
0.20
0.16
0.12
Menthol
-
-
Dime thylbenzylcarbinol
3.1
1.2
1.2
Phenylethylalcohol
0.18
0.11
0.12
Compound
0.2 1
3.8
Wine (5.3 % Eth.)
Wine (8 % Eth.)
LDPE
LDPE
HDPE
HDPE
I 100
1000
5000
Camphor
-
-
-
Linalylacetate
-
-
-
-
2100
2300
830
1600
Limonene
Diphenylmethane lsoamylacetate
4.5
Citronellol
5.9
Diphenyloxide Eugenol Aldehyde C 14
74 2.4 34
5.4 13 125 2.8 77
4.7 5.1 28 18
12
5.3 12 61 4.7 190
cis-3-Hexenol
0.08
Menthol
4.6
Dimethylbenzylcarbinol
0.34
0.67
0.44
0.65
Phenylethylalcohol
0.15
0.30
0.20
0.22
0.20 18
0.09 7.1
0.20 18
In Fig. 9-7 the concentrations of styrene in either aqueous ethanol or milk versus the percentage ethanol or fat are plottcd in a bar chart (O'Neill et al., 1994). The values were measured after 10 days contact at 30 "C with identical PS samples in contact
280
Piringer
-milk
nethanollwater
I %
fat content
ethanol percentage
Figure 9-7: Concentration of styrene in aqueous ethanol and milk after lOdays in contact with PS at 30°C.
with the same volumes of the two liquid phases. This result further confirms the similarity between whole milk with 3.5 % fat and 50 % aqueous ethanol with respect to the partition of low polarity substances in such systems. Like the size of the K values of the model substances, the partition process plays a role in mass transfer in packaging material/milk systems only for extremely non-polar substances. The loss of volatile milk components, mostly low molecular weight alcohols and ketones, through the packaging has no practical significance because of the small K values expected. On the other hand, this relationship plays a big role in the transfer of substances contained in the packaging into the food. The migration of dioxin into the milk fat phase is an example of this. The partition coefficients of this group of substances are very small in the polyolefin/milk system because of the fat phase in comparison to the polyolefin/water system. In comparison, significant losses of a number of wine components must be expected when in contact with polyolefins because of the large K values for non-polar compounds. Packaging wine in polyolefin-coated containers, which for example is the case for bag-in-box packaging, does not appear to make sense. Quality decreases can occur not only by loss of the aroma but by the alteration of the aroma character due to different K values for different aroma compounds. The uptake (scalping) of non-polar compounds like limonene from fruit juices by polyolefins has been experimentally confirmed (Hirose et al., 1988; Mannheim et al., 1988). While permeation of organic substances through a plastic container occurs very slowly, the enrichment of product components in the plastic near the material’s surface can occur after just a short contact time for plastic/product systems with large K values. When suffering a loss in quality, the product component need not necessarily be transported through the container wall and into the external atmosphere. The use of a thicker wall of the same plastic is not the solution in such a case. More important here is the selection of polymer, which should have a diffusion coefficient as small as possible, so that the thickness of the diffusion front in the plastic stays as small as possible during the intended storage time.
Permeation of gosees, writer vapor and volatile organic cornpoitndh
281
Partition processes like the types described above play as big a role in liquid cosmetics and cleaning formulations as in packaged foods. Table 9-14 contains the relative permeability coefficients P, of various aroma compounds through LDPE in contact with a liquid dish-washing detergent (with water as its main component), a skin cream and with methanol, all containing the same aroma compounds. Most of the values are much higher in the detergent than in methanol. This can be easily described using explanations found in the above discussion. The more unpolar the aroma compound, the greater the difference between the detergent and methanol. In comparison to both of these phases the P, values of aroma compounds in the same LDPE in contact with the skin cream are almost all much smaller. Because the product components are so soluble in a fat phase they remain in the cream. Table 9-14: Relative permeability coefficients of several aromas in the systems LDPElcleaning agent, LDPElmethanol and LDPElskincreme at 23 "C. Compound
Cleaning agent
Methanol
Skincreme
P, . 10"cm2/s 1 2 3 4
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
-
-
-
-
-
-
-
-
33 46 68 57 20 7.3 28 20 91 114 20 150 87 38 70 22 2.3 8.6 0.6 2.3 310 20 22 56 21 21 364 23
-
0.11 0.17 2.4 0.27
-
1.9 10 32 5.4 29 1 4.5 2.2 1.1 34 12 3.6 3.3 4.3 42 -
2.7 52 11 8.3 9.9 4.4 5.5 35 3.9
-
0.27 0.12 0.36 0.51 0.59 0.22 0.29 0.23 0.14 1.7 -
282
Piringer
The consequences of partitioning processes in package/product systems must also be considered in the case of returnable and recycled packaging. Because diffusioncontrolled transport processes take place relatively slowly, one cannot rule out the transport of product components absorbed during the previous use storage eventually diffusing back into the freshly filled product, even if the container was washed between uses. Such substance traces can also include reaction products of earlier absorbed components with oxygen and can lead to diminished quality in the newly filled product through the creation of off-odors. Traces of substances absorbed during the storage of various chemicals can have negative consequences in recycled materials. In general such cases have seldom been observed. Model studies in our laboratory have shown that mass transfers of this type are as a rule very small and can at most exert an influence from only the sensory point of view. Nevertheless, mass transfer of substances in lower density polyolefins is more likely to lead to negative influences because of the high D values. In view of the variety of molecular structures and the very different use conditions that need to be considered with regard to interactions, one is forced towards the idea of developing partition estimation methods that have adequate accuracy for practical purposes. Estimations based on experimental data collections are possible. Several simple expressions have already been presented for estimating D and S values for gases. In Chapter 4 estimation methods for partition coefficients are treated in more depth. In conclusion it must be emphasized here that the values of partition coefficients of permeating substances cover a range of more than 9 orders of magnitude (lo-* to 10’) dependent on their structure and the polarity of the filled product and packaging material (e.g. polyolefinsiwater); and this is only for a single polymer (e.g. LDPE). This means that in practice, the importance of the partition coefficient in the permeation of organic compounds is often not given the attention it deserves.
9.3.4 The significance of diffusion coefficients Compared to the partition coefficients the values of the diffusion coefficients of organic compounds in a given polymer cover a relatively small range (approximately three orders of magnitude for the values of the compounds listed in Table 9-7 in LDPE at the same temperature). At the same time the D values for a given permeant depend on the nature of the polymer, like that shown for the simple gases, and can range over 8 orders of magnitude. Given that P = S D or P, = K D, there theoretically results an enormous range of values for the permeation coefficient as a function of permeant molecular structure, product and packaging. In practice the extreme values do not lie so far apart because the tendency of the diffusion and partition coefficients to oppose each other reduces the differences between permeation values. The good solubility of a permeant in a polymer is due to a relatively strong attraction between permeant and macromolecule. At the same time the mobility of the permeant molecule and consequently its D value decreases. Such a case was mentioned in the discussion of water vapor permeation. In the development of estimation methods for D values, two independent contributions must be taken into consideration: on one side, the size and shape of the per-
Permerttioti of gases. wnler vapor and voIniiIe orgrmic conipoiinds
283
meant molecule and on the other, the attractive forces between the permeant and macromolecule. If the concentration of a highly soluble permeant increases so much in a polymer that swelling takes place, diffusion is made easier through a loosening of the polymer matrix. For this reason methanol and ethanol were selected as the contact phase for studying permeation of organic compounds in polyolefins. When one compares the D values in Table 9-15 for undecane in LDPE in contact with methanol, acetone and hexane, then the increasing solvent swelling effects with decreasing polarity can be plainly seen. The difference between hexane with and without pre-swelling of the polymer matrix shows the time-dependent character of the swelling process. Tahle 9-15: Solvent dependence of the diffusion coefficients of undecane in LDPE at 23 "C. Solvent
D . 10" (crn2/s)
n-Hexane (pre-swelling)
530
n-Hexane
66
Acetone
13 9.0
Methanol
When one plots the D values of various different compounds versus their relative molecular mass, M,., for a given polymer, then the values for the n-alkanes lie on the upper limit of diffusion (Fig. 9-8). This result means in practice that one has a maximum value for a variety of compounds with similar molecular weights when the nalkane diffusion coefficients are known. In a first approximation one can assume the ratio of the D values between a gas, for example carbon dioxide, and a n-alkane with the molecular weight M, to be constant and independent of the polymer. Given the existence of values for simple gases in a large number of polymers (Table 9-2) the
1 Of
0
10-5
t I
1
1
1
1
1
I
I
I
I .
lb u
M,
Figure 9-8: Diffusion coefficients of organic compounds in LDPE depending on their relative molecular mass. M,. C-6 to C-24 are hexane to tetracosan: 1: undecalactone, 2: phenylethyl alcohol. 3: isoamyl acetate, 4: diphenyl methane. 5: diphenyl ether, A: 7-OH to 18-OHare alcohols (heptanol to 1-octadecanol).
284
Piringer
order of magnitude of D values can be estimated for compounds in polymers for which no experimental data exist. This is particularly the case for barrier plastics whose diffusion measurements can be very time consuming (see Chapters 6 and 15). Equation (9-16) is valid for permeation through laminate structures. Even though our measurements for a series of coextruded laminate films gave good agreement with calculated values it was clear that for example the use of adhesives (Ad) in laminates can lead to deviations. The type of problems that can occur as a result can be described using a PE/Ad/OPP laminate film as an example. In Table 9-16 the relative permeability coefficients P, measured for PE and OPP homopolymers as well as the laminate are compared with the calculated P, values of a hypothetical PE/ OPP laminate (without adhesive Ad). Because according to Eq. (9-16) the total permeation of a laminate is determined by the lowest permeability of a material in the laminate, the OPP layer must be the layer controlling the permeation process. A “disturbance free” permeation process was measured and compared to the result calculated for a laminate containing no adhesive using Eq. (9-16). It was found that the P, value for the actual laminated film was a factor 3 to 40 times larger. Table 9-16: Relative permeability coefficients P, [cm2/s] . 1012 of 7 aroma compounds with different polarities (solved in methanol) in a laminate PEIAdlOPP of 62 pm (40/2/20)at 23 “C. Measured Compound
Isoamylacetate Limonene
Monofoil
Calculated Laminate
Laminate
PElAdlOPP (40/2/20)
PE/OPP (40/20)
PE
OPP
215
0.50
6.9
1.5
1651
2.16
20.9
6.5
cis-3-Hexenol
17.6
0.09
2.0
0.3
Linalylacetate
53.9
0.07
2.0
0.2
Menthol
10.4
0.01
1.2
0.03
8.3
0.01
1 .o 10.6
0.03
Citronellol Diuhenvloxide
595
1.20
3.6
Resulting from a comparison of the measured and calculated partition coefficient values K, the laminate containing adhesive dissolved significantly more aroma compounds than the PE/OPP laminate without adhesive (Table 9-17). Relatively high K values can be calculated for the adhesive layer. Due to the uncertainties connected with the calculation of K values in an extremely thin and possibly non-homogeneous adhesive layer, these values must be cautiously interpreted. The characteristics of the contact layer between the two mono films cannot be differentiated between an extremely thin and discrete adhesive layer at high permeant concentration and a mixed phase diffuse mono adhesive layer with a somewhat lower permeant concentration. One last possibility leading to a reduction in the effectiveness of the barrier layer could be the possible swelling effect occurring at the surface of the contact layers. This at the same time explains the higher observed P, values and appears to be more plausible (Thalmann, 1990). In any case the observed enrichment of the permeant in the region of the adhesive can have detrimental effects on the properties of the packa-
285
Perntearion of gases, wciter vnpor nnd volatile organic conipounds
ging. Along with more or less expressed changes in permeability, delamination (cloudiness, bubble formation) can occur as a result. The above example underscores once more the importance of distribution processes between the packaging and products which does not occur in the case of simple gases with very low solubility. Tablc 9-17: Partition coefficients K . lo2 of 7 aroma compounds with different polarities between a laminate PE/Ad/OPP with 62pm thickness (40/2/20)and methanol at 23 "C. Measured Compound
lsoamylacetate Limonene
Monofoil
Calculated Laminate
Laminate
PE
OPP
PE/AdlOPP (40/2/20)
PE/OPP (40120)
Ad
3.9
8.4
10.5
5.4
164
52.4
68.8
64.8
57.9
272
cis-3-Hexenol
0.2
0.9
4.9
0.5
137
Linalylacetate
5.2
10.1
11.9
6.9
163
Menthol
0.6
1.7
5.8
1.0
150
Citi onellol
0.2
1.3
5.3
0.5
147
13.5
1Y.6
25.7
15.5
332
Diphrnyloxide
References Becker K., Koszinowski J.. Piringer 0. 1983, Dt,sc.h.Lebensni.-Rundsch. 79 257-266. Brandrup J., Immergut E.H. (eds.) 1989, Polymer Hiindhook 3'd ed. John Wiley & Sons. Demertzis P.. Kontominas M. G., Voudouris E.K. 1985,J Food Technol. 20 419428. Felder R. M.. Huvard G.S. 1980. Permeation, diffitsion and sorption of gases and vapors in Methods of experimental physics, 16e. 315-377, Academic Press Inc. Franz R. 1993, Packag. Technol. Sci. 6 91. Hennessy B.. Mead J.. Stening T. 1966. The permeability of plastics films, London: The Plastic Institute. Hirose K.. Harte B. R., Giacin J. R., Miltz J., Stine C. 1988. in: Hotchkiss J. 1988, Food and packaging interactions, Am. Chem. Soc.. Washington, p 2841. Koszinowski J.. Piringer 0. 1986, in: Mathlouthi M. (ed) 1986, Food packaging and preservation. Theory and practice, London, Elsevier Applied Science. Koszinowski J., Piringer 0.1989, Verpackungs-Rrmdrch.40 3 9 4 4 (techn-wissensch. Beilage). Leibl S., Ewender J., Piringer 0. 1990, Verpack.-Rirndsch.41.1-3 (techn.-wissensch. Beilage). Mannheim C. H., Milk J., Passy N. 1988, in: Hotchkiss J. 1988, Food ond packaging interactions, Am. Chem. Soc., Washington, p 68-82. O'Neill E.T.. Tiohy J.J., Franz R. 1994,Inr. Dairy J. 4 271. Salame M. 1961, Trans folym. Eng. Sci.1 153. Thalman W.R. 1990,Packaging TechnoLand Science 3 67-82. Till D.. Schwope A,.. Ehntholt D., Sidman K., Whelan R., Schwartz P., Reid R. 1987, CRC Critical Reviews in Toxicology 18 161-188. Van Krevelen D. W. 1990, Properties of polymers. Their correlation with chemical structrire; their numerical estimation and prediction from additive group contributions (3th ed). Elsevier, Amsterdam.
Reactivity in Molecular Crystals Edited by Yuli Ohashi Copyright @ K d a o r h a Ltd .Tokyo. 1999
10 Migration of plastic constituents Roland Franz
10.1 Principles of migration testing The purpose of migration testing is to ensure food safety and protect the consumer, by controlling the levels of undesirable constituents from the packaging entering foodstuffs. Applicants and users of migration tests are in the first instance industrial laboratories, such as from polymer or plastic additives producers. But manufacturers of packaging materials such as bottle and film producers as well as converters also apply or commission migration testing to demonstrate compliance with food law, for quality assurance purposes or for submission of new product petitions. Finally and, in principal, with highest responsibility, the end-users of food packaging, the food industry themselves, need migration tests. However, normal practice is that they request and receive food law compliance certificates from the industries mentioned above. As another group of laboratories involved in migration testing, independent certifying laboratories as well as public or governmental control and surveillance labs must be mentioned. Before proceeding in the discussion about migration test principles, one needs to establish some definitions. The term “migration” is used to describe the process of mass transfer from a food packaging material to its contents. During the migration process a packaging material, in general, withstands the food contact conditions and does not alter its mechanical or diffusion properties too significantly. The term “extraction” is often used in the same sense as “migration” which may lead to confusion in the context with solvent extraction of packaging materials. Therefore the term “extraction” is defined in the following as a very intensive interaction process between a packaging material where solvent penetrates the packaging material and alters its mechanical and diffusion properties significantly and even extremely. If one reduces the migration process to the diffusion in and from plastics then the migratability of plastics constituents (organic substances) corresponds predominantly to the volatility or molecular weight of these organic substances and to the basic diffusivity of a polymer type. For a given plastic this means that the mobility of a migrant decreases with increasing molecular weight. For a given molecule this means that its mobility in different polymers is dependent on the elasticity or thermoplastic properties of the polymer. Once a molecule has moved to and arrived at the interface between plastic and foodstuff, the extent of mass transfer into the food depends on its viscosity and, very crucially, on its fat content. Since most of plastic constituents do have a lipophilic rather than hydrophilic character, migration increases strongly with increasing fat content; and especially so in the case where the fat or oil represents the outer phase of the food matrix. The toxicologically relevant molecular weight range for migrants is considered to end at a molecular weight of 1000 daltons. Larger molecules are considered from a biophysical point-of-view not to be physiologically resorbed in the gastrointestinal tract.
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Franz
In order to underpin these more general descriptive approaches to migration by appropriate physico-chemical arguments, the parameters controlling migration will be presented and discussed in more depth in the following chapter.
10.1.1 Parameters determining migration Besides the geometric dimensions of a given food/packaging system which influence migration, mass transfer from a plastic into food consists essentially of kinetic (diffusion in the polymer and foodstuff) and thermodynamic (equilibrium partitioning between packaging and food) factors. It is common practice in migration evaluations to start as a worst assumption with a total mass transfer scenario, using a case where the initial concentration of a migrant in the packaging is known. However, if this relatively simple calculation provides a scenario which exceeds a migration limit, then it is advisable and necessary to achieve further refinements to the total mass transfer approach by taking into account the effect of the partition coefficient K and considering the role of the diffusion coefficient D as important material-specific parameters for migration. The role of the partition coefficient K The value of the partition coefficient K of a substance between two phases depends mainly on the polarity of the substance and the polarity of the two media. Applying the rule "like dissolves like", when considering a plastic packaging material for instance for contact with an aqueous product, one would as a consequence select a non-polar polymer (e.g. polyolefin) that will not be attacked by water. In such a system strongly polar substances prefer the product phase and non polar substances prefer the packaging material. However, when filling a fatty product into the same hydrophobic polymer type, a completely different partitioning behaviour from polymer into foodstuff takes place. Values for the partition coefficient KP,&defined as the concentration ratio at equilibrium of a migrant in the polymer, cP,,, divided by that at equilibrium in the foodstuff or food simulant, cF,,, range over several orders of magnitude depending on the polarities of polymer involved, the food simulant and the nature of the migrant. For instance, the partition coefficient KP,F = cp,, / c F , ~for limonene, a nonpolar substance (hydrocarbon), in the LDPE/water system at 23 "C was found to be higher than 5000 (Chapter 9, Table 9-13). This makes it retained in the polymer, whereas a much more polar compound like cis-hexenol shows a much lower value of 0.33, causing considerable transfer into the water. Numerous experimentally determined KeF-values have been described (Piringer 1993). Also estimative approaches for calculating Kp,F-valueshave been published (Baner and Piringer 1991,1994). An important quantity which can be calculated at equilibrium conditions is the amount of substance migrated into the food or food simulant at equilibrium, mF.e. Provided that the migration potential in the polymer, i.e. the initial amount of migrant dissolved in the polymer, mp,o, is known then from mass balance calculations the following equation can be derived: (10-1)
Migration of plastic constituents
289
The volumes of the polymer material of the packaging and food simulant are given by Vp and VF, the contact surface area between the two phases is given by A and the layer thickness of the polymer (for single sided contact) is given by dp In general, the package to food ratio is Vp/VF << 1 so that at equilibrium for Kp.F 2 1 practically the entire quantity of potential migrants will be found in the simulant, i.e. mEe = mP,().However, if the potential migrant is much more soluble in the polymer than in the simulant, i.e. K ~ . F>> 1, then at equilibrium only a small fraction will have migrated into the simulant so that mF.e << mp.o.As a rule, this second case occurs for migration into aqueous foods and, as a consequence, leads to a much lower substance transfer than into foods containing fat where, as a rule, Kp,F 2 1. The role of the diffusion coefficient D in the polymer Since practically the entire amount of migrant in the polymer can migrate into a fatty food or fatty food simulant at equilibrium, the most important variables which control migration of the substance are the contact time t and the temperature T. It was found in numerous migration tests that the majority of measurements could be represented as being approximately proportional to the square root of time t and proportional to the initial concentration of migrant in the polymer, cP,().With the assumption that material transport obeys the laws of diffusion (Chapter 7) then the following equation can be applied to describe approximately the migration of a substance from a polymer into a food (simulant) for situations where mEt/ mEe 5 0.5: (10-2) Here DP is the actual diffusion coefficient of the migrant in the polymer with a homogeneous distribution of the migrant at an initial concentration cp.0. It must not be confused with the effective diffusion coefficient for the complete polymer/migrant/ contact medium system presented by (Till et al. 1983,1987). All influences of the food or other contact medium that lead to a reduction in the migration value resulting only from migration in the polymer are contained in the constant k I 1 in Eq. (10-2). The constant k is therefore a measure of the influence of factors that lie outside the polymer/migrant system and has by definition a value of k = 1 in the absence of such influences (e.g. for contact with ethanol and oil) as long as no polymer swelling takes place. A practical application of this equation is that for cases with k = 1, the actual diffusion coefficients of migrants in the polymer can be determined from kinetic measurement of mEt from systems with known or measured values for c ~ ,Afterwards, ~. these DP values can then be used to estimate the k values for other foods. It is also necessary to describe mass transport in the opposite direction in order to understand the migration processes occuring with the use of different simulants in migration testing. More specifically, this means the migration of substances from the food or simulant or the simulant itself into the polymer. In analogy to Eq. (10-2) the amount of a substance, mp,t,migrating into the polymer from the food or simulant during the contact time t can approximately be described by the following equation: (10-3)
290
Frnnz
Where cE0 is the initial concentration of the migrating component in the simulant. In contrast to Eq. (10-2) the partition coefficient K plays an important role here, where the sorption of component into the polymer is proportional to KP,~. It is necessary to discuss the following relationship to achieve a better understanding of the influence of a simulant on migration. The average migration distance made by the diffusing additive i in the polymer during time t should be designated xi and its diffusion coefficient be DP,i. Analogously, xj should be considered to be the distance which the migration front of the simulant has moved in the polymer during the same time t and Dp,, be the diffusion coefficient of the simulant in the polymer. From the theory of diffusion the following ratio for xi/xj can be derived: (10-4) Now, in the case of xi << xj then the polymer additive i will be “overrun” by the simulant before it can migrate out of the polymer. Depending on the solubility of the simulant in the polymer (Kp,jvalue), the migration behaviour of i will then be influenced in an accelerated way. In the case, however, that xi >> xj then the migration of i from the plastic is not influenced by the migration of the simulant. From the above equations (10-1 to 10-4) the following conclusions can be drawn with respect to the selection of a food simulant: 1. When significant interactions occur between fat or oil and a plastic (Piringer, 1990) two borderline cases must be distinguished: Case la): Di >> Dj which means that according to Eq. (10-4) the previously mentioned case occurs where xi >> xj and the migration from the packaging is not affected by the uptake of fat by the plastic. The migration of substances whose molecular weights are much less than that of triglycerides remains unaffected by the uptake of fat because, as a rule, the diffusion coefficient decreases with increasing molecular weight. The molecular weights of the triglycerides in question lie between approximately 600 and 1000. Substances with molecular weights up to and including this range can be considered to meet this assumption. Case lb): When Di << D, , then according to Eq. (10-4) migration in the polymer is controlled by the fat penetration meaning the sorbed fat leads to higher migration values (Vom Bruck et al. 1986). 2. For volatile food simulants with low molecular weights, e.g. heptane, iso-octane. ethanol, the relationship D i << D j is valid for practically all polymer constituents. However, here again, two borderline cases must be differentiated as well: Case 2a): If the partition coefficient of the simulant Kp,j = 1 (i.e. the simulant is well dissolved by the polymer) the amount of sorbed simulant mp,tof j is so large according to Eq. (10-3) that it causes severe swelling of the polymer. As a consequence, total extraction of the migrant i from the polymer takes place provided that the solubility of migrant in the simulant allows that. This is for example the case where iso-octane comes into contact with non-polar polyolefins. Case 2b): For KP,, << 1 the sorption of j is so low according to Eq. (10-3) that the Dp.i value and consequently the migration of migrant i is not significantly influenced. This is for example the case where polar ethanol comes in contact with non-polar polyolefins at normal test temperatures (up to 40°C). At higher temperatures the solubility of ethanol (as well as that of fat) increases in polyolefins. However, by dilut-
Migration of’plustic consririientx
291
ing the ethanol with water, the undesired increase in migration due to higher temperatures can be avoided and a situation with a diffusion control in the polymer according to case 2b) be achieved again (Piringer 1993). If one wishes to use a volatile simulant as a lower molecular weight alternative to the natural edible oils or synthetic triglycerides, then one must determine according to the above discussion whether the simulant belongs to case 2a) or 2b). In the case of 2a) a time factor (in a n accelerated sense) must be considered because of the extraction effect caused by swelling. This means a series of studies must be carried out to determine at which contact time according to Eq. (10-2) does the same mass transfer take place compared to oil or actual food. Moderate temperature increase can also be used at the same time as a further variable. In the case of 2b) the time factor does not need to be considered as long as the test temperature is the same or very similar for the simulant as it is for the oil.
10.1.2 Migration control methodologies Any migration control procedure must be linked either directly or indirectly to the measurement o r evaluation of the concentration of an undesired compound in a foodstuff migrating from a package under given food contact conditions. This concentration, cEt, represents the toxicologically relevant target parameter for any migration control methodology. This toxicological parameter , c ~ ,which ~ , can be measured, controlled or assessed in different ways must then be compared to relevant migration limits as set up by laws such as the Commission Directive 90/128/EEC or by (juridically non-mandatory but practically binding) recommendations such as the German BgVV (Bundesinstitut fur gesundheitlichen yerbraucherschutz und yeterinarmedizin, formerly BGA) system. In this context it should be remembered that migration limits as set up in the European Directives have been derived from toxicological data in connection with some conventional assumptions. The migration limit, expressed in milligrams per kilogram food (simulant), is calculated from the toxicological magnitudes AD1 or TDI (acceptable daily intake o r tolerable daily intake, each expressed as milligrams per kilogram body weight per day) by multiplication with the factor 60 which (in kilograms) is the conventionally assumed body weight of an average European person. It is further assumed that this average person eats 1 kg food per day which is packed by 6 dm2 plastic material (Ashby et al. 1997). It should be kept in mind that specific migration limits (SML) established in this way d o contain inbuilt safety margins in the range of 100 to 1000 relative to so-called “No toxic effect levels” (Katan 1996 a)). SML values range typically from the 10-20 pg/kg (ppb) level for specific substances of toxicological concern such as vinyl chloride, butadiene, acrylonitrile and others up to the lower mgikg (ppm) level for less toxic principals such as bisphenol A (3 ppm), ethylendiamine (12 pprn ) or I-octene (15 ppm) and others. On the other hand, food packaging legislation or regulation has also set up restrictions on the packaging material side. Especially, the above mentioned BgVV system is mainly built on this strategy of setting maximum allowable concentrations in the packaging material. Such compositional limits in plastics are given as QM (maximum quantity) limits in the minority of compounds listed by EU Directives, especially in such cases where the migrant is chemically not stable enough in food simulants or may bc lost in migration testing due to its volatility. A typical example is butadiene
292
Franz
which is listed in 90/128/EEC with both a SML value (not detectable) and a QM value of 1 mg/kg polymer. It has been the experience of many experimentators that the SM determination of butadiene in aqueous food simulants is practically impossible in a reliable and reproducible way. The reason for this practical difficulty is the high volatility of this compound and its very unfavourable (from a sample handling point of view) partition coefficient KP,F, estimated to be in the range of limonene or higher (see above). Both factors contribute to immediate and significant losses of butadiene from aqueous migration solutions during sample handling. Similar observations have been reported for other volatile migrants (Rijk 1993). The question by which test methodology migration should best be controlled cannot be answered by recommending only one and the same test principle for all cases. Nowadays a number of options, including mathematical modelling of diffusion processes, are available and all of them can be justified for application under certain circumstances. However, as a general strategy, it is wise not to start in all cases of compliance testing immediately with a specific migration test but to consider the materialrelated, geometric and time-temperature application parameters of the individual food/packaging system to be evaluated. More specifically, it is wise to consider the migration potential of a given migrant in a plastic before initiating a long-term and time-consuming migration test. Or with other and more simplistic words: Initial considerations to any compliance testing should always start with the question “Can a given migration limit be exceeded or even reached at all?”. The second consideration should then address the question “What is the most economic way to demonstrate that a migration limit cannot be exceeded?”. This however goes without saying that it must not be the expectation of any compliance test that migration limits cannot be exceeded. Undoubtedly, the relevant maxim is “Consumer’s safety must not be compromised”. However, also undoubtedly, this approach helps to economise migration control and to allow more tests per unit of time and cost - a principle which has been proven to increase consumer safety. In the following, several options for migration control testing are described briefly with a focus only on the essential parts of each strategy. The options are given in a sequence which tries to meets in the best way the considerations made above.
Indirect migration assessment by compositional analysis of plastics Assessment by worst-case assumptions of total mass transfer Quantitative determinations of migrating analytes in food simulants and especially in the more complex matrices such as olive oil or other fatty simulants or foodstuffs themselves in many cases require relatively time-consuming sample preparation and very sensitive and selective methods of analysis. So the a priori most reasonable way is to carry out a compositional analysis in the plastic to determine the initial concentration of a migrant in a polymer, c ~ ,This ~ . value is equivalent to the migration potential and can be assessed in different ways with respect to the corresponding specific migration (SM). The most simplistic and direct approach is to assume total mass transfer into a foodstuff or simulant and compare this worst-case value with a given SML restriction. Vice versa, a given SML restriction can be transformed into a corresponding QM value, again under the assumption of total mass transfer, and compared to the
Migration of plastic constituents
293
experimentally determined c ~ ,This ~ . represents the worst-case modification of socalled QM/SML relationships (Baner et al. 1996) and does not take any partitioning or kinetic effects into account. Conventionally, QM/SML or cp.$3M ratios of 100 have been assumed and even implemented in the legislation - as an example the European vinyl chloride restrictions of QM = lmg/kg and SML = not detectable at 0.01 mg/kg may be cited. However, even under total mass transfer assumptions, the thickness of the respective polymer layer must be taken into account. It is obvious that for very thin film thicknesses a measured cP,(]value may exceed a given QM value without posing any health risk to a consumer. With other words, the cp,,JSML ratio is a function of the film thickness and for very thin films may end up at ratios orders of magnitude higher than the conventional one of 100 (compare also Figure 10-l)(Baner et al. 1996). And this, to be well remembered, under the assumption of total mass transfer. Since these relationships have been recently demonstrated (Franz and Rijk 1997) and specifically in the case of coatings and laquers on metal substrates, another understanding and definition of QM values has been developed. What is meant here, are area-related QM values where the maximum allowable migration is given as mass [mg] of migrant per food contact area [dm’] of the packaging. This new approach, which is currently being introduced into European legislation (EU Commission 1999), is extremely helpful especially in those cases where film thicknesses cannot be determined. In all cases under the premise of total mass transfer where an indirect migration assessment demonstrates the impossibility of exceeding a given legal SML restriction criterion, full compliance testing has been achieved and no further migration assessment or testing is necessary. Assessment by mass balance considerations under equilibrium conditions
In those cases where the above assessment leads to an uncertain conformity status, then mass balance calculations can be applied according to Eq. (10-1) provided that reliable values for the respective partition coefficient Kp,F are known. Figure 10-1
K = 1000
K = 100
K=10 K= 1 0
50
100
150 dp
(w)
200
250
300
Figure 10-1: QM/SML ratio versus laver thickness dp as a function of the partition coefficient KP,F under equilibrium conditions.
294
Franz
shows a set of generalized curves presenting calculated QM/SML values versus the layer thickness dp as a function of the partition coefficient and assuming a constant surface area to mass food ratio of 6 dm'lkg. One important relationship evident from this figure is that the variations of the partition coefficient over a range from 1 to 10 (typical for partitioning of substances between polymers and fats or oils) has no significant effect on the migrated amount. Furthermore, for a partition coefficient range from 1 to 100, there is a large effect of material thickness on the migration whereas for K , , > 100 the curve becomes practically insensitive to the material thickness (Baner et al. 1996) Assessment by application of complex mathematical models
As described in Chapters 7, 11 and 15 of this book predictive mathematical models for migration estimation based on diffusion theory and considering partitioning effects have been developed in the past few years. Although such models are currently still under scientific discussion (Reynier et al. 1999) and refinement or further development they have been proven in whole classes of polymer types such as the polyolefins to work very satisfactorily in terms of providing worse case migration scenarios. This is a prerequisite to finding general acceptance for being used in the field of food packaging compliance testing. The use of these diffusion models to progress the evaluation process of a food packaging plastic will be discussed shortly. In those cases where assessment by mass balance considerations under equilibrium conditions, including partitioning effects, does not provide a clear picture of the plastics conformity status, then the different diffusivities of polymer types and the influence of the migrant molecule size or its molecular weight on its mobility within a plastic can be taken into account to achieve more distinguished views on QM/SML ratios. Based on diffusion theory (Chapters 7 and 15) QM/SML ratios can be described as a function of the migrant molecular weight, for different polymer types as given in Fig. 10-2. For illustration reasons, this figure (Baner et al. 1996) provides two scenarios (i) diffusion controlled migration from different plastics under standard test conditions of 10 days/4O0C under the assumption of infinite thickness and (ii) as for given thicknesses (of any plastic) under the assumption of total mass transfer (KP.F=l). It can be recognised (again) that complete migration transfer calculations are dependent on the material thickness. It should also be noted that complete migration transfer lines are independent of migration test time and temperature conditions. Figure 10-2 shows that for some combinations of polymer type and thickness and substance molecular weight, there are cases where mass balance calculations yield higher QMlSML ratios than diffusion-controlled migration calculations. This is only a virtual contradiction and can be explained by the infinite thickness assumption of the diffusion model. This situation is particularly given in the case of high diffusion coefficients, i.e. high diffusivity of the plastic and/or migrants with low molecular weights. Figure 10-2 can be used to provide an acceptable estimated initial concentration of a substance in a polymer where a related SML value cannot be further exceeded. For example: a migrant with molecular weight 750 has a corresponding QM/SML value of approximately 1000 for the HDPE/PP curve. Now, multiplying this QM/SML value by the legally prescribed SML value will give its maximum acceptable QM in the polymer.
Migration of plastic constituents
i 4
l.e+7
295
Rigid PVC
I I .
/
l.e+6
I /
/
l.e+O t0
1
250
500
i Non-polyolefins JLDPE
-
750
1000 1250 1500
Molecular weight of migrant
Figure 10-2: QMlSML ratio versus molecular weight under standard test conditions (10 days/40 "C) for different polymer types under the assumption of infinite thickness as well as for given thicknesses under the assumption of total mass transfer.
Another attempt t o demonstrate the usefulness of employing diffusion models is made with Fig. 10-3. A dimensionless migration curve can be found for a given food packaging, to allow a quick look-up of possible migration values, for instance for plausability considerations related to measured migration test results or for the design of new plastics additives. This figure is based on the diffusion model presented in Chapter 15 and applies the migration Eq. (7-51) for an individually given food packaging application. It models the migration under standard test conditions of 10 days/40 "C as a function of cRo and the migrant's molecular weights from a HDPE container of thickness dp = 0.06 cm, assuming a surface/volume ratio of 6 dm2/kg and a partition coefficient KP,F= 1 (high solubility in the foodstuff). Analogous figures can be derived for any other food packaging application. With respect to the curve given in this figure, it should be noted that the packaging system under the applied test conditions can be considered nearly infinite or semi-infinite for migrants down to molecular weights of approximately 150. At lower molecular weights where the curve turns down from the steep line, the thickness of the material controls the shape of the migration curve. This particular situation can be considered an intermediate phase between infiniteness and mass balance as discussed above and presented in Fig. 10-2. As an example of how to make use o f Fig. 10-3, a migrant of molecular weight 47.5 may be selected; and the curve then provides a value of 0.5. If this migrant is, for instance, present in the polymer at C P , ~=~200 ppm then migration into the foodstuff can be calculated at 1.0 mg/kg from the equation given on the y-axis.
296
Franz
-
3,s
B
3
E
Y
0
2,5 e
=
9
2
Y
29
1,5
0
10 1 1
5
0,5
I
.v
$
V
0 0
100 200 300 400 500 600 700 800 900 1000
molecular weight of migrant
Figure 10-3: Estimation of migration (standard test conditions of 10 days/4O0C) as a function of CP,,) and in dependency of molecular weight of migrant from a HDPE container of thickness dp = 0.06 cm at a surfacelvolume ratio of 6 dm2/kg assuming a partition coefficient KP.F= 1.
Migration assessment by analysis of mass transfer from plastics Until today, the control of transfer from plastics packaging materials into foods has mainly been based on the measurement of the substance(s) in the food or simulant after certain specified, and in most cases standardized, contact conditions. Here, in principal, it can be distinguished between: (i) conventional direct migration measurements where a sample is placed in contact with a food or simulant in a manner representing the contact conditions of actual conditions in use; and (ii) alternative semi-direct migration test approaches where a sample is kept in contact with an appropriate simulant in such a manner that a strong interaction between simulant and plastic takes place (“more severe test conditions”) and - although shorter contact times are then applicable - at least equal or exaggerated extents of migration are obtained. Direct migration measurement The principle of direct migration measurement is, as the term reveals, to measure either directly in foodstuffs or more commonly mimic as closely as possible a given food packaging application, using agreed and authorised food simulants (Chapters 11 and 12). Results obtained with food simulants represent either directly the real rnigration values or can be correlated by the use of so-called reduction factors. The advantage of direct measurement is that the results can be directly and definitely compared with legally prescribed migration limits, thus allowing immediately a statement of conformity or disapproval of the test sample. The disadvantage of direct measurement has been recognised more and more during recent years: analysis of migrants in com-
Migration of plastic constititents
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plex food simulants such as oils and fats is often very time-consuming and costly and at the same time relatively poor in terms of analytical sensivity and precision. This occurs not only in the case of specific migrants such as antioxidants or other non-volatile polymer constituents, but also in the case of overall migration determinations. It is extremely so in contact with oils as fatty food simulants and especially so in the case of high temperature testing and polar plastics. It should be noted that the legally allowed analytical tolerance in oils is stated at 20 mg/kg in relation to 60 mg/kg as the overall migration limit itself. This is really remarkable, taking into account that low diffusivity plastics such as PET release, as a rule, maximum overall migrations which are lower than the analytical tolerance itself. Overall migration testing, carried out according to the methods in the EN (European Standard) or ENV (European Prestandard) 1186 series of CEN (European Committee for Standardization) standards and described in numerous papers and books (Ashby et al. 1997; Katan 1996b; de Kruijf and Rijk 1988; CEN 1998a; Tice 1997), will not be taken up in detail here. Only the major problems related to overall migration testing in contact with oils will be mentioned here; these are: - inherent imprecision of the method due to substracting high values obtained by weighing the sample in order to determine a much smaller overall migration value; - moisture conditioning of polar plastics; - oil uptake by the sample and incompleteness of back extraction; - analytical determination of the absorbed amount of oil due to many possible GC/ FID interferences (according to the amendments of 90/128/EEC some 40 or 50 interfering compounds are in the positive list); - performance and handling at high temperature testing. Numerous examples of measured overall migration values have been collected and the interested reader can find a published data compilation summarized for different polymer types (Van Battum 1996). The whole area of specific migration determinations can be subdivided in two phases: (i) the pre-analytical migration exposure phase, which is more or less identical to that necessary for overall migration determination; and (ii) the pure analytical phase, where the specific migrant must be determined in the respective food or simulant as precisely and reproducibly as possible. This pure analytical migration test phase comprises many considerations to be made and includes so many technical possibilities that it deserves to be described in an own comprehensive section (see Section 10.2). Semi-direct, alternative migration tests The principle of these tests is to apply more severe test conditions by using volatile solvents with strong interactions towards the plastic, to enhance the migration rate from the plastic. Thus, the extraction test is based on an accelerated mass transport mechanism where the diffusion coefficients of migrants are increased by several orders of magnitude compared to the original migration test. As a rule, extraction tests are designed such that they make use of the following principle: I
Polar polymer
+ polar migrant + polar solvent
= worse case = non-polar polymer + non-polar migrant
+ non-polar solvent
I
298
Franz
Following this principle, semi-direct and generally quick extraction tests can be established with the aim of determining the migration potential for assessment of the worse case migration. These tests, which do not need to be as exhaustive as for instance necessary for a cp.0 determination, can be considered to be semi-direct because they produce an extraction value which can be directly compared to a legal restriction. But at the same time this value is an exaggerated one and does not always correspond to the real (lower) migration value. For example, a rapid extraction test for overall migration assessment into fatty food simulants, proposed as part 15 of the EN/ENV 1186 series of CEN standards, is presented as follows (CEN 1998b; Berghammer et al. 1994). The method is based on the determination of the extraction of migratable substances from plastics which are intended to come into contact with foodstuffs. It uses total immersion in non-polar isooctane and/or polar ethanol solvents depending on the polarity of the packaging material. According to results obtained by this method and taking physico-chemical considerations into account, the obtained extraction efficiency was generally found to be equivalent to or higher than overall migration results obtained under these test conditions: 10 days at 40"C, 2 h at 70"C, 1 h at 100°C, 30 min at 121 "C and 30 min at 130 "C, as specified in Council Directive 82/711/EEC and its subsequent amendments. To ensure as complete as possible an extraction of the potential migrants requires a strong interaction, e.g. swelling, of the sample by the extraction solvent. For this purpose, iso-octane is used as an extraction solvent for plastics materials and articles containing non-polar food contact layers, such as polyolefins. For test samples with polar food contact plastics such as polyamide and polyethyleneterephthalate, 95 % (v/v) aqueous ethanol is used. For polystyrenes, plasticised PVC and other polymers where the identification or polarity of the polymer is not clear, two parallel extraction tests are conducted using both of the proposed extraction solvents and taking into account the higher value obtained as the relevant result. In the case of unsymmetric structures such as plastics laminates and co-extruded plastics, the nature of the food contact layer determines the selection of the extraction solvent(s). Table 10-1 gives an overview of the allocation of extraction solvents and test conditions to polymer types. Table 10-1: Use of extraction solvents and test conditions in relation to polymer types. Polymer type of the food contact layer
Extraction solvent
Extraction conditions
Polyolefines
iso-octane
24 hours at 40°C
Polyamides
9.5 % ethanol
24 hours at 40 "C
Polystyrene
iso-octane and 95 YO ethanol
24 hours at 40°C
Polyethylene terephthalate
95 YOethanol
24 hours at SO "C
Polyvinyl chloride (plasticised)
iso-octane and 95 Y' O ethanol
24 hours at 40 "C
Polyvinyl chloride (rigid)
95 %, ethanol
24 hours at 50 "C
In case of doubt or unknown
iso-octane and 95 TOethanol
24 hours at SO "C
The test principle is such that the extraction of migratable substances from a sample of the plastics is determined as the mass of non-volatile residue after evaporation of the solvent following immersion. Test specimens of at least 1 dm2 (single side considered) are immersed in the extraction solvent at the specified test conditions and then
Migration o f plastic constitirents
299
removed. The extraction solvent is evaporated to dryness, the mass of the non-volatile residue is determined and the result is expressed as milligrams per square decimetre of surface area of the test specimen. The measured value is compared to the overall migration limit given by Directive 90/128/EEC (and amendments) and taking the analytical tolerance of this method (1 mg/dm') into account. The rapid extraction test was primarily developed for flexible packagings less than 300 ym in thickness. However, if this extraction test is applied to materials with higher thickness than 300 pm and the result does not exceed the allowed overall migation limit, then the material can be considered t o be in compliance with E C regulations. If the test result exceeds the allowed overall migration limit, regardless of the film thickness of the test material, then the extraction test may be repeated. However. in single-sided mode (using a test cell) or the conventional fat test or another alternative test may be used. In any case the rapid extraction test was designed to demonstrate compliance in the case of extraction values lower than the overall migration limit. The test cannot disapprove a material whose extraction value exceeds the limit. Conditions differing from those described above are of course possible as are much quicker tests. But in all cases, a reliable relationship between the short test and the full migration test must be established. In addition, it is also of practical and economic interest to design these tests so that they can be applied as broadly as possible, i.e. in most laboratories without too high an investment. Another quick extraction test has been proposed, especially tailored for rigid PVC material. Treating the samples with methanol for 2 hours under reflux conditions provided values which were considerably higher than those achieved under conventional olive oil conditions but still remained far below the overall migration limit, thus demonstrating fully legal conformity of the test materials (Tice and Cooper 1997). It should be noted here that quick cxtraction tests in general produce higher migration values and are therefore unfavourable when it comes to correlating such a value with the reputation of a test sample. However, when the testing costs can be decreased in this way by 50% to 70% and conformity can still be shown, although with somewhat higher results, then it seems to be only a question of getting accustomed t o extraction values. Substitute fat tests as defined by table 4 of E U Directive 97i48iEC are a further example of semi-direct migration tests. These tests are applicable in cases where technical or analytical difficulties are connected with the regular fatty food simulants. They apply iso-octane and 95 Oh ethanol under conventional test conditions such that an accelerated test based on (swelling) interactions between substitute test solvent and the polymer is conducted. For instance, an analytically impossible 10 daysi40 "C olive oil test on polyolefins can be replaced by a 2 days/2O0C extraction with isooctane. In this case a suitable time point has been chosen on the kinetic curve of an extraction process where an empirically satisfying agreement has been found between isooctane extractions and fat migration tests into olive oil. Another example is where a substitute test is carried out at lower temperatures compared to the required regular test temperatures. For instance, a high temperature fat test under test conditions of 2 hours/l5O0C can be replaced by a 3 hours/60"C iso-octane extraction. In this case again, a semi-direct test strategy is applied, empirically based on corresponding comparative test results. However, it is important to note that nearly all of these comparative long termlhigh temperature migration versus short terniflow temperature extraction measurements have focused more or less on just the overall migration and do not include sufficiently specific migrations. As a consequence, further research work is
300
Franz
necessary to correlate substitute test conditions for specific migration purposes where the chemical and thermal stability of migrants as well as the possible formation of break-down products and solubility questions related to individual migrants must all be taken into account.
10.2 Analysis of specific migrants 10.2.1 The positive list system within the European Union Legislation As described more in detail in Chapter 12, the European regulations on plastics for food contact are characterised by a consolidated positive list system which contains authorized monomers as well as additives for manufacturing or incorporation into any plastic type. This so-called “Plastics Directive” 90/128/EEC and its 5 amendments contain, as an essential element, numerous specific restrictions for listed substances either in terms of specific migration limits (SML values) and/or maximum quantities in the finished food contact material (QM values). Currently, out of approximately 200 listed monomers, nearly 80 are listed with a restriction, in most cases a SML value. Even more SML and/or QM values are expected for the additives’ list with restrictions, which was recently finalized at Commission level as a further (Sh)amendment of the “Plastics Directive” (EU Commission 1999). This situation immediately poses the question of enforcability of this law, since appropriate analytical methods have not been published or referenced in synchrony with the appearance of the positive list system. Although there is a general need for the availability of workable and validated analytical methods for food law compliance testing, the European Union legislative system requires special attention with respect to the analysis of specific migrants.
10.2.2 General requirements to analytical methods for compliance testing When selecting a method of analysis, some pre-considerations are obligatory. The volatility of the analyte must be taken into account as well as the nature of the matrix to be analyzed and, especially, the expected concentration range of the substance being measured. While analysis in aqueous food simulants and some plastics is relatively simple to perform, it is exceptionally difficult in many foods due to their complex chemical composition. As a result of these pre-considerations, a decision is taken about the choice of the most appropriate sample preparation procedure and a suitable chromatographic system. The envisaged analysis can also have various purposes or objectives. The aim may be to achieve a quantitative analysis (e.g. concentration determination) of one or several substances. The concentration range to be measured can be in the range of several mg/kg (ppm) or a few ng/kg (ppt). Analysis for the presence of groups of substances with defined structural characteristics (e.g. epoxides) or the identification of unknown substances may also be desirable. Already from these introductory notes, the very different structures of various analytical laboratories are becoming apparent. Analytical laboratories for small and medium-sized food packaging manufacturers and food producers, in general pay particular attention to the routine control of several substances and as a rule make use of a limited selection of methods. In contrast to this type of laboratory, governmental sur-
Migration of plastic constitiients
301
veillance laboratories, research institutes and central analytical facilities in industry are equipped with the latest state-of-the-art technology and are much more flexible in making use of any kind of analytical methods. Many analysts in these industry, private and public research, governmental and enforcement laboratories are involved in compliance testing of plastics for food contact. The methods applied may vary from sophisticated gaschromatography/mass-spectrometry (GUMS) techniques to classical methods like colorimetric determination. In many cases laboratories apply their own house analytical methods, often without any method validation. However, the use of different methods of determination will most likely lead to discrepancies in the results. In addition, for methods which have never been validated in inter-laboratory studies, no generally accepted analytical tolerances have been established. Consequently, enforcement of legal restrictions given by SML or QM values is poorly or even not possible at all, if validated and generally accepted methods are not available. However, in order to enable proper compliance testing, such methods of analysis commonly accessible and with well-defined analytical tolerances are indispensable. The requirements which must be addressed to analytical methods depend on their purpose. Routine methods for industrial quality control, for instance, need to be quick, cheap, robust and completely reproducible. It is not urgently required to determine a true value but to determine the homogeneity in manufacturing a certain industrial product. Therefore, the measurement of the corresponding parameter must be very precise, even though it may be wrong. On the other hand, very sophisticated, highly technical and expensive methods may be needed when it comes, for instance, to the determining the migration of a polymer constituent of analytically exotic character for the purpose of delivering a technical dossier for a petition to the authorities. In this case, the analytical method need not be cost-efficient in the first place but must provide a true value with high accuracy, or the best approach to it in order to allow decision-making about the need for toxicological testing. A complete intra-laboratory validation is another important requirement in this case. Due to the complexity of this specialised method it may never again find application in another laboratory, such as governmental surveillance methods. In between these two cases, however, the whole class of frequently used methods for food law compliance testing can be placed. Ideally, the major requirement here is: standardized methods should be published as norms and fully validated in inter-laboratory collaborative trials. However, being realistic and pragmatic, one has to recognize that realization of this demand will be more the exception than the rule. Furthermore, the methods should not be at the cutting edge of analytical hardware technology but make use of the state-of-the-art technology available in most analytical laboratories. Only under this premise, as much as possible will laboratories be able to apply the method, thus guaranteeing the most effective quality control and consumer protection. Generally, these methods should allow one to quantify the monomer or plastics additive at the required restriction limit in all relevant food simulants and/or in the polymer, respectively. That means an optimization in sensivity must be achieved, targeted to the necessary range of the method’s limit of detection (LOD), at or well below a given restriction criterion. It should be noted here that optimized methods of known performance and broad applicability with respect to food simulants as matrices may find their limit of workability when applied to real foodstuffs, due to interference problems. However, as a general rule, one can say that at least headspace sampling GC methods for volatiles are applicable and workable in every case.
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10.2.3 Establishing (juristically) valid performance of methods The need f o r validated analytical methods It is generally recognized and accepted that analytical methods must be suitable for the intended use. Furthermore, EU Directives 85/591/EEC, 89/397/EEC and 93/99/ EEC state that analytical procedures for compliance testing with food laws are to be carried out on the basis of validated methods. Method validation is known as the process used to confirm that a procedure is fit for a particular analytical purpose. This process, an essential part of analytical quality assurance, can be described as the set of tests used to establish and document performance characteristics of a method. The performance characteristics of a method are experimentally derived values for the fundamental parameters of importance in assessing the suitability of the method (Horwitz 1988, 1995; Thompson and Wood 1993, 1995; Eurachem 1996; FA0 1998: US EPA 1995; US FDA 1993a). These parameters include:
Applica:bility:
Includes the matrix, analyte and species being measured, concentration ranges and the purpose for which it is suited, limitations of the method. Selectivity: The ability to discriminate between the target analyte and other substances in the test sample. Calibration: The calibration curve is a graphic representation of the detection system’s response as a function of the quantity of analyte. Accuracy: The closeness of agreement between a test result and the accepted reference or true value. Precision: The closeness of agreement between independent test results obtained under stipulated conditions. Range: The interval of concentration within which the analytical procedure demonstrates a suitable level of precision and accuracy. Limit of quantification: The lowest amount or concentration of analyte in a sample which can be quantitatively determined with an acceptable level of precision and accuracy. The smallest amount or concentration of analyte in a sample Limit of detection: that can be reliably distinguished, with stated significance, from the background or blank level. A measure of the magnitude of the response caused by a cerSensivity: tain amount of analyte. Ruggedness: The resistance to change of an analytical method when minor deviations are made in the experimental conditions of the procedure. Practica bility: The ease of operation, in terms of sample throughput and costs, to achieve the required performance criteria and thereby meet the specified purpose. Internationally accepted protocols have been established for the “full” validation of a method of analysis by collaborative trial (Horwitz 1988, 1995; I S 0 1994). These protocols require a minimum number of laboratories and test materials to be included in the collaborative trial to fully validate the analytical method. However, before
Migration ofplustic constituents
303
entering the ring trial, the method must undergo pre-validation within a single laboratory, normally the the one which develops or modifies the method. Inclusion of a second laboratory to confirm the performance obtained is another practise used for method pre-validation. Statistical tools for validation and evaluation of analytical methods Even when all conditions required for correctly carrying out an analysis are fulfilled, different values within a certain scatter range will be obtained within a laboratory for repeated measurements of identical samples. As a rule, the differences or scattering will be still larger if different laboratories are involved in the comparison exercise using identical samples. It is therefore necessary to apply statistical tools in order to verify the maintenance of limit values and eventually to evaluate the accuracy of disputed estimates. For this reason standards for measurement precision and accuracy are defined at national level (e.g. ASTM in U.S.A.,DIN in Germany) and at international level by I S 0 (International Organization for Standardization). Clearly, in view of the harmonization of the legal regulations in Europe, standardized methods of analysis and validation principles and certified reference materials are becoming more important. Moreover, due to the globalization of markets, these have worldwide relevance. A relevant juristical statement about the precision of a method can only be made after defining the performance characteristics obtained from a round robin or interlaboratory trial study, as for instance described in I S 0 5725 (IS0 1994). This study is used to determine the statistical key data about the precision of a method. The international standard I S 0 5725 has been adopted by many countries. I S 0 uses two terms, “trueness” and “precision”, to describe the accuracy of a measured value. “Trueness” refers to the closeness of agreement between the average value of a large number of test results and the true or accepted reference value. “Precision” refers to the closeness of agreement of test results, or in other words the variability between repeated tests. The standard deviation of the measured value obtained by repeated determinations under the same conditions is used as a measure of the precision of the measurement procedure. The repeatability limit “r” (an intra-laboratory parameter) and the reproducibility limit “R” (an inter-laboratory parameter) are calculated as measures of precision. Again, “precision” and “trueness” together describe the accuracy of an analytical method. Particularly important definitions and terms for the evaluation of analyses from I S 0 5725 will be briefly discussed in the following section. If the test result as an average of several individual measurements is obtained with the same method from an identical test sample, in the same laboratory, by the same analyst, with the same instrumentation, over a short period of time, then the study takes place under “repeatability” conditions. On the other hand, “reproducibility” conditions occur when the measurements take place following the same procedure and using identical samples but in different laboratories using different analysts with different instrumentation. The parameters describing the scattering of a test result under repeatability and reproducibility conditions are the corresponding standard deviations. The repeatability limit, “r”, is the within-laboratory precision and describes the maximum expected value of the difference between two individual test results obtained under repeatabil-
304
Franz
ity conditions at a defined significance which is in most cases a probability level of 95 %. Similarly, the reproducibility limit, “R”, describes the analogous between-laboratory precision. An important assumption for the use of r and R in practice is that they have been determined in an inter-laboratory test in which the participating laboratories represent those potential candidate appliers of the particular analytical procedure. For the determination of r and R, the method of analysis must be described very clearly and in detail to eliminate as many differences between laboratories as possible. Particular precautions are necessary with regard to the homogeneity and stability of the sample to be studied in the inter-laboratory test. Clearly the sample must withstand transport conditions and arrive unaltered at the participating laboratories. The statistical model for estimating the precision of the analytical method assumes that every individual measurement result y is the sum of three components: y=m
+B+
(10-5)
e
Here m represents the average of all values for the material studied (the characteristic level), B is the scattering between the laboratories and e the random deviation in results occurring in every measurement. The characteristic level m must not necessarily agree completely with the true value. There may be a difference (m - my) from the true value due to a systematic error in the measurement procedure (bias). For contributions B and e, it is assumed that they approximately follow the normal distribution. Then the variance of B, var(B), is the variance between laboratories (02). This include the scattering between different analysts and different instruments. The variance of e, var(e), is referred to as the internal variance of a laboratory (o’,). The average of all the internal variances of the participating laboratories in an inter-laboratory test is expressed as the repeatability variance 0:.While r depends only on the repeatability variance, R is determined by the sum of the repeatability variances and the variance between all laboratories. The standard deviations of repeatability and reproducibility are given by or and OR = (0: + o : ) ~ ’and ~ it follows that: r = f 2 1 / 2 ~ , and R
=f
2’120,
(10-6)
The factor 2”* is based on the fact that r and R are related to the difference between two measurement results. For distributions which are approximately normal and in the case of not too small a number of measurements, the factor f does not vary much from 2 and one can use the approximate value of 2.8 for f .21‘2. Because in practice the true repeatability and reproducibility standard deviations are not known, they are replaced with estimated values s, and sR from the inter-laboratory study and one obtains then: r = 2.8 s, and R = 2.8 SR
(10-7)
The precision of a standard measurement method is expressed using the values of r and R. More specifically, the range of measured values (from ... to ...) or a typical result should be given together with the corresponding estimated value of the standard deviation s, and sR as well as r and R for the corresponding range. The precision of the analytical method can be verbally described as:
Migration of plastic c.on.~titiient.s
305
The difference between two individual measurement results, which an analyst obtained on the identical sample material with the same instrument within the shortest time span possible, will on average not exceed the repeatability limit r more than once in 20 cases, provided the measurement procedure has been correctly carried out. The difference between two individual measurement results, reported by two laboratories for identical sample material, will on average not exceed the reproducibility limit R more than one time in 20 cases provided the measurement procedure has been correctly carried out. For probability levels other than 95 %, the values for r and R must be multiplied by the factors in Table 10-2. Table 10-2 Factors to adapt r and R to various probability levels. Probability level P %
Factor
90
0.82
9s
1.00
98
1.16
99
1.25
99.5
1.40
Various critical difference parameters can be derived from r and R as illustrated by the following examples: In one laboratory two measurements are carried out.
In one laboratory two groups of measurements are carried out under repeatability conditions whereby the first group of nl measurements gives an average value of y1 and the second group of n2 measurements gives an average value of y2. With r being the repeatability limit (for two individual measurement results), the critical difference CTD~~(Y~ is -then: Y~)
(10-8) In the case of nl = n2 = 1 then by definition one obtains r as the critical difference.
Two laboratories conduct more than one measurement each. One laboratory carries out nl measurements with an average of y1 while a second laboratory obtains an average of y2 for n2 measurements. The critical difference between the two is then: r2 (I -
(1 0-9)
By definition, for the special case where nl = n2 = 1 the formula simplifies to R and for nl = n2 = 2 one obtains:
(10-10)
306
Franz
The mean value from one laboratory is compared with a given value. One laboratory has carried n measurements under repeatability conditions and obtained an average value y which is compared with a given value mo (e.g. a specific migration limit). Then one obtains the critical difference as:
& [R2 - r2 (e)] 112
Cr%(Ifl
- mol) =
(10-11)
The mean value of several laboratories is compared with a given value. A number of p laboratories have carried out ni measurements and obtained the average values yi (i = 1,2, ..., p). The overall mean value over yi, 7,is compared with a given value mo. One obtains the following expression for the critical difference:
'cyi
R2 - r2 (1 - ' C L)]1'2, = y= (10-12) (W' P i "i P i If, when making a comparison between two averages or between an individual value and a given value, the measured difference between two values exceeds the corresponding critical difference, then this deviation should be considered suspect. There could be a specific reason why the critical difference is exceeded and this should be rationalized. In particular, if the given or reference value is a true or correct value, then the suspected difference can point to a bias in the measured result. In the case that the given value is a specific migration limit then the critical difference evaluation system allows the decision whether a legal restriction criterion has been exceeded or not. CrD95(Jy - mu[) =
[
10.2.4 A practical guide for developing and pre-validation of analytical methods Validation of analytical methods -both in-house and standard methods - has been the focus of many scientific, industrial and regulatory activities and working groups (US EPA 1995; US FDA 1987,1993a; Wegschneider 1996). As a consequence, numerous parameters for method validation have been defined and recommended. However, there is no official or generally accepted guiding document such as an I S 0 standard available which de- and prescribes a sequence of individual working steps for the development and validation of analytical methods. In the following, a practical guide for a step-by-step procedure is presented to establish a validated method of analysis both for determination of a specific migrant in a food simulant and the residual concentration in a plastic. This procedure was first developed and then applied in a European project (Franz and Rijk 1997) and found to be very practical. It should be considered as a recommendation based on the great practical experience of the analysts involved. The development procedure consists of the following 8 steps: 1. Scope of the method
Basically, two types of method must be taken into account: Analysis of a specific migrant in a food simulant (SML-methods) - Analysis of a specific migrant in a polymer (QM-methods).
-
Migration of plnstic corzstitirents
307
Generally, the method to be developed should allow quantitative analysis of the analyte at the required restriction limit in all the official food simulants, including substitutes or alternatives and/or in the polymer, respectively. That means that for very low SML values which are assumed to be in the range of the detection limit, the aim should be to obtain a detection limit equal to o r even lower than the restriction criterion. For other, higher SML and QM values, the aim should be to obtain a detection limit at least ten times below the legal or self-defined restriction criterion. It should also kept in mind that the method description should provide the relevant intra-laboratory precision data (at the required SML/QM value) according to I S 0 5725 -(IS0 1094). The most suitable analytical methodology should be selected based on the required performance characteristics. A sound literature search is always of great help with respect to known methods for the respective analyte and matrices. In most cases the search results will not directly provide the method wanted but will allow the most likely successful analytical approach to be set up. In this context, pre-considerations should address the most appropriate sample work-up procedure as well as the suitable analytical separation and detection system. The question of direct analysis of the analyte o r a derivate formed after chemical reaction should be clarified. And finally, some thoughts should already be given to the question of chemical stability of the analyte in the given matrices under the applied conditions.
2. Setting up the chromatographic and detection system First of all, it should be noted by the reader that it is not within the scope of this chapter to give more background and details on analytical chemistry. The corresponding scientific knowledge and technical information have been described elsewhere (for instance Schomburg 1984; Lee et al. 1984; Chapman 1986 and many other lecture books). Having rationalized the most suitable analytical principle as a result from step 1, it is necessary t o demonstrate the adequate specifity and sensivity of the analytical system. This aim can be achieved by carrying out an initial feasibility study where the following points need in-depth consideration: - availability and purity of reference standards; - purity requirements for chemicals, reagents and solvents; - safety considerations; - selection of sampling and chromatographic instruments; - choice of separation column; - suitable detection system; - optimization of instrument parameters; - appropriate internal standard; - solvent to be used for preparation of stock and standard solutions. The feasibility exercise should include preparation of a concentrated (stock) solution as well as diluted standard solutions of various concentrations and establishing a first calibration curve. From the data obtained, preliminary conclusions should be drawn with respect to the approximate precision, its working range and limit of detection. Finally, the results should provide sufficient evidence with respect to the workability of the intended analytical approach. If the method appears inappropriate, it must be optimized by methodological improvements, instrument changes or applica-
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tion of a completely different analytical technique. If no satisfactory improvements can be achieved, a possible way out of the problem may be through compromising the acceptance limits.
3. Preparation and measurement of calibration samples When the initial study has been sucessfully completed, the performance characteristics should be investigated. As a first step on this way, calibration samples should be prepared in order to prove the calibration with respect to fulfilling general acceptance limits for linearity and repeatability performance. Starting from two independent stock solutions, two sets of analyte calibration solutions should be prepared. The solutions should preferably consist of the same medium (i.e. either food simulant for SML methods or swelling/extraction solvent for QM methods) to be used for the final determination of the specific migration or the residual amount in the plastic. Since the method’s performance characteristics are to be established in relation to the intended use, it is not necessary to check the method’s linearity over the full range of the equipment. Therefore, at least five concentration levels are required spanning the given restriction criterion value from 0.1 x value to 2.0 x value, provided this is within the LOD. Solutions without any analyte (blanks) should be analyzed as well. In the case of standard addition procedures, five levels should also be analyzed spanning the QM restriction value by standard additions ranging from 0.5 x value to 5.0 x value. All calibration and blank samples should be measured in triplicate (three injections of one sample) and the calibration graph should be constructed by plotting the detection signal obtained for the analyte (preferably peak area rather than peak height) relative to that of the internal standard versus analyte concentration. With respect to the correlation coefficient obtained (usually “R”)from the - in most cases - linear regression line, a minimum value of R = 0.9996 should be defined as a general acceptance limit. Deviation from this minimum requirement to linearity should only occur in exceptional cases. On the basis of 95 % probability level, the corresponding confidence bounds should be calculated and the within-laboratory LOD determined according to Fig. 10-4. The statistical methodology may be taken from the literature, for instance (DIN 1994). The two independently prepared sets of calibration samples should coincide with the upper and lower confidence bounds as another general acceptance limit with respect to repeatability performance. Full statistical evaluation of the calibration graph provides useful data about the method’s performance characteristics over the applied calibration range such as the standard error of the procedure, sx, or the standard error of estimate, sy 4. Within laboratory (repeatability conditions) precision according to I S 0 5725
The precision of an analytical method is the degree to which individual determinations of a series of standards agree. Since in general only one laboratory is involved in the development of the method the precision, as determined by one laboratory by one operator over a relatively short time, is defined as repeatability “r” ( I S 0 1994; compare also Section 10.2.3). For determining “r”, the following procedure is recommended: SML methods: for conventional or alternative food simulants at least 6 samples should be prepared, having the same concentration at the restriction criterion (SML value). All the samples should be measured by at least double injections and the
309
Migration ofplastic constituents
Y ......-.................. standard error of the analytical procedure s, standard error of estimate s, calibration regression curve
4
concentration
A
LOD Figure 10-4: Calibration curve and relevant precision parameters.
detector signals obtained should be evaluated using the calibration graph established as described under 3 above. QM methods: for the analysis of polymer matrices, 12 samples should be prepared for headspace sampling technique or 6 samples for liquid injection, respectively. In each case the series of samples should be prepared in the polymer/swelling solvent system with all samples using the same concentration at the restriction criterion (QM value). Headspace samples are measured only once and liquid injection samples in duplicate. If possible, analyte-free polymer should be used here. Again the spiked concentrations should be verified by standard addition calibration procedure carried out as described above under 3. When conducting an additional series of measurements using only the swelling solvent as the matrix without polymer and comparing results to those obtained above, the influence of the polymer matrix on the detection of analyte can be investigated. From the results obtained the repeatability standard deviation “S,” as well as the repeatability limit “r” can be calculated on a 95 % probability level according to Eq. (10-13). r = 2.8 S,
(10-13)
In addition, the results can also be used to calculate the mean recovery % as (the ratio of measured concentrationhominal concentration) * 100 and its standard devia-
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Franz
tion in the case of direct analyte determinations without any sample work-up. In cases where a sample work-up procedure such as extraction or chemical derivation has been applied, the mean recovery can be determined by comparing the detector response for the analyte signal after sample work-up with the response obtained from the appropriate standard dissolved in pure solvent.
5. Development of an appropriate confirmation procedure Whenever a measured value exceeds a certain threshold (an internally defined limit or a legal restriction criterion) then a confirmation procedure is recommended or even necessary. The purpose of confirmation analysis is to prove or disapprove the measurement result obtained by the usual analytical method. Generally, the difference from the confirmation procedure compared to the usual test method should be due to only either the use of a completely different separation column (with completely different retention behaviour) in the same detection system or the use of an alternative detection method with sufficient sensivity. For the latter case and especially for GC methods, the prefered procedure should be to apply analyte selective mass spectroscopy (MS) detection. In some cases, derivatisation of the analyte followed by MS detection can also be the method of choice. In the case of HPLC methods, different polarity of another column in connection with full exploitation of modern UV diode array detection systems may be useful to selectively allow confirmation of the analyte. It is extremely important to make sure that the confirmation procedure works at the restriction criterion level or other self-defined concentration limit!
6 . Stability check on stock and standard solutions Stability tests are understood to be time-dependent measurements of a stock and a standard solution at different temperature conditions, for instance at ambient temperature (approx. 22 "C), normal refrigerator conditions (2-8 "C) and at deep freezing temperatures (approx. -20 "C). Stability tests should always be carried out with the exclusion of light. Under these storage conditions, stock and standard solutions should be monitored for constancy of initial analyte concentration. This can be achieved by comparison against freshly pepared solutions. Storage time should be extended to at least three months or until a decrease of 50 % or more has been observed. Sampling frequency depends on the decrease rate of the solutions. It is wise to commence stability checks early enough when starting method development work. The aim here is to find out the optimum storage conditions and maximum practical storage time. Internal standards, if applied, should also be investigated.
7. Workability of the test method under practical conditions After successful completion of all the development steps described above, the analyst still cannot be sure that the developed method will work under realistic conditions. The workability of the method therefore has to be proved. There are two major reasons why this workability test has to be carried out: First of all, it should be demonstrated that the method is not affected by interferences migrating from the polymer matrix. Secondly, it needs to be clarified whether the analyte is stable under the contact conditions applied during the migration exposure, to avoid false-negative migration results. Therefore, a suitable plastic material containing a high residual level of the analyte under investigation should be available for the following experiments:
Migration of plastic constitiients
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SML methods: The selected polymer sample should be brought in contact with the food simulants under the relevant time/temperature conditions. In general, a migration test applying the total immersion principle using olive oil and 15 % ethanol at test conditions of 10 days at 40°C is sufficient. The determination should be performed in triplicate with double injections for analysis of the food simulants. In cases where the analyte level in the migration solutions is found to be below the detection limit, the migration solutions should be fortified with the migrant at the restriction criterion level or some other concentration of concern and measured again. In parallel, to check for migrant stability in the migration solutions, the relevant food simulants should be fortified at the level of concern to ensure that it is sufficiently higher than the LOD. If the test level concerned is in the range of the LOD, then the threefold concentration should be applied. The food simulants spiked in this way should be stored under appropriate timeitemperature conditions and recovery of the analyte determined by cross checking against freshly prepared solutions. QM methods: Triplicate determination of the concentration of the analyte in the selected polymer sample should be performed by the standard addition procedure using the polymer/swelling solvent system. The comparison to a calibration curve of the analyte in the pure swelling solvent only allows significant polymer matrix effects to be recognized. Again the stability of the analyte in the swelling solvent should be studied by fortification at the QM concentration or other relevant level and determination of recovery under the applied swelling and polymer extraction conditions. 8. Method description and reporting
Once the method has been established and validated, it should be described in full detail such that it can be carried out by any other analyst. Besides the numerous experimental details relating to the chemicals, solvents and solutions used and the chromatographic parameters, important observations such as for instance the findings about the stability of standard solutions should be laid down appropriately in the method description as notes or remarks. But potential health risks to the analytical operator should also be addressed, for instance in a warning note at the beginning of the method description. The following structure of a method description, which was agreed upon as a CEN standard format, is a recommended example.
Foreword: 1. Introduction:
2. Scope: -3. Principle:
4. Reagents:
Optional paragraph explaining about the background or history of the method. This chapter gives a rationale why it was necessary to establish this method. In this section the range of applications for the method should be indicated. This paragraph summarizes the applied analytical principle, including sample preparation techniques. It is necessary to describe in full detail the origin and purity of chemicals and solvents, the preparation of stock and standard solutions or other solutions, such as the mobile phase in the case of HPLC analysis. In conjunction with a given set of analytical parameters, the chromatogram obtained or at least an indication of retention times obtained for the analyte and the internal standard should be presented.
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5. Apparatus:
This chapter should describe the complete set of instrumental and other analytical parameters as well as special laboratory equipment and analytical accessories such as size and type of sample vials, pipettes and syringes etc., standard laboratory glassware and equipment excepted. 6. Samples: In this section, the preparation of test samples, blanks and calibration samples has to described, together with an indication of the minimum number of samples needed. If necessary, precautions should be mentioned, for instance to avoid cross-contamination of samples in the case of volatiles or to minimise chemical degradation in the case of unstable analytes etc. Here it is necessary to provide details as to how the analytical 7. Procedure: measurement of test, blank and calibration samples is executed and how the obtained data are evaluated. The measured concentration of the analyte obtained in this way may need further transformation into a different dimension and this should also be addressed in this section. 8. Confirmation: When a certain critical concentration value has been measured and found excessive, then it may be recommendable or even necessary to confirm the result or the identity of the quantified analyte by means of another analytical technique, for instance by specific detection using mass spectrometry. This confirmation procedure should be clearly presented in this paragraph. 9. Precision data: This chapter should give an insight into the validation procedure applied and report the most important performance characteristics: - the achieved limit of detection (LOD) or LOD range, - the achieved repeatability criteria, i.e. the r-values in the different food simulants or in the polymer matrix and the concentration range where they have been determined, - if available the determined reproducibility, i.e. the R-value and the critical difference, i.e. the CrD95-value, as obtained in the most usual situation, i.e. one laboratory carries out n measurements (Eq. 10-11). 10. Test report: The test report should contain all necessary documentation such as - date of analysis and reporting, - clear identification of the test laboratory and the responsible analyst, - analyte and method of test, including references, - sample details like origin and specification, type of food/simulant/material/article, reception date and storage conditions, - results expressed in mg analyte per kg food simulant or plastic material, - details of confirmation procedure, if any, and - reasons for modifications introduced into the test method, if any.
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10.2.5 Availability of (pre)validated methods in Europe About the economical impossibility of meeting the requirements of I S 0 5725 and the need f o r pragmatic solutions
Ideally, and strictly speaking also legally prescribed, the positive list system in Directive 90/128/EEC and its follow-ups would formally only be enforcable on the basis of fully validated analytical methods for specific migration determinations (compare discussion in Section 10.2.3). However, since full collaborative trials according to I S 0 5725 are very time-consuming and expensive and because of the large number of SML values to be validated, it is immediately quite obvious that achieving this ideal situation is an economical impossibility. In addition, the time frame to fulfill such a task would exceed the dimensions of any real life requirement. Furthermore, many of the positively listed plastics constituents obviously have such a low commercial relevance that the question of absurdity would also be raised in these cases. As a consequence, there is clearly a need for pragmatic solutions to this problem. Since provision of “fully validated” methods turns out to be impossible, certain minimum requirements to method validation should be agreed upon at an European level to produce so-called “generally agreed or accepted” methods. Possible ways out of the situation are in-house validation procedures carried out by one laboratory, which however has to fulfill generally agreed requirements for single laboratory validation and as a basic formal prerequisite needs an accreditation to EN45000 (Eurachem 1993). This strategy may be assisted by the definition of minimum requirements for test method precision based on the so-called Horwitz trumpet (Horwitz 1988,1995) which links repeatability to concentration. As an economic alternative to I S 0 5725 and obeying full validation ring trials, small collaborative trials with two or three laboratories can also be considered. Currently, a task group (TG7) within CEN TC194/SCl is investigating the feasibility of such alternative approaches. Among the criteria to be considered, the aspects of practicability and cost-efficiency have also been selected. About the availability of generally accepted or standard methods in Europe In the European Member States there are many laboratories such as research organisations, industry, private, governmental and enforcement laboratories, involved in the measurement of specific migration of monomers and additives from polymeric packaging materials into foods and food simulants. Most of these laboratories apply analytical methods developed by themselves and in most cases without appropriate validation. Dependent on the analytical equipment and level of education within the laboratory, the methods applied may vary from sophisticated and highly selective techniques such as GUMS to classical and often unspecific methods such as colorimetric tests. In other words: laboratories are currently far from applying generally accepted and validated test methods for the determination of specific migrations. As a consequence, the results obtained from different laboratories for a given migration test are likely to vary in such a way that comparable, accurate and precise migration results are hardly obtainable for supporting a successful argument in court. However, also from an economical standpoint viewing a free European market, the requirement of available and generally accepted test methods was and remains essential.
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Vinylchloride EU Directives:
As a consequence of ELI Directive 781142/EEC, which introduced a limitation of vinyl chloride monomer both as residual amount in final articles (QM: lmg/kg) intended to come into contact with foodstuffs and in migration to food (SML not detectable; LOD: 0.01 mg/kg), the corresponding necessary analytical methods were developed between several European expert laboratories and laid down as agreed methods in EU Directives 80/766/EEC and 81/432/EEC, respectively. This piece of the EU harmonization process was too time- and work-consuming to continue in this way. The vinyl chloride Directives therefore remain a unique feature in E U food packaging legislation since this was found to be impractical for generalization.
CEN TCI 94/SCl: Validation and standardization of analytical methods is a recognized basic task of the European Committee for Standardization (CEN). Within the CEN organisation, a working group, CEN TC 1941SC11WG2, has produced fully validated methods for 15 plastics monomers which have been published as European pre-norms (ENV) within the ENV 13130 series (CEN 1999). Whereas Part 1 of this multipart standard gives general guidance t o the specific migration test methodology prior to analysis of the specific migrant, the remaining seven Parts are pure analytical methods for the determination of monomers in food simulants or plastics. Table 10-3 gives an overview of the ENV13130 series. Table 10-3: Overview of CEN ENV13130 standard. No.
Title
Restriction
Part 1 Guide to the test methods for specific migration of substances from plastics into food and food simulants and the determination of substances in plastics and the selection of conditions of exposure to food simulants Part 2 Determination of terephthalic acid in food simulants
SML: 7.5 mg/kg
Part 3 Determination of acrylonitrile in food and food simulants
S M L not detectable. LOD: 0.02 mg/kg
Part 4 Determination of 1,3-butadiene in plastics
QM: 1 mg/kg
Part 5 Determination of vinylidene chloride in food simulants
SML: not detectable, LOD: 0.05 mg/kg
Part 6 Determination of vinylidene chloride in plastics
QM: 5 mg/kg
Part 7 Determination of monoethylene glycol and diethylene glycol in food simulants
SML (T): 30 mg/kg
Part 8 Determination of isocyanates in plastics: - 2,6-toluene diisocyanate - diphenylmethane-4,4'-diisocyanate - 2.4-toluene diisocyanate - hexamethylene diisocyanate - cyclohexyl isocyanate - 1 $naphthalene diisocyanate - diphenylmethane-2,4'-diisocyanate - 2,4-toluene diisocyanate dimer - phenyl isocyanate
QM (T): 1 mgikg (expressed as NCO)
Migrution o,f plastic constititents
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BCR (S,M & T )project “Monomers”: During the period 1993-1996 a European project was conducted within the Standards, Measurements and Testing programme of DG XII. The scope of this project was to fill the tremendous gap in analytical methods by development and pre-validation of methods of analysis for 36 monomers selected from the “Plastics Directive” positive lists. The project was carried out by a European consortium of 13 laboratories from 9 different Member States, under the co-ordination of the “Fraunhofer-Institute of Process Engeneering and Packaging” (FhIVV) Freising, Germany, and the main partner “TNO-Nutrition and Food Research” Zeist, The Netherlands. From the 36 target monomers (see Table 10-4) the project has elaborated 33 pre-validated methods of analysis for the determination of the specific migration of a selection of monomers listed with a restriction in Directives 90/128/EEC and 92/39/EEC (Franz and Rijk 1997). Since it was the original intention of the project to establish the developed analytical methods as ENVlEN standards within the European Committee for Standardization (CEN), the project structure included the involvement of CEN, in particular the Technical Sub-committee CEN TCl94/SC1 “General chemical methods of test for materials intended to come into contact with food’. Within this CEN sub-committee a working group, WG2, “Methods of test for monomers” is active in which more than 25 European expert analysts in the field of specific migration are collaborating in order to develop and standardize specific migration test methods. As most of the project participants were involved in the work of CEN TC194/SCl/WG2, it was decided in agreement with the “Standards, Measurements & Testing” Programme and DG 111 (Industry) of the European Commission to consult and disseminate the project results to the CEN working group in order to allow the establishment of Europe-wide accepted and agreed test methods. The mechanisms of consultation and dissemination were the following: Before the practical project work started, the project participants were required to deliver for each of their assigned monomers a rationale about the intended analytical procedure. These rationales were then circulated to the CEN group for discussion and expert comment. Only after there was agreement in the CEN group did the practical work start. In t h e course of the project, the CEN group was continuously informed about progress. As soon as a method of analysis was experimentally completed within the project, a draft written in CEN format was circulated to the WG2 members for discussion at the next biannual meeting. In these meetings the methods were either directly approved by the working group as technically suitable for publication as pre-norms, or if necessary after inclusion of the given comments and proposals for amendments. Finally, however, it turned out that CEN WG2 was overloaded with standardization tasks within the funding of the EU mandate for this work. Therefore, the developed and WG2 agreed pre-validated methods of analysis could not be processed forward to EN/ENV standards. Taking the multi-national project structure and the above involvement of CEN TCl94/SCl/WG2 into account, the co-ordinators and all other project participants considered the methods presented (see Table 10-4) to be accepted as Europe-wide agreed analytical methods for specific migration determination of the respective monomers. The project consortium proposed the methods to the European Commission for recommendation as “generally agreed” or as “useful” methods of analysis for the Member States.
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Table 10-4: Overview of BCR project “Monomers” methods of analysis. PM/-Ref. No.
Monomer
10120
Acetic acid, vinylester
10630
Acrylamide
0.01
12788
0.01
13480
11-Aminoundecanoic acid 1.3-Benzenedimethaneamine 2,2-Bis(4-hydroxyphenyl)propane
13510
2,2-Bis(4-hydroxyphenyl)propane,bis(2,3-epoxypropyl)ether
13000
Restriction [mgkg]
QM
SML 12
0.05 3 and
0.02
(BADGE) 136M)
3,3-Bis(3-methyl-4-hydroxy-phenyl)2-indolinone
13630
1.3-Butadiene
1.8 0.02
14200
Caprolactam
15
14230
Caprolactam, sodium salt
15
14380
Carbonyl chloride
15880
1.2-Dihydroxybenzene
6
15910
1,3-Dihydroxybenzene
2.4
15940
1,4-Dihydroxybenzene
0.6
15970
Dihydroxybenzophenone
6
16000
4,4-Dihydroxybenzophenyl
16150
Dimethylaminoethanol
16750
Epichlorohydrin
16960
Ethylenediamine
17005
Ethyleneimine
17020
Ethylene oxide
17260
Formaldehyde
18460
Hexamethylenediamine
6 18
12 0.01
15 2.4
18670
Hexamethylenetetramine
15
19540
Maleic acid
30
19960
Maleic anhydride
30
21490
Methacrylonitrile
0.02
22150
4-Methyl-1-pentene
0.02
22660
1-Octene
23050
1,3-Phenylenediamine
24010
Propylene oxide
25150
Tetrahydrofuran
25360
Trialkyl (C5-Cl5) acetic acid. 2.3-epoxypropylester
25420
2,4,6-Triamino-1.3,5-triazine
25600
1,l.l -Trimethylolpropane
15
0.6 6 30 6
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Methods of analysis in petitions to the European Commission: As another source of analytical methods for monomers and additives, the numerous technical dossiers submitted to the Scientific Committee of Food (SCF) through many European companies should be mentioned. According to the Commission’s request to the petitioners, these methods should have been written in a CEN standard format and meet current analytical requirements. Normally, however, these methods were established in assessing front line human exposure under the envisaged contact application, and were not always suitable for general control purposes. Nevertheless, there seems to be a large potential for technically suitable methods to be further evaluated and processed to a generally agreed level of validation on the Europe-wide scale.
10.2.6 Practical examples During method development and validation, a number of practical difficulties may occur and need control. An already well-known major phenomenon which can cause problems to the analyst is for instance insufficient or even zero recovery of analytes from the migration test solution. Possible reasons for that may be: (i) the chemical instability of analytes under migration test conditions due to oxidation, chemical binding to food simulant, (acid catalyzed) hydrolysis or ethanolysis; or (ii) volatilization during migration exposure and sample preparation (Rijk 1993). To illustrate and put into practise what has been said so far, several examples of methods of analysis are presented in the following, together with some specific difficulties and problems related to SM determination methods.
Acrylnnitrile ( S M L = not detectable at 0.02 nig/kg) The ENV13130-3 standard method (CEN 1999) to determine the specific migration of acrylonitrile in food simulants and foodstuffs originates from the German official BgVV (former BGA) collection of analytical methods according to $35 LMBG. It was already fully validated in Germany within a IS0 5725 collaborative trial before it was translated into English and editorially rearranged to fit into the CEN standard format. Acrylonitrile, CH2=CH-CN (CAS No. 107-13-1; PM/Ref. No. 12100) is a monomer commonly used as a co-monomer with styrene and butadiene to make ABS or SAN plastics for food contact articles such as kitchen utensils, rigid containers, measuring jugs, refrigerator linings, trays and fittings, coatings for nylon and polycarbonate films etc. It should be mentioned that acrylonitrile is a hazardous substance and volatile at room temperature. It requires corresponding precautions with respect to health risk for the analyst and cross-contamination during sample preparation. The method is not only applicable to the EU-official aqueous and fatty food simulant but also to foodstuffs such as beverages and soft margarine. Indeed the collaborative trial included fruit juice, wine and sunflower oil. The level of migrated acrylonitrile is determined by headspace gas chromatography, preferably with automated sample injection and using a nitrogen specific detector, for instance an alkali flame ionization detector (AFID). This gives the method the necessary sensivity to meet the
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restriction criterion requirement “not detectable at 0.02 mg/kg”. Quantification is achieved using propionitrile as an internal standard with calibration against a blank sample matrix fortified with defined amounts of acrylonitrile. Numerous suitable G C columns are described in the method, for instance: - 2 m x 3 mm internal diameter stainless steel column packed with 15 YOpolyethylene glycol 1500 on 60 mesh to 100 mesh diatomite support; or - 12 m x 0.20 mm internal diameter, fused silica capillary column with 0.33 pm film thickness of free fatty acid phase (modified polyethylene glycol). In the case of a measured concentration exceeding the restriction criterion, confirmation of acrylonitrile levels is carried out either by combined gas chroamtography/ mass spectrometry (GUMS) or by re-analysis on a second GC column of different polarity. It should be noted that the GUMS confirmation is considered more appropriate. The procedure makes use of the selected ion detection mode and quantifies acrylonitrile by monitoring the ions m/z = 53 for acrylonitrile and m/z = 55 for propionitrile. It is stated in the method that the level measured in this way shall be the true value which may be lower and in compliance again with legislation despite the initially determined value. Concerning the limit of detection (LOD), the collaborative trial revealed that the participating laboratories could achieve LODs in the range between 0.005 mglkg and 0.02 mglkg. So, in order to allow 95 YOof laboratories to achieve the same LOD, the upper limit, i.e. 0.02 mg/kg, was agreed as relevant for any laboratory. Based on the r (0.005 mg/litre) and R (0.011 mg/litre) values determined in the collaborative trial, a critical difference threshold CrDg5of 0.006 mg/litre can be derived for a duplicate determination in the same laboratory. Consequently, the restriction criterion “not detectable” must be considered to be exceeded when a laboratory measures a concentration higher than 0.026 mg/litre on the basis of a duplicate determination.
1,J-Butadiene ( S M L = not detectable at 0.02 mg/kg, Q M
= Img/kg)
Butadiene, CH2=CH-CH=CH2 (CAS No. 106-99-0; PM/Ref. No. 13630) is commonly copolymerized with styrene and acrylonitrile to make ABS or BS food contact plastics (for applications see acrylonitrile). Butadiene is a suspected carcinogen with extreme volatility (bp 4 . 5 “C) and low water solubility. This makes it very difficult to handle migration and calibration samples where the matrix is of highly aqueous character such as the aqueous food simulants. The Plastics Directive foresees 2 restrictions for this monomer. The reasons for that will be recognized after the following discussion. The method developed in the BCR project (Franz and Rijk 1997) to determine butadiene in all of the official food simulants and probably also in real foodstuffs was pre-validated by a collaborative trial with three laboratories. It was found appropriate in principle for the quantitative determination of butadiene at a range of 0.01 to 0.1 mg/kg in food simulants. Indeed the limit of detection was found to be in the range 4 to 9 pg/kg, thus being even in the worst case significantly lower than originally presumed when establishing the Plastics Directive limit of 0.02 mg/kg. The working principle is as follows: The level of butadiene in a food or food simulant is determined by headspace gas chromatography (HSGC) with automated sample injection and by flame ionisation detection (FID). Quantification is achieved using an internal standard (n-pentane) with calibration against relevant food simulant samples fortified with known amounts of butadiene. Confirmation of butadiene levels is car-
Migrotion of plastic constituents
319
ried out by combined gas chromatography/mass spectrometry (GUMS). In contrast to the acrylonitrile standard, it was agreed in the BCR project that the confirmation is qualitative in the sense that it should demonstrate the correct identity of the measured peak and the absence of interferences. If the G U M S analysis clearly indicates the absence of interferences, then the migration result as obtained by the HSGC/FID method is taken as the true value. In the case of interferences occurring, the peak area ratios of the specified ions obtained from the G U M S method are used to calculate the relevant butadiene level in the food simulant. During the method development and validation work in the project, severe problems had been observed with respect to volatilization of butadiene. Therefore, it is important and crucial to take the following into account when planning and designing a migration test: From migration experiments carried out at 10 days for 40°C it was recognized that irreproducibly considerable loss (up to 90 %) can result from volatilization of 1,3-butadiene when using aqueous food simulants. Just opening and closing vials containing calibration solutions caused significant headspace losses of the volatile analyte. which is due to very unfavourable partitioning from the aqueous phase to the head space. On the other hand olive oil samples were found to provide satisfactory recoveries, due to the much better solubility of butadiene in this non-polar matrix. As a consequence. migration exposure of plastic materials to an aqueous food simulant in a test cell o r glass container combined with sampling steps to prepare food simulant aliquots for analysis will most likely lead to irreproducible results due to uncontrollable loss of analyte. Of course, one can argue that this occurs also in real life with a food package. However, when thinking about reproducibility of analytical standard methods, such an argument must be excluded in the first instance but taken into account again when it comes to the interpretation or down-correction of a reproducibly measured analytical result obtained under conditions without uncontrolled analyte loss. This topic has been discussed many times so far but no concrete solution has been agreed. A very pragmatic solution to this problem could be to divide a specific migration result obtained under controlled conditions by a factor of two to take care of real life losses of analyte into the environment of a food package. Obviously, this kind of problem had been foreseen when the idea of two restriction types for butadiene was born. Indeed, compliance testing with respect to the QM limit of butadiene in plastic according the ENV13130-4 standard method which also originates from the German official BgVV (former BGA) analytical methods according to $35 LMBG, is in all cases highly recommendable since this method is much easier and straight-forward and therefore, much less error-prone.
BADGE ( S M L = not detectable at 0.02 mg/kg, Q M = lmg/kg) 2,2-Bis(4-hydroxyphenyl)propane-bis(2,3-cp~~xypropyl) ether o r bisphenol A diglycidyl ether (BADGE), C21H2404, (CAS No. 1675-543, PM/Ref. No. 13510) is commonly used as a bifunctional monomer or cross-linker in epoxy-based coatings very widely used in food contact applications such as lacquer coatings on food cans, plastic storage vessels e.g. wine vats, or in adhesives for laminates, printing inks and others. For the molecular structure of B A D G E and known reaction products in food simulants see Fig. 10-5 (Philo et al. 1997). The analyst who plans to carry out migration testing for B A D G E is often confronted with the question how to obtain a suitable B A D G E sample, since it is not
320
Franz
(4)
Figure 10-5: Molecular structures of BADGE and hydrolysisiethanolysis products: (1) Bisphenol A diglycidyl ether (BADGE);(2) Bisphenol A (2,3-dihydroxypropyl ether) diglycidyl ether (did-epuxide); (3) Bisphenol A di-(2,3-dihydroxypropyl ether) ( d i d - d i d ) ; (4) Bisphenol A (3-ethoxy-2-hydroxypropyl ether) diglycidyl ether (ether-epoxide); ( 5 ) Bisphenol A (3-ethoxy-2-hydroxypropylether) (2.3-dihydroxypropyl ether) (ether-did).
commercially available on the market of fine chemicals. For this purpose, the analyst may contact national or international reference collection systems as for instance the “Plastics Reference Collection” of the British MAFF Central Food Science Laboratory in Norwich (Bush et al. 1994) which has been established largely within a BCR project funded by the European Commission. On request, this collection provides a 1 g reference standard or solution free of charge to the applicant. Many studies have been published describing the isolation and determination of BADGE monomer from polymer articles, oils or foodstuffs. A number of these papers also give attention to the formation of hydrolysis or other reaction products of BADGE (Roubtsova et al. 1997, Simal Gandara et al. 1993, Paseiro Losada et al. 1993). The BCR project has also provided Europe-wide agreed pre-validated methods both for QM and SML control purposes (Franz and Rijk 1997). The SML method: the scope of this method comprises the determination of BADGE monomer in all four of the official food simulants with a LOD of 0.005 mg/ kg. The method should also be applicable to other, alternative food simulants. The principle is to determine BADGE in aqueous simulant test samples directly by high performance liquid chromatography (HPLC) with fluorescence detection. Determination of BADGE in fat simulant is also conducted by HPLC, after isolating of BADGE from the oil by extraction using acetonitrile. The identity of BADGE may be confirmed either from its fluorescence emission spectrum (1st option) or from the ratio of the areas of its peaks in chromatograms obtained with fluorescence and ultraviolet detection (2nd option), in both cases by comparison with authentic samples. A third option is to use an analytical column with a different selectivity. Although the method was found to be applicable in all food simulants, the observed rapid hydrolysis of BADGE must be taken into account. As expected, BADGE is sen-
Migration of plastic
constituents
321
sitive to hydrolysis in contact with aqueous foodstuffs (Paseiro Losada 1993), so special attention was given in this BCR project study to the stability of BADGE under usual migration test conditions such as 10 days at 40 "C. The formation of mono- and di-hydrolysis products is shown in Fig. 10-5. These investigations were carried out using food simulants spiked in the restriction value range (0.02 to 0.04 mg/kg) and it was found that BADGE was completely hydrolyzed in all the three aqueous food simulants after 10 days at 40°C. On the other hand quantitative recovery was obtained in the case of olive oil under the same test conditions. A kinetic study revealed the following approximate half-lives in aqueous food simulants under the conditions mentioned above: Table 10-5:Hydrolysis of BADGE in aqueous food sirnulants at 40 "C. Food simulant
Half-life time
Distilled water
1.1 days
3 % (wlv) Acetic acid
0.15 days
15 % (vlv) Ethanol
I .4 days
Therefore, the scope of the method seems to be limited only to very short and mild contact conditions in the case of aqueous food simulants, but the method is fully applicable to olive oil and other oils or fats as well as to non-proton-active alternative simulants such as iso-octane. It is important to note that the above study was carried out under the premise of a given SML restriction of 0.02 mglkg. From this, a highly challenging situation existed with respect to the target detection limit. In the meantime the Scientific Committee on Food (SCF) for the Commission has updated its opinion on BADGE (Internet: http://europa.eu.int/en/comm/spc/spc.html). According to this opinion, the restriction included in the Shamendment of the "Plastics Directive" now reads: " S M L = lmg/kg in foodstuffs or in food simulants or Q M ( T ) Irng/6dm2 in FP Both limits shall include the mono-hydrolysisproduct of BADGE, if any. However in aqueous food sirnidants, the S M L should also include the di-hydrolysis product unless the material or article is labelled for use in contact with those foods and/or beverages for which it has been demonstrated that BADGE and its mono-hydrolysisproduct cannot exceed I mg/kg. Since it is also reported in the above SML method that the HPLC method after some modification also allows the detection of two BADGE hydrolysis products, the method may nevertheless be very useful to fulfill the latest regulatory requirements. The QM method: This describes the determination of BADGE monomer in polymers expressing the measured levels as (mg BADGE)/(kg of polymer) or as (mg BADGE)/(dm* food contact area) depending on the type of test material. BADGE is extracted from the polymer with refluxing chloroform and determined by high performance liquid chromatography (HPLC) with fluorescence detection after transfer from chloroform into 90 % (v/v) methanol to obtain a solution compatible with the HPLC mobile phase (acetonitrile/water = 65:35 (v/v)). Quantification is achieved relative to external standards. Confirmation of the identity of BADGE is achieved in the same way as described for the SML method. This is appropriate for the quantitative determination of BADGE at a minimum level of 0.15 mg/kg in the polymer.
322
Frcmz
The method development work was done under the premise of a BADGE QM restriction of 1 mg/kg. However, BADGE is mainly used in coatings on non-plastic supports. Therefore, the amount of coating on a final article (e.g. coated can) can generally not be determined with sufficient accuracy. Consequently, this leads to severe problems with respect to determining the QM restriction in mg/kg coating. Therefore, the idea of determining a surface area related BADGE “concentration”, in mg BADGE per dm2 food contact area was born and followed in this project work. Indeed, as mentioned above, the SCF has now proposed a surface area related QM value of 0.16 mg BADGE per dm2. The method already takes account of this situation and is capable of meeting the most recent BADGE QM restriction. In spite of the fact that two very suitable test methods were available for BADGE determination in food simulants, the need for a sensitive and convenient control method for real foodstuffs was not yet satisfied. This need originated from the socalled BADGE problem observed first in Switzerland (Biedermann et al. 1996) and then in many European countries. Control laboratories found BADGE very frequently exceeding the legal restriction values in samples drawn from the market. It is well known in the area of analysis of complex matrices such as foodstuffs that one of the major problems and in many cases an insurmountable difficulty arises from possible analytical interferences from the oily or fatty foodstuff matrix. In principal, a possible way-out of this problem is application of (i) a separation system which allows elution of the interesting analyte fraction separate from that of the oil matrix or (ii) very specific detection in the presence of oil matrix interference which allows compensation of poor chromatographic separation of the analyte fraction. The latter can be achieved in many cases by modern LC-MS-MS analysis using the atmospheric pressure chemical ionisation (ACPI) technique and operated in single reaction monitoring mode (SRM). Based on this technique, a rapid, convenient and very sensitive method for BADGE determination has been described for foodstuffs such as canned fish products and goulash soup and with general applicability to many other food types (Roubtsova et al. 1997). In t h e following, the HPLC fractionation of the analyte from a fatty matrix and selective MS-MS quantification is described in more detail. In order for the oil matrix fraction to by-pass the mass spectrometer (a Finnigan TSQ-7000), a 6-way-valve was installed after the C18 reversed phase HPLC column. The elution conditions were: Isocratic elution with 100 % methanol (MeOH) from 0-3 minutes. then 100 % tetrahydrofuran (THF) from 3-8 minutes and again 100 % methanol from 8-20 minutes. In this way the column was capable of separating the oil matrix fraction from the analyte fraction. The fraction containing BADGE was eluted from the column within the first 3 minutes during the MeOH elution, followed by the oil fraction being washed during the THF elution. While the column was THF-washed. the 6-way-valve was switched to pass the eluent flow to the waste reservoir in order to avoid the oil matrix entering the mass spectrometer.The mass spectrometer parameters were optimized for the most sensitive detection of BADGE possible. Under these conditions BADGE was detected in the MS mode as a molecular ion-water cluster m/z = 358.1 [M + H20]+ (see Fig. 10-6). In the coupled MS-MS mode a corresponding fragment ion with m/z = 191.0 (Fig. 10-6) was found to be the most intensive. For quantification in the applied SRM mode. only one parent ion ( d z = 358.1 [M + H201’) was selected for fragmentation and only one fragment ion (daughter ion m/z = 191.0) was detected. While in the MS mode both the analyte molecule ion and other matrix molecules with the
I mlz= 358.1
K+ 05 1.17
m/z = 191
1.K + O 3 0.41
I
Figure 10-6: Mass spectrum of BADGE [M + HzO] at n ~ / z= 358.1 (upper) and its fragment ion n?/z = 191 (lower) selected as daughter ion for SRM detection.
324
Franz
,
P.04
a.903
m/z = 358.1
9+04 3.961
I,
mlz = 191
Figure 10-7: Selective analysis of BADGE in a food sample: detection of the parent ion t d z = 358.1 in the MS mode (upper) and daughter ion d z = 191 in the MS-MS mode (lower).
Migration of plastic constituents
325
same m/z = 358.1 value are detected, the SRM mode detects only the specific BADGE fragment. In this way it was possible to detect BADGE very selectively in the HPLC analyte fraction. The advantage of detection in the SRM mode is illustrated by Fig. 10-7. The same sample of fortified “herring in vegetable sauce” was detected in MS mode, where the m/z =358.1 was monitored (Fig. 10-7: upper mass chromatogram), and in the SRM mode where the fragment m/z = 191.0 was monitored (Fig. 107: lower mass chromatogram). This demonstrates impressively how a selective detection procedure allows suppression of the matrix influence for unambigous detection and quantification of the analyte. In contrast, conventional HPLC/UV or HPLC/fluorescence detection systems will be disturbed in such a case by many interfering peaks originating from the food matrix. It may even be difficult or impossible to recognize the analyte peak, especially when there is no blank food sample (free of BADGE) available for comparison. The described HPLC-MS-MS method was also found to be capable of detecting selectively the BADGE hydrolysis and ethanolysis products in foodstuffs. This is highly advantageous over the BCR project SML method since it is much more suitable for meeting the analytical requirements derived from the updated SCF opinion on BADGE.
Carhonyl chloride ( Q M
= 1 rng/kg)
Carbonyl chloride, CI-C(=O)-C1, (CAS No. 75-44-5; PM Ref. No. 14380), also known as phosgene, is an important starting compound in the production of intermediates and end products in many branches of large-scale industrial chemistry due to its high chemical reactivity. Carbonyl chloride is mainly used for the production of diisocyanates as starting materials for polyurethane chemistry. A large part of carbonyl production is also used for the manufacture of polycarbonate plastics (polycarbonates), produced by the reaction of 2,2-bis(4-hydroxyphenyl)propane (bisphenol A) with carbonyl chloride. Typical food packaging applications are multi-trip containers for drinking water and milk products, coatings for cookware, tableware, containers for automatic dispensers and baby feeding bottles (Bush et al. 1994, Gmeiner et al. 1998). For the analyst it is important to note that carbonyl chloride is an extremely acute toxic substance (irritant capable of producing delayed pulmonary edema) and is gaseous at room temperature (b.p. 7.5 “C/1013 mbar).Therefore, all processes in which carbonyl chloride may be liberated must be carried out in a fume cupboard. Skin and eye contact with carbonyl chloride solutions and especially the inhalation of carbonyl chloride vapour must be avoided. It is recommended not to work with pure carbonyl chloride but with commercially available solutions, for instance 20 % carbonyl chloride in toluene (density at 20 “ C 0.935 kg/l) corresponding to a concentration of 1.93 Mol per litre or 191 g/l. Stock solutions and standard solutions should be prepared and stored in closed containers. The analytical method developed in the BCR project (Franz and Rijk, 1997) to determine residual carbonyl chloride monomer in polymers was pre-validated by two laboratories and found appropriate for the quantitative determination of carbonyl chloride with a LOD = 0.3 mglkg below and in the range of the restriction criterion of 1 mg/kg polymer, with observed repeatability values of r = 0.23 and 0.32 mg carbonyl chloride/kg polymer, respectively. The method is applicable to polycarbonate as well as to other polymers and copolymers where these are soluble in methylene chloride.
326
Franz
Working principle of the method: The level of carbonyl chloride in the polymer is determined by dissolution of the polymer in methylene chloride and concurrent derivation with 2-aminophenol to form 2-benzoxazolinone (Box) under hydrochloric acid elimination (see Fig. 10-8).
2-arnincphend
carbonyl chloride
2-benzoxazolinone (Box)
Figure 10-8: Chemical derivation of carbonyl chloride with 2-aminophenol
Whereas carbonyl chloride itself is very moisture sensitive and requires the corresponding precautions such as efficiently dried glassware and solvents, the Box derivative is very stable and can be analysed by high performance liquid chromatography (HPLC) with ultra violet (UV) detection at 270 nm. Quantification is achieved by the standard addition procedure spiking carbonyl chloride into the test polymer solution. However, since Box is a commercially available chemical, it is advisable to work also with Box standards, especially when the method is used for the first time and when problems are experienced in the HPLC determination or the derivation procedure. The standards of the carbonyl chloride derivative are particularly useful to establish the analytical system and to check linearity of detector response as well as for the recovery check. For illustration purposes, in the following the determination of carbonyl chloride in test sample is described in detail. From the measurements of the calibration samples prepared according to the standard addition procedure a calibration graph is obtained as depicted in Fig. 10-9.
rng carbonyl chloride added per kg polymer
Figure 10-9: Calibration graph obtained from the standard addition procedure
Migration of plastic constituents
327
Graphically, the determination can be achieved as follows: The carbonyl chloride concentration of the test sample can be read from the calibration graph by back extrapolation to the x-axis where the magnitude of the intercept Z is equal to the carbonyl chloride concentration. The sample concentration can also be calculated from the regression parameters, specifically from the regression line of the calibration graph including the sample value, which is given by the following equation: y=ax+b
(10-14)
The residual carbonyl chloride concentration in the test Sample Ccarhonyl chloride. po~ymer is then obtained from the regression parameters a and b where y = 0 according to: Ccarhonyl chloride. polymer =
b/a
(10-15)
From both procedures the carbonyl chloride concentration in the test material is obtained directly in mg of carbonyl chloride in 1 kg polymer. In the BCR project it was agreed that the method applying calculation from the regression parameters should be preferred. In case of measured concentrations exceeding the QM limit, confirmation of the identity of carbonyl chloride is carried out by diode array detection. This is achieved by recording the spectral profiles of the samples, blanks and calibration samples over the wavelength range of 200-320 nm at the front, apex and tail of the peak identified as the carbonyl chloride derivative. Box can be identified as having an absorbance peak maximum at 272 nm and a minimum at 245 nm with an absorbance ratio of 40 (at 260 nm) : 100 (at 272 nm) : 70 (at 280 nm). I f the peak is pure, the overlaid spectral profiles of the front, apex and tail of the peak should be identical. Therefore, if the three profiles are normalized, they should superimpose on top of each other. A pecularity observed during method development,and which illustrates what the analyst must be aware of when working with a derivation procedure was the following: After some remarkable and confusing experiences indicating that the HPLC peak of Box in the completely worked-up sample was still increasing with time and inhibiting reproducible results, it was found that the derivation agent 2-aminophenol is capable of reacting not only with carbonyl chloride but also at a much slower rate with oligomers or the polymer residues dissolved in the sample solution. The final evidence for this was derived from the following control experiment: A polycarbonate sample was dissolved and re-precipitated to ensure a polymer matrix completely free of carbonyl chloride monomer. This purified polymer sample was then treated by the derivation procedure with 2-aminophenol but without removal of the excess derivation reagent with hydrochloric acid after the standard derivatisation reaction. The sample was then analysed for Box as a function of time and in comparison against both, a polymer blank (without derivation reagent) and a reagent blank (without polymer). The results obtained after 2 hours and 13hours storage time of the HPLC sample vial at room are depicted in Fig. 10-10. They demonstrate clearly an effect which can only be explained by the chemical reaction of 2-aminophenol with residual polycarbonate oligomers or polymer present in the sample solution. In conclusion and as a consequence, the method requires from the analyst a timely and very disciplined sample preparation, including the need €or acidic removal of the stochiometrically excess aminophenol.
328
Franz 3.27-
3.27-
(a) 3.17-
3.17-
2sri 5.w
,
,
,
700
8.00
n.w
I
2.67-
m 7 4
I
1
I
I
5.00
7.w
9.00
ll.W
,
,
, 5w
7.w 9w AarcnUon Urn h mdfwces
I
, n.w
Figure 10-10: HPLC chromatograms of phosgene-free polycarbonate samples derived with 2-aminophenol as a function of time: (a) sample after 2 hours, (b) sample after 13 hours, (c) polymer blank, (d) reagent blank.
Epichlorohydrin ( Q M = lmg/kg) Epichlorohydrin (l-chloro-2,3-epoxypropane), C3H50C1, (CAS-No 106-89-8; PM/ Ref.No 16750) is a toxicologically important starting substance, reacting for instance with bisphenol A to form bisphenol A diglycidyl ether (BADGE, see above) used for the production of epoxy lacquers. It is also used for epoxy resins with p-hydroxybenzoic acid and resins with dimethylamine. Food contact applications are coating cans for fruit, vegetables and beverages as well as coating storage vats and silos for wine, beer, fats and dry foods. Another application is its use for adhesives. The “Plastics Directive” foresees a QM value as a restriction criterion for ECH. As a consequence a pre-validated QM method was developed in the BCR project entitled “Determination of the residual content of epichlorohydrin (ECH) in coatings”. Similar to the BADGE discussion to justify determination of an area-related QM value, in this method it is stated that epichlorohydrin is mainly used in coatings on a non-plastic support. Therefore the amount of coating on a final article (e.g. coated cans) cannot be determined within an acceptable accuracy and, in consequence, the amount of residual epichlorohydrin should be measured and related to the area and given in mg/ dm2. The method was found to be appropriate for the quantitative determination of ECH at 1pg per dm2 of coating. In general this allows for the detection of ECH at the level of 1 mglkg polymer.
Migrution of plastic constitirents
329
The working principle of the method is to extract the sample material with dioxane for 6 hours at room temperature. It is important to note that the dioxane quality used must be of the highest purity (>99.5 YO)with a water content ~ 0 . 0 YO 1 (dried over a molecular sieve). From a practical standpoint, the extraction of ECH can be carried out in the case of cans by filling with 50 ml dioxane and closing the can with an epoxide-free coated plate and, in the case of other coated packaging material, by cutting 2 dm2 coated material into pieces and immersing them in the extraction solvent. Typical surfacelvolume ratio is 2.5 dm2 packaging material area per 50 ml extraction solvent. After extraction, the extract is distilled by means of a micro-distillation depicted in Fig. 10-11. In the distilled fraction thus obtained, the concentration of epichlorohydrin is determined by derivation of the epoxide with an aromatic sulphonic acid, i.e. 9,lOdimethoxyanthracene-2-sulphonic acid (DAS), followed by reversed phase HPLC with fluorescence detection (HPLC column: stainless steel 250 mm x 4.6 mm, filled with C8 coated silica, particle size 5 pm, load of 10 % carbon and end capped; acetonitrile-water gradient elution; fluorescence detector set to hexcltation 262 nm and hemission 490 nm). The DAS solution prepared in acetonitrile is only stable for one day at room temperature and must be prepared freshly before use and protected against light. Depending on the quality and type of the HPLC column, it is possible to separate the two isomers formed in the derivation reaction of epichlorohydrin with DAS. In this case, for calibration and quantification purposes the sum of both peak areas has to applied. Quantification is achieved by means of external standard calibration using dioxane solutions fortified with known amounts of epichlorohydrin. Confirmation of ECH identity is carried out by straight phase HPLC with fluorescence detection. A conclusion drawn from the BCR project work was the following: Expression of the measured ECH concentration in mg/kg in final product is difficult or even impossible because data on thickness and weight of the coating in food contact materials are often missing. Since the determination of the area weight of the coating layer is troublesome, it was proposed to the E U Commission to set a maximum content limit of 20 pg ECH per 6 dm2 food contact area which translates to 20 ppb (pg/kg) food in the case of total mass transfer.
Cold waterlice
bath
Hot plate and magnetic stirrer
Figure 10.11: Schematic picture of the micro-distillation of epichlorohydrin from the dioxane extract of the polymer in vial A into cooled vial B: (1) Vial A; (2) Vial €3; (3) PTFE lined septum; (4) Sleeve of PTFE tube for isolation; (5) Stainless steel tubing. ends are injection needle type sharpened. Int. diameter 1 mm,lenght approx. 20 cm; (6) Injection needle for venting; (7) 3 ml mark.
330
Franz
However, due to the rapid decomposition of ECH in aqueous foods the migration measurements for such products are very problematic and not reproducible (Piringer 1993,1980). Bronsted had already studied the kinetics of the ring opening of epoxides over 60 years ago. Because of the large ring tension, epoxides are very reactive and indeed react in water with nucleophilic substances at any pH-value. The hydrolysis mechanism occurs according to the so-called S$ mechanism. In alkaline and neutral media the chemical reaction can be described by the following equation (Fig. 10-12).
yLk
0+
OH
\/c-c I
OH-
OH
1 0 \
slow
OH
\I /c-c
HzO
1 0
+
OH'
\
fast
0-
OH
\,c-cI
0
*
I\
slow
,\c-cI
/ I\
fast
OH
H,O+
Figure 10-12: Alkalineheutral hydrolysis of epichlorohydrin.
In acidic media the nucleophilic attack on the epoxy ring proceeds by a proton attachment. The intermediate species formed very quickly in step a) is present in very low equilibrium concentrations and favors the rate determining nucleophilic ring opening b) whereby the acid functions as a catalyst for the whole process (Fig. 10-13) H
0
O+
H
yzk
b)
OH
OH
+
HzO
slow
\/c-c I
/c-c
0
I\
'I
fast
H,O+
OH
Figure 10-13: Acidic hydrolysis of epichlorohydrin.
The hydrolysis product of ECH in neutral and acidic aqueous media is 3-chloro-1,2propanediol and at high pH values the reaction proceeds up to the formation of glycerine (Fig. 10-14). 0
/ \
C-C-C-CI
OH OH
-I H', HzO
I
C-C-C-CI
-I OH-
OH C-C-C
0
/ \
OH OH
-I OH-
I
C-C-C-OH
Figure 10-14: Hydrolysis products formed from epichlorohydrin.
The hydrolysis reaction follows a first order mechanism with respect to ECH: (10-16)
Migration ofplastic constiriients
331
where kECHrepresents an overall rate constant which contains the contributions of all nucleophilic reaction partners present in the system as well as that of water. Numerous publications in earlier years dealing with the kinetics of this reaction were limited by the analytical determination in ECH concentration ranges of 0.01-0.2 mol/l. The control of these residual monomcrs. however, requires methods and knowledge of the reaction process in the trace amount concentration region of approximately 1 . mol/l for pH values from 2 to 12. Combined GUMS using headspace and SIM techniques allows the quantitative determination of ECH at a limit of detection of 0.5. moll1 (40 ppb ECH in aqueous solution). Values obtained for halflife times t 1 / 2 of the hydrolysis using this method are given in Table 10-6. Table 10-6: Halflife times tl,z [hours] for ECH in different aqueous systems and foodstuffs in dcpendency of temperature.
20 "C
tli2 PI 40 "C
60 "C
148
23
4.4
62
10
2.0 1.6
Matrix 10 % Ethanol in water ( p H = 7)
NaOH in water (pH
=
12)
3 % Acetic acid in water (pH = 2.5)
79
10
Sunflower oil
45.000 (5.1 years)
-
Sunflower oil + 1 ' 6 water
15.000 ( I .7 years)
-
106
13
Green beans Pectin 5 6 ' (pH = 7)
41
8.2
Processed tomatoes
44
5.6 6.4
Beef + vegetable
41
Mackerals + tomatoes
38
6.2
Sardines in oil
33
4.7
Egg yellow
34
6.0
Egg white
1')
2.6
The hydrolysis of ECH is so rapid at 40 "C, even in neutral aqueous media (water, 10 YOethanol) as well as acidic (3 YOacetic acid, 0.01 N HCl) and alkaline (0.01 N NaOH) media, that specific determination of this residual monomer migration from epoxy lacquers into these media causes inconsistent and erroneous results. Due the fact that the overall rate of hydrolysis contains the sum of all contributions from nucleophiles present in aqueous systems, one can find a rapid decomposition of ECH even in foods with neutral pH, due to their complex composition.
Ethylenediamine (SML = 12 mg/kg) and hexamethylenediamine (SML = 2.4 mg/kg) The two homologous aliphatic diamines are commonly used as bifunctional monomers for polycondensation reactions. Hexamethylenediamine or 1,6-diaminohexane, ChHlhN2(CAS No. 124-09-4, PM Ref.No. 1840), which is most well-known as a polyamide (Nylon 66) monomer, is also copolymerized with sebacic acid to form Nylon 6/ 10, or with isophthalic acid. Besides that, it is applied as a curing agent for expoxy
332
Franz
I
350.00-
i I
300.00
250.00 200.00-
150.0U 1OO.OD
50.00
7
A--LI-
I
I
I
1
I
I
1
160.0F
120.0cF
80.00-
40.00-
0.00
10.00
20.00 30.00 40.00 Retention time In minutes
50.00
60.00
70.00
Figure 10-15: SFCiFID analysis of olive oil before (upper) and after reaction (lower) with a EDA/ HMDA mixture.
Migration of plastic constiti4ents
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resins. Practical packaging applications are vacuum and modified atmosphere packs, boil-in-packs for packaging meat, fish, coffee and snack foods. In the field of rigid containers, monolayer or multilayer bottles for refilling with soft drinks and water are on the market. Ethylenediamine or 1,2-diaminoethane, CzHgN2 (CAS No. 107-15-3, PM Ref. No. 16960) is also used to make some nylons and thermosetting resins. It finds application as a reactive hardener in epoxy resins and in stabilizing rubber latexes. Examples of practical applications are adhesives, moisture barrier coatings for paper, cellophane or others, and corrosion inhibitor for aluminium alloys. In the BCR project, a group method was developed for both diamines HMDA and EDA in the same way (Franz and Rijk 1997, Demertzis et al. 1995). During the project work a remarkable observation was made: Stability tests in olive oil as a food simulant carried out under test conditions 10 daysi20 “C and 10 days140 “C indicated that both diamines could no longer be recovered, whereas in aqueous food simulants nearly 100 Yo recovery was obtained under the same test conditions. To investigate the mechanism of diamine disappearance a model experiment was carried out. A 1:l mixture by mass of olive oil and diamines was stored for 10 days at 40°C. Then the mixture was analyzed by supercritical fluid chromatography (SFC) using FID detection and compared with the original olive oil SFC pattern. The result is depicted in Fig. 10-15. It can be recognized that the original olive oil triglyceride peaks are nearly completely transformed into a series of different SFC peaks with lower molecular weights. The only reasonable explanation is that the triglycerides react with the diamines to form transamidation products. This was confirmed by LC-MS analysis which demonstrated that the products formed contain the moiety of the diamines. An important conclusion from these findings was that even though this analytical method works in principle with olive oil as a food simulant, the migration test using olive oil or another fat simulant can provide false-negative results. Therefore. the method should only be applied in the case of short exposure periods with olive oil. If the method is carried out with olive oil. a recovery check with spiked olive oil applying the same timehemperature migration test conditions is necessary. In the case that such a recovery check indicates “loss” of HMDA andlor EDA, then alternatively 95 YOethanol or iso-octane should be used as substitute fatty food simulants. As a consequence of these findings, the scope of the analytical method was extended from the determination of the diamine monomers in the aqueous food simulants and in olive oil to the substitute food simulants 95 YO(vh) ethanol and iso-octane. The working principle of the method is as follows: The level of HMDA and EDA in a food simulant is determined by derivation of the free diamine using ethyl chloroformate as derivation agent (see Fig. 10-16) followed by analysis of the resulting diurethane by gas chromatography using automated sample injection and flame ionisation detection (FID). Quantification is achieved using propylenediamine (PDA) as an internal standard with calibration against relevant food simulants samples fortified with known amounts of HMDAIEDA. Confirmation of HMDNEDA levels is carried out by combined gas chromatography/ mass spectrometry (GUMS) of the diurethane. 0 CI H,N-(CH,),-NH,
-CII-OEt
0
II
EtO-C-HN-(CH,),-NH-C-OEt
0
II
EDA (n = 0 ) HMDA (n = 4) Figure 10-16: Chemical derivation of diamines EDA and HMDA with ethyl chloroformate.
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As a result of the pre-validation work, which included a within-laboratory precision experiment carried out in two different laboratories at concentrations of 2.1 mg HMDA and 12.1 mg EDA per kg food simulant, the performance characteristics in Table 10-7 were obtained at the 95 OO/ probability level. Table 10-7: Repeatability values r [mglkg] obtained from two laboratories for HMDA and EDA at concentrations close to the SML values. Food simulant’)
HMDA
EDA
Water
0.30/0.67
0.37/1.5
3 % Acetic acid
0.17/0.62
0.56l0.8
15 % Ethanol
0.13/0.37
0.49/0.7
Olive oil
0.1710.64
0.6810.7
’)
For the substitute food simulants 95 % ethanol and iso-octane a precision experiment has not been carried out. However, from experience with establishment of calibration curves, r-values can be expected to be in the same range as with the other food simulants.
The within-laboratory limit of detection for HMDA was found to be in the range 0.1 to 0.5 mg HMDA/kg (substitute) food simulant depending on the type of food simulant. In case of EDA, the LOD was not determined exactly but was found to be lower than 1 mg EDA/kg (substitute) food simulant regardless of the type of food simulant.
10.2.7 The concept of functionality of validation procedures and precision data for compliance testing As mentioned earlier (Section 10.2.5), there exists a clear need for pragmatic and cost effective solutions to specific migration testing. One possible way to reduce the analytical workload without compromising the requirement of consumer protection with regard to food packaging safety is to follow the policy of functionalizing the extend of validation work and the degree of precision data required. This concept for which the term “ j k c t i o n a l validation & precision” (FVP) is introduced, means that the degree of validation steps to be applied and the amount of necessary precision data to be provided is a function of the analytical demands and the relevance of the migrant or analyte concerned. With respect to FVP, as a general rule, the following maxim is applicable: the more challenging a legal restriction, i.e. the lower the SML or QM value is, the more necessary and justified is the time and work expenditure for validation and production of precision data. and vice versa. The consequence is: in the first place, the analyst has to carry out some basic considerations regarding a healthy ratio between expected benefits and invested time/work load prior to designing and carrying out the analytical validation work. In the following the concept and practical consequences of FVP are explained in more depth. However, first of all, one needs to examine some considerations deviating from the classical analytical understanding. First of all and as a matter of principle, the reader should accept the following premise as a modified understanding of an analytical method: An analytical method may be understood predominantly as a tool for
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compliance testing or, more specifically and since this is the normal case, as a comparative method to prove that a SML or QM value is not or cannot be exceeded. The analytical method may not be understood primarily in the classical sense, i.e. as a tool to determine precisely the exact concentration of an analyte. In principle, the compliance testing analyst has to deal with 3 main categories of legal restrictions: Category I: Authorized compounds on positive lists with very low restrictions. for instance at or very close to the analytical detection limit. In this highly challenging situation the analytical method has to fulfil its classical task, which is to determine the target concentration as accurately as possible and the full extent of validation work is necessary. It is obvious that this does not deserve further explanation, as compromise with respect to the required precision data is not acceptable. Category ZZI: At the other end of the positive list spectrum, are analytes with SML values in the 15 mg/kg to 30 mglkg range such as the PET monomers mono- and diethyleneglycol (MEG and DEG). Such compounds can even be controlled by the overall migration (OM) test itself. So if, for instance, an OM value in the typical range of 6 to 12 mglkg has been obtained for a PET sample, then this could already be considered to be the whole validation process and full set of precision data which is required. In this case, compliance proof has already been achieved with the OM test result. It is important to note that from a purely food regulatory point of view, the accurate MEGlDEG concentration obtained in the migration test is of no interest as long as it can be localized far below the restriction criterion. It should also be noted that this approach is based on experience and supported by modern diffusion models (compare Chapter 15) by which the maximum MEGlDEG migration can be estimated in the 1 pprn range in a food simulant. Taking this into account, development of analytical CEN standard methods for MEG/DEG (ENV 13130 - part 7) (CEN 1999) appear to be a wrongly placed investment. Category ZZ: In between the 2 cases mentioned above, the spectrum of SML values contains numerous “small and medium sized” restrictions. Consequently, category I1 may be subdivided into several subcategories with different requirements for validation and precision. Depending on the target concentration values, more or less validation work may be necessary. This is characteristic of “FVP” and needs to be defined case by case. However, one approach for dealing with this question in a very pragmatic and costefficient way is the method of direct comparative analysis using only one calibration point as a benchmark, at or below the legal restriction concentration. Provided that appropriate safety margins are guaranteed, compliance testing could be achieved in this way very time and cost effectively without posing any risk to consumer health. Logically, the corresponding validation work would be dramatically reduced. The following gives an example to provide a better principal understanding of this approach in practical terms: The relevant migrant or analyte shall have a SML value of 5 ppm (mglkg) and be analyzed by GClFID in food simulants. From the chemical structure and the physico-chemical properties of the migrant the analyst would not foresee any great analytical difficulties and would expect normal linear FID response behaviour. In this case, compliance testing and validation could be achieved simply by fortifying the blank food simulant to a certain concentration. This can be, for instance, 3 ppm (60 70of the SML) or even at 5 ppm (100 70SML), for obtaining just one calibration sample. Then this calibration sample would be analyzed (for instance GC/
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FID) under the same analytical circumstances and in the same test run (same sample preparation etc.) as the migration solution (of the same food simulant) and the blank solution. One must be made certain that all other analytical parameters are kept constant in the different sample solutions and the only variable is the analyte concentration. In the case that an analyte peak in the migration solution is significantly smaller than that of the calibration point, this would demonstrate compliance Of course, depending on the closeness of the calibration sample concentration to the SML, an appropriate one-sided analytical tolerance between the sample and calibrant peaks needs to be defined. What happens in the case that the analyte concentration is in the critical range where it is not smaller than the legal restriction and indeed likely to exceed it? In such a case (which is the exception rather than the rule) a confirmation analysis has to be carried out. This is also the usual practice with standard methods such as the acrylonitrile CEN method where the result of the confirmatory GUMS procedure is taken as the true or relevant value, although this GUMS method has never been approved in a ring trial according to IS0 5725. The confirmatory analysis may be such that the one point calibration is replaced by a full set of calibration points, but using the same analytical principle (GC/FID). If compliance is not clearly shown after that, then confirmatory analysis in the conventional sense, i.e. applying GUMS or another method has to be carried out. In the context of this discussion, it is important to note that the FVP concept can also take account of the plastic type (diffusivity of the polymer) in analogy to the “QM/SML” concept (see Section 10.1.2). In this way, very quick and cost efficient validation strategies based on extraction methods of more severe test character can then be considered. But in depth explanations of such strategies would exceed the frame of this chapter.
10.3 Safety assessment of modern food packaging applications The E U Directive 94/62/EEC on packaging and packaging waste (European Commission 1994) sets out requirements and targets for the reuse and recycling of waste packaging to reduce waste and to save resources. One of the options to meet these requirements is the reuse of food packaging in the sense of refilling used and returned bottles. Well-known examples for many years have been glass milk bottles and in more recent times also plastic containers such as the returnable PET bottle used for soft drinks. Reuse of food packaging in a wider sense can also mean chemical or physical reprocessing, which has been applied for a long time for glass waste and for used cellulosic fibres from paper and board. In the area of food packaging plastics, this topic is of growing concern and its feasibility is under investigation. Indeed and as a matter of fact, considerable progress has been made in this field and different pilot attempts have already entered the European market. Of course, the use of recycled plastic materials in packaging applications has to comply with the regulations and must not be at the expense of public health, nor should it alterate the filling’s quality. But from manufacture to recycling of a package the plastic material is exposed to various influences which may change its composition e.g. uptake of compounds, commingling with other resins and degradation. Particularly plastics are vulnerable to an uptake of contaminants because of their permeable nature. Refilling plastic bottles and recycling plastics for packaging applications for sensitive products such as food-
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stuffs is therefore limited to excellent performance plastics and requires thorough and careful suitability and compliance testing. In the following examples, such modern food packaging applications are presented together with the inherent problems and difficulties in their food safety assessment.
10.3.1 Recycling used packaging plastics into new food packaging Due to modern environmental packaging requirements the question of recyclability of used packaging plastics into new food packaging applications is of increasing interest. This question is currently still enforced since usual market applications for recycled plastics in the non-food area seem to approach saturation. Indeed, recycled plastics have already been used in food-contact plastics for several years around the world. However, these cases must be considered to have more pilot character than real market value and, in most cases, the mass fraction of recycled plastics in these applications was relatively low, due to blending with virgin plastics or sandwiching with functional barrier layers of relatively high thickness extruded also from virgin polymer. Although considerable progress has been made from a scientific point of view in understanding and physico-mathematical modeling of diffusion processes for adventitious hazardous compounds from a recycled plastic in direct contact with food or from a core layer across a functional barrier (Scheirs 1998, Begley and Hollifield 1995, Franz et al. 1994,1996, Laoubi and Vergnaud 1995, 1996, Laoubi et al. 1995, Piringer et al. 1998), the translation of this knowledge about migration into action, i.e. into industrial solutions remains still in a waiting position. One of the reasons has more “European” character, substantiated by the fact that the European legal requirements in this respect are not yet precisely defined. However, in the US a very concrete concept, the so-called “threshold-of-regulation” principle has been established and adopted by FDA. Another reason is clearly the non-availability of simple and economic test methods which in addition would need to be at least generally accepted procedures and, at best, standard test procedures. Due to the lack of regulations within the currently harmonized Europe, the Member States treat this modern challenge individually according to national laws or recommendations. In Germany for instance, it is in principle not forbidden to use recycled materials for direct-contact foodstuff packagings. A statement ( B g W 1995) in a document from the “Kunststoffkommission des Bundesinstituts fur gesundheitlichen Verbraucherschutz und Veterinarmedizin” stressed that the reuse of recycled plastics in foodstuff packaging is legally not excluded. However, the document demands that recycled plastics have to meet the same legal regulations as required for virgin plastics, particularly the requirements of $3 30-32 of the “Lebensmittel- und Bedarfsgegenstandegesetzes (LMBG)” and those of the “Bedarfsgegenstandeverordnung” (which is the nationally implemented European Directive). The BgVV document further demands explicitly that there must not be any risk of health danger to the consumer from any goods made with recycled materials. Moreover, no measurable sensory damage or impairment to the product should result from use of the recycled packaging material. Finally, the document states that it is the responsibility of the company using the recycled packaging to prove that it is suitable from a legal standpoint. It should also be noted that the BgVV document clearly provides no hindrance to the introduction of a suitable test method.
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In the USA, there are also no specific decrees or directives for packaging made from recycled materials. However, the Food and Drug Administration (FDA) has published some basic information about the conditions of use of recycled plastics in food packaging applications (US FDA 1992). This information is based on current legislation in the USA and has the backing of American industry (US NFPA 1995). The safety and quality assurance principles involved here concern three fundamental elements: - Control of the source of raw materials (recycling control), - The effectiveness of the purification steps in the recycling process, - Conditions for the application of the recycled packaging materials. As a judgement criterion, the FDA uses the so-called “Threshold-of-Regulation” concept (US FDA 1993b) which orientates itself on the maxim “De minimis non curat lex”. This concept is backed up by extensive scientific evaluation of toxicological data (Rulis 1986) and also tolerates the transfer of unknown substances into foodstuffs as long as a threshold concentration is not surpassed. This threshold, relating to average dietary intake, is set at 0.5 ppb (0.0005 ppm) and is primarily independent of packaging type and packaging material. By applying so-called “Consumption Factors” (CF) which take account of the percentage of plastics types used in food packaging, the concentrations actually allowed are increased (depending on polymer type). For example, in the case of PET (CF=O.OS), the concentration permitted, for instance in a soft drink, is increased by a factor of 20 to 0.01 ppm (10 ppb).
10.3.2 Recycled plastics covered by functional barriers First of all it should be mentioned that the so-called functional barrier concept corresponds to nothing more than the well-known important classical function of a food packaging material, which is to protect the food against external influences. The requirements are that the food contact layer has to act as a barrier against contamination from the packaging’s environment in general and more specifically from the recycled core layer or outer compartments of the multilayer packaging structure. The published studies on functional barriers to migration have focused predominantly on the question of reusability of recycled plastics for food packaging. This unfortunately, generated such a very rigid link between the terms “recycled plastics” and “functional barrier” that it is often forgotten that the functional barrier concept has general relevance and is applicable to any multilayer structure. It is well known that there is only a very limited number of packaging materials which provide absolute protection properties against penetration by chemical compounds. Therefore, the mass transfer from outside through a packaging (permeation) or from a packaging into the food (migration) can generally not be limited to zero. As a consequence, in most cases an unavoidable mass transfer occurs to a certain extent. This must be understood as a functional quantity which, however, must also comply with food regulations, for instance Article 2 of Framework Directive 89/109/EEC. Therefore, functiona1 barrier efficiency needs to be defined beyond the toxicological meaning (requirement: US-FDA threshold-of-regulation concept) to cover also purely organoleptic food quality considerations. Concerning the efficiency definition of a functional barrier, different understandings seem to exist. On the one hand and in most of the published cases in the litera-
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ture, functional barrier efficiency is related to the mass migrating into a foodstuff, thus allowing a comparison of resulting measured concentrations in the foodstuff with given legislative limits. On the other hand, there is also a time-related understanding which links the F B efficiency to the lag time for the start of migration. The latter definition seems to be questionable since the lag time itself is a priori not linked with a migration-related concentration in a foodstuff or simulant. Exceeding a lag time docs not automatically also mean exceeding a threshold concentration. But a threshold concentration can already be exceeded before the lag time (understood in the classical sense) has been reached. Physically, this can be explained by the non-idealistic behaviour of the migration front and can be recognized from the initial part of a typical permeation curve before the steady state has been achieved (Chapter 7). In the published literature only a few attempts have been made to tackle the functional barrier problem by experimental and theoretical approaches. Most of the papers present a mathematical model solution based on the assumption that the contaminated recycling layer was burried by a contuminunt-free virgin functional barrier layer just after its manufacture. However. other studies (Franz et al. 1997, Piringer et al. 1998) have recently demonstrated that, since multi-layer plastic structures are mostly manufactured under coextrusion conditions where extreme temperatures far above the melting point of the plastic arc applied, a significant inter-diffusion is in reality occurring between the in situ formed polymer layers. Taking into account coextrusion temperatures up to 280 “C it can be estimated, depending on the polymer type and thickness, that middle layer contaminants are penetrating the functional barrier layer partially or completely within a time range of seconds down to fractions of one second. As a consequence, more or less significant impurification of a “virgin” functional barrier layer is likely to occur during manufacture, which compromises and reduces the originally designed functional barrier efficiency. It can even result in the possibility of complete penetration, with the consequence of already having direct food contact with contaminants originating from the middle layer at the start of migration, i.e. after the time point when the foodstuff is filled into the packaging. From the above discussion, one can summarize that functional barrier efficiency does not correspond to an absolute barrier requirement but is related to a “functional” quantity in terms of mass transfer which is dependent of the technological and application-related parameters of the respective food-packaging system. These parameters are: - manufacture conditions of the package - thickness of the functional barrier layer - type of functional barrier plastic - molecular weight and chemical structure of penetrants (contaminants) - concentration and mobility of contaminants in the matrix behind the functional barrier - time period between manufacture of packaging and filling - type of foodstuff, i.e. fat content, polarity etc. - filling conditions and storage (time, temperature) of the packed foodstuffs
How cun the efficiency of functional barriers he verified or tested? Currently, there are two different test principles which have been described and applied in practice:
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A. Migration testing of deliberately contaminated packaging structures using incorporated model contaminants or surrogates. B. Migration testing of real-life recycling packaging structures by monitoring inherently present recycling-related substances. Procedure A has been proposed by the US-FDA and incorporates model contaminants or so-called surrogates into the packaging material. This approach is probably the best choice for individual functional barrier efficiency testing of a given test structure. Despite its individual test character, this procedures also allows the collection of fundamental knowledge on functional barrier packaging design. In fact, recent studies have applied this test approach to validate a physico-mathematical model which is able to describe migration across functional barriers even when they are already partially impurified due to the extrusion process-related in-situ contamination (Franz et al. 1997, Piringer et al. 1998). This migration model subdivides migration out of a contaminated core layer into two separate steps theoretically, one of them being migration from the core-layer into the functional barrier and the other being migration into the foodstuff itself. The other and much more essential key element of the model is to give a solution to the problem of the remaining functional barrier efficiency after the manufacture process. An important conclusion from this study is that the crucial impurification step of the functional barrier occurs during co-extrusion. Compared to this effect, room or slightly increased temperature storage of the packaging material before the time point of filling can be considered negligible. Finally, it was discussed that on the basis of the presented model, migration prediction seemed to be feasible also for functional barrier packaging structures, thus also here offering (and not only with monolayer plastics) a possibility of applying QM/SML relationships for food regulatory purposes in future (see Section 10.1.2). A remarkable drawback of procedure A, however, is that working with surrogates for incorporation in packaging materials is a very laborous process and only possible with special precautionary measures. Therefore this test approach, which has to be applied case by case, again implicates an economically disadvantageous situation. In addition, enforcement laboratories cannot make use of this method. Procedure B has been developed and proposed by Fraunhofer I W (Franz et al. 1994) without incorporating model contaminants. It is a “black-box’’ approach which monitors inherently present recycling-related substances and is applicable to a readyto-use food contact article. In this way, the procedure meets not only the R&D and quality assurance requirements of the manufacturer but also offers a test possibility for enforcement labs. Essentially, procedure B consists of two experimental key steps: (i) Extraction of the packaging material for determination of the migration potential and characterization or identification of recycling specific substances which can serve as indicator compounds to be monitored in the migration test (ii). (ii) Migration testing both under prescribed and more severe conditions. The extent of test work depends on several factors, such as the test packaging structure, the migration potential found under (i) and the practical application itself, i.e. type of foodstuff, filling and storage conditions. In the most advantageous case, only step (i) is required. Important information can be obtained during key step (ii) from additional migration testing under more severe conditions (for instance higher temperature and/or stronger extracting solvent). This introduces a kinetic factor into the test and allows one to consider a possible lag phase effect of the functional barrier layer. From the findings measured under the exaggerated test conditions, migration
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test results likely to be obtained under normal or application-related conditions can be extrapolated down to concentrations far below analytical detection limits. To explain: if one obtains data from two migration tests where one is carried out at 20 "C and the other at 40 "C (under otherwise the same conditions), in each case using the analytical detection limit (which in both cases is the same) as a migration test result, then the real migration value at 20°C must be much lower than the concentration corresponding to the analytical detection limit achieved. The following describes a typical case study representative for test principle B (Franz et al. 1994): Test material was a coextruded three-layer polypropylene (PP) cup of symmetrical structure with recycled post-consumer PP in the middle layer (mass fraction 50 Yo)and virgin food grade PP in the adjacent layers. The recycled PP, which contained about 95 YO PP and 5 YO PS, was completely under return control in the recollection system and had been used in its prior application for packaging yoghurt. The intended application for the recycled material was again packaging milk products such as yoghurt with storage for short times under refrigerated conditions. The point of interest was the functional barrier efficiency of the virgin PP food contact layer under the intended storage conditions. In addition, it was the aim of this R&D research work to establish a simple and cost efficient quality test procedure for future production. This was one of the reasons why procedure A using incorporated model contaminants was not applied. Therefore, the working strategy was to compare the recycled plastic with new, food grade plastic material of the same type. This comparison experimentally included three investigation levels: (1) Compositional analysis of the raw materials (virgin and recycled PP granules), (2) compositional analysis of the food contact articles (virgin and recycled cups), ( 3 ) migration testing on both types of cup (virgin and recycled) under prescribed (10 days/20"C with 3 YOacetic acid) and more severe test conditions (10 days/ 40°C with 3 YOacetic acid, 35 YOethanol or 80 YOethanol). First of all, from levels (1) and (2) the intention was to characterize and if possible to identify and quantify recycling-related (R) polymer components (migrants). Then, R-components with relatively high concentrations should serve as indicator substances to be monitored in migration measurements on level (3). The realization of this principle is demonstrated in Fig. 10-17. In the upper and middle gas chromatograms it compares the components extracted from a virgin and a R-PP cup. This comparison allows immediately assignment of R-substances. In the lower gas chromatogram of Fig. 10-17 one can recognize which of the R-substances really migrate in measurable amounts under the most severe test conditions applied in this investigation. Migrating R-substances are only such with short retention times, i.e. low molecular weight and volatile components. The major component among them was identified as limonene, an aroma or flavour compound which can be found in many foodstuffs and also in the non-food area. The results obtained in this study can be summarized as follows: None of the R-substances could be analytically detected in the food simulant (at a detection limit of 13 ppb) under prescribed migration test conditions. However, from the results obtained under more severe test conditions, it could be concluded finally that the R-substance with the highest migration, limonene, could not migrate into a milk product with a concentration higher than 1 ppb. This concentration is more or less equal to the US-FDA threshold-of-regulation concentration (TRC). With regard to the other R-substances it could be estimated that they migrate far below the TRC. Concerning further quality assurance tests, it turned out that it
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A
A B.0
5.0 4.0
3.0
0.00
eo.oo
10.00
R
7 . 0
R. 30.00
40.00
0
5.Q A.0
3.0 0.00
20:oo
10.00
4-
40100
t
I1
3.8
A
(Limonene) R
3.2
3 .O O D D
8
10.00
I 20.00
8
8
30.00
40.00
Retention time [min]
Figure 10-17: Gas chromatograms of extracts of a virgin (upper) and a recycling PP cup (middle) as well as a migration solution (80 % ethanol, 10 days/4O0C) obtained from a recycling cup (lower picture). Abbreviations: 0 = Oligorner; A = antioxidant: R = recycling-related substance; b = interfering peak from the solvent.
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would suffice to carry out only compositional analysis of the raw materials comparing any future recycled PP granules with the reprocessed PP material of this study as a reference material. The two princicpal test approaches A and B should not be considered suitable only for multilayer plastic structures. Other packaging structures can be tested by the same principles: for instance polymeric coatings on paper and paperboard where the question of functional barrier efficiency is also very important. However, due to the fact that paper as a core layer material is completely different to a polymer and that in most cases very thin films of polyolefins are used as food contact layers, correspondingly specific considerations have to be taken into account. One of the interesting issues in this context is related to the diffusion of inorganic compounds across these very thin polyolefin films. The permeation of organic compounds across such films has been extensively investigated, with the result that plain polyolefin films do not provide efficient barrier properties against organic compounds such as toluene, limonene etc. However, there is very little published about the permeation behaviour of inorganic compounds. Recently, a study was presented about the diffusion behaviour of CuC12, dissolved in various ethanol-water mixtures, across LDPE films at different temperatures (Hampe and Piringer 1998). It was found that the diffusion was very dependent on ethanol concentration. Only at very high ethanol concentrations (8s-100 YO)and relatively high temperatures (60 "C) could measurable permeation results be obtained. The values for the diffusion coefficient measured at 60 "C in 85 YO to 100 YOethanol ranged from 3.4 x cm% to 1.2 x lo-" cm2/s. From the values measured at 60 "C and 40 "C, diffusion coefficients at 20 "C can be estimated for high percentage ethanol in water (80 YOto 100 YO)to range between 1 x cm2/s to 3 x lo-'' cm2/s. For highly aqueous systems (0 YOto 20 YO)such an estimation is nearly impossible. However, the diffusion coefficients are likely to be much smaller than 3 x cm2k (possibly orders of magnitude lower). An attempt to estimate lag times from this for inorganic compounds like CuCI2 across thin LDPE films under practical conditions, i.e room temperature and highly aqueous systems, would lead to predicting a range between over 2 years up to 50 years or even more depending on the film thickness (10 to 50 pm). This demonstrates impressively the barrier properties of polyolefin films against inorganic structures in general. As already mentioned above, the question of reusability of plastics represents only one specific modification of functional barrier packaging design. Mass fractions of recycled plastics burried in this way range currently between 25 YOand 50 YOof the whole package structure. However, it is obvious that the economic benefit correlates with increasing the recycled mass fraction. In the almost ideal case, a homogeneous recycled plastic layer would be covered by extremely thin films with high barrier properties. Such developments have been on the market already for a long time, produced however with another intention: for instance barrier coated polymer films such as metallized, biaxially oriented polypropylene films or acrylic- or PVDC-coated films. Such thin layers were found to improve barrier properties against organic compounds by a factor of 1000 compared to the plain BOPP film (Franz 1995). From these results it can be assumed that such barrier principles are likely also to provide functional barrier efficiency against recycling-originating contaminants. The ideal case and most efficient recycled plastics packaging design, however, is the plain recycled mono-layer with direct food contact. This situation is described in the next section.
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10.3.3 Recycling of post-consumer PET for direct food contact As discussed in 10.3.1, there is an observable industrial hesitation to introduce environmentally friendly packaging solutions to the market based on recycled materials such as the closed-loop bottle recycling. Reasons for that have also been mentioned. Another reason for this hesitation can be found in the current lack of simple and economic test methods which in addition would need to be at least generally accepted procedures and, at best, standard methods. Currently available are the guidelines developed by the FDA and the US Food and Plastics Industry some years ago. These guidelines, however, were established on the basis of a very conservative approach in order to avoid any risks for the consumer. From today's point of view and with our knowledge increasing all the time, these guidelines prove too conservative and require unnecessarily enormous efforts in the performance of the underlying tests. These test schemes, also known as challenge tests, are challenging a recycling process by the artificial introduction of model contaminants, so-called surrogates. They check the cleansing efficiency or surrogate removal potential of this process including, if necessary, migration testing of food contact articles deriving from recycled plastics. In Europe, the results obtained from a European Project, AIR2-CT93-1014 (Castle 1997, Jetten et al. 1999), dealing with the question of recyclability and re-usability of food contact plastics for new food packaging applications, have been taken into consideration by a Packaging Material Expert Group on Plastic Recycling Guidelines. As a result, this expert group has recently published its conclusions on this topic as a guideline document more appropriate to the current state of the art in this matter (ILSI Europe 1998).
A challenge test case study and evaluution scheme The following describes a research work investigating the feasibility of recycling post-consumer PET into new direct food packaging (Franz et al. 1998). One of the interesting points in this study was the purification potential of modern industrial recycling processes, which are able to produce high quality recycled PET granules. Another point of interest was the question how far the actual knowledge about diffusion and migration estimation can be applied to evaluate the suitability of the recycled PET materials at the level of the granulate itself, in order to decide whether or not there is a need to carry out additional migration tests with the food contact articles manufactured from the recycled raw material. Probably the best way to investigate these items is to apply challenge tests to the recyling processes of concern. Therefore another aim of this work was to draw up a modified challenge test for post-consumer poly(ethy1ene terephthalate) PET material in order to make the test more economic and user-friendly, for instance by shortening the FDA-recommended 14 days/40 "C sorption or soaking conditions for the surrogates. A further point of interest was to design the contamination scheme in such a way that only the minimum amounts of solvent and chemical contaminants were necessary, thus avoiding production of unnecessary amounts of hazardous waste. With such optimized framework parameters, the main intention was then to evaluate the cleansing efficiency of a new commercial recycling process for postconsumer PET material collected from used soft drink bottles with the simplified challenge test. The results were expected to give a better understanding of the contaminant removal potential of the particular recycling process.
Migration of plustic. constiricents
345
The recycling process The process consisted essentially of three key steps: washing and heat-drying the incoming PET flakes obtained from grinding used soft drink bottles, (ii) remelting the PET flakes from (i) for extrusion to form new PET granules and (iii) additional solid-phase condensation, using a high vacuum high and temperatures nearly up to the melting point of PET.
The challenge test For challenging the recycling process, virgin PET flakes obtained from ground bottles were contaminated with model contaminants or so-called surrogates of different chemical structures and physical properties. The surrogates were chosen such that they represented the four FDA general categories of chemical compounds: volatile and non-polar, volatile and polar, non-volatile and non-polar and, finally, non-volatile and polar. Additionally, a wide range of functional groups was used in order to reflect the different chemical and physical properties of real-life contaminants (see Table 10-8). Table 10-8: List of the surrogates used for thc contamination cocktail, with chemical structures and properties. ~
~~
~~~
~
Substance
Structure
Functional group
Properties
l.l,l-Trichloroethane
CHyCCI3
Halogenated hydrocarbon
Volatile. polar, aggressive to PET
Hydrocarbon
Volatile, non-polar
Halogenated hydrocarbon
Volatile, medium-polar, very aggressive to PET
Hydrocarbon
Non-volatile. non-polar
Toluene
Chlorobenzene
Phenylcyclohexane
a,
I "
0
6
Non-volatile, polar
1-0ctadecanol
Methyl stearate
CH~CHZ)I.IOH CH3(CH2),,COOCH3
Alcohol
Non-volatile, polar
Ester
Non-volatile. polar
The contamination and the challenge test were carried out several times, starting at three different initial concentration levels of surrogates in PET flakes in order to check the purification efficiency over a wide concentration range. The expectation was that this test scheme would allow an extrapolation of the results to higher or lower initial concentration levels not actually measured in our challenge test. The contaminated PET flakes were then processed through the industrial purification process, entering the process at step (ii) and omitting the washing and heat drying procedure. This protocol was justified by the fact that the cleansing efficiency of a normal wash-
346
Franz
ing step is well known and well documented in the literature and because the washing conditions of the investigated process were no different to conventional washing procedures. Therefore, step (i) was omitted with the contaminated PET flakes going directly into the remelting/extrusion process. It should be noted in this context that even when the flakes are not homogeneously contaminated after contact with the surrogates, such a procedure leads automatically to a homogeneous distribution of the surrogates in the extruded granules. PET samples were taken at the beginning and at sampling points during this process and analysed to determine the concentration of surrogates in the PET material both before introduction into the process and at any relevant stage during the process. Table 10-9 summarizes the results obtained by presenting the relative concentrations of surrogates as a percentage of the initial concentration after step (ii), i.e. remelting to granulate and after step (iii), i.e. in the post-condensed final product. Table 10-9: Percentage recovery of the initial concentration in ppm of the surrogates in the PET material after remelting in the granulate (step (ii)) and in the final product (step (iii)). ~
Initial concentration Toluene
Chlorobenzene
Benzophenone
Octadecanol
Methyl stearate
granules after step (ii)
17
<<2.4 Yo
57
<<0.7 yo
93
<<0.4 %
31
5.2 %
88
5.5 Yo
146 Phenyl cyclohexane
8
~~
~
Per cent of the initial concentration found in final product after step (iii) <<2.4 Yo 0 <<1.2 o/o
<<0.7 Yo <<0.4 Yo <1.3 Yo
0 5.5 Yo
<0.5 Yo
5.8 %
<0.3 Yo
I3 Yo
<5.0 Yo
32
6.9 Yo
3.9 Yo
s4
37.6 Yo 13.0 yo
200
26.9 Yo
4.0 %
960
33.4 %
2.8 %
45
72.7 Yo
5.1 Yo
I17
14.4 Yo
154
I 17.5 Yo
383
72.1 Yo
5 90
40.') Yo
6.5 %
1753
56.0 %
5.4 %
16
22.7 Yo 51.7 %
1234
13.8 Yo
96
12.9 %
546
27.4 %
1989
38.2 %
0 <0.7 Yo
1.1 Yo
177
66
0 <<1.2 %
0 21.8 Yo
1.2 Yo
0 3.0 %
2.9 %
0 51.8 %
11.0 %
0 7.6 Yo
3.5 %
0 29.4 Yo
2.0 %
0 2.0%
0.4 Yo 4.3 %
0 26.2 %
3.9 70 3.3 Yo
0 3.8 %
Migration of plastic cotzstitueniJ
347
The table shows that the process can eliminate volatile compounds much more efficiently than non-volatile substances. Volatiles. like toluene and chlorobenzene, are already efficiently removed by step (ii) alone. Toluene was no longer measurable at a detection limit of 0.4 ppm. The other volatile, chlorobenzene, was recovered at 5.5 YO of the initial concentration after the extrusion step. After the post-condensation step, the amount of toluene in the final product was likely to be far below the limit of detection since the detection limit was already determined after the extrusion step. Chlorobenzene also could not be found above the limit of detection. These results show very impressively that a conventional recycling process (consisting of steps (i) and (ii)) for post-consumer PET removes volatile real-life contaminants very efficiently, for example solvents and fuel. An additional vacuum treatment during solid-phase post-condensation further decreases any level of volatile compounds in the final product. Elimination of non-volatile substances like phenylcyclohexane, benzophenone, octadecanol and methyl stearate turned out to be much more difficult. An average of 22 YOof the initial concentration of phenylcyclohexane remained in the granules after step (ii). But in the post-condensed final product only 3 YOof the initial concentration of phenylcyclohexane was measured. Very similar figures were obtained for octadecano1 and methyl stearate. The most challenging compound was found to be benzophenone. Half of the initial concentration (52 YO)remained after remelting and extrusion whereas 8 % was determined in the final product. Another interesting finding was that the purification effect was independent of the initial concentration of the model contaminants within the investigated contamination range (100-2000 ppm). This concentration-independence most likely permits an extrapolation of the results to real concentration levels as they occur in commercial PET recyclates from conventional recycling facilities. Verification of this correlation is still in progress within a European project (FAIR-CT98-4318) and needs further measurement, but certainly real contamination levels can be found far below our investigated contamination range (Franz and Welle 1999). Such knowledge would allow one to draw conclusions on maximum or average real life exposures of the consumer to specific recycled compounds deriving from recycled PET bottles. The following describes an example (Fig. 10-18) of how food regulatory evaluation of recycling processes and products can be achieved, taking modern knowledge of diffusion and migration models into account (Chapters 7, 8, 12 and 15). If one assumes maximum concentrations of 500 ppm (which is very conservative) for high volatility and low volatility substances in real PET charges which are introduced in step (i) of the recycling process, then one can expect concentrations of ca 50 ppm in the washed and dried flakes (Komolprasert and Lawson 1995). Steps (ii) and (iii) of the investigated process further reduce the concentration of highly volatile substances (e.g. toluene) in the condensed final product to levels below the detection limit. Substances of lower volatility (e.g. benzophenone) are reduced in concentration to about 2.5 pprn (5 '30of the initial concentration). During the manufacture of a PET bottle from the final product, a further decrease in the concentration of contaminants is to be expected (Franz et al. 1996). Considering a worst-case scenario however, i.e. no decrease in concentration during the bottle manufacturing process, then there would be 2.5 pprn contaminants in a PET bottle of mass ca 80 g and volume 1 litre. Assuming complete transfer of the contaminants, this would result in a maximum concentration of ca 0.2 ppm low volatility substances in the foodstuff. This purely arithmetic migration value (totally removed from reality) considerably exceeds the FDA allowed limit
348
Franz
U 500 ppm
Raw material PET flakes
ca 90%
step (i) washing and drying of the flakes
Washed and dried PET material step (ii) and (iii) extrusion and solid-phase condensation
M 95%
2.5 ppm
Final product of the recycling process
manufacture of a PET-softdrink bottle with a mass of 80 g and a volume of 1 litre PET-softdrink bottle Assumption: complete migration into the foodstuff Calculated concentrationin the foodstuff
I
2.5 o m
I Assumption: diffusion-controlledmigration into the foodstuff Calculated concentration in the foodstuff (aqueous or oily foodstuffs, respectively)
Figure 10-18: Scheme of a scenario based on an initial contamination of 5MJ ppm of a non-volatile substance in unwashed PET-recycling material with respect to the consequences for a softdrink bottle produced from this material and migration into the foodstuff.
of 0.01 ppm (10 ppb) and would make an experimental determination of contaminant migration necessary. With the help of scientifically recognised models for estimating diffusion out of plastics and considering a migration test according to EU Directives 82/71UEEC and 85/572/EEC (contact conditions: 10 days at 40 "C), it is possible to estimate migration values of 0.002 ppm in olive oil as a food simulant or lower than 0.001 ppm in 3 % acetic acid as the appropriate food simulant for soft drinks. The PET bottle produced from this post-consumer PET material would therefore fulfill FDA regulations with these migration values. This would be true not just for soft drinks but also for fatty foodstuffs under room temperature contact conditions. Vice versa, migration models allow a back calculation to maximum permissible contaminant concentrations in recycled PET bottle starting with the FDA prescribed migration upper limit of 0.01 ppm (10 ppb) in the foodstuff. Table 10-10 shows the calculated situation for three of the model contaminants used, based on the above mentioned diffusion model. In practical terms, this means that the investigated recycling process is able to produce recycled PET material suitable for contact with foodstuffs, as long as an initial concentration of real contaminants of 500 ppm per substance is not exceeded. However, it must be stressed that 500 ppm represents an extremely high contamination of the PET material being returned for recycling (far higher than in practice). This
Migration of plastic constitirents
349
Table 10-10: Calculated values for the maximum residual concentrations of contaminants in materials for PET bottles corresponding to a migration of 0.01 ppm in food. Model contaminant
Food simulant Olive oil
Food siniulant 3 % acetic acid
Benzophenone
9 PPm 15 PPm
20 PPm 27 PPm
Stearic acid methylester
24 PPm
40 PPm
Toluene
already follows from purely statistical considerations of the frequency of return of highly contaminated bottles and the resulting very high dilution effect. Certainly, the misuse of one PET soft-drink bottle by filling with and storage of solvents or fuel would lead to a very high concentration of this chemical in the particular PET bottle material (similar as the concentrations of the soaking experiment according to the FDA proposal). But the grinding and the mixing with uncontaminated soft-drink bottles dilute real contaminants down to a maximum in the lower pprn range. If lower concentrations of contaminants are considered (e.g. 100 ppm before washing the flakes), then under otherwise identical conditions one can expect maximum concentrations of low volatility contaminants in the final PET product of only ca 0.5 pprn and correspondingly lower migration values will be obtained. The inherent low diffusivity of PET is another safety factor here, which does not allow such high initial concentrations as discussed above to be established in real life. Concerning the FDA recommended evaluation procedure, it can be critically noted that it does not sufficiently consider the individual migration potential of different contaminants. It is, however, well known today that volatile substances in packaging materials are readily transferred to contents (due to their high diffusivitiy). On the other hand, substances having low volatility (high diffusion resistance) can only diffuse to a much lesser extent into the contents. The fact that high volatility substances having a high capacity for migration are almost completely removed in modern recycling processes is worthy of note. Finally, it must be noted that the predictive evaluation scheme as presented has recently been verified and confirmed by carrying out migration tests using PET bottles produced from a challenge-test-accompanied recovery process (Franz and Welle 1998).
10.3.4 Safety aspects related to refillable plastic bottles Refillable plastic containers composed of polyethylene terephthalate (PET) polycondensate are used for packaging beverages such as carbonated soft drinks. PET is particularly suitable for this purpose because it has a very good resistance to CO2 permeation losses, compared to other plastics materials (Steingiser 1978). But also from an ecological point of view, i.e. to reduce waste from food packaging material, refillable PET containers offer great advantages. Due to the underlying principle of a plastic bottle refill system, i.e. circulation between bottler and consumer, and due to the intrinsic interactivity of plastics with contacting chemicals, a special and possibly even unique situation arises concerning
350
Franz
the question of testing compliance with food regulations. Of course, it is well known that major soft drink manufacturers employ quality assurance practices which include visual and electronic inspections, cleaning and sanitation of these plastic refillable bottles. Concern about potential consumer misuse of such bottles, resulting in possible contamination, has led to additional safeguards during the refilling process to protect product quality, specifically through the use of in-line detection systems. Prior to cleaning, a detector system “sniffs” each bottle for the presence of volatile materials and rejects it when detected. However, there are neither any specific national or EU regulations nor a standard test currently available which could be applied by industry or enforcement laboratories. As a consequence, the food safety quality control of washed and refilled PET bottles before they go out again to the consumer is practically completely in the hands of the bottle fillers, based on their internal test regimen. Many studies, some of them highly time-consuming, have been made for determining the transfer of pollutants from possible misuse into the food (Feron et al. 1994 and literature given therein). The potential public health risks in connection with possibly misused PET refillable bottles have also been reviewed and summarized (Feron et al. 1994). From the results of all misuse studies carried out so far and from probability considerations, it is generally concluded that returnable PET bottles can be safely reused, provided that food manufacturing procedures, including visual and electronic inspection systems, are employed to eliminate abused bottles. The results elaborated so far at tremendous cost by work- and cost-intensive contamination procedures and re-migration testing of whole batteries of bottles give a more or less statistical picture of the possible range for emigration from abused bottles into refilled soft drinks. The principal disadvantage of any chemical misuse testing of refillable plastic bottles is the impossibility of mimicing the real-life situation (which cannot be defined). Consequently, common practice was and still is to select “real-life-relevant” misuse chemicals, which however means nothing more than applying representatives or model contaminants. Concerning the conditions of bottle contamination, an analogous situation occurs. In many studies, exposure conditions between 2 weeks at 40 “C and several months at room temperature have been applied (Feron et al. 1994). Furthermore, the concentrations of contaminants selected for artificial bottle contamination range from the pure, undiluted compound or commercially available formulation with a high concentration of active ingredients (and formulation solvents), to the lower concentrations of user-strength dilutions as applied in the practical situation. The question of what are the misuse conditions really cannot be answered. This remains another field of probability for consideration. The only conclusion from all this is that any chemical misuse testing has to live with conventionally agreed test protocols (which by the way is common sense and practice for any migration testing of food contact articles). As a consequence of this state of the art, the need and justification for establishing a conventional method for reproducible inertness testing of refill-bottle materials was identified in our laboratory a few years ago. In our opinion, a practical, cost-efficient and relatively quick standard test procedure which could also be used by surveillance labs was worth development. Within an European project (Castle 1997, Jetten et al. 1999), an investigation was undertaken to elucidate the feasibility of such a quick test method for refillable PET bottles, with respect to evaluating their inertness concerning the uptake and subsequent release of chemicals and sensory-active compounds. Before starting method development, the following considerations were made and
Migration of plastic constitiienls
35 1
taken into account. A principal conclusion following from the above discussion was to apply a selection of model contaminants under well-defined contamination conditions, to determine in a reproducible and comparable way the interactivity of a given PET material and to compare it directly with another. Another more pragmatic conclusion was to use only strips from the wall instead of whole bottles and to relate the measured interactivity to the contact surface area. Such a test scheme (see Fig. 10-19) would allow working with small amounts of chemicals and solvents compared to whole bottles, yet give relatively quick answers to the question what is the uptake of a chemical by the PET material in question and what is the potential for re-migration after refilling. Another aspect of this work was to find a reasonable compromise for the contamination conditions. In any case these should be always the same standard contamination conditions to allow for real comparative testing. Our approach to working with mixtures of model contaminants having different chemical structures (which however can be tested in one analytical gas chromatography run) rather than with a number of individually selected compounds (which needs much more work) may be criticized using the following argument: To justify working with mixtures of model contaminants, one needs to demonstrate how such mixture-derived values correlate with single-compound contamination results. This, however, is a critical argument in any case because all known artificial and unknown real-life contaminations have been carricd out irreproducibly at different conditions and concentrations. For instance, if at a high contaminant concentration incompatibility with the test material might be visually observed (e.g. swelling effect), the same contaminant can diffuse at lower concentrations into the bottle wall without optically changing it. The relevant question arising here is: Where is the borderline concentration which just does not lead to swelling of the polymer? This situation is the most critical one since it cannot easily be recognised by optical inspections. And it should be borne in mind that at such a borderline concentration (before reaching a plasticizing effect) the diffusion characteristics of the individual compounds are not too much influenced by each other, which justifies application of mixtures of model contaminants at lower concentrations. Further, in real life misuse with mixtures is much more likely than with single compounds. From this again a selection of model contaminants is justified, but at such concentrations as to leave the polymer visually still intact. ----+
I I I I
u1 1 ,
11 rnrn
I I
I I
I
1. Sorption phase using a set of model compounds
I
$-
I I
I
2. Extraction of absorbed
model compounds
II
I
J 3. GUFID analysis of extract
I I
Figure 10-19: Principle of chemical inertness testing of refillable PET bottles.
352
Franz
The model contaminants used then for this work (Demertzis et al. 1997) have been selected under different aspects: - Variation of chemical structureslpolarities - Variation of molecular weights - Comparison of aromatic versus non-aromatic structures - Consideration of strongly interactive compounds - Consideration of surrogates proposed by US-FDA for challenge tests - Simple analysis of all model contaminants using only one method (GCIFID). As a consequence, three sets (A, B and C) each of six model contaminants and a mixture of two chlorinated chemicals strongly interactive with polymers (Set D) were selected (see Table 10-11). Table 10-11: Sets A to D used for chemical inertness testing (molecular weight). Set A: alcohol-t ype compounds
Set B: estedketone-type compounds
Set C: hydrocarbon-type compounds
Set D: strongly interactive chlorinated compounds
Propylene glycol (76) Phenol
Toluene
Chlorobenzene (112) 1.1 ,l-Trichloroethane (133)
Menthol (156) 1.2-Decandiol
Ethyl acetate (88) Cyclohexanone (loo) iso-Amy1 acetate (130) Benzophenone (182) Linalyl acetate (196) Methyl stearatc
(174)
(299)
(218)
(94)
n-Hexanol (1 02) 2-Phenylethanol (122)
(92)
n-Heptane (100) p-Xylene (106) Limonene (136) Phenyl cyclohexane (160) Phenyl decane
Sets A and C were applied as mixtures prepared from equal weight parts of each of the contaminants. In sets B and D, the mixtures had to be diluted in a ratio 1:5 with polyethylene glycol 400 (PEG 400). This was done to reduce vapour pressure and the agressiveness of set B and D compounds, because these compounds are sorbed to a relatively high degree into the PET matrix thus swelling the material. From the sorption experiments carried out in this way, it became evident that chemicals can be absorbed into the bottle wall of refillable PET bottles to varying extents depending on the chemical nature and molecular weight of the chemical compound. The results indicated that under given standard contamination conditions the sorbed amounts and the sorption patterns obtained can be used to evaluate the inertness of a PET plastic bottle. This was found to be a crucial key element for a quick inertness test procedure. Comparative checks between the behaviour of bottle wall strips and whole bottle tests indicated also satisfying correlations between strip and bottle tests which might be an interesting tool for predicting whole bottle behaviour (Nielsen et al. 1997) . Finally, the results confirmed that, due to sorption into the bottle wall a remigration potential can be established therein, which could be transferred later to the foodstuff after refill if not removed by washing and passing the electronic/optical inspection system of a refill line.
Migration of p~asricconslitiients
353
On the basis of these results the PET inertness test has been further developed, simplified and standardized within another European project, SMT4-CT96-2129. The principle of the test is to apply only one cocktail of model compounds and to determine quantitatively the absorbed amounts of model compounds as a final bottle-specific interactivity value in mg sorbed compound per dm2 bottle wall area (Palzer and Franz 1998). For illustration, Fig. 10-20 shows graphically a direct comparison of two commercial PET grades with regard to their chemical inertness. From this figure it can be recognised that this standard test can easily be used to check improvements in inertness behaviour of PET materials, an aspect which gains increased importance today when bottle fillers are changing more and more from glass bottling systems to PET, even for very off-taste sensitive products like mineral water. It should also be noted that the test is most useful in the comparative mode and that any reference material can be used. In order to have access to a general reference material, this European project aims also to produce a reference material with certified interactivity values. Finally, once an acceptable and safe interactivity value has been agreed upon, the method could also provide a manageable test basis for legal compliance testing of refillable plastic bottles drawn from the market. (0
-.-
....
.
-.
...
I
Qt
.....................
......................
............
7
...........
.............
.................................................... .................................................. ....................
toluene
phenol
limene
menthol
phenykydo- benzophenon hexane e
Model compounds Figure 10-20: Comparison of two different PET materials with respect to their interactivity to model compounds.
354
Franz
References Ashby R. Cooper I, Harvey S and Tice P. 1997,Food Packaging Migration and Legislation. Pira International, Leatherhead 1997. Baner L, Brandsch J, Franz R and Piringer 0. 1996. The application of a predictive migration model for evaluating the compliance of plastic materials with European food regulations. Food Additiv. Contam. 13 (5). 587401. Baner L and Piringer 0 G, 1991. Prediction of solute partition coefficients between polyolefins and alcohols using the regular solution theory and group contribution methods. Ind. Eng. Chem. Res.. 30 (7). 1 5 0 ~ 1 5 1 5and references given there. Baner L and Piringer 0 G. 1994, Liquidlgas partition coefficients of aroma compounds and n-alkanes between aqueous ethanol mixtures and nitrogen. J. Chem. Eng. Data 1994,39 (2). 341-348 and references given there. Begley T H and Hollifield H C, 1995, Food Packaging Made from Recycled Polymers: Functional Barrier Considerations. In: Plastic, Rubber and Paper Recycling: A pragmatic approach. C.P. Rader, S.D. Baldwin. D.D. Cornell, G.D. Sadler and R.E. Stockel (eds.) ACS Symposium Series 609, American Chemical Society: Washington DC. 1995.pp. 445457. Berghammer A, Biicherl T and Malter C. 1994. Rapid extraction method for the determination of potential migrants from flexible packaging coated materials. Verpack.-Rundsch. 45 (7). 4145. Biedermann M. Grob K, Bronz M, Curcio R, Huber M and Lopez-Fabal F, 1996. Bisphenol-A-diglycidyl cther (BADGE) in edible-oil-containing canned foods: determination by LC-LC-Fluorescence detection. Mitt. Gebiete Lebensm. Hyg. 87. 547-558. Bush J. Gilbert J and Goenaga X, 1994, Spectra for identification of monomers in food packaging. Kluwer Academic Publishers, Dordrecht - Boston - London 1994. BgVV, 1995, Statement of the German Commission on Plastics of the BgVV Bundesgesundheitsblatt 1995,38,73-74. Castle L. 1997. Final Report of EU project AIR2-CT93-1014 “Program to establish criteria to ensure the quality and safety of recycled and re-used plastics for food packaging.” Brussels: Agro-Industrial Research Programme, December 1997 (available from [email protected]). CEN, 1998a), European Standards ENlENV 1186. Materials and Articles in contact with foodstuffs Plastics, Part 1 - 14. European Committee for standardization, Brussels, August 1998. CEN. 1998b), European Standards ENlENV 1186. Materials and Articles in contact with foodstuffs Plastics, Part 15 (draft version). European Committee for standardization, Brussels. August 1998. CEN, 1999, European Standards ENV 13130. Materials and Articles in contact with foodstuffs - Plastics, Part 1 - 8. European Committee for standardization. Brussels, 1999. Chapman J R, 1986, Practical organic mass spectrometry. John Wiley & Sons, New York 1986. Dc Kruijf N and Rijk M A H 1988. Iso-octane as fatty food simulant: possibilities and limitations. Food Additiv. Contam. 5,467483. Demertzis P G, Simal-Gandara J and Franz R, 1995. A convenient group method for the gas chromatographic determination of aliphatic diamines in the four official EC food simulants. Deutsche Lebensmittel-Rdsch. 91 (2), 35-38. Demertzis P G. Johansson F. Lievens C and Franz R, 1997, Studics on the development of a quick inertness test procedure for multi-use PET containers - sorption behaviour of bottle wall strips. Packaging Technology and Science 10.45-58. DIN, 1994. Deutsche Norm DIN 32645: Chemische Analytik: Nachweis-, Erfassungs- und Bestimmungsgrenze: Ermittlung unter Wiederholbedingungen: Begriffe. Verfahren, Auswertung. Deutsches Institut fur Normunge.V., Berlin. 1994. European Commission, 1994. Council Directive 94/62/EEC on Packaging and Packaging Waste. Official J. European Communities 1994. L365, 1&23. European Commission. 1999. Draft Slh Amendment of EU Directivc 90/128/EEC, DGIII, 26Ih April 1999. EURACHEM. 1993, Guidance Document No. WELAC and No. WGD 2: Accreditation for chemical laboratories: Guidance on the interpretation of the EN 45000 series of standards and ISO/IEC Guide 25. 1993. EURACHEM secretariat, PO Box 46. Teddington. Middlesex. T W l l ONH, UK. EURACHEM. 1996. Method validation - a laboratory guide. EURACHEM Secretariat. Laboratory of the Government Chemist, Teddington. UK, 1996. FAO, 1998. Validation of analytical methods for food control. Report of a Joint FAOlIAEA Expert Consultation. December 1997,F A 0 Food and Nutrition Paper No. 68, FAO. Rome. 1998. Feron V J, Jetten J. de Kruijf N and van den Berg F, 1994. Polyethylene terephthalate bottles (PRBs): a health and safety assessment. Food Additiv. Contam. 11(5). 571-594. ~
.
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Franz R, Huher M and Piringer 0 G, 1994, Testing and evaluation of recycled plastics for food packaging use - possible migration through a functional barrier. Food Additives and Contaminants 1994, 11 (4). 479496. Franz R. 1995. Permation of flavour compounds across conventional as well as biodegradeable polymer films. In: Ackermann, Jagerstad and Ohlsson (eds.): “Foods and Packaging Materials - Chemical Interactions”. The Royal Society of Chemistry. Cambridge. 199.5,pp. 45-50. Franz R, Huher M. Piringer 0 G, Damant A P, Jickells S M and Castle L. 1996. Study of Functional Barrier Properties of Multilayer Recycled Poly(ethy1ene terephthalate) Bottles for Soft Drinks. J. Agric. Food Chem. 44,892-897. Franz R, Huher M and Piringer OG , 1997, Presentation and experimental verification of a physicomathematical model describing the migration across functional barrier layers into foodstuffs. Food Additiv. Contam. 14 (6-7). 627440. Franz R and Rijk R, 1907, Development of methods of analysis for monomers and other starting suhstances with SML andlor QM limits in Directives 90/128/EEC and 92/39/EEC. European Commission BCR information: Chemical analysis. EU report 17610 EN. ECSC-EC-EAEC, Brussels Luxembourg 1997. Franz R, Huber M and Welle F, 1998, Recycling of post-consumer poly(ethy1ene terephthalate) for direct food contact application - a feasibility study using a simplified challenge test. Deutsche Lebensm-Rdsch. 94 (9). 303-308. Franz R and Welle F, 1998, Submission CTS 59489 to US FDA, Division of Petition Control, HFS-215. Office of Premarket Approval, Washington DC. 1998: Results published in Deutsche Lehensm.Rundschau 95 (10). 424427. Franz R and Welle F, 1999, Analytical screening and evaluation of post-consumer PET recyclate materials from the market with respect to reuse for food packaging application. Deutsche Lebensm-Rdsch. 95 (3). 94100. Gmeiner M. Demertzis P and Franz R, 1998. Development of a HPLC method for the sensitive determination of carhonyl chloride in polycarbonate for food contact articles. Deutsche Lehensm.-Rdsch. 94 (2). 4145. Hampe D and Piringer 0, 1998, Studies on the permeation of inorganic salts through plastic films. Food Additives and Contaminants 15 (2). 209-216. Horwitz W. 1988. Protocol for the design. conduct and interpretation of method performance studies. Pure and Applied Chem. 60,855464. Horwitz W. 1995. Protocol for the design, conduct and interpretation of method performance studies. Pure and Applied Chern. 67.331-343. ILSI Europe, 1998, Recycling of plastics for food contact use. Guidelines prepared under the responsihility of the ILSI Europe Packaging Material Task Force, Brussels, Belgium May 1998. ISO. 1994. International Standard I S 0 5725: “Accuracy (trueness and precision) of measurement method and results”. 1994-12. Jcttcn J. de Kruijf N and Castle L, 1999, Quality and safety aspects of reusable plastic food packaging materials: A European study to underpin future legislation. Food Additiv. Contam. 16 (1). 25-36. Katan L L. 1996 a). Effects of migration. In: L.L. Katan (ed.): Migration from food contact materials. Blackie Academic & Professional London 1996 (Chapter 2). Katan L L (ed.), 1996 h). Migration from food contact materials. Blackie Academic & Professional London 1996. Komolprasert V and Lawson A, 1995. Residual contaminants in recycled poly(ethy1ene terephthalate) effects of washing and drying. In: ACS Symposium series 609. Plastics. Rubber and Paper Recycling: A pragmatic approach. K.W. Hutchinson and N.R. Foster (editors), American Chemical Society: Washington DC, 1995, pp. 435444. Laoubi S. Feigenbaum A and Vergnaud J M. 1995. Safety of Recycled Plastics for Food Contact Materials: Testing to Define a Functional Barrier. Packaging Technology and Science 8. 17-27. Laoubi S and Vergnaud J M, 1995, Process of Contaminant Transfer Through a Food Package Made of a Recycled Film and a Functional Barrier. Packaging Technology and Science 8,97-110. Laoubi S and Vergnaud J M, 1996, Theoretical treatment of pollutant transfer in a finite volume of food from a polymer packaging made of a recycled Film and a functional barrier. Food Additives and Contaminants 13 (3), 293-306. Lee M L. Yang F J and Bartle K D. 1984, Open tubular column gas chromatography. Theory and practice. John Wiley & Sons, New York 1984. Nielsen T, Damant A P and Castle L, 1997. Validation studies of a quick test for predicting the sorption and washing properties of refillable plastic bottles. Food Additiv. Contam. 14 (6-7), 685493.
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Patzer G and Franz R, 1998, Chemical inertness of multi-trip PET beverage bottles. Kunststoffe plast europe 88 (6). 2&21. Paseiro Losada P, Simal Lozano J, Paz Abuin S, Lopez Mahia P and Simal Gandara J. 1993, Kinetics of the hydrolysis of bisphenol A diglycidyl ether (BADGE) in water-based food simulants. Fresenius J. Anal. Chem. 345,527-532. Philo M R, Jickells S M, Damant A P and Castle L, 1994, Stability of plastics monomers in food-simulating liquids under European Union migration test conditions. J. Agric. Food. Chem. 42,1497-1501. Philo M R, Damant A P and Castle L, 1997, Reactions of epoxide monomers in food simulants used to test plastics for migration. Food Additiv. Contam. 14 (1). 75-82. Piringer 0, 1980, Kinetik der Hydrolyse von Epichlorohydrin in verdiinnten wasserigen Losungen. Deutsche Lebensm.-Rdsch. 76 (1). 11-13. Piringer 0, 1990, Ethanol und EthanollWasser-Gemische als Priiflebensmittel fur die Migration aus Kunststoffen. Dtsch. Lebensm.-Rundsch., 86 (2), 35-39. Piringer 0 G (ed.), 1993, Verpackungen fur Lebensmittel - Eignung, Wechselwirlungen. Sicherheit. VCH Verlagsgesellschaft Weinheim-New York-BaseLCambridge (Chapter 4). Piringer 0,Franz R, Huber M, Begley T H and McNeal T P, 1998, Migration from food packaging containing a functional bamer: mathematical and experimental evaluation. J. Agric. Food Chem. 46, 1532-1538. Reynier A, Dole P and Feigenbaum A, 1999, Prediction of worst case migration: presentation of a rigorous methodology. Food Additiv. Contam. 16 (4), 137-152. Rijk R, 1993, Migration cells to test volatile substances. Proceedings International Conference “Materials for Food Packaging”, March 10 and 11,1993, PACKFORSK Gothenburg, Sweden. Roubtsova S, Hollander J and Franz R, 1997. A rapid and convenient method for the quantitative determination of bisphenol A diglycidyl ether (BADGE) in foodstuffs. Deutsche Lebensm.-Rdsch. 93 (9). 273-276. Rulis A M. 1986, De minimis and the threshold of regulation. In: Food Protection Technology, C.W. Felix (ed.), Chelsea, Michigan, USA: Lewis Publishers 1986, pp. 29-37. Scheirs J, 1998, Polymer Recycling - Science, Technology and Aplications. John Wiley & Sons, Chichester - New York - Weinheim - Brisbane - Singapore -Toronto 1998. Schomburg G, 1987, Gaschromatographie - Grundlagen, Praxis, Kapillartechnik. 2. Auflage. VCH Verlagsgesellschaft mbH, Weinheim, 1987. Simal GAndara J, Lopez Mahia P, Paseiro Losada P, Simal Lozano J and Paz Abuin S, 1993, Overall migration and specific migration of bisphenol A diglycidyl ether monomer and m-xylylenediamine hardener from an optimized epoxy-amine formulation into water-based food simulants. Food Additiv. Contam. 10 (5). 555-565. Steingiser S, Nemphos S P and Salame M. 1978, Barrier polymers. In: Kirk-Othmer Encyclopedia of Chemical Technology, 3rdedn, John Wiley/lnterscience, New York 1978. Summerfield W. Goodson A and Cooper I. 1998, Survey of Bisphenol A diglycidyl ether (BADGE) in canned foods. Food Additiv. Contam. 15 (7), 818-830. Tice P, 1997, European Committee for standardization (CEN) - Progress with standard test methods. In: R. Ashby, I. Cooper, S. Harvey and P. Tice: Food Packaging Migration and Legislation. Pira International, Leatherhead 1997 (Appendix to Chapter 2, p 37). Tice P and Cooper I, 1997, Rationalizing the testing of food contact plastics. In: R. Ashby, I. Cooper, S. Harvey and I? Tice: Food Packaging Migration and Legislation. Pira International, Leatherhead 1997 (Chapter 5, p 155). Thompson M and Wood R, 1993, The International harmonised protocol for the proficiency testing of (chemical) analytical laboratories. Pure and Applied Chem. 65,2123-2144. Thompson M and Wood R. 1995, Harmonised guidelines for internal quality control in analytical chemistry laboratories. Pure and Applied Chem. 67,49 56. Till D E, Ehnthold D, Schwope A D, Sidman K R, Whelan R H and Reid R C, 1983, A study of indirect food additive migration. Final summary report. Arthur D. Little Inc. 1983 (Chapter 4). Till D, Schwope A, Ehnthold D, Sidman K, Whelan R, Schwartz P and Reid R, 1987, Indirect food additive migration from polymeric food packaging materials. CRC Critical Reviews in Toxicology,18 (3). 161-188. US EPA, 1995, Guidance for methods development and methods validation for the Resource Conservation and Recovery Act (RCRA) Program, Washington, USA, 1995. US FDA, 1987, General Principles of Validation, Center for Drug Evaluation and Research (CDER), Rockville, Maryland, USA, May 1987.
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US FDA, 1992, Food and Drug Administration: Points to consider for the use of recycled plastics in food packaging: chemistry considerations. Chemistry Review Branch, Office of Pre-market Approval, HFS-247. Washington DC, December 1992. US FDA, 1993 a), Technical Review Guide: Validation of chromatographic methods. Center for Drug Evaluation and Research (CDER), Rockville, Maryland, USA, 1993. US FDA, 1993 b), Food and Drug Administration:. Food Additives: threshold of regulation for substances used in food contact articles. Federal Register 1993.58.52719-52729. US NFPA, 1995, Guidelines for the safe use of recycled plastics for food packaging applications. Plastics Recycling Task Force. National Food Processors Association. Washington DC: Society of Plastics Industry Inc., March 1995. Van Battum D, 1996. Alternative Fatty Food Simulants - A fact finding exercise. EU Commission Research Report N33, Revision 1,February 1996. Vom Bruck C.G., Bieber W-D and Figge K. 1986. Interactions between food and packaging materials and its consequences on migration. In M. Mathlouti (ed.): Food packaging and preservation. Theory and practice. Elsevier Applied Science London 1986, 3946. Wegscheider W, 1996, Validation of Analytical Methods. In: H. Guenzler (ed.): Accreditation and quality assurance in analytical chemistry. Springer Verlag. Berlin, Germany, 1996.
Reactivity in Molecular Crystals Edited by Yuli Ohashi Copyright @ K d a o r h a Ltd .Tokyo. 1999
11 Migration from food packaging: Regulatory considerations for estimating exposure Timothy H. Begley
11.1 Introduction The law governing food packaging in the United States is the Federal Food, Drug and Cosmetic Act of 1958, as Amended. Since 1958 this law has required premarket approval of all food packaging materials because these materials meet the general definition of a food additive. That is, food packaging materials are considered food additives because during the intended use of these materials, substances from these materials may reasonably be expected to become a component of the food, therefore affecting the characteristics of the food. Because of these properties, food packaging materials are subject to regulation in the US. These regulations are specified in the Code of Federal Regulations, chapter 21, parts 170-199. Regulations for food additives are established by petitioning the Food and Drug Administration (FDA) for permission to market the food packaging material. The FDA evaluates the food packaging material for safety and, if it can be concluded from the evidence presented in the food additive petition, that there is a reasonable certainty of no harm to the consumer, the packaging material can be marketed. Safety assesments are made from dietary exposure estimates from migration data contained in the petition. The petition generally contains the following information: a. Identity of the additive/polymer: The name and all pertinent information concerning the additive/polymer that is the subject of the petition, including the chemical identity and composition of the substance: its physical, chemical, and biological properties and the specifications prescribing the minimum content of the desired component(s), and identification of the reaction byproducts and other impurities which must be limited must be supplied. The information on chemical identity and composition should include the systematic chemical name, preferably in accordance with Chemical Abstracts Service (CAS) nomenclature guidelines or IUPAC name, and should also include a representative chemical structure (s) and a CAS registry number(s) . For polymers, information on the weight average (M,)and number average (M,)molecular weight, the molecular weight distribution, and the methods used for their determination is submitted. If the molecular weight is not readily obtainable, other properties of the polymer that are functions of the molecular weight, such as the intrinsic or relative viscosity or the melt flow index, are supplied. b. Use: The maximum use levels of the additive and the types of food-contact articles in which it may be used must be provided. For additives “use level” refers to the concentration of a substance in the food-contact article, not in the food itself. The range of possible uses of the additive (e.g., films, molded articles, coatings, etc.) should be described. The maximum thickness and density is also required. Detailed informa-
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tion on the stability of the additive or polymers relating to the intended conditions of use is also included. Lists of the types of food (with examples) expected to be used in contact with the food packaging materials and the maximum temperature and time conditions of the food in contact, as classified in Tables 11-1 and 11-2 must also be supplied. Table 11-1: Classification of raw and processed foods.
I.
Nonacid, aqueous products; may contain salt or sugar or both (pH above 5.0). e.g. raspberries, maple syrup, consomme, ripe olives.
IT.
Acid, aqueous products: may contain salt or sugar or both, and including oil-in-water emulsions of low- or high-fat content, e.g. vinegar, mayonnaise, orange juice, cream dressing.
111. Aqueous, acidic, or nonacid products containing free oil or fat; may contain salt, and
including oil-in-water emulsions of low- or high-fat content, e.g. crab, lobster, ground beef, bacon, chicken. oleomargarine. IV.
Dairy products and modifications: A. Water-in-oil emulsions, high- or low-fat, e.g. chedar cheese, swiss cheese, butter. B. Oil-in-water emulsions, high- or low-fat, e.g. milk, ice cream, cottage cheese, sweet cream (40 %).
V.
Low-moisture fats and oil, e.g. Lard, peanut oil
VI.
Beverages: A. Containing up to 8 % of ethanol, e.g. beer B. Nonalcoholic, e.g. soda C. Containing more than 8 % of ethanol. e.g. distilled spirits
VII. Bakery products other than those included under Type VIII or IX, e.g. wheat bread, waffels, doughnuts, sugar cookies, mince pie, biscuits
VIII. Dry solids with surface containing no free fat or oil, e.g. macaroni, shreaded wheat, corn meal, coffee.
IX. Dry solids with the surface containing free fat or oil, e.g. potato chips, french fried potatos, broiled meat and fish, fried chicken, popcorn.
c. Intended technical effect: Data showing the additive or polymer can achieve the intended technical effect and that the proposed use level is the minimum level required to accomplish the effect must be presented. For a food contact substance, “technical effect” refers to the effect on the food package or processing equipment, not on the food. An example is the effect of an antioxidant on a particular polymer. In the case of a new food-contact polymer, data must be presented that demonstrate the particular properties of the polymer are useful for food-contact applications. This information is frequently available in product technical bulletins.
Migriztion from food packaging: Regitlotory consirlerations for estimating exposure
361
Table 11-2: Conditions of Use and General Testing Protocols for Food Packaging. A.
High temperature, heat sterilized or retorted above I0O"C (212 O F ) .
10 % Ethanol" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
121 "C (250 "F) for two hours
50 % Ethanol. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71 "C (160°F) for two hours
Food Oil ( e g . corn oil) or HB307 or Miglyol 812TM.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
121 "C (250°F) for two hours
or 50 % or 95 % Ethanol"
................
121 "C (250°F) for two hours
After two hours at elevated temperatures, continue the tests at 40°C (104°F) for 238 hours to a total or240 hours (10 days). Analyze the test solutions at the end of the initial two hour period, and after 24, 96 and 240 hours.
"
B.
Boiling water sterilized. The protocol remains the same as for Condition of Use A except that the highest test temperature is 100°C (212 O F ) .
C.
Hot filled or pasteurized above 66 "C (150 OF). Add solvents to the test samples at 100°C (212"F), hold for 30 minutes, and then allow to cool to 40°C (104°F). Maintain the test cells at 40°C (104°F) for ten days with samples taken for analysis after the intervals indicated for the previous protocols.
Alternatively, perform migration studies for 2 hours at 66°C (150°F) followed by 238 hours at 40°C (104°F). The longer time at the lower temperature (2 hours at 66°C vs 30 minutes at 100°C) compensates for the shorter time at 100°C. D.
Hot filled or pasteurized below 66°C (150°F).The protocol is analogous to that for C except that all solvents are added to the test samples at 66°C (150°F) and held for 30 minutes before cooling to 40°C (104°F).
E.
Room temperatiire filled and stored (no thermal ireatmeni In {he container). Conduct migration studies for 240 hours at 40 "C (104 O F ) . Analyze the test solutions after 24,48,120 and 240 hours.
F.
Refrigerated storage ('no thermal treatment in the container). The protocol is identical to that for E except that the test temperature is 20°C (68°F).
G.
Frozen storage (no thermal treatment in the container). The protocol is identical to F except that the test time is five (5) days.
H.
Frozen or refrigerated storage; ready-prepared foods intended to he reheated in container at time of irse:
10 YO Ethanol. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
100°C (212°F) for two hours
Food Oil (e.g., corn oil) or HB307 or Miglyol 812TM.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
100°C (212°F) for two hours
or 50 % or 05 % Ethanol. . . . . . . . . . . . . . . . . . . . . . . . . . . .
100°C (212 O F ) for two hours
d. Migration and analytical methodology: The petition should also provide sufficient information to estimate of the daily intake of the additive, i.e., consumer exposure. The estimated daily intake of the additive in the daily diet is obtained through simulations of time and temperature conditions designed to imitate the processing and storage of food. From analyzed or estimated levels of an additive in food or foodsimulating solvents, the concentration of the additive expected in the daily diet is calculated.
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Begley
The concentration of an additive in the daily diet, and hence exposure, may be determined from measured levels in food, or in food-simulating solvents, or estimated based on formulation or residual levels of the substance in the food contact article and the assumption of 100% migration of the food contact substance to food. Although FDA has always accepted reliable analyses of additives in real foods, in practice, many analytes are difficult to measure in food. As an alternative, petitioners may submit migration data obtained with food-simulating solvents, that can reproduce the nature and amount of migration of the additive into food. Because food packaging may contact many foods with different processing conditions and shelf lives, the migration data submitted must reflect the most severe temperaturehime conditions to which the food-package containing the additive food will be exposed. Migration studies should be carefully designed to reflect the intended uses of the food package.
11.2 Estimating the exposure to components of food packaging The major purpose for performing migration studies is to estimate exposure to food packaging components. Exposure is calculated to determine an estimate of daily intake (EDI). The ED1 for a particular migrant is compared with the acceptable daily intake (ADI) of the migrant, as determined by FDA toxicologists. An estimate of the exposure to an additive in the diet is determined by combining migration data from food simulants or actual foods with information on the uses of food packaging that may contain the additive. This information includes food type distribution factors, and the fraction of the daily diet expected to contact specific packaging materials i.e., consumption factors (CF). Consumption factors are obtained by using information on U.S. food packaging markets to estimate the fraction of the diet likely to contact broad categories of food packaging (i.e., glass, metal, plastic, paper) as well as specific types of food-contact polymers. These values are used by FDA, unless there is justification for the use of other more appropriate values. To account for the variable nature of food contacting each packaging material, food type distribution factors (fr),are calculated for each material to reflect the fraction of all food contacting each material that is aqueous, acidic, alcoholic and fatty. The concentration of the additive in each type of food with which it comes in contacts is obtained by multiplying the individual f r value by the amount of migration measured or calculated by using a food simulant appropriate for that food type. By summing over the four broad food types (aqueous, acidic, alcoholic, and fatty ), a weighted average of migration is obtained. Multiplying this value by the CF gives the concentration of the migrant in the total diet. The total dietary concentration is calculated as follows: 4
Dietary Concentration = CF . C (Mi . fT) i=l
(11-1)
where M iis the concentration of the migrant in the ith food-simulating solvent. The values FDA uses for CF and f T are listed in Tables 11-3 and 11-4. With these values and the migration values, dietary concentrations can be calculated for exposure estimates.
363
Migration from food packaging: Regulrtory corisidrrations for estiniating exposure Table 11-3: Consumption Factors used for Estimating Exposures (CF). CF"
Package Category
CF'
Glass
0.1
Adhesives
0.14
Metal- Polymer coated
0.17
Retort pouch
0.05
Metal- Uncoated
0.03
Microwave susceptor
0.01
Paper- Polymer coated
0.2
Paper- Uncoated
0.1
Polymer
0.4
Package Category A. General
B. Polymer Pol yolefins"
0.35
PVC
0.1
LDPE
0.116
- rigid
0.05
LLDPE
0.064
- semirigid
0.05
HDPE
0.133
Polyester
0.05
PP
0.040
Cellophane
0.01
0. I
Nylon
0.02
0.15
Polystyrene -
impact
0.04
Acrylics, phenolics, etc.
-
non-impact
0.06
EVA
0.02
All Others'
0.05
Except for metal-polymer coated, polyolefins, acrylics, and phenolics, these Cfs have been rounded lo one significant figure from those reported in the 1988 Recommendations. '-The CF for polyolefins is currently subdivided as follows: LDPE, 0.18; HDPE, 0.13; PP, 0.02. If polyolefins coverage only involves PP. a minimum CF of 0.05 is used. '- As discussed in the text. a minimum CF of 0.05 will he used initially for all exposure estimates.
"-
364
Begley
Table 11-4: Food-type distribution factors (fT). Package Category
Food-Type Distribution
(fT)
Aqueous"
Acidic"
Alcoholic
Fattv
A. General Glass
0.08
0.36
0.47
0.09
Metal- Polymer coated
0.16
0.35
0.40
0.09
Metal- Uncoated
0.54
0.25
0.01h
0.20
Paper- Polymer coated
0.55
0.04
0.01h
0.40
Paper- Uncoated
0.57
0.01h
0.01h
0.41
Polymer
0.49
0.16
0.01h
0.34
Polyolefins
0.67
0.01h
0.01h
0.31
Polystyrene
0.67
0.01h
0.01"
0.31
-impact
0.84
0.016
0.04
0.10
-nonimpact
0.5 1
0.01
0.01
0.47
Acrylics, phenolics, etc.
0.17
0.40
0.3 1
0.12
PVC
0.01h
0.23
0.27
0.49
Acrylonitrile. ionomers, PVDC
0.Olh
0.01"
O.Olh
0.97
Polycarbonates
0.97
0.01h
0.01h
0.01b
Polyesters
0.01h
0.97
0.01h
0.01h
EVA
0.30
0.28
0.28
0.14
Wax
0.47
0.01h
0.01h
0.51
Cellouhane
0.05
0.01h
0.01h
0.93
B. Polymer
"-For 10 % ethanol as the food simulant for aqueous and acidic foods, the food-type distribution factors should be summed. h- 1 % or less
11.3 Establishing a threshold policy for regulating food contact materials In some food packaging applications, the amount of migration can be considered so small as to be negligible and therefore presents no public health or safety concern. In an effort to improve and speed the food additive petition process and focus resources on issues of major public health impact, FDA has adopted a threshold policy (Federal Register, 1995) that defines this negligible exposure from migration. To develop this policy on negligible exposure, FDA considered the following. Toxicological data have shown that carcinogenic and noncarcinogenic toxic effects caused by the ingestion of chemical substances occur in predictable dietary concentration ranges. Specifically, carcinogenic potencies are know to be lognormally distributed (Rulis, 1992). Because these potencies have a wide distribution, it is possible to
Migration from food packaging: Regulatory cotzsiderations for estiniating exposure
365
probablistically define a specific level of dietary exposure or a “threshold of regulation” that is well below the range of dietary concentrations that typically induce toxic effects. As a result, those substances present in the daily diet at levels at or below the threshold would not require the extensive safety review and rulemaking process that are normally required to obtain an amendment to the food additive regulations. The dietary concentration chosen as the threshold of regulation must be low enough to ensure that the public health is protected, even in the event that a substance exempted from regulation as a food additive is later found to be a carcinogen. Carcinogens and substances that may be carcinogens are excluded from the regulation (Code of Federal Regulations, 170.39 (a)(l)) because the use of carcinogens as food additives is prohibited by the Delaney Clause of the US Federal Food, Drug and Cosmetic Act (section 409 (c)(3)(A)). Because the likelihood of a substance posing a health hazard depends on its dietary concentration and toxic potency, the agency considered both of these factors in establishing a threshotd of regulation level. FDA reasoned that the degree of effort expended in its review of the safety of a substance should be related to the health risk and has infrequently required long-term toxicity testing for substances migrating into food at low levels. Thus in selecting a threshold of regulation level, FDA initially considered short-term toxicity data. Although many of the unstudied substances that will be reviewed under the regulation will not have been subjected to toxicological oral feeding studies, by using a probablistic approach, the range of toxic potency for an unstudied compound can be predicted based on an analysis of the toxic potencies of a large number of representative compounds. A probablistic approach used to analyze data on 18000 acute oral feeding studies in rats and mice showed that all the acute toxic effects occurred above 1000 pg/kg on a dietary basis (Rulis, 1989).The large number and wide variety of chemicals used in this analysis, make it representative of the substances used in the manufacture of food-contact articles. Therefore, this probablistic analysis was used to predict the upper-bound dietary concentration at which an unstudied chemical (i.e., one that has not been the subject of toxicological feeding studies) is likely to cause acute toxic effects. The agency also considered the toxic effects that result from chronic exposure to chemical substances. The results of chronic oral feeding studies of 2-years duration on 220 compounds have shown that only five of the 220 chemicals exhibited toxic effects below 1 mg/kg. All five of the chemicals that were toxic at levels below 1 mg/kg, on a dietary basis, were pesticides, compounds that would, based on their pesticidal activity, be expected to be more toxic than most substances (Frawley, 1967). However, even among these 5 pesticides, none exhibited toxic effects at dietary concentrations below 0.1 mgkg. On the basis of the results of these analyses, FDA concluded that the noncarcinogenic toxic effects caused by the majority of unstudied compounds would be unlikely to occur below dietary concentration of 1 mg/kg. To provide an adequate safety margin, however, the dietary concentration chosen as a level that presents no regulatory concern should be well below 1 mg/kg. Therefore, FDA established a dietary concentration of 0.5 pg/kg (0.5 ppb) as the threshold of regulation for substances used in food contact articles. A 0.5 pg/kg (0.5 ppb) threshold is 2000 times lower than the dietary concentration at which the vast majority of studied compounds are likely to cause noncarcinogenic toxic effects and 200 times lower than the chronic exposure level at which potent pesticides induce toxic effects. FDA believes that these safety margins,
366
Begley
which are larger than the 100-fold safety factor that is typically used in applying animal experimentation data to humans (21 CFR 170.22), support a conclusion that substances consumed in a dietary concentration at or below 0.5 pg/kg are not of concern. An additional consideration in establishing a threshold of regulation is that a substance that has not been tested for carcinogenicity may later be found to be a carcinogen. FDA used potency data on a large number of known carcinogens to estimate the risk of this possibility. These data were obtained from a carcinogenic potency data base (Gold et al., 1984, 1986, 1987) that included data on more than 3500 long-term chronic animal studies of 975 chemicals. FDA restricted its analysis to 477 animal carcinogens that were the subject of oral feeding studies showing a statistically significant increase in the incidence of animals with specific neoplasms (p<0.01) (Rulis, 1992). In those cases where multiple studies had been carried out on a specific chemical, the carcinogenic potency chosen represented the most sensitive speciesisexiorgan combination. Finally, in assessing the appropriate dietary concentration level to use as the threshold of regulation level, FDA has assumed that the distribution of carcinogenic potencies of the 477 chemicals studied is representative of all known and unknown carcinogens, and that it is very unlikely that an unstudied compound would both be a carcinogen and have an intrinsic carcinogenic potency greater than observed for the studied compounds. On the basis of the range of potencies exhibited by these 477 animal carcinogens, FDA has determined that most known carcinogens pose less than one in a million lifetime risk if present in the diet at 0.5 pglkg (Rulis, 1992). Therefore, a 0.5 yg/kg dietary concentration takes into consideration the possibility that a substance exempted from regulation as a food additive is later shown to be a carcinogen. FDA also concluded that establishing a 0.5 pg/kg dietary concentration as the threshold of regulation is appropriate because it corresponds to a migration level that is above the measurement limit for many of the analytical methods used to quantify migrants from food-contact materials. Thus, decisions are usually made based on dietary concentrations that result from measurable migration into food or food-simulating solvents rather than on worst-case estimates of dietary concentration based on the detection limits of the methods used in the analysis.
11.4 Evaluating migration from food packaging materials The first step in evaluating the exposure and safety of food packaging materials is to understand the mechanism by which components of food packaging enter the food and the amount of these components in the food. Historically the major detailed studies on the migration from food packaging materials started in the 1970s. During the 1970s Figge (1972, 1980) studied the migration of antioxidants from HDPE, PVC and PS into food oils and fat simulants. These studies showed that the migration to the oils and fat simulants was generally predictable. The migration of the antioxidant butylated hydroxy toluene (BHT) and two hydrocarbons (C18H38and CZ3Hbh)from polyolefins (LDPE, HDPE, PP, and polyethylene with 5 % and 13 % vinyl acetate copolymer [EVA]) into heptane, water, ethanollwater solutions, n-octanol, n-octadecane, corn oil, HB307, tributyrin, and trioctanoin at temperatures from 24" to 60°C was studied by Chang et al. (1982) and Chang (1984), at the National Institute of Standards and Technology. The objective of this study was to characterize migration from typical food packaging and determine which mathematical relation-
Migration from ,food packuging: Regiilntory considerations for estinmting exposure
367
ship may be applied for evaluating migration. In particular, Chang et al. (1982), evaluated the migration in the finite polymer-finite food system to determine if Fick’s 2nd Law was obeyed. Mathematically this has been described in J. Cranks Mathematics of Diffusion (Crank, 1975) as follows: Finite polymer - finite food
(1 1-2)
M,, is the mass of solute that migrates at time t; M E x is the mass of solute that migrates at infinite time; D, is the diffusion coefficient in the polymer with thickness Lp; where tan qn = -aq,, and cx = a/K (Chapter 7). Here a is the ratio of the food volume to the volume of polymer and K is the partition coefficient. In the absence of partitioning between the polymer and the food, c1 expresses the volume of food to volume of polymer. Typical values for the value of a in the absence of partitioning are given in Table 11-5. It is evident from this table that values of cx for real food packaging are much greater than 1. Practically, this means that the solution to Eq. (11-2) is very similar to the solution to the case where the polymer and food are assumed to be infinitely thick. This is illustrated in Figure 11-1 which shows the overlay of many soluTable 11-5: Experimental values of a, assuming no partitioning (K=l).
a
Food Package Type PET (soft drink or water bottle)
29
PP (yogurt cup)
15
Aseptic Box (fruit juice, milk)
414
PET (salad dressing or condiment bottle)
11
PC (reusable baby bottle)
12
PVC (peanut oil bottle)
14
PET (soybean oil bottle)
18
HDPE (corn oil jug)
26
PVC (dry powder jar)
38
PVC (food barrel)
46
HIPS (food tray)
41
HIPS (cup)
31
Epoxy-coated can (soup)
1089
PVC lined bottle cap (3.78 1 glass bottle)
10026
LDPE (single serving cheese wrapper)
59
PET (bag in a box, 5 1)
169
PET (peanut butter jar)
19
PS (cookie tray)
32
Expanded PS ( foam cups)
7
HDPE (juice, milk or water bottle, 3.78 I ) Average a = 608 Values for typical migration experiments a
50
=
5-25
368
Begley
l1-
inf-inf alphas28 alphac7 alpha4
0.0001
0.001
0.01
1
0.1
10
DVL~
Figure 11-1: Predicted relative migration using Equations (11-2) and (11-3) (V) for many values of Dt/L’ and a.The relative migration assuming finite polymer to a finite amount of food and an infinite polymer and infinite amount of food is illustrated.
tions to Fick’s 2nd Law for the finite polymer-finite food system and the infinite-infinite polymer food system given in Eq. (11-3) where: (11-3)
M,, is the mass that migrates at infinite time. It is clear from this figure that over most values Dt/L2, and for typical values of a found in food packaging, the solutions are equivalent. In many practical cases M , , can be considered the total amount of solute in the polymer at t=O. That is, it is essentially possible for all of a solute to migrate out of a polymer. This was tested and demonstrated by Chang et al. (1982) and is illustrated in Figs. 11-2 and 11-3. Here essentially 100% of BHT and n-octadecane is shown to migrate from LDPE at 30°C and HDPE at 60°C. Because essentially all the solute 1 0.8 0
n0.6
z
5 0.4 \
0.2
0 0
10
20
30
40
Square Root Time (hours) Figure 11-2: Migration of n-octadecane from HDPE into 50 % ethanol/water at 60°C. Mp,o is the total amount of n-octadecane in the HDPE polymer.
Migration from food packaging: Regulatory considerations for estimating exposure
369
1 0.8 0
0.6
0
10
5
20
15
30
25
35
Square Root Time (hours) Figure 11-3: Migration of BHT from LDPE into corn oil at 30°C. Mp.0 is the total amount of BHT in the LDPE polymer.
has been shown to migrate, Eq. (11-3) can be modified with Mr,==Cp,0 . A . L, where A is the polymer area and Cp," is the solute concentration (w/v). The study by Chang et al. (1982 and 1984), concluded that migration of antioxidants is predictable. The amount of migration is controlled by diffusion through the polymer according to Fick's 2nd Law and diffusion follows Arrhenius type behavior. In another extensive study on migration of polymer additives into foods and liquids, AD Little, 1983 evaluated the migration of BHT, Irganox 1010, styrene, an organo-tin stabilizer, and the plasticizer dioctyl adipate from HDPE, LDPE, PS, high-impact-PS, PVC and EVA. The details of this study are given in numerous publications (Till et al. 1982a, 1982b, 1982c; and Schwope et al. 1986,1987a, 1987b, 1 9 8 7 1988). ~ Typical data from this study are shown in Fig. 11-4 which shows the migration of BHT from HDPE into corn oil, orange juice and milk at 4 "C. This figure clearly shows the total amount of migration is affected by the nature of the food. The objective of this study was to determine the relationship, if any, between the migration to foods and food simulating solvents and to determine accelerated migration testing conditions into solvents that would correlate to the solute migration to food. Additionally, results from this study 0.1 0.08
x0.06
E z
0.04 0.02
0 0
10
30
20
40
Square Root Time (hours)
*
Orange Juice
=
Milk
A
Corn Oil
Figure 11-4: Migration of BHT from HDPE into corn oil, orange juice and milk at 4 "C. Mp.0 is the total amount of BHT in the HDPE polymer.
370
Begley
10
8
2
0 0
10
20 30 Square Root Time (hr)
40
50
Figure 11-5: Migration of styrene into water and corn oil at 40°C.
also show the magnitude of partitioning effects, which can be seen in Fig. 11-5. This illustrates the magnitude of the styrene partitioning between polystyrene and water versus migration to corn oil. It is evident from this figure that partitioning has a terminating effect on the migration of styrene to water and assuming no partitioning (i.e. the migration to corn oil) ensures a conservative safety evaluation of this food packaging material. From this 1983 A D Little study ( Till et al., 1982a, 1982b, 1982c; and Schwope et al. 1986, 1987a, 1987b, 1987c, 1988) it can be concluded that migration is predictable and the amount migrating to food will always be less than that to the food simulants. The migration to food oils generally represents a worst case. Additionally, the AD Little studies classified migration to foods into 12 mass transfer categories for the purposes of predicting migration. These groups are listed in Table 11-6. This table of mass transfer groups was also formulated into a migration decision tree, Fig. 11-6 (Reid et al., 1983), which indicates when certain mass transfer effects become important and dominant in controlling migration to food. In this figure, T = D, t/L2, the relative time for diffusion, p = K(De /D, )" , the ratio of diffusion in the food (D,) to diffusion in the polymer, and Y = kK(tfD,)% ,the ratio of mass transfer (k) to diffusion in polymer. In 1989, a very detailed migration study on the migration of BHT and Irganox 1010 from HDPE and LDPE, (Gandek et a1.,1989) showed migration could be accurately predicted if all parameters which control migration are known. This study used measured values for the diffusion coefficient (Dp) of the additive in the polymer, the mass transfer coefficient (km) (mixing coefficient), partition coefficient (K) of the additive between the polymer and the food, and the reaction rate constant (k,) for the degradation of the additive in the food (which effects the partition coefficient) to demonstrate that migration from the polymer is predictable within experimental error. Most of the detailed systematic migration studies performed before 1990 were at low temperatures, i.e., less than 60 "C.In 1990, migration of antioxidants from polyolefins (the most common food packaging material) to the food simulants corn oil, 95 YO ethanol, water, 8 YO ethanol and food was studied at high temperatures in the range
37 1
Migration from food pncknging: Regirlritory cotisiderntions for estimrrting exposiirr Table 1 1 -6: Categories for mass transfer to food. Domain
Extent of Phase Polymer Food
Mass transfer resistance Polymer Food
Parameters
I (MII) 2 (MIF)
infinite infinite
infinite finite
diffusive
none
DQ
diffusive
none
DP
3 (MFI)
finite
infinite
diffusive
none
DQ
4 (MFF) 5 (BII)
finite infinite
finite infinite
diffusive diffusive
none b. layer
D, Dp
K km
k", K
K
6 (BIF)
infinite
finite
diffusive
h. layer
D,
7 (BFI)
finite
infinite
diffusive
h. layer
DQ k,
8 (BFF) 9 (DII)
finite infinite
finite infinite
diffusive diffusive
b. layer diffusive
Dp D,,
km K D, K
10 (DIF)
infinite
finite
diffusive
diffusive
D,
D,
11 (DIF)
finite
infinite
diffusive
diffusive
D,
D,
K K
12 (DIF)
finite
finite
diffusive
diffusive
D,
D,
K
D, is the diffusion of the solute in the polymer. D, is the diffusion of the solute in the external phase (food). K is the partition coefficient of the solute between Ihe polymer and the external phase. b. layer is the convective boundary layer resistance. That i s the bulk fluid is of uniform composition. but a small stagnant region is assumed to exist in the liquid ncxt to the polymer.
77-135 "C (Goydan et al. 1990; AD Little, 1990). This work expanded the temperature range of known migration data for polyolefins to 135 "C. One aspect of these high temperature studies was to determine if small amounts for flavor components in aqueous systems would enhance migration from polyolefins. These effects have been shown to occur in polystyrene (Phillips 1979). Table 11-7 lists the migration results relative to food oils for the possible effects of flavor components enhancing migration from polyolefins. It is clear from this table, for these test solutions, that migration was not enhanced by flavor components. The foods evaluated in these high temperature Table 11-7: Effect of flavor components on migration at high temperature. Migration of Irganox 1076 from HDPE into aqueous solutions and food oils at 121 "C, 2 hours. ~
Solution Water
Amount Percent Migrated ugldm' 14
0.4
Oil
Amount ug/dm2
Percent Migrated
Butter oil
2219
69 56
Salt water (0.7.5 % salt)
13
0.35
Cod liver oil
1996
Sugar water (40 YOsugar)
12
0.34
Cornoil
3090
88
Acid water (0.75 % Citric Acid)
17
0.48
Olive oil
2407
68
d-Limonene in water (0.035 YOd-limonene)
12
0.33
Peanutoil
2298
65
0.035 YOd-Limonene in 8 % ethanollwater
22
0.61
Soybean
2002
58
Polysorbate 60 in water (0.15 %)
44
1.2
HB307
2377
68
Polysorbate 60 in water (0.3 Yo)
123
3.4
372
Begley
Assume 100% migration
kaume partition equilibrium
No
YeS
YeS
I 5: BII 1
16: BIF
I 1 7: BFI I
YCS
18: BFF]
DifPusive
Boundary Layer T < 0.2?
Well-Mixed Figure 11-6: Migration decision tree illustrating the 12 migration categories for migration from food packaging.
migration studies and the amount of migration found are illustrated in Figs. 11-7, 11-8 and 11-9. These figures illustrate in all cases the migration to oil represents the worse case. This study showed, as did the other studies, that migration was predictable and migration to food was less than the migration to food simulants.
Migration ,fromfood packaging: Regirlatory considerations for estimnting expositre
373
Tcmpcrarurc = I 3S0C I
4.000
3.000
2.000
1.000
Figure 11-7: Migration of Irganox 1076 (molecular weight = 531 daltons) from PP into different foods after 1.5 hours contact at I35 "C.
0
Figure 11-8: Migration of lrganox 1010 (molecular weight = 1178 daltons) from LDPE into different foods after 1.5 hours contact at 95 "C. 2,500
%
2,M)o
-...................................................................................
f,SW
-...................................................................................
1.m
-...................................................................................
4 e
.Q
B
5
P <
Figure 11-9: Migration of Irganox 1010 (molecular weight = 1178 daltons) from PP into different foods after 1.5 hours contact at 100 "C.
374
Begley
11.5 Using migration modeling to estimate exposure to components of food packaging The critical parameter that must be determined or estimated to increase the use of migration modeling for exposure estimates in regulatory work is the diffusion coefficient. All parameters in Eq. (11-2) are generally known or easily measured except for the diffusion coefficient which is generally unknown and must be measured in some type of kinetic experiment (permeation, sorption, or desorption experiments). These kinetic experiments can be time-consuming, costly and error-prone. Recently, an alternate approach for estimating diffusion coefficients in a number of different polymers was developed (Piringer 1994; Baner et al. 1996). An empirical correlation approach was used where known diffusion coefficients were fit to an Arrhenius type equation resulting in Eq. (11-4): Ap - a . MW
-
1
(11-4)
b(+)
where the coefficient A, accounts for the effect of the polymer on diffusivity, MW is the additive/contaminant's molecular weight, T is the temperature in K, and a and b are correlation constants for molecular weight and temperature effects on diffusion with values of 0.010 and 10450 (Chapter 15) respectively. The A, coefficients are 9 for LDPE, -3 for PET and 5 for HDPE and PP. Another semi-empirical diffusion model has been developed (Limm and Hollifield, 199%) which is based on the simplification of existing diffusion theories by Pace and Datyner (1979) and the generalized trend found by Berens and Hopfenberg (1982) for the diffusion of small molecules in polymers (Chapter 5). From these studies it is possible to arrive at the following relationship:
InDp(MW,T) = InA+a(MW)'/'-
K (MW)'/~ T
(11-5)
where D,, is the diffusion coefficient of a contaminantladditive, MW is the molecular weight of the contaminant/additive, T is the temperature in K and A , a and K are constants determined from experimental data. Typical values obtained for diffusion coefficients in LDPE, HDPE and PP at 40 "C in using the approach by Limm and Hollifield are illustrated in Fig. 11-10. This figure clearly shows that as the molecular size, i.e. molecular weight, increases the diffusion through the polymer decreases. This general trend has been experimentally measured in polymers by Storey et al. (1989). Comparative results for calculating diffusion coefficients in LDPE at 40 "C by using the methods of Baner et al. (1996) and Limm and Hollifield (1996) are illustrated in Fig. 11-11. This figure illustrates similar results are obtained by using both approaches (Chapter 15). Generally, LDPE is used to estimate the worst case migration from polyolefins. Using modeling to evaluate potential migration and to help make regulatory decisions should always be referenced to typical migration found to food simulating liquids and food. Historically, migration testing to food simulating liquids was developed to mimic actual worst case migration to food in a shorter time with higher temperatures. For example, the migration condition of 40 "C for 10 days is to represent migration to food at 21 "C.Because it is generally accepted that migration to food simulat-
Migration from fond packaging: Regtilatory considerations for estimating exposure
-12
~~
----L-3\
________________
375
PP 4
-7 -8 +
-
Fraunhofer FDA
-10 -11
0
200
400
600
800
1000
Molecular Weight Figure 11-11: Comparative calculated diffusion coefficients at 40 "C versus molecular weight for molecules in LDPE using the models by Baner et al. ( l Y Y 6 ) and Limm and Hollifield (1996).
ing liquids exaggerates migration typically measured to foods, then comparative data between calculated migration and measured migration to food simulating liquids can serve as an indicator of the utility of migration modeling for evaluating the safety of food packaging materials. Appendix 11-I lists calculated and experimental migration data to food simulating liquids for 25 different polymer additives in different polymers. The molecular structures for the chemicals listed in Appendix 11-1are illustrated in Appendix 11-11. The data in the table of Appendix 11-1 indicate that the calculated values are almost always greater than or equal to the experimental migration values to food simulants. In some instances, the calculated values are much greater than the experimental values. These cases are usually for aqueous food simulating systems where solubility is the major parameter controlling migration. Incorporating a partition coefficient into the migration calculations can improve the correlation
376
Begley
between calculated and measured migration values for those systems where solubility of the additive in the food is very low. As with any form of simulated migration testing or calculation, a reference should be made to what is actually measured in real foods. For comparitive purposes, Appendix 11-111lists reported literature values for actual migration of polymer additives to foods. In general, these migration data show migration into food oils is greater than into other foods and that the calculated values in Appendix 9-1 on similar materials and under similar conditions are greater than the migration to food. References Arthur D. Little, Inc.. 1983, A Study of Indirect Food Additive Migration, Final Summary Report. FDA contract number 223-77-2360, Washington DC. Arthur D. Little Inc., 1990. High Temperature Migration of Indirect Food Additives to Foods, Final Summary Report, FDA Contract 223-89-2202. July. Baner, A.L.. Franz, R. and Piringer, O., 1994. Alternative methods for the determination and evaluation of migration potential from polymeric food contact materials. Deutsche Lehensmittel-Rundschau, 90(5). 137-143. and 90(6), 181-185. Baner, A,, Brandsch, J., Franz R.. and Piringer 0..1996.The application of a predictive migration model for evaluating the compliance of plastic materials with European food regulations. Food Additives and Contaminants, 13 (S), 587401. Berens, A.R.. and Hopfenberg, H.B.. 1982, Diffusion of organic vapors at low concentrations in glassy PVC, polystyrene and PMMA. Jorirnal of Membrane Science 10,283-303. Chang, S.S.. Senich, G.A. and Smith, L.E. 1982. Migration of Low molecular weight Additives in Polyolej n s and Copolymers, Final Report, NBSlR 82-2472, National Institute for Standards and Technology, Washington, DC. Chang, S. 1984, Migration of low molecular weight components from polymers: 1. Methodology and diffusion of straight-chain octadecane in polyolefins. Polymer Vol. 25.209-217. Crank, J., 1975, The Mathematics o,fDiffusion.Clarendon Press, Oxford, 2nd edn. Federal Register, 199.5,Vol. 60, No. 136,36582-36596. Figge. K. 1972, Migration of Additives form Plastics Films into Edible Oils and Fat Simulants. Food Cosmetic Toxicology, 10.8154328. Figge, K. 1980, Migration of Components from Plastics-Packaging Materials Into Packed Goods - Test methods and Diffusion Models. Progress Polymer Science, 6. 187-252. Frawley, J.P., 1967, Scientific Evidence and Common Sense as a Basis for Food-Packaging Regulations. Food and Cosmetic Toxicology, 5,293-308. Gandek. T.P., Hatton, T.A. and Reid, R.C., 1989, Batch extraction with Reaction: Phenolic Antioxidant Migration from Polyolefins to Water. 1. Theory. and Batch extraction with Reaction: Phenolic Antioxidant Migration from Polyolefins to Water. 2. Experimental Results and Discussion. Industrial & Engineering Chemical Research, 28 10361045. Gold, L.S., Sawyer C.B., Magaw R., Backman G.M., DeVeciana M.. Levinson R., Kim Hooper N., Havender R., Bernstein L., Peto R.. Pike M., Ames b., 1984, A Carcinogenesis Potency Database of the Standardized Results of Animal Bioassays. Environmental Health Perspectives, 58,9-319. Gold, L.S., deVeciana M., Backman GM., Magaw R., Lopipero P., Smith M., Blumenthal M., Levinson R., Bernstein L., Ames B., 1986, Chronological Supplement to the Carcinogenic Potency Database: Standardized Results of Animal Bioassays Published Through December 1982. Environmental Health Perspectives, 67, 161-200. Gold, L.S., Magaw R., Backman G.M.. DeVeciana M., Levinson R.. DaCosta M., Lopipero P., Blumenthal M., Ames B., 1987, Second chronological Supplement to the Carcinogenic Potency Database: Standardized Results of Animal Bioassays Published Through December 1984 and by the National Toxicology Program through May 1986. Environmental Health Perspectives, 74,237-329. Goydan, R., Schwope A. D., Reid R.C., and Cramer G., 1990, High temperature Migration of Antioxidants from Polyolefins. Food Additives and Contaminants 7,323-337. Limm, W., and Hollifield, H.C., 1996. Modeling of additive diffusion in polyolefins. Food Additives and Contaminants 13, No. 8,949-967. Pace, R.J.. and Datyner, A.J., 1979, Statistical mechanical model of diffusion of simple penetrants in polymers. I. Theory. Journal of Polymer Science: Polymer Physics Edition 17,437452.
Migration froni food packaging: Regirlatory considerations for estiniating exposirre
377
Phillips. M., 1979, Lemon-Tea Drinkers-A group at Risk. New. Eng. J. Medicine. 302, 18,1005. Piringer, O., 1994, Evaluation of plastics for food packaging. Food Additives and Contaminants 11. No. 2.221-230. Rulis, A., 1989, Establishing a Threshold of Regulation. Risk Assessment in Setting National Priorities. Edited by Bonin. J., and Stevenson, D., Plenum Publishing Corp., 271-278. Reid. R.C., Schwope. A.D., Sidmar, K.R., 1983. Fouth International Conference on Migration, Hamburg, November. Rulis. A. 1992. Threshold of Regulation: Options for Handling Minimal Risk Situations. Food Safety Assessment, Edited by J.W. Finley, S.F. Robinson. and D.J. Armstrong (American Chemical Society. Symposium Series 484). 132-139. Schwope, A.D.; Reid, R.C., 1988, Migration t o dry foods. Food Add. Contam.: 5 (Suppl. 1) 445454. Schwope, A.D.; Till, D.E.; Ehntholt, D.J.: Sidman. K.R.: Whelan. R.H.: Schwartz, P.S.: Reid R.C., 1987. Migration of Irganox 1010 from ethylene-vinyl acetate films to foods and food-simulating liquids. Food. Chem. Tox.: 25 (4) 327-330. Schwope, A.D.; Till, D.E.; Ehntholt. D.J.: Sidman, K.R.; Whelan. R.H.; Schwartz, P.S.; Reid R.C.. 1987, Migration of BHT and Irganox 1010 from low-density polyethylene (LDPE) to foods and food-simulating liquids. Food Chem. Tox.; 25 (4) 317-326. Schwope, A.D., Till. D.E., Ehntholt, D.J.. Sidman. K.R.. Schwartz. P.S., Reid, R.C.. 1987, Migration of BHT from Impact Polystyrene to Foods and Food-Simulating Liquids. Ind. Eng. Chem. Res. 26. 1668-1670. Schwope, A.D.; Till, D.E.: Ehntholt, D.J.; Sidman. K.R., Whelan. R.H., Schwarz, P.S., Reid, R.C., 1986. Migration of an organo-tin stabilizer from polyvinyl chloride film to food and food simulating liquids. Deutsche-Lebensmittel-Rundschau; H2 (9) 277-282. Storey, R.F., Mauritz, K.A. and Cox B.D., 1989. Diffusion of Various Dialkyl Phthalates in PVC, Macromolecules, 2,289-294. Till, D.E., Reid, R.C., Schwartz, P.S.. Sidman, K.R., Valentine. J.H.. and Whelan R.H. 1982, Plasticizer Migration from Polyvinyl Chloride Film to Solvents and Food. Food Cosmet. Tox. 20,153-175. Till. D.E., Ehntholt, D.J., Reid, R.C., Schwartz, P.S., Sidman, K.R., Schwope, A.D.. Whelan. R.H. 1982, Migration of BHT antioxidant from high density polyethylene to foods and food simulants. Ind. Eng.Chem. Prod. Res. Devel. 21 (1) 1 0 6 113. Till, D.E.. Ehntholt, D.J., Reid, R.C., Schwartz. P.S., Schwope, A.D.. Sidman, K.R., Whelan, R.H.. 1982, Migration of styrene monomer from crystal polystyrene to foods and food simulating liquids. Ind. Eng. Chem. Fund.; 21 (2) 161-168, Till, D.E.. Reid, R.C., Schwartz. P.S.. Sidman, K.R., Valentine, J.R., Whelan. R.H.. 1982 , Plasticizer migration from polyvinyl chloride film to solvents and foods. Food Chem.Tox.: 20 (1) 95-104. Till, D., Schwope, A.D., Ehntholt, D.J., Sidman. K.R., Whelan, R.H., Schwartz, P.S., and Reid R.C., 1987, Indirect food addtive migration from polymeric food packaging materials. CRC Critical Reviews in Toxicology. Vol. 18, No. 3,215-243.
Appendix 11-1
Migration data submitted for exposure estimates. Calculated versus Experimental. Calculated amount using Ma = 2C0 (DP and 1.55 gkm' food to package surface. Additive
MW Solvent
Polymer Tcmp. "C + time
Model Calc. D, M,
Exp. Mt
Cp.,, Ppm
L cm
mg/kg mglkg
I . Antioxidant 2. Contaminant in antioxidant 3. Antioxidant I stabilizcr 4. Process stabilizcr 4. Process stabilizer 4. 4. 5. 5. 6. 6. 6. 7. 7.
Process stahilizer Process stabilizer Colorant Colorant Stabilizer Stabilizer Stabilizer Proccss stabilizer Process stabilizer X. Colorant 8. Colorant 9. UV stabilizer 9. UV stabilizer 9. UV stabilizer 9. UV stabilizcr 9. UV stabilizer 9. UV stabilizcr 10. UV stabilizer 10. UV stahilizer 10. UV stabilizer 10. UV stabilizer 11. Process stabilizer 11. Process stabilizer 11. Process stabilizer 11. Process stabilizer 11. Process stabilizer 12. Clarifying agent 12. Clarifying agent 13. Antioxidant 13. Antioxidant 14. Light stabilizer 14. Light stabilizer 14. Light stabilizer 14. Light stabilizer 14. Light stabilizer 15. Stabilizer 15. Stabilizer 16. Optical brightncr 17. Clarifying agent
450 YS%ETOH LLDPE 66.2h+40.10d 262 95 %ETOH LLDPE 66.2h + 40,10d
FDA FDA
852 10 %ETOH LLDPE 66.2h, + 40. 10d FDA 1465 corn oil PP 121.2h, + 49,10d FDA 1465 corn oil IOO. 2h +49, IOd FDA coHDPE 1465 corn oil LLDPE 100,2h. + 49,10d FDA 1465 water LLDPE 100.2h. + 49, I0d FDA 525 95 %ETOH LDPE 77.2h. + 49, 10d FDA 525 8%ETOH LDPE 100.2h+49. 10d FDA 346 8 %ETOH PVC 120.2h. + 49.10d Fraun 346 HB307 PVC 120.2h. + 49.10d Fraun 346 HB307 PVC 120.2h. + 49, 10d Storey 512 95%ETOH PP 100.2h+49,10d FDA 512 8%ETOH PP 121.211+49, IOd FDA 381 95%ETOH LDPE 100.2h+49.10d FDA 3x1 X %ETOH LDPE I M I . 2h + 49,10d FDA 1300 8 %ETOH LDPE 66.2h + 49.238h FDA 1300 95 %ETOH LDPE 66.2h + 49,238h FDA 1300 8 %ETOH HDPE 100 0.5h + 49.238h FDA 1300 95 %ETOH HDPE 100 0.Sh + 49.23811 FDA 1300 8 %ETOH CO-PP' 121.2h + 49.238h FDA 1300 95 %ETOH CO-PP 121.2h + 49.23811 FDA 2716 water LDPE 100.2h + 49,32811 FDA 2716 3 % Acetic LDPE 100.2h +49.382h FDA 2716 8 %ETOH LDPE 71.2h + 49,382h FDA 2716 water LDPE 100.2h + 49,382h FDA 514 X %ETOH LDPE 100.2h + 49. 10d FDA 514 HB307 LDPE 100,2 hr FDA 514 HB307 LDPE 49,10d FDA 514 HB307 FDA PP 49. IOd 514 HB307 PP 100.2hr FDA 414 8%ETOH PP 121.2h+4Y. IUd FDA 414 95YoETOH PP 121.2h +49. 10d FDA 632 8 %ETOH LLDPE 100.2h. + 49.10d FDA 632 95 %ETOH LLDPE 100,2h + 49.10d FDA 121.2h +49, 10d Fraun 425 X %ETOH PET 425 olive oil PET 121,2h +49. 10d Fraun 425 8 %ETOH PC 121.2h +4Y. 10d Fraun 425 olive oil PC 121.2h +49. IOd Fraun 425 olive oil PET 121.2h +4Y. 10d FDA 741 R%ETOH PP 121,2h+49,10d FDA 741 SO%ETOH PP 71.2h+49, 10d FDA 430 HB307 HDPE 121.2h+49,10d FDA 508 95 %ETOH HDPE 71.2h + 49. 10d FDA
4.7' 0.04"
2.2 0.04
1000 ,008 10 ,008
2.8* 9.0 1.6
ND 6.2 0.85
1000 .04x
14.6 14.6 284* 284* 0.14 0.14
15.4 1.0 0.1 0.28 ND 2.2 2.2 11.7 1.3 ND ND 2.8 7.1 0.2 0.5 2.0
5.1*
21.9 29.6* 241* 241* 19.7 19.7 5.1 5.1 47 47 31.7 31.7 31.7 31.7 89* 53 85 34 30 151"
Ion0
.oos
1000 ,051 loo0 ,051
loo00 loo00 2600 2600 4800 4x00 4700 4700 3000 3000
.038 ,038 .05 .05 .05 .05
9.4 0.25
360 0.1 3000 0.1
3.6 .006 37 59 15
11
1.2 16
.09 0.2 ND 0.4 ND ND 0.4
3.0 3.0 7.2 44 19.7 9.5 14.9
IOOO .04x loo0 .048 10000 0.5 I l r n 0.5 lo00 ,005 1000 ,005
0.01 0.9
0.18 0.5 0.21
IS*
3.0
Loo0 ,048
.05 .05 ,044 ,044 3(Kx) ,044 3000 ,044 3000 .05 3000 .ns 3000 .05 3000 ,005 3000 ,005 4000 .w 4000 .064 500 ,005 500 ,005 5000 ,0025 5000 .0025 5000 ,0025 5000 ,0025 SO00 ,0025 3000 ,025 3000 .025
1I.X
151* IS* 3.0
600 0.37
Migration f r o m food pnckriging: Regiilntorv corisirierntions for estirniiting e-rposiire Additive
MW Solvent
Polymer Temp. "C + time
Model Calc. D,, M,
Exp. M,
Cp.,, ppm
379 L cm
mg/kg mg/kg 18. Light / thermal stabilizer 2286 95%ETOH PP
18. Light / thermal stahilizer 19. Colorant 19. Colorant 20 Stabilizer 20. Stabilizer 22. dispersant-siloxane 22. di$pcrsant-siloxane 23. UV stabilizer 23. UV stabilizer
2286 520 520 414 414 17nn 1700 1300 1300
23. uv stabilizer 23. UV stabilizer 23. liv stabilizer 23. UV stabilizer
1300 1300 1300 1300
23. lJV stabilizer 23. UV stabilizer 23. LJV stabilizer 23. UV stabilizer
1300
23. IJV Ytahilizer 23. LJV stabilizer 24. Antioxidant 24. Antioxidant 24. Antioxidant 25. Stahilizcr 25. Stabilizer
13(M 1300 13W
1300 1300 582 582 582
424 424
8 %ETOH 10 % ETOH 95 %ETOH X%ETOH 95%ETOH 10% ETOH 95% ETOH water 3% Acetic acid 50% ETOH ~6307 water 3% Acetic acid 50% ETOH HB307 water 3% Acetic acid 50% ETOH HB307 10% ETOH 50% ETOH 95% ETOH 109G ETOH 50% ETOH
* indicates 100 Yo migration should occur ND no migration detected co-PP contains 14 wt.% ethylene as comonomer
'
LDPE LDPE LDPE PP PP LDPE LDPE LDPE LDPE
121.2h +49.10d 100.2h + 49, 10d 100.2hr + 40.238h 100.2hr + 40,238h 121.2h+49. IOd 121.2h+4Y.lOd 65.2h t 40, 10d 65.2h + 40.10d 65.2h. 49. 10d 65.2h. 49, 10d
FDA FDA FDA FDA FDA FDA FDA FDA FDA FDA
7.5 8.3 189
LDPE LDPE HDPE HDPE
65.2h. 49. 65. 2h. 49, 65. 2h. 49. 65.2h. 49.
10d 10d 10d 10d
FDA FDA FDA FDA
HDPE 65.2h. 49. 10d HDPE h5.2h. 49.10d 65.2h. 49. 10d PP PP 65.2h. 49. 10d
FDA FDA FDA FDA
PP PP HDPE HDPE HDPE HIPS HIPS
FDA FDA FDA FDA FDA Fraun Fraun
65.2h. 49. 10d 65.2h. 49. 10d IOO. 2h. 49, 10d X I . 2h. 49. IOd 71.211.49, 10d 121.2h. 49.10d 121.2h.49. 10d
2.1 ND 0.35 0.19 I .2 16 0.016 0.3 4.3
600 8lK)
.05 .05 .076 ,076 .064 ,064
3.9
5000 5000 4000 4000 3000 3000 3000 0.51 3000 0.51
23 23 0.97 0.97
6.4 15.8 I .7 1.9
3000 3000 3000 3000
0.5 I
0.97 0.97 5.1 5.1
2.8 5.6
3000 3000 3000 3000
0.51 0.51 0.51
5.1
2.6 3.2 0.88
3000 3000 1500 1500
0.51 0.51 0.10 0.10 0.10 0.05 0.05
189 151*
151* 9.2 9.2 23 23
5.1 8.7 4.6 4.0 18.0
18.0
1.8
2.0
1.1 3.1
0.1 2.5
1500
1600 1600
0.51 0.51 0.51
0.51
380
Begley
Appendix 11-II
8-
u
r:B
/
Po
Y
$ + I-Z o
c1
,* 0 u
1
I
K,*
0
00
Migration from food pcickaging: Regti lcirory considercrtions for estimating exposure
381
n
"
I
gv f0
0
I
+ 1
I
-
0
0
I
0=0
I
r" 0
f 0
#-
Y
Q#
Y
P
302
Begley
N
I
I
=+
I
I + t
2 X N
* N
s
Migration from food packaging: Regulaiory considerations for estimating exposirre
Appendix 11-III
The Amount of Migration to Food reported in the Literature. Polymer
Migrant
PP PP PP PP PP PP PP PP PP PP PP PP PP PP PP PP PP PP PI' PP PP PP PP PP PP LDPE LDPE LDPE LDPE
lrganox 1076' lrganox 1076 lrganox 1076 Irganox 1076 lrganox 1076 lrganox 1076 lrganox 1076 Irganox 1076 lrganox I076 Irganox 1076 Irganox 1076 Irganox 1076 lrganox 1076 lrganox 1076 Irganox 1076 Irganox 1076 Irganox 1076 Irganox 1076 Irganox 1076 Irganox 1076 lrganox 1076 Irganox 1010 lrganox 1010i Irganox 1010 lrganox 1010 lrganox 1076 Irganox 1076 lrganox 1076 lrganox 1076
HDPE HDPE LDPE LDPE LDPE LDPE IDPE PS PS PS PS PS PS PS
T"C
Food
mg/kg
0.5 0.012 0.12 0.6 1 .5 1.2 0.05 0.6
9.5
Chiken hroth Evap. Skim milk Newburg sauce Corn oil Gravy 10 o/, fat Chicken broth Evap. Skim milk Newburg sauce Corn oil Evap. skim milk Liquid Nutrient Newburg sauce Chicken ala king Chicken hroth Gravy 10 % fat Corn oil Chicken hroth Bahy food. turkey Baby food hanana Beef, stew Corned Beef hash Chicken hroth Evap. skim milk Newburg sauce Corn oil Corn oil Chicken hroth Evap. sklm milk Newburs sauce
BHT' BHT Irganox 1076 lrganox 1076 Irganox 1076 Irganox 1076 lrganox 1076
I0 20 23 23 23 23 23
cheese mayonnaise cheese mayonnaisc chocolate emmental chceae margarine
6 6 0.06 1.3 I .8 4 3.5
Styrene Styrene Styrene Styrene Styrene Styrene Styrene
66
66 4 4 4 4 4
tea coffee milk cream beef gelatin margarine
0.006 0.006 0.018 0.019 0.032 0.001 0.03 1
77 77 71 17 100
100 100 100 100
121 121 121 121 121 121 I21 135 135 135 135 135 100
100 100 100 95
95 95
1.5 0 15
0.14 0.74 0.94 2.1 2.1 2.8 3.5 3.8 0.16 4.4 1.8
0.7 0.21 0.52 0.88 8.9 1.2 0.05 2.1
pg/dmz 385 8.9 87 443 I089
907 36 452 1096 112 103 553 701 1583 1596 209 I 2680 2873 122 3271 1321 554 163 410 696 6766 908
37 1587
10 198
279 620 555
' Octadecyl3,5-bis(l.l-dimethylethyl)-4-hydroxyt~enzenepropanoate
0.X
0.8 4.6 4.8 3.2 0.2 4.7
Reference
AD Little. 1990 AD Little. 1990 AD Little, 1990 AD Little. 1990 AD Littlc. 1990 AD Little, 1990 AD Little. 1990 AD Little, 1990 AD Little, 1990 AD Little. 1990 AD Little, 1990 AD Little, 1990 AD Little. 1990 AD Little, 1990 AD Little. 1990 AD Little, 1990 AD Little. 1990 AD Little. 1990 AD Little, 1990 AD Little, 1990 AD Little. 1990 AD Little, 1990 AD Little. 1990 AD Little, 1990 AD Little. 1990 AD Little, 1990 AD Little. 1990 AD Little. 1990 AD Little. 1990 Figge, Koch, el. al. 1978 Figge. Koch, et. al. I978 Figge, 1980 Figge. 1980 Figgc. 1980 Figge. 1980 Figge, 1980 Varner & Breder. 1981 Varner & Breder. 1981 Till. D.E. el al. 1982.a Till, D.E. et al. 1982.a Till. D.E. ct al. 1982.a Till, D.E. et al. 1982.a Till, D.E. el al. 19823
* Tetrakis[3-(3',5'-di-tert.-butyl-4'-hydroxypheny1)-propionyloxymethyl]-methane Butylated hydroxy toluene
383
384 ~
Begley ~~
~
~
Polymer
Migrant
T T
PS PS PS
Styrene Styrene Styrene
4 21
HDPE HDPE HDPE HDPE HDPE HDPE HDPE HDPE HDPE
BHT BHT BHT BHT BHT BHT BHT BHT BHT
PVC PVC PVC PVC PVC PVC PVC
DOA~ DOA DOA DOA DOA DOA DOA
4
LDPE LDPE LDPE LDPE LDPE LDPE LDPE
Irganox 1076 Irganox 1076 Irganox 1076 Irganox 1076 Irganox 1076 Irganox 1076 Irganox 1076
5 5
IPS IPS IPS IPS IPS IPS IPS
Irganox 1076 Irganox 1076 Irganox 1076 lrganox 1076 Irganox 1076 Irganox 1076 lrganox 1076
HDPE HDPE HDPE HDPE HDPE HDPE
lrganox 1076 Irganox 1076 lrganox 1076 Irganox 1076 Irganox 1076 Irganox 1076
PP PP PP PP PP PP
Irganox 1076 Irganox 1076 lrganox 1076 Irganox 1076 Irganox 1076 Irganox 1076
Dioctyladipate
21 4
21 4 21 21 4
21 4
21
4 4 4 4 4 4
in 10 15 20
20 5 5 10 10 15
20 20
5 10 10 15 20
20 5 10 10 15
20 20
~
Food
~~
nig/kg
pgidm'
mayonnaise vanilla frosting chocolate
0.042 0.013 0.008
4.2 6.1 2.0
Till, D.E. et al. 1982.a Till, D.E. et al. 1982,a Till. D.E, et al. 1982.a
milk milk, powdered orange juice pickle juice corn oil margarine mayonnaise whipped topping chicken soup mix
0.008 0.68 0.032 0.082 0.41 0.016 0.27 0.018 0.83
2 17 7 11 45 2.4 36 0.9 50
Till. D.E. el al. 1982.b Till. D.E. et al. 1982.b Till, D.E. et al. 1982.b Till, D.E. et al. 1982,b Till. D.E. et al. 1982.h Till. D.E. et al. 1982.b Till. D.E, et al. 1982,b Till, D.E. et al. 1982.b Till, D.E, et al. 1982.h
ground beef lean beef beef fat chicken breasts fish fillet apples carrots spread. pork sausage liver sausage yoghurt fresh cheese margarine hard cheese processed cheese spread, pork sausage liver sausagc yoghurt fresh cheese margarine hard cheese processed cheese liver sausage yoghurt fresh cheese margarine hard cheese processed cheese liver sausage yoghurt fresh cheese margarine hard cheese processed cheese
14 1.X 36
20 2.9 0.3 0.06
12OOO 1400
29OOO 19ooo 2400
220 40
1.4
212
1.2
1x5 3.9 471 1331 1652 13.9
0.025 3.1 8.6 10.6 0.089
~
Reference
Till, Reid, et al. 1982 Till. Reid. et al. 1982 Till. Reid, et al. 19x2 Till, Reid. et al. 1982 Till, Reid, et al. 1982 Till, Reid. et al. 1982 Till, Reid. et al. 1982 Bieber. Figge. Koch. 1985 Bieber, Figge, Koch, 1985 Bieber, Figge, Koch, 1985 Bieber. Figge. Koch, 1985 Bieber. Figge. Koch. 1985 Bieber. Figge. Koch, 1985 Bieber, Figge, Koch. 1985
Bieber, Figge. Koch. 1985 Bieber, Figge. Koch, 1985 0.19 Bieber. Figge, Koch. 1985 6.4 Bieber. Figge. Koch. 1985 9.4 Bieber. Figge, Koch, 1985 84.4 Bieber, Figge, Koch, 1985 1 .9 Bieber, Figge, Koch. 1985 5.5 6.3
Biebcr. Figge. Koch, 1985 Bieber, Figge, Koch, 1985 Bieber, Figge, Koch, 1 985 187 Bieber. Figge. Koch. 1985 232 Bieber. Figge. Koch. 1985 10.9 Bieber. Figge, Koch, 1985 28.6 3.3 66.1
39.4 0.94 30.7
221 192 4.8
Bieber, Figge, Koch. 1985 Bieber. Figge. Koch. 1985 Bieber, Figge. Koch. 1985 Bieber. Figge. Koch, 1985 Bieber, Figge, Koch, 1985 Bieber, Figge. Koch. 1985
Migration from food packaging: Regirlatary considerations for estimating exposure Polymer
Migrant
PVC rigid PVC rigid PVC rigid PVC rigid PVC rigid PVC rigid PVC rigid EVA EVA EVA EVA EVA EVA EVA
Sn stabilizer' Sn stabilizer Sn btabilizer Sn stabilizer Sn stabilizer Sn stabilizer Sn stabilizer IrganoxlOlO IrganoxlO10 IrganoxlOlO IrganoxlOlO Irganox 1010 IrganoxlOlO Irganox1010
T"C
4 4 4 21 21 21 21 4 4 4 21 21 21 21
milk margarine processed cheese winc. Chablis cola whiskey mayonnaisc milk processcd cheese hologna bread. whitc wine, Chablis soup mix, dry corn oil
Food
mgikg
0.024 0.055 0.065 0.135 0.052 0.316 0.059 0.002 0.047 0.120 0.096 0.001 0.66
IPS IPS IPS IPS IPS IPS IPS IPS IPS IPS IPS
BHT BHT BHT BHT BHT BHT BHT BHT BHT BHT BHT
4 4 4 4 4 4 4 4 21 21 21
sour cream yogurt cottage cheesc vanilla pudding beef liver gelatin/ sugar gelatin/ no sugar margarine corn oil mayonnaise apple jelly
0.w 0.002 0.003 0.014 0.023 0.012 0.002 0.022 0.33 0.008 0.003
p tr
vodka
0.03
PET PVCiPVDC PVC/PVDC PVCIPVDC PVClPVDC PVCIPVDC PVCiPVDC PVCiPVDC PVCiPVDC PVClPVDC
40 tcrephthalic acid PET oligomers I75 micro ATBC' ATBC micro ATBC micro ATBC micro ATBC micro ATBC micro ATBC micro micro ATBC ATBC micro
PVC PVC PVC PVC PVC
D EH A DEHA DEHA D EH A DEnA
PVC PVC PVC
1.5
pgldm'
6.1 8.8 7.1 37.8 13.0 79 14.7 0.6 5.2 12.4 2.4 0.3 13.2 155
0.5 0.2 0.4 1.6 3.1 1.5 0.2 3.3 36.4 1.1 0.4
Reference Schwope et al., 1986 Schwope et al., 1986 Schwope et al., 1986 Schwope et al.. 1986 Schwope et al., 1986 Schwope et al., 1986 Schwope ct al., 1986 Schwope. et al., 1987 Schwope, et al.. 19x7 Schwope. et al., 1987 Schwope. et al.. 1987 Schwope, et al., I987 Schwope. et al., 1987 Schwope. et al., 1987 Schwope. et al., 1087. b Schwope, ct al., 1987. b Schwope, e t al., 1987. b Schwope. et al., 1987. b Schwope, et al.. 1987. b Schwopc, et al.. 1987, h Schwope. et al., 1987. b Schwope. e t al., 1987. b Schwope, et al., 1987, b Schwope. et al., 1987. h Schwope, et al., 1987. h Ashhy. 1988
35 22 22 47 23
Ashby, 1988 Gilbert. et al.. 1988 Gilbert. et al.. 1988 Gilbert, et al.. 1988 Gilbert. et al.. 1988 Gilbert. et al.. 1988 Gilbert, et al.. 198X Gilbert, et al., 1988 Gilbert. et al., 1988 Gilhert, et al.. 1988
5 micro micro
sandwich cheese cake chicken biscuit
41 246 226 46 362
Gilbert. et al.. 1988 Gilbert. et al.. 1988 Gilbert, et al.. 19x8 Gilbert, et al.. 1988 Gilbert. et al.. 1988
placticizer. polymeric(pp)
5
sandwich
3
Gilbert, et al.. 1988
PP PP
5 5
cheese cake
12 54
Gilbert, et al.. 1988 Gilbert, et al., 1988
11.3
5
olive oil soup pork chops pudding beef meal pizza bread cakcs biscuits cake
di(n-octy1)tin-bis(isooctylrnercaptoaceta1e)
' acetyl tributyl citrate
400 0.4 1.4 2.7 0.8
385
386
Begley
Polymer
Migrant
T"C
Food
PVC PVC
PP PP
micro micro
chicken biscuit
PVC PVC PVC PVC PVC
ESBO' ESBO ESBO ESBO ESBO
PVC PVC PVC PVC PVC PVC PVC PVC PVC PVC PVC PVC PVC PVC PVC PVC
ATBC ATBC ATBC ATBC ATBC ATBC ATBC ATBC ATBC ATBC ATBC ATBC ATBC ATBC ATBC ATBC
micro micro micro micro micro micro micro micro micro micro micro micro micro
LDPE LDPE LDPE LDPE LDPE LDPE LDPE LDPE LDPE LDPE LDPE LDPE
BHT BHT BHT BHT BHT BHT BHT BHT BHT BHT BHT BHT
4 4 4 4 4 4 4 21 21 21 21
LDPE LDPE LDPE LDPE LDPE LDPE
Irganox 1010 lrganox 1010 Irganox 1010 lrganox 1010 Irganox 1010 lrganox 1010
PP (printed) PP (printed) PP (printed)
DBP~ DBP DCHP'
'
epoxidized soy b e a n oil di-butyl phthalate di-cyclohexyl phthalate
5 5
5 micro micro
5 5
5
sandwich cheese cake chicken biscuit soup chicken breasts pork chop hot bread spinach sweetcorn hrussel sprouts stcam puding cake5 [scones) chocolatc cake peanut biscuits roast beef meal pizza cheese slices cake sandwich
mdkg
40 90 8 3 200
Gilbert, et al., 1988 Gilbert. et al.. 1988 Gilbert, et al.. 1988 Gilhert, et al., 1988 Gilbert. et al.. 1988
0.4 12.4 I.4
22.0 24.7 3.9
100
2.7 22.3 22.6 79.8 0.8 35.0 29.9 3.2 2.6
600
0.002 0.006 0.031
21 21
milk orange juicc margarine processed cheese dry soup mix white rice
20 20 20
chocolate sweets snack food snack food
4
4 4
100
300 400 600 I on 2w
0.9
0.29 0.43 0.71 0.45
4
Reference Gilbert, et al.. 1988 Gilbert, et al.. 1988
milk orange juice margarine apple squash. pre-peelcd chicken breast processed chccsc white rice dry chicken soup brown sugar powdcrcd milk french fries. frozen
-18
pg/dm2
8 37
0.16
0.052 0.14 1.2 1 .I)
0.27 0.7 0.07
0.019 1.6 0.017
9.2 14.1 IX.6
17"
2400 5100 6W 4900
600 200 1on
65 96 114 4s 16 21 53 I68 135 25 85 10
Castle. et al.. 1988 Castle. et al.. 1988 Castle, et al.. 1988 Castle, et al., 1988 Castle. et al., 1988 Castle, et al.. 1988 Castle. et al., 1988 Castle, et al., 1988 Castle. et al.. 1988 Castle. et al., 1988 Castle, et al., 1988 Castle. et al.. 1988 Castle, et al.. 1988 Castle. et al.. 1988 Castle, et al.. 1988 Castle. et al.. 1988 AD Littlc. 1983 AD Little. 1983 AD Little, 1983 AD Little. 1983 AD Littlc, 1983 AD Little. 1983 AD Littlc. 1983 AD Little. 1983 Schwopc and Reid. 1988 AD Little, 1983 AD Little, 1983 AD Little. 1983
0.5 AD Littlc, 1983 1.3 AD Little, 1983 5.0 AD Little, 1983 2.1 AD Little, 1983 9.7 AD Little. 1983 2.0 AD Littlc. 1983
Castle et al. 1989 Castle et al. 1989 Castle et al. 1989
Migration from food packaging: Regtilatory considerations for estimating exposure Polymer
Migrant
PP (printed) PP (printed)
DEHP DEHP'"
T T 20 20
PVC PVC
DEHA DEHA
4 20
PET PET PET PE -i PET
PET oligomers PET oligomers PET oligomers PET oligomers PET oligomers
PVC PVC PVC PVC PVC PVC
DEHA DEHA D EH A DEHA DEHA DEHA
5 5 5
PVC PVC PVC
ESBO ESBO ESBO
4 4 4
PVC PVC
ESBO ESBO
4 4
PVC PVC PVC PVC PVC PVC PVC PVC PVC PVC PVC PVC PVC
ESBO ESBO ESBO ESBO ESBO ESBO ESBO ESBO ESBO ESBO ESBO ESBO ESBO
4 4 4 4 micro micro micro micro micro micro micro micro
PVC PVC PV" PVC
ESBO ESBO ESBO ESBO
PV" PVC PVC PV(' PV('
D EH A DEHA DEHA DEHA DEHA
Food
mgikg
@dm2
387
Reference
~
"'
di-(2-ethylhexyl) phthalate
I75 204 micro
5
5
5
micro
Chocolate bar Potato crisps Cheese Bread Gin Ginger Ale Olive oil Lasagne French fries
2.3 1.4 429 325
Pizza Curry Pastry Potato Meal
Kozyrod and Ziaziarib, 1089 Koiyrod and Ziaziaris, 1989
0.29 0.08 4.2 1.47 2.13
Castle et al. 1989 Castle et al. 1989 Castle et al, 1989 Castle et al. 1989 Castle et al. 1989
I520 1350 540 550 870 Ill0
Mercer et al.. 1990 Mercer et al.. 1990 Mercer CI al., 19YO Mercer et al.. 1990 Mercer er al.. 1990 Mercer et al.. 1990
14ou 400 6300
Castle et al.. 1990 Castle et al., 1990 Castle et al.. 1990
600 2100
Castle et al.. 1990 Castle el al., 1990
1200 2300 400 3200 4000 6600 4son 700 500
0.6 4.1 0.3 3.2
Castle et al.. 1990 Castle et al.. 1990 Castle et al., 1990 Castle et al.. 1990 Castle et al., 1990 Castle et al.. 1990 Castle el al.. 1990 Castle et al.. 1990 Castle et al.. 1990 Castle et al.. 1990 Castle et al.. 1990 Castle et al., 1990 Castle et al., 1990
7.6 0.4 0. I 0.5
Castle et al., 1990 Castle et al.. 1990 Castle et al., 1990 Castle et al., 1990
Cheese Salami Chicken Beef Swiss roll Avocado Ground beef Chicken leg Roast boneless chicken Beef salad sandwich Cheese and lumato roll Tuna salad sandwich Leicester cheese Brie cheese Swiss cheese slices Peanut biscuits Pizza Cornish pastry Hamburgcr Apple crumble Baby fovd (rice) Bahy food (lamb) Baby food (desert) Baby food (vegetable) Bahy food (chicken) Baby food (pudding) Baby food (yoghurt) Baby food (custard)
Castle et al. 1989 Castle et al. 1989
4 1
22 10
27 19 23 4 32 85 16.3 10.6 2.6 1.8
27 0.9 7 2.6 0.6
1350 80 470 220 60
Castle et al., 1990 Castle et al.. 1990 Castle et al., 1990 Castle et al.. 1990 Castle et al.. 1990
388
Begley
Polymer
Migrant
T"C
Food
PVCIPVDC PVC/PVDC PVCPVDC PVClPVDC PVC/PVDC
ATBC ATBC ATBC ATBC ATBC
micro
Pina Meal Bread Cakes Biscuits
35 29.9 22.0 22.3 79.8
4900
PET PET PET PETIadhesive PET PET PET
Cyclic trimer Cyclic tetramer DEGDB" BADGEI2 Cyclic trimer Cyclic trimer Cyclic trimer
micro micro micro micro micro
French fries
6.8 0.53 11.0 1.33 5.9 2.1 1.I
418 32 677
Jute Sacks
Mineral oil
room
Milk CartodPE dioxins
4
Meat pie Popcorn Pizza Fish sticks Coffee Milk
mglkg
pgldm2
600
600 1700 5100
Reference Castle et al., 1990 Castle et al.. 1990 Castle et al., 1990 Castle et al.. 1990 Castle et al.. 1990 Begley and Hollifield. 1990 Begley and Hollifield, 1990 Begley and Hollifield, 1990 Begley et al., 1991 Begley et al., 1990 Begley et al.. 1990 Begley et al., 1990
230
Grob et al.. 1991
1 . 0 in4 ~
Ryan. e t al. 1991
Lead crystal
lead (Pb)
room
Alcoholic beverages
2.5
Falcone. 1991
PVC PVC PVC PVC PVC
poly-adipate poly-adipate poly-adipate poly-adipate poly-adipate
4 4 4 micro micro
Cheese Sandwich Cake Pizza Pastry
9.8
Castle, et al. 1991 Castle, et al. 1991 Castle, et al. 1991 Castle. ct al. 1991 Castle, et al. 1991
PE PE
polyisobutylene polyisobutylene
Tuna sandwich Egg sandwich
2 4
Elastic netting
nitrosamines
Cured pork
0.52
PS PS ABS PS
mineral oil mineral oil mineral oil mineral oil
WAX coating WAX coating WAX coating WAX coating
mineral oil mineral oil mineral oil mineral oil
Edam cheese Gouda cheese Bavarian smoked Jarlberg cheese
PP PP PP PP PP
DBP DEHA DEHA DBP DEHP
Chocolate bars Chocolate bars Biscuits Biscuits Confectionery
'I l2
4 4 4 4
diethylene glycol dibenzoate diglycydyl ether of bisphenol A
Cream Milk Sunflower oil Sunflower oil
0.5 5.0 4.3 1.2
84 93
<3.0 140 5.4 2.5 1.3 1.3 0.81 0.3X 0.1 1
0.60 0.67
0.07 Castle et al., 1992 0.09 Castle. et al. 1992 Sen et al.. 1993 3600 3ooO
Castle et aL.1993 Castle. et al. 1993 Castle, et al. 1993 Castle, et al. 1993
1900 1400 300 800
Castle et al.. 1993 Castle et aL.1993 Castle et aL.1993 Castle et al.,lY93 Nerin Nerin Nerin Nerin Nerin
et al., 1993 et al., 1993 et al.. 1993 et al.. 1993 et al., 1993
Migration from food packnging: Regit latory considerations for estimating exposure Polymer
Migrant
T”C
Food
polyester polycster
Styrene Ethylbenzene
175 175
Belly. pork . Belly pork
PVC PVC
DEHA
PET/adhesive
BADGE
Epoxy coating
5 5 micro
mglkg
Danbo cheesc (45 %) 150 Danbo cheese (30 %) 53 Pizza
0.67
Bisphenol A
Infant formula
0.013
polycarbonate
Bisphenol A
Water
4.7
Polyamide
Nylon oligomer 200
Chicken
PS
Styrene
4
Yoghurt
PVC gaskets
ESBO ESBO ESBO ESBO
PVC PVC PVC PVC PVC PVC PVC PVC PVC PVC PVC PVC PVC PVC PVC PVC PVC
DEHA DEHA DEHA DEHA DEHA DEHA DEHA DEHA DEHA DEHA DEHA DEHA DEHA DEHA DEHA DEHA DEHA
PS PS PS PS PS PS PS PS 1’s
Styrene Styrene Styrene Styrene Styrene Styrcne Styrcne Styrcne Styrcne
23 5
micro
-18 4
-10 100
4 4 4 4
Chicken Ham Salami Beef Sandwich Chocolate Swiss roll Madeira Battenburg Avocado Grapefruit Chicken breast Pork (spare-ribs) Carrots (boiled) Biscuits (peanut) Cheesecake Pizza
12000 4000
Petcrsen et al., 1995 Petersen et al.. 1995
70
Sharman et al.. 1995
1.1 Biles et al., 1997 Biles et al., 1997 Gramshaw et al.. 1998 Nerin et al., 1998
0.0085
Hammarling. et al., 1998 Hammarling, et al., 1998 Hammarling, et al., 1998 Hammarling. et al.. 1998
23.1 19.1 21.1 11.3
.
Whole milk Skimmcd milk Pudding, whole milk Ice cream Soup (3.6 % fat) Yogurt (3.5 “10fat) Rice with milk Mozzarella Checse( 13.5 % fat)
75 107 181 78 23 4 125 34 6 53 3 106 351 2 435 1 I7 11.0
0.003 <0.001 n.oo9 0.024 0.015 0.044 0.032 0.069 0.062
Reference Gramshaw, Vandenburg, 1995 Gramshaw, Vandenburg, 1995
16.1
Baby. beef Baby. chicken Baby, fish Baby, carrots 5
yg/dm2
2.4 0.034
389
5400 2800 13500 5500 1300 400 8700 2000 500 11100
300 14100 24000 300 17300 9500
Startin et al. 1987 Startin et al. 1987 Startin et al. 1987 Startin et al. 1987 Startin et al. 1987 Startin et al. 1987 Startin et al. 1987 Startin et al. 1987 Startin et al. 1987 Startin et al. 1987 Startin et al. 1987 Startin et al. 1987 Startin et al. 1987 Startin et al. 1987 Startin et al. 1987 Startin et al. 1987 Startin et al. 1987
0.4 Tawfik and Huyghebaert, 1998 ~ 0 . 1 Tawfik and Huyghcbaert. 1998 0.14 Tawfik and Huyghebaert. 1998 0.3 Tawfik and Huyghebaert. 1998 2.0 Tawfik and Huyghebaert, 1998 6.0 Tawfik and Huyghebaert, 1998 3.0 Tawfik and Huyghebaert, 1998 11 Tawfik and Huyghebaert. 1998 10 Tawfik and Huyghebaert. 1998
390
Begley
References for Appendix I1-IlI
Migration values into Food. AD Little Inc.. 1990, High Temperature Migration of Indirect Food Additives to Foods, Final Summary Report,, FDA Contract 223-89-2202, July. Ashby, R., 1988. Migration from polyethylene terephthalate under all conditions of use. Food Add. Contam. 5 (Suppl. 1)485492. Begley, T.H.. Biles, J.E., and Hollifield. H.C., 1991, Migration of an Epoxy Adhesive Compound Into a Food Simulating Liquid and Food From Microwave Susceptor Packaging, J. Agricultural and Food Chem., November, 1944-1945. Begley, T.H.. and Hollifield, H.C.. 1990, Migration of Dibenzoate Plasticizers and Polyethylene Terephthalate Cyclic Oligomers from Microwave Susceptor Packaging into Food-Simulating Liquids and Food. Journal of Food Protection. Vol. 53, No. 12,1062-1066. Begley. T.H., Dennison, J.L. and Hollifield, H.C., 1990, Migration into Food of Polyethylene Terephthalate (PET) Cyclic Oligomers from PET Microwave Susceptor Packaging. Food Additives and Contaminants. Vol. 7. NO. 6,797-803. Bieber. W.D., Figge, K.. Koch J., 1985, Interaction between plastics packaging materials and foodstuffs with different fat content and fat release properties. Food Add. Contam. 2 (2) 113-124. Bieber, W.D., Freytag W.. Figge K., Bruck, C.G. vom, 1984, Transfer of additives from plastics materials into foodstuffs and into food simulants a comparison. Food Chem. Tox. 22 (9) 737-742. Biles, J.E., McNeal, T.P., Begley, T.H., 1997. Determination of Bisphenol-A Migrating From Epoxy Can coatings to Infant formula Concentrates. J of Agric. Food Chemi. 1997,45,46974700. Biles. J.E., McNeal. T.P., Begley, T.H., and Hollifield, H.C., 1997, Determination of Bisphenol-A in Reusable Polycarbonate Food-Contact Plastics and Migration to Food Simulating Liquids. J. of Agric. Food Chem. Vol. 45, No. 9,3541-3544. Castle, L., Mayo, A., Crews, C., Gilbert, J., 1989, Migration of poly(ethy1ene terephthalate) (PET) oligomers from PET plastics into foods during microwave and conventional cooking and into bottled beverages. Journal of Food Protection; 52 (5) 337-342,lS. Castle, L., Jickells, S.M., Shaman, M., Gramshaw, J.W., Gilbert, J., 1988, Migration of the plasticizer acetyltributyl citrate from plastic film into foods during microwave cooking and other domestic use. J. Food Prot. 51 (12) 916-919. Castle, L., Cloke, H.R., Startin. J.R., Gilbert, J., 1988, Gas chromatographic determination of monoethylene glycol and diethylene glycol in chocolate packaged in regenerated cellulose film. Journal of the Association of Official Analytical Chemists; 71 (3) 499,502. Castle, L., Mercer, A.J., Gilbert, J., 1988, Gas chromatographicmass spectrometric determination of adipatebased polymeric plasticizers in foods. J. Assoc. Off. Anal. Chem. 71 (2) 394-396. Castle, L., Mercer, A.J., Gilbert, J., 1988, Migration from plasticized films into foods. 4. Use of polymeric plasticizers and lower levels of di-(2-ethylhexyl)adipate plasticizer in PVC films to reduce migration into foods. Food Additives and Contaminants: 5 (3) 277-282. Castle, L.. Mercer, A.J., Startin, J.R., Gilbert, J., 1988, Migration from plasticized films into foods. 111. Migration of phthalate, sebacate, citrate and phosphate esters from films used for retail food packaging. Food Add. Contam.5 (1) 9-20. Castle, L., Mayo, A., Gilbert, J., 1990,Migration of epoxidised soya bean into foods from retail packaging materials and from plasticised PVC film used in the home. Food. Add. Contam. 7 (1) 29-36. Castle, L., Jickels, S.M., Gilbert, J., Harrison, 1990. Migration testing of plastics and microwave-active materials for high-temperature food-use. Food Add. Contam. 7,6,779-796. Castle, L., Mayo, A,, Gilbert, 1990, Migration of epoxidised soya bean oil foods from retail packaging materials and from plasticised PVC film used in the hame. Food Add. Contam. 7, I , 29-36. Castle, L., Mercer, A.J., Gilbert, J., 1991 Migration from Plasticized films into Foods. 5. Indentification of individual species in a polymeric plasticizer and their migration to food. Food Additives and Contam. 85,565-576. Castle, L., Kelly. M., Gilbert, J.. 1993, Migration of mineral hydrocarbons into foods. 11. Polystyrene, ABS, and waxed paperboard containers for dairy products. Food Add. Contam. 10 (2) 167-174. Daun, H., Gilbert, S.G., 1977, Migration of plasticizers from polyvinylchloride packaging films to meat. JournalofFoodScience; 42 (2) 561-562. Falcone, F., 1991, Migration of Lead into Alcoholic beverages During Storage in Lead Crystal Decanters. J. Food Protection, 54.5.378-380. Figge, K., Koch, J., Freytag, W., 1978, The suitability of simulants for foodstuffs, cosmetics and pharmaceutical products in migration studies. Food Cosmet. Tox. 16 (2) 135-142.
Migration f r o m food packaging: Regiilatory cot~siderationsf o r estimating exposicre
391
Figge. K., 1980, Migration of components from plastics-packaging materials into packed goods - test methods and diffusion models. Prog. Polym. Sci., 6. 187-252. Gilbert, J., Castle, L., Jickells, S.M., Mercer, A.J.. Sharman. M.. 1988. Migration from plastics into foodstuffs under realistic conditions of use. Food Add. Contam. 5 (Suppl. 1) 513-523. Gramshaw, J.W., Soto-Valdez, H., 1998, Migration from polyamide microwave and roasting bags into chicken. Food Add. Contam. 15,3.329-335. Gramshaw. J.W., and Vandenburg, H.J., 1995. Compositional analysis of thermoset polyester and migration of ethylbenzene and styrene from therniosct polyester into pork during cooking. Food Add. and Contam. 12,2,223-234. Grob. K., Lanfranchi, M.. Egli. J., and Artho, A.. 1991. determination of food Contamination by Mineral oil from Jute Sacks Using coupled LC-GC. J. Assoc. Off. Anal. Chem. Vol. 74,506-512. Hammarling, L., Gustavsson, H.. Svensson. K., Karlsson. S., Oskarsson, A,. 1998, Migration of epoxidized soya bean oil from plasticized PVC gaskets into baby food. Food Add. Contam. 15,2,203-208. Kozyrod, R.P., and Ziaziaris. J., 1989, A survey of Plasticizer Migration, J. Food Protection, Vol. 52.578580. Mercer. A., Castle, L., Comyn, J.. Gilbert, J.. lYY0. Evaluation of pridictive mathematical model of di(2ethylhexyl) adipate palsticizer migration from PVC film inot foods. Food Add. Contam. 7. 4, 497507.
Nerin. C., Rubio, C., Cacho, J., Salafranca, J., 1998, Parts-per-trillion determination of sytrene in yoghurt by purge-and-trap GC with mass spectrometry detection. Food Add. Contam. 1 5 3 , 346-354. Nerin. C.. Cacho, J.. and Gancedo, P., 1993. Plasticizers from printing inks in a selection or food packaging and their migration to food. Food Add. Contam. 10,4,453-460. Petersen. J.H., Naamansen, E.T., Nielsen, PA., 1995, PVC cling film in contact with cheese: health aspects related to global migration and specific migration of DEHA. Food Add. Contam. 12 (2) 245253. Ryan, J.. Panopio. L., Lewis, D., and Weber F., 1991, Polychlorinated Dibenzo-p-dioxins and Polychlorinated dibenzofurans in Cow’s Milk packaged in Plastic-coated bleached paperboard. J Agric. Food Chem. 39,218-223. Schwope, A.D., Reid, R.C., 1988, Migration to dry foods. Food Add. Contam.; 5 (Suppl. 1) 445454. Schwope, A.D., Till, D.E., Ehntholt, D.J., Sidman, K.R.. Whelan, R.H., Schwartz. P.S., Reid, R.C., 1987, Migration of lrganox 1010 from ethylenevinyl acetate films to roods and food-simulating liquids. Food and Chemical Toxicology; 25 (4) 327-330. Schwope, A.D., Till, D.E.. Ehntholt, D.J., Sidman, K.R.. Whelan, R.H., Schwartz. P.S., Reid, R.C., 1987, Migration of BHT and Irganox 1010 from low-density polyethylene (LDPE) to foods and food-simulating liquids. FoodandChemicalToxicology;25 (4) 317-326. Schwope, A.D., Till, D.E., Ehntholt, D.J., Sidman, K.R.. Schwartz, P.S.. Reid, R.C., 1987, Migration of BHT from Impact Polystyrene to Foods and Food-Simulating Liquids. Ind. Eng. Chem. Res. 26, 1668-1670. Schwope, A.D., Till, D.E., Ehntholt, D.J., Sidman. K.R.. Whelan. R.H., Schwartz, PS., Reid R.C., 1986, Migration of an organotin stabilizer from polyvinyl chloride film to food and food simulating liquids. DeutscheLebensmittel Rundschau; 82 (9) 277-282. Sen. N.P., Baddoo, P.A.. and Seaman, S.W., 1993, Nitrosamine in cured pork products packaged in elastic rubber netting: An update. Food Chemistry 47,387-390. Sharman. M., Honeybone, C.A., Jickells, S.M.. and Castle. L., 1995, Detection of residues of the epoxy adhesive component bisphenol A diglycidyl ether (BADGE) in microwave susceptors and its migration into food., Food Add. Contam. 12,6,779-787. Startin, J.R., Sharman, M., Rose. M.D., Parker. 1.. Mercer, A.J., Castle. L., Gilbert, J., 1987, Migration from plasticized films into foods. I. Migration of di-(2-ethylhexyl)adipate from PVC films during homeuse and microwave cooking. Food Additives and Contaminants; 4 (4) 385-398. Startin, J.R., Gilbert, J.. 1984. Single ion monitoring of butadiene in plastics and foods by coupled mass spectrometryautomatic headspace gas chromatography. Journal of Chromatography; 294,427-430 Tawfik, M.S., and Huyghebaert, A,, 1998, Polystyrene cups and containers: styrene migration. Food Additives and Contaminants, Val. 15, No. 5 , SY2-599. Till, D.E.. Reid, R.C., Schwartz, P.S., Sidman, K.R., Valentine, J.H., and Whelan, R.H. 1982, Plasticizer Migration from Polyvinyl Chloride Film to Solvents and Food. Food Cosmet Tox. 20,153-175. Till. D.E.. Ehntholt, D.J., Reid, R.C.. Schwartz, P.S., Sidman, K.R., Schwope. A.D., Whelan, R.H., 1982. Migration of BHT antioxidant from high density polyethylene to foods and food simulants. Industrial & Engineering hemistry, Product Research and Development; 21 (1) 106-113.
392
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Till, D.E., Ehntholt, D.J., Reid, R.C., Schwartz, PS., Schwope, A.D., Sidman, K.R.. Whelan, R.H., 1982, Migration of styrene monomer from crystal polystyrene to foods and food simulating liquids Ind. Eng. Chem. Fund.: 21 (2) 161-168, Till, D.E., Reid, R.C., Schwartz, P.S., Sidman, K.R., Valentine, J.R.. Whelan, R.H.. 1982 , Plasticizer migration from polyvinyl chloride film to solvents and foods. Food Chem.Tox.; 20 (1)95-104. Till, D., Schwope, A.D., Ehntholt, D.J., Sidman, K.R., Whelan, R.H., Schwartz, P.S., and Reid, R.C., 1987, Indirect food addtive migration from polymeric food packaging materials. CRC Critical Reviews in Toxicology, Vol. 18, No. 3,215-243. Vamer, S.L., Breder, C.V., 1981, Headspace sampling and gas chromatographic determination of styrene migration from food-contact polystyrene cups into beverages and food simulants. J. Assoc. Off. Chem. 64 (5) 1122-1130.
Reactivity in Molecular Crystals Edited by Yuli Ohashi Copyright @ K d a o r h a Ltd .Tokyo. 1999
12 European Community legislation on materials and articles intended to come into contact with food Luigi Rossi
12.1 Introduction At the end of the 1950s, following the first legal provisions adopted by the US Food and Drug Administration (FDA) in the sector of plastics intended to come into contact with foodstuffs, the German and Italian authorities began issuing their first regulations in the field of migration. These regulations were designed to avoid excessive release into foodstuffs of the substances contained in the materials, especially in plastics, and above all to rule out the possibility of a health hazard to the consumer as a result of the toxicity of some of the substances used to manufacture these materials. One need only think of the migration of certain monomers regarded as carcinogenic (e.g. vinylchloride, acrylonitrile), the release of certain highly toxic metals like lead and cadmium from ceramic surfaces, the presence of nitrosamines in certain types of rubber used for teats and soothers, etc. Subsequently France, the Netherlands and Belgium also issued similar laws, although each provision differed from the other not so much in the objectives behind them (consumer protection) as in the ways of achieving those objectives. In the European Community the differences in the provisions adopted at national level soon began to create problems for packaging companies, which were forced to adjust production to the country of destination and apply for authorization to use a new material. This led to a growing need to approximate (“harmonize”) the various laws and thereby remove legal barriers to Community trade in packaged food which, with the abolition of customs duty and the new systems of sales (supermarkets) and lifestyles (pre-packaged food), had developed enormously. In addition to this need there was the growing awareness on the part of the press and public opinion of everything to do with health protection and the ever more pressing demand for regulation from the professional associations, who wanted to have legal safeguards and to be able to advertize their products as products recognized as safe by the law. This explains the proliferation of national laws and the need to harmonize them. In 1972 the Commission of the European Communities drew up a broad programme of action designed to harmonize all existing laws in the field of materials intended to come into contact with food (plastics, paper, ceramics, rubber, etc.). In practice, rather than harmonizing laws and standards which were often too different to be reconciled, this meant drawing up a Directive (= Community legal act requiring a national implemention law) to replace national laws and recommendations (in Germany and the United Kingdom). There has so far been little recourse to Article 30 of the Treaty of Rome, which prevents a Member State from prohibiting the importation of a product conforming to the legislation of the exporting country. The main reason
394
Rossi
for this is that application of this article has been complicated by the existence of a clause which gives a Member State the possibility of opposing the importation of products with a harmlessness very much open to question. In addition, for one thing the procedure under Article 30 provides for appeal to the Court of Justice in cases of dispute, which is very time-consuming, and for another the validity of the judgment is limited to the case in dispute. In the following pages w e will look at the main aspects of current Community legislation on materials and articles intended to come into contact with foodstuffs.
12.2 Harmonization of national regulations Table 12-1 lists all the directives applicable to each type of material and Table 12-2 gives the dates of enforcement and the bibliographic references. The directives adopted can be divided into three categories: 1. directives applicable to all materials and articles; 2. directives applicable to one category of materials and articles: 3. directives relating to individual substances. Table 12-1: The main directives already adopted in the sector of materials intended to come into contact with foodstuffs (subdivided by subject). DIRECTIVES APPLICABLE TO ALL MATERIALS New framework Directive
891109lEEC
Symbol
80/590/EEC
DIRECTIVES APPLICABLE TO INDIVIDUAL MATERIALS AND SUBSTANCES PLASTICS Base Directive: monomers - 1st amendment - 2nd amendment - 3rd amendment - 4th amendment Directive on the basic rules for migration tests - 1st amendment - 2nd amendment Directive on the list of simulants
901128lEEC 92139lEEC 93/9/EEC 95/3/EEC 96/11/EEC 82/71llEEC 93/8/EEC 97/48/EC 85I572lEEC
Directive on vinylchloride monomer (VCM)
781142lEEC
Directive on the method for determining VCM in PVC
80/766/EEC
Directive on the method for determining VCM in foods
821432EEC
REGENERATED CELLULOSE FILM Base Directive
93/10/EEC CERAMICS
Base Directive
84/500/EEC ELASTOMERS
Nitrosamines in teats and soothers
93/11/EEC
Ellropeon Community legislation on rnnterials and orticles to come into contact .._
395
Table 12-2: Directives already adopted in the sector of materials intended to come into contact with foodstuffs (in chronological order). Directive N o
Adoption
Entrv into force
OJ No
761893lEEC
First framework Directive
Subiect
23.1 1.1976
26.11.1978
L 341 9.12.1976
7811421EEC
Plastics: VCM limits
30.1.1978
26.11.1979
L 44 15.2.1978
80/590lEEC
Symbol
9.6.1980
1.1.1981
L 151 19.6.1980
80/766/EEC
Plastics: methods for determining VCM in PVC
8.7.1980
1I . 1.1982
L213 16.8.1980
8114321EEC
Plastics: methods for determining VCM in food
29.4.1981
1.10.1982
L 167 24.6.1981
82/71UEEC
Plastics: basic rules for migration testing
18.10.1982
1.1.1991
L 297 23.10.1982
831229lEEC
Regenerated cellulose
25.4.1983
1.1.1985
L 123 11.5.1983
851572lEEC
Plastics: List of simulants
19.12.1985
1.1.1991
L 372 3 1.12.1985
86/388/EEC
Regenerated cellulose
23.7.1986
1.4.1987
L 228 14.8.1986
8911091EEC
New framework Directive
21.12.1988
10.7.1990
L 40 11.2.1989
9011281EEC
Plastics: monomers
23.2.1990
1.1.1991
L 75 21.3.100
9211SIEEC
Regenerated cellulose: 2nd amendment
11.3.1992
30.6.1993
L 102 16.4.1992
921391EEC
Plastics: monomers 1st amendment
14.5.1992
31.12.1992
L 168 23.6.1992
93/8/EEC
Plastics: 1st amendment to 82/71l/EEC
15.3.1993
1.4.1994
L 90 14.4.1993
93I9IEEC
Plastics: monomers 2nd amendment
15.3.1993
1.4.1904
L 90 14.4.1993
93110lEEC
Regenerated cellulose: codification
15.3.1993
1.1.1994
L 93 17.4.1993
931111EEC
Elastomers: nitrosamines
15.3.1993
1.4.1994
L 93 17.4.1993
9513lEC
Plastics: monomers 3rd amendment
14.2.1995
1.4.1996
L 41 23.2.1995
9611 1IEC
Plastics: monomers 4th amendment
5.3.1996
1.1.1997
L 61 12.3.1996
97/48/EC
Plastics: 2nd amendment to 82/71 1/EEC
29.7.1997
1.9.1997
L 222 12.8.1997
396
Rossi
12.2.1 Directives applicable t o all materials and articles The Commission initially drew up a framework Directive, 76/8931EEC, which establishes two general principles: a) the principle of the “inertness” of the material and the “purity” of the foodstuffs, whereby the materials and articles must not transfer any of their constituents to foodstuffs in quantities which could “endanger human health and bring about an unacceptable change in the composition of the foodstuffs or a deterioration in the organoleptic characteristics thereof.” It should be pointed out that the regulation applies not only to packaging but to all articles whose surface can come into contact with food at any stage of production, storage, transport and consumption. For practical reasons the only plants excluded from this are water supply plants. b) the principle of “positive labelling”, whereby materials and articles intended to come into contact with foodstuffs must be accompanied by the words “for food” (or an appropriate symbol) or, where there are restrictions on their use, with some indication of the limitations in question so that consumers or users are informed of the potential use and limitations of the materials and articles they buy. Only for materials and articles which by their nature are clearly intended to come into contact with foodstuffs do Member States have the option of not imposing such labelling at the retail stage. In 1980 the framework Directive was completed by an implementing Directive 80/ 590/EEC, laying down the symbols to affix to materials and articles (see Fig. 12-1). In 1989 the framework Directive 76/893/EEC was replaced by Directive 89/109/ EEC, which, in confirmation of the principles set out above, laid down the sectors in which the Commission is asked to establish Community rules (see Table 12-3) and the criteria and procedures to be followed in the drafting in specific directives, which can be summarized as follows: a) the Commission must, as far as possible, satisfy rigorous health criteria and thus consult the Scientific Committee for Food (SCF)’ on any regulation with implications as regards health;
Figure 12-1: Symbol. 1 The Scientific Committee for Food, set up in 1974 by a Commission Decision, is an independent advisory
body consisting of leading figures from the fields of toxicology, nutrition, medicine, etc. (Decision 74/234/ EEC, 01 No L 136, 20.5.1974, amended by Decision 86/241/EEC, OJ No L 163, 19.6.1986).
European Community legislation on materials and articles to come into contact ...
397
b) specific directives and amendments to existing directives will be adopted by the Regulatory Committee procedure, in this instance the Standing Committee on Foodstuffs (CPDA)*. Table 12-3: Groups of materials requiring legislation. 1. Plastics, including varnish and coatings
2. Regenerated cellulose 3. Elastomers and rubber
4. Paper and board
5. Ceramics
,
6. Glass
7. Metals and alloys
8. Wood, including cork 9. Textile products
10. Paraffin and micro-crystalline waxes
Framework Directive
Ceramics
Plastics
Regenerated cellulose
Glass
Elastomers
Paper and board
Metals
Surface coatings
Figure 12-2: Harmonisation plan.
2 Council Decision 69/414/EEC of 13 November 1969, OJ No L 291, 19.11.69, and its rules of procedure
published in document III/3938/93.
398
Rossi
12.2.2 Directives applicable to one category of materials and articles Having defined the general framework, the Commission began to study three of the principal materials to be dealt with at Community level, these being regenerated cellulose film, ceramics and plastics. One of the reasons for this choice had to do with the possibility of using the rules for these three sectors as models for other, similar, ones (see Fig. 12-2). The main results obtained are described below.
Directive on regenerated cellulose film The first specific “sectoral” Directive was adopted in 1983, this being Directive 831 229/EEC on regenerated cellulose film. Based on a number of existing national regulations, the Community Directive lays down rules which differ from those laid down for plastics (see below). The technical impossibility of applying migration tests to these materials based on simulating liquids, limited use of this material in food packaging (only for solid or semi-solid foodstuffs) because of its technological properties, and the possibility of using a limited number of substances in the manufacture of the finished material were the reasons for treating regenerated cellulose film differently from plastics. For the preparation of the Directive the Commission collected the documentation and evaluated about 150 products considered necessary to manufacture the finished article by the CIPCEL (European professional association in the sector), and then evaluated the risk associated with using them3. The Directive, which has solved the main problems of technical barriers in the sector, established (see Table 12-4): - a list of authorised substances (positive list); - restrictions on the composition of the material. Table 12-4: Rules for regenerated cellulose film. Positive list of authorised substances (114 substances: 72 compounds and 42 groups of substances) Restrictions applicable to authorised substances, expressed in maximum quantity in the finished product except for the limits for MEG and DEG expressed as specific migration limits (= 30 ppm in foodstuffs)
Only for monoethylene glycol (MEG) and diethylene glycol (DEG), which under certain circumstances can be transferred in unacceptably high quantities, have migration limits in food been provided for in Directive 86/388/EEC. The positive list has been amended on two occasions (Directives 86/388/EEC and 92/15/EEC) and the Commission took the opportunity of a third amendment (Directive 93/1O/EEC) to codify all the directives adopted. Now the positive list contains 72 compounds and 42 groups of substances, i.e. 114 chemical products.
Directive on ceramics
In 1984, after some ten years of discussion, Directive 84/500/EEC on ceramic articles was approved; it lays down the specific migration limits for lead and cadmium, according to their intended uses, along with the essentials of the method for checking 3 CEC, Reports of the Scientific Committee for Food, 6th Series, 1978.
European Commitnity legislation on niatuials
~ i i articles d
to come into contact ...
399
those limits (see Table 12-5). The analysis method, on the other hand, is contained in an EEC standard4. In this sector, too, it can be said that the present Directive removes the main technical barriers to intra-Community trade. Table 12-5: Specific migration limits for lead and cadmium. Type of article
Category
Lead
Cadmium
0.8 mg/dm2
0.07 mg/ dm2
Category 1
Non-fillahle articles and fillable articles of internal depth not exceeding 25 mm
Category 2
All other fillable articles
4.0 mg/l
0.3 mgll
Category 3
Cooking utensils; packagings with a capacity of more than 3 litres
1.5 mg/l
0.1 mgll
The test is carried out in total darkness at 22°C lor 24 hours using 4 % acetic acid (v/v) as the simulating liquid.
12.3 Directive on plastics materials Finally, the Commission began to draw up rules for the most complex and important area of packaging, that of plastics materials. With the wide divergence of national regulations, their poor scientific basis and the need imposed by the legislative procedure to consult a whole series of committees and to come to an agreement first of all unanimously and then, after the adoption of the Single Act which revised the decision making procedures, by a qualified majority, the Commission has been obliged to take a very cautious, step-by-step approach towards harmonization. Community legislation has now established: - a list of authorized substances at the Community level; - restricted use of certain substances; - a system of checking migration. It should be said here that the legislation currently applies only to materials and articles made up of one or more layers exclusively of plastics material. The large surface coatings sector is therefore outside its scope.
12.3.1 Community list of authorised substances This list, contained in Directives 90/128/EEC, 92/39/EEC, 93/9/EEC, 95/3/EEC and 96111/EEC, concerns monomers and most types of additives, including substances which constitute the means of polymerization. Colours and catalysts are excluded from the Community lists. As regards monomers, the list is complete and contains 206 substances or groups of substances. Accordingly, it rules out the use of an unlisted monomer at the Community level (positive list). Member States may, however, authorise the use of monomers which appear in Section B of Directive 90/128/EEC until 31 December 2001 (78 sub-
4 EN 1388-1: 1995
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stances or groups of substances). These monomers have to wait for evaluation by the SCF of the new toxicological data that are already available or about to become available. For additives, on the other hand, the list is a partial list currently comprising 289 substances fully evaluated by the SCF whose toxicological characteristics do not necessitate the imposition of any restriction on use other than the overall migration limit. 204 additional substances, fully evaluated by the SCFand 185 of which require a restriction on their use according to the SCF, will be added to the list before long. All of the more important information on the evaluation of substances is to be found in the document entitled “Synoptic” which is to be distributed on the Internet (address: http://cpf.jrc.it/webpack/). Restricted use The legislation in force provides for two types of restriction. The first, applying to all substances, provides that they may not be released alone or together with others in quantities greater than 60 mg/kg or 10 mg/dm2per material or article. This is an overall migration limit which is designed on the one hand to impart a certain inertia to the material intended to come into contact with the food so as to guarantee its purity and on the other hand to avoid setting a special migration limit for each substance. The second type of restriction, which applies to isolated substances, provides that they must not migrate in quantities higher than a certain value fixed according to the toxicological characteristics of each of them. This is what is called the specific migration limit (SML), the value of which is generally established according to the acceptable daily intake (ADI) or the tolerable daily intake (TDI) laid down by the SCF for the substance and the quantity of food containing the substance released by the plastics material and assumed to be ingested by a person in one day. For reasons of prudence this quantity is conventionally put at one kilogram. Assuming, then, that a person weighs 60 kg, the SML is obtained by multiplying the AD1 and the TDI by 60. The following rules have also been used for establishing the Community restrictions: - for substances classified by the SCF in category 4A (“Substances for which it was not possible to establish an AD1 or a TDI but which could be used if the substance which migrates in the foodstuffs or in food simulants were not detectable by an acknowledged sensitive method”) a detection limit of 0.01 mg/kg has been set in the Community directives, sometimes together with an analytical tolerance of 100 %; - for substances classified in category 6 (“Substances for which there is suspicion as to their toxicity and for which data are lacking or insufficient...”) a migration limit of 0.05 mg/kg has been set in the Community directives. Since the SCF recently subdivided list 6 into two categories 6A (“Substances suspected to have carcinogenic properties”) and 6B (“Substances suspected to have toxic properties other than carcinogenic”), the limit of 0.05 mg/kg shall apply only to substances of category 6A because in the case of substances of category 6B the restriction proposed by SCF will be applied. However, the detection limits of 0.01 and 0.05 mgkg are replaced in certain cases by residue limits of the substance in the finished product of 1mgkg and 5 mg/kg respectively if the intended use is restricted and thus exposure is low or if the substance is subject to chemical transformation in conventional migration tests (e.g. hydrolysis) and hence the
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migration limit loses its significance. Replacing the specific migration limit by the residual limit in the finished product assumes that the migration in food or simulating liquids is not greater than 1 YO of the residual quantity in the finished product, as is borne out by data available for certain monomers found in plastics.
12.3.2 Authorization of new substances For new substances to be included in the Community lists the industry has to submit a special request accompanied by a technical file containing a set of data which will enable the SCF to evaluate the risk associated with the use of that substance. These data, shown in Table 12-6, were laid down b the SCF in a document entitled “Guidelines of the Scientific Committee for Food”! With regard to the most important data, i.e. the toxicity data, in principle the SCF requires a long-term study plus data on mutagenesis, reproduction, metabolism, etc. (see Table 12-7). It will be noted that the data to be supplied depend on the scale of the migration (see Table 12-8). Finally, as an aid to the industry the Commission has drawn up a document entitled “Practical Guidetf6which contains all the texts necessary for preparing the technical file and supplies explanations, suggestions and model letters for the transmission of documents. This document will also soon be available on the Internet (address: http:// cpf.jrc.it/webpack/) Table 12-6: Data necessary for the toxicological evaluation of a substance. Identity Physical, chemical and other properties Use Migration data Toxicological data
Table 12-7: Full set of essential toxicological tests. -
a 90-day study of oral administration
-
three mutagen studies: i) a mutagenicity test o n bacteria; ii) a mutagenicity test o n mammalian cell culture; iii) a test to detect chromosomal aberrations in mammalian cell culture in vitro
-
long-term toxicity andlor carcinogenicity studies
-
reproduction studies
-
teratogenicity studies
-
studies of absorption, distribution, metabolism and excretion
5 CEC, Reports of the Scientific Committee for Food, Series N. 26 (1992). 6 “Practical Guide No 1’: EC document with the reference CS/PM/2024 of 2 April 1993 and its updated ver-
sion: “Compilation of all amendments to Practical Guide No 1’: available in English only.
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Table 12-8: Reduced set of toxicological tests for individual cases. Conditions: migration data (ppm)
Toxicological tests required by the Usual decision of the SCF SCF
0-0.0s
3 mutagenesis tests
0.05-5
3 mutagenesis tests
-
no bioaccumulation
90-day oral administration test
-
no toxic effect presumed
hioaccumulation test
540
Full set of essential toxicological tests, unless there are good reasons for dispensing with them
-
if results are positive : use prohibited
-
if results are negative: R* = 0.05 ppm
depends on toxicological results
depends on toxicological results
R*= restriction recommended by SCF which may be expressed in a specific migration limit or a value expressed in mg/kg p.c. or in some other way.
12.4 Directives on the system of checking migration In 1982 the first directive in the sector, Council Directive 82/71I/EEC, laying down a precise reference framework for the system of checking specific and/or overall migration, was adopted. It establishes what simulating liquids (i.e. liquids which can simulate the extractive capacity of foodstuffs), contact times and temperatures are to be used in migration tests performed under standardized conditions. This reference framework, which may seem unduly rigid given the innumerable conditions of contact in reality, was made flexible by the inclusion of a clause which permits Member States to depart from the standard conditions where these prove to be inadequate in the case in question either for technical reasons or because they are too different from the real conditions. Moreover, the first amendment to it, Council Directive 93/8/EEC, made the standard conditions for migration tests more flexible by allowing a greater number of possible combinations of times and temperatures and the use of other simulants for the “fat test” in cases where it is not possible to use those previously provided for. Table 12-9 shows the conditions which now apply. A second amendment, Directive 97/48/EEC, laid down the conditions of use of volatile solvents, e.g. isooctane and ethanol, as test liquids in the “fat test”. It provided that these solvents may replace olive oil or the other fat simulants (HB 307, sunflower oil, etc.) if the fat test is not applicable in its basic version for technical reasons or in routine checking. These conditions are shown in Tables 12-10 and 12-11. Directive 82/71UEEC, which specifies the simulating liquids to be used in the case of materials and articles intended to come into contact with food products of all kinds or with foods not known u priori to the manufacturer, was followed by another directive, 85/572/EEC, laying down the simulating liquids to be used for materials or articles intended to come into contact with only one food product or with one specific group of food products. Table 12-12 gives examples of the application of this Directive.
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Table 12-9: Conditions for migration tests. Conditions of contact in actual use
Test conditions
Contact time t I 0.5 hours 0.5 h < t I 1 hours 1.0 h < t I 2 hours 2 h < t I 2 4 hours t > 24 hours Contact temperature T I 5°C 5 "C < T I 20°C 20 "C < T 5 4 0 ° C 40 "C < T I 70 "C 70 "C < T 5 100 "C 100 "C < T I 121 "C 121 "C I T 5 130 "C 130 "C < T 5 150 "C T > 150 "C
Test time 0.5 hours 1 hour 2 hours 24 hours 10 days Test temperature 5 "C 20 "c 40 "C 70 "C 100 "C or reflux temperature 121 "C" 130 "c': 150°C"" 175 TL*
* Use simulant C at reflux temperature. ** Use simulant D at 150°C or 175 "C in addition to simulants A, B and C used as appropriate at 100 "C or at reflux temperature. Table 12-10: Conventional conditions for substitution tests. Test conditions with simulants D 10 d - 5°C 10d-20"C 10 d 40°C 2h-70"C
Test conditions with isooctane 0.5d-5°C 1 d-20°C 2d-20"C 0.5 h-40°C
Test conditions with ethanol 95 YO 10 d - 5°C 10 d - 20 "C 10 d - 40 "C 2.0h-60°C
Test conditions with MPPO'
0.5 h - 100°C 1 h - 100°C 2 h - 100°C 0.5 h - 121 "C 1 h-121°C 2h-121"C 0.5 h - 130°C I h - 130°C 2h-150°C 2 h - 175°C
0.5 h-60°C* 1.0 h-60"C* 1.5 h - 60 "C* 1.5 h - 60 "C* 2.0 h - 60 "C* 2.5 h - 60 "C* 2.0 h - 60 "C* 2.5 h - 60 O C * 3.0 h - 60 "C* 4.0 h - 60 "C*
2.5 h - 6 0 ° C 3.0 h - 60"C* 3.5 h - 60 'C* 3.5 h - 60 "C* 4.0 h - 60 "C* 4.5 h - 60"C* 4.0 h - 60 OC* 4.5 h - 60 "C* 5.0 h - 60"C* 6.0 h - 60 "C*
0.5 h - 100°C 1 h-100°C 2 h - 100°C 0.5 h - 121 "C 1 h-121°C 2 h - 121 "C 0.5 h-130°C 1 h-130°C 2 h - 150°C 2 h - 175 "C
-
_ _ .
-
_ _ _ _
(*) Volatile test media are used up to a maximum temperature of 60 "C. It is a precondition for substitution testing that the material or article should withstand the test conditions applied with simulants D. Immerse a test specimen in olive oil in the appropriate conditions. If the physical properties are changcd (e.g. melting or deformation), the material is considered to be unsuitable for use at that temperature. If the physical properties are not changed, carry out substitution tests using new specimens.
7 MPPO = modified polyphenylene oxide.
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Table 12-11: Conditions for using alternative fat tests. It is possible to carry out alternative tests using isooctane or ethanol or other solvents if the following conditions are satisfied:
(a) the values obtained in a “comparative test” are higher than or equal to those obtained in the test carried out with olive oil or other fat simulants; (b) the detection limits are not exceeded. By way of derogation from condition (a), the comparative test may be dispensed with if there is conclusive evidence based on experimental scientific results that the values obtained in the alternative test are equal to or higher than those obtained in the migration test.
Table 12-12: Some examples taken from the Directive laying down the list of simulants to be used in the migration tests. Simulants to be used Water
3 Oh acetic acid
Non-alcoholic beverages, etc.
X
Chocolate, chocolate-coated products, etc.
-
Fresh, chilled, salted or smoked fish
15 % ethanol
Olive oil
X
-
-
-
-
XI5
X
-
-
XI3
Animal and vegetable fats and oils, etc. Vinegar
-
-
-
X
-
X
-
-
Fried Dotatoes. fritters and the like
-
-
-
XI5
Description of foodstuffs
Only the simulant indicated by an “X” may be used. When “X” is followed by an oblique stroke and “3” or “5”. the result of the migration tests should be divided by the number indicated. known as the “reduction factor”. This figure is conventionally used to take account of the greater extractive capacity of the simulant for fatty foods compared with other types of foods.
12.5 Other complementary Community initiatives To help the supervisory authorities and industry to verify the conformity of products with the directives, the European Commission started a number of initiatives which resulted in: - plastics reference materials with a certified overall value for migration into the four simulants; - a bank of standard samples of substances contained in the Community lists, accompanied by corresponding spectral and physical data, to facilitate the identification and quantitative determination of these substances; - standard methods for evaluating overall migration into the four simulants and certain specific migrations or contents in the finished products. For this the Commission gave CEN a special mandate. Other specific evaluation methods have been developed as part of the activities of the “Standards, measurements and testing” Unit of the Directorate-General for Research, pending their eventual standardization.
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Future programmes For the time being the Commission will probably seek to add to the present Community legislation other directives which should have as their immediate objectives: - completion of the list of additives; - extension of the scope of Directive 90/128/EEC to cover most of the products which are excluded from it at present, in particular surface coverings such as varnished materials on any kind of backing; - laying down specific rules for recycled materials. In the longer term, rules will be adopted where necessary for colourings, adhesives, inks, catalysts, etc.
12.6 Directives concerning individual substances While legislating on a broad scale, i.e. in relation to various sectors of production, the Commission has also been obliged to lay down rules for individual substances which have been the cause of considerable public concern. This applies to the vinylchloride monomer used in PVC and the mono (MEG) and diethylene glycol (DEG) used in regenerated cellulose film.
Directives on vinylchloride A directive was adopted in 1978 regarding exclusively materials and articles containing free vinylchloride monomer (Directive 78/142/EEC). It lays down the maximum quantity of free monomer permitted in the finished article as 1 mg/kg and states that such materials and articles must not release to the foodstuffs with which they are in contact any amount of vinylchloride detectable by a method of analysis with a detection limit of 0.01 mg/kg. In 1980 and 1981 two further directives were adopted which lay down the method of analysis for vinylchloride in the finished article and in foodstuffs respectively (Directives 80/766/EEC and 81/432/EEC).
Directive on M E G and DEG in regenerated cellulose film In 1985, following application of the safeguard clause by the Federal Republic of Germany, which had observed excessive migration of monoethylene glycol and diethylene glycol from regenerated cellulose film under certain circumstances, the Commission proposed a directive, promptly adopted by the Council (Directive 861 388/EEC), amending the conditions of use of these substances and establishing a migration limit in foodstuffs of 50 mg/kg for both of them, which was reduced t o 30 in Directive 93/10/EEC. Draft directive on nitrosamines in rubber teats and soothers On 15 March 1993 the Commission adopted Directive 93/11/EEC concerning the migration of N-nitrosamines and N-nitrosatable substances from elastomer or rubber teats and soothers. This Directive stipulates that these articles must not release any Nnitrosamine and N-nitrosatable substance detectable by a validated method able to
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detect 0.01 mg/kg of total N-nitrosamines and 0.1 mg/kg of total N-nitrosatable substances. It also specifies the method to be used although a detailed description of the analytical procedure is left to the CEN’s TC252/WG5.
12.7 Activities of other institutions connected with the Community Directives A full analysis of current legislation in the European Community should also take into account the national rules and recommendations in force in certain countries on articles or materials not yet harmonized by Community directives, which this report does not do. The Council of Europe, however, prepares resolutions to which the Member States of the Community often refer in the absence of Community directives or national legislation. The Council of Europe has made the following resolutions in the areas not covered by Community directives: - Resolution of the Council of Europe AP (89) 1 relating to the use of colorants in plastics intended to come into contact with foodstuffs; - Resolution of the Council of Europe AP (89) 2 relating to ion-exchange resins used in the processing of foodstuffs; - Resolution of the Council of Europe AP (92) 2 on control of aids to polymerisation for plastics materials and articles intended to come into contact with foodstuffs. - Resolution of the Council of Europe AP (96) 5 on varnishes intended to come into contact with foodstuffs. The main activities in progress are as follows: - draft resolution on paper and board; - draft resolution on ink.
12.8 Conclusions Harmonization of legislation at the Community level is moving forward slowly but surely. Progress is often slow because the technical and scientific data necessary for selecting the most appropriate measures are not available. Also, the Member States and the professional organizations require problems to be solved at the Community level which have never been solved at the national level, so the Commission has to provide for expensive and complex prenormative research or standardization programmes which will make it easier to secure agreement on legislative proposals or reduce negative preconceptions. However, over the last few years the Member States have shown a firm resolve to speed up progress and the Commission is currently preparing a series of texts which should make it possible for legislation on plastics to be fully harmonized at the Community level by the year 2000.
Reactivity in Molecular Crystals Edited by Yuli Ohashi Copyright @ K d a o r h a Ltd .Tokyo. 1999
13 Sensory problems caused by food and packaging interactions Otto Piringer and Monika Riiter
Off-flavors in food packages are not only a legal but also often an economic problem, when market recalls have to be made. Off-odors are due to the presence of one or several substances whose strong odors affect the food’s specific aroma. This chapter deals with solutions for several kinds of off-flavor problems arising from interactions between packaging and food.
13.1 Problems with off-odor compounds An off-odor can be caused by a single substance or by a mixture of several substances. Difficulties in describing an off-odor occur particularly in the second case where the smallest change in the mixture composition can lead to a complete palette of odor nuances. The individual substances leading to the formation of off-odors can be classified according to different viewpoints: source, odor thresholds and chemical structure. The main components from raw materials, contaminants as well as aroma compounds are differentiated by their origin from substances that can be taken up by the packaging from the surrounding atmosphere. Off-odor forming residual raw materials can be further subdivided into residual monomers, e.g. styrene, vinyl acetate, acrylic esters, and residual solvents e.g. ethyl acetate. The presence of such residual raw materials can be deduced from knowledge of the chemical composition of the packaging, which allows them to be specifically searched for and quantitatively analyzed. The prediction of the occurrence of the other category of undesirable aroma compounds is very difficult because they can be products of widely varying reactions between components of the packaging through oxidation, condensation, dehydration etc. In most cases these reactions occur unexpectedly. For this reason and because of their often extremely low odor thresholds t h e identification and clarification of the cause of their formation is connected with significant time and cost expenses. It often happens in practice that the off-odor is found in the packaged product after it has been distributed in the market, leading to consumer complaints. This happens since the formation of off-odors occurs very slowly or because they require longer times to diffuse through the packaging material. Despite these difficulties with the identification of the off-odor sources, most offodor problems have several typical characteristics in common: - In general off-flavors occur sporadically but from different directions. Often the causes can be found in new production methods, especially for the packaging material or package.
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Presently, changes in the packaging material for ecological reasons, e.g. reduction or elimination of proven barrier layers play an important role. Often substitutions of packaging materials are carried out for environmental reasons and are not fully developed technically. The contamination of raw materials like e.g. plastic granulates widely distributes off-flavors to many converters. In order to solve the off-odor problem in food packaging, all the packaging materials used as well as their raw materials and additives have to be considered. Very often one has to deal with contaminated packages, the history of which is unknown. Lack of knowledge about the life cycle of a package, its packed product and their individual components makes the solution of the off-odor problem tremendously difficult. Not infrequently there is an absence of good reference samples since the complete production run shows off-flavor. In this case the solution of the off-flavor problem is significantly more difficult since there are no samples for comparison in sensory and analytical analyses. The testing of these off-flavor problems requires a systematic approach where prior experience is necessary. In spite of the best instruments and long years of experience, numerous difficulties can occur during the solution of off-flavor problems: - Numerous substances have the same odor. Table 13-1 shows examples of the odor descriptions ‘musty’, ‘painty’ and ‘plastic’ which are used for a number of different substances. It is therefore obvious that for example the description ’musty’ of an off-flavor does not give any concrete reference to the kind of the off-odor substance involved. Table 13-1: Possible chemical compounds related to specific sensory descriptors (Saxby 1993). Descriptor
chemical compound
musty
2,6-Dimethyl-3-methoxypyrazine 2-Methoxy-3-isopropylpyrazine 2,4-Dichloroanisole 2,6-Dichloroanisole 2,3,6-Trichloroanisole 2,4,6-Trichloroanisole 2,3,4,6-Tetrachloroanisole Pentachloroanisole 2,4,6-Tribromoanisole Geosmin 2-Methylisoborneol 1-Octene-3-01 Octa-1.3-diene a-Terpineol 4,4,6-Trimethyl-1,3-dioxane
painty
he pane-Zone trans,trans-Hepta-2,4-dienal trans-l,3-Pentadiene 2-(2-Pentenyl)furane
plastic
Benzothiazole Methylacrylate Methylmethacrylate trans-2-Nonenal Styrene
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- The same substance shows different odors depending on its concentration. Table
13-2 shows the variation of the flavor description of trans-2-nonenal depending on its concentration in water. Table 13-2: Variation of taste description of trans-2-nonenal with concentration in water Concentration [I@]
Taste description
0.2 0.42.0
Plastic Woody Fatty Cucumber
840
1000
- Another effect which makes the solution of off-flavor problems significantly more
difficult is the fact that different odor active substances overlap with one another to form an unspecified global odor. One of the biggest difficulties in such overlapping mixtures is the very different and sometimes very low odor thresholds of these substances.
13.2 Identification of off-odor compounds The threshold limits of chemical compounds can lie over a range of 10 orders of magnitude or more (Table 13-3). The saturated hydrocarbons and organic solvents have high threshold limits and are as a consequence relatively odorless. Esters of acrylic acid and a$-unsaturated ketones and aldehydes belong to intensive aroma compounds. Descriptions of several methods of analysis are given in the following because of their relationship to sensory properties. These methods are not applied for the simple case mentioned in the introduction where a specific substance is studied and only its quantitation is of interest. The beginning of an investigation of an off-odor always includes a qualitative and quantitative global sensory analysis. A global sensory analysis emphasizes as detailed as possible a description of the odor impression and its intensity. Afterwards the sample is placed in a closed glass container to test if the odor prefers water, fat or a powder with high adsorption capacity, e.g. lactose, after diffusion through the gas headspace. A comparison of the odor and taste in these test medium with a sensory neutral control sample in many cases gives an indication of its partitioning characteristics. From this, conclusions can be drawn as to the polarity of the aroma compound. The extraction of the aroma compound from the packaging sample and its concentration follows as the next step. Different techniques are used for this, for example steam distillation, extraction with organic solvents or desorption with the help of a stream of gas followed by sorption in a solid or liquid. Some compounds, e.g. unsaturated carbonyl compounds, can be extracted from the packaging using water and afterwards desorbed from the aqueous solution using a stream of gas in a counter current column. The advantage of this method comes from the selectivity of the process for the polar compounds. This method selects against non-polar hydrocarbons for example which are only slightly soluble in water, are present in high concentrations in
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many packaging materials and cover up the odor compounds in the subsequent GC separations (Piringer, Skories, 1984). Table 13-3: Absolute odor threshold (OT,) concentrations of different chemical compounds.
OT, mdm3
Compound
103
Heptane, Octane, Nonane
102
Ethanol, Acetone
10'
Isopropanol (50).Ethylacetate (50). n-Butanol(30), Methylethylketone (30). Ethylglycol (20). Toluene (20), Ethylglycolacetate (lo), lsopropylacetate (10). Methacrylic acid
10"
Butylacetate, Vinylacetate, Acetic acid, Acrylic acid. 2-Ethylhexylmethacrylate, 2-Ethylhexylacrylate, Methylmethacrylate
10-1
Styrene, Mesithyloxide, n-Butylmethacrylate. Ethylmethacrylate, Methylacrylate
10-2
n-Butylacrylate, Eugenol, Butyric acid, Chlorophenol
10-3
Ethylacrylate, 2-Nonena1, Ethylmercaptane
101'
1-0ctene-3-one (Mushroom-ketone), Pentylmercaptane
10-6
Vanillin
The odor compounds retained on a sorbant are desorbed with a volatile solvent, e.g. ether, and after concentrating the solution are separated with a gas chromatograph (GC). It is necessary in this case to split the carrier gas stream coming off the column into two streams. One stream is directed to a mass spectrometer or other physical detector (Fig. 13-1) and the other stream is available for sniffing. With this detection method three cases shown in the figure can occur: 1. One obtains a physically detectable signal but no odor impression at the same retention time. 2. An odor is found simultaneously with the detector signal. 3. In spite of smelling an odor no physical signal is detected. Of the two interesting cases 2 and 3, the third case requires further concentration and enrichment of the sample until a physically measurable signal is obtained. In case 2 it is possible to deduce the structure of the substance with the combination of the mass spectrum with the retention time. It must be mentioned that often false interpretations are made using this method when the physically measured peak from a sufficiently concentrated sample contains overlapping peaks of an odorless substance and an odor active substance. The description of the off-odor, identified at the beginning of the study in the global sensorial evaluation, which has been separated into several components by the gas chromatographic sniffing method can have seemingly large deviations in the descriptions of the individual components from the initial off-odor description. When one is fortunate enough to have an idea of the structure of one or several odor producing substances then the next step is to synthesize the substance or substances or reproduce them using another way. Only when the same retention time, the same mass spectrum and the same odor impression are obtained as in the sample material can the identification be considered to be assured.
Sensory prohlenis criiiserl by food and packaging interactions 1
2
41 1
3
Detector
Nose
-
m
t(rnin)
Figure 13-1: Separation and identification of odor compounds by means of physical and physiological dc tectors.
Often the most difficult step follows the identification of the odor substance: finding the cause of the presence of this substance in the packaging in order to avoid future quality problems. To do this it is advantageous to have as much information as possible on the chemical composition, treatment, and complete history of the package. With this information, it is sometimes possible to discover a reaction pathway for the offending substance or substances. If one or more possible paths are found that could lead to the formation of the offodor, then the most likely path must be determined using a model study. Only then can the problem be considered as solved (Piringer 1993).
13.3 Case studies In the following, several examples have been selected from actual case studies carried out in previous years in the author’s laboratory. One of the experiences made is that at certain times specific off-odors seem to occur for different manufacturers, in other words “the flavor of the month”. This is apparently due to the widespread use of some technology for a particular application at a certain point in time.
13.3.1 Off-odor from styrene-butadiene coatings An earlier off-odor problem that surfaced was the presence of 4-phenyl-cyclohexene in styrene-butadiene coated paper (Koszinowski et al. 1980). This compound was created by a Diels-Alder condensation reaction involving a molecule of styrene and butadiene and is differentiated by its odor from the isomeric 3 and t-phenyl-cyclohexene compounds which cannot be formed by such a condensation reaction. The recognition threshold of this compound in the headspace over an aqueous solution lies around a concentration of 10 pgikg (10 ppb). The typical odor of this compound at concentrations of 4-phenyl-cyclohexene in paper over 4 mg/kg (4 ppm) is easily identified. A GC determination in this concentration range is also possible without difficulty and its identification with MS using the relative molecular mass of 158 and one of the retro Diels-Alder decomposition product fragments at m/e = 104 (styrene) and m/e = 54 (butadiene) is definitely possible. From the investigation of different off-odor influencing factors it was determined that the off-odor problems in coated papers become more intense with increasing moisture content.
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13.3.2 Off-odor from printing In another off-odor complaint, a customer suspected that methoxy-propanol from printing of the film or a contaminant in it was causing the off-odor (Koszinowski, Piringer 1986). With help of the above mentioned selective enrichment of the off-odor using extraction with water and desorption with gas two components were found by GC separation (Fig. 13-2a). Of these two components, the second reproduced the offodor. Using MS in selective ion monitoring (SIM) mode, the relative molecular mass m/e = 126 and the characteristic mass fragments of m/e = 97 and m/e = 69 were measured (Fig. 13-2b). The mass spectrum was characteristic of 5-methyl-4-heptene-3-on and results from a a splitting of a carbonyl group and loss of an ethyl group. A further contribution to the 97 fragment with the highest intensity (base peak) resulted from the splitting on the tert C-atom and loss of the other ethyl group from the molecule. The cis and trans isomers of the unsaturated bond correspond to the same mass spectrum for both components and the two components could only be differentiated from their different GC retention times. a
b
2 1
1
2 126
97
69
-t - t Figure 13-2 Gaschromatogram (a) and SIM-spectrum (b) of two isomers of an unsaturated ketone after selective enrichment. d e = relative molecular or fragmental mass; t = time.
Sensory problems caused by food and packaging interactions
413
The formation of the ketone by an Aldol condensation reaction from methylethylketone (MEK), a commonly used solvent, was suspected based on its structure. A systematic study of all raw materials used for the manufacture of the contaminated packaging led to the printing ink used. Traces of the Aldol condensation product were found only in the printing ink containing MEK. However, the trace amount of the above ketone found in the MEK was too little to be the source of the concentration found in the packaging and to account for the odor intensity. A further test of the printing ink showed that the polyvinyl butyral stabilized with NaOH and used as a binding agent functioned as a catalyst for the Aldol condensation. The white pigment used in the printing ink acted finally as a dehydration catalyst:
0 II
CH3-CH2-C-CH3
0
+ CH3-CH2-C II -CH3 1 OHOH I
(Polyvinylbutyral)
0 II
CH3-CH2-C-CH2-C-CH2-CH3 I
CH3 1 -HzO (Ti021 CH3 I CH3 - CHI - C = CH - C - CH2 - CH3 II 0
As a conclusion it results that neither the suspected methoxy propanol nor the
MEK used as solvent could contain a high enough concentration of the off-odor-causing ketone. The off-odor developed first after printing and subsequent evaporation of the solvent. Because of its relatively low solubility and good solubility in the plastic the unsaturated ketone was slowly set free during further storage of the packaging.
13.3.3 Unsaturated carbonyl compounds A packaging material with exceptional importance for food is PE. Depending on the source of this plastic, water brought in contact can produce various nuances of a characteristic odor as well as flavor changes. The description of this “PE odor” ranges from candle-like, stale, stuffy, musty, to soapy or rancid. For this reason PE used for food applications has particularly high quality standards set. It is well known for example in the saturated LDPE polymer chains that a certain number of double bounds exist which can be measured with IR spectroscopy. By extraction with non-polar solvents and GC separation, numerous alkanes and alkenes can be identified which are dissolved in small concentrations in the PE. The odor thresholds of these compounds are in general so high that these hydrocarbons play no sensory role. As a result no correlation can be made between the total amount of volatile compounds isolated from PE or the “fingerprint” chromatogram from a GC separation and the sensory properties of a sample. The relevant sensory compounds as a rule are the (order of magnitude) less concentrated oxygenated compounds in the
414
Piringer
volatile fraction. They are sensory-perceptible because of their extremely low threshold levels, even though they are covered up by the much more concentrated hydrocarbons in chromatography even with the use of high resolution separation columns. One sees there is a large amount of work necessary to separate and obtain suitable examples of olefin oxidation products to study the numerous possible olefin structures. From the three different general types of structure RCH=CHR', RR'C=CHz and RCH=CH2, where R is an unbranched residue, it was decided to study only the last one due to practical considerations (Koszinowski, Piringer 1983). The goal of this study was to measure the threshold levels of several selected oxidation products of 1-alkenes, along with their instrumental identification and determination in trace amounts using GC and MS. Different concentration relationships of several components in this class of substances are responsible for individual PE odor nuances. This was determined by the manufacture of different mixtures followed by subsequent sensory evaluation. By selective enrichment, a$ unsaturated carbonyl compounds could be detected in PE-containing packaging materials. The oxidation of the 1-alkene occurs most likely through the formation of a free radical from the splitting off of hydrogen on the third C-atom (allylic CH-compound). It is expected that the oxygen subsequently attacks i n the 1 and 3 position due to the allylmesomerism: -H' __+
++
.
CH3 -(CH,),-CH
- CH=CH2
CH3 - (CH,),-CH=CH - CH;
With this, the formation of the 2-alkene-1-01, 2-alkene-1 -al, 2-alkene- 1-carboxylic acid, 1-alkene-3-01and 1-alkene-2-one is predestined. Since the odor thresholds of 1-alkene-1-ole and 1-alkene lie several orders of magnitude over those of the a$ unsaturated carbonyl compounds, an exact sensory determination of the threshold is possible only using GC separation. Traces of unsaturated aldehydes or ketones dissolved in 1-alkene or alkenol, can easily be formed by oxidation. These traces are easily confused with odors not coming from the alkene and alkenols during threshold determinations using the usual methods that do not separate the mixtures into individual components. Table 13-4 shows the threshold levels found. Values are given for lowest amount of substance detected by sniffing at the end of the GC column as well as the threshold level concentrations in air. The threshold value for trans-2-alkenal in air could be taken from the literature and used to calculate the threshold value from the GC determination. While the threshold levels are independent of the apparatus and can be compared with literature values, the smallest amount of compound that is still detectable can be used for a comparison of the physical detection limits. A common characteristic of the homologous series of oxygen derivatives is the minimum threshold level for molecules with 9 carbon atoms. The value of the aldehyde lies one order and the alcohol lies two to three orders of magnitude higher than the corresponding ketone. The values of the alkenes, 1-heptene to 1-decene were practically constant and 5 to 6 orders of magnitude over the alkenones derived from them. 1-nonene-3-one is consequently an odor compound with an extremely low threshold value.
415
Sensory problems crtrrsed by food and packaging interactions
Tablc 13-4: Absolute odor thresholds (ng) and OT, concentrations (mgim’) of alkenes and the corresponding alcohols and unsaturated carbonyl compounds. The number of C-atomes in the molecule is designated with n. ~~~
1-Alkenes
1-Alkene-3-oles
~~~
I-Alkene-3-ones
~~
2-Alkenales
ng
mg/m’
5
-
-
900
0.66
28
6
-
-
100
0.07
1
0.0007
45
0.033
7
50000
37
100
0.07
0.9
0.0007
45
0.033
8
50000
37
150
011
0.15
0.0001
9
0.007
9
50000
37
60
0.04
0.025
0.00002
1.6
0.001
10
50000
37
11
-
-
500 500
0.37 0.37
1.5 1.5
0.001 0.001
12
-
-
15
-
-
n
ng
5000 200000
mg/m’
3.7 150
ng
250 4000
mg/m’ 0.02
0.18 2.Y
ng -
mg/m’ -
11 18
0.008 0.013
-
-
-
-
Some of the carbonyl compounds and alcohols form important aroma components in various foods. 1-0ctene-3-one and 1 -octene-3-01 are the main components of fresh mushroom aromas. From the series of aldehydes, 2-heptenal to 2-decenal are found in potato chips, and 2-nonenal forms an important component of the aroma in carrots. Through a combination of selective enrichment, G U M S analysis and sensory analysis when considering structure characteristic retention times and molecule fragments. the presence of 1-heptene-3-one and 2-nonenal could be identified in several PE-containing packaging materials. These compounds were the main cause of the offodors present in these samples. Furthermore they were not found in any of the PE granulates studied. In addition several low molecular weight carbonyl compounds and higher molecular weight alcohols were identified which contributed a leek-like as well as soapy note to the total odor. These compounds play only a subordinate role because of the volatilities of the former and the low odor intensities of the latter. A source for unsaturated carbonyl compounds in PE-containing packaging material are alkane traces coming from PE. The alkane traces, whose concentrations are below the threshold levels, can be transformed into unsaturated carbonyl compounds by ageing processes under light and the influence of oxygen or under high temperatures during processing. This could be shown to occur by storage of pure 1-alkene in which all derivable oxidation products were found. There are other sources, independent of PE, for these classes of unsaturated carbonyl compounds which can lead to the same or very similar odor impressions. An example of this is the above mentioned l-heptene3-one formed from 2-ethyl-hexanol in paperboard samples. The importance of the unsaturated carbonyl compounds as potential causes of offodors in packaging has been shown in the results of the preceding study. The properties of the compounds responsible are the following: 1. The a$ conjugation of a C=C bond with the carbonyl group give this class of substances a relatively high stability. 2. Numerous reactions of trace concentrations of sensory-harmless substances lead to the formation of this group of substances.
416
Piringer
3. All representatives of this class have relatively low threshold levels, particularly those with 8 and 9 carbon atoms. 4. The retention of these substances in the packaging is in general very strong because of their relatively low volatility and not high polarity. 5. The partly very low threshold levels of this class of compounds complicate instrumental analysis because the concentrations necessary to form off-odors are so low that they are covered up by other trace components. Only the combination of instrumental and sensory analysis methods leads to successful solving of the problem. In addition to the somewhat comprehensive treatment of alcohols and carbonyl compounds, the carboxylic acids can also play a role in the sensory properties of packaging materials. Because of their very low volatility their contribution is mainly to the taste of aqueous solutions.
13.3.4 Off-odors caused by halogenated phenols and anisols Due to their extremely low sensory threshold levels, chloro- and bromoanisoles have been clearly identified for years as the cause of off-odors. The following case shows how new variations and combinations of unpredictable events can lead to a problem whose solution requires a great amount of work. A few years ago there was a series of off-odor problems in packed food over a relatively short time period, occurring in different types of packaging and materials related to one another through the use of a polymer granulate. Even though each problem had a different nature, all of the samples studied had several similar characteristics: 1. The description of the off-odor matched that for trichloro- (TCA) as well as tribromoanisole (TBA). 2. In all cases the packaging contained some polyethylene. 3. The number of samples affected was relatively small which means they came from a relatively small batch. Together with the seemingly simultaneous occurrence, these characteristics point to a common cause. Since there was no technical reason to assume formation of TCA or TBA in PE, the study was directed to the PE granulate because it was the simplest matrix. The discovery of TCA led to the suspicion that the granulate had become contaminated in some way. However, the occurrence of the contamination in granulates from different manufacturers could not be explained. The TCA and TBA found in PE coated cartons came from the PE and not from the paperboard. Finally, these substances were found in food that was packed in pouches containing PE. The cause of these problems was eventually traced back to the presence of halogenated phenols in several of the wooden pallets used for transport. One difficulty in solving the case was finding wood samples contaminated with such phenols, since in international transportation the wooden pallets are stored for only a short time in one place and no reserves exist. The testing of wood samples with obvious off-odors and those without gave a clear correlation with an analytical analysis of the wood extracts using GC separation with halogene-specific detection. The formation of TCA and TBA from the corresponding halogenated phenols by microorganisms is known and likewise the use of such phenols as wood preservatives
Sensory problems catrwd b-y food and pnckagitig intermtioris
417
(Whitfield et al. 1991). If by chance a bag containing PE granulate lies on a wood pallet containing halogenated phenols it is possible that contamination of the PE layer adjacent to the wood occurs by diffusion of the anisole. Given the tremendously low threshold levels on one hand and the low thickness of the PE layers needed for food packaging on the other, it would be possible for example that several thousand packages are affected from a bag containing 25 kg contaminated granulate. With the high sensitivity of today’s mass spectrometers trace amounts down to approximately 50 ppt (ng/kg) of TCA or TBA can be detected in the affected packaging (Ewender et al. 1995).
13.3.5 Methylmercaptopentane as an interaction product between packaging and food A complaint of an off-odor that smelled like cat urine occurred practically simultaneously in two different cooked ham products. Both products were cooked and packed in polyamide/ionomer laminate films coming from different film manufacturers with different sources for the PA but the same source for the ionomer. One of the two cooked ham producers used two different printing inks on the same laminate and received complaints only for one of the two packages. The simultaneous complaint cases as well as the observed dependence on the printing ink pointed to a complex relationship for the mechanism needed to describe the formation of the off-odor (Franz et al. 1990). A search of the literature revealed several chemical structures that produced catlike odors which are shown as molecules I to V in Fig. 13-3. The tertiary mercaptoamyl group is common to all 5 structures and likely t o be responsible for the typical odor. Structure I, a H2S adduct of mesityloxide with an extremely low threshold level, was involved in several off-odor problems. For example the compound was found the cause of off-odors in a freshly painted slaughterhouse, in sulfur-containing vegetables and in waste water. Even though no packaging problem was known to exist with this compound, structure I immediately appeared as a likely candidate as the source of the off-odor in the cooked ham. In this case mesityloxide itself or a chemical precursor like acetone or diacetone alcohol (DAA) must have been used in the printing ink of the film under complaint and it subsequently migrated into the laminate. A GC study of the film for volatile components was able to confirm the fact that in both of the problem films DAA was detected (3 mg/dm2 and 9 mg/dm2) while the good film was found to contain none. At the same time mesityloxide itself was not found in any of the films.
I
Figure 13-3: Several chemical structures with “cat-like” odor.
418
Piringer
2
1
I
I
4
6
8
I
-
I
10 12 t [min]
I
14
Figure 13-4: Gaschromatogram of the off-odor-compound.
To confirm that structure I was in fact the cause of the off-odor, compound I was produced synthetically by a reaction of hydrogen sulfide with mesityloxide. Also the off-odor from the problem ham was first extracted with methanol and hexane and then concentrated. Subsequent study with GC showed the synthesized compound 1 (Fig. 13-4), whose structure was confirmed by MS, had the same FID retention time as the substance producing the off-odor at the end of the GC column identified by sniffing the ham extract. With this result the identity of the cat-like off-odor was explained, but not the mechanism of formation. The unanswered question was: did the DAA used contain a large enough amount of mesityloxide impurity to form the off-odor or was the DAA that migrated into the film converted into mesityloxide through splitting off of a hydrogen. The GC analysis of technical DAA showed a mesityloxide content of 1 %. Under the consideration that only a fraction can permeate into the cooked ham and there only a small fraction of the permeated amount reacts to form compound I, it was suspected that a chemical conversion of DAA to mesityloxide was taking place in the polymer laminate. The fact that the ionomer has a Lewis as well as a proton-acid character tends to lend credence to this suspicion. Corresponding model studies in which DAA-saturated laminate films as well as DAA-saturated mono films were heated under the cooking conditions confirmed the suspected dehydration reaction of DAA by the ethylene ionomer. This gave an logical explanation for the mechanism of formation for the 4-methyl-4-mercaptopentane-2one off-odor (Fig. 13-5). As further proof of the model study a laminate containing DAA was heated in the presence of an odorless cooked ham or in the presence of cystein, a sulfur-containing amino acid, to produce the off-odor. The identity of this off-odor was then characterized by G C separation with subsequent sniffing detection and comparison with the retention time of compound I. The consequence of the knowledge gained from this study was that when printing ionomer films or laminates containing ionomer in which foods with sulfur-containing proteins are to be packed, the absence of mesityloxide and its chemical precursors like acetone and diacetone alcohol must be guaranteed.
Sensory problems carised by food and packaging interactions
419
Print
>,K I OH
printed PAtlonomerlaminate
Diacetone alcohol
1
I
t
-
lonomer layer
0
t Ham as H2 S - souw
I
0
SH
Figure 1.7-5: Formation mechanism of the off-odor-compound.
The cases described in these examples confirm the variety of interaction possibilities between components of the packaging and filled product. In addition these components must be considered in extremely low trace amounts for the quality assurance of the product.
13.4 Parameters determining odor and taste Article 2 of the framework directive 89/109/EEC forbids the alteration of the sensory properties of food by the transfer of substances from food contact materials. However, this does not represent absolute sensory neutrality. This principal is not defined just for the packaging but is rather a function of the properties of the packaging, the food and their compatibility. The avoidance of complaints and damages is the reason for desiring knowledge of threshold limits of sensory-active substances in packaging materials. With this knowledge, instrumental quality control analysis of packaging materials can be carried out as a preventive measure. Whether or not a certain substance in a given application leads to a perceptible quality change and with it a violation of food regulations depends on numerous parameters. Therefore, no generally valid limit value can be assigned to a substance in comparison to toxicologically relevant substances. The influence of a sensory active component from the packaging on the product is largely determined by the following parameters (Granzer et al. 1986):
420 -
Piringer
Concentration of component in packaging material.
- Solubility of component in packaging material
(partition gas phase/packaging material). Solubility of component in food (partition gas phase / food). Sensory threshold level of component. Type and intensity of food aroma. Diffusion rate of component in packaging material. - Diffusion rate of component in food. - Time and temperature of storage. - Ratio of amount of packaging material to amount of food. Knowledge of these parameters makes it possible for a case by case determination of the limits for avoiding a reduction in quality. The lowest concentration of a substance in air sufficient to give a perceptible odor is defined a the absolute threshold level and is designated OT, in the following (see Table 13-3). A criterion for the selection of a solvent for use in packaging manufacture, e.g. for printing inks, is a possible high OT, value between 10 and 100 mg/m3. The threshold levels of solvents contained in parenthesis in Table 13-3 serve to give a slightly better differentiation between different solvents. The published threshold levels from various authors can in general vary over three orders of magnitude for a given compound. This widely scattered range is partly due to the imprecise definition of the perceptible sensory concentration as either a stimulation- or recognition-threshold and partly due to the different study set-up for the determination of OT, values and the sensitivity of the test participants. In addition, formerly the olfactometer was used almost exclusively for the determination of absolute threshold levels. With this equipment it is not possible to separate the substance being studied from traces of odor active contaminants and therefore to eliminate the possibility that the presence of such contaminants may lead to completely wrong OT, values. The possibility of separating contaminants from the main odor active substance using GC eliminates the largest source of error in these measurements. However, several requirements must be fulfilled to obtain reproducible investigations. The values listed in Table 13-3 are averages of several measurements and published values. The partition coefficient is important in the sensory influence of an aroma compound on food (Chapters 4 and 9). The partition coefficients includes those of the substance between the gas (atmosphere) and packaging material, KGIP = cG/cR and as well as the resulting partition coefficient between the gas and food, KG/F = CG/CF, between the packaging material and food, K ~ / = F KG/F/KG/~ = CP/CF= S,. Here the corresponding concentrations in the packaging material, food and gas are cR cF and CG In Table 13-5 the K G values ~ and diffusion coefficients, DF, are given for several solvents in a selection of liquid, fatty and solid foods at 23°C. It is notable that the limits for the parameters lay four orders of magnitude apart in comparison to the narrow range of the relative molecular masses M, and boiling points TB of the pure solvents. The K values of a strongly polar solvent, e.g. ethylene glycol, can vary over three orders of magnitude depending on the polarity of the food (related to the food’s water content), while a medium polar solvent has a much smaller range. The KG/Fvalues in aqueous systems for the solvents listed in Table 13-5 can be used as approximate values for other solvents with similar structures. The aromatic hydrocarbon, toluene, is in this respect an exception where its partition coefficient in the aidwater system has a value of KGIF= 0.5.
-
421
Sensory problems caiised by food and packaging interactions
Table 13-5: Partition (KCIF)and diffusion (DF)coefficients of several solvents in a selection of liquid, fatty and solid foods at 23 "C. M, = relative molecular mass. T s = boiling point. Solvent
Food
Mr
TB
K ~ , lo3 ~ .
"C
Ethylacetate
Coconutfat
88
77
Sof tcheese
Buttercookies Water Methylethyl ketone
Coconutfat
72
80
Softcheese Buttercookies
Ethanol
Ethylglycol
DF. 10' cm*/s
1.5
1.3*
4.0
0.3
15.0
3.0
5.3
-
1.3
1.5*
1.9
0.5
12.0
3.0
Jam
7.7
-
Water
1.7
-
Coconutfat
46
78
7.7
0.9*
Softcheese
0.59
1.2
Buttercookies
9.1
3.1
Jam
0.91
-
Water
0.29
-
0.23
-
Softcheese
0.02
0.5
Buttercookies
2.2
-
Jam
0.53
-
Water
0.006
-
Coconutfat
90
135
* at 0°C Compared to the KG/F values, the DF values can hardly be differentiated. The measured values in the order of magnitude of l.104 cm2/s lay between that for liquids and those for plastics (< lo-'). These values are in agreement with the firmness of the fatty food studied. The small variation of the diffusion coefficient allows the values in Table 13-5 to be used for other solvents as well. The DF values investigated allow a simple estimation of the rate of penetration of the solvent into the fatty food with the help of the formula (Chapter 7):
(13-1) where dF.tis the average penetration distance of the solvent into the food up to time t. A diffusion coefficient DF = 1.2 . lo4 cm2/s for ethanol in soft cheese corresponds to a penetration of approximately 0.5 cm/day or 8.7 cm/year at 23 "C. Attention should be given when determining odor or taste threshold levels for a substance in a food or other testing medium, that during the "taste test" the compound studied can be detected in the gas headspace in contact with the food where the partition coefficient KG/Fplays an important role.
422
Piringer
One defines the relative threshold level of a substance over a food to be the lowest concentration of the substance in food leading to a perceptible odor in the gas headspace over the food at equilibrium. The relative threshold level is designated by OT, and has the relationship: (13-2) The density of the food is designated pF. The relative threshold values of solvents in several foods are contained in Table 136. The values were determined by placing a dilution series of solvent in weighed amounts of food in sealable glass containers and equilibrating overnight at 23 "C. Each test series was composed of a minimum of eight dilution levels (Ruter, 1992). A scattering of the threshold levels over an order of magnitude is due to the different sensory sensitivity of individual test persons. This relatively narrow region allows the formation of mediated values for the establishment of simple characteristic numbers. However, for sensory evaluation, the lowest value of the most sensitive tester must be given consideration since complaints often originate because of complaints from such sensitive consumers. The sensory evaluation differentiates between the stimulation threshold (a just detectable level where a perceptible but not yet definable deviation of the sample from the standard is observed) and the recognition threshold, a level where the odor is identifiable or creates odor problems (a no longer tolerable quality deterioration caused by a definite off odor andlor taste). The difference between a perceptible and identifiable level is usually only one to two steps of a geometric dilution series. Therefore, only undifferentiated odor and taste thresholds are given in Table 13-6, because of the very different sensitivities of individual testers. The perceptible (stimulation) levels of a less sensitive tester can overlap with the identifiable (recognition) level of another more sensitive tester. Table 13-6: Relative odor and taste thresholds of several solvents in different food. OTJmglkg]. Potatochips Solvent
Odor
Cyclohexane 50-100
Taste
Coffee Odor
Jelly-Bears
Taste
100-1000 SO(k1MW) 200-500
Toluene
20-500
Acetone
20-1000 1W2000 100-2000 1000-5000
20-100
100-500
Methylethylketone
50-200
Taste
20-50
500-1000
Odor
Taste
100-500
1GOG2000
20-25
20-25
100-SOO IOW-2000
20-100
50-100
500-loo0
50-100
100-500
50-500 100-500
200-300
50-100
10-50
20-50
500-2000
20-100
50-100
10
5C.500
500-looO
20-50
50-100
Ethylacetate
10-50
10-100 100-1000
Isopropylacetate
1GS0
50-200
Ethanol
10-20
Odor
100&3000 100-2000
Chocolate
50-100
200-1000 200-2000 500-2000 5000-20000
Isopropanol IW1000 1000-3000 500-1000
500
1-Ethoxy-2- 100-1000 500-2000 500-1000 200400 propanol
2000 1W500 500
1000-2000 500-2000 1000-2000 2000
500-1000 1GOG2000
1000-2000 500-loo0
5Oo-lOOO
Sensory p r o b l e m caitsed by food and packaging interactions
423
Ethyl acetate, one of the most common presently used solvents for printing food contact materials, could cause many sensory problems with its very low odor threshold of 10 mg/kg. Assuming a complete transfer of ethyl acetate from the packaging into the product, it is calculated that the threshold level in Table 13-6 is reached with a package surface area to product mass of > 1 m2/kg based on a content in the material of 10 mg ethylacetate per m2. This could only be the case for small packages or for foods with a low fill weight (e.g. potato chips). With the present state-of-the-art technology the residual amounts of ethylacetate are usually under 10 mg/m2 and can be monitored analytically without difficulty. The relative threshold levels of acrylates and methylacrylates in test foods are contained in Table 13-7. The threshold levels pass through a minimum at the ethyl esters. The values of the acrylates lay approximately an order of magnitude lower than the methylacrylates. The influence of the partition coefficient KG,F can be easily seen when comparing the threshold levels of 2-ethyl-hexylacrylate and acrylic acid. Even though the relative threshold level of acrylic acid is only three times higher than that of the ester, the relative threshold level of the acrylic acid in water is 100 times higher than the ester. This is the consequence of the good aqueous solubility of the polar acrylic acid and the small K G / F values. In sunflower oil the K C / F value of the unpolar ester is much smaller than that of the large acrylic acid value, although the relative threshold levels of the two compounds are practically identical. The relatively small values of acrylic acid in the presence of ethanol as well as acetic acid can be caused by a partial ester formation and a small amount of dissociation along with a high partial pressure over the solution. Table 13-7: Relative odor thresholds of acrylates and methacrylates in test foods, OT, [mg/kg]. Compound Methy lacrylate Ethylacrylate
Water 0.005-0.01 0.0001-0.002
Sunflower-oil
0.005-0.2
0.00141.0s
0.001-0.01
0.01-0.1
0.000541.000~
0.0054.2
0.24
0.014.2
0.01-0.1
0.5-10
0.5-10
0.05-2
0.05-1
0.054.5
0.2-10
0.05-1
0.054.5
0.002-0.02
0.1-1
2-Ethyl-hexylacrylate
0.0054.2
Methylmethacrylate
3 v-% Acetic acid
0.005-0.1
n-Butylacrylate
Acrylic acid
10 v-% Ethanol
0.0054.2
0.05- I
0.02-0.2
0.01-0.1
n-Butylmethacrylate
0.01-0.1
0.14
0.05-0.5
0.05-0.5
2-Ethyhexylmcthacrylate
0.02-0.5
0.5-10
0.05-0.5
0.054.5
Et hylmethacrylate
Methacrvlic acid
0.002-0.05
2-1 00
2- 100
13.5 Derivation of threshold concentrations of sensory-active compounds A finished packaging material for a specific food, e.g. a roll of printed laminate film, often possesses a certain individual odor. Even though from a food regulatory view only the transfer of odor substances to the food is important and not the individ-
424
Piringer
ual odor of the food contact material, the package filler will often evaluate the incoming package material for odors. This case becomes important when a more sensoryneutral product is offered by another manufacturer or when samples from previous deliveries are found to have less odor. Here the interesting question becomes the total amount of sensory-active substance that can be transferred to the packed food. It is simplest analytically to determine the mass of the odor compound per unit mass of packaging material, cp, in mg/kg (ppm) or the mass based on the unit surface area of packaging cb in mg/m2. It should be mentioned here that in the case of packaging material (e.g. laminate films) with a impermeable aroma barrier in the packaging material, transfer is important only in the permeable layer between the food and barrier layer. On the other hand in the case of a semipermeable packaging material a fraction of the odor compound contained in it is lost into the atmosphere during storage. In the derivation of an allowable upper limit for the concentration of a certain odor in a packaging material, it is assumed in the first approximation that a complete transfer of the odor compound into the food occurs. The maximum value of the odor concentration in the food by complete transfer from the package (which can practically never be reached for the above mentioned reasons) is: (13-3) where mF and mp are the mass of the food and packaging material and A is the inner surface area of the packaging material. Setting c b A / m ~equal to the relative threshold level OT, from equation 13-2 then one obtains the maximum allowable amount of an odor substance in a packaging material c;.,,~: (13-4) The threshold level of a substance can be decreased by the presence of less sensorically active substances. In a mixture of ethanol, ethylacetate, ethyleneglycol monoethylether and toluene, the odor threshold level of ethyl acetate was reduced to half and in the case of cookies a factor of 5 decrease was observed. A reason for this finding may be the adsorption process taking place in the solid food. Compared to the solution processes in the complete food, the influence of other components on the ethyl acetate partition coefficient during a simple adsorption on the surface is likely to be larger. The repulsion of ethyl acetate from the surface increases its partial pressure over the food. In the previous discussion of the limit value concentration, the influence of solubility of the odor compound in the packaging material on the limit value has been ignored. When one takes into consideration the KP/F value than in equilibrium one gets instead of Eq. (13-4): (13-5) This expression is a realistic approximation even though it is assumed here that no diffusion of the aroma substances into the atmosphere takes place. The relative solubility KPF of the aroma substance in the packaging material can play an important role in critical cases (high A/mF values) where the ratio mP/mFassumes a maximum
425
Sensory proh1erii.s cniisecl bjl food cind packaging interactions
value for a certain packaging material. If polyolefin packaging material is used for aqueous foods then Kp/F > 1 particularly in the case of weakly polar odor compounds, e.g. toluene. The threshold level concentration of the odor compound can also be greatly increased by its high solubility in the packaging. The threshold level according to Eq. (13-5) are not established regulatory levels. However, when these levels are exceeded, their negative influence on the food and subsequent conflict with Article 2 of the Directive 89/109/EEC cannot be ruled out. In the above discussion it is assumed that during storage a partition equilibrium is established between the packaging and food. However, this is not always the case. Given the time tllz, which is the time required for half of solvent contained in the packaging material to be transferred to the food, then one gets: (13-6) where dp is the thickness of the packaging layer and DP is the diffusion coefficient of the odor compound in the packaging material. It is assumed that single sided migration from the material layer takes place. The tliz values for different DP values are found in Table 13-8. It can be seen from this that with packaging materials with DP < lo-'' cm2/s,for example the polyolefins, the residual solvent can be transferred to the product in a relatively short time. Table 13-8:
dp
1PmI
t1,2
values for different Dp values.
10-8
10-9
Dp [ c m b ] lo-"' lo-.l
I
10-'2
10-13
tu2
10
[hl 0.005
[hl 0.05
SO
0.14
1.4
14
100
0.54
5.4
54
200
2.2
222
22
[hl 0.54
[days1 0.23
5.7
Pays1
2.2
Pays1
23
57
570
23
223
2250
91
910
9100
As already shown above, diffusion in a solid food, e.g. a soft cheese, occurs very slowly and as a consequence the equilibrium state is not reached during the storage time. For time t < t1,2 one calculates the penetration depth dEt of the odor compound in t h e food with Eq. (13-1). The diffusion coefficient of the odor compound in food is given by DF. The average concentration cEt of the odor compound in the outer layer of the food having a thickness of dEt can be estimated by the equation (Chapter 7): (1 3-7) Upon further storage, the concentration in the outer layer decreases until it reaches the equilibrium concentration. The duration of this decrease depends on the DF value and this can decrease rapidly with decreasing temperature. Because of this it is possible to get a concentration of odor compounds in a thin external layer of frozen foods.
426
Piringer
Upon rapid thawing of the food the high concentration of odor compounds in the outer food surface layer it is possible to experience a perceptible sensory effect that may exceed the threshold concentration of c;,,,~. Given a 50 pm thick film with a density of pp = 1 g/cm3, a residual solvent concentration of 100 mg/dm2, DP = 1.10-* cm%, a package area to food mass ratio of 6 dm2/ kg and DF = 1.104 cm2/s,one calculates the initial concentration in the food at tl12to be cE1= 160 mg/kg in the food layer thickness of 313 pm in contact with the packaging material, assuming transfer occurs only into the food from the packaging. This concentration falls to 10 mg/kg after 1.3 days and after 13 days when cool, if one assumes that the diffusion slows down by a factor of 10 at the cooler storage temperature. A final comment is needed on the sensory influence of residual solvents where sensory-active substances present in printing inks can lead to off-odors, for example components in mineral oil used for offset printing. The isolation, identification and quantitative analysis of such traces is very difficult due to the complex composition of the printing inks in which most of the relevant sensory compounds are covered up by unimportant compounds. As a rule no satisfactory correlations have been shown to exist between the total amount of volatile substances or the amount of substances with functional groups and the actual sensory active components. The best way in this application is the testing of the finished package for its global odor and then the transfer of this odor to test foods (e.g. grated milk chocolate). It is furthermore recommended that the paperboard packaging of chocolates and confections in particular be printed with as thin a coating as possible and not completely printed. These types of odors, having low volatility, are strongly retained particularly by relatively thick packaging layers. References Ewender J., Lindner-Steinert A., Riiter M., Piringer 0. 1995, in: Ackermann P., Jagerstad M., Ohlsson T. (Eds), Foods and Packaging Materials - Chemical Interactions. The Royal Society of Chemistry. Thomas Graham House, Cambridge. Franz R., Kluge S., Lindner A., Piringer 0. 1990. Packaging Technology and Science 3,89-95. Granzer R., Koszinowski J.. Robinson-Mand L.. Piringer 0. 1986, Verpack.-Rundsch. 37, tech.-wissensch. Beilage, 53-58. Koszinowski J.. Miiller H.. Piringer 0. 1980, Coating 13,310-314. Koszinowski J., Piringer 0. 1983, Drsch. Lebensm.-Rundsch. 79,179-183. Koszinowski J., Piringer 0. 1986, J. Plasfic Film & Sheeting 2,4C!-SO. Piringer O., Skories H. 1984, in: Schreier P.(Ed.), Analysis of volatiles Walter de Gruyter et Co.. Berlin. Piringer 0..1993, Verpackungen fur Lebensmitte. Eignung, Wechselwirkungen, Sicherheit. VCH-Verlagsgesellschaft mbH, Weinheim, New York. Riiter M. 1992, Verpack.-Rimcfsch.43, techn.-wissensch.Beilage. Saxby M., J. 1993, Food Paints and Off-Flavours,BIackie Academic & Professional, Glasgow. Whitfield F. B.. Ly Nguyen T. H., Last J. H . 1991. J. Sci. Food Agric. 54,595.
Reactivity in Molecular Crystals Edited by Yuli Ohashi Copyright @ K d a o r h a Ltd .Tokyo. 1999
14 Case study: styrene monomer migration into dairy products in single serve portion packs Albert L. Baner
14.1 Introduction The potential problem of styrene taint in foods is well known and documented in the literature (Saxby 1996). Styrene (see Chapter 2) is the monomer that is polymerized to make polystyrene (PS) (also known as general purpose or GPPS grade). It is also commonly used with butadiene rubber (5-20% w/w) as a block copolymer to form high impact polystyrene (HIPS). In addition there are less common copolymer grades such as acrylonitrile-butadiene-styrene (ABS) having a mixture of 25 %, 1525 YO and 50-65 YO of each monomer respectively or a copolymer with acrylonitrile (styrene-acrylonitrile, SAN).
14.1.1 Content of residual styrene monomer in polystyrene containing food contact materials The level of unpolymerised residual styrene monomer in commercial grades of polystyrene material has been reduced over the years from 1000 mg/kg (0.1 YO w/w) to a target level of 500 mg/kg (0.05 % w/w) by more complete devolatilization after the polymerization step (Brighton 1982). The legal limits for styrene monomer in materials can be much higher (e.g. Australia 2500 mg/kg, AS 2070.3-1992). Hernpel and Riidt (1988) carried out a survey of residual volatiles found in polystyrene and polystyrene copolymers whose results are summarized in Table 14-la. The results of a recent survey by the Inspection Health Protection/Food Inspection Department, Utrecht, Netherlands (van Lierop, Wildervanck 1996), shown in Table 14-lb, found an average residual styrene monomer content of 224 mg/kg in 31 different polystyrene containing food contact articles and packaging. The two highest contents found were 888 and 1459 mgikg and in 14 articles less than 150 mglkg was found. A comparison of the results of the two studies from 1988 and 1996 supports the stated industry objective of reducing styrene monomer contents and shows an overall downward trend. Low monomer content PS materials are commercially available with specified styrene monomer levels of 150 ppm (mg/kg) that have actual contents of 100 ppm (ex. BASF 0 suffix materials 168 NO, 143 10). These materials can be used for injection molding or extrusion and are priced above normal styrene monomer content materials (those where styrene < 500 mg/kg). High impact polystyrene copolymer materials (HIPS) use normal monomer level polystyrene since there has been n o commercial market for such materials.
428
Baner
Table 14-la: Survey of volatile substances in polystyrene materials (Hempel and Riidt, 1988). Type of Polymer
Number of Samples
PS
PS block and mixed copolymer (HIPS, ABS. SAN)
44
Styrene monomer level (mg/kg) range and average 55-2272, Ave. 401
Potential off-flavor substance: frequency measured, range and levels in material (mgW Toluene 33.6-213, Ave. 45 Ethylbenzene, 41.8-473. Ave 50 Cumene, 34, 10-257, Ave. 27 n-Propylbenzene, 28.8-178, Ave. 29
12
320-1281. Ave. 550
Toluene, 12,26-128, Ave. 70 Ethylbenzene. 12.61-202, Ave. 84. Cumene, 12,18-210, Ave. 34 n-Propylbenzene, 11,31-3541, Ave. 56 a-Methylstyrene, 2, Ave. 527 4-Methylstyrene, 4,58-250, Ave. 80 Acrylonitrile, 4,25-116, Ave. 60.
Table 14-lb: Market survey of styrene content (mglkg) in 31 polystyrene material samples in Netherlands (van Lierop and Wildervanck, 1996). Analysis Number
Sample Description
Styrene content (mg/kg)
1418 1421 1549 1561 1582 1564 1565 1761 1762 1763 1763 1763 1791 1792 1793 1797 2037 2340 2494 2582 2863 2886 2887 2288 2898 2890 2892 2893 2894 2895 2869
Tray
198 106 137 238 n.a. 157 229 141 148 18 71 22 340 202 209 67 110 346 888 246 145Y 179 326 175 170 114 109 133 224 164 113
CUP CUP Plate Foam cup Separation sheets for meat CUP CUP CUP CUP Brown Cup Black Cup Tray for hamburger Pizza tray 1 kg tray Hamburger tray Salad tray Small meal tray Dessert plate Yogurt container Meat plate Pudding container Pudding container Curd cheese package Pudding container Spreadable cheese package Spreadable cheese package Pudding container Whipping cream package Yogurt container Curd cheese package
Case study: styrene monomer migration into dairy products ...
429
Polystyrene is quite stable during forming processes and does not readily decompose to produce styrene monomer. At normal thermoforming process conditions for example ( z 120 “C) styrene monomer levels do not increase. PS first starts to decompose at very low levels only after several hours at temperatures greater than 240°C. In general however, injection molding is a more severe process and the monomer content may increase slightly during processing which reflects food industry experience. In addition to styrene migration from the primary package, polystyrene containing toys, surprises and other items packed inside a package together with product can also be a source of styrene monomer off-flavor. The polystyrene used may or may not be food grade and the overwrap for the item is usually not a barrier to the transmission of styrene into the food.
14.1.2 Taste threshold levels for styrene monomer in foods The toxicity and safety of styrene has been extensively studied and is of no health consequence at the levels commonly found in foods. The current European legislation sets no specific migration limits (SML) for styrene in food which means its content is then controlled by the overall migration limit of 60 mg/kg in the food (Chapter 12). The overall migration limit is never reached because the styrene creates a strong astringent “chemical plastic” off-taste at levels in the food much lower than 60 mg/kg. As such styrene monomer migration into foods is more of an organoleptic/quality problem than a health and safety issue. In fact recent surveys of styrene levels in foods by the Ministry of Agriculture Foods and Fisheries (MAFF) in England have led to the conclusion that there is no toxicological concern considering the levels (< 1 to 134 pgikg) found in foods (MAFF, 1994). The residual styrene monomer remaining in the finished material can cause taints by transferring to the packed product in amounts that exceed the taste threshold concentration level in that particular food. Each food matrix has a characteristic styrene concentration (threshold concentration) above which the styrene taint becomes evident (Chapter 13). A series of sensory taste threshold concentrations taken from the literature for different foods are shown in Table 14-2. Ethylbenzene is commonly used as a solvent diluent during the polystyrene polymerization process. It can be found in the finished material and can be a source of taints as well. As seen in Table 14-2 the sensory taste threshold concentrations for ethylbenzene are 2 to 3 times higher than those for styrene. Other volatile compounds found in polystyrene containing packages but of less sensory significance can be 2-methyl-2-propen-I -01, P-methylstyrene, trimethyl- and tetramethylbenzenes. In general, the higher the fat content of the product the higher the taste threshold concentration (Chapters 4, 9, 13). vom Bruck and Hammerschmidt (1977) developed an equation that relates the fat content of the food product to the taste threshold concentration: threshold (mg/L styrene) z 0.0025 . (80. %fat in food
+ % water in food)
Conversely, water and products with high water contents (juices, skim milk etc.) have lower taste thresholds usually on the order of 50 ppb.
430
Baner
Based on taste threshold's published in the literature as well as food industry experience, an average acceptable taste threshold level of styrene monomer in a variety of food products ranges around 0.3 ppm. Table 14-2: Taste thresholds for styrene and ethylbemene in foods. Food
Taste threshold ( m d k d
Reference
Odor threshold in air Water Water Tea Java-Broken Tea Mixture Apple Juice
0.050 0.037 0.022 0.20 0.2 0.050 styrene > 0.10 ethylbenzene 0.025 1:1 styrenekthylbenzene 0.2
Fazzalari 1978 Rosent et al. 1963 Linssen et al. 1991 Jenne 1980 vorn Bruck, Hammerschmidt, 1977 Durst and Laperle 1990
0.50 0.20' 0.30 - 0.50 0.036' 0.099' 0.171' 0.005 0.5
Jenne 1980 Jensen 1972 vom Bruck, Hammerschmidt, 1977 Linssen et al. 1993 Linssen et al. 1993 Linssen et al. 1993 Miltz et al. 1980 vom Bruck, Hammerschrnidt, 1977
0.3 1.2 1.2 2-6 33 5.0 0.001 styrene 0.003 ethylbemene 0.001 1:l styrene/ethylbenzene 0.20' 0.65' 1.18' 1.40' 1.56' 2.08' 2.3 1.82 2.22 0.5 - 2.02 0.5 - 2.02
vom Bruck, Hammerschmidt, 1977 Jenne 1980 vom Bruck, Hammerschmidt, 1977 vom Bruck, Hammerschrnidt, 1977 vom Bruck, Hammerschrnidt, 1977 CSIRO 1969 Linssen et al. 1995
Orange fruit juice drink (0 % fat) Yogurt Yogurt 3 YOFat Yogurt (1.5 % fat) Yogurt (0.1 YOfat) Yogurt (0.15 % fat) Yogurt (0.3 YOfat) Sour cream Vanilla-almond pudding (2.0 %! fat) Skim milk (0 % fat) Whole milk Whole milk ( = 3.8 YOfat) Condensed milk (10 % fat) Cream (33 % fat) Butter 5 YOOil-in-water emulsions
3 YOOil-in-water emulsions 10 % Oil-in-water emulsions 15 YO Oil-in-water emulsions 20 YO Oil-in-water emulsions 25 % Oil-in-water emulsions 30% Oil-in-water emulsions 30 % Oil-in-water emulsions Cocoa powder (10 YO fat) Cocoa powder (20 YOfat)
Milk chocolate flakes Plain chocolate flakes
vom Bruck, Hammerschmidt, 1977
Linssen et al. 1993 Linssen et al. 1993 Linssen et al. 1993 Linssen et al. 1993 Linssen et al. 19Y3 Linssen et al. 1993 Linssen et al. 1Y90 Linssen et al. 1991 Linssen et al. 1991 Linssen et al. 1991 Linssen et al. 1991
1 SO % taste recognition threshold concentration values (TRTC) 2 Recognizable difference from control sample not a true threshold concentration mglL, mg/kg = ppm to convert from liter to kg assume density of liquids % 1.0 g/ml
Case study: styretir tnononier rnigrution into dairy products ...
431
14.1.3 Analytical methods for measuring styrene Although there are methods for analyzing styrene in materials in the literature (Hempel and Rudt, 1988a, Sugita et al. 1996) and as standard methods (ISO, 1974) there are no official or standard methods available for determining styrene in foods. There are however numerous published methods for measuring styrene in foods (Rossli and Marek, 1977, Hempel and Rudt, 1988b, Durst and Laperle 1990, Linssen et al. 1991, Nerin et al. 1996). For measurements in materials ISO-2561 first dissolves the PS material in chloroform, then the dissolved polymer is precipitated using methanol and water. The level of styrene monomer is quantified by injection of the chloroform solution into a gas chromatograph (GC). The method of Rossli and Marek (1977) uses GC determination of styrene after isolation by co-distillation with water and continuous extraction of the distillate with hexane.
14.2 Case study: styrene taint in coffee creamers and condensed milk packed in portion packs An example of a product that has had styrene taint problems over the years has been dairy products such as coffee creamer and condensed milk packed in thermoformed PS single serve portion pack containers holding 5-10 g of product. The high package mass and surface area ratio to product and high fat content of the product make this packageiproduct system a challenging system to optimize. MAFF carried out a trade survey in 1994 (MAFF, 1994) of 22 coffee creamer portion packs and found styrene monomer levels in the product ranging from 23 to 223 pgikg (ppb) with an average of 134 pglkg. These levels have decreased significantly since an earlier market survey in 1992 of 7 coffee creamers that had styrene monomer concentration ranges from 265-665 pgIkg with an average of 430 pg/kg (MAFF, 1994). There was no indication in this survey if the products were refrigerated or shelf stable. Although the problem has become less severe due to the trend towards reducing residual monomer content in materials there is still potential for taint problems to occur in products. Total styrene content in current materials varies within a range of 250 to 350 ppm (even for laminate materials), Of the commonly polystyrene containing portion pack materials mono-material PS has the greatest migration followed by PSiPE and the material with the lowest migration is from PSIEVOHIPE. Surprisingly, even product packed in PSIEVOHIPE barrier material can contain styrene at a sensory significant level at the end of shelf life despite the EVOH barrier layer between the PS layer and product. The explanation for the styrene in the product comes from the fact that the styrene from the PS layer transfers to the inner PE layer while the material is shipped and stored in role form before forming. This is entirely possible in a few days given the relatively high diffusion coefficients of PS and PE. Measurements of refrigerated products (shelf life unknown) have shown practically no taint. Lower temperatures and shorter shelf life can reduce the amount of styrene transferred to the product.
14.2.1 Threshold concentration of styrene in coffee creamers and condensed milk From experience it has been established that the sensory threshold for coffee creamer and condensed milk products is on the order of 0.1 mglkg (ppm) of styrene in the product. This observation is only partly supported by threshold values from the literature in Table 14-2 where values range from 0.2 ppm for 3 YO yogurt, 1.2 ppm for 3.8 YO fat milk and 2-5 pprn for condensed milk. This points out two problems with threshold concentration values caused by the way they are determined (e.g. experimental methods) and the definition of the threshold value being the value at which the substance is correctly identified by SO Y of the panelists (versus other possible ways of measuring/defining the taste threshold). The intended use of the product also plays a role in the importance of the threshold concentration value. Coffee creamers and condensed milk are not intended to be consumed alone but added to coffee and tea drinks. Taking a threshold forstyrene in tea of 0.2 ppm from Table 14-2, a simple mass balance calculation shows that in a 150 ml cup (vending machine cup size) the 7.5 g cream in a portion pack could contain up to 4 ppm styrene monomer before the styrene becomes noticeable in the tea drink. One could assume that coffee would have a higher threshold concentration level due to a more robust flavor versus tea. However, one should also consider unforeseen uses of the product or package such as the current fad in Europe of collecting creamer lidding material printed with different pictures and designs. The common practice is for people to lick the cream from the lid before placing it in their pockets!
14.3 Estimation of styrene migration from PS The simplified approach to the estimation of migration described in Chapters 7 and 15 can be used to estimate the migration of styrene from polystyrene into the packed food. By estimating the migration of styrene a priori one can make a better initial material selection (e.g. level of residual monomer in material) for a given product application. Afterwards, filling and storage studies can be carried out on the final package system to confirm the material choice.
14.3.1 Mass balance estimation of worst case styrene migration The simplest estimation of migration is to use the mass balance calculation shown in Eq. (14-1) below. This equation assumes that all of the styrene found in the polymer will migrate into the food instantly. This is of course not realistic but the estimation gives an upper limit to the possible migration that could occur at the end of the product's shelf life.
(14-1) where: cF,& the concentration of styrene in the food after a long time (mg kg-'), cp.0 is the initial concentration of styrene in the material (mg kg-'),
Case study: styrene nionorner migration into dairy products ...
433
IF is the thickness of the material (cm), pp is the density (g cm-3) of the PS,
6is the package surface area A (cm2) to food mass ratio (mF = VF. pF in g wsere VF is the volume of the food or simulant (cm"). mF = PF . VF and mp = pp . Vp are the masses of the foodstuff and polymer. The ratio can be the actual package surface area to food mass ratio or a conmF ventional ratio like 0.6 cm2 g-' (6 dm2 kg-') (used in the European Union) or 0.645 cm2 g-' (1 in2/10 g) (used by the US. FDA). The density of polystyrene is approximately 1.08g ~ r n - ~ . The initial concentration of styrene in the polymer (P), cp.0 (rng kg-'), is known either from the manufacturer of the material or has been determined by analysis of the material. In the absence of initial styrene monomer concentration data one could assume as a worst case a level of 1000 mg/kg which is the highest level usually seen in commercial PS materials. Usually the level found in the material is 500 mg/kg or less which is the industry standard for food grade polystyrene. For simplification one can assume the density of the polymer and food are approximately equal to one, PF "- pp "- 1.0,without large error. Example 14-1:Calculate the amount of styrene monomer that could migrate from a PS coffee creamer portion pack (7.5 g) with a residual styrene monomer content of 1000 ppm (mg/kg) into a coffee creamer containing 10 % fat. 1 ) take pp = 1.08 for average PS density ( g cm-3) from Table 14-1 2) measure wall thickness of portion pack (bottom is thickest part giving worst case) = 0.48 mm 3) calculate surface area of package in contact with food area cylinder = h . JT. r2 = 1.5 . IT (1.55)2= 11.3 cm2 4) enter values into the mass balance equation (14-1): A 11 3 C F . ~= -. pp . I p cp.0 = I s . 1.08.0.048 . 1000 = 78 mg/kg (ppm) mF
Interpretation of result: Assuming complete migration of styrene at this styrene monomer level in the PS, the taste of styrene monomer will be readily detected in the product based on a threshold of 0.1-0.3 ppm. Discussion: In this case the package area to food ratio is extremely high since this is a single serving portion pack (the EU standard package area to food ratio is 0.6 cm2/g compared to ratio here of 1.5). Realistically, one could also assume that since migration occurs in both directions that half of the initial monomer in the material would be lost into the environment (assuming no package overwrap). Even with the current European polystyrene manufacturer specification of < 500 mgikg styrene in the finished material (actual range from 300-400 mgl kg), the styrene concentration would still be 23-31 mgikg in the creamer.
14.3.2 Effect of partitioning on mass balance If there are significant partitioning effects occurring between the PS and product, then the amount of styrene migrating may reach a thermodynamic upper limit (Chapter 4). The partition coefficient is the ratio of the concentration of the migrant in the polymer cp,, to the concentration of migrant in the food C F , ~at equilibrium (long times):
434
Baner
It is possible that styrene will never reach the mass balance migration limit specified by Eq. (14-1) in certain foods because of partitioning effects. The systems most likely to have partitioning effects, i.e. when K >> 1, are those for styrene between aqueous foodstuffs and PS. Migration is usually highest into fats and oils since styrene is readily soluble in both the fats and polymers so that K 5 1. A guide for estimating the general behavior of partition coefficients is “like dissolves like”. Thus styrene, a relatively nonpolar hydrocarbon, will tend to remain in a nonpolar polystyrene polymer if the package contains a polar aqueous food (Chapter 9). Incorporating the effect of the partition coefficient into a mass balance Eq. (14-1) gets (Chapter 7):
(14-3) Note that as K becomes very small (the styrene partitions very readily in the food phase as opposed to the polymer phase, e.g. fatty foods) then Eq. (14-3) simplifies to Eq. (14-1) which assumes complete migration into the food. For this reason migration into foods with high fat contents is generally best estimated using Eq. (14-1). Example 14-2:Taking the same package in Example 14-1 (7.5 g PS portion pack) assume that skim milk is packed in this package instead of coffee creamer product with 10 % fat. In this case, since skim milk contains very little fat, the partition coefficient may limit the transfer of styrene monomer to the product. Assume the same residual styrene monomer content of 1000 ppm (mg/kg) in the PS. 1) Use the same package dimensions and polymer density given in Example 14-1. 2) Assume the partition coefficient for styrene monomer between PS and skim milk to be approximately equal to that for toluene/PS/water (K = 800) (Gavara et al. 1996). 3) Using Eq. (14-3):
The effect of the partition coefficient on the transfer of styrene into an aqueous product is dramatic, the estimated potential migration is reduced by 60 times compared to Example 14-1. However, the taste threshold for styrene in low fat products is lower (around 0.40 mg/kg). In order to be sure no styrene taint will be detected in the product, one would have to reduce the initial concentration of styrene in PS. Rearranging Eq. (14-3) one can estimate the maximum allowable styrene monomer concentration in the material that would ensure the concentration in the product would not exceed 0.4 mg/kg:
This level is within the range of the commercially available PS styrene contents and it should be possible to pack skim milk in a high quality polystyrene that would virtually exclude the likelihood of styrene tainting of the product.
Case sriirly: styrcwe tvotzonler migration into dairy products ...
435
14.3.3 Time dependent styrene migration One can assume that styrene migration out of PS into food is slowed down or braked by the diffusion of styrene in the plastic material (P). Eq. (14-4) the simplified expression for the estimating the concentration, cF,, (mg kg-'),of the styrene in the food (F) at time t can be used:
(14-4) where: c;., is the estimated styrene concentration (as opposed to the true concentration, which would be experimentally measured) (mg kg-' ), Db is the estimated diffusion coefficient of styrene in the plastic material (cm2 s-l) using Eq. (14 - 9 , t is the expected shelf life (s). The statement c;,~ 2 cF., in Eq. (14-4) indicates the tendency of the estimation to overpredict the actual migration due to the estimation of Dp and some simplifications made in deriving Eq. (14-4) (see Chapters 7 and 15). The value calculated for c;,, can be used for comparison with regulatory migration limits (e.g. specific migration limits, SML, given in EU legislation) to evaluate the material's suitability for the intended application with respect to food packaging regulations. Note that the initial concentration o f styrene in PS , c ~ . ~in, Eq. (14-4) must be experimentally determined or given in the material's specifications. The other inputs are readily available except for the diffusion coefficient which can be estimated as explained below or taken from the literature.
14.3.4 Estimation of styrene diffusion coefficient in PS Where no experimental diffusion coefficient data in the polymer is available an estimation for the upper limit diffusion coefficient D; can be made using the empirical correlation given in Eq. (15-1) (Chapter 15):
Dp
4
exp(Ap - a . M ,
-
b.T-])
(14-5)
where: Ap accounts for the effect of the polymer on diffusivity, GPPS = -4, HIPS = -3 M, is the substance's molecular weight T is the temperature in Kelvin (K C + 273) a and b are correlation constants for molecular weight and temperature effects on diffusion. The values of the coefficients a and b are 0.01 and 10454 High impact polystyrene (HIPS) is a mixed or block copolymer with 8 to 20% (w/w) rubber (polybutadiene). In general HIPS has a higher diffusion coefficient than simply pure PS. In some types of copolymers the rubber is present in lamellae layers in the PS matrix and these lamellae can act like capillaries increasing the diffusion of styrene. One must also be aware that the presence of mineral oil plasticizers in the HIPS material can also lead to higher diffusion coefficients as well (Lickly et al. 1997). =O
436
Baner
Table 14-3: Experimental diffusion coefficients for styrene in polystyrene materials Material (monomer content)
Temperature ("C)
Diffusion Coefficient (cm2/s)
1:l H1PS:GPPS (285 f 6 mgikg)
10
4.7
io-lh
1:l H1PS:GPPS (285 f 6 mglkg)
20
2.8
10-1~
1:l H1PS:GPPS (285 k 6 mglkg)
30
0.9 10-14
Linssen et al. 1992
1:l H1PS:GPPS (285 f 6 mg/kg)
40
5.1
Linssen et al. 1992
1:l H1PS:GPPS (285 f 6 mglkg)
50
1.5 x
Linssen et al. 1992
GPPS (800 mg/kg)
40
2-5
Till et al. 1982
GPPS (4260 mglkg)
40
2-3 x lo-"
PS/EVOH/PE
20
1.02 x 10-15.
PS/PE
20
1.03 10-14.
PS
20
5.5
GPPS (-)
23
3.10 x i0-l'
Eq. (14-5) (AP= 4)
GPPS (-)
40
2.10
10-13
Eq. (14-5) (AP = 4)
HIPS (-)
23
8.19
10-l~
Eq. (14-5) (A,, = -3)
HIPS (-)
40
ExDandedPS
25
10-14
x
10-14. b
Activation Energy (Jlmol)
Reference
12 104. a
Linssen et al. 1992 Linssen et al. 1992
Snyder and Breder (1 985)
-
3.01 x
Eq. (14-5) (AP = 4)
5.57 x 10-13
Eq. (14-5) (AP = -3)
2.05 x lo-"
Eq. (14-5) (AP= 4)
5.5 10-14.h
-
GPPS = general purpose polystyrene HIPS = high impact polystyrene a) 1:l H1PS:GPPS diffusion coefficient equation: I n D = 15.61 - 14 500 . ( l / T ( K ) ) b) apparent diffusion coefficient calculated from experimental migration data.
1
Example 14-3:Continuing with the preceding examples for the migration of styrene from polystyrene, this time assume the migration is diffusion controlled. Assume the product has a 6 month shelf life at room temperature (23 "C). 1) Use same portion package described in Example 14-1 2) Assume no partitioning effects (K = 1) 3) Calculate the upper limit diffusion coefficient for styrene in polystyrene using AP = 4 from Table 14-3. Dp = 10000 e x p [ 4 - (0.01 x 104) - (10454/296)] = 3.10 x (cm2/s) 4) Using Eq. (14-4): A 11.3 =_ . 1.08.1000. 4 3 . 1 0 x ' (6.3.24.3600) c:,, = -. mF p p 'cpg 7.5 = 1.0 mg/kg (or 0.3 mg/kg for = 300 mg/kg)
Case study: styrene tminomer migrotion into clniry products .._
437
5) Using the experimental diffusion coefficient data for 1:l GPPS:HIPS from Linssen et al. 1992 and Eq. (14-4): nD = 15.61 - 14500. (l/T()) = 15.61 - 14500(1/296) = -33.38.D = 3.2 x 10-ls(cm2/s) A 11.3 = __. 1.08 1000. J3.2. x . ( 6 . 3 0 ' 2 4 ' 3600) c;,~ = -. pp . cp.0 . mF 7.5 = 0.36 mg/kg (or 0.11 mg/kg for cp.0 = 300 mg/kg) fnterpretation of result: The calculated migration values here are realistic since results cal:dated using Eq. (14-4) cannot be larger than the mass balance result (Example 14-1). The :aiculated amount of styrene is still above the assumed sensory threshold limit of 0.1 mg/kg n the product for the worst case in step 4 but is equal to the estimation using the experimental diffusion coefficient in step 5. f i i s points out the difficulties of finding reliable experimental data on diffusion. The data of Linssen et al. are about one order of magnitude smaller than that of other researchers. The actual diffusion coefficient for styrene monomer in polystyrene probably lies in between the Estimated upper limit value of 3.01 x (cm2/s) and the experimental value of 3.2 x (cm2/s). Another use of Equation (14-4) is to estimate the length of time before the amount of styrene reaches 0.1 mglkg in product. Solving Equation (14-4) for time one gets: I
1 = -.
Db
(=)*=
A-pp c p g
~.
1
(-)
5 0.1
3 1 0 ~ 1 0 Il.3~1.OX~lOOIl ~ ~ ~
2
= 54147 s =
15.0 hours
As a worst case this result means the product can be expected to develop a styrene off-flavor almost instantly. If the initial amount of styrene in the material is reduced by 1/3 to 300 mg/kg then one will see a 9 times increase in the expected time to 5.8 days before a taint is detected. IJsing the experimental diffusion coefficient from Linssen et al. (1992) the shelf life would be 6 days and 55 days for PS containing 1000 and 300 ppm styrene.
Example 14-4 Using Eq. (14-4) and (14-5) it can be shown that one can pick accelerated migration testing conditions for diffusion controlled migration from packaging into foods that give migration equivalent to that experienced over long term room temperature storage. The US and E U accelerated migration test conditions for long term ambient storage, 10 d at 49°C and 10 d at 40°C. yield equivalent migration values to those calculated in Example 14-3 for ambient storage at 23 "C for six months: 1) Use same package described in Example 14-1 2) Assume no partitioning effects (K = I ) 3) Calculate the upper limit diffusion coefficient for styrene in polystyrene using Ap = -4 from Table 14-3 for 49 "C and 40 "C. DI. = 10000 exp[-4 - (0.01 x 104) - (10450/322)] = 5.1 x (cm2/s) DP = 10000 e x p [ 4 - (0.01 x 104) - (10450/313)] = 2.0 x lo-'' (cm2/s) 4) Using Eq. (14-4) with 10 d at 49 "C: 11.3 = ~. 1.08' 1000. J S . 1 x '864000 c;,, = mF pp . cp.0. 7.5 = 1.1mg/kg (or 0.68 mg/kg at 40 "C)
4.
Interpretation of result: These results show that these accelerated migration testing conditions for ambient storage can be useful for accelerated storage testing of packaged product. This could be quite useful for testing package product compatibility without having to wait 6 months to observe packaging related taints in the product. Note that these accelerated conditions are not intended as accelerated testing conditions for the food product itself.
438
Baner
14.3.5 Functional barrier: estimating the time it takes for styrene to travel through a material The time it takes for styrene to travel through a material of thickness (I) can be estimated using the following equation (Chapters 7 and 9): t
=
2
1
2,Dp
(14-6)
where: I is the thickness of the material (cm) t is the time ( 5 ) required for styrene with a diffusion coefficient of D p to travel through the material Using Eqs. (14-5) and (14-6) the approximate break through times for styrene (M, = 104) to migrate through different materials and different thickness can be calculated. This will give an idea of the type (i.e. diffusion coefficient) and thickness of the functional barrier material needed to protect the product. Equation (14-6) can also be rearranged to estimate the thickness of the material needed to provide protection against styrene breakthrough contamination for a given length of time and D p :
1=Jm
(14-7)
14.3.6 Estimation of allowable styrene concentration in polymer Given the acceptable threshold concentration for styrene in a given product, one can calculate a maximum acceptable initial concentration of residual styrene in the food contact material (QMcalc).c;,~ is replaced with the threshold concentration (TC) in Eq. (14-4) to yield Eq. (14-8) or C F , is ~ replaced with TC in Eq. (14-3) to yield Eq. (14-9). (14-8) (14-9) As long as the initial concentration, c ~ ,of~ styrene , in the material is not larger than the largest QMcalcvalue calculated from Eq. (14-8) or (14-9) the taste threshold in the product will not be exceeded.
1
Example 14-5: Calculate the maximum allowable amount of styrene monomer (M, = 104.2) that can be allowed in a PS thermoformed portion pack with Coil lid (7.5 g product) for condensed milk (see Example 14-1). Assume that based on experience a concentration above 300 pglkg in the product will produce an off-flavor and lead to consumer complaints. The package surface area to food mass ratio (A)is % = 1.5 cmz g-'. The product is shelf stable and has an intended shelf life of 6 monthsmF
Case study: styretie nimonier migration into dairy products ...
439
I ) Calculate a general DP for styrene in PS at 23 "C using Eq. (14-5). DP = 10000 exp[-4 - (0.01 x 104) - (10450/296)] = 3.10 x (cm'ls) 2) 1 d = 86400 s + 90 d = 7776000 s 3) Put the numbers into Eq. (14-8): 7.s
1
mt
QMcalc= G . SML .
= 380 mg/kg o'3 ' I OX d3 I lb-14.777hOol) 4) Compare this with the mass balance resull using Eq. (14-9) (in a high fat product one can assume partitioning is not significant): mF 1.5 = 3.8 mg/kg QM,,,, = SML . = 0.3 . ~
P
~
A-PPdp
P
-
m=
'
A
11.3-l.0X 0 IWX
Interpretation of results: Diffusion controlled migration results in step 3 compared to the results in step 4 assuming a mass balance, show that the diffusion of the styrene in the polymer acts to slow down mass transfer into the product. These calculations also show that the relationship in Eq. (14-1) is still valid (mass balance calculations represent the maximum possible amount of migration). QMCaI,means the maximum allowable concentration of the substance in the polymer that will not exceed the specific migration limit in the food for given time and temperature storage conditions. Note that a polystyrene material with a level o f 3x0 mglkg residual styrene is readily commercially available. If taint problems still occur in the product most likely the threshold level may be too high. Another explanation may be that the product is filled in the portion pack after the material has been heated for thermoforming. Portion packs are thermoformed and filled in line at a rates of approximately 25 cycleshin. The sheet stock PS material is heated to its softening temperature of 100 "C (temperature for low monomer PS) by contact with heated platens having temperatures of about 120°C. The package is then filled with product and a coated aluminum lid is heat sealed onto it for 1 s. The plastic is still likely to be warm when filled. Assuming a temperature of 60°C for the plastic the rate of diffusion could be 1000 times higher than at room temperature. A solution in this case may be to use a material with a lower styrene monomer content or use an alternative thermoformable material like PP for this package.
14.4 Estimation of styrene transfer from portion pack into food 14.4.1 Estimation of shelf life based on taint development in creamer portion packs Figures 14-1 and 14-2 show estimations of shelf life in a 7.5 g PS containing portion pack before two different taste threshold concentrations (2 and 0.1 mg/kg) of styrene are exceeded in the product. In each graph the diffusion coefficients from Linssen et al. (1992) for a 1:1 PS:HIPS polymer blend at room temperature (23°C) and refrigeration temperature (4 "C) are used. The estimation using Eq. (14-5) at 23 "C and 4 "C and an calculated apparent diffusion coefficient for PSlPE and PSlEVOHlPE structures (see Table 14-3) are used in Eq. (14-4) (see example 14-5) to calculate the days before a styrene taint is detected in the product. The shelf life is decreased by a factor of the square of the increase in the material's residual styrene content. As seen in Figures 14-1 and 14-2 a reduction in the taste threshold by a factor of ten means almost a 100 times decrease in the shelf life.
440
Baner
100oOoo
8
10000
1000
1001
'
'
,
8
'
'
'
'
'
'
'
'
'
Styrene content in ps (mplkg) Figrue 14-1: Shelf-life (days) before 2 mgkg taste threshold is reached. 100oOoO 100000 10000 1000
-------
I00
10
1 0.1
Styrene content in PS ( m k g ) Figure 14-2: Shelf-life (days) before 0.1 mg/kg taste threshold is reached.
Figure 14-2 shows a good representation of the shelf life for creamers and condensed milk in portion packs. A PS/PE material with the normal residual styrene content of 300 ppm has a shelf life of 40-50 days while the PSIEVOHIPE material has a shelf life of 200 days. The PS material shelf life is similar to that for PSIPE. Figure 142 shows for a given material how reducing the temperature by refrigeration (23 "C to 4 "C)one can increase shelf life by over 10 times. Furthermore, Figure 14-2 shows the importance of low monomer PS material for avoiding taints at the end of shelf life. Drastic increases in shelf life are gained by reducing the styrene monomer content in the material to less than 100 ppm. The PS/PE material could give a one year shelf life without styrene taint if the material had a residual styrene monomer of 100 or below.
Case study: styrene n~ononiermigration into dairy prodiicls ...
441
1o.wo
2cn
1.000
'li
1n
.-=
0.100
1
0.010
-_._-.--
P
0.0014:. 0
8 r
I
I
I
I
t
b
I
.
I
I
D Q t
I
I
S
8
8
9
0
I
I
t
r
Styrene content in PS (mgikg)
Figure 14-3: Styrene migration from portion pack at 6 months.
Figure 14-3 shows more clearly how the styrene content varies as a function of the residual styrene content in the material assuming a desired shelf life of 6 months. If one knows the threshold concentration in the product (e.g. 0.1 mg/kg for dairy creamers) then the necessary initial styrene concentration in the PS material can be selected to give a shelf life of 6 months before a styrene taint develops in the product.
14.4.2 Selecting appropriate polystyrene packaging materials for specific packaging applications Given the initial concentration of styrene residual monomer in the packaging material, the styrene threshold concentration in the product and the desired shelf life of the product one can estimate whether or not a given polystyrene material will cause taints in a given packaging application. Without this information accelerated storage studies should be carried out using the officially recognized accelerated migration testing conditions and the actual product package system. To do this the package/product system is first stored under accelerated conditions (see Table 14-6) and then a sensory comparison test is carried out with a reference product sample that has been stored under the same conditions but not in contact with any packaging. If a styrene taint is detected after storage under these conditions then the amount of styrene in the material should be determined and a material with lower residual styrene monomer then used. These accelerated storage conditions will avoid lengthy room temperature shelf life trials during package development. Care must be taken not to use test temperatures and conditions that may lead to dangerous spoilage of the product. Note that these accelerated storage conditions are generally agreed upon conventions and are not always exactly comparable to actual long time room temperature storage tests. They are useful as guidelines for designing accelerated migration tests
442
Baner
and are legally recognized accelerated migration testing conditions. The US and EU testing conditions differ slightly, the US being slightly more severe conditions than EU is probably due to the higher average temperature experienced in the US in summer. It may be appropriate to consider even more severe conditions in desert and tropical climates. Styrene can cause off-flavors in food products packed in polystyrene packaging materials. Each food product has a different sensitivity to styrene off-flavors and thus each food package system needs to be evaluated individually. The formation of styrene off-flavor in a given package/product system can be estimated a priori given the styrene threshold concentration in the food, the initial residual styrene monomer concentration in the packaging material and the desired shelf life. If this information is not readily available then accelerated storage tests followed by a sensory comparison can be carried out to evaluate the potential of off-flavor formation in the product. Table 14-4 Storage/filling conditions and their equivalent accelerated testing conditions. Actual storage/filling conditions: Temperatures for different contact times
EU Migration test conditions'
FDA Migration test conditions'
T15"C
10 d at 5 "C
5 d at 21 "C
5° C < T I 20°C
10 d at 20°C
10d at 21 "C
5 "C < T < 40°C
10 d at 40°C
10 d at 49 "C
long term storage
hot fill I sterilization plus long term storage 2 h I t + t > 24 h hot fill (T > 66 "C)
2hat70"C+l0dat4O0C
30min.at 100"C+10dat49"C
boiling water sterilized (70 "C < T 6 100°C)
1 h a t l W o C + 10 d at 40°C
2 h at 100°C + 10 d at 49°C
pasteurizatiotdsterilization (100"C
0.5 h at 121°C + 10 d at 40°C
2 h at 121 "C + 10d at 49°C
sterilization ( T = 121 "C)
2 h at 121 "C + 10 d at 40°C
2 h at 121 "C + 10 d at 49°C
sterilization (121 "C < T I 130°C)
2 h at 130°C
+ 10 d at 40°C
Microwaveablelovenable (130"C
2 h a t 150°C
2 h a t 100°C (for package T < 121°C)
(150"C
2 h a t 175°C'
-
1 EU Directive 93/8/EEC (amendment to 82/711/EEC) 7 appendix, chapter 11, test conditions. 2 Recommendations for chemistry data for indirect food additive petitions. Center for Food Safety and Applied Nutrition, FDA, Washington. D.C. September 1988 v. 1.1 3 non polyolefin materials only
Case study: styrene riiononier migration into dairy products ...
443
References AS 2070.31992 Australian Standard. Plastics Materials for food contact use. Part 3: Styrene plastics materials. Brighton, C., 1982. Styrene Polymers and Food Packaging. Food Chemistry 8:97-107. vom Bruck, C., Hammerschmidt. W. 1977. Ermittlung der Fremdgeschmacksschwelle in Lebensmitteln und ihre Bedeutung fur die Auswahl von Verpackungsmaterialien. Technisch-wissenschaftliche Beilage in Verpackungs-Rundschau 28( 1):14. CSIRO. Division of Dairy Research. 1969. Examination of taints caused by shipping containers, CSIRO Australia Annual Reports. P. 35. Durst, G., Laperle. E. 1990. Styrene monomer migration as monitored by purge and trap gas chromatography and sensory analysis for polystyrene containers. J. Fd. Science. 55:522-524. FaGalari, F. (ed.) 1978. Compilation of Odor and Taste Threshold Values Data. American Society of Testing and Materials. DS 48A. Philadelphia. Gavara R., Hernandez R., Giacin J. R., 1996. Mcthods to determine psrtition coefficients of organic compounds in water/polystyrene systems. J Food Science, 61 ( 5 ) 940-952. Hempel. G., Rudt, U. 1988a. Bestimmung von monomeren fliichtigen Anteilen in Polystyrol und StyrolMisch- und Pfropfpolymerisaten. Deutsche Lebensmittel-Rundschau. 84(8):239-242. Hcmpel, G.. Riidt, U. 198Xb. Bestimmung von monomeren fluchtigen Anteilen in Pruflebensmittel. Deutsche Lehensmittel-Rundschau. 84(9):28&290. I S 0 2561-1974 Plastic Materials - Determination of residual styrene monomer in polystyrene by gas chromatography. ISO, Geneva, Switzerland. Jenne, H. 1980. Polystyrol und Polypropylene als Spritzguss- und Tiefziehmaterial fur Molkereirproduktc. Deutsche Molkerei Zeitung 51/52:1906-1910. Jensen. F. 1972. Determination of monomers of polystyrene in milk products. Annali dell' Instituto Superiore di Sanita 8:443448. Lickly. T. D.. Rainey M. L.., Burgert L. C., Breder C. V.. Borodinsky L. 1997, Using a simple diffusion model to predict residual monomer migration - considerations and limitations, Food Additives and Cntaminants, 14.65-74. Lierop, J. van. Wildervanck. J. 1996. Styrene in packings for food. Report No. UT/CH2N/96-3. Health ProtectionlFood Inspection Department, Utrecht, Netherlands. Linssen, J. Legger-Huysman, a. Roozen, J. 1990. Threshold concentrations of migrants from food packages: styrene and ethylbenzene. In: Flavour Science and Technology, ed. Bessiere Y. & Thomas A. John Wiley & Sons, Chichester, UK pp 359-362. Linssen, J.. Janssens. A., Reitsma, H., Roozen. J. 1991. Sensory analysis of polystyrene packaging material taint in cocoa powder for drinks and chocolate flakes. Food Additives and Contaminants. 8( l):l7. Linssen, J., Janssens. A., Reitsma, H.. Bredie, W., Roozen. J. 1993. Taste Recognition Threshold Concentrations of Styrene in Oil-In-Water Emulsions and Yogurts. J. Sci. Food Agric. 61:457462. MAFF. 1994. MAFF UK - Survey of Styrene in Food. Food Surveillance Information Sheet. No. 38. October. Miltz, J., Elisha, C., Mannheim, C. 1980. Sensory threshold of styrene and monomer migration from polystyrene food packages. J. Food Processing and Preservation. 4:281-289. Nerin, C. Rubio. C . Cacho, J.. Salafranca. J. 1996. Determination of Styrene in Yogurt by an Automatic Purge and Trap System Coupled to GC-MS. Prescnted at ILSI International Symposium "Food Packaging Ensuring the Safety and Quality of Foods" Budapest. Hungary. 11-13 September. Rosen. A,, Skeel, M., Ettinger. M. 1963. J. Water Poll. Control Fed. 35:777. Riissli, M., Marek. B. 1977. Mitt. Gebiete Lebensm. Hy 68.440-447. Saxby. M. (ed.). 1996. Food Taints and Off-Flavours. 2""ed.'Blackie Academic & Professional. London. p. 5Y. 247. Sugita, T.. lshiwate H., Kawamura. Y., Baha, T.. Umehara, T., Morita, S., Yamada. T. 1996. Headspace Gas Chromatographic Analysis of Residual Volatile Substances in Polystyrene Food Containers. J. Food Hygienic Society of Japan. 36(2):263-268.
Reactivity in Molecular Crystals Edited by Yuli Ohashi Copyright @ K d a o r h a Ltd .Tokyo. 1999
15 Possibilities and limitations of migration modeling Johannes Brandsch, Peter Mercea, Otto Piringer
One of the principal aims of regulations for food contact materials and articles is the protection of consumer health. World-wide investigations over the last 20 years have demonstrated that interactions between polymers and foodstuffs occur under foreseeable physical processes (Chapter 1 1). Standardization of migration measurements is based on this knowledge. However, with regard to consumer safety it has to be pointed out that it is not possible to carry out all desirable tests. The reasons for this are the variety of substances to control and the necessary time and cost requirements to carry out the analysis (Chapter 10). Fortunately mass transfer from a plastic material into foodstuffs is predictable, derived from the fact that mass transfer from plastics in the most cases obey Fick’s laws of diffusion (Chapter 7). Modeling of potential migration is already used in the United States as an additional tool to help make regulatory decisions (Chapter ll), and the European Union (Chapter 12) also intends to introduce this tool as a quality assurance instrument. In the Practical Guide, a document with no legally binding value (EU-Commission 1999), some guidelines have been given on the use of mathematical models to replace migration testing. In Annex 1 to Section 6 in the guidelines covering the enforcement of legislation and method of analysis it is indicated that: “When it can be demonstrated b y generally recognized diffiision models that the amount of substance in the material is such that the limit(s) cannot be exceeded in any foreseeable conditions” the migration tests can be avoided. As a consequence of this generally agreed principle, the Commission intends to insert a clause which could appear in a future Amendment of Directive 90/128/EEC: “The verification of compliance with the specific migration limits ( S M L )provided in the Directives may be replaced b y the verification of compliance with the maximum permitted quantity of substance in the finished product ( Q M ) , which corresponds to the S M L . The correspondence between the specified S M L and the Q M shall be established by a calculation based on adequate experimentation of the finished product or by the application of generally recognized diffiision models. However, if the limit of Q M is exceeded, f o r a judgement of non compliance of the material or article, it is necessary to obtain a confirmation that the S M L has been exceeded”. The text of this clause is yet provisional and will be improved later. To develop and validate a migration estimation model for the above purpose, the Commission approved a project entitled: “Evaluation of Migration Models to be Used under Directive 90/128/EEC”. A final objective of this project is a proposal of a validated migration model to the European Committee of Standards (CEN) for standardization. The following discussion summarizes the current state of knowledge regarding migration modeling.
446
Brandsch
15.1 Migration modeling for polyolefins In food packaging the polyolefins, especially polyethylene (PE) and polypropylene (PP) are the most widely used plastic materials (Chapter 2). Because PE and PP exhibit a low glass transition temperature, T,, it is legitimate to assume that, under normal conditions of use, the migration of substances in and from packaging made from these materials obey Fick’s laws (Chapters 7, 9, 10, 11). Therefore for a reasonable prediction of migration in many practical cases the availability of data for two fundamental constants is needed: i) the partition coefficient, Kp,F, of a migrating compound between the plastic P and the foodstuff or simulating liquid F (Chapter 4) and ii) the diffusion coefficient, DR of the compound in P (Chapters 5 and 6). Assuming that data for KP,Fand DP exist or can be predicted with sufficient accuracy, a considerable reduction is possible in the analytical work, time and effort currently spent on compliance applications (Chapter 10). Whereas both of the above parameters play a crucial role in determining the level of migration in a real situation, from the regulatory stand point a “worst case” scenario is of primary interest.
15.1.1 Estimation of diffusion coefficients for regulatory purposes To set up a worst case scenario, in a first approximation the following two assumptions can be made: i) the solubility of the migrant in food is high and ii) the diffusion coefficient of the migrant has an “upper bond” value, D;, that means a value which, with a given statistical certainty, is larger than any possible real DP for the migrant. Whereas the first assumption leads to a simple relation, Kp,F I 1, the second one is much more difficult to cm2 s-’ down to about quantify. This is because a real DP may range from about 1@l8 cm2 s-l. Therefore the primary task is to find a procedure for predicting Dp-values which in combination with the diffusion equations (Chapter 7 and 8) and Kp.F = 1provide a guarantee that calculated migration values are equal to or above the real migration value under the same conditions. Because all experimentally obtained data, including the specific properties of a specific plastic material, scatter more or less around a mean value, a guarantee for avoiding underestimations can only be expressed in statistical terms Whereas from a regulatory point of view an “upper bond” limit for DP with sufficient safety for the calculated migration value can be established without difficulties, this limit must be defined in concordance with the practicable concentrations of the migrants from a technological standpoint. Too high overestimations can be useless in practice if the resulting calculated QM-value is much lower than the minimum technologically required concentration of the migrant in the plastic material. The direct consequence from the above consideration is the need for prediction of diffusion coefficients which provide a sufficiently high safety margin for the consumer and a realistic domain for technological applications. The best way to achieve this aim is to develop diffusion coefficient prediction methods that give maximum degree of precision. However, at the same time it must not be forgotten, that highly sophisticated diffusion coefficient models (Chapter 5) are, at least today, so complicated that their application requires more time and cost than the simple migration experiments needed to conform to the regulatory requirements. Such complicated theoretical methods are consequently prohibitive and the only way to come to arrive at results is to start with much simpler estimation procedures.
Possihiliiirs and liriiitntions of niigriiiiori modeling
447
In this respect one solution for the estimation of a Dp-value is to correlate the diffusion coefficient with the relative molecular mass, M,, of the migrant and with matrix specific parameters at a given temperature T in Kelvin. This approach has already been successfully used (Piringer 1993,1994: Limm and Hollifield 1996). The estimation of the diffusion coefficient can be achieved for example using the following heuristic correlation (Piringer 1994; Baner et al. 1996):
(
Dp = 104exp Ap
-
bM,
-
+)
=
104exp(Ap - 0.01Mr -
y)cm2sc1
(15-1)
The parameter AP accounts for a specific contribution of the plastic material to the diffusion process. Phenomenologically speaking AP has the role of a “conductance” of the polymer matrix towards the diffusion of the migrant (Chapter 6). Higher values of AP in such polymers as PE lead to increased Dp-values while in stiff chain polymers such as polyesters and polystyrenes lower Ap-values account for smaller diffusion coefficients for the same migrant. The parameters b and c account for the specific contributions of the migrant and the diffusion activation energy respectively. Three experimental observations support Eq. (15-1): i) within a moderate mass range the logarithm of DP decreases approximately linearly with increasing M,; ii) a (hypothetical) n-alkane with the molecular weight M, exhibits a Dp which is generally larger than the DP of any other organic migrant with the same M,; iii) the exponential temperature dependence of DP In order lo calculate migration rates with a sufficient safety margin from the regulation standpoint, one can match the parameters AH b and c in Eq. (15-1) to yield a DG instead of the real DP Due to the above mentioned scatter of experimental values, the usc of D; 2 DP can avoid underestimations with a certain statistical degree of assurance. But the greater the scatter, the higher the upper limit for Dp* must be set. This statistical assurance is a matter of convention and can be established from a regulatory point of view. It was shown (Piringer 1993; Baner et al. 1996) that for all polymers one can take in a first approximation b = 0.01 dalton-I and c = 104.54 K (Chapter 6). Therefore the task to calculate a D; for a given polymer reduces to specification of its AP Starting for example with AP = 11 for LDPE, practically all values calculated with Eq. (15-1) for substances with M, < 1000 at room temperature are Dgvalues, that means they are higher than real Dp-values for these conditions (Fig. 15-2). In Chapter 11 it was shown that Limm and Hollifield (1996) proposed a somewhat similar approach to calculate DP for migration estimation purposes: I13
(15-2) ( The results obtained are in a reasonable agreement with experimental data. To calDp
=
Doexp aM;/’
-
K F ) (cm2 s-I)
culate the DP one needs for each polymer a set of values for the three parameters, Do, K and a, which are obtained from experimental diffusion data. For polyolefins the following sets of values are given: Tablc 15-1: Empirical constants for the diffusion model of Limm and Hollifield (1996).
Polymer PP
K 1335.7
a 0.597
HDPE
1760.7
0.819
0.90
LDPE
1140.5
0.555
4.16
In Do -2.10
448
Brandsch
To pursue the goal of obtaining a simple formula for the estimation of DR which does not rely on experimental diffusion data, reference Eq. (6-20) for all plastic materials was developed (Brandsch et al. 1999). The theoretical assumptions for this equation are given in Chapter 6. Following the approach treated in Chapter 6 a refined equation for DP resulted: Ap - 0.1351Mf13+ 0.003Mr - ’0+54) ~
(cm2s-1)
(15-3)
where AP is generally a function of temperature: AP = Ap‘ - T/T. The additional parameter T accounts for the deviation of the diffusion activation energy in the considered polymer from the reference activation energy, EA= 10454 R = 86.9 kJ mol-’ in Eq. (6-20). Most currently available diffusion coefficient data are for polyolefins. Appendix I provides a comprehensive list of Dp-values taken from the scientific literature for LDPE, HDPE and PP.The diffusion data presented in the three tables of Appendix I were critically (i.e. not based on subjective decisions) selected from several hundreds of papers and reports published over the last four decades. A similar publication, but with far less data, was published more than 15 years ago (Flynn, 1982). In comparison with Flynn (1982) the criteria used to select the data in Appendix I were primarily based on considerations linked to relevance of the data for predicting migration into and from food packaging made from these polymers. The inclusion of experimental diffusion data in the present collection required that: - the materials, experimental procedures and conditions used to determine the diffusion coefficients are clearly defined and well presented; - the mathematical algorithms derived from the experimentally measured data and the reported diffusion coefficients are clearly given. The data collected in Appendix I can be used to derive values for the athermal term AP’ and for z in order to use Eq. (15-3) for D; calculations. Table 15-2 contains these values for polyolefins. Table 15-2: Plastic specific parameter-values for D ii n polyolefins,
Plastic
AD’
LDPE HDPE PP
11.5
0
14.5
1511
13.1
1511
t
With the above set of plastic specific parameters for polyolefins, a Dgvalue can be calculated using Eq. (15-3) for each molecular mass up to about 4000 dalton and temperature T,>T>T,, where T, is the melting temperature of the polymer. As shown in Chapter 7, the diffusion coefficient appears in all migration rate formulas in the form of its square root. That means for example that, if Dp* is a four-fold over-estimation of DR this will produce only a two-fold over-estimation of the migration rate. Consequently the ratio (D;/Dp)’12 is equivalent with the ratio (mG,t/mF,t)of estimated to measured migration amounts. Most data in Appendix I are for LDPE at room temperature. Figure 15-1 shows the distribution of the ratio (D;/Dp)1’2 for LDPE at room temperature, obtained by using Eq. (15-3) for calculation of DG and Appendix I for extracting the corresponding
449
0
-
0,5 0,8
>0,8 -1,O
-
>1,0 2,O >2,0 - 5,O *5,0
- 10,O >lO,O - 20, >20,0 - 50,
Ratio intervals
Figure 15-1: Distribution of the ratio (Di/Dp)”’ for LDPE at room temperature.
450
Brandsch
experimental Dp-values. The distributions show a sharp maximum for Dp ratios between 1.0 and 5.0. Underestimations below 0.8 are obtained in less than 5 % of cases, whereas the underestimations in the range of 0.8 to 1.0 are at the limits of the precision of the experimental DP In Fig. 15-2 the dependence of the diffusion coefficient, log(Dp*),from M,2'3 calculated with Eq. (15-1) and Ap=ll (curve 2) and with Eq. (15-3) and Ap'=11.5 (curve 1), respectively, is shown in comparison with the experimentally obtained Dp-values extracted from Appendix I for LDPE at room temperature. One can see from this figure that in Eq. (153) with increasing molecular masses, the decrease of the diffusion coefficients is slower than for low molecular masses (Chapter 6). This finding is in agreement with experimental data collected for the diffusion of heavier compounds in polyolefins. With Eq. (15-2) (Limm and Hollifield, 1996) a similar curve as (1) in Fig. 15-2results. Figure 15-2 contains also the curve representing the theoretical reference equation (6-20), which shows a linear decrease of log DP with increasing M:/3. Recently Reynier et al. (1999) measured diffusion coefficients by the film to film method for a series of compounds in polyolefins at 40°C. An advantage of this method lies in the absence of possible interaction (swelling) processes produced from a liquid phase in contact with the polymeric sample. Moreover, using the same procedure and the same sample for a series of migrants, some sources for scatter of results could be avoided. Such scatter of experimental data often results when one compares results obtained in different laboratories with different samples and different experimental methods. The results obtained by Reynier et al. (1999) for HDPE and PP are compared in Fig. 15-3with
-7
-
-8 -9
-
B -10 0
-'
-11
-
-*'
n
-
-12 - ' -13
.-
I
0
20
40
60
80
t
I
100
120
MF3 Figure 15-2: Dependence of the diffusion coefficient from M ": in LDPE at room temperature. Calculated values: (1) with Eq. (15-3). (2) with Eq. (15-1) and (3) with Eq. (6-20); experimental points from Appendix 1-1.
+
451
Possibilities and litnitations of migration modeling
D:-values calculated using Eq. (15-3) and the parameters given in Table 15-2. From this figure one can see that D;-values calculated with Eq. (15-3) show a good agreement with the experimental Dp-values.That means, the D;-values deduced from the data collection in Appendix I are true upper limits but are at the same time quite close to the real values. From a legal view point as presented at the beginning of this Chapter, this is a very important feature of the proposed formula for D;. a) - 7 3 -
-8-A
(.logDpG' log DP calc
f
A
*
;
A
*.
A
- 8 3 --
p"
-m 0
-9
.
c A
**
A
--
A
A A
4
* *
A
A
-95
A
--
A
A
A
-10 --
A
-10,5
300
250
200
350
I 450
400
Mr
b) -8,s
.
T
A
A
*
-9
--
A
**
A A
r
s
* f
0" m
-0
- 9 3 --
A
A A A
** A
A
A
-10 --
A
A
A
452
Brandsch
15.1.2 Estimation of migration values From the above results one can conclude that migration values calculated with the general diffusion equations developed in Chapter 7 can be assumed to come quite near to actual migration values, if the condition Kp,F = 1 is realistic. In cases when large differences exist between calculated m&- and measured mF,,-values when using assumptions for the migration equation (Chapter 7), this means that one or more of those assumptions are violated. Such discrepancies are a natural consequence of applying equations based on a limited set of assumptions to more complex practical situations. On the other hand, discovering the sources of these deviations can lead to a deeper understanding of the processes occurring during migration. In the following DG-values calculated with the refined Eq. (15-3) and partition coefficients Kp,F assumed to equal 1 are used for estimating worst case migration rates for additives from polyolefins with Eq. (7-51). These estimated values are compared with experimentally obtained migration values carried out under well defined conditions for several additives from HDPE and different PP-types (Table 15-3a) into olive oil (O'Brian et al., 1999 and 2000). The results are summarized in Table 15-3b. Table 15-3a: Measured additive concentrations in HDPE and PP. Ranges of concentrations are shown in parenthesis. ~
No.
Chemical name
M,
cP,"[mg/kg]
Polymer
2-Hydroxy -4-n-oct yloxy-benzophenone
326
1540 ( 1400- 1720)
HDPE
Adipic acid, bis(2-ethylhexy1)ester
370
4820 (3970-5640)
HDPE
Octadecyl-3-(3,5-di-t-butyl-4-hydroxyphenyl)propionate 531
840 (77s930)
HDPE
2-(2-Hydroxy-3-t-butyl-5methyl phenyl)-5-chlorobenzotriazole
316
1500 (1400-1670)
HDPE
2-H ydroxy-4-n-octyloxy-benzophenone
326
1470 (136CL1570)
PP
Adipic acid, bis(2-ethylhexy1)ester
370
5260 (SOlG.5730)
PP
890
PP
Octadecyl-3-(3,S-di-t-butyl-4-hydroxyphenyl)propionate531
(72G980)
2-(2-Hydroxy-3-t-butyl-5-methyl pheny1)-5-chlorobenzo-
316
1480 (1420-1560)
PP
43 1
500 146k540)
PP
triazole
2.5-Bis(5-tert-butyl-2-benzoxazolyl)thiophene
The average cP,()values from Table 15-3a were used for calculation in order to compare the estimated migration values in Table 15-3b with the average experimental values. As shown in Table 15-3b, overestimation resulted for all average values and the smallest differences between calculated and measured values appeared at higher temperatures. One reason for the higher overestimation at lower temperatures lies with high probability in the partition coefficients for additives which are in general noticeable increasing with decreasing temperature (Chapter 4). From the quality assurance
453
Possibilities and limitations of migration modeling
Table 15-3b: Measured and calculated migration values [mglkg] of some additives from HDPE and PP into olive oil. ~~~
~
Migration conditions Additive no.
Polymer
1
HDPE
2h/70°C
6h / 7 0 T
exp.
calc.
7.5
19
(5.6-9.8) 2
HDPE
3
HDPE
19
48
HDPE
5.0
20
2
PP
PP PP
42
98
(30-58) 7.2
3.4
8.4
(2.8-4.3)
8.4
34
11
40
(7.9-17)
2h/70"C
10d/40°C
exp.
calc.
exp.
calc.
83
6.8
8.6
9.5
185
240
(5-1 I ) 14
25
(6-17) 23
51
121 13
(9-28) 20
31 7.7 (5.9-11)
1.9
(1244) 2.1
(1.2-3.1) 88
(25-44) 5
39
calc.
(12-18) 4
19
41
(94- 166)
PP
84
4.2
calc.
exp. (33-55)
3
32
exp. (14-24)
(5.5-12)
2 h / 121"C PP
33
(3.1-5.4)
(3.5-7.2)
1
16
(24-41) 4.1
(1.8-4.4) 4
calc.
(8.7-1 7)
(15-25) 3.0
10 d / 40°C
exp.
4.3
9.1
(3-8) 17
0.9 (0.6-1.7)
2.4
4.2
(1.3-4.2) 5.2
19
(3-10) 1.8
1 .o
3.6
(0.5-2)
point of view overprediction is not a concern, however from a technological standpoint more accurate estimation of partition may be of great interest in order to allow predictions closer to actual experimental data. Conclusions can be drawn by making comparisons of estimated migration values with data from experimental data banks containing migration values obtained from petitions for additives in food contact materials (Chapter 11). In Table 15-4 some of the data extracted from migration studies collected in the BgVV (formerly BGA), over the last two decades, are compared with estimated values under the same conditions. In this section data for polyolefins are discussed and the estimation results are based on D;-values calculated with the refined diffusion coefficient estimation Eq. (15-3). The discussion of non-polyolefins is found in the following section. In all cases presented in Table 15-4 the thickness of the plastic samples and the experimental conditions provided a migration process far from reaching the equilibrium state. Here only data obtained with fatty food simulants denoted as D (Chapter 12), that means olive or corn oil or a synthetic fat and in some cases ethanol/water-mixtures are discussed.
454
Brandsch
Table 15-4.Migration data extracted from the data bank of BgVV for several plastic materials. Polymer LDPE LDPE HDPE
dr (cm) M, 0.4 0.2 0.06
43 1 ZOO0 5.53
HDPE
0.2
35 1
HDPE PP PP PP
0.2 0.2 0.2 0.2
39") I178 4.1 1 604
PP
0.2
553
PP
0.2
1465
cP,"(mgikg) 1000 2800 1000 2000 1000 1000 1000 750 6000 10000 100
2500 1000 IOW ZOO0 3000
Food simulant D Eth. 95 % D
D Eth. 95 Yo D D D
D D
T "C 40 49 40
t 1Od 1Od 1Od
100
100
Ih 1Od 2h 2h 3.5h 1Od 1Od 10d 10d Ih
40
1Od
100
Ih 1Od 2h 3.5h 1 Od 10d 10d 2h I Od Ih 1Od 2h 0.5t 2h Id 4d 1Od IOd 1Od 2h 1Od 2h 1Od 2h 10d Ih 2h 1Od Ih 2h 10d Ih 1Od lh I Od
40 70 70 60 40 40 40 40
40 100
PP PS
0.2 0.1
3900 587
6000 2000
IPS
0.2
395
5oou
IPS
0.2
425
2000
IPS
0.2
439
2000
D
IPS
0.2
549
5000
Eth. 95 %
Eth. 95 % D
PVC PVC
0.1 0.1
330 604
loo00 8600
D D
PVC
0.1
513
5700
D
9400 PET
0.1
448
2500
D
60 40 10 40 70 40 100 40 70 66 49 49 49 49 40 40 70 40 70 40 70 40 100
5000
D
40 100
PET
0.2
587
2500
D
5000
D
1500
Efh. SO Yo D
40
100
POM PA 6.6
PA 12
0.2 0.2
0.2
553 587
587
5000
5000
D Eth. SO Yo D Eth. SO Yo
40 100 40 40 100 40 100 49 49 40 49 49
IOd
Ih 1Od Ih 1Od 1Od 1Od 1Od 1Od
mF,, (mg/dm') calc. mF.,(mg/dmz) exp. 6.93 0.34 1.52 3.1 2.1 3.7 1.8 1.4
0.0027 0.93 1.2 I .5 0.59 0.84 1.4 2.0 0.13 0.27 0.0013 0.0084 0.0014 0.055 0.15
0.022 0.13 0.018 0.05 -
0.21 0.047 0.030 0.042 0.030 0.069 0.052 0.01 1 0.045
n.n@ 0.021 0.090 0.13 0.015
0.10 0.030 0.21 -
0.076 0.072 0.038 0.060 0.060 -
0.15 0.24 -
2.79 0.89 0.015 0.038 0.13 0.23 0.25 0.16 0.0064 0.18 0.19 0.32 0.17 0.62
0.027 0.48 0.1 0.I 5 0.0084 0.0031 0.0013 0.0072 0.050 0.060 0.40 0.009 0.047 0.183 0.2 13 0.068 0.0 10 0.23 0.008 0.018 0.0016 0.016 0.0031
0.033 0.001 0.019 0.021 0.0014 0.041
0.052 0.0056 0.11 0.012 0.26 0.26 n 023 0m7 0.0015
0.021 0.016 10.3 0.016 0.077 12.6
Possibilities cind limitations of migration modeling
455
From Table 15-4 one can see that, whereas a two-fold overestimation resulted for the migrant with M, = 431 from LDPE into olive oil, an underestimation resulted for an additive with a mean molecular weight M, = 2000 from LDPE into 95 % ethanol. In this later case the additive was a mixture of oligomers with a mass distribution around 2000 dalton. The analysis of oligomeric species was specific for the structure but could not distinguish between their different masses. This is important because at 2000 dalton an estimated migration amount of m*F,t= 0.34 mg dm-2 results and at 1500 dalton m*F,t= 1 mg dm-' is obtained. That means for high molecular weight additives made up of oligomer distributions containing different masses, the mass distribution must be known in order to allow accurate estimation. The species with lower masses diffuse more easily and therefore play a more important role in the mixture than do the higher masses when measuring migration. From Table 15-4 we can see that the calculated migration amounts from HDPE are more or less overestimated in comparison with the measured values, depending on how the migrant partitions itself between the plastic and food simulant. The migration calculated for the additive with M, = 553 is greatly overestimated because this additive has a low solubility in food simulant D. Using a partition coefficient K ~ , J= 10000 instead of 1, which is used for the worst cases, the calculated migration amounts are mF,t = 0.016 and 0.032 mg dm-' for the initial additive concentrations in the plastic sample of ~ ~ ~ ~ ~ and = 1 02000 0 0 mg kg-I. These values are very close to the measured amounts at 40 "C. At 100 "C similar results are obtained with an estimation using a partition coefficient, Kp,F = 1000, mF,t= 0.129 mg dm-2 compared with 0.127 mg dm-' measured after 1 h. The decrease of the KeF-value with increasing temperature means a higher solubility in the simulant at higher temperature. The underestimation in the case of the additive with the main component molecular weight 3900 has the same explanation as that given for the 2000 M, additive in LDPE. It is a mixture of several species with a mass distribution in which the lowest mass provides the highest relative contribution to the overall amount of migration. As in the case of polyethylene, the calculated migration amounts for additives from PP are over estimations. This overestimation is especially high for the additive with M, = 553 at 40 "C, due to a larger partition coefficient as it was shown for HDPE. Due to the higher solubility of the additive at 100°C the degree of overestimation is decreased.
15.2 Migration modeling for non-polyolefins In contrast to the polyolefins, much less well defined migration data are available for non-polyolefins. Therefore if one intends to develop for non-polyolefins a similar approach to estimate Dp*-values as given above for polyolefins the lack of data is a real handicap for predictions requiring a degree of precision. An additional difficulty is the much higher glass temperature, T,, for most non-polyolefins in comparison to the polyolefins. For the most important food packaging non-polyolefins the T,-values are between 50 and 100 "C, that means the temperatures fall between the conditions of food contact at room temperature and hot-fill, pasteurization and sterilization temperatures. In the transition region from the glassy to the rubbery state of the plastic
456
Brandsch
generally a significant change in the activation energy of diffusion occurs. Referring to terms defined for Eqs. (15-1) and (15-3), this change must be taken into account by selecting adequate Ap-values for each state of the plastic phase. Despite these limitations and problems encountered with non-polyolefin materials in Table 15-5 a set of provisional Ap-values can be presented. These Ap-values apply only in the simplified Eq. (15-1). Table 15-5: Ap-values for some non-polyolefins. Polymer
Temperature range ("C)
AP
PS, IPS
< 70
4
HIPS
< 70
-3
PS, IPS, HIPS
2 70
0
PET
5 70
-6
> 70
-3
< 50
4
PBT PVC
2 50
0
< 70
-3 -4
2 70 POM
0
PA 66
< 70
-3
2 70
-2
PA 12
< 70
0
> 70
2
With the set of Ap-values given in Table 15-5 most of the calculated migration amounts from Table 15-4 are overestimations compared with the measured values. The considerable influence of the food simulant can be observed in many cases for non-polyolefins. For example, the migration of an additive with M, = 549 from IPS into 50 % ethanol in water in Table 15-4 shows a decrease of the migration amount measured at 49 "Cafter an initial contact temperature of 66 "C.This phenomenon cannot be explained by changes in diffusion. The decrease in migration must be a consequence of a strong increase of the partition coefficient, KKF,with decreasing temperature that shifts the equilibrium concentration of the migrant to the plastic phase. Other frequent phenomena are strong interactions between the plastic sample and the simulant. For example, the additive with M, = 587 shows a 20-fold enhanced migration from PBT into 50 % ethanollwater at 40 "C compared to olive oil. The interaction effect is dramatic with PA, as can be seen from the migration of the same additive into 50 % ethanol (mEt = 12.6 mg dm-') compared to olive oil (mEt = 0.077 mg dm-') after 10 days at 49 "C. A very important fact is the difference observed between the migration amount measured with IPS samples by full immersion compared with one-sided migration cells (Lickly 1997, Figge 1988). Due to the two-phase structure of the plastic matrix, the normally homogeneous polystyrene-phase near the interface in a real food contact material is destroyed in the material edges after cutting. The consequence is an enhanced migration through the rubbery phase in these regions.
Possibilities mid lirnitutions of migrotion inodeliizg
457
Last but not least, an aging effect of the polymeric samples can produce significant overestimations in modeling, especially in the case of low molecular migrants (Lickly et al., 1997). During long storage periods of packaging materials in the open atmosphere, considerable loss of the migrant occurs near the interface and consequently the migrant is no longer homogeneously distributed in the plastic, as assumed in theory. As a conclusion, careful examination of all migration measurements is necessary for a correct evaluation of estimation results, because many processes are possible which are in direct conflict with the assumptions of the mathematics behind the simplified migration equations (Chapter 7). Overlooking these conflicts between assumptions and experimental behavior produces many pitfalls (Piergiovanni et al. 1999).
15.3 Optimization of modeling From the point of view of compliance applications the use of Eq. (15-3) and the parameters from Table 15-2 for migration estimation may in principle lead to two types of results. The first case occurs when it is found that for a given polyolefin the worst case scenario by using KP,F = 1 and Df. from Eq. (15-3) and Table 15-2 leads to calculated QM values which are within the limits of the technologically required concentrations. The second case is when it is found that the above migration estimation approach leads to QM's which are impractical (too low) from a technological point of view. From a legislative standpoint in such a case for a compliance application with the real polymer it will be necessary to perform experimental migration tests. However, it must be emphasized that often this later case is caused because the worst case scenario developed above overestimates too strongly the migration amount in the actual polymer-migrant system. Thus it is legitimate to ask: what can be done when a more precise migration prediction is desired for a specific additive from an unknown or newly developed plastic formulation ? With the theoretical and experimental background accumulated until now and the discussions in this book, it is in fact not too difficult to provide the needed information quickly with a minimum of experimental effort, get still provide enough precision for modeling all necessary practical applications. The following example outlines an approach applied to polyethylene samples obtained from different manufacturers containing the additives shown in Table 15-6. The aim of this exercise was to demonstrate how precise such investigations can actually be using only generally available laboratory equipment. The initial concentrations, cpv0,shown in Table 15-6 were measured after dissolving the polymer sample in toluene under reflux, precipitating of the polymer with ethanol, filtration, solvent evaporation and dissolving the residue in 95 % ethanol. All additives were analyzed by high performance liquid chromatography (HPLC) on a Spectra Physics chromatograph (Thermo Quest). A Nucleosil 100-5C 18 H D column with a 125 mm length and an inner diameter of 4 mm was eluted using 100 '10 acetonitril as mobile phase at a flow rate of 1 ml min-' at 30°C. 20 pl of the ethanol solution was injected and the UV detector monitored at 195 nm. Under these conditions retention times of 8.2, 12.5, 20.9 and 23.2 min were obtained for Irganox 1330, Irgafos 168 ox, Irganox 1076 and Irgafos 168, respectively (Fig.15-4) (Brandsch et al. 1999).
458
Brandsch
Table 15-6 Polyethylene samples with different densities, pP (g/cm3), and additives with relative molecular masses, M,, and initial concentrations,cp.0 (mg/kg). Polymer LLDPE
PP
1
0.905
Additive Irganox 1076 Irgafos 168
Mr 531 646
2
LDPE
0.918
Irganox 1076 Irgafos 168
531 646
220
3
HDPE
0.946
Irganox 1010 Irgafos 168
1177 646
220 1070
4
LDPE
0.918
Irganox 1330
775
585
No.
__
m
CP.U
130 540 760
W1000-lSSnm
15
Vdb'O,
S
lrgafos 168 ox. 1
0
4,. ,
,
..
,
,
,
.,
,
.________l_.l_,
, , , ,,,, , , _ , ,
, ,
,, ,
-
,.,, ,
,
.,,
,,,, ,_
,
,
, ,
,
,
, ,,
,,
,, , ,,
,
,
,
___
Figure 15-4 HPLC-Chromatogram obtained with a migration solution containing Irgafos 168, oxidized Irgafos 168, Irganox 1076 and Irganox 1330.
Possibilities arid limitations of migration modeling
459
For each migration experiment two pieces measuring 9.8 x 4.9 cm2 were cut from the 0.2 cm thick polymer samples and placed in a double sided glass migration cell (Greiner & Gassner GmbH, Glastechnik Munchen) with an inner diameter of 6 cm. The pieces were covered with 130 ml of 9.5 % ethanol. The surface area of the total immersed pieces in contact with the liquid was 192.08 cm2. The contribution of the edge surface area was about 12 cm2, representing 6 % of the total surface area. This additional 6 % surface area was neglected in the evaluation of the results. This leads to an overestimation, which is acceptable from a regulatory standpoint. For polyethylene the amount of migration per surface area, mF,,/A, from the edges and the contact surface area are of the same magnitude. However, this must not be true in all cases, as will be mentioned later. The migration experiments were conducted at 40°C for 10 d and at 80°C for 6 h. The analysis of the additives from the migration solutions were performed with HPLC as described above. The determination of the migrated amounts was performed using corresponding calibration curves for each additive. In Table 15-7 the migrated amounts per surface area, mF,,/A, are shown in the second column for Irgafos 168 from HDPE with pp = 0.946 g cm-j at 40 “C(Brandsch et al. 1999). The amounts represent the sum of phosphite and phosphate (Irgafos 168ox). Tahle 15-7: Comparison of experimentally measured and calculated migration values, mF,,/A (pg dm ’) for Irgafos from HDPE into 95 % ethanol at 40°C.
~
~
~~
~
~
~
~
~
1
33
707
21
27
0.82
33
1.00
2
43
999
23
40
0.Y3
45
1 .05
4
59
1411
24
57
0.97
61
1.03
10
89
2222
25
91
1.02
88
0.99
All calculated mF,,/A-values were obtained using Eq. (1.5-3) in conjunction with Eq. (7-51). A recently developed software was used for all calculations (Mercea et al. 1997). The calculation was started taking AP from Table 15-2 for 40 “C, which gave an “upper bond” Df; = 1.15E-10 cm2 s-l. Using this D; and taking Kp,F = 1 - the worst case scenario - one can calculate the migrated amount and its ratio against the experimental one. The results obtained are shown in columns 3 and 4 of Table 15-7 from where one can see a 20-fold overestimation of the migrated amount. In other words this means that for this type of HDPE the “conductance” corresponding to an AP = 9.46 was too high. Therefore in a second calculation an adjusted AP = 3.1 was taken and the results obtained are given in columns 5 and 6 of Table 1.5-7. In this case the estimated values are much closer to the experimental ones. But in this and the previous case too, a systematic increase with time is found in the mF,l,ca~c/mF,l.exp ratios. This may be caused by the fact that the real partitioning coefficient is higher than the worst case one. Therefore, adjusting again with Kp,F = 380 and AP = 3.8 the results obtained in columns 7 and 8 show a very good agreement between experiment and modeling.
460
Brandsch
The following conclusions can be immediately drawn from the above results: the actual state of the art in analytical equipment allows very precise determination of the specific migration of some widely applied additives, such as Irgafos 168 in volatile food simulants. The special advantage of this additive is that the phosphate (Irgafos 168 ox) is the only oxidation product. This can be determined in the same analytical run along with the initial phosphite. The migration rates of the two species are practically the same and a full recovery and mass balance is possible. The initial concentration, c ~ ,is~also , the sum of the two species and so one important assumption for Eq. (7-51) (Chapter 7) is fulfilled. Another conclusion is the very sensitive reaction of the calculated amounts to different partition coefficients, Kp,F. Although only less than 20% of the additive is migrated after 10 days from the polymer into the ethanol, a partition influence can be easily detected. The relatively high Kp,F-valuesfor many plastic/liquid-systems,especially at lower temperatures are the reason for high overestimations using the worst case value of KEF = 1. In Table 15-8 experimental (exp) and calculated (calc) migration values for Irganox 1076 and Irganox 1330 from LDPE with pp = 0.918 g cmP3at 40 “C are given. Table 15-8: Migration amounts, mF,,/A (kg dm”) obtained with Irganox 1076 and Irganox 1330 from LDPE into 9.5 % ethanol at 40 “C. t (days) 1
mF,,/Aexp Ire. 1076
mF.,/Acalc AP = 8.6
mErcalci
mF,,/Aexp Ire. 1330
mF,,/Acalc AP = 9.0
mF.1 calc/
142
145
1.02
188
187
0.99 1.02
mFr
exu
mF, exu
2
210
204
0.97
259
265
4
290
288
0.99
366
374
1.02
10
459
454
0.99
593
59 1
1.00
In these two runs, KP.F= 1 was used in Eq. (7-51) and as can be seen, no systematic deviation between the calculated and experimental values occurs with increasing of time. In both cases using AP = 11.5 from Table 15-2 one obtains an overestimation because the estimated DG is larger than the real DF The best fit with experimental values is obtained if one lowers AP to about 9 and then calculates an adjusted Dp < Df. and mF,,/A with Eq. (15-3) and Eq. (7-51) respectively. Phenomenologically the lowering of AP from 11.5 to 9 means that the LDPE sample exhibits a smaller “conductance” for the migrant than that corresponding to the worst case scenario quantified by the parameters given in Table 15-2. It is well known that the density, pR of a polymer plays an important role in determining the mobility and hence the DP of a migrant in its matrix. It is well established by experimental evidence that for a given polymer type the increase of pp leads to a decrease of DP (see for example Appendix I). To illustrate this feature in Table 15-9 the experimental and estimated amounts of migration for Irgafos 168 from three polyethylene samples with different densities into 95 % ethanol at 80°C are given. The first two PE’s are LDPE while the third one is a HDPE sample. In all three cases it was assumed that KP,F= 1 and the DG-values were calculated using Eq. (15-3) and the data from Table 15-2. With these data Eq. (7-51 ) can be used to estimate the migrated amount under the worst case scenario. The results obtained show an overestimation of m,,/A which for the HDPE sample is about 8-fold. On the other hand the overestimations show no systematic deviation with increasing of time which is an indication of
461
Possibilities arid limitations of migration niodeling
the fact that the assumption Kp,F = 1 is valid. Therefore in order to bring the estimated migration amounts closer to the experimental ones it is again necessary to adjust (lower) the Ap-values. In Table 15-9 it is shown that taking AP = 9.9, 9.05 and 5.75 respectively yields a good agreement between experiment and estimation. This is also in agreement with the above phenomenological picture, i.e. a higher density in PE determines smaller diffusion coefficients to which then correspond smaller Ap-values than those given for LDPE and HDPE in Table 15-2. Although a significantly higher amount of Irgafos 168 migrated from HDPE after 6 h at 80°C in comparison to the values obtained after 10 days at 40 "C, the ratio between calculated and experimental value are equal to one at 80 "C. Table 15-9: Migration values, mF.,/A(pg dm-2),of lrgafos 168 from three polyethylene samples with different densities into 95 % ethanol at 80°C.
1
536
578
1.08
534
539
1.01
148
148
2
786
815
1.04
756
761
1.01
210
210
1 .OO
3.5
1077
1075
1.00
979
1010
1.03
284
279
0.98
6
1399
1403
1.00
1310
1314
1.00
394
366
0.93
1.00
This reduced "conductance" of the investigated PE's results in a great part from the interaction between the structure of this additive and the plastic. For additives with a more alkane-like structure, significantly higher migration amounts are found from HDPE and correspondingly the lowering of AP will be less severe. From the above examples and discussions one can derive a general scheme to be used for migration estimations from new polymers (polyolefins in our case) for which experimental diffusion or migration data are not yet available. In such cases a quick migration experiment is recommendable at 80 "C with 95 o/' ethanol, using an incorporated additive (which in many cases is a phosphite or phenolic antioxidant similar to the above examples). From several measurements after different contact times (up to a few hours) the experimental mF,t values must be compared with values calculated with Eq. (7-51) using Eq. (15-3), where in a first approximation Dp* is calculated with AP = 11.5 (as for LDPE) and using Kp,F = 1 (worst case scenario). If the calculated mF.,-values show no systematic deviation from the experimental values for increasing contact times, then the assumption KeF = 1 is valid. On the other hand if the estimated values show an overestimation, this indicates that the new polyolefine requires a smaller real AP than that from Table 15-2. After a few repeated calculation runs with lower Ap-values quickly provide the correct Ap-value. Once the adjusted Ap is found so that there is a good agreement between experiment and calculations, this new value can be used in combination with Eq. (15-3) and Eq. (7-51) to estimate the migration at any temperature T 2 80 "C and for any migrant with any molecular weight, M,, and a similar structure to that of the additive incorporated in the above PE samples. This scheme is valid for a wide range of initial migrant concentrations, c ~ ,in~the , new polyolefine. Most likely this range will cover the technically practicable amounts of additives in the new plastic.
462
Brandsch
15.4 Migration modeling with new polymer-migrant systems From a practical point of view it is useful to develop a scheme as reliable and as simple as possible to model theoretically the migration in new polymer migrant systems for which experimental data are not yet available. In the following such a step by step scheme will be presented. As a first step it is useful to test the interaction between the plastic and food simulants that differ as much as possible from the plastic in their polarities. A quick overview about the absorption behavior of the plastic is obtained by immersion of samples into olive or corn oil at the highest desired used temperature for 1-2 hours and then determining the amount of oil absorbed gravimetrically. In Table 15-10 some results obtained in this way with several plastics are shown. The most important result from this table is the high absorption of olive oil into HDPE and PP at 121" after 2 h. Due to the strong interaction with this fat simulant the actual conditions required in the regulations (Chapters 12 and 11) for migration testing at sterilization conditions using pure fat phases seem to be inadequate. The migration of additives when such strong interaction occurs leads to exaggerated overestimation conditions compared with foodstuffs in practice. In practice the absorption process is greatly reduced by water present in the system. It must not be forgotten, that packaging materials for food are only admissible if interaction processes are negligible in order to fulfill the requirement of inertness (Chapters 11 and 12). Once an adequate simulant is selected which shows no or only little interaction with the plastic, the next step is to perform a migration experiment using a well known additive as a reference compound. This selected additive must be well soluble in the chosen food simulant in order t o give a guarantee of a partition coefficient as low as possible (Chapter 4). In most cases one can select for this purpose an additive used in the plastic sample under investigation and run the migration experiment as shown in the previous section. Once these two experimental steps are done their results can be used to obtain the necessary specific parameters in Eq. (15-3),which then can be used in conjunction with Eq. (7-51) to perform migration estimations for a new or unknown plastic material. There are many possibilities for selecting the most adequate conditions for such determinations. But by such a combination of a few experimental measurements with the existing theoretical background, the actual limitations in modeling could relatively easily be overcome and much loss of time and expensive effort can be avoided. Finally a few remarks are necessary with respect to the analytical procedures required for migration studies. Whereas chromatographic separations in the gas and liquid phases are currently state of the art, additional selective methods will be of considerable importance for future studies. Among these, direct mass spectrometry using for example an electro-spray- ionization (ESI) or API ion source can quickly provide data for several species migrating into a simulant in one run. The whole mass range occurring in practice can be covered in a single measurement. For example, Figs. 15-5 to 15-7 show three applications which demonstrate the necessity of using specific analysis for complex additives such as mixtures of oligomers. Older results obtained using global methods, like radiolabeling, could not distinguish between species with different masses. As a result these methods give results which conflict in many cases with predictions made using the mean molecular weight, as was shown above. The ESI-MS is especially well suited for complex nitrogen-containing and phenolic structures. Fortunately, combinations of HPLC with ESI-MS or API-MS also provide a very powerful tool.
Possibilities imcl linzitations o f migration modelitzg Table 15-10: Oil absorption into several plastic materials. __
Polymer
Simulant
LDPE
Miglyol812
Test conditions [hI"C] 240140 240150 240160
Olive oil
HDPE
Miglyol812
Olive oil
PP
Miglyol812
Olive oil
IPS
Miglyol812
i-Octane Ethanol
ABS
Miglyol812 Ethanol
PBT
Miglyol812
2/70 1 1100 21100 41100 I/lo0 21100 411 00 11120 21I20 4/120 11120 21120 41120 11120 21120 41 120 11120 21120 41120 48/40 96140 168140 240140 240160 2170 240140 2170 240140 2/70 240140 2/70 0.51100 lil00 21100 0.51150 11150 21150
Absorbtion
["/.I 1.2 1.4 1.6 1.0 17.2 27.9 30.4 3.5 5.3 8.3 9.2 10.1 11.7 1.9 2.8 4.3 9.7 12.0 14.2 1.3 2.0 2.5 9.2 11.7 15.0 16.5 54.5 49.8 1.1 1.5 0 0 7.1 8.9 0 0 0 0 0 0
463
464
Brandsch 481.6
100.1
h
80
i
482.5
n
2ol
II 1I m/Z
Figure 15-5: Mass spectrum of Tinuvin 770 obtained with the ESI-MS method.
1: 4.5 1214.:
a) 1009590-
9
=P
i
80-
7570-
65-
605550-
3 5
65-
2
504540-
8
45-
.-
40-
3530-
6055-
fY 3530-
25-
25-
20-
20-
15105- 1182
-.
x
0
0.5
85-
7570-
3 5 5
8
90-
8580-
0
10095-
b'
-*
837.5
880.9
Figure 15-6: Mass spectrum of a) the double charged and b) the threefold charged HAS molecule with M, = 2426 obtained with the ESI-MS method.
Possibilities and limitations of migration modeling
465
A very effective class of photoantioxidants and long-term heat stabilizers are hindered amine stabilizers (HAS) (Chapter 3). Mononuclear and high-molecular-weight polynuclear compounds of this structure type are used as commercialized stabilizers. In Fig. 15-5 a mass spectrum of the binuclear HAS (Chapter 3, structure 31), bis(2,2,6,6-tetramethyl-4-piperidyl) sebacate (TINUVIN 770), with M, = 480.6, is shown. It was obtained after 10 days migration at 40 "C from HDPE into 95 % ethanol. After adding 10 pl glacial acetic acid to 1 ml of migration solution and dibutylamine (not shown in Fig. 15-5) as an internal standard the migration solution was directly introduced into the ESI-MS with a flow rate of 10 pl min-'. The signal obtained is an average of 25 mass scans. The peak with the masslcharge ratio, mlz = 481.6, represents the (M,+l)+-ion obtained by addition of one proton. The relative abundance of the signal represents a concentration of 0.48 pg ml-' migration solution, corresponding to 0.4 pg dm-* of HDPE. This method is very sensitive, specific and quick. In Fig. 15-6a the positive signal at m/z = 1214 of a double charged ion (M,+2)2+ corresponds to a HAS-molecule with M, = 2426 and in Fig. 15-6b the signal at m/z = 810 is that of a threefold charged HAS-molecule with the same structure. The signals were obtained in the same manner as for the previous case. The additional advantage of the ESI-MS in this example is the possibility to measure mixtures of additives with a large range of molecular masses, including impurities and degradation products with much lower molecular weights as the additive (Chapter 3) in a single run. The above mentioned possibility for direct analysis of a mixture of migrants is shown in Fig. 15-7. In this case a mixture of oligomers was analyzed, representing polyethoxylated alcohols. A difference of 44 dalton between two consecutive ionpeaks represents a structure unit CH2-CHZO-. 7. 705 3
4
661 2
881.1
35352 302
20 z
6
-.
..
...-
900 mlr
Figure 15-7 Mass spectrum of a mixture of polyethoxylated alcohols obtained with the ESI-MS method.
466
Brandsch
Only with such modern analytical tools is it possible to give correct answers to the many problems occurring in interactions between plastics and food. Some of the results obtained with ill-suited analytical methods for high molecular additive mixtures can be re-evaluated in this manner. In addition, answers can be given about the mechanism of degradation and the nature of decomposition products (Chapter 3). Last but not least a much faster determination of low migrants concentrations is possible in many cases. This is an important assumption for quality assurance with low thresholds of concentrations for regulation.
15.5 Modeling of migration from multilayer structures In many examples discussed in this book an actual practical situation is reduced to some kind of an “idealized” plastic migrant system in which the plastic material is a single layer structure with a finite thickness and a homogeneously distributed concentration of the migrant. That means the initial and boundary conditions for analytical solutions of the diffusion equation are fulfilling the assumptions described in Chapter 7. There it is already mentioned that for structures and initial and boundary conditions which deviate from such a relatively simple picture of the migration process the analytical solution for the diffusion equation is very difficult if not impossible. In such cases only the numerical mathematics leads to the desired results (Chapter 8). To exemplify such a problem the migration of an impurity from a core layer into and through a functional barrier made from an identical raw material was analyzed. In the majority of cases in food packaging with multilayer structure different materials are combined 100000
I d
2 10000--
I000
3d -
--
4d
--8d
flP I00
10
---
--
4d
I,
5;
8d p2
1
, p3
jF I
Figure 15-8: Migrant concentration profiles in a three layered laminate as a function of time and spatial coordinate.
Possibilities atid limitations of migrnrion modeling
467
33T
o ! 0
I 1
2
3
4
5
6
7
8
d Figure 15-9: Concentration of a substance migrated from a laminate into a food simulant as a function o f time.
in a laminate, e.g. polymers, polymeric glues and varnish. Migration modeling in such cases is possible only by numerically solving the diffusion equations. The following example shows modeling results obtained recently with a three layered laminate (Tosa et al. 1999). The system consisted of a thin layer PI with a thickness dl = 1 pm, which adheres with the left side to an impermeable layer (e.g. aluminum) and with the right side to a thicker layer P2 (d2 = 2.7 pm). This second layer adheres to the food contact layer P3 (d3 = 30 pm). While PI and P3 are made of quite similar polymeric raw materials and do not contain initially any potential migrant, the layer Pz is made of a plastified polymeric material which contains a potential migrant with a initial concentration, c2.0 = 12.5 %. The solubility of the migrant in PI and P3 is about the same but it is lower than in P2. That means the partition coefficients, K1,2 = 0.01 and K2,3 = 100 are assumed for the migrant between PI-P2 and P2-P3, respectively. The diffusion coefficient of the migrant at room temperature is D1 = D3 = 1E-12 cm2 s-l and D2 = 1E-10 crn2s-I. In this example it is assumed that the migration starts when the contact between packaging and food is established. An initial storage time of the laminate can also be considered (Tosa et al. 1999). It was further assumed that the migrant has the same solubility in the food simulant F as in P3, that means, K ~ , = F 1. The volume VF/A = 10 cm3 cmP2.This value is exaggerated in comparison with actual VF/A ratios, but it allows a better illustration of the process in Fig. 15-8. The results obtained (Fig. 15-8) show clearly the important role of the partitioning during the migration through the multilayer structure. The effect of the diffusion
468
Brandsch
process through P3 is illustrated after one day. As the migration proceeds, one can see that the concentration of the migrant in P2 decreases rapidly as it migrates through P3 into F. In Fig. 15-9 one can see that after 8 days the system reaches equilibrium, which is shown by the horizontal concentration profiles in PI, P2 and P3 in Fig. 15-8 and the asymptotic value, cF,~= 3.37 ppm in Fig. 15-9. Thus at equilibrium about 336 ppm of the migrant remain “trapped” in Pz, despite the much lower concentration of the migrant in the food simulant. This is due to the effect of the partition between P2 and P3, a result which has an important practical value. There are many cases where it is technologically necessary to include into one of the layers a considerable amount of a migrateable compound (a binding agent from ink or a varnish component). To hold this migrant as long as possible in the laminate it is important to place between the layer containing the migrant and the food another layer (functional barrier) in which the migrant has a considerably smaller solubility that in the parent layer and a diffusion coefficient as small as possible. The above example is a relative simple case of modeling migration in a laminate. But it illustrates the power of numerical mathematics (Chapter 8). The possibilities in modeling with easily available hard- and software opens a large field of complex applications. However, it must be emphasized that such principally simple modeling problems may offer many difficult to solve details and pitfalls. Consequently specialized software offered for migration modeling may be a great help for all people interested in plastic-food interactions. MIGRATEST Lite (1997, 1999), COATINGTEST (1999) and MIGRATEST (2000) are examples of such tools. References Baner A. L., Brandsch J., Franz R., Piringer 0.1996, Food Additive;, and Contaminants 13 587401. Brandsch J., Piringer O., Riiter M. 1999 (unpublishedresults). EU Commission 1999, Practical Guide, Internet. http:l/cpf.jrc.it/webpack. Figge K, 1988, Food Additives and Contaminants 5 397420. Flynn J. H. 1982. Polymer 23 1325-1344. Lickly T.D., Rainey M. L., Burgert L. C., Breder C. V., Borodinski L. 1997, Food Additives and Contaminants 14 65-74. Limm W., Hollifield H. C. 1996. Food Addirives and Contaminanrs 13 949-967. Mercea P, Piringer 0..Petrescu L., 1997, MIGRATESTLite, FABES, Munich. O’Brien A,, Goodson A., Cooper I. 1999, Food Additives and Contaminants 16 367-380 and 2000 (in print) Piergiovanni L., Fava P., Schiraldi A. 1999, Food Additives and Contaminants16 353-359. Piringer 0.1993, Verpackungenfur Lebensmittel, VCH-Verlag, Weinheim. Piringer 0. 1994, Food Additives and Contaminants 11 221-230. Reynier A., Dole P.. Feigenbaum A. 1999, Food Additives and Contaminants 16 137-152. Tosa V.,Mercea P., Piringer 0.1999. (unpublished results).
Reactivity in Molecular Crystals Edited by Yuli Ohashi Copyright @ K d a o r h a Ltd .Tokyo. 1999
Appendices Appendix I Table 1: Diffusion data for low molecular weight organic substances in Polyethylenes (PE). Low Density Polyethylene (LDPE) and Linear Low Density Polyethylene (LLDPE) 470 Table 2: Diffusion data for low molecular weight organic substances in Polyethylenes (PE). Medium and High Density Polyethylenes (MDPE & HDPE) 498 Table 3: Diffusion data for low molecular weight organic substances in various types of Polypropylenes (PP) 51 1
Appendix I1 Table 1: UNIFAC group volume (Rk) and surface area
(ak)parameters
531
Table 2: UNIFAC group interaction parameters for prediction of vapour-liquid equilibria at temperatures between 250 and 425 K 539
Appendix I11 Table 1: Trivalent phosphorus antioxidants
565
Table 2: Major commercial hindered amine stabilizers 566 Table 3: Major commercial hindered phenolic antioxidants
567
Methane Methane Methane Methane Methane Methane
Name
where:
(dalton) 16.0 16.0 16.0 16.0 16.0 16.0
Molec. weight Mr (gkm') 0.894 (25) 0.914 (25) 0.894 (25) 0.914 (25) 0.916 (25) 0.915 (25)
PP
-
D D D D D D
(%)
("C) 15 : 45 5 ;55 25 25 15 ; 50 5:50
Experiment Type of Temp. diffusion range of coefficient experim.
29.0 43.0 29.0 43.0 54.0 44.0
-
Polymer Density Cristal@ ("C) linity
:''
Diffusing Species
diffusion coefficient not measured but extrapolated to 23 "C diffusion coefficient at the temperature given in column 6 (other than 23 "C) diffusion coefficient at the temperature. "C, given in the upperscript.
(*
concentration independent average diffusion coefficient diffusion coefficient at "zero" diffusant concentration diffusion coefficient determined from inverse gas chromatography diffusion coefficient in a polymeric sample in contact with a solventkimulant diffusion coefficient in a swollen polymeric sample diffusion coefficient at the gashapor pressure given in the subscript self-diffusion coefficient of the substance in the PE matrix diffusion coefficient extrapolated on the basis of structure relationships
D D, Dg,=, D, Dsw DIatm DSf Dth
Table 1: Diffusion data for low molecular weight organic substances in Polyethylenes (PE's) Low Density Polyethylene (LDPE) and Linear Low Density Polyethylene (LLDPE) [Densities up to 0.930 g/cm5 (at room temperature)].
Peter Mercea
Appendix I
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do Ed Drxp (cm2/s) x lo-' (kJ/mol) 46.4 1.421 43.94 1 17.0 1.282 45.62 1 54.0'** 1 19.3'"" 1 1.93 0.556 46.86 2 15.8 1.546 47.30 3
4
0
4
P
Methane Methane Methane Methane Ethylene Ethylene Ethylene Ethane Ethane Ethane Ethane Ethane Ethane Ethane Ethane Ethane Ethane Ethane Ethane Methanol Methanol Methanol Methanol Allene Allene Allene Allene
Name
Diffusing Species
(g/cm3) 0.915 (25) 0.918 0.921 (23) 0.920 (23) 0.918 0.918 0.923 (25) 0.894 (25) 0.914 (2.5) 0.894 (25) 0.914 (25) 0.920 (23) 0.918 0.910 (25) 0.918 (2.5) 0.919 (25) 0.921 (25) 0.924 (25) 0.916 (25) 0.918 (23) 0.917 (23) 0.920 (25) 0.919 0.894 (25) 0.914 (25) 0.894 (25) 0.914 (25)
(dalton) 16.0 16.0 16.0 16.0 28.1 28.1 28.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 32.0 32.0 32.0 32.0 40.1 40.1 40.1 40.1 29.0 43.0 29.0 43.0
-
50.0
-
-
-
48.0 -
45.0 45.0 48.0 29.0 43.0 29.0 43.0 -
44.0 45.0 52.1 -
(%)
Polymer Density Cristal@ ("C) linity PP -
Molec. weight M,
-
D D, D Dsw D D D D D
D
Dc 0 D~a,m D Dc + 11 D D D D D D D D D D D D
D
-
23 : 73 5 ; 5s 5 : 55 2s 25 33 : 48 -26 : 25 0 : 50 25 ; 50 0;50 25 ; 50 20 ; 60 25 23 23 15 ;35 30 10:50 10 : 50 25 25
5;35
5;35 125.2 35.50 5 ; 35
7J C L
("C)
Experiment Type of Temp. diffusion range of coefficient experim. 18.0'** 29.8 2500.0'** 17.9'* 13.4 18.1 12.5 21 .0 5 87 24.0"6.8"" 9.3'* 7.9 4.98 4.8'* 4.95 3.48(* 5.38 5.4'** 4.8 1.94 1.6 3.30'*' 27.4 9.16 31 .O(** 10.5"*
-
45.20 49.80 -
-
-
44.36 1.414 1.750
-
-
-
0.031
-
-
34.46 56.52 53.29 55.66 64.07 60.36 51.89 -
-
-
-
-0.948 2.874 2.101 2.505 4.001 3.194 1.888
6 4 4 7 1
1 1 1
1
6 8 9 9 9 9 10 11 12 13 14 15
1 1 1
5 -
28.52 61.11 67.62 39.18 49.38 53.57
3 4
-1.712 3.913 5.191 0.01023 2.036 2.222
43.93
1.226 -
-
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do Ed D,," (Crn*/S);; 10-8 (kJ/mol)
Propylene Propylene Propylene Propylene Propylene Propane Propane Propane Propane Propane Propane Propane Propane Propane Propane Ethanol Propionitrile Isobutylene Isobutylene Acetone Butane Butane Butane n-Butane n-Butane Neopentane n-Pentane
Name
Diffusing Species
(dalton) 42.1 42.1 42.1 42.1 42.1 44.1 44.1 44.1 44.1 44.1 44.1 44.1 44.1 44.1 44.1 46.1 55.1 56.1 56.1 58.1 58.1 58.1 58.1 58.1 58.1 72.1 72.1
Mr
Molec. weight
0.924 (25) 0.922 (25) 0.924 (25) 0.915 (23) 0.921 (23) 0.918 (25) 0.918 (25)
-
0.922 (25) 0.922 (25)
-
(g/cm3) 0.894 (25) 0.914 (25) 0.894 (25) 0.914 (25) 0.920 (25) 0.920 (25) 0.894 (25) 0.914 (25) 0.894 (25) 0.914 (25) 0.915 (25) 0.915 (25) 0.918 0.920 0.920
-
-
60.0 60.0 50.0 51.0 46.0 50.0
-
-
0
0
D D D D Dsf D,r D D
-
D D D, n
Dc
D D D D D D Dc D D
-
D
-
D D D D D
-
("c) 10 ; 50 10 ; 50 25 25 0 : 22 0 : 2s 10 ; 50 10;50 25 25 25 25 ; 55 5 ;35 25 30 ;48 49.1 25 -8 ; 30 -8 : 30 25 30 ; 60 25 25 23 23 25 ; 50 25 : 50
Experiment Type of Temp. diffusion range of coefficient experim.
29.0 43.0 29.0 43.0 44.0 44.0 45.0 -
29.0 43.0 29.0 43.0 -
(Yo)
Polymer Density Cristal@ ("C) linity PP -
10.7'* 6.65 10.4 2.76 12.04'' 3.22'*' 2.6'** 2.1'* 5.2 2.0(" 1.98'* 0.027'** 0.5'** 4.0 2.6 0.7'*" 4.2" 1.95"* 1.4'** 10.0 6.0 0.16(' 0.805"
5.8(**
(cm2/s) x lo-' 17.5 5.0 20.0(**
uexp
6.503 4.836
I
-0.4437
4.102 3.607 -
86.73 13.27
-
-
39.25
-
65.16 63.41
-
45.20 -
-
63.19 57.86
3.491 2.929 0.2135 -
-
38.0 23.3 52.31 55.66 -
4.260 -7.176 2.248 2.264 -
-
-
-
(kJ/mol) 48.13 52.31
1.737 1.933
4 6 6 17 18 19 19 18 10 20 20 21 21 9 9
3
1 1 16 16 1 1 1 1 3
. 1
1
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ .r(23 "C) lg DO Ed
r
B 2'
7
b
%
N
!?j
n-Pentane n-Pentane n-Pentane n-Butylaldehyde n-Butylaldehyde Butanal Butanal Butylalcohol B utylalcohol Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene
n-Pentane
Name
Diffusing Species
72.1 72.1 72.1 72.1 72.1 72.1 72.1 74.1 74.1 78.1 78.1 78.1 78.1 78.1 78.1 78.1 78.1 78.1 78.1 78.1 78.1 78.1 78.1 78.1 78.1 78.1
(dalton) 72.1
Molec. weight M,
(23) (23) (23) (25) (25) (25) (25) (25) (25) (25) (25) (25)
0.918 (25) 0.920 (25) 0.920 (25) 0.915 (23) 0.918 (25) 0.918 (25) 0.918 (25) 0.916 (25) 0.917 (25) 0.917 (23)
0.916 (25) 0.916 (25) -
-
0.919 0.921 0.928 0.922 0.924 0.919 0.919 0.922 0.922 0.922 0.922 0.922
(g/cm7) 0.915 (23)
PP
-
-
-
50.0 51.0 60.0 60.0 60.0 70.0 54.0 54.0 70.0 54.0 45.0 45.0 42.0 45.0
-
46.0 48.0 50.0 55.0 50.0 51.0 -
(%)
-
Polymer Density Cristal(3 ("C) Iinity
23 23 23 25 25 25 25 25 25 0 0 0 25 ; 50 25 25 ; 45 23 25 30 ; 40 30 : 40 23 25 ; 45 25 ; 45 25 25 : 35 25 25
LJ
71
(T)
Experiment Temp. Type of diffusion range of coefficient experim.
I'
%'
x
9.2 6.0 4.0 27 1 18'** 1.05". 0.28" 4.12'' 1.08' 0 90'' 0.19' ' 0.33'" 1.05" ' 0.99' 1.29*1.08" 3.0 1.98' 1.41'' 13 5'x 0.38 1.05' 8 26'" 0.4'** 0.14'* 0.82'** I 72'''
(cm /s)
+P
-
-
-3.309
-
4.603 -0.130
-
0.4730 0.9698
-
3.841 -
3.369
-
-
-
-
-
(kJimol)
21 20 20 22 22 20 20 19 19 19 17 24 24 25 26 27 27 28 29 29 30 31 32 33
21
21 21
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) lg Do Ed
4 W
P
4
F'
4
2
b h
Diffusing Species
Benzene Benzene Benzene Benzene Benzene Benzene Dimethylsulfoxide (DMSO) 1-Hexene 2-Hexene Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Methylenechloride Methylenechloride Met hylenechloride Methylenechloride Pentanal Pentanal n-Hexane n-Hexane
Name
(dalton) 78.1 78.1 78.1 78.1 78.1 78.1 78.1 84.2 84.2 84.2 84.2 84.2 84.2 84.2 84.2 84.2 84.2 84.2 84.2 84.9 84.9 84.9 84.9 86.1 86.1 86.2 86.2
Molec. weight M,
0.919 (20) 0.912 (25) 0.917 (25) 0.924 (25) 0.924 (25) 0.919 (25) 0.919 (25) 0.918 (25)
0.918 (25) 0.915 (23) 0.915 (23) 0.922 0.922 0.921 (25) 0.920 (25) -
-
-
(glcm') 0.918 (25) 0.919 (25) 0.921 (25) 0.922 (25) 0.928 (25) 0.919 0.915 (25) 0.919 (20)
PP
70.0 -
-
-
-
50.0 45.0 36.5 47.0 50.2 52.0
-
36.5 70.0 70.0 54.0 42.0 42.0 -
(%)
-
Polymer Density Cristal@ ("C) linity
-
(OC) 25 25 25 I5 ; 35 25 30 30 :45 25 : 50 25 : SO 25 ; 50 25 23 23 25 ; 30 25 :30 15 ; 35 15 ; 35 25 30 : 45 25 25 25 25 25 25 25 ; 50 25 ; 45
Experiment Type of Temp. diffusion range of coefficient experim.
Diffusion Parameters Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do Ed Dexp (cm2/s) x lo-' (kUmol) 2. 15'" 1.68(** 1.48"' 0.99 2.187 57.75 0.69'"* 0.83'"' 0.29" 1.768 58.35 59.8'* 26.38 -1.568 0.71'* 54.40 1.452 0.40'* 61.10 2.388 0.61'*' 0.20 0.80 0.18'77.00 4.848 3.5'* 40.99 -0.2207 1.04 0.5264 48.20 47.9 15.90 -3.514 4.15(** 24.1'" 32.78 -0.834 9.2'** 8.2'** 7.0'** 7.1''" 0.7"* 1.76'** 0.53'" 3.249 65.29 0.84'. 61.10 2.706 32 38 38 38 39 22 22 23 29
37
33 14
36
33 33 33 33 33 15 34 35 23 23 26 28 28 36
Ref.
c
L
2 7 $
P
n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane 3-Methylpentane 3-Methylpentane Neohexane Tetrafluormethane Ethylacetate Ethylacetate Ethylacetate Ethylacetate
Name
Diffusing Species
(dalton) 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 88.0 88.1 88.1 88.1 88.1
Molec. weight M, (g/cm3) 0.918 (25) 0.918 (2.5) 0.918 (25) 0.918 (25) 0.915 (23) 0.919 (23) 0.921 (23) 0.928 (23) 0.928 (23) 0.922 (25) 0.924 (25) 0.918 (25) 0.915 (25) 0.918 (25) 0.928 (25) 0.920 (25) 0.919 (20) 0.919 (20) 0.919 (20) 0.918 (25) 0.922 (25) 0.924 (25) 0.906 (30) -
PP
54.0 46.0 48.0 50.0 55.0 55.0 50.0 51.0 45.0 43.2 44.7 51.7 50.0 45.0 36.5 41.5 70.0 36.5 70.0 45.0 50.0 51.0 35.8 45.0
-
-
-
(%)
-
Polymer Density Cristal@ ("C) linity
-
(T) 25 : 35 25 ; 35 25 ; 50 25 : 45 23 23 23 23 23 25 25 25 25 25 25 15 ; 35 25 30 ;SO 30 $0 25 :50 30 :50 25 ; 50 20 ; 50 25 25 30 25
Experiment Type of Temp. diffusion range of coefficient experim.
1.05'*0.90'"' 0.3"" 1.32'** 1.40'** 0.797'** 62.8 13.2(** 37.6'* 37.6(* 0.41" 34.5'* 0.28'" 0.79 5.3'" 4.7'"3.0'** 3.2'"*
(cm2/s) x lo-' 27.2" 0.14'' 1.04'' 1.05(* 9.0 6.1 4.1 3.4 3.1
Dexp
-
-
-
27.15 23.53 61.94 33.17 64.86 63.15 -
-
-1.633 -1.833 2.547 -0.608 2.900 3.043 -
23.44
-
-
-
-
-
-2.065
-
-
-
-
-
-
-
-
-
-
-
(kJ/mol) 48.46 21.71 60.56 65.40 1.985 -5.034 2.703 3.563
-
29 31 40 26 21 21 21 21 21 20 20 30 41 41 41 14 37 35 35 23 35 23 42 20 20 43 37
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do Ed
VI
P 4
4
r;'
3 9
x
a h
p-Dioxane 1-Pentan01 2-Pentanol Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Phenole Methylbromide Methylbromide Methylbromide Methylbromide Methylcyclohexane Methylcyclohexane n-Heptane n-Heptane n-Heptane n-Heptane n-Heptane
Name
Diffusing Species
(dalton) 88.1 88.2 88.2 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 94.1 95.0 95.0 95.0 95.0 98.2 98.2 100.2 100.2 100.2 100.2 100.2
Molec. weight M,
0.919 (25) 0.919 (25) 0.918 (25) 0.918 (25) 0.920 0.918 (30) 0.919 (30) 0.918 (30) 0.918 (30) 0.910 (70) 0.891 (70) -
0.918 (23) 0.919 (20) 0.922 (25) 0.922 (25) 0.918 0.918 0.919
0.920 (25) 0.918 (23) 0.918 (23) 0.919 (25) 0.922 (25) -
-
-
-
-
40.6 36.5 -
-
-
58.0 60.0
-
45.0 35.0 50.0 40.6
-
54.0 54.0 45.0 47.3 48.0 -
-
-
-
(%) 70.0
-
(g/cm')
PP
Polymer Density Cristal@ ("C) linity
("c) 25 ; 50 25 25 25 25 ; 45 30 : 50 30 30 30 30 70 70 25 15 : 35 30 23 0 : 30 0 -3.0 15 ; 60 30 30 ;50 25 ; 30 25 ; 30 25 ;35 25 ; 50 30
Experiment Type of Temp. diffusion range of coefficient experim.
0.12(* 0.90(* 1.10'**
8.8'*
34.2'** 52.2"* 31.0'** 73.5 2.13'** 0.45 6.05 1.1 2.9('* 8.48 0.58(** 36.9(* 0.44'*
17.0'**
24.05 61.38 59.69 21.47 70.99 -
-2.189 2.480 3.478 -5.122 4.484 -
42.45 -
-
52.58 -
12.55 -
-
-
0.419 -
-
-3.91 9 2.061 -
-
-
Diffusion Parameters Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do Ed *Dev (cm /s) x lo-' (kJlmol) 0.41(* 4.912 75.33 0.64'"' 0.97'** 1.81'1.43'' 7.508 87.00 1.37" 1.604 53.64 4.1(" 3.6"* 4.3"*
23 22 22 26 26 27 44 44 45 45 46 46 47 14 48 12 19 19 49 49 48 35 36 36 31 40 15
Ref.
3
*c
;L
x.o"
m
$ !
n-Heptane n-Heptane n-Hexylaldehyde n-Hexylaldehyde cis-3-Hexen-1-01 Hexanal Hexanal Ethylpropionate Hexylalcohol Hexylalcohol I-Hexanol 1-Hexanol 2-Hexanol Hexylalcohol Hexylalcohol o-Xylene m-Xylene p-Xylene o-Xylene p-Xylene N-Methylaniline p-Cresole An iso1e n-Octane n-Octane n-Octane n-Octane
Name
Diffusing Species
(dalton) 100.2 100.2 100.2 100.2 100.2 100.2 100.2 102.1 102.2 102.2 102.2 102.2 102.2 102.2 102.2 106.2 106.2 106.2 106.2 106.2 107.1 108.1 108.1 114.2 114.2 114.2 114.2
Molec. weight M, (%)
46.0
-
42.0 50.0 51.0
-
-
-
-
-
-
-
-
-
-
-
so.0 51.0
0.922 (25) 0.924 (25) 0.919 (25) 0.919 (25) 0.919 (25) 0.922 (25) 0.924 (25) 0.918 (25) 0.918 (25) 0.918 (25) 0.918 (25) 0.918 (25) 0.924 (25) 0.918 (23) 0.918 (25) 0.922 (25) 0.924 (25) 0.918 0.915 (23)
-
40.6 36.5 50.0 51.0 -
-
(gicm') (23) (20) (25) (25) (23) (25) (25)
0.918 0.919 0.922 0.925 0.918 0.919 0.919
Polymer Density Cristallinity @ ("C) PP -
30 30 : 50 25 25 23 25 25 30 25 25 25 25 25 25 25 25 25 25 25 : 50 25 ;50 50 23 25 25 25 25 : 50 23
("c)
Experiment Temp. Type of range of diffusion coefficient experim. 0.79"" 30.9(* 0.8'*' 0.6(** 1.40 0.03(** 0.31** 1.22'** 0.7'** 0.5' '* 1.44'** 3.21'*' 0.405'** 0.6'"' 0.5'" 0.94(** 1.46(*" 1.57(** 12.2'* 38.1(** 4.2(** 0.23 1.8(** 0.68(** 0.60('* 0.71(* 5.5
48 35 20 20 50 22 22 51 20 20 22 22 22 20 20 26 26 26 52 52 53 12 54 20 20 40 21
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do Ed Dexp (cm'is) x IO-* (kJimol)
P 4 4
4
r;'
4
%
b 'D
Diffusing Species
n-Octane n-Octane n-Octane n-Octane n-Octane iso-Octane iso-Octane 2,2.4-Trimethylpentane Ethylbutyrate Ethylbutyrate Ethylbutyrate Ethylbutyrate Heptanol Heptanol Heptanol Heptanol 1-Heptanol 2-Heptanol 2,3-Benzopyrole (Indole) Chlorophorm Chlorophorm Chlorophorm Phenylmethylketone (Acetophenone) Mesitylene Mesitylene n-Propylbenzene n-Propylbenzene
Name
114.2 114.2 114.2 114.2 114.2 114.2 114.2 114.2 116.2 116.2 116.2 116.2 116.2 116.2 116.2 116.2 116.2 116.2 117.1 119.4 119.4 119.4 120.1 120.2 120.2 120.2 120.2 0.918 0.918 0.918 0.918 0.919 0.919 0.918 0.918 0.922 0.928 0.918 0.920 0.920 0.920 0.920
(23) (23) (23) (23) (25) (25) (23) (25) (25) (25) (23) (25) (25) (25) (25) 45.0 45.0 45.0 45.0
-
-
-
50.0
-
-
-
-
-
-
-
50.0 51.0
-
48.0 50.0 55.0 55.0 36.5 40.6 36.5
-
(23) (23) (23) (23) (20) (23) (20) (25) (25) (25)
-
0.919 0.921 0.928 0.919 0.919 0.918 0.919 0.918 0.922 0.924
(glcm?)
(dalton) (Oh)
Polymer Density Cristal@ ("C) linity PP -
Molec. weight Mr -
23 23 23 23 25 ;50 30 30 : 50 25 : 50 25 25 23 20 ; 40 23 23 23 23 25 25 23 25 25 ;50 25 ; 50 23 30 : 50 30 : 50 30 : 50 30 ; 50
("c)
Experiment Type of Temp. diffusion range of coefficient experim.
Diffusion Parameters Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig D,, Ed Dexp (cm2/s) x (kJ/mol) 4.0 2.5 1.85 1.7 29.59 26.7'* -1.351 0.52("* 8.29'* 0.634 43.72 0.23'' 6.113 83.59 2.2'" 1.75"" 1.79 1.86 -6.291 8.16 0.53 60.9 63.2 0.55 0.049'** 0.139'*' 0.55 1.78'" 17.7'* 4.162 14.68 15.4'" -3.540 18.54 1.10 0.74'* 0.6019 49.47 3.26'" -1.584 33.45 1.16(* 1.083 51.10 20.91 6.2'" -3.517 12 22 22 50 26 58 58 50 27 27 27 27
57
57 57
56
21 21 21 21 35 48 35 40 20 20 55
Ref.
h
h
; 2
b
5 co
Diffusing Species
N,N-Dimethylaniline N,N-Dimethylaniline N.N-Dimethylaniline N,N-Dimethylaniline N,N-Dimethylaniline N.N-Dimethylaniline (DMA) N,N-Dimethylaniline (DMA) N.N-Dimethylaniline (DMA) NNDimethylaniline (DMA) N.N-Dimethylaniline (DMA) N.N-Ethylaniline Cresylmethylether 2-Phenylethylalcohol 3-Octen-2-one (Methylheptenone) n-Octylaldehyde n-Octylaldehyde n-Octanal (Aldehyde C,) n-Octanal (Aldehyde C,) Octanal Octanal Octanal Ethylvalerate Octylalcohol Oct ylalcohol Amylaceticester (Isoamylacetate) Trichloroethylene Trichloroethylene
Name
~
(dalton) 121.2 121.2 121.2 121.2 121.2 121.2 121.2 121.2 121.2 121.2 121.2 122.2 122.2 126.2 128.2 128.2 128.2 128.2 128.2 128.2 128.2 130.2 130.2 130.2 130.2 131.4 131.4
Molec. weight M,
0.919 (25) 0.919 (25) 0.922 (25) 0.924 (25) 0.918 (23) 0.922 (25) 0.928 (25)
50.0 51.0 -
42.0 42.0 50.0 50.0 50.0 -
25 : 45 25 ; 45 15 :34 15 :35 15 :35 50 23 23 23 25 25 23 23 25 25 20 ; 40 30 25 25 23 25 ; 70 25 ; 70
so
25 25 25 25
(T)
D
(%) 29.031.0 35.0 42.0 -
(gicm') 0.916 (25) 0.917 (25) 0.917 (25) 0.918 (25) 0.924 (50) 0.918 (25) 0.918 (25) 0.920 (25) 0.920 (2.5) 0.920 (25) 0.924 (SO) 0.918 (23) 0.918 (23) 0.918 (23) 0.922 (25) 0.924 (25) 0.918 (23) -
Experiment Type of Temp. diffusion range of coefficient experim.
Polymer Density Cristal@ ("C) linity PP -
Diffusion Parameters Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do Ed Drxp (cm'is) x (kJimo1) OX'** 0.87'** 0.82(** 0.72(** 6.29'** 69.99 0.38'' 3.934 65.70 0.51(* 3.301 63.19 0.741 3.021 43.58 -0.0702 1.73 15.70 44.2 -3.583 4.54'** 1.20 0.43 0.73 0.43'** 0.40' * * 0.23 0.00196 0.009" * 0.041'*' -4.312 22.39 0.54 LO(** 0.47'** 0.40(** 0.17 25.7'* -3.370 18.25 25.3" -3.951 14.99
20 20 50 55 22 22 56 51 20 20 50 58 58
so
50
so
59 53 60 60 61 14 14 53
59
59 59
Ref.
Diffusing Species
Tetralin 1,l.l - Trichloroethane 1,1,1- Trichloroethane p-Isopropyltoluene (p-Cymene) 2-(2-Ethoxyethoxy) ethanol n-Butylbenzene N-Propylaniline 2,4,6Trimethylphenol 4-Isopropenyl-1 -methyl-1-cyclohexene (Limonene) 4-lsopropenyl-I-methyl-1 -cyclohexene (Limonene) 4-Isopropenyl-1-methyl-I-cyclohexene (Limonene) 4-Isopropenyl-1 -methyl-I-cyclohexene (Limonene) 4-Isopropenyl-1 -methyl-1-cyclohexene (Limonene) 7-Methyl-3-methylene-1.6-octadiene (Myrcene) 7-Methyl-3-methylene-l.6-octadiene(Myrcene) 2-Methyl-benzoic acid (Phenylacetate) 3-Phenyl-1-propano1 2,6,6-Trimethylbicyclo(3,l,l)hept-2-ene (alpha - Pinene) 2,6,6-Trimethylbicyclo(3,l,l)hept-2-ene(alpha - Pinene) 6,6-Dimethyl-2-methylenebicyclo (3,lJ)heptane-ropinene (Beta - Pinene)
Name
23 20 : 40 23 20 ;40 23 23 23 20 :40
-
0.918(23) 0.918 (23) 0.918 (23) 0.918(23) -
0.918 (23)
136.2 136.2 136.2 136.2 136.2 136.2 136.2 136.2 136.2
-
25 ;45
0.930 (25)
23
25 ;45
23 23
50
25 ;50 23 23 30 ;60
136.2
115 ; 140 25 ; 50
(T)
0.923 (25)
-
136.2
(%)
Experiment Q p e of Temp. diffusion range of coefficient experim.
0.922 (25) 0.928 (25) 0.918 (23) 0.918 (23) 0.920 (25) 0.924 (50) 0.918 (23) 0.918 (23)
(gkm') -
Polymer Density Cristal@ ("C) linity PP -
132.2 133.4 133.4 134.2 134.2 134.2 135.2 136.2 136.2
(dalton)
Molec. weight Mr
lo4
0.14
2.18
0.70 1.04 0.25 0.28 0.14
1.10
0.00571
0.04(*
0.042("
9.6('15 6.0'' 4.75(* 0.54 0.38 0.64(* 6.51'"' 0.23 0.43
(cm2/s) x
Dexp
-
-
-
-4.169
-
-
-
56 50
-
50
50
50
50 56
56
55
63
63
50
27 53 12
50 50
58 58
62
19.79
20.76 -
-4.320
19.25
-
23.54
4.546
-
-5.243
39.31
-
-
-2.436
-
49.33
-
42.34 27.83 26.04
(kJ/mol)
0.514
-1.318 -2.309 -2.728
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23"C) Ig Do Ed
+
F'
9
%
1
0
&
Diffusing Species
3,7,7-Trimethyl-bicyclo[4.1 .0]hept-2-ene (Carene) 2,4-Dimethyl-3-cyclohexene-l -carboxyaldehyde cis-Decalin trans-Decalin n-Nonanal (Aldehyde C,) n-Decane n-Decane n-Decane n-Decane cis-3-Hexen-I-yl-acetate 7-Methylchinoline Ethylhexanoate Ethy lhexanoate Ethylhexanoate Nonanol 1.2-Benzopyrone (Cumarin) I -Methoxy-4-(1-propeny1)benzene (Anethol) -nitrile cis,truns 3,7-Dimethyl-2,6-octadiene-l (Citralva) N,N- Di-ethylaniline (DEA) 3,4-Methylene-dioxybenzaldehyde(Heliotropine) Benzylacetate 2,3.5.6 Tetramethylphenol Dimethylbenzylcarbinol
Name
150.2 150.2 150.2
149.2 150.1
138.3 138.3 142.2 142.2 142.2 142.2 142.2 142.2 143.2 144.2 144.2 144.2 144.3 146.2 148.2 149.2
-
0.918 (23)
0.918 (23)
0.918 (23)
50.0
0.920 (25)
(23) (23) (23) (23)
0.918 (23)
0.918 0.918 0.918 0.918
0.918 (23) 0.918 (25) 0.922 (25) 0.924 (2.5) 0.918 (23) 0.918 (23) 0.922 (25) 0.924 (25) -
-
23 23 23
20 ; 39 23
122 ; 132 122 ; 140 23 25 ; 50 25 25 30 ; 80 23 23 25 25 30 23 23 23 23
23
0.918 (23)
138.2
Experiment Type of Temp. diffusion range of coefficient experim.
("C) 23
-
Polymer Cristallinity
(dalton) 136.2
M,
Molec. weight
-
24.12 -
-
4.213
-
-
-
-
0.70 0.16 0.075
2.635
0.21
-
-
-
-
-
-
-
-
-
-
-
-
06.83
8.644 -
-
37.34 38.21 -
-
-
(kJ/mol)
-2.088 -1.919
-
-
0.087
0.81(** 0.40 0.54 0.50 0.17
0.18 0.36'* 0.42'* 0.37" * 0.34' 0.93 0.43 0.90'" 0.27'**
10.1('20)
,39(120)
0.11
1.O
50
50
62 62 50 40 20 20 32 50 50 20 20 51 12 50
50
64
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 " C ) Ig DO Ed x IO-' (cm-is) >DCXP
Diffusing Species
0.918 (23) 0.918 (23) 0.918 (23)
154.2 154.2 154.2
154.2
154.2
0.919 0.922 (25) 0.928 (25) 0.929 (25) 0.918 (23)
&xp
0.21 0.31
23 23
0.27
0.00139
0.10 0.10 0.19
(cm2/s) x 0.11 0.36 0.00320 0.222 0.15 0.08(" 0.66'** 0.29" 0.69'*" 8.0'' 7.63'* 7.53'4" 0.048
0.918 (23) 0.918 (23)
20 : 40
23
23 23 23
(T) 23 23 23 20 : 40 23 25 25 25 : 50 30 25 ; 70 25 ; 70 40 : 60 23
0.21 0.15
-
-
-
-
-
-5.39 1
-
-
-
-
-
-3.009 -3.496 -2.104
-
6.092
-
-0.899 -
-
-
-
-
(kJ/mol)
50 50
50 50
56
55
50 50 50
50 50 55 56 50 30 26 23 15 58 58 65 50
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23°C) Ig Do Ed
23 23
("10)
-
Experiment Type of Temp. diffusion range of coefficient experim.
0.918 (23) 0.918 (23)
-
-
0.918 (23) 0.918 (25) 0.918 (25) -
-
(gicm') 0918 (23) 0.918 (23)
PP
Polymer Density Cristal@ ("C) linity
(dalton) 150.2 152.2 152.2 152.2 152.2 153.8 153.8 153.8 153.8 153.8 153.8 153.8 154.2
Molec. weight Mr
154.2 2-cis-3,7-Dimethyl-2,6-octadiene-l-ole (Nerol) 154.2 2-trans-3.7-dimethyl-2.6-octadiene-8-ole (Geraniol) 154.2 2-Isopropyl-5-methylhexanone(Menthon) cis-2[2-Methyl-l-propenyl]-4-methyltetrahydro-154.2 pyran (Roseoxyde L)
1001)
3.7-Dimethyl-l.6-octadiene-3-ylacetate (Lina-
1001)
3.7-Dimethyl-1,6-octadiene-3-ylacetate (Lina-
1001)
Ethylbenzoate cis,trans 3,7-Dimethyl-2,6-octadienal(Citral) &,trans 3,7-Dimethyl-2,6-octadienal(Citral) cis,trans 3,7-Dimethyl-2,6-octadienal(Citral) 1.7.7-Trimethyl-2.2.1 heptane-2-one (Campher) Carbontetrachloride Carbontetrachloride Carbontetrachloride Carbontetrachloride Carbontetrachloride Carbontetrachloride Carbontetrachloride 1.7,7-Trimethylbicyclo2.2,1 heptane-2-one (Borneol) 3,7-Dimethyl-6-octene-1-al (Citronellal) 1.8-Epoxy-p-Mentone (Eukalyptol) 3,7-Dimethyl-1.6-octadiene-3-ylacetate (Lina-
Name
I
s
h
5
N
&
0.24'"' 0.21'"" 0.26 0.14 0.016'** 0.153'*' 1.66'** 1.90'** 0.9 6.6 0.15 0.12 10.7'" 10.4(* 0.47 0.69(** 0.29"* 0.22'** 0.092 0.13 0.44 0.079 0.26
25 25 23 23 25 25 40 40 23 23 23 23 25 ; 70 25 :70 23 30 25 25 23 23 23 23 23 0.922 0.924 0.918 0.918 0.919 0.919
156.3 156.3 156.3 156.3 156.3 156.3 156.3 156.3 156.3 156.3 156.3 157.0 157.0 158.2 158.2 158.3 158.3 158.3 158.3 160.2 164.2 164.2
156.3
0.086
20 ; 40
-
0.922 0.924 0.918 0.918 0.918 0.918 0.918
-
0.918 0.918 0.918 0.918 0.922 0.928 0.918
-
-
(25) (25) (23) (23) (23) (23) (23)
(23) (23) (23) (23) (25) (25) (23)
(25) (25) (23) (23) (25) (25)
0.22
154.2
-
23
PP
0.918 (23)
(kJ/mol)
20 20 50 50 22 22 66 66 57 57 50 50 58 58 50 51 20 20 50 50 50 50 50
56
50
Diffusion Parameters Ref. Diffusion Pre-expon. Activation energy coefficient coefficient @ (23 "C) Ig Du Ed
154.2
Experiment Temp. Type of range of diffusion coefficient experim.
1-Methyl-4-isopropyl-l-cyclohexene-1-01 (Terpineol) 1-Methyl-4-isopropyl-1-cyclohene-1-01 (alpha Terpineol) n-Decylaldehyde n-Decylaldehyde 3,7-Dimethyl-6-octene-l-ol (Citronellol) n-Decanal (Aldehyd Clo) Decanal Decanal Undecane Undecane Undecane Undecane 2,6-Dimethyl-7-0ctene-2-01 (Dihydrornyrcenol) 2-Isopropyl-5-methylcyclohexanole(Menthol) Bromobenzene Bromobenzene 2-Methoxynaphthalene (Yara Yara) Ethylheptanoate Decylalcohol Decylalcohol 3,7-Dimethyl-l-octanol 3,7-Dimethyl-octane-3-o1 Diethylmalonate Dimethylphenylethylcarbinole Methoxy-4(2-propenyl)phenol (Eugenol)
Polymer Density Cristallinity @ ("C)
Molec. weight
Diffusing Species
Name
Diffusing Species
2-Methoxy-4-prophenylphenol (Isoeugenol) 1-Phenylethylacetate 2-Phenylethylacetate Tetrachlorethylene Tetrachlorethylene Perchlorethylene n-Undecene-2-al (Aldehyd C,,) cis-Undecene-8-al (Aldehyd C, 1 inter) Diphenylmethane 1,1,2,2 - Tetrachlorethane 1,1,2.2 - Tetrachlorethane Diphenyloxide Ethyloctanoate Ethy loctanoate n-Undecylaldehyde (Aldehyde C, ,) n-Dodecane n-Dodecane n-Dodecane Dodecane (Alcane CL2) Dodecane (Alcane C12) n-Dodecane n-Dodecane n-Dodecane n-Dodecane 2,4-Di-t-butylphenol 2.6-Di-t-butylphenol Ethyl-Naphtylether (Bromelia)
Name
164.2 164.2 164.2 165.8 165.8 165.8 168.3 168.3 168.3 169.9 169.9 170.2 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.5 170.5 172.2 (23) (23) (23) (25) (25) (23) (25) (25) (23) (25) (25) (23) (23) (23)
(23) (23) (23) (25) (25)
0.918 (23) 0.918 (23) 0.918 (23)
-
-
-
-
0.918 0.918 0.918 0.922 0.928 0.918 0.922 0.924 0.918 0.922 0.924 0.918 0.918 0.918
-
0.918 0.918 0.918 0.922 0.928
PP
(g/cm3)
(dalton) (%)
-
Polymer Density Cristal@ ("C) linity
Molec. weight M,
23 23 23 25 ; 70 25 : 70 25 23 23 23 25 ; 70 25 : 70 23 25 25 23 25 25 23 6 : 40 6 ; 40 40 40 40 40 23 23 23
(T)
Experiment Type of Temp. diffusion range of coefficient experim. uexp
0.155 0.29 0.57 15.S(* 14.2(* 6.2'** 0.096 0.090 0.48 2.88'' 2.59'" 0.37 0.32'** 0.28(** 0.10 0.33'** 0.29(** 0.27 0.26 13.6 1.86'** 1.23'"* 0.99'** 0.78( * 0.012 0.098 0.39
(cm2/s)x 10" -
(kJ/mol) 50 50 50 58 58 37 50 50 SO 58 58 50 20 20 50 20 20 67 67 67 66 66 66 66 12 12 50
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @n (23 "C) Ig D,, Ed
4
k
%
b
2
h
P
Diffusing Species
(dalton)
Molec. weight M,
nellal) Methyleugenol Butyrated hydroxyanisole (BHA) Butyrated hydroxyanisole (BHA) Butyrated hydroxyanisole (BHA) 2-Methoxy-4-propenylanisol (Methylisoeugenol) Diphenylmethanone (Benzophenone) n-Dodecylaldehyde (Aldehyde C12) 2-Methyl-undecanal (Aldehyde C I 2MNA) n-Undecalacton (Aldehyde C14) n-Dodecylaldehyde n-Dodecylaldehyde Citronellylformiate Tridecane Tridecane Tridecane Tridecane 2,6-Di-t-butyl-4-methylphenol Dodecanol 3-Methoxy-4-hydroxy-benzaldehyde(Verdyla. cetate) 2-Methyl-3-(4-isopropyl)phenylpropanal (Cyclamen aldehyde) Dimethylbenzylcarbinylacetate (DMBCA) 4-[2,6,6-Trimethyl-2-cyclohexene-l-yl]-3butene-2-one (Ionone) 0.918 (23) 0.918 (23) 0.918 (23)
190.3 192.3 192.3
-
(23) (23) (23) (23) (25) (25) (23)
0.918 (23) 0.918 (23) 0.918 (23)
0.918 0.918 0.918 0.918 0.922 0.924 0.918
0.918 (23)
0.918 (23) 0.912 (31) 0.927 (31) -
PP
-
Polymer Density Cristallinity 0 ("C)
182.2 184.3 184.3 184.3 184.3 184.3 184.3 184.4 184.4 184.4 184.4 184.6 186.4 190.2
178.2 180.2 180.2 180.2 178.2
3,7-Dimethyl-8-hydroxyoctanal ( H y d r o x y c i K 172.3
Name
23 23
23
23 23 23 23 25 25 23 40 40 40 40 23 23 23
23 31 31 137 ; 169 23
("C) 23
Experiment Temp. Type of diffusion range of coefficient experim.
1.09 0.12
0.12
0.49 0.019 0.018 0.027 0.19(** 0.16(** 0.23 1.60(** 1.86"' 1.44"" 0.90'** 0.066 0.11 0.21
0.30 0.34(** 0.38'" 6.1(I3O 0.26
-
-
-
41.56
-
-1.828 -
-
-
-
so so
50 68 68 62 50
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy 0 (23 "C) Ig Do Ed Dexp (cmz/s) x IOU' (kJ/mol) 0.055 so
& VI
D i h i n g Species
0.920 (25) 0.918 (23) 0.918 (23) 0.918 (23) 0.918 (23)
-
-
-
-
50.0 -
-
-
50.0 51.0 44.0
-
-
-
0.918 (23) 0.918 (23) 0.918(23) 0.918 (23) 0.918 (23) 0.922 (25) 0.924 (25) 0.918 0.918 (23) 0.918 (23)
Ds Ds D, D,
D S
D D D*
D
24 ; 43 23 23 23 23
D,
-
0.918 (23)
Ds
0.12
23
Ds
-
0.918 (23)
23 6 : 40 6 :40 23 23 25 25 20 : 70 23 23
0.12
23
Ds
-
0.918 (23)
DS DS Dsw Ds DS
0.23
23
Ds DS
-
0.918 (23) 0.918 (23)
Allyl-3-cyclohexylpropionate 196.3 2.6-Dimethyl-2.6-octadiene-8-yl-acetate (Gera196.3 nylacetate) 1,7,7-Trimethylbicylo-1,2.2-naphtanyl-2-acetate 196.3 (Isobromylacetate) 3,7-Dimethyl-1,6-octadiene-3-yl-acetate 196.3 (Linalylacetate) 1-Methyl-4-isopropyl-l-cyclohexene-4-yl196.3 acetate (Terpinylacetate) Tetradecane (Alcane C14) 198.4 Tetradecane (Alcane CI4) 198.4 Tetradecane (Alcane CI4) 198.4 3,7-Dimethyl-6-octene-l-yl-acetate 198.3 p-tert.-Butylcyclohexylacetate (Oriclene extra) 198.3 Et hyldecanoate 200.3 Ethyldecanoate 200.3 Methylundecanoate 200.3 Am ylcinnamicaldehyde 202.3 3-[4-tert.-Buthylphenyl]-2-methylpropanale 204.3 (Lilial) 205.3 N.N-Di-n-butyl-aniline (DBA) 2.4-Di-tert-but ylphenole 206.3 2.6-Di-tert-butylphenole 206.3 3-Methyl-3-phenylglycidate (Aldehyde C l h ) 206.3 5-(2,6,6-Trimethyl-2-cyclohexene-1 -yl)-3-methyl- 206.3 3-butene-2-one (Methyljonone-alpha)
0.12(* 0.012 0.098 0.22 0.066
0.25 0.19 10.1 0.29 0.12 0.21'** 0.17"" 1.18 0.14 0.14
0.24 0.16
23 23 23
-
0.918 (23)
("c)
-
-
50
-
-
-
-
-
61 12 12 50
50
50
67 67 67 50 50 20 20 69
55.01
-
-
60.39
-
-
0.8007
-
-
2.73
-
-
-
-
-
73.70 59.84
-
4.282 3.565
-
50
-
-
-
50
-
-
-
50
-
-
50 50
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23°C) Ig Do Ed Dexp (cm2/s) x lo-' (kJ/mol) 0.19 50
D,
(gkm')
(dalton)
Experiment Type of Temp. diffusion range of coefficient experim.
(%)
Polymer Density Cristal@ ("C) linity PP -
Molec. weight M,
194.2
Dimethylphthalate (DMP)
Name
P 00
Lc
3&
3
b
6\
Diffusing Species
2,6-Di-tert-butyl-4-methylphenol 2,6-Di-tert-butyl-4-methylphenol(BHT) 2.6-Di-tert-butyl-4-methylphenol (Ionol) 2,6-Di-tert-butyl-4-methylphenol (Ionol) 2,6-Di-tert-butyl-4-methylphenol (Ionol) 2,6-Di-tert-butyl-4-methylphenol (BHT) 2,6-Di-tert-butyl-4-methylphenol (BHT) 2,6-Di-tert-butyl-4-methylphenol(BHT) 2,6-Di-tert-butyl-4-methylphenol (BHT) 220.4 220.4 220.4 220.4 220.4 220.4 220.4 220.4 220.4
-
0.918 (25) 0.920 (25) 0.917
-
0.918 (25) 0.918 (25)
-
-
0.918 (23)
-
0.918 (23) 0.918 (25) 0.918 (23)
-
0.920 (25) 0.920 (25)
-
-
30 : 60
1o:so 5 ; 60
-
-
39.22
-2.321
-
0.832 3.842 9.260 -
1.7'60 0.081 3.45(7" 0.09'** 0.10 0.048 0.012'*
4.150 5.902 6.639
-
74.47 86.23 93.83
54.82 73.28 109.8
-
0.066
-
66.83 -
-
71.67 77.30
-
3.760
-
-
-
2.995 4.210
50 66 66 66 66 70 71 71 72 12 69 50 62 12 72 73 74 74 75 76 77 78
-
-
50 50
-
0.15'""
0.022 0.037" 0.42'" 0.05'"' 0.082 0.93 0.16 3.9'i3n
-
-
-
1.15'** 1.23'"'
1.50'**
-
-
0.32
-
0.77'**
23 40 40 40 40 5 ;loo 35 ; 75 44 25 23 20 ; 70 23 137 : 169 23 25 65 ; 95 23 ; 74 75 ; 90 25
0.918 (23) -
0.21 0.012
(T)
23 23
-
0.918 (23) 0.918 (23)
(Yo)
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) lg Do Ed D,," (cm2/sj; 10-* (kJ/mol) 0.086 50
23
(g/cm3)
(dalton)
-
Experiment Temp. Type of range of diffusion coefficient experim.
0.918 (23)
PP
Polymer Density Cristallinity @ ("C)
Molec. weight Mr
4-(2,6,6-Trimethyl-2-cyclohexene-l-yl)-3-meth-206.3 yl-3-butene-2-one (Methyljonone-gamma) Iso-amylsalicilate 208.3 4-[4-Methyl-4-hydroxyamyl]-3-cyclohexene-ca- 210.3 rboxaldehyde (Lyral) Benzylbenzoate 212.3 212.4 Pentadecane 212.4 Pentadecane 212.4 Pentadecane 212.4 Pentadecane 214.2 2,4-Dihydroxybenzophenone 2.4-Dihydroxybenzophenone 214.2 2,4-Dihydroxybenzophenone 214.2 214.2 2,4-Dihydroxybenzophenone (DHB) Tetradecanol 214.4 Methyllaureate 214.4 2-Hexyl-3-phenylpropenal (Jasmonal) 216.3 220.3 2,5-Tert-butyl-4-hydroxy-toluene (BHT)
Name
228.2 228.4 240.3 242.3 242.4 244.3 244.3 244.3 252.7 252.7 254.4 254.4 254.5 254.5 254.5 254.5 254.5 254.5 254.5 254.5
sorb 90) 2-Hydroxy-4-methoxybenzophenone Methyltridecanoate Phenylethylphenylacetate Hexadecanol Methylmiristate Nonane-l,3-dioldiacetate (Jasmelia) Triphenylmethane Triphenylmethane Brornoforrn Brornoform Hexadecanone Hexadecanone n-Octadecane (Alcane Ci8) n-Octadecane (Alcane CIS) n-Octadecane (Alcane CIS) n-Octadecane (Alcane CIS) n-Octadecane Octadecane Octadecane n-Octadecane
Molec. weight M,
2,6-Di-tert-butyl-4-methylphenol (BHT) 2,6-Di-tert-butyl-4-methylphenol(BHT) Hexadecane (Alcane Clh) Hexadecane (Alcane C l h ) Tetradecanamide 2-Hydroxy-4-methoxybenzophenone(Chima-
Diffusing Species
(dalton) 220.4 220.4 226.4 226.4 227.4 228.2
Name
(23)
(25)
(25) (23) (23)
0.917
-
0.922 (25) 0.928 (25) 0.918 (25) 0.918 (25) 0.918 (23) 0.918 (23) 0.918 (23) 0.917 0.914 -
-
-
0.918 0.918 0.918 0.918 0.918
-
-
-
(g/cm') 0.917 0.917 0.918 (23) 0.918 (23)
PP
(%)
-
Polymer Density Cristal@ ("C) linity
-
70 ;90 20 ; 70 23 23 20 ;70 23 40 40 25 ; 70 25 ;70 30 ; 45 48 ; 70 23 6 ; 40 6 ; 40 30 ; 60 40 ; 90 40 40 30 ; 60
30 ; 60 60 6 : 40 6 ; 40 118 25
(T)
Experiment Type of Temp. diffusion range of coefficient experirn.
4.27(" 0.78 0.30 0.064 0.63 0.082 0.385 0.152(** 3.3(* 3.1(* 0.28" 3.86(4" 0.12 0.095 5.50 0.035(* 1.19(* 0.60'"' 0.40(** 0.078(*
(cm2/s) x lo4 3.03(* 0.83(** 0.10 7.5 280(** 0.70(**
UtXp
-
78.01 62.77 4.773 3.952 -
-
81.82 65.49 70.74 53.3 83.80
-
5.416 4.295 3.034 1.491
5.678
-
-
-
-2.428 -2.401 9.550 2.770
-
73.15
28.62 28.91 102.6 61.0
4.710 -
0.2787 4.350 -
50.22 70.60 -
-
-
-
(kJ/mol) 55.44
2.265
81 69 50 12 69 50 66 66 58 58 69 69 67 67 67 79 82 66 66 78
78 79 67 67 80 75
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23°C) IgDo Ed
*
2
2
1
%
%
Diffusing Species
nzctadecane n-Octadecane 2-H ydroxy-4-ethanediolbenzophenone 1,3,4,6,7.8-hexahydro-4.6,6,7.8,8-haxamethylcyclopenta-2-benzopyrane (Galaxolid) 7-Acetyl-1,1,3,4,4,6-Hexamethyl-tetrahydronaphthaline (Tonalid) N,N'-Diphenyl-p-phenylene-diamine (DPPD) Cedrylacetate Trichlormethylphenylcarbinylacetate (Roseacetol) 2.6-Dinitro-l -methyl-3-methoxy-4-tert.-butylbenzene (Moschus Ambrette) Tetramethylpentadecane Tetramethylpentadecane Dicumilperoxyde Dicumilperoxyde 2-Hydroxy-4-n-butoxybenzophenone Octadecanol Methylpalmitate Stearylalcohol Stearylalcohol Di-butyl-phthalate (DBP) Trans-9-octanacide Trans-9-octanacide Eicosane (Alcane C20) Eicosane (Alcane C2")
Name
(%)
(g/cm3)
22 23 23 23 40 40 40 : 70 70 70 : 90 23 30 : 70 40 40 20 :40 20 ; 40 43 : 65 23 6 : 40
-
0.918 (23) 0.918 (23) 0.918 (23) -
260.3 264.4 267.5 268.3 268.3 268.3 270.2 270.2 270.3 270.5 270.5 270.5 270.5 270.5 282.5 282.5 282.6 282.6
0.918 (25) 0.918 (25) 0.918 (23) 0.918 (23)
-
-
0.918 (23) 0.918 (25)
-
0.929 (25) 0.929 (25)
-
23
30 ; 60 5 ;lo0 23
0.918 (23)
(T) 30 : 60
258.4
-
Experiment Type of Temp. range of diffusion coefficient experim.
0.918 (23)
0.917 0.917 -
-
PP
Polymer Density Cristal@ ("C) linity
254.5 254.5 258.3 258.4
(dalton)
Molec. weight Mr
0.56'"' 0.37(** 1.02'~" 32.0'** 2.04"O 0.048 0.44 0.304'** 0.109(** 0.0001 8 0.034 2.4(4s 0.047 0.063
0.074
0.087"" 0.041 0.082
0.038
2.49(* 0.0163(' 0.021 0.044
-
-
-
-
87.88
-
81.45 128.1 55.95
-
-
6.306
2.635 13.14 1.58
-
-
-
72.36
4.410
68.63
124.4 -
-
2.763 -
-
12.450
-
-
-
-
-
-
-
-
-
-
-
71.89 57.67 71.56
5.083 0.389 2.949
66 66 85 86 81 12 69 66 66 87 69 69 67 67
50
84 50 50
50
78 83 70 50
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do Ed Dexp (cm2/s) x lo-' (kJ/mol)
Diffusing Species
D D
-
-
44.0 44.0
-
44.0 44.0 -
48.0 -
0.918 (23) 0.918(23) 0.918 (25) 0.918 (25) 0.918 (23) 0.918(23) -
0.918 (25) 0.918 (25) 0.918 (23) -
0.918 -
-
-
DS
44.0 44.0 44.0 48.0
0.918(25) 0.918 (25) 0.918 (25) 0.918
D D
D D D
D D D D DS
Dsw
D,
D,
D D D D D
D
-
Dsw
-
-
-
(%)
-
(g/cm3)
(dalton)
-
5
;loo
94
40 40 30 ; 60
20 ; 38 40 ; 60 6 : 40 6 ; 40 40 40 20 ;40 40 ;70 23
23
23
6 ; 40 90; 140 85 40 ; 70 70 ; 90 30 ; 80 30 ; 60
(T)
Temp. range of experim.
Experiment Type of diffusion coefficient
0.918 (23) -
PP
Cristallinity
Polymer Density @ ("C)
Molec. weight M,
282.6 Eicosane (Alcane C2") Octadecanamide 283.4 Octadecanamide 283.4 Stearic acid 284.3 Stearic acid 284.3 Methyl Heptadecanoate 284.5 Methylester 3-(3,5-di-tert.-butyl-4-hydroxy292.2 phenyl) propionic acid 2,6-Dinitro-3.5-dimethyl-l-acetyl-4-tert.-butyl-294.3 benzene (Moschus Ketone) 2,4.6-Trinitro-1,3-dimethyl-5-tert.-butylbenzene 297.3 (Moschus Xylol) Metylstearate 298.5 Metylstearate 298.5 Docosane (Alcane CZ2) 310.6 Docosane (Alcane Czz) 310.6 Docosane 310.6 Docosane 310.6 Methylnonadecanoate 312.5 Methylnonadecanoate 312.5 2-(2-hydroxy-3-t-butyl-5-methylphenyl)-5-chlo- 315.8 ro-benztriazol (Tinuvin 326) Heptadecylbenzene 316.4 Heptadecylbenzene 316.4 Propylester 3-(3,5-di-tert.-butyI-4-hydroxyphe- 320.2 nyl) propionic acid -325 Homogenized paraffin 326.4 2-Hydroxy-4-octoxybenzophenone
Name
(cm2/s) x lo-*
0.32'** 0.051
0.49(** 0.38(** 0.023"
0.12 1.58'40 0.035 2.45 0.135'** 0.096'" 0.11 2.73(40 0.02
0.057
0.035
3.70 102'" 28.0(** 0.082'4" 6.49(" 0.31" 0.028'*
Uexp
2.754
6.167
-
-
12.091 6.260 -
-
13.940 6.550 7.227 5.203
-
-
7.530 2.800 6.580 5.803
-
4.699 -1.958
-
@ (23°C)
-
Pre-expon. coefficient Ig Do
68.28
-
89.60
-
-
-
119.4 85.0
-
-
129.5 86.0 94.54 72.61
-
89 70
66 66 88
66 66 69 69 12
67
69 69 67
50
50
-
-
96.38 65.58 85.50 87.00
Ref.
67 80 80 69 69 69 88
68.72 28.01
(kJ/mol)
Activation energy Ed
Diffusion Parameters Diffusion coefficient
4
7-
%2
h
6
0
59.0 44.0 44.0
-
Dexp
2.08('" 0.072 1.37'4" 0.022'** 0.0067 1.62 0.125"" 50 ; 80
50 ; 90 10 ; 70
5 ; 100
Dsw
D D D
D
-
2.236 5.84 -
0.224"" 0.02 0.0038'**
20 ;40 40 ; 80 5;70 45 ; 70 10 ; 70 10
D D D D D D
43.0 48.0 44.0 -
44.0 44.0 48.0 44.0 44.0
0.923 (25) 0.918 (25) -
0.918 (25) 0.918 (25) 0.918 (25) 0.917 (25) 0.918 (25) 0.918 (25)
340.4 340.4 346.4 354.5 354.5 357.5 358.0 358.5 358.5
44.0
-
0.918 (23) 0.916(25)
0.033 0.96"" 0.016
0.009
0.022
0.042'4"
-
12.22 5.09 6.770
3.461
8.240
4.95
3.725 6.332 4.430
-
-
-
0.924 11.77 5.221
4.250
5.950
-
19.88 2.002
0.918 (25) 0.918 (25) -
D D D D D
70 :90 20 : 40 40 ; 80 40 5 : 100 5:40
0.051("' 2.48"" 0.15'** 0.11
fcm2/s)x
0.84'40
5 ; 40
25
35 ; 50 60 ; 75
f°C)
-
65.32 88.09
123.0 78.55 93.83
76.54
101.4
85.83
78.75 80.03 79.89
-
56.50 118.5 78.4
73.86
84.37
-
88.14 61.23
(kJ/rnol)
74 93
92
69 69 74
70
74
91
81 69 69 66 70 67 91
74
90 90 72 74
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23"C) Ig Do Ed
40;70
D
D D D D
-
Experiment Type of Temp. diffusion range of coefficient experim.
326.4 326.5 326.5 326.6 332.4 338.6 340.4
44.0
0.918 (25)
2-Hydroxy-4-n-octoxybenzophenone Methyl Eicosanate Methyl Eicosanate Behenyl-alcohol 2-Hydroxy-4-ethandiol-thioacetic acid ester Tetracosane (Alcane C21, 2-2-Methylene-bis-(4-methyl-6-t .-butylphenol (Plastanox 2246) 2-2-Methylene-bis-(4-methyl-6-t.-butylphenol) (Plastanox 2246) 2-2-Methylene-bis-(4-methyl-6-t.-butylphenol) (Plastanox 2246) 2-Hydroxy- 4 - ethandiol methylthioacetic acid ester Methyl Docosanate Methyl Docosanate 2(2-hydroxy-3-5-di-tert.-butyl-pheny1)-5-chloro-benzotriazole (Tinuvin 327) 4.4'-thio-bis-(3-rnethyl-6-tert-butylphenol) 4-4-Thio-bis-(6-t.-butyl-metacresol) (Santonox) 4-4-Thio-bis-(6-t.-butyl-metacresol) (Santonox)
-
-
44.0
uv 531)
uv 531)
43.0 43.0
0.919 0.919
0.918 (25)
f%l
326.4
(dcm3)
Polymer Density Cristal@ ("C) linity PP -
2-Hydroxy-4-octoxybenzophenone (Cyasorb
fdaltonl
Molec. weight Mr
326.4 326.4 326.4 326.4
Diffusing Species
2-Hydroxy-4-octoxybenzophenone 2-Hydroxy-4-octoxybenzophenone 2-Hydroxy-4-octoxybenzophenone (HOB) 2-Hydroxy-4-octoxybenzophenone (Cyasorb
Name
P
.r
3
p
2
Diffusing Species
Hexylester of 3(3,5-di-tert.-butyl-4-hydroxyPhenYl) N-amido bis(2,2,6,6-tetramethyl-4-piperidinyl)p-animo propionamide Hexacosane (Alcane C26) Tri-cresyl-phosphate (TCP) 2-2-Methylene-bis(4-ethyl-6-t.-butyl-phenol) (Plastanox 425) Methyl Tricosanate Methyl Tricosanate 2-Hydroxy-4-n-dodecoxy benzop henone 2-Hydroxy-4 ethandiol t-butylthioacetic acid ester Di-octyl-phthalate (DOP) Octacosane Octacosane Octacosane (Alcane CZ8) 2,2,6,6 -Tetramethyl-4-piperidinol(Dastib 845) 2,2,6,6 -Tetramethyl-4-piperidinol (Dastib 845) 2,2,6,6 -Tetramethyl-4-piperidinol(Dastib 845) 2,2,6,6 -Tetramethyl-4-piperidinol(Dastib 845) 2-2-Methylene-bis-(4-methyl-6-methyl-cyclohexyl-phenole) (Novox WSP) Squalane Squalane Triacontane (Alcane C30) 4-4-Methylene-bis-(2-6 di-tert. butyl-phenole) (Ionox 220)
Name
-
44.0 44.0
-
0.918 (25) 0.918 (2.5) 0.918 (25)
-
-
0.918 (23) 0.918 (25)
422.6 422.6 422.7 424.5
-
0.918 (23) 0.921 0.921 0.921 0.917 (25) 0.918 (25)
390.6 394.6 394.6 394.6 411.2 411.2 411.2 411.2 420.5
44.0
-
-
-
23.0 44.0
-
-
-
-
-
59.0 -
-
-
44.0
-
0.918 (23)
366.7 368.4 368.5 368.5 368.5 382.5 388.5
D
-
0.921
-
uexp
-
D D Dsw D
Dc (1 D D Dsw D D D, D D
40 40 5 : 40 5;70
20 ; 40 40 40 5 : 40 50 : 75 23 20 ; 40 25 : 60 5 : 70
20 ; 40 42 : 80 70 ; 90 5 : 100
D D D D
0.146(** 0.073'** 0.34 0.010
0.000047 0.0246(** 0.0141'** 0.59 1.99'" 0.069 0.104 0.018(* 0.0063
0.015 1.47'40 1.6'70 0.0008
0.94 0.00004'** 0.0087
5 : 40 40 5:70
+
Dsw D, o D
(cm2/s) x lo4 0.0066'* 1.02'~~
(T) 30 : 60
9.503 7.96
7.970 1.550 7.902 1.54 7.42
-
18.66 -
14.99 1.930 1.127 4.400
6.744 8.89
-1.60
10.45
-
101.8 101.8
95.68 64.0 99.85
-
91.81 57.20
-
175.6 -
140.6 58.50 58.59 87.85
107.4
-
83.70
38.30
(kJ/mol) 116.9
Ed
66 66 67 74
87 66 66 67 94 94 95 96 74
69 69 81 70
67 87 74
94
88
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23°C) lg Do
49 ; 80
D
366.6
-
(YO) 48.0
-
Experiment Type of Temp. diffusion range of coefficient experim.
(g/cm3) 0.918
PP
Polymer Density Cristal@ ("C) linity
(dalton) 362.4
Molec. weight M,
%
$
2
b
%
8
Diffusing Species
(Uvitex OB) 3,5-di-tert.-butyl-4-hydroxy-benzoic acid- (2.4di-tert-butyl-phenyl) ester (Tinuvin 120) Methyloctacosanate Methyloctacosanate 2-Hydroxy-4 ethandiol n-octylthioacetic acid ester Dodecylester- 3(3,5-di-tert.-butyl-4-hydroxyphenyl) propionic acid Saturated Hydrocarbon (Ceresin 100) Normal paraffin Dotriacontane (Alcane C3z) n-Dotriacontane n-Dotriacontane n-Dotriacontane bis[2,2,6,6-tetramethyl-4-piperidinyl)-sebacate (Tinuvin 770) bis[2,2,6,6-tetramethyl-4-piperidinyl-l-oxy]sebacate bis[2,2,6,6-tetramethyl-4-piperidinyl1-oxy] sebacate 1,1,3-tris(2-methyl-4-hydroxy-5-butyl phenyl) butane (Topanol) Didodecyl-3-3-thiodipropionate(DLTDP) Didodecyl-3-3-thiodipropionate(DLTDP) Didodecyl-3-3-thiodipropionate(DLTDP) Didodecyl-3-3-thiodipropionate (DLTDP)
2.5 di(5-tert-butyl-2-benzoxazolyI)thiophene
Name
0.918 (23) 0.918 (25) 0.918(25) -
0.918 -
0.918(23) 0.917 0.917 0.917 0.921
0.917 0.922 0.918 (23) 0.918 (25) 0.918 (25) 0.916 (25) 0.916 (25)
438.6 438.6 438.6 445.5 446.3 -450 -450 450.7 450.9 450.9 450.9 480.7 511.3 511.3
512.6 514.4 514.4 514.4 514.4
430.5
-
2uexP
0.003 0.95'40 0.003
20 :40 40 ; 80 5 ;loo
0.17'4u
40 : 80 23
24.0
44.0 44.0 43.0 43.0
5 ; 40 40 ;70 20 ; 50 50 ; 90
0.20(~"
40 : 80
23.0
0.20 0.00064'* 0.02'* 0.2'*' 0.054"
0.85""
0.002
o.55'40
0.053
0.00054
56.3('*' 7oo(isri
120 ; 130 150 : 200 5 ; 40 30 : 60 30 ; 60 60 20 ;40
-
0.013'"
0.0018
0.0204(**
(cm I S ) x
23
22
(T)
9.940 6.230 15.40 2.740
-
3.683
6.840
-2.873 -2.260 10.28 12.69 16.58 3.587
6.891
14.65 2.21 1.611
-
-
-
108.9 86.8 147.8 66.6
-
74.5
93.1
72.83
-
25.40 23.44 107.5 135.32 148.90
95.06
142.7 61.3 68.92
-
-
(kJ/mol)
74 74 91 91
12
96
96
97 98 67 78 78 79 95
88
69 69 70
12
84
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient energy coefficient @ (23"C) Ig Do Ed
30 ; 60
-
Experiment Type of Temp. diffusion range of coefficient experim.
48.0
44.0 44.0 -
-
-
(YO)
(dalton)
(g/cm3)
Polymer Density Cristal@ ("C) linity PP -
Molec. weight M,
Diffusing Species
Didodecyl-3-3-thiodipropionate(DLTDP) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,S-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3.5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxy phenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3.5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) 1- 1-3-tris(2-rnethyl-4-hydroxy-5-tert. -butylpheny1)butane (Topanol CA) 1-1-3-tris(2-methyl-4-hydroxy-5-tert-butylpheny1)butane (Topanol CA)
Name
(g/cm3) 0.928 (25) 0.918 (25) 0.918 (25) 0.918 (25) 0.916 (25) 0.924 (25) 0.928 (25) 0.916 (25) 0.924 (25) 0.928 (25) 0.918 (23) 0.918 0.918 0.918 0.909 (45)
531.4 531.4 531.4 531.4 531.4 531.4 531.4 531.4 531.4 531.4 53 1.4 544.5 544.5
(T)
50 ; 80 45 ; 80
D D
Dsw
D
44.0 32.5
Ds
48.0
48.0
44.5
45 :80
5 ;70
49; 110
50 ; 77
50 ; 80
D
48.0
Ds
50 ; 80
D
43.0
51.0
30 ; 50
30 ; 50
D
51.0
D
30 ; 50
D
43.0 48.0
40 ; 70
5 ; 40
50 ; 90 30 ; 60
D
D
D D
-
Experiment Type of Temp. diffusion range of coefficient experim.
44.0
44.0
51.0 48.0
(%)
Polymer Density Cristal@ ("C) linity PP
(dalton) 514.4 531.4
Molec. weight M,
1.35'4Q
0.0078
0.149'4"
0.174(40
0.063'4'
0 . 0 6 4 '~ ~
0.12'~~
0.48'50
0.00052'*
0.001I(*
0.008'*
0.38(4"
0.01 1
(crn2/s) x 0.27'50 0.0066"
uexp
-
-
-1.558
6.230
3.690
2.950
4.909
6.75
4.37
1.77
18.54
14.71
10.18
3.46
9.15
2.470 8.170
37.81
92.6
75.0
70.17
84.54
98.6
82.1
62.4
169.0
145.5
114.9
71.2
108.2
(kJ/mol) 68.2 104.0
Ed
102
74
101
100
99
91
91
91
91
91
91
74
74
91 88
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do
+
S'
b
%2
P
Diffusing Species Molec. weight M,
(dalton) 1-1-3-tris(2-methvI-4-hvdroxv-5-tert-butvl-uhe544.5 I . ny1)butane (Topanol CA) 2-Hydroxy-4-ethandiol n-dodecylthio acetic 557.5 acid ester 2-Hydroxy-4-ethandiol n- octadecylthio acetic 585.5 acid ester N,N -Dioctadecyl-aniline (DODA) 597.6 N.N -Dioctadecyl-aniline (DODA) 597.6 Oligomeric hindered amine -600 Oligorners from PE -600 Saturated Hydrocarbon (Ceresin 80) -600 2.2-Thiodiethyl-bis-[3-(3.5-di-tert-butyl-4-hydr- 643.4 oxy pheny1)-propionat] (Irganox 1035) 2,2-Thiodiethyl-bis-[3-(3.5-di-tert-butyl-4-hydr-643.4 oxy pheny1)-propionat] (Irganox 1035) 2,2-Thiodiethyl-bis-[3-(3,5-di-tert-butyl-4-hydr-643.4 oxy pheny1)-propionat] (Irganox 1035) Docosanyl Docosanate 649.1 Docosanyl Docosanate 649.1 Behenyl Behenate 649.1 Distearyl-thio-dipropionate (DSTDP) 682.5 1.3,5-Trimethyl-2,4,6-tri(3,5-di-tert-butyl-4-hy- 774.6 droxy benzy1)benzene (Ionox 330) 1.3,5-Trimethyl-2,4.6-tri(3,5-di-tert-butyl-4-hy- 774.6 droxy benzy1)benzene (Ionox 330) Terephthalate-2-2-methylene-bis(4-methyl-6810.6 tert-butyl) phenole (HMP12) Pentaerythrityl-tetrabis-(3,5-di-tert-butyl~4-hy- 1176.0 droxy-cinnamate)
Name
-
-
42.0 42.0 23.0
-
-
0.918 (25) 0.918 (2.5) 0.921 0.918 -
44.0 44.0 44.0 -
42.8 43.0 44.0 44.0 44.0 20.0
-
0.918 (25) 0.918 (25) 0.918 (25) -
0.916 (30) 0.916 (25) 0.918 (25) 0.918 (25) 0.918 (25) -
-
44.0
(%)
-
(g/cm3) 0.918 (25)
PP
Polymer Density Cristal@ ("C) linity
0.00058
5 : 40
40; 70 40 $0
D D D D D~am D D
D
D
D
80
5 ; 70
10
90 40 : 80 5 ; 70
80 ; 110
26.0' 0.00004'*'
-
0.15'" 0.041'* 0.01'-
25 : 45 25 ; 45 25 40 100; 120 10
D D Dth D, Dc 0 D
0.013(*'
0.00024
0.0000135~""
0.40'40 0.0079
-
16.78
-
6.12 6.43
-
6.903 -2.0
0.18(40
35.1@' 15.6(""
4.14
14.00
-
-0.6720
-
160.9
-
87.0 93.7
-
93.7 30.1
77.7
143.0
-
42.22
-
-
-
66.96 11.66
69.92
70.01
3.002 -7.323
1.602
1.807
0.15'4"
0.02""
0.0018
0.0028
5 ;loo
5 ;loo
D
105
74
93
80 104 91 74
80
74
74
60 60 95 103 97 93
70
70
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig DO Ed Dexp (cm2/s) x (kJ/mol) 93 0.0014'**
D
10
D
(T)
Experiment Type of Temp. diffusion range of coefficient experim.
Diffusing Species Molec. weight M, PP
0.028'** 0.00037
0.013'"' 0.000268'**
80 80
80
80 80 5 ;70
45 $0 25 49 45 : 110 10
D
D D
D D D
D
D
D D
D
23.3 25.1 28.7
31.5 32.4 44.0 43.0
-
45.0
O.ooo0436(**
0.000502'"
0.0046'40
0.068'"'
0.081(**
0.016(**
0.0105(**
0.012'**
(T) 80
D
(%)
DtXp (cm2/s) x 10" -
107
-
93
75 -
-
106
130.6
101
74
115.5
-
205
105 -
-
105
105
-
105
105 -
-
(kJ/mol)
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23"C) lg Do Ed
20.0
Experiment Type of Temp. diffusion range of coefficient experim.
-
-
Polymer Density Cristal@ ("C) linity
(dalton) (gkm?) Pentaerythrityl-tetrabis-(3,5-di-tert-butyl-4-hy- 1176.0 droxy-cinnamate) Pentaerythrityl-tetrabis-(3,5-di-tert-butyl-4-hy-1176.0 droxy-cinnamate) Pentaerythrityl-tetrabis-(3,5-di-tert-butyl-4-hy- 1176.0 droxy-cinnamate) Pentaerythrityl-tetrabis-(3,5-di-tert-butyl-4-hy- 1176.0 droxy-cinnamate) Pentaerythrityl-tetrabis-(3,5-di-tert-butyl-4-hy- 1176.0 droxy-cinnamate) 1176.0 Pentaerythrityl-tetrabis-(3,5-di-tert-butyl-4hydroxy-cinnama te) Tetrakis(3-(3,5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 0.918 (25) propionyloxymethy1)- methane (Irganox 1010) Tetrakis(3-(3,5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 0.921 (23) propionyloxymethy1)- methane (Irganox 1010) Tetrakis(3-(3,5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethy1)- methane (Irganox 1010) 0.924 Tetrakis(3-(3,5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethy1)- methane (Irganox 1010) Tetrakis(3-(3,5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethy1)- methane (Irganox 1010) Tetrakis(3-(3,5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethy1)- methane (Irganox 1010)
Name
4
2
2
b
%
& 6\
Diffusing Species
Molec. weight M,
(dalton) Tetrakis(3-(3,5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethy1)- methane (Irganox 1010) Tetrakis(3-(3.5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethy1)- methane (Irganox 1010) Tertakis[methylene-3-(3',5'-di-tert-butyl-4-hy- 1178.0 droxy-phenyl) propionate]-methane Oligomenc hindered amine -1200 Polyethylene segments -2000 Deuterated polyethylene segments -2280 Deuterated polyethylene segments -2440 Deuterated polyethylene segments -3600 Deuterated polyethylene segments -4600 Deuterated polyethylene segments -8000 Deuterated polyethylene segments -11000 Deuterated polyethylene segments -17000 Deuterated polyethylene segments -20000 Deuterated polyethylene segments -23000 Polvethvlene segments -45000
Name
176 125
-
150
-
176
0.000048'** 0.55"2" 31.0'" 20,0('5"
25 120 ; 130 150 150 : 200 176 176 150 176
0.917 (23) -
0.081'** 0.15'**
3.2'** 0.34'** 0.15'*" 0.4"*
1.86'**
3.0'**
0.133("
55 :75
0.0056'**
0.917 ( 2 5 )
(T) 30
-
-
111
80
110
80 80 -
110 -
110 110 80 80
95 109
92
108
-
329.1 28.0 -
-
48.44
-
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23"C) Ig DIl Ed Dexp (cm2/s) x IO-' (kJ/mol) 0.00021'** 77
25
-
DS
(%)
45.0
-
Experiment Type of Temp. diffusion range of coefficient experim.
0.917 (23)
(g/cm3) 0.920
PP
Polymer Density Cristal@ ("C) linity
diffusion coefficient not measured but extrapolated to 23 "C diffusion coefficient at the temperature given in column 6 (other than 23 *C) diffusion coefficient at the temperature, "C. given in the upperscript.
Methane Methane Methane Acetylene Ethane Ethane Ethane Ethane Ethane Ethane Ethane Ethane Ethane
Name
Diffusing Species
PP
(glcm') 0.964 (25) 0.931 (25) 0.951 (25) UHO 0.964 (25) 0.950 (25) 0.951 (25) 0.951 (25) 0.963 (25) 0.964 (25) 0.941 (23) 0.954 (23) 0.964 (23)
Molec. weight M, (dalton) 16.0 16.0 16.0 26.0 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 -
D
73.0
(T) 15 : 55 25 : 50 25 24 ; 65 5;55 0;so 25 ; 50 -5 ; 50 25 :50 25 :50 23 23 23
Experiment Type of Temp. diffusion range of coefficient experim.
(%)
-
Polymer Density Cristal@ ("C) linity
-
ultra highly
(cm /s) x 10" 5.06 2.28" 8.2'** 0.000045" 1.26 1.8 2.06'* 2.72 0.72" 0.93'* 3.4 2.1 1.35
2u,xp
-
-
-
-
80.94 52.31 53.57 58.68 48.91 67.68 53.27
-
(kJ/mol) 43.52 48.13 1.941 1.333 1.711 2.668 1.064 3.803 1.372
0.384 0.851
-
1 3 9 112 1 9 9 9 9 9 113 113 113
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ .r(23 "C) Ig Do Ed
Abreviations for the type of polymer where no data about the density and cristallinity are given: IS - isotropic, OR - oriented, CD - cold drawn, CM - compression moulded, QR - quenched & rolled, UHM - ultra high modulus. UHO oriented
(40
(* (**
-
Table 2: Diffusion data for low molecular weight organic substances in Polyethylenes (PE) Medium and High Density Polyethylenes (MDPE & HDPE) [Densities larger than 0.930 g/cm3 (at room temperature)]. where: D concentration independent average diffusion coefficient D, 0 diffusion coefficient at "zero" diffusant concentration D, diffusion coefficient in a polymeric sample in contact with a solvent/simulant Dsw diffusion coefficient in a swollen polymeric sample DI,,, diffusion coefficient at the gadvapor pressure given in the subscript
rr,
F'
3(L
$:
b
\o 00
P
Ethane Ethane Ethane Ethane Ethane Ethane Ethane Ethane Allene Cyclopropane Cyclopropane Propylene Propane Propane n-Butane n-Butane Butane Butane Butane Butane Neopentane Neopentane Neopentane n-Pentane n-Butylalde hyde n-Butylaldehyde Butanal
Name
Diffusing Species
30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 40.1 42.1 42.1 42.1 44.1 58.1 58.1 58.1 58.1 58.1 58.1 72.1 72.1 72.1 72. I 72.1 72.1 72.1
44.1
(%)
(glcm") 0.971 (23) 0.972 (23) 0.973 (23) 0.952 (25) 0.955 (25) 0.969 (25) 0.939 (25) 0.948 (25) 0.964 (25) 0.965 (25) 0.965 (25) 0.964 (25) 0.965 (25) 0.940 (25) 0.965 (25) 0.965 (25) 0.951 (25) 0.935 (25) 0.944 (25) 0.958 (25) 0.967 (25) 0.967 (25) 0.9.51 (25) 0.9.51 (25) 0.935 (25) 0.944 (25) 0.939
(dalton)
-
59.0 65.0
-
-
-
-
59.0 65.0 71.4
-
-
-
73.0 73.0 58.0
-
-
73.0
-
-
67.5 71.8 79.2
-
-
-
-
Polymer Density Cristal@ ("C) linity PP
Molec. weight M,
D D D D D D D
DZatIll
D D D D D D D D Dsw D D D D D
D D D
D D
-
23 23 23 25 25 25 43 ; 73 60 : 70 5 : 55 30 : 57 120 : 160 5 : 5s 5 : 50 0 : 40 35: 50 120; 160 25 25 25 23 50 : 80 120 : 140 35 : 50 25 : 50 25 25 25
("C)
Experiment Type of Temp. diffusion range of coefficient experim.
0.27'' 0 64' 0 44'I* 0 36'"
0 24(30
31 1 ' I Z I l
0.36' * 1.o' 0.7' 34.5 0.20'"'
67502"
0 SY""
0 92 0.42 8.24
5.7 2.80 1.55 1.83' 1.63' " 1.16'** 13.6'4" 15.8'"' 2 18 1 40' 930(120
-
-
-
-
-
-
-
-
54.91 76.53
87.47 26.91
-
5.900 -1.930 0.845 4.933
-
-
-
57.33 16.86 52.31 56.92 52.66 62.36 18.Y6 2.260 -2.790 1.194 1.667 2.208 2.70 -2.65
39.74 43.36
-
0.233 3.081
-
-
-
-
-
-
9 9 20
117 115 115
113 113 113 114 114 114 115 115 1 11s 115 1 1 116 115 115 9 20 20
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do Ed D,," (cm*/s); I 0 Y (kJ/mol)
+
2
2
b b
Tetrahydrofuran Tetrahydrofuran Butylalcohol Butylalcohol Benzene Benzene Benzene Methylenechloride Methylenechloride Methylenechloride Methylenechloride Methylenechloride Methylenechloride Pentanal n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n -H exa ne n-Hexane n-Hexane
Name
(Dichlormethane) (Dichlormethane) (Dichlormethane) (Dichlormethane) (Dichlormethane) (Dichlormethane)
Diffusing Species
(dalton) 72.1 72.1 74.1 74.1 78.1 78.1 78.1 84.9 84.9 84.9 84.9 84.9 84.9 86.1 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2
Molec. weight Mr
0.939 0.944 0.934 0.937 0.943 0.944 0.948 0.949 0.963 0.964
-
(25) (25) (25) (25) (25) (25) (25) (25) (25) (25)
0.940 (25) 0.940 (25) 0.945 (25) 0.949 (25) 0.949 (25) 0.940 (25) 0.949 (20) IS 0.939 (25) 0.938 (25) 0.954 (25)
(g/cm3) IS OR 0.935 (25) 0.944 (25) -
68.0 75.0 90.0 59.0 65.0 55.8 57.3 62.0 62.5 64.9 66.2 74.9 75.8
-
-
68.0
81.0 71.8 71.8 -
59.0 65.0 90.0 35.0 -
-
-
(%)
Polymer Density Cristallinity @ ("C) PP -
50 50 25 25 23 20 ; 40 22 ; 50 25 25 25 22 25 ; 55 25 25 0 0 23 25 25 25 25 25 25 25 25 25 25
("c)
Experiment Type of Temp. diffusion range of coefficient experim. (cm'/s) x 10'" ll.o't 0.19' 0.48' 0.25' 0.40 0.40 4.5 2.66' 2.7' 7.8' 8.9' ' 0.99' l.l('* 0.28" 0.49'*' 0.23'* 0.30 0.60'** 0.38' 0.301' " * 0.247'*' 0.71(" 0.417'" 0.262'** 0.130(** 0.143(" 0.243(**
ucxp
-
(kJ/mol) 118 118 20 20 25 119 120 121 122 122 120 123 118 22 19 19 25 20 20 41 41 41 41 41 41 41 41
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (_23"C) Ig Do Ed
I
%3
5
b
0
Diffusing Species
n-Hexane n-Hexane n-Hexane Ethylacetate Ethylacetate 1-Pentanol 2-Pentanol Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene cis-1.2-Dichloroethylene [runs-1,2-DichIoroethylene 1,2-Dichloroethane n-Hexylaldehyde
Name
(dalton) 86.2 86.2 86.2 88.1 88.1 88.2 88.2 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 97.0 97.1 99.0 100.2
Molec. weight M, (glcm') 0.965 (25) 0.989 (25) 0.992 (25) 0.939 (25) 0.944 (25) 0.939 (25) 0.939 (2.5) 0.932 0.941 0.954 0.956 CD QR QR QR QR CM CM 0.948 (25) 0.948 (25) 0.940 (2.5) IS OR 0.942 (25) 0.942 (25) 0.940 (25) 0.935 (25)
59.0
-
-
70.0 70.0
-
-
-
-
57.0 63.0 71.6 72.9 -
-
(%) 76.5 92.8 94.8 59.0 65.0
Polymer Density Cristal@ ("C) linity PP -
-
-
-
-
-
-
-
D D, n D, + (I Dc 11 D, o Dc 0 Dc 0 Dsw Dc 0 Dsw Dc o Dsw Dc 0 Dsw Dsw Dsw Dsw Dsw Dsw Dsw D
D
Dc I) Dc 0 Dc u D D
-
-
25 25 25 25 30 30 30 30 30 30 30 30 30 30 30 70 70 22 : 50 50 50 30 30 22 : 50 25
25
25 25
("c)
Experiment Type of Temp. diffusion range of coefficient experim.
-
45.0'** 2.4 0.7'**
18.0'**
0.143(** 0.014(** 0 084'** 0.29'** 0.20'** 0.293'** 0.253'" 2.3'** 1.2'** 1.0'*? 0.61( '* 0 42" * 0 90'"* 5 22"" 0.69'** 3.59'*" 0.34'** 5.53'"" 9.2(** 28.0'** 7 73 13.0'** 0.16'**
(cm2/s) x lo4
4 , p
-
(kJ/mol) 41 41 41 20 20 22 22 44 44 44 44 124 124 124 124 124 124 124 46 46 120 118 118 125 125 120 20
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do Ed
fJl
e
-
3
f
b b
106.2 114.2 114.2 114.2 114.2 116.2 116.2 116.2 116.2 119.4 121.2 122.2
p-Xylene n-Octane n-Octane n-Octane Heptanal Ethylbutyrate Ethylbutyrate 1-Heptanol 2-Heptanol Chloroforrm N,N-Dimethylaniline 2-Phenylethylalcohol
106.2
100.2 100.2 100.2 102.2 102.2 102.2 102.2 104.1 106.2
(dalton) 100.2 100.2
Molec. weight M,
106.2 106.2 106.2
Diffusing Species
cis-3-Hexene-1-01 n-Heptane n-Heptane Hexylalcohol Hexylalcohol 1-Hexanol 2-Hexanol Styrene (Vinylbenzene) p-Xylene p-Xylene o-Xylene p -Xy 1ene p-Xylene
n-Hexylaldehyde Hexanal
Name
0.957 0.939 0.944 0.937 0.939 0.939 0.944 0.939 0.939 0.948 0.945 0.956
(25) (25) (25) (25) (25) (25) (25) (25) (25) (25) (25) (23)
0.956 (23) 0.948 (25) 0.948 (25) 0.939 (25) 0.944 (25) 0.939 (25) 0.939 (25) 0.940 (25) 0.975 0.942 (25) 0.942 (25) 0.955 (25) 0.955 (25)
(g/cm3) 0.944 (25) 0.939 (25)
71.9 -
-
59.0 65.0 -
-
70.0 70.0 59.0 65.0 -
-
65.0
(%)
Polymer Density Cristal@ ("C) linity PP -
Dsw D D D D D D D D Dsw D D5
-
-
DS Dc 0 Dsw D D D D Dsw Dsw Dsw Dsw D, n Dsw
D D
12.7'" 0.34'** 0.215'" 0.26 0.079'** 1.05"" 0.89'** 0.036'** 0.077'" 6.79" 0.168'"' 0.023
25 : 70 25 4 : 45 25 25 25 25 25 25 : 50 25 23
25
0.15 4.8'20.0''A 0.3(** 0.1 85'** 0.112'** 0.144(** 5.24 3.41'** 1 LO'** 5.9'** 0.38'"* 11.1'-
(cmZ/s)x lo-* 0.285'" 0.171'**
Dexp
-
-
-
-
-
-
-
-
-
22.85 -
-
-
-
-3.136
-
-
-
-
79.97
-
5.535 -
-
-1.145 -
32.59
-
-
-
34.08 -
-
-
-1.266
-
-
-
-
-
-
-
(kJ/mol)
-
-
-
-
52 20 20 20 22 20 20 22 22 58 59 57
56 46 46 20 20 22 22 120 126 125 125 127 127
20 22
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do Ed
23 70 70 25 25 25 25 22 ;50 30 30 30 30 30
(T) 25 25
Experiment Type of Temp. diffusion range of coefficient experim.
c
f&
b
b
8
-
Diffusing Species
n-Octylaldehyde n-Octylaldehyde Octanal Naphthalene Octylalcohol Octylalcohol Amylaceticester (Isoamylacetate) Amylacetate (Isoamylacetate) Amylacetate (Isoamylacetate) Trichlorethylene 1.1.1-Trichlorethane 1,1,2-Trichloroethane 4-Isopropenyl-1methyl-I-cyclohexene (Limonene) 4-Isopropenyl-1-methyl-1-cyclohexene (Limonene) Decahydronaphthalin (Decalin) n-Decane n-Decane Ethylhexanoate 2-Methylnaphthalene Dimethylbenzylcarbinol Brornobenzene 1,7,7-Trimethyl-2,2,1-heptane-2-one (Carnpher) Carbonte trachloride Carbonte trachloride 3.7-Dimethyl-6-octene-1-al (Citronellal)
Name
-
-
0.948 0.948 0.940 0.956
n IJ,,p
0.021(~" 0.219** 0.14"* 2.02"" 0.36'*= 0.0045 3.49': 0.0022 0.046" 2.63'* 0.0053
80 : 100 25 25 50 25 23 25 : 70 23 25 ;65 25 : 70 23 90.0 59.0 65.0 59.0
(UHM) 0.939 (25) 0.944 (25) 0.939 (25) 0.940 (2.5) 0.9.56 (23) 0.948 (25) 0.956 (23) 0.952 (25) 0.948 (25) 0.956 (23)
138.3 142.2 142.2 144.2 144.2 150.2 150.7 152.2 153.8 153.8 154.2 -
-
70.0
-
-
-
-
0.05
(cm2/s) x 0.20(** 0.175'** 0.031(** 3.33(** 0.20'** 0.135'*' 0.085 0.91(** 0.305'** 12.3'* 1.61'* 1.52 0.057 23
(OC) 25 25 25 50 25 25 23 30 33 25 : 70 25 : 50 22 : 50 23
-
5.800 -1.801
-
-1 345
-
-
-
-
85.77 32.75
-
31.80
-
-
-
-
-
88.12 -
-
-
22.16 41.61 50.16
-
-
3.740
-
-
-2.999 -0.451 1.033
-
-
-
-
-
-
-
-
-
-
(kJ/mol)
-
-
-
-
30 58 57
58 57
130 20 20 120 20 57
129
120 20 20 57 128 128 58 58 120 57
20 20 22
Diffision Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23°C) Ig Do Ed
-
-
-
-
-
Experiment Temp. Type of diffusion range of coefficient experim.
-
(25) (25) (25) (23)
-
-
59.0 65.0
-
-
(g/cm3) 0.939 (25) 0.944 (25) 0.939 (25) 0.940 (25) 0.939 (25) 0.944 (25) 0.956 (23) -
(%) 59.0 65.0
Polymer Density Cristal@ ("C) linity PP -
136.2
(dalton) 128.2 128.2 128.2 128.2 130.2 130.2 130.2 130.2 130.2 131.4 133.4 133.4 136.2
Molec. weight Mr
Diffusing Species
n-Decylaldehyde n-Decylaldehyde Decanal Undecane 2-Isopropyl-5-methylcyclohexanole(Menthol) Decylalcohol Decylalcohol Methoxy-4(2-propenyl)phenol (Eugenol) Tetrachlorethylene Tetrachlorethylene Tetrachlorethylene Diphenylmethane 1,1,2,2-Tetrachlorethane Diphenyloxide Ethyloctanoate Ethyloctanoate 4-Hydroxyundecanlactonidacide n-Dodecane n-Dodecane Dodecane (Alcane ClZ) Dodecane (Alcane C12) n-Dodecane 2-Tert-butyl-4-methoxyphenol(BHA) n-Dodecylaldehyde (Aldehyde Clz) 3,7-Dimethyl-1,6-octadien-3-ylacetate (Linalyl. acetate) p-Aminoazobenzene (pAAB)
Name
-
0.952 (30)
197.3
68.0
-
59.0
-
-
59.0 65.0 -
-
59.0 65.0
-
-
68.0 68.0 -
-
59.0 65.0
-
-
(YO) 59.0 65.0
-
0.956 (23) 0.939 (25) 0.944 (25) 0.956 (23) 0.948 (25) 0.945 (25) 0.945 (25) 0.956 (23) 0.948 (25) 0.956 (23) 0.939 (25) 0.944 (25) 0.956 (23) 0.939 (25) 0.944 (25) 0.956 (23) 0.956 (23) 0.954 (25) 0.939 (25) 0.956 (23)
0.939 (25) 0.944 (25) 0.939 (25)
(glcm')
PP
Polymer Density Cristal@ ("C) linity
156.3 156.3 156.3 156.3 156.3 158.3 158.3 164.2 165.8 165.8 165.8 168.3 165.8 170.2 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 180.2 184.3 196.3
(dalton)
Molec. weight Mr
-
-
0.035 0.74" 0.039
23 25 : 70 23 25 25 23 25 25 23 23 40 10 : 50 25 23 80
8.0'*"
25
5.92'**
0.125'** 0.064 3.8 0.423'** 0.0355 0.073'"" 0.0082'*
-
-
-
65.28
-
-
-
-
-
-
0.17'**
-
-
45.48
-
-
-
24.03
-
-
-
-
-
(kJImol)
0.16'** 0.0048
-
0.19'**
0.08'**
0.013 5.06'" 0.9'**
x
10-' 0.135'** 0.103'** 0.018'** 1.03'** 0.0057 0.15(*'
(cm IS)
*uexp
104
20 20 22 66 57 20 20 57 58 131 131 57 58 57 20 20 57 20 20 67 67 66 132 20 57
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23"C) Ig Do Ed
25 25 25 40 23 25 25 23 25 ; 70 25
("c)
Experiment Type of Temp. diffusion range of coefficient experim.
b
'r,
22
'c1
b
g
226.4 226.4 226.4 228.2 240.4 244.2 252.7
201
Hexadecane (Alcane Clh) Hexadecane (Alcane CI6) Hexadecane 2-Hydroxy-4-methoxybenzophenone Heptadecane Triphenylmethane Bromoform
(dalton)
Molec. weight Mr 198.4 198.4 200.3 200.3 200.3 212.4 214.2 214.2 214.2 220.3 220.3 220.3 220.3 220.3 220.3 220.3 220.3 220.3 225.3
Diffusing Species
Tetradecane (Alcane CI4) Tetradecane (Alcane C14) Ethyldecanoate Ethyldecanoate Ethylcaprate Pentadecane 2,4-Dihydroxybenzophenone 2,4-Dihydroxybenzophenone 2,4-Dihydroxybenzophenone 2.6-Di-tert-butyl-4-methylphenol 2.6-Di-tert-butyl-p-cresole 2.6-Di-tert-but yl-4-methylphenol 2,6-Di-tert-butyl-4-methylphenol 2,6-Di-tert-butyl-4-methylphenol 2,6-Di-tert-butyl-4-methylphenol 2,6-Di-tert-butyl-4-methylphenol 2,6-Di-tert-butyl-4-methylphenol 2,6-Di-tert-butyl-4-methylphenoI 2-(2'-hydroxy-5'-methyl-phenyl)-2H-benzotna-
Name
~
-
0.978
-
-
0.948 (25)
-
70.0
-
-
-
-
-
0.956 (23) 0.956 (23)
-
-
-
-
-
0.964
-
-
-
0.978
68.0 72.0 72.0 64.0 54.0
0.953 0.959 0.959 0.948 (25) 0.934
59.0 65.0 68.0
-
-
-
(23) (23) (25) (25) (30)
(%)
-
0.956 0.956 0.939 0.944 0.952
(g/cm3)
Polymer Density Cristal@ ("C) linity PP -
-
23 23 40 80; 110 40 40 25 : 70
23 23 25 25 90 40 60 ; 75 43 ; 75 44 5 : 60 20 : 80 23 30 : 60 30 ; 60 30 : 60 30 ; 60 40 100 40
("c)
Experiment Type of Temp. diffusion range of coefficient experim.
0.029 1.90 0 637' 0.02'x" 0.586' 0 0698' 0 90'
I(
0.049 3.2 0.14'* 0.11'*' 37.3'* 0.778' 0 0783"" 0.041'4" 0 0099' * 0 00027 0 133 0 0138 0 00046' 0.00048' 0.0004" 1.91' 0 01' 12 0' 0 136(
(cm'ls) x I O Y
Dcxp
-
-
-
-0.3476
43.62
-
-
72.82 -
-
-
-
2.477
-
-
-
-
-
-
-
102.60 77.56 106.77 40.71 -
-
6.768 3.372 7.449 4,534
-
-
175.80 54.82
-
102.10 93.32 -1 1.88 0.800
7.406 6.184
-
-
-
-
(kJ/mol) -
-
-
58
81 66 66
67 66
6
79 79 78 78 134 78 66
77 133 75
104 66 71 71 71
67 20 20
67
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do Ed
Diffusing Species
Stearyl alcohol Eicosane (Alcane C20) Eicosane (Alcane CzO) Docosane (Alcane (222) Docosane (Alcane C22) Docosane Caprylcaprate Ethylstearate Heptadecylbenzene 2-Hydroxy-4-n-octoxybenzophenone 2-Hydroxy-4-octoxybenzophenone 2-H ydroxy-4-octoxybenzophenone Behenyl alcohol Tetracosane
2-Hydroxy-4-n-butoxybenzophenone
n-Octadecane (Alcane CIR) n-Octadecane (Alcane Clx) n-Octadecane n-Octadecane n-Octadecane n-Octadecane n-Octadecane Octadecane n-Octadecane n-Butyllaureate Te tramethylpentadecane
Name
(dalton) 254.5 254.5 254.5 254.5 254.5 254.5 254.5 254.5 254.5 256.4 268.6 270.3 270.3 282.6 282.6 310.6 310.6 310.6 313.5 313.4 316.2 326.4 326.4 326.4 326.4 338.6
Molec. weight M,
-
(23) (23) (23) (23)
-
0.953 0.959
-
-
0.952 (30) 0.952 (30)
-
0.956 0.956 0.956 0.956
-
-
-
0.934 0.Y52 (30)
23 23 40 90 90 40 80; 110 55 ;75 55 ; 75 40 40
23
(T) 23 23 24 : 60 24 ; 60 30 ; 60 30 : 60 30 ; 60 40 20 ; 100 90 40 80: 110 40 23
-
(YO)
(g/cm3) 0.956 (23) 0.956 (23) 0.978 0.978 0.978 0.978 0.978
Experiment Type of Temp. diffusion range of coefficient experim.
Polymer Density Cristal@ ("C) linity PP -
-
-
-
4.602 16.81 14.98
0.042"" 0.0066"" 0.0013'4" 0.0169'** 0.0527(**
-
-
90.40 166.90 155.00
-
0.12'**
-
-
-
-
-
-
-
-
-
0.50 0.0033 0.20 0.0417'"" 9.72' * * KO(**
'
Diffusion Parameters Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 " C ) Ig Do Ed Dexp (crn2/s)x lo-' (kJ/rnol) 0.019 1 I6 0.0035' 9.466 112.86 I .45' 0.337 46.32 0.03 1 -2.838 37.81 7.519 100.15 0.005' 0.0088' 7.029 96.79 0.2 16' 1.4 1.300 51.89 2 I .5' 0.102' 0.029"" 2.919 77.42 0.0819' 0.009
66
66
90
66 104 104 66 81 90
81 66 67 67 67 67
133 104 66
78 78 83 79 79 66
67 67
Ref.
3
4
2 2
2
b
m
Diffusing Species
Di-octyl-phthalate (DOP) Squalane 2,5-Bis-(5-tert-buthyl-benzoxazol-2-yl)-thiophene n-Dotriacontane n-Dotriacontane n-Dotriacontane Laurylstearate Bis-[2,2,6,6-tetramethyl-4-piperidinyl-l-oxy] sebacate Didodecyl-3-3-thiodipropionate(DLTDP) Didodecyl-3-3-thiodipropionate(DLTDP) Didodecyl-3-3-thiodipropionate(DLTDP)
Di-(2-ethylhexyl)-phthalate
(Plastanox 2246) 2-2-Methylene-bis-(4-methyl-6-t.-butyl phenol) (Plastanox 2246) 2-2-Methylene-bis-(4-rnethyl-6-t.-butyl phenol) (Plastanox 2246) n-Butylstearate N-Octadecyl-1-diethanolamine (N-ode) Phenylstearate Lauryllaureate Lauryllaureate Lauryllaureate Lauryllaureate 2-Hydroxy-4-n-octadecoxybenzophenone
Name
68.0 54.0 68.0 70.0 71.0 72.1 85.5 70.0 -
-
0.952 (30) 0.934 (25) 0.952 (30) 0.956 (30) 0.957 (30) 0.964 (30) 0.977 (30)
-
0.978 0.978 0.978 0.952(30) 0.943 0.937 0.952 0.9.54
341.4 357.4 361.4 369.6 369.6 369.6 369.6 382.5 390.6 390.6 422.7 430.5 450.9 450.9 450.9 453.6 511.0 514.4 514.4 514.4
-
-
57.0 68.0 69.0
68.0 46.0
-
69.0
0.954 (25)
340.4
-
68.0
0.952 (25)
-
Polymer Density CrislalC3 ("C) linity
340.4
Molec. weight
0.000029'* 0.014'" 0.000064(* 5.77'"' 0.074(60 0.25(b" 0.12'6" 0.12'fJ"
60 : YO 60 : 90 60 : 90
0.0136'"' 0.0016'*" 0.0345"" 0.00933'""
0.08""
7.55' 0.26 7.62'** 1.60'"' 1 1 2'"' 0.9'** l.l(**
0.0062'7"
0.0048'"'
7.387
84.00 83.90 70.0
-
105.30
-
4.580 4.260 2.070
154.40 166.99 144.00
-
-
-
-
14.71 19.629 13.22
-
-
-
-
1.431
71.14
-
-
-
-
52.73
91 91 91
78 78 79 104 96
81 66 87 66 66
135
104 133 104 104 104 135
51.47 -
91
91
91
111.30
112.38
95.79
(kJimol)
0.477
0.500
-
7.800
7.840
6.030
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23"C) Ed lg Do
30 : 60 30 : 60 30 ; 60 90 60:100
90 20 ; 78 90 60 : 90 90 85 85 80 ;110 40 70 40 40
50 ; 80
50 :80
Experiment Type of Temp. diffusion range - of coefficient experirn.
Diffusing Species
Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3.5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Stearylstearate 1-1-3-tris(2-methyl-4-hydroxy-5-tert-butylphenyl) butane Laurin Docosanic acid docosanyl ester (Behenyl behenate) Docosanic acid docosanyl ester (Behenyl behenate) Behenyl behenate
Didodecyl-3-3-thiodipropionate (DLTDP) Didodecyl-3-3-thiodipropionate
Name
(g/cm3)
(dalton)
65.0 65.0 65.0 68.0 54.0 68.0 72.1 85.5
0.963 0.963 0.963 0.9.52 (30) 0.934 0.952 (30) 0.964 (30) 0.977 (30) 0.952 (30)
531.4 531.4 531.4 537.6 544.5 639.1 649.1 649.1 649.1
68.0
91
87.67
69.0
0.954(25)
531.4
51.06 -
75.95
7.819 10.330 4.300 -
2.601
0.00062'40 0.0033'70 3.75'** 0.28""
49 ; 110 77 : 135
30.96 -
-12.705 -
0.75'Rn 2.75'**
85 : 95
90
90
1.14(** 0.23@'
114.0
85 ; 95
90 56 ; 100
130.1
9.568
0.0022(~~) 50 ; 121
125.1
4.44 0.018(~0
50 ; 90
91
171.42
18.24 0.000098''
30 ; 50
69.0
0.954 (25)
531.4
13.9
104
135
104 135
133
104
136
101
100
91
102.82 6.550
0.0083's0
50 ; 90
68.0
0.952 (25)
531.4
91
147.27
0.00008("
30 ; 50
68.0
0.952 (25)
91
91.44
18.57
0.5
5.33
91 133 91
157.50 51.89 171.6
(kJ/mol)
18.67
-
0.035'sn
531.4
Dexp
(crn2/s) x lo4
50 ; 90
57.0
0.937 (25)
531.4
(T)
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23°C) Ig Do Ed
0.075" 3.9'70 0.00019'*
D
-
Experiment Type of Temp. diffusion range of coefficient experim.
30 ; 60 78 ; 100 30 ; 50
68.0 54.0 57.0
0.952 0.934 0.937 (25)
514.4 514.4 531.4
(%)
Polymer Density Cristal@ ("C) linity PP
Molec. weight M,
i?:
3
B
-6
5A
%
v1
Diffusing Species
(g/cm')
(dalton)
diene Deuterated polyethylene Three-arms star branched deuterated polybutadiene
-5000 -9300
Tetrakis[3-(3-5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethyl]-methane (Irganox 1010) Linear deuterated Polybutadiene (PBD) -2600 Deuterated polyethylene -3000 Three-arms star branched deuterated polybuta-3100
propionyloxymethyl]-methane (Irganox 1010) Tetrakis[3-(3-5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethyl]-methane (Irganox 1010) Tetrakis[3-(3-5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethyl]-methane (Irganox 1010)
-
-
-
-
-
-
-
-
65.0
-
-
0.963
65.0
-
70.0 71.O 57.0 68.0 68.0 69.0 68.0 68.0 68.0 68.0
(%)
-
0.963
0.956-(30) 0.957 (30) 0.937 (25) 0.952 (25) 0.952 (25) 0.954 (2.5) 0.952 (30) 0.952 (30) 0.952 (30) 0.952 (30) 0.963
PP
Polymer Density Cristal@ ("C) linity
Molec. weight M,
649.1 649.1 Distearyl-thio-dipropionate (DSTDP) 682.5 Distearyl-thio-dipropionate (DSTDP) 682.5 Distearyl-thio-dipropionate (DSTDP) 682.5 Distearyl-thio-dipropionate (DSTDP) 682.5 Myristin 723.2 847.2 Dioctadecyl Octadecanedioate Stearin 891.3 Didocosyl Eicosandioate 988.2 Tetrakis[3-(3-5-di-tert-butyl-4-hydroxy-phenyl) 1177.8
Behenyl behenate Behenyl behenate
Name
-
176 176
176 176 176
50 ; 130
25
49 ; 135
80 ;125 90 60 : 90 30 :60 60 : YO 60 ; YO 90 90 90 90 49 : 135
("c)
Experiment Type of Temp. diffusion range of coefficient experim.
2.2'** 0.23(**
10.5'** 3.5'** 2.1(**
0.000044~50
0.000502(**
0.0000018'40
4.02(90 2.17'** 0.12'"' 0.00035" 0.088''O 0.072"" 0.74'** 1.22'** 0.61(*' 1.02'" 0.000014'""
-
-
-
-
-
-
12.394
-
13.98
11.16
7.15 20.94 3.90 4.46
-
-
-
-
-
153.0
-
166.0
143.8
67.38 99.31 183.55 80.10 84.11 -
2.368
139 138
138 139 138
100
75
101
104 104 91 91 91 91 104 104 104 104 137
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23"C) Ig Do Ed Dcxp (cm'/s) x lo-' (kJlmol)
\o
5
1
Diffusing Species
Deuterated Polyethylene Linear deuterated polybutadiene (PBD) Deuterated polyethylene Linear deuterated polybutadiene (PBD) Three-arms star branched deuterated polybutadiene
Name
-
-
(dalton) 10200 108oO 18000 -53000 -66300
Molec. weight M,
-
-
-
-
-
(%)
-
-
-
(g/crn') -
Polymer Density Cristallinity @ ("C) PP -
(T) 176 176 176 176 176
-
D D D D D
Experiment Temp. Type of range of diffusion coefficient experim.
Diffusion Parameters Ref. Pre-expon. Activation Diffusion coefficient coefficient energy @ (23°C) lg Do Ed Dexp (cm2/s) x lo-' (kJlmo1) 0.13'" I39 0.85'** 138 139 0.075(** 0.04(*" 138 0.001(** 138
$
&
B3
"D
a
0
diffusion coefficient not measured but extrapolated to 23 "C diffusion coefficient at the temperature given in column 6 (other than 23 "C) diffusion coefficient at the temperature. "C,given in the upperscript.
(* (**
(4"
concentration independent average diffusion coefficient diffusion coefficient at "zero" diffusant concentration diffusion coefficient in a polymeric sample in contact with a solventlsimulant diffusion coefficient in a swollen polymeric sample diffusion coefficient at the gaslvapor pressure given in the subscript
D D, D, Dsw D,,,,
Diffusing Species
Ethylene Methanol Methanol Ethanol Ethanol Ethanol Acetone Dimethylcarbinol(2-Propanol) Benzene Benzene Benzene Cyclohexane Dichloromethane Dichloromethane
Name
(dalton) 28.1 32.0 32.0 46.1 46.1 46.1 58.1 60.1 78.1 78.1 78.1 84.2 84.5 84.5
Molec. weight Mr
-
-
0.902 (23) -(HO) 0.910 (25) 63.0 10.0 (aT) 0.883 47.0 (iT) 0.883 47.0 (iT) 0.883 47.0 (iT) 0.883 47.0 (iT)
-
-
-
64.0 BO BO
(%)
-
-
-
-
(glcm') 0.892
PP
Polymer Density Cristal@ ("C) linity
D
(T) 25 23 23 20 20 10 ; 25 10 ; 25 23 25 15 ; 40 25 25 25 25
Experiment Type of Temp. diffusion range of coefficient experim.
Diffusion Parameters Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ed Ig Dd Drxp (cm'is) x to-' (kJ/mol) 0.45'** 0.0009 0.0004 0.084'** 1.5(** 15.335 140.3 0.038 -8.572 4.99 0.035 0.0012 0.085(*' 0.72 6.557 83.33 19.6'** 10.6(** 0.22'*" 13.0'" -
Abreviations for the type of polypropylene: aT - atactic, iT - isotactic, HO - homopolymer, CO -copolymer, BO - biaxially oriented, UO - uniaxially oriented, SB - stereoblock polymer,
where:
Table 3: Diffusion data for low molecular weight organic substances in various types of Polypropylenes (PP)
140 141 142 142 142 143 143 144 30 145 146 146 146 146
Ref.
Diffusing Species
bis-(2-Chloroethyl)-sulfide Methylcyclohexane Methylcyclohexane Methylcyclohexane Methylmethacrylate
bis-(2-Chloroethyl)-sulfide bis-(2-Chloroethyl)-sulfide
Methylenechloride n-Hexane n-Hexane n-Hexane n-Hexane Tetrafluormethane Tetrafluormethane Tetrafluormethane Tetrafluormethane Tetrafluormethane Tetrafluormethane Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene bis-(2-Chloroethyl)-sulfide
Name
(%)
-
- (BO) 60.3 (iT) 60.3 (iT) 74.0 (iT) - (iT) 65.0(iT) 56.9(iT)
-
0.889 (25) 0.889 (25) 0.890 0.905 0.897(25)
0.883 47.0 (iT) 0.910(25) 63.0 43.0 (iT) 43.0 (iT) 0.883 47.0 (iT) 0.895 (25) 47.8 (iT) 0.915 (25) 73.0 (iT) 0.895 (25) 47.6 (iT) 0.914 (25) 72.5 (iT) 0.906 (25) 61.8(iT) 0.915 (25) 72.6 (iT) 74.0 (iT) 0.904 64.0(UO) 0.904 64.0(UO) 0.916 0.916 78.0(OP) 0.883 47.0 (iT) 0.890 - (iT) 0.905 65.0(iT)
(g/cm3)
(dalton)
84.5 86.2 86.2 86.2 84.5 88.0 88.0 88.0 88.0 88.0 88.0 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 96.5 96.5 96.5 96.5 98.2 98.2 98.2 100.1
PP
Cristallinity -
Polymer Density @ ("C)
Molec. weight Mr
n
25 25 30 ;60 30 ;60 25 40 ;70 40 ;70 40 ; 70 40 ; 70 40 ; 70 40 ; 70 0;50 30 30 30 30 25 40 40 25 ;45 25 : 45 20 : 40 20 ; 30 0;so 40 40 60
(T)
-
D,
Temp. range of experim.
Experiment Type of diffusion coefficient
0.0204" 0.0091 0.0093 0.0165 30.0('* 10.2(" 0.91'**
0.10''
0.43'3n 0.60('0 0.43(3" 0.67'3n 0.12 0.056(** 42.0"" 0.0028'*' 0.0097'** 10.0(" 78.1"' 33.2'**
0.60'3"
0.24("' 0.06'" 4.68" 400(' 27.0(** 0.51(30
-
-
-
-
-
-
-
30.24 31.13 94.60 93.07 76.3 -
-
-3.654 4.196 6.657 6.394 3.683
-
-
53.64 45.84 65.62 65.97 69.38 62.56 67.95 66.55 57.61 -
-
-
-
3.024 3.155 3.598 2.659 3.348 3.297 1.262
-
2.136 2.691
-
-
(kJ/mol) -
Activation energy Ed
Diffusion Parameters Diffusion Pre-expon. coefficient coefficient @ (23"C) Ig Dd Dexp (cm2/s) x lo-* -
152 152 155
150
147 30 148 148 146 149 149 149 149 149 149 150 151 151 151 151 146 152 152 153 153 154 154
Ref.
+
$
9
b
%
N
p
VI
Diffusing Species
Methylmethacrylate Methylmethacrylate Methylmethacrylate Methylmethacrylate Methylme thacrylate Methylmethacrylate Methylmethacrylate Methylmethacrylate Methylmethacrylate Methylmethacrylate n-Heptane cis-3-Hexene-1-01 cis-3-Hexene-1-01 cis-3-Hexene-1-01 p-Xylene p-Xylene o-Xylene o-Xylene Chlorobenzene 2,2,4-Trimethylpentane 2.2.4-Trimethylpentane Chloroform Chloroform 2-Phenylethylalcohol 2-Phenylethylalcohol 2-Phenylethylalcohol 2-Phen ylethylalcohol
Name
100.1 100.1 100.1 100.1 100.1 100.1 100.1 100.1 100.1 100.1 100.2 100.2 100.2 100.2 106.2 106.2 106.2 106.2 112.6 112.6 112.6 119.4 119.4 122.2 122.2 122.2 122.2
(dalton)
Molec. weight M,
-
0.900 0.902 0.900 0.902
(23) (23) (23) (23)
(25) (25) (25) (25) (25) (25) (25) (25) (25) (25)
(%)
-
-
(CO)
- (HO) - (CO) - (HO)
-
62.4 (iT) 65.2 (iT) 66.1 (iT) 68.0 (iT) 74.5 (iT) 75.4 (iT) 76.3 (iT) 77.3 (iT) 56.9 (iT) 68.0 (iT) 74.0 (iT) 0.900 (23) - (CO) 0.902 (23) - (HO) 0.902 (23) - (HO) 0.890 - (iT) 0.905 65.0 (iT) - (iT) 0.890 0.905 65.0 (iT) 0.883 47.0 (iT) 0.890 - (iT) 0.905 65.0 (iT) 0.883 47.0 (iT)
0.902 0.904 0.905 0.907 0.912 0.913 0.914 0.915 0.897 0.907
(g/cm')
PP
Polymer Density Cristal@ ("C) linity -
60 60 60 60 60 60 60 60 20 : 60 20 ; 60 0 : 50 23 23 23 40 40 40 40 25 40 40 25 25 ;SO 23 23 23 23
("c)
Experiment Type of Temp. diffusion range of coefficient experim.
155
155 155 155 155 155 155 150 57 57 144 152 152 152 152 146 152 152 146 58 57 57 57 57 -
0.68'*"
0.32'" 0.24' * ' 0.056 0.0064 0.037 0.017 0.015 0.012 70.0'** 28.0(** 38.0(** KO(** 13.0(** 25.0'** 5.0'** 10.6'** 23.7(* 0.0026 0.0017 0.0016 0.0013
155 155 155
-
-
-
-
14.09
-
-
-
-
-
-
-
-
-
-
62.44 66.22 75.2
-
-
-
-
-
(kJ/mol)
-
-
0.77'"* 0.49"* 0.28'** 0.14(** 0.88'"
(cm2/s) x
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Dd Ed Dexp
b
t;
u l
3
-
2
"0
2-Phenylethylalcohol Amylaceticester (Isoamylacetate) Amylaceticester (Isoamylacetate) Amylaceticester (Isoamylacetate) Amylaceticester (Isoamylacetate) Amylaceticester (Isoamylacetate) Trichlorethylene 1J.1-Trichlorethane 4-Isopropenyl-I-methyl-1-cyclohexene (Limonene) 4-Isopropenyl-I-methyl-1 -cyclohexene (Limonene) 4-Isopropenyl-I-methyl-I-cyclohexene (Limonene) 4-Isopropenyl-I-methyl-] -cyclohexene (Limonene) 4-Isopropenyl-I-methyl-] -cyclohexene (Limonene) 4-Isopropenyl-1-methyl-1-cyclohexene (Limonene) 4-Isopropenyl-1-methyl-1-cyclohexene (Limonene) 4-Isopropenyl-I-methyl-1-cyclohexene (Limonene) 4-Isopropenyl-1-methyl-1-cyclohexene (Limonene) 4-Isopropenyl-I-methyl-1-cyclohexene (Limonene)
Name
Diffusing Species
156 156
4.3'" 0.17(""
0.6 1 (**
30 30
30
51.0
51.0
63.0(UO)
-
-
136.2
-
-
-
-
136.2 136.2 136.2 136.2 136.2
136.2
23
- (HO)
0.902 (23)
- (UO)
24
30
30
66.0(BO) 66.0(BO)
30
63.O(UO)
157
156 0.594(** 0.0003(**
156
156
156
141
0.042(*'
0.151('*
0.000375
144
136.2
0.0025
23
- (HO)
0.902 (23)
136.2
144 57 57 57 57 144 58 58 57
- (HO)
("c) 23 23 23 23 23 23 25 ;70 25 ;50 23
0.902 (23)
-
Ds
-
-
-
-
(HO) (CO) (HO) (CO) (HO) (HO) -
(YO)
Ref.
-
-
-
Diffusion Parameters Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Dd Ed Dexp (cm2/s) x IO-' (kJ/mol) 0.0089 0.0068 0.0038 0.0045 0.0024 0.003 30.3'' 9.90.0032
-
(g/cm3) 0.902 (23) 0.900 (23) 0.902 (23) 0.900 (23) 0.902 (23) 0.902 (23)
PP
Experiment Type of Temp. diffusion range of coefficient experim.
(dalton) 122.2 130.2 130.2 130.2 130.2 130.2 131.4 133.4 136.2
Molec. weight M,
Polymer Density Cristal@ ("C) linity
+
h
3 B
b
%
VI
,A P
Diffusing Species
4-Isopropenyl-1-methyl-1-cyclohexene (Limonene) Ethyleneglycolmonophenylether (EMPhE) n-Decane bis-(2-Chloroethyl)-ether bis-(2-Chloroethyl)-ether Dimethylbenzylcarbinol Dimethylbenzylcarbinol Dimethylbenzylcarbinol Bromobenzene 1.7,7-Trimethyl-bicyclo12.2.11 heptane-2-one (Camphor) 1,7,7-Trimethyl-bicyclo[2.2.1] heptane-2-one (Camphor) 1,7,7-Trimethyl-bicyclo[2.2.1] heptane-2-one (Camphor) 1,7,7-Trimethyl-bicyclo12.2.11 heptane-2-one (Camphor) 1,7,7-Trimethyl-bicyclo[2.2.1] heptane-2-one (Camphor) Carbontetrachloride Carbontetrachloride Carbontetrachloride 3,7-Dimethyl-6-octene-l-al (Citronellal) 3,7-Dimethyl-6-octene-l-al (Citronellal) 3,7-Dimethyl-6-octene-l-al (Citronellal) 3,7-Dimethyl-6-octene-l-ol (Citronellol) 2-Isopropyl-5-methyl-cyclohexanole (Menthol)
Name
0.900 (23) 0.902 (23) 0.900 (23) 0.902 (23) 0.902 (23) 0.910 (25) 0.883
152.2 152.2 152.2 152.2 153.8 153.8 153.8 154.2 154.2 154.2 156.3 156.3 0.900 0.902 0.902 0.902 0.900
-
-
(23) (23) (23) (23) (23)
0.900 (23) 0.902 (23) 0.900 (23)
-
(g/cm3) -
(UP)
(%)
Polymer Density Cristal@ ("C) linity PP -
138.2 142.3 143.0 143.0 150.2 150.2 150.2 150.7 152.2
136.2
(dalton)
Molec. weight Mr
25 25 25 ; 70 23 23 23 23 23
23
23
23
0.02"* 11.0(** 11.3'* 0.0013 0.00071 0.00043 o.ooo5 0.00066
0.00024
0.00039
0.00071
0.00033
25 ; 60 70; 110 25 ; 45 25 ; 45 23 23 23 25 ;70 23 23
0.00046'* 0.53(70 0.171'" 0,029'" 0.00092 0.001 1 0.0012 11.9(* 0.00044
24
DS
0.016'**
(T)
-
-
-
-2.306
-
-3.934
-
11.715 3.644 4.318 4.994
-
57 57 144
-
-
-
-
-
26.17 -
144
58 57 57 57
30 146
51
-
-
58 57
143 81 153 153 57 57 57
157
17.11 -
-
-
130.6 78.28 25.21 25.76 -
-
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Dd Ed D'Xp (cm2/s) x (kJ/mol)
D
Experiment Type of Temp. diffusion range of coefficient experim.
s. *
4
%
g
2-Isopropyl-5-methyl-cyclohexanole (Menthol) 2-Isopropyl-5-methyl-cyclohexanole (Menthol) Undecane Methoxy-4(2-propenyl)phenol (Eugenol) Methoxy-4(2-propenyl)phenol (Eugenol) Methoxy-4(2-propenyl)phenol (Eugenol) Methoxy-4(2-propenyl)phenol(Eugenol) Tetrachlorethylene Diphenylmethane Diphenylmethane Diphenylme thane Diphenylmethane Diphenylme thane Diphenylamine (DPA) Diphenylamine (DPA) Diphenylamine (DPA) 1,1,2,2-TetrachIoroethane Diphenyloxide Diphenyloxide Diphenyloxide Diphen yloxide Diphenyloxide n-Dodecane (Alcane C12) n-Dodecane (Alcane C,?) n-Dodecane (Alcane C12) n-Dodecane (Alcane Clz) n-Dodecane
Name
Diffusing Species
156.3 156.3 156.3 164.2 164.2 164.2 164.2 165.8 168.3 168.3 168.3 168.3 168.3 169.2 169.2 169.2 169.9 170.2 170.2 170.2 170.2 170.2 170.3 170.3 170.3 170.3 170.3
(dalton)
M*
Molec. weight
-
(%)
-
-
-
(aT) -
0.900 (23) - (CO) 0.902 (23) - (HO) 0.900 (23) - (CO) 0.902 (23) - (HO) 0.902 (23) - (HO) 0.900 (23) -(CO) 0.902 (23) - (HO) 0.900 (23) - (CO) 0.902(23) - (HO) -
-
-
0.900 (23) - (CO) 0.902 (23) - (HO) 0.900 (23) - (CO) 0.902 (23) - (HO) 0.900 (23) - (CO) 0.902 (23) - (HO) 0.900 (23) - (CO) 0.902 (23) - (HO) 0.902 (23) - (HO) - (aT) - (aT)
-
(HO) 0.902 (23) - (HO)
(g/cm3) 0.902(23)
PP
Polymer Density Cristallinity @ ("C)
D,
-
40
40 23 23 23 23 25 ;70 23 23 23 23 23 40 ;60 40 :60 40 25 ;70 23 23 23 23 23 23 23 23 23
(T) 23 23
Experiment Type of Temp. diffusion range of coefficient experim.
0.00026 0.0013 0.212'** 0.0024 0.0015 0.0021 0.00105 16.9'* 0.0029 0.0016 0.0022 0.0015 0.00125 0.073(40 0.51(4" 0.78(** 3.6(* 0.0038 0.002 0.0021 0.0013 0.0018 0.011 0.0059 24.0 34.0 0.0934'*'
(cm2/s) x I O - ~
Uexp
-
(kJlmo1)
57 144 66 57 57 57 144 58 57 57 57 57 144 158 158 158 58 57 57 57 57 144 67 67 67 67 66
Diffusion Parameters Ref. Diffusion Pre-expon. Activation energy coefficient coefficient @ (23 Ig Dd - "C) Ed
4
52
h b
o\
p
VI
Diffusing Species
y-Undecanlactone Tridecane Methyl decanoate Methyl decanoate 3,7-Dimethyl- 1,6-octadiene-3-ylacetate (Linalylacetate) 3.7-Dimethyl-l,6-octadiene-3-ylacetate (Linalylacetate) 3,7-Dimethyl-1,6-octadiene-3-ylacetate (Linalylacetate) 3,7-Dimethyl-l,6-octadiene-3-ylacetate (Linalylacetate) Phenylbenzoate (PB) Phenylbenzoate (PB) Tetradecane (Alcane C14) Tetradecane (Alcane CI4) Tetradecane (Alcane CI4) Tetradecane (Alcane C14) Phenothiazine 4-Hydroxyundecanelactone acid 4-Hydroxyundecanelactone acid 4-Hydroxyundecanelactone acid Dimethyl-3,3'-thiodipropionate Dimethyl-3,3'-thiodipropionate Dimethyl-3.3'-thiodipropionate 2.6-di-tert-butyl-4-phenylphenol 2,4-Dihydroxybenzophenone
Name
~
- (CO) - (HO) - (CO) 16.0 63.0 (iT)
(aT) - (CO) - (HO) - (CO) - (HO) - (iT) -
-
-
0.898 (25) 56.0 (iT)
-
0.900 (23) 0.902 (23) 0.900 (23) -
-
0.900 0.902 0.900 0.902
(23) (23) (23) (23)
-
198.2 198.2 198.4 198.4 198.4 198.4 199.3 200.4 200.4 200.4 206.3 206.3 206.3 212.3 214.2
40 ;60 40 23 23 23 23 70 ; 110 23 23 23 20 ; 40 80 ; 110 140 40 50 ;75
23
0.902 (23)
196.3
(HO)
23
(CO)
-
0.900 (23)
196.3 -
23
(HO)
-
0.902 (23)
196.3
(T) 23 40 50 ; 100 50 ; 100 23
(HO) 64.0(HO) 64.0(HO) 0.900 (23) - (CO)
-
-
(%)
Experiment Temp. Type of diffusion range of coefficient experim.
0.902 (23)
(g/cm3)
Polymer Density Cristal@ ("C) linity PP -
184.3 184.3 186.3 186.3 196.3
(dalton)
Molec. weight M,
0.27'4') 0.56(** 0.0082 0.0043 22.0 28.0 1.08(7" 0.0011 0.00062 0.0007 0.141 0.35"' 32.4(*" 0.204(" 0.00078'4'
0.0002
0.0012
0.00078
-
142.3
-
79.93 71.56 -
-
131.2 -
-
-
-
-
-
84.0
12.64
-
5.255 2.447
-
-
-
12.01
-
5.447
-
-
-
-
-
-
Diffusion Parameters Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Dd Ed Dexp (cm2/s) x (kUmol) 0.0007 0.112(** 0.00117'4' 133.0 11.27 0.00135(4' 128.7 10.614 0.0014
1.58 158 67 67 67 67 160 57 57 57 81 161 162 66 71
144
57
57
144 66 159 159 57
Ref.
2,4-Dihydroxybenzophenone Dibenzylsulphide (DBS) Dibenzylsulphide (DBS) Methyllaureate Methyllaureate 2,5-Di-tert-butyl-4-hydroxy-toluene 2,6-Di-tert-butyl-p-cresol (BHT) 2,6-Di-tert-butyl-p-cresol (BHT) 2.6-Di-tert-butyl-4-methylphenol (BHT) 2,6-Di-tert-butyl-4-methylphenol (BHT) 2.6-Di-tert-butyl-4-methylphenol (BHT) 2,6-Di-tert-butyl-4-methylphenol(K4) 2,4-Dihydroxybenzophenone (DHB) 2-(2'-Hydroxy-5'-methylphenyl)-benzotriazole 2-(2'-Hydroxy-5'-methylphenyl)-benzotriazole 2-(2'-hydroxy-5'-methylphenyl)-benzotriazole 2-(2'-Hydroxy-5'-methylphenyl)-benzotriazole Hexadecane (Alcane C16) Hexadecane (Alcane Clh) Hexadecane (Alcane C16) Hexadecane (Alcane Clh) Hexadecane Hexadecane 2-Hydroxy-4-methoxybenzophenone 2-Hydroxy-4-methoxybenzophenone 2-Hydroxy-4-methoxybenzophenone
Name
Diffusing Species
(dalton) 214.2 214.3 214.3 214.4 214.4 220.3 220.3 220.3 220.3 220.3 220.3 220.3 222.2 225.2 225.0 225.3 225.0 226.4 226.4 226.4 226.4 226.4 226.4 228.2 228.2 228.2
M,
Molec. weight
-
-
-
-
-
-
-
-
(CO) (HO) (CO)
- (HO) - (iT) (iT) 63.0 (iT) -
-
-
-
48.0 (iT) 48.0 (iT) -
0.900 (23) 0.902 (23) 0.900 (23) 0.902 (23)
0.899 0.899 -
-
-
- (iT)
-
-
-
-
-
-
-
-
-
-
-
(aT)
64.0(HO) 64.0(HO) - (iT) 54.0
-
56.0 (iT)
(YO)
-
-
(g/cm') 0.898 (25)
Polymer Density Cristal63 ("C) linity PP -
D D
D
DS Dc-n Dsw D D D D D D Ds Dsw D D D D D D Ds D, Dsw Dsw D D
(T) 44 40 : 60 40 50 ;lo0 50 ;loo 60 : 110 70 ; 100 80 : 120 25 30 ;60 30 ;60 140 25 80: 120 40 ; 120 40 ; 120 115 : 160 23 23 23 23 40 70 ; 110 70 ;85 80 ; 110 40 : 90
Experiment Type of Temp. range of diffusion coefficient experim. (cm2/s) x IO-* 0.0055(*" 0.25'4" 0.58'** 0.0007(40 0.00068'4" 0.115'5" 0.116'70 0.446(70 0.005''" 0.00028'' 0.93" 40.1(*' 0.0005'" 1.62'70 0.0083(3" 0.0093(30 4.0"" 0.0074 0.0037 22.0 25.0 0.133'** 0.39(70 2.32'70 0.168'70 0.00237'30
uexp
-
-
3.839 0.0792 2.826 10.473
80.42 50.64 76.17 122.4
-
-
-
-
74.67 96.07 94.57 76.35 -
-
-
105.7 64.41
3.583 6.481 6.274 3.299 -
-
-
134.3 135.5 94.31 108.8 104.1 11.27 11.45 6.312 7.631 7.503 7.096 3.335
-
-
80.0
-
(kJ/mol)
-
4.748
-
67 66 81 81 161 168
78 78 162 72 165 166 166 167 67 67 67
71 158 158 159 159 160 163 164 72
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy 63 (23 "C) Ig Dd Ed
.c
2
b
2
cc,
+L
VI
Bromoform n-Octadecane (Alcane Cis) n-Octadecane (Alcane CIS) n-Octadecane (Alcane Clx) n-Octadecane (Alcane CI8) Octadecane n-Octadecane n-Ocatdecane n-Ocatdecane 2.6-Di-tert-butyl-4-n-butylphenol 2,6-Di-tert-butyl-4-tert-butylphenol
2,6-Di-tert-butyl-4-i-propylphenol
228.2 228.2 228.4 228.4 228.4 234.3 236.4 239.3 240.4 242.3 242.4 242.4 244.3 247.4 252.7 254.5 254.5 254.5 254.5 254.5 254.5 254.5 254.5 262.4 262.4
2-Hydroxy-4-methoxybenzophenone 2-Hydroxy-4-methoxybenzophenone Ethyllaureate Ethyllaureate Ethyllaureate 2.6 -Di-tert-butyl-phenylphenol 2.6-Di-t-butyl-4-methoxy phenol (Topanol354) 2-(2'-Hydroxy-5'-ethylphenyl)benzotriazole Heptadecane 2-Hydroxy-4-ethyl-benzophenone Methylmiristate Methylmiristate Triphenylmethane
(dalton)
Molec. weight M, 228.2
Diffusing Species
2-Hydroxv-4-methoxybenzophenone (Cyasorb
Name
-
0.900 0.902 0.900 0.902
-
-
(iT) (iT) (iT)
-
-
(CO) - (HO) - (CO) - (HO) -
64.0(HO) -
64.0(HO)
-
-
-
- (iT)
(%)
-
-
(23) (23) (23) (23)
(g/cm3)
PP
Polymer Density Cristal@ ("C) linity
Dsw D D
DS
DS
D
Dsw Dsw
Ds
D D Dsw D Dsw D D D D D D D D D Dsw DS
D
-
25 : 70 23 23 23 23 40 30 ; 60 30 : 60 30 : 60 140 140
140
120 ; 160 60 ; 120 20 20 20 140 120 : 130 80 : 120 40 60 : 120 50 ; 100 50 ; 100 40
30 ; 70
(T)
Experiment Type of Temp. diffusion range of coefficient experim.
S.6"O0 0.283"" 0.015"* 0.0014"" 0.033(** 27.2'** 6.5("" 0.199'70 0.133'" 0.282(5" 0.00038'4'' 0.000404'" 0.0129(** 31.7'** 3.6'" 0.0066 0.0034 23.0 25.0 0.0867'" 0.012(* 0.00086" 3.29'' 14.6'** 3 1.O'**
0.0014'*
-
-
-
-
38.78 121.8 56.37 -
-3.084 10.429 2.466 -
-
27.72
-2.546
-
-
-
73.54 141.3 140.3
3.343 12.17 12.02
-
53.40 82.83
0.099 3.915
-
-
-
-
-
-
66.11 77.45
112.4
2.01 3.980
8.970
167 165 170 170 171 162 172 165 66 165 159 159 66 162 58 67 67 67 67 66 83 78 78 162 162
169
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Dd Ed D,"" (cm2/sj; (kJ/mol)
v1
I
$
Diffusing Species
2-(2'-Hydroxy-5'-t-butylphenyl)-benzotriazole Tetramethylpentadecane 2-Hydroxy-4-n-butoxybenzophenone 2-Hydroxy-4-n-butoxybenzophenone 2-Hydroxy-4-n-butoxybenzophenone Methylpalmitate Methylpalmitate Stearyl alcohol Dibuthylphthalate (DBP) Dibuthylphthalate (DBP) Dibuthylphthalate (DBP) Eicosane (Alcane CzO) Eicosane (Alcane Cz0) Eicosane (Alcane CzO) Eicosane (Alcane C,,,) 2,6-Di-tert-butyl-4-cyc4ohexylphenol 1-Amnio-2-pentyl-antraquinone(Dye I) 1-Amnio-2-pentyl-antraquinone (Dye I) 2-(2'-Hydroxy-5'-cyclohexyl phenyl) benzotriazole 2.6-di-tert-butyl-4-benzyI-phenol Methyloleate Methyloleate Methyloleate Methyloleate
2-(2'-Hydroxy-5'-t-butylphenyl)-benzotriazole
2-(2'-Hydroxy-5'-n-butylphenyl)-benzotriazole
Name
296.4 296.5 296.5 296.5 296.5
(dalton) 267.3 267.3 267.3 268.4 270.3 270.3 270.3 270.4 270.4 270.4 278.3 278.3 278.3 282.6 282.6 282.6 282.6 288.4 293.3 293.3 293.4
Molec. weight M,
-
24.0(SB) 63.0 (iT) - (iT)
-
-
-
- (CO) - (HO) - (CO) - (HO) - (iT) - (iT)
-
64.0(HO) 65.9(HO) 68.0(HO) 70.1 (HO)
-
0.900 (23) 0.902 (23) 0.900 (23) 0.902 (23) -
-
-
-
-
-
-
64.0(HO) 64.0(HO)
-
-
-
48.0 (iT)
0.899
D D D D D
D
Dsw Dsw D D D
Ds
D D D D D D D D D D D D D Ds
(iT) (iT)
-
-
-
-
140 70 ; 90 70 ;90 70 ; 90 70 : 90
80 40 70 $5 80 ;110 60 : 120 50; 100 50 ; 100 40 20 20 20 23 23 23 23 140 60 ;70 70 ; 90 80 ; 120
(T) 80 $20 80 ;120
Experiment Type of Temp. diffusion range of coefficient experim.
(YO)
(g/cm3) -
PP
Polymer Density Cristal@ ("C) linity
4.26(** 0.004(60 0.00375(m 0.0049(60 0.00276'60
0.000194(4" 0.00028'4o 0.021 1(** 0.0051'*' 0.0051("* 0.0051"* 0.0061 0.0031 20.0 17.0 5.8'"" 0.032'50 9.3'70 0.0548(70
0 .0 4 5 0
(cm2/s) x lo-' 0.199(70 0.428'70 1.35'** 0.0278('* 1.21(70 0.104(70
ucxp
-
-
-
11.19 10.494 7.711 10.321
-
27.73 15.28 4.674
-
-
137.6 133.4 114.8 133.1
-
230.2 146.5 91.50
-
-
-
-
-
-
-
62.36 81.61 91.26 142.2 143.3 -
-
-
(kJ/mol) 82.83 82.58
1.580 3.447 5.363 12.02 12.38 -
-
-
3.915 4.209
162 159 159 159 159
165 165 166 66 81 161 165 159 159 66 87 87 87 67 67 67 67 162 173 173 165
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Dd Ed
+
&
k
20
3 0
48.0 (iT)
0.899
318.5 323.4 323.4
butyl)-pheny1)-benzotriazole 2-(2'-Hydroxy-3'-t-butyl-S'-(l"-methyI-
propy1)-pheny1)-benzotriazole 2-(2'-Hydroxy-3',5'-di-t-butyl-phenyl)-benzotriazole 2-(2'-Hydroxy-3',5'-di-t-butyl-phenyl)-benzotriazole
-
48.0 (iT)
-
0.899 0.899
323.4 323.4
0.899
(CO) (HO)
(iT)
48.0 (iT)
48.0 (iT)
48.0 (iT)
-
- (CO) - (HO) - (iT)
-
-
D
D
D
D D
D D
D
D Ds Ds Dsw Dsw D D
D
- (iT)
0.899
(23) (23) (23) (23)
D D D
-
50 ; 80
60 ; 80
80
140 80
40 80
92; 115
140 23 23 23 23 40 80 : 120
90 : 110
5 0 ; 110 50 : 110 65 : 90
(T)
Experiment Type of Temp. diffusion range of coefficient experim.
64.0(HO) 64.0(HO) - (iT)
(YO)
-
316.6 316.6
-
-
0.900 0.902 0.900 0.902
-
-
-
-
(g/cm')
PP
Polymer Density Cristal@ ("C) linity
-
310.5 310.6 310.6 310.6 310.6 310.6 315.4
307.4
298.3 298.3 307.4
(dalton)
Molec. weight M,
316.5
Diffusing Species
Methylstearate Methylstearate 1-N-Methylamino-2-pent yl-antraquinone (Dye 11) 1-N-Methylamino-2-pentyl-antraquinone (Dye 11) 2,6-di-tert-hutyl-4-(1-pheny1ethyl)phenol Docosane (Alcane C22) Docosane (Alcane C22) Docosane (Alcane C22) Docosane (Alcane Crr) Docosane 2-(2'-Hydroxy-5'-( 1" -phenylethyl) phenyl) benzotriazole 1-(3'-methyl-4'-hydroxy)phenyl-4-phenyl-disazobenzene (Yellow 7) Heptadecylhenzene 2-(2'-Hydroxy-3'-t-butyl -5'-methyl-phenyl)-5benzotriazole 2.6-di-tert-butyl-4-n-octylphenol 2-(2'-Hydroxy-5'-(1",1",3",3"-tetrametyhl-
Name
0.0067'"'
0.031(h"
0.613'**
1.95'" 0.319'"*
0.0524'** 0.0537'**
16.0""'
3.89'" 0.0029 0.0026 15.0 13.0 0.0245"" 0.01'~"
60.5""
0.00013'4" 0.000178'4" 7.07"'
(crn2/s) x
ULTp
P.
10.556
9.722
-
128.2
122.5
-
-
-
-
-
133.9
99.24
-
71.14
144.2 147.0 111.3
(kJ/mol)
-
-
-
11.96
5.123
-
4.018
12.180 12.79 9.8
-
166
166
166
162 166
66 166
173
162 67 67 67 67 66 165
173
159 159 173
Diffusion Parameters Ref. Diffusion Pre-expon. Activation energy coefficient coefficient @ (23°C) Ig Dd Ed
Y
h)
cn
%
3 i?: 2
b
Diffusing Species
,
I
L
r
(CAO-5) 2,6-di-tert-butyl-4-dimethylbenzylphenol 2-Hydroxy-4-n-octoxybenzophenone 2-Hydroxy-4-octoxybenzophenone 2-Hydroxy-4-n-octoxybenzophenone 2-Hydroxy-4-octoxybenzophenone (HOB) 2-Hydroxy-4-octoxybenzophenone (UV531) 2-Hydroxy-4-n-octoxybenzophenone 2-Hydroxy-4-(2’-ethyIhexyl)benzophenone 2-Hydroxy-4-octoxybenzophenone 2-Hydroxy-4-octoxybenzophenone 2-Hydroxy-4-octoxybenzophenone 4-Alkoxy-2-hydroxybenzophenone (Cyasorb UV 531) 2-Hydroxy-4-octoxybenzophenone (Cyasorb UV 531) 2-(2’-Hydroxy-5’-(2”-phenyl-2”-propyl) phenyl) benzotriazole Tetracosane (Alcane Cz4) Tetracosane (Alcane CZ4) Tetracosane Di-n-hexyl-3,3’-thiodipropionate Di-n-hexvl-3.3’-thiodi~ro~ionate
2-(2’-Hydroxy-3’,5’-di-t-butyl. .pheny1)-benzo. triazole 2-(2’-Hydroxy-5’-n-octyl phenyl) benzotriazole 2-(2’-Hydroxy-5’-t-octylphenyl) benzotriazole 2.2’-Methylene bis(4-methyl-6-t-butyl phenol)
Name
-
(iT)
338.6 338.6 338.6 346.5 346.5
- (HO) 24.0 (SB) 63.0 (iT)
-
(CO)
Dsw Dsw D D D
D -
(iT)
23 23 40 70 ; 85 80 ;110
80 : 120
30 ; 100
329.5
140 70 ; 85 44 ; 75 80 ; 110 25 125 60 ; 120 60 : 120 30 ; 125 75 ; 90 75 ; 90 60 ; 90
80 ; 120 80 : 120 120
(T) 80 ; 120
D D D D D D D D D D D D
D D D
D
D
35.4 48.4 58.0
-
- (iT) - (iT)
-
24.0 (SB) 56.0 (iT) 63.0 (iT)
-
(iT) - (iT) - (iT) -
(iT)
(%) -
-
Experiment Type of Temp. range of diffusion coefficient experim.
-
(g/cm’)
Polymer CristalDensity linity @ (“C) PP -
326.5
324.5 326.4 326.4 326.4 326.4 326.4 326.4 326.4 326.5 326.5 326.5 326.5
324.4 324.4 324.5
(dalton) 323.4
Molec. weight M,
14.0 10.0 0.0561(”* 10.4(7n 0.153(70
0.01(~~’
0.00012‘*
3.58(** I .34”’ 0.0091‘40 0.055‘7” 0.0015(** 20.0‘** 0.00045‘so 0.00079(50 0.00197‘* 0.355‘7” 0.772‘70 0.32‘H’
0.0079(70 0.079‘70 25.0(**
80.35 77.84
5.255 3.041
-
99.24
107.00
120.5 121.2 96.80 119.9 115.0 82.92
69.89 93.99 87.05 -
-
106.43 84.53
5.114
6.948
8.135 8.499 6.377 9.81 9.346 4.513
-
-
2.771 5.648 4.000
-
6.107 3.769 -
67 67 66 81 161
165
169
172 165 165 168 168 168 174
162 81 90 161 72
165 165 172
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 “C) Ig Dd Ed Dexp (cm2/s) x lo-’ (kJ/mol) 0.0146‘7n 7.322 112.64 165
*
k
39
G
k
h)
Diffusing Species
2.4-Dihydroxy-n-dodecoxybenzophenone 2,4-Dihydroxy-dodecoxybenzophenone 2-Hydroxy-4-dodecyloxybenzophenone(Aduvex 2412) 2-Hydroxy-4-n-dodecyloxybenzophenone 2-Hydroxy-4-(2'-ethylhexyl)-5-t-butyl-benzophenone Di-(2-ethylhexyl)-phthalate Phthalic acid bis(2-ethylhexyl ester) (DOP) Octacosane (Alcane Cza) Octacosane (Alcane CZR) Octacosane 2.2.6,6 -tetramethyl-4-piperidinol (Dastib 845) 2.2.6.6 -tetramethyl-4-piperidinol (Dastib 845) Squalane
2,4-Dihydroxy-n-dodecoxybenzophenone
2-(2'-Hydroxy"',5'-di-(l,"l"dimethyl propy1)pheny1)-benzotriazole n-Octadecyldiethanolamine 2-(2'-Hydroxy-3'.5'-di-t-butyl-phenyl)-5-chlorobenzotriazole n-Amido bis(2.3.6.6-tetramethyl-4-piperidinyl)amino Hexacosane (Alcane CZ6) Hexacosane (Alcane CZh) Tritolylester phosphoric acid (TCP) 2-(2'-Hydroxy-5'-n-dodecylphenyl) benzotriazole
Name
-
-
-
382.5 382.5 382.5 382.5 382.5 382.5 390.4 390.6 394.6 394.6 394.6 411.2 411.2 422.5
-
0.900 (23) 0.902 (23)
366.7 366.7 368.4 379.5
0.899 0.905
-
0.900 (23) 0.902 (23)
-
-
-
- (CO) - (HO) - (iT)
0.905
366.6
(CO) (HO) 48.0 (iT) - (iT)
-
-
0.00377'" 0.00013'4' 10.0 6.9 0.0178(** 0.000074" 0.126'6' 0.0099' '*
40 40 : 70 23 23 40 25 ; 60 60 ; 90 40 D D Dsw Dsw D D D D
-
0.0332"" 0.0032""
100 :120 80; 120 D D
(iT) (iT)
2.14'70 0.04"' 0.0062"' 0.00052"
70 3 5 80:llO 40 ;90 30 ; 70
13.0 7.2 0.00002" 0.0074'7"
0.12(70
0.29"' 0.347(**
0.621'*'
D D D D
80 ; 90
Drxp
(crn2/s)x lo-'
24.0(SB) 63.0 (iT) -
D
78 : 135 80
80
(T)
149.7 109.0 -
14.29 8.201 -
-
-
-
-
85.52 -
-
104.38 132.47
83.70 89.14 92.56 118.2
61.83
2.386
-
5.141 9.683
5.079 4.179 5.749 9.578
4717
66 96 94 66
66 87 67 67
165 165
81 161 168 169
165
-
67 67 87
-
-
94
133 166 87.64
-
166
4.432
85.72 -
-
-
4.156
(kJ/mol)
-
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 " C ) Ig Dd Ed
23 23 70 80: 120
(iT)
D
Dc n
-
D
-
Experiment Type of Temp. range of diffusion coefficient experim.
Dsw Dsw D D
-
60.0 48.0 (iT)
-
0.899
357.6 357.9
48.0 (iT)
(%)
0.899
(gkm')
Polymer Density Cristal@ ("C) linity PP -
351.5
(dalton)
Molec. weight M,
Diffusing Species
1,4-di-(2'-Hydroxy-4'-oxy-benzophenone)-nbutane
bis[2,2,6,6-tetramethyl-4-piperidinyl)-sebacate (Tinuvin 770) bis[2,2,6,6-tetramethyl-4-pipetidinyl)-sebacate (Tinuvin 770)
2-Hydroxy -4-n-octadecoxybenzophenone 2-Hydroxy -4-n-octadecoxybenzophenone
2,6-di-tert-butyl-4-n-octadecylphenol
Triacontane (Alcane C30) Triacontane (Alcane C3") 2,5-di(5-tert-butyl-2-benzoxazolyl) thiophene (Uvitex OB) 2,5-di(5-tert-butyl-2-benzoxazolyl) thiophene (Uvitex OB) 2,5-di(5-tert-butyl-2-benzoxazolyl) thiophene (Uvitex OB) 2.5-bis(5-tert-butyl-benzoxazol-2-yl)-thiophene 2-(2'-Hydroxy-3',5'-di-(dimethylbutyl)-phenyl)benzotriazole 2-(2'-Hydroxy-3',5'-di-(dimethylbutyl)-phenyl)benzotriazole Saturated Hydrocarbon (Ceresin 100) Dotriacontane (Alcane C32) Dotriacontane (Alcane &) Dotriacontane Dotriacontane
Name
D D D
48.0 (iT) - (aT) (HO) 24.0(SB) 24.0(SB) 48.0 (iT) (iT)
- (iT)
0.899 -
0.899 0.905 -
447.6 -450 450.9 450.9 450.9 450.9 458.8 466.7 466.7 480.7 480.7 482.5
-
-
-
-
-
-
-
-
48.0 (iT)
0.899
0.902 (23)
D D
-
-
430.0 447.6
D5 Ds Dsw D D D
D,-o Dsw
D
D
(iT)
-
-
430.5
Dsw Dsw D D
-
-
430.5
-
(CO) (HO)
-
70.8"*" 3.9 0.063'** 0.000056'* 0.67'" 0.112'0.65(7" 0.022'~~ 0.00018'* 0.022'5"
120 : 130 23 60 30 : 60 30 : 60 140 70 ; 85 80 ; 110 40 : 80 57 : 83
0.0104(s"
0.0089'h0
60 : 120
60 ; 120
0.0045"* 0.01'6"
6.0'**
0.6'**
5.4 0.00712""
-
6.700
5.802
103.14
95.6
76.17 99.18
3.415 5.491
155.83 78.3
-
-
45.49
113.1
109.1
-
-
94.72
-
1.524 5.645
-
-
-0.103
7.698
7.112
-
-
-
5.172
-
(kJlmol) -
165
94
97 67 79 78 78 162 81 161 96
166
166
66
172
175
67 67 168
Diffusion Parameters Ref. Diffusion Pre-expon. Activation energy coefficient coefficient 3 '2 (23°C) Ig Dd Ed
40 60: 120
120
130
23 23 50 : 125
("C)
Experiment Type of Temp. range of diffusion coefficient experim.
(iT)
-
-
(%)
0.900(23) 0.902(23) -
(gicm')
Polymer Density Cristallinity @ ("C) PP
422.7 422.7 430.5
(dalton)
Molec. weight M,
+
h'
33
h
b
3 P
Diffusing Species
phenone)-n-butane Saturated hydrocarbon (Ceresin 80) 1.4-di-(2'-Hydroxy-5'-t-butyl-4'-oxy-benzophenone)-n-octane bis-(2-Hydroxy-3(2'-benzotriazole-5(1',1",3",3"-tetramethyl-buthyl) pheny1)methane 1,4-di-(2'-Hydroxy-S'-(l"-phenyl-ethyl)-4'-oxybemophenone)-n-butane Hexanediol-di-3-(3'-(2''-benzotriazole)-4'hydroxy-5'- t-butyl-pheny1)-propionate
1,4-di-(2'-Hydroxy-5'-t-butyl-4'-oxy-benzo-
3-(3'-(5"-chloro-2'-benzotriazole)-4'-hydroxy5'-t-butyl-phenyl-propionate bis[2,2.6,6-tetramethyl-4-piperidinyl-l -oxy] sebacate Didodecyl-3-3-thiodipropionate(DLTDP) Di-n-dodecyl-3-3-thiodipropionate (DLTDP) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) 1.4-di-(2'-Hydroxy-4'-oxy-benzophenone)-noctene 1-1-3-tris(2-methyI-4-hydroxy-5-tert-butylphenyl) butane
Name
-
0.900 0.900
0.900 -
514.4 514.4 53 1.4 531.4 531.4 538.5
(iT)
-
0.899
690.8 760.9
(iT)
48.0 (iT)
-
48.0 (iT)
(iT)
-
0.899
-
-
-
-
(iT)
60.0
-
60.0
-
658.9
-600 650.9
594.5
544.5
60.0 63.0(iT) 60.0
0.899
512.0
60.0
D
48.0 (iT)
0.899
-
D
D
D
D
Dc
D
D
D
D,
Ds
D D D,
D
(%)
48.0 (iT)
(gicm')
o
80
80 ; 120
80
100 ; 120 80 ; 120
80 ; 120
100 ; 150
60;100
4.740
5.067
6.567
I
4.559
3.931 3.756 1.908
6.223
0.106""
0.0025('"
0.0771'**
-
9.528
-
-1.571 32.1"0° 0.0028'~~ 4.960
0.0027""
0.093('O0
0.0195'so
18.8""
0.01'40
50 ; 135
135
0.011(~~
0.00341's0 0.066'7"
0.052'70
166
97 165
165
133
165
136
100
101
133 161
96
-
166
132.18 165
-
35.14 101.88
100.48
100.66
100.64
-
87.23
82.85 84.95 71.0
101.8
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23"C) Ig Dd Ed Dexp (cm'is) x (kJimol) 0.18'"' 166
56 ; 135 80 ; 110 49 ; 121
70 ; 121
80
(T)
Experiment Type of Temp. diffusion range of coefficient experim.
486.0
Polymer Density Cristal@ ("C) linity PP
(dalton)
Molec. weight M,
+ L
wl
h)
wl
*
3$
h
Diffusing Species Molec. weight M,
(dalton) 2,4,6~Tris(2,6-di-t-butyl-4-hydroxybenzyl)-l.3,5-774.6 trimethylbenzene (Ionox 330) 774.6 1,3,5-(3,5-di-tert-butyl-4-hydroxy benzyl) mesitylene (Irganox 1330) N,N,N-Tris(2,6-di-t-butyl-4-methyl pheny1)iso- 777.0 cyanurate (Goodrite 31 14) 999.0 N,N,N"-Tris(ethyl[3,5-di-t-butyl-4-hydroxy phenyll-propionate) isocyanurate (Goodrite 3125) Tetrakis[3-(3-5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethyl]-me thane (Irganox 1010) Tetrakis[3-(3-5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethyl]-methane (Irganox 1010) Te trakis[3-(3-5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethyl]-methane (Irganox 1010) Tetrakis[3-(3-5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxyrnethyl]-methane (Irganox 1010) Tetrakis[3-(3-5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethyl]-methane (Irganox 1010) -2000 Polyethylene segments Atactic polypropylene segments -8000
Name
48.0
(aT) (iT)
0.900 -
D
48.0
0.900
-
-
-
-
-
0.000247(40
50 : 135
60.0
0.900
100 : 135
5.6'** 0.028""
0.39'""
120 : 150 100
11.15
0.0013(7" 70; 105
2.890
-
2.011
10.397
8.609
5.380
-
-
7.492
-
-
0.000013(4"
49 : 135
0.000054(*
49 ; 121
60.0
0.900
1.0'*'
0.0038(70
2.0(**
0.7'**
-
-
120
80 ; 120
(T) 120
De*p (cm2/s) x
97 177 .
-
88.8
108
108
137
136
76.4
144.6
139.4
121.1
101
172
-
100.0
172
176
172
-
117.63
-
(kJ/mol)
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @(23"C) IgDd Ed
120
(iT)
-
-
-
Experiment Type of Temp. diffusion range of coefficient experim.
(iT)
-
(iT)
(%) -
-
-
(g/cm3)
Polymer Density Cristal@ ("C) linity PP -
4
2
22
b
m
Appendix I
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50.
5I . 52. 53. 54. 55.
to Appendix
527
I
Michaels, A. S., Bixler, H. J., J. Polym. Sci., 50 (1961) 413. Kanitz, P J. F., Huang, R. Y. M., J. Appl. Polym. Sci.. 14 (1970) 2739. Bixler, H. J., Michaels, A. S., Salame, S., J. Polym. Sci., A l(1963) 895. Kulkarni, S.S., Stern, A. S., J. Polym. Sci., Polym. Phys. Ed. 21 (1983) 441. Lundberg, J.L., Wilk, M.B., Huyett, M.J., J.Polym.Sci., 57 (1962) 275. MacDonald, R. W., Huang, R. Y. M., J. Appl. Polym. Sci., 26 (1981) 2239. Beret, S., Hager, S. L., J. AppLPolym. Sci., 24 (1979) 1787. Evnochides, S. K.. Henley, E. J., J. PolymSci., A-2.8 (1970) 1987and AIChE Journal, 17 (1971) 880. Brandt, W. W.. J. Polym. Sci., 41 (1959) 403 and 415. Robeson, L. M., Smith, T. M.. J. Appl. Polym. Sci., 11 (1967) 2007 and 12 (1968) 2083. Yasuda. H., Stannett, V.T., Frisch, H.L., Peterlin, A,. Die Makromolekulare Chem., 73 (1964) 188. Koszinowski, J., J. Appl. Polym. Sci., 31 (1986) 27 11. Podkowka, J., Puchalik, A,. J. Appl. Polym. Sci., 27 (1982) 1471. He, Z . , Hammond, G.S., Weiss, R.G.. Macromolecules. 25 (1992) 1568. Izydorczyk. Salwinski, J. Appl. Polym. Sci.. 29 (1984) 3663. Dos Santos, M.L., Leitao, D.M., J. Polym. Sci., A-2 10 (1971) 769 and 10 (1972) 1. Thalmann, W.R., Packaging Tech. Sci., 3 (1990) 67. Cuttler, J. A., Kaplan, E., McLaren, A. D., Mark, H., TAPPI, 34 (1951) 404 and 36 (1953) 423. Rogers, C. E., Stannett, V., Szwarc, M., J. Polym. Sci., 45 (1960) 61. Shimoda, M.. Matsui, T., Osajima, Y., Nippon Shokuhin Koyo Gakkaishi, 34 (1987) 402 and 535. Fleischer. G., Holstein, P., Acta Polymerica, 35 (1984) 738. Johanson, F., Leufvkn, A.. J. Food Sci.. 59 (1994) 1328. McCall. D. W., Schlichter, W. P.,J. Am. Chem. SOC80 (1958) 1861. Fels, M., Huang. R. Y. M., J. Appl. Polym. Sci., 14 (1970) 523 & 537. McCall, D. W., J. Polym. Sci., 26 (1957) 151. Saleem, M., Asfour, A.-F. A., De Kee, D.. Harrison, B., J. Appl. Polym. Sci., 37 (1989) 617. Doong, S. J.. Ho. W. S. W., Ind. Eng.Chem. Res., 31 (1992) 1050. Fleischer, G., Polym. Comm.. 25 (1985) 20. Huang, R. Y. M., Rhim. J.-W., J. Appl. Polym. Sci.. 41 (1990) 535. Kreituss. A., Frisch, H. L., J. Polym.Sci., Polym. Phys.Ed., 19 (1981) 889. Aboul-Nasr, O.T., Huang, R. Y. M., J. Appl. Polym. Sci., 23 (1979) 1819, 1833 and 1851. Gray, D. G., Guillet, J. E.. Macromolecules. 6 (1973) 223. Takeuchi, Y., Okamura, H., J. Chem. Eng. Japan. 9 (1976) 136. Stern, A. S.. Britton, G. W., J. Polym. Sci., Part A-2 10 (1972) 295. Peeters, H.. Vanderstraten, P.. Verhoeye, L., J. Chem. Tech.Biotechnol., 29 (1979) 581. Fels, M., AIChE J., Symposium Series, 120 (1970) 49. Chalkyh. A.Ye., Krivoshei, V.N., Vysokomol. Soed., A24 (1982) 1640. Araimo, L., De Candia. F.,Vittoria, V., Peterlin, A,, J. Polym. Sci., Polym. Phys. Ed., 16(1978) 2087. De Candia, F., Russo, R., F., Vittoria,V., Peterlin. A,, J. Polym. Sci.. Polym. Phys.Ed.. 20 (1982) 269. Asfour, A.-F. A., Saleem, M., De Kee, D., Harrison, B., J. Appl. Polym. Sci., 38 (1989) 1503, Hedenqvist, M., Angelstok, A., Edsberg, L.. Larsson, P.T., Gedde, U.W., Polymer, 37 (1996) 2887. Stern. A. S., Sampat, S. R., Kulkarni, S. S., J. Polym. Sci., Part B Polym. Phys., 24 (1986) 2149. Phillips. J.C., Peterlin, A,, Polym. Eng. Sci., 23 (1983) 734. Ng. H. C.. Leung. W. P., Choy, C. L.. J..Polym.Sci., Polym.Phys. Ed.. 23 (1985) 973. Markevich, M.A., Stogova, V.N., Gorenberg, A.Ya., Vysokomol. Soed.. A33 (1991) 132. Liitzow, N., Tihminlioglu, A,, Danner. R.P.. Duda, J.L., DeHaan, A,, Warnier, G., Zielinski, J.M., Polymer, 40 (1999) 2797. Corbin, G.A.. Cohen, R.E., Baddour, R.F., J. Appl. Polym. Sci.. 30 (1985) 1407. Ghosh. S.K., J. Appl. Polym. Sci., 27 (1982) 331. Sobolev, I., Meyer, J.A., Stannett, V.T., Szwarc. M., Ind. Eng. Chem., 49 (1957) 441. Koszinowski, J., Piringer, O., Verpackungs Rundschau, 41 (1990) 15. Strandburg, G., De Lassus, P. T., Howell. B. A,. in “Barrier Polymers and Packaging”, Ed. Koros. W. J.. ACS Symposium Series, Nr., 423, Washington DC, 1990, pp. 333. Michaels, A.S., Baddour,R.F. ,Bixler,H.J... Choo. C.Y.. Ind. Eng. Chem.,Proc. Des. Dev., l(1962) 14. Serota, D.G., Meyer. M.C., Autian, J., J. Pharm. Sci.. 61 (1972) 416. He, Z., Hammond. G.S., Weiss. R.G.. Macromolecules, 25 (1992) 501. Theodorou, E., Paik, J. S., Packaging. Techn. Sci.. 5 (1992) 21.
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530
Appendix I
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3
3
4
4
“ACH”
“ACCH2”
“ACCH2”
2
2
2
2
“ACH”
‘.C=c”
“C=C“
“C-C”
“C-C”
13
12
11
10
9
8
7
6
5
4
1
“CH2”
2
2 3
1 1
“CH2” “CH2”
“C-C”
1
1
“CH2”
Sub Group Number
Main Group Number
Main Group
Sub Group
1.0396
1.2663
,3652
,5313
,6605
,8886
1.1173
1.1167
1.3454
,2195
,6744 ,4469
27.044 26.036
.66
12.01
13.018
24.020
25.028
26.036
26.036
27.044
12.010
14.026 13.018
15.034
Group Molecular Weight
Sub
,968
.12
.4
,485
,676
,988
367
1.176
0
.54 ,228
,848
,9011
(Rk)
Surface Area (Qr)
Volume
Group
Table 1: UNIFAC group volume (Rk) and surface area (Qk) parameters.
Appendix I1
2-methyl propane 3 C H 3 , l CH Neopentane 4 CH3,l C Hexene-l 1 CH3.3 CH2.1 CH2=CH Hexene-2 2 CH3.2 CH2.1 CH=CH 2-methyl-1-hutene 2 CH3,l CH2.1 CH2=C 2-Methyl-1-hutene 2 CH3.1 CH=C 2.3-dimethylhutene 4 CH3,l C=C Naphthaline 8 ACH. 2 AC Styrene 1 CH2=CH. 5 ACH, 1 AC Toluene 5 ACH. 1 ACCH3 Ethylbenzene 1 CH3.5 ACH, 1 ACCH2
Hexane 2 CH3.4 CH2
Example
Reactivity in Molecular Crystals Copyright @ K d a o r h a Ltd .Tokyo. 1999
Edited by Yuli Ohashi
43.044 42.036 29.018 59.044 58.036 45.018 31.034 30.026
1.448 1.18 .948 1.728 1.42 1.188 1.088
.78
1.6724 1.4457 .998 1.9031 1.6764 1.242 1.145 ,9183 ,6908 ,9183
19 20 21 22 23 24 25 26 27 28
“CWCO”
“CH2CO”
THO“
“CH3COO”
“CHZCOO”
“HCOO”
“CH30”
“CH20”
“CH-0”
“FCH2O”
9
9
10
11
11
12
13
13
13
13
“CH2CO”
“CH2CO”
“CHO”
“CCOO”
“CCOO”
“HCOO”
“CH20”
“CH20”
“CH20”
“CH20”
30.026
29.018
.68
3952
18
“‘ACOH”
8
“ACOH”
1.1
18.016
1.4
.92
17
“H20”
7
“H20”
29.018
32.042
1.432
1.4311
16
“CH3OH’
6
“CH30H”
,468
17.GO8
1.2
1
15
“OH”
5
“OH”
25.028
,348
,8121
14
“ACCH”
4
“ACCH2”
(Qk)
(Rk)
Sub Group Molecular Weight
Surface Area
Group Volume
Sub Group Number
Sub Group
Main Group Number
Main Group
Cumene 2 CH3.5 ACH. I ACCH Propanol-2 2 CH3.1 CH, 1 OH Methanol 1 CH30H Water 1H20 Phenol 5 ACH, 1 ACOH Butanone 1 CH3.1 CH2.1 CH3CO Pentanone-3 2 CH3,l CH2,l CH2CO Propionic aldehyde 1 CH3.1 CH 2, l CHO Butyl acetate 1 CH3,3 CH2.1 CH3COO Methyl propionate 2 CH3.1 CH2COO Ethyl forrnate 1 CH3,l CH2.1 HCOO Dimethyl ether 1 CH3.1 CH3CO Diethyl ether 2 CH3,l CH 2, l CH2 0 Diisopropyl ether 4 CH3.1 CH, 1 CHO Tetrahydrofuran 3 CH2.1 THF
Example
F’ 2
a.
k-
3m
t d
wl w
1.3692 1.1417
30
31 32 33 34 35
36 37 38 39 40 41 42 43
“CH2NH2”
“CHNH2”
“CH3NH”
“CH2NH”
“CHNH”
“CH3N”
“CH2N”
”‘ACNH2”
“CSH5N”
“CSH4N”
“C5H3N”
“CH3CN”
TH2CN”
“COOH”
14
14
15
15
15
16
16
17
18
18
18
19
19
20
“CNH2”
“CNH2”
“CNH”
“CNH”
“CNH”
(C)3N”
“( C)3N”
“ACNH2”
“pyridine”
“pyridine”
“pyridine”
“CCN”
“CCN”
“COOH”
“
1.5959
29
“CH3NH2”
1.3013
1.6434
1.8701
2.667
2.8332
2.9993
1.06
,9597
1.1865
,9795
1.207
1.4337
(Rk)
14
“CNH2”
Group Volume
Sub Group Number
Sub Group
Main Group Number
~
Group
Main
1.224
1.416
1.724
1.553
1.833
2.113
,816
,632
.94
.624
,936
1.244
,924
1.236
1.544
(ad
Surface Area
Sub
45.018
40.044
41.052
77.082
78.090
79.098
28.034
28.034
29.042
28.034
29.042
30.50
29.042
30.50
31.058
Molecular Weieht
Group
Methylamine 1 CH3NH2 Ethylamine 1 CH3.1 CHNH2 Isopropylamine 2 C H 3 , l CHNH2 Dimethylamine 1 CH3,l CH3NH Diethylamine 2 C H 3 , l C H 2 , l CH2NH Diisopropy lamine 4 CH2,l CH. 1 CHNH Trimethylamine 2 CH3,l CH3N Triethylamine 3 CH3.2 CH2,l CH2N Aniline 5 ACH, 1 ACNH2 Pyridine 1 CSHSN 2-Methylpyridine 1 CH3,l C5H4N 2,3-Dimethylpyridine 2 CH3.1 C5H3N Acetonitrile 1 CH3CN Propionitrile 1 CH3.1 CHZCN Acetic acid 1 CH3.1 COOH
Example
wl w w
1.448 2.41 2.184 2.91 ,844 1.868
1.8016 2.87 2.6401 3.39 1.1562 2.0086
50 51 52 53 54 55 56 57 58
”CC12”
“CHC13”
“CC13”
“CC14”
“ACCl”
“CH3N02”
“CH2N02”
“CHN02”
”ACN02”
22
23
23
24
25
26
26
26
27
“CC12”
“CC13”
“CC13”
“CC14’
“ACCI“
“CN02”
“CN02”
“CN02”
“ACN02”
1.4199
1.104
1.248
1.684
2.0606
49
“CHC12”
22
“CC12“
1.5544
1.988
2.2564
48
“CH2C12”
22
“CC12”
1.56
47.467
.724
1.0106
47
“CCI”
21
“CCI”
1.7818
48.475
,952
1.238
46
“CHCI”
21
“CCI”
58.018
59.026
60.034
61.042
47.467
153.838
118.381
119.389
82.924
83.932
84.940
49.483
1.264
1.4654
45
“CH2Cl”
21
“CCI”
46.026
1S32
1.528
44
“HCOOH”
20
(Qk)
(Rk)
“COOH”
Sub Group Molecular Weight
Surface Area
Group Volume
Sub Group Number
Sub Group
Main Group Number
Main Group
Formic acid 1 HCOOH Butane-1-chloro 1 CH3.2 CH2,l CH2CI Propane-2-chloro 2 CH3.1 CHCI 2-Methylpropane-2-chloro 3 CH3,l CCI Methane-dichloro 1 CH2C12 Ethane-1,I -dichloro 1 Ch3.1 CHC12 Propane-2.2 dichloro 2 Ch3.1 CC12 Chloroform 1 CHC13 Ethane-l,l,l-trichloro 1 CH3.1 CC13 Methane-tetrachloro 1 CC14 Benzene-chloro 5 ACH, 1 ACCl Nitromethane 1 CH3N02 Propane- 1-nitro 1 CH3.1 CH2,l CH2N02 Propane-2-nitro 2 Ch3.1 CHNO2 Benzene-nitro 5 ACH. 1 ACN02
Example
P
w
VI
,784 2.472
1.0613 2.8266
66 67 68 69
“CH-C”
“C-C”
“Me2SO”
“ACRY ’‘
.‘CI(C=C)’.
34
34
35
36
37
38
“C-C”
“C-C”
“Me2SO”
“ACRY”
“CICC”
“ACF”
“DMF”
“DMF’
71.09 2.12
2.6322
73
“DMF-2”
39
73.09 2.736
72
“DMF-1”
39
3.0856
,6948
71
“ACF”
35.45 31.01
,724
,791
70
53.06
78.131
24.020
25.028
60.052
96.090
Molecular Weight
,524
2.052
2.3144
1.088
79.916
,832
.9492
65
“Br”
33
“Br” 1.292
126.92
.YY2
1.264
64
“I”
32
“I”
2.248
2.4088
63
“(CH20H)2”
31
“DOH”
2.484
3.168
62
“furfural”
30
“furfural”
47.100
1.368
1.651
61
“CH2SH”
29
“CH3SH”
48.108
1.676
1.877
60
“CH3SH”
29
“CH3SH”
76.142
1.65
2.057
59
“CS2”
28
“CS2”
(Qk)
(Rk)
Sub
Group
Surface Area
Group Volume
Sub Group Number
~
Sub Group
Main Group Number
Main Group
N.N-Diethylformarnide 2 CH3.1 HCON(CH2)2
1 DMF
Carbon disulfide 1c s 2 Methanethiol 1 CH2SH Ethanethiol 1 CH3.1 CH2SH Furfural 1 furfural 1,2-Ethanediol 1 DOH Iodoe thane 1 CH3.1 CH2.1 I Bromoethane 1 CH3,l CH2.1 Br Hexyne-1 1 CH3.3 CH2. I CH=C Hexyne-2 2 CH3,2 CH2.1 CkC Dimethylsulfoxide 1 DMSO Acrylonitrile 1 acrylonitrile Ethene-trichloro 1 C H X , 3 CI-(C=C) Hexafluorobenzene 6 ACF N.N-Dimethylformamide
Example
84 85
86 87 88
“COO”
“SiH3”
“SiH2”
“SiH”
“Si”
“SiH20”
“SiHO”
“SiO”
“NMP
“CCL3F”
“CCL2F”
“HCCL2F”
41
42
42
42
42
43
43
43
44
45
45
45
“COO”
“SiH2”
“SiH2”
“SiH2”
“SiH2”
“SiO”
“SiO”
‘SO”
“NMP”
“CCLF”
“CCLF’
“CCLF’
83
2.4060
2.2287
3.0356
3.981
1.1044
1.303
1.4838
1.047
81 82
1.2853
1.4443
1.6035
1.38
1.0105 .615
80
79
78
77
75 76
“CF2” “CF”
40 40
“CF2” “CF2”
2.116
102.924
101.916
137.36
2.644 1.916
99.13
44.085
,4657 3.2
45.093
46.101
.7639
1.0621
28.086
29.094
,7494 .4099
30.102
1.0063
31.110
44.010
1.2 1.2632
50.01 31.01
.92 .46
69.01
1.38
1.406
74
“CF3”
40
(Qk)
(Rk)
“CF2”
Sub Group Molecular Weight
Surface Area
Group Volume
Sub Group Number
Sub Group
Main Group Number
Main Group
Perfluorometh ylcyclohexane 1 CF3,5 CF5, 1 CF Methyl acrylate 1 CH3.1 CH2=CH, 1 COO Methylsilane 1 CH3.1 SiH3 Diethylsilane 2 CH3.2 C H 2 , l SiH2 Heptamethyltrisiloxane 7 CH3.2 SiO, 1 SiH Heptamethyldisiloxane 6 C H 3 , l SiO, 1 Si 1,3-Dimethyldisiloxane 3 CH3.1 SiH20,l SiH2 1,1,3,3-Tetramethyldisiloxane 4 CH3.1 SiHO, 1 SiH Octamethylcyclotetrasiloxane 8 CH3.4 SiO N-Methylpyrrolidone 1 NMP Trichlorofluoromethane 1 CC13F Tetrachloro-1.2-difluorethane 2 CC12F Dichlorofluorome thane 1 HCCL2F
Perfluorohexane 2 CF3.5 CF2,l CF
Example
o\
wl w
61.051 60.053 47.098 46.090
1.904 1.592 1.368 1.060
2.1226 1.8952 1.6130 1.3863
100 101 102 103
“C2H502”
“C2H402”
“CH3S”
“CH2S”
47
47
48
48
“OCCOH”
“CH2S”
“CH2S”
“OCCOH”
70.069
1.812
2.4054
99
“CON( CH2)2”
46
“CON”
71.077
2.120
2.6322
98
“CONCH3CH2”
46
“CON”
72.085
2.428
2.8589
97
“CON( CH3)2”
46
“CON’
58.059
1.488
1.9637
96
“CONHCH2“
46
“CON”
59.067
1.796
2.1905
95
“CONHCH3”
46
“CON”
44.033
1.248
1.4515
94
“CONH2”
46
“CON”
120.914
2.376
2.6243
93
“CCL2F2”
45
“CCLF”
104.459
2.100
2.1721
92
“CCLF3”
45
“CCLF”
86.469
1.828
1.9670
91
“HCCLF2”
45
”CCLF”
85.461
1.8174
1.648
90
”CCLF2”
45
“CCLF”
67.471
1.416
45
“CCLF”
1.6493
89
“HCCLF”
Sub Group Molecular Weieht
(Qk)
Surface Area
Group Volume (Rk)
Sub Group Number
Sub Group
Main Group Number
Main Group
1-Chloro-I .2.2,2-tetrafluoroethane 1 CF3. 1 HCClF 1,2-Dichlorotetrafluoroethane 2 CCIF2 Chlorodifluorome thane 1 HCCIF3 Chlorotrifluorornethane 1 CClF3 Dichlorodifluoromethane 1 CC12F2 Acetarnid 1 CH3.1 CONH2 N-Methylacetamid 1 CH3.1 CONHCH3 N-Ethylacetamid 2 CH3.1 CONHCH2 N.N-Dimethylethylacetamid 2 CH3.1 CON(CH3)2 N.N-Methylethylacetamid 2 CH3,l CONCH3CH2 N.N-diethy lacetamid 3 CH3.1 CON(CH2)2 2-Ethoxyethanol 1 CH3.1 CH2,l C2H502 2-Ethoxy-1-propano1 2 CH3.1 CH2.1 C2H402 Dimethylsulfide 1 CH3.1 CH3S Diethylsulfide 2 CH3.1 CH2.1 CH2S
Example
4
w
VI
4
9$
b h
C4H3S
C4H3S
49
50
SO
50
Morpholine
Thiophene
Thiophene
Thiophene
C4H3S
Morph
“CHS”
48
“CHZS”
Sub Group
Main Group Number
Main Group
108
107
106
105
104
Sub Group Number
2.5241
2.6908
2.8569
3.4740
1.580
1.860
2.140
2.796
,748
(Qk)
(Rk) 1.1589
Surface Area
Group Volume
82.125
83.133
84.140
86.110
45.082
Sub Group Molecular Weight
Diisopropylsulfide 4 CH3,l CH. 1 CHS morpholine 1 Morph Thiophene 1 C4H4S 2-Methy lthiophene 1 CH3.1 C4H3S 2.3-Dimethylthiophene 2 C H 3 , l C4H2S
Example
B
b ‘ci
00
wl w
Appendix II
539
Table 2: UNIFAC group interaction parameters for prediction of vapor-liquid equilibria at temperature between 250 and 425 K. (Hansen et al., 1991)
I “CH2” 1 “CH2”
1 “CH2” 1 “CH2”
1 “CH2” 1 “CH2”
1 “CH2” 1 “CH2”
1 “CH2”
I “CH2” 1 “CH2” 1 “CH2”
1 “CH2” 2 “C=C” 2 “C=C” 2 “C=C” 2 “C=C” 2 “C=C” 2 “C=C” 2 “CXC” 2 “C=C” 2 “C=C” 2 “C=C” 2 “C=C” 2 “C=C” 2 “C=C”
1 “CH2” 0 5 “OH” 986.5 9 “CH2CO” 476.4 13 “CH20” 251.5 17 “ACNH2” 920.7 21 “CC1” 35.93 25 “ACCI” 11.44 29 “CH3SH” 184.4 33 “Br” 479.5 37 “CICC” 4.189 41 “COO” 387.1 45 “CCLF” -5.869 49 Morpholine 216.1
2 “CZC” 86.02 6 “CH30H” 697.2 10 T H O ” 677 14 “CNH2” 391.5 18 “pyridine” 287.7 22 “CC12” 53.76 26 “CN02” 661.5 30 “furfural” 354.5 34 “C-C” 298.9 38 “ACF” 125.8 42 “SiH2” 450.4 46 “CON” 390.9 50 Thiophene 92.09
3 “ACH” 61.13 7 “H20” 1318 11 “CCOO” 232.1 15 “CNH” 255.7 19 “CCN” 597 23 “CC13” 24.9 27 “ACNO2” 543 31 “DOH” 3025 35 “Me2SO” 526.5 39 “DMF’ 485.3 43 “SiO” 252.7 47 “OCCOH” 553.3
4 “ACCH2” 76.5 8 “ACOH” 1333 12 “HCOO” 507.0 16 “(C)3N” 206.6 20 “COOH” 663.5 24 “CC14” 104.3 28 “CS2” 153.6 32 “I” 335.8 36 “ACRY” 689 40 “CF2” -2.859 44 “NMP” 220.3 48 “CH2S” 187
1 “CH2” -35.36 5 “OH” 524.1 9 “CH2CO” 182.6 13 “CH20” 214.5 17 “ACNH2” 749.3 21 “CCI” -36.87 25 “ACC1” 100.1 29 “CH3SH” 0 33 “Br” 183.8 37 “CICC” -66.46 41 “COO” 48.33 4s “ C C L F 0 49 Morpholine 62.56
2 “C=C” 0 6 “CH30H” 787.6 10 T H O ” 448.8 14 “CNH2” 240.9 18 “pyridine” 280.5 22 “CC12” 58.55 26 “CN02” 357.5 30 “furfural” 262.9 34 “C-C” 31.14 38 “ACF” 359.3 42 “SiH2” 0 46 “CON” 200.2 50 Thiophene 0
3 “ACH” 38.81 7 “H20” 270.6 11 “CCOO” 37.85 15 “CNH” 163.9 19 “CCN” 336.9 23 “CC13” -13.99 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 179.0 39 “DMF” -70.45 43 ‘ S O ” 0 47 “OCCOH” 268.1
4 “ACCH2” 74. 15 8 “ACOH” 526.1 12 “HCOO” 333.5 16 “(C)3N” 61.11 20 “COOH” 318.9 24 “CC14” -109.7 28 “CS2” 76.3 32 “I” 0 36 “ACRY” -52.87 40 “CF2” 449.4 44 “NMP” 86.46 48 “CH2S” -617
540
Appendix I I
3 “ACH” 3 “ACH” 3 “ACH” 3 “ACH” 3 “ACH” 3 “ACH” 3 “ACH” 3 “ACH” 3 “ACH” 3 “ACH” 3 “ACH” 3 “ACH”
3 “ACH”
4 “ACCH2” 4 “ACCH2” 4 “ACCH2” 4 “ACCH2” 4 “ACCH2” 4 “ACCH2” 4 “ACCH2” 4 “ACCH2” 4 “ACCH2” 4 “ACCH2” 4 “ACCH2” 4 “ACCH2” 4 “ACCH2”
1 “CH2” -11.12 5 “OH” 636.1 9 “CH2CO” 25.77 13 “CH20” 32.14 17 “ACNH2” 648.2 21 “CCI” -18.81 25 “ACCI” 187.0 29 “CH3SH” -1 0.43 33 “Br” 261.3 37 “CICC” -259.1 41 “COO” 103.5 45 “CCLF’ -88.11 49 Morpholine -59.58
2 “C=C” 3.446 6 “CH30H” 637.3 10 “CHO” 347.3 14 “CNH2” 161.7 18 “pyridine” 4.449 22 “CC12” -144.4 26 “CN02“ 168 30 “furfural” -64.69 34 “C-c“ 0 38 “ACF” 389.3 42 “SiH2” 432.3 46 “CON” 0 50 Thiophene -39.16
3 “ACH” 0 7 “H20” 903.8 11 “CCOO” 5.994 15 “CNH” 122.8 19 “CCN” 212.5 23 “CC13” -231.9 27 “ACN02” 194.9 31 “DOH” 210.4 35 “Me2SO” 169.9 39 “DMF” 245.6 43 “SiO” 238.9 47 “OCCOH” 333.3
4 “ACCH2” 167 8 “ACOH” 1329 12 “HCOO” 287.1 16 “(C)3N” 90.49 20 “COOH” 537.4 24 “CC14” 3 28 “CS2” 52.07 32 “I” 113.3 36 “ACRY” 383.9 40 “CF2” 22.67 44 “NMP” 30.04 48 “CH2S” 0
1 “CH2” -69.7 5 “OH” 803.2 9 “CH2CO” -52.1 13 “CH20” 213.1 17 “ACNH2” 664.2 21 “CCI” -114.1 25 “ACCI” -21 1.8 29 “CH3SH” 393.6 33 “Br” 210.0 37 “CICC’ -282.5 41 “COO” 69.26 45 “ C C L F 0 49 Morpholine -203.6
2 “C=C” -113.6 6 “CH30H” 603.2 10 T H O ” 586.6 14 “CNH2” 19.02 18 “pyridine” 52.8 22 “CC12” -111 26 “CN02” 3629 30 “furfural” 48.49 34 “C-C” 0 38 “ACF’ 101.4 42 “SiH2” 0 46 “CON” 0 50 Thiophene 184.9
3 “ACH” -146.8 7 “H20” 5695 11 “CCOO” 5688 15 “CNH” 49.29 19 “CCN” 6096 23 “CC13” 80.25 27 “ACN02” 4448 31 “DOH” 4975 35 “Me2SO” 4284 39 “DMF’ 5629 43 “SiO” 0 47 “OCCOH” 421.9
4 “ACCH2” 0 8 “ACOH” 884.9 12 “HCOO” 197.8 16 “(C)3N” 23.5 20 “COOH” 87.23 24 “CC14 -141.3 28 “CS2” -9.451 32 “I” 259.0 36 “ACRY” -1 19.2 40 “CF2” 0 44 “ N M P 46.38 48 “CH2S” 0
Appendix
5 “OH” 5 “OH” 5 “OH”
5 “OH” 5 “OH” 5 “OH” 5 “OH”
5 “OH” 5 “OH” 5 “OH” 5 “OH“
5 “OH” 5 “OH”
6 “CH30H” 6 “CH30H” 6 “CH30H” 6 “CH30H” 6 “CH30H” 6 “CH30H” 6 “CH30H” 6 “CH30H” 6 “CH30H”
6 “CH30H” 6 “CH30H” 6 “CH30H” 6 “CH30H”
II
1 THY 156.4 5 “OH” 0 9 “CH2CO” 84 13 “CH20” 28.06 17 “ACNH2” -52.39 21 “CC1” 75.62 25 “‘ACCI” 123.5 29 “CH3SH” 147.5 33 “Br” 133.4 37 “ C I C C 225.8 41 “COO” 190.3 45 “CCLF’ 72.96 49 Morpholine 104.7
2 “C=C“ 457 6 “CH30H” -1 37.1 10 “CHO” -203.6 14 “CNH2” 8.642 18 “pyridine” 170 22 “CC12” 65.28 26 “CN02” 256.5 30 “furfural” -120.5 34 “C-C” 727.8 38 “ A C F 44.78 42 5 H 2 ” -817.7 46 “CON” -382.7 50 Thiophene 57.65
3 “ACH” 89.6 7 “H20” 353.5 11 “CCOO” 101.1 15 “CNH” 42.7 19 “CCN” 6.712 23 “CC13” -98.12 27 “ACN02” 157.1 31 “DOH” -318.9 35 “Me2SO” -202.1 39 “ D M F -143.9 43 ‘ S O ” 0 47 “OCCOH” -248.3
4 “ACCH2” 25.82 8 “ACOH“ -259.7 12 “HCOO” 267.8 16 “(C)3N” -323 20 “COOH” 199 24 “CC14” 143.1 28 “CS2” 488.9 32 “I” 313.5 36 “ACRY” 74.27 40 “CF2” 0 44 “NMP” -504.2 48 “CH2S” 0
1 “CH2” 16.51 5 “OH” 249.1 9 “CH2CO” 23.39 13 “CH20” -128.6 17 “ACNH2” 489.7 21 “CCI” -38.32 25 “ACCI” -25.25 29 “CH3SH” -17.50 33 “Br” 106.3 37 “CICC” 33.47 “COO” 165.7 41 “COO” -52.1 49 Morpholine -59.4
2 “C=C” -12.52 6 “CH30H” 0 10 ‘ T H O ” 306.4 14 “CNH2” 359.3 18 ”pyridine” 580.5 22 “CC12” -1 02.5 26 ”CN02” 75. I4 30 ”furfural” 0 34 “C-C” 0 38 “ACF” 48.25 ’‘ SiH2” 0 42 “SiH2” 0 50 Thiophene 46.01
3 “ACH” -50 7 “H20” -181 11 “CCOO” -10.72 15 “CNH” -20.98 19 “CCN” 53.28 23 “CC13” -139.4 27 “ACNO2” 0 31 “ D O H -119.2 35 “Me2SO” -399.3 39 “DMF” -172.4 “SiO” 0 43 “SiO” 0
4 “ACCH2” 44.5 8 “ACOH” -101.7 12 “HCOO” 179.7 16 “(C)3N” 53.9 20 “COOH” -202.0 24 “CC14” 44.76 28 “CS2” -3 1.09 32 “I” 212.1 36 “ACRY” -5.224 40 “CF2” 0 “NMP 0 44 “NMP” 37.63
541
542
Appendix II
7 “H20” 7 “H20” 7 “H20” 7 “H20” 7 “H20” 7 “H20” 7 “H20” 7 “H20” 7 “H20’ 7 “H20” 7 “H20” 7 “H20” 7 “H20”
8 “ACOH” 8 “ACOH”
8 “ACOH” 8 “ACOH” 8 “ACOH”
8 “ACOH”
8 “ACOH” 8 “ACOH”
8 “ACOH” 8 “ACOH” 8 “ACOH” 8 “ACOH” 8 “ACOH”
37 “CICC” 0 41 “COO” -197.5 45 “ C C L F 0 49 Morpholine 407.9
2 “CZC” 496.1 6 “CH30H” 289.6 10 T H O ” -1 16.0 14 “CNH2” 48.89 18 “pyridine” 459 22 “CC12” 370.4 26 “CN02” 220.6 30 “furfural” 188 34 “C-C’ 0 38 “ACF’ 0 42 “SiH2” -363.8 46 “CON” 835.6 50 Thiophene 0
3 “ACH” 362.3 7 “H20” 0 11 “CCOO” 72.87 15 “CNH” 168 19 “CCN” 112.6 23 “CC13” 353.7 27 “ACNO2” 399.5 31 “DOH” 12.72 35 “Me2SO” -139 39 “DMF” 319 43 “SiO” 0 47 “OCCOH” 19.6
4 “ACCH2” 317.6 8 “ACOH” 324.5 12 “ H C O O 0 16 “(C)3N” 304 20 “COOH” -14.09 24 “CC14” 497.5 28 “CS2” 887.1 32 “I” 0 36 “ACRY” 160.8 40 “CF2” 0 44 “NMP’ 452.2 48 “CH2S” 0
1 “CH2” 275.8 5 “OH” 451.6 9 “CH2CO” -356.1 13 “CH20” -162.9 17 “ACNH2” 119.9 21 “CCI” 0 25 “ACCI”
2 ‘‘C=C’’ 217.5 6 “CH30H” -265.2 10 “CHO” -271.1 14 ”CNH2” 0 18 “pyridine” -305.5 22 “CC12” 0 26 “CN02”
3 “ACH” 25.34 7 “H20” 401.8 11 “CCOO” 49.4 15 “CNH” 0 19 “CCN” 0 23 “CC13” 0 27 “ACN02”
4 “ACCH2” 244.2 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 408.9 24 “CC14” 1827 28 “CS2”
691.5 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO” 494.2 45 “CCLF” 0 49 Morpholine 0
0 30 “furfural” 0 34 “C- C” 0 38 “ A C F 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 1005
0 31 “DOH” 487.1 35 “Me2SO” 0 39 “DMF” 0 43 ‘ S O ” 0 47 “OCCOH” 0
8484 32 “1” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP’ 459.0 48 “CH2S” 0
1 “CH2” 300 5 “OH” -229.1 9 “CH2CO -195.4 13 “CH20” 540.5 17 “ACNH2” 243.2 21 “CCI” 325.4 25 “ACCI” 133.9 29 “CH3SH” 0 33 “Br” 0
Appendix II
9 “CH2CO”
9 “CH2CO” 9 “CH2CO“ 9 “CHZCO” 9 “CH2CO” 9 “CH2CO”
9 “CH2CO” Y “CH2CO”
9 “CH2CO” 9 “CH2CO” Y “CH2CO”
Y “CH2CO” 9 -’CH2CO”
10 T H O ” 10 “CHO”
10 T H O ” 10 T H O ” 10 T H O “
10 “CHO“
10 “CHO” 10 T H O ” 10 T H O ” 10 T H O ” 10 ‘ T H O ” 10 “CHO” 10 “CHO”
1 “CH2” 26.76 5 “OH” 164.5 9 ”CH2CO” 0 13 “CH20” -103.6 17 “ACNH2” 6201 21 “CCI” -191.7 25 “ACCI” -1 19.8 29 “CH3SH” 46.28 33 “Br” 245.2 37 “CICC’ -34.57 41 “COO” -18.8 45 “CCLF” 0 49 Morpholine 0
2 “C=C” 42.92 6 “CH30H” 108.7 10 T H O ” -37.36 14 “CNH2” 0 18 “pyridine” 7.341 22 “CC12” -130.3 26 “CN02” 137.5 30 “furfural” -163.7 34 “C-C“ -246.6 38 “ACF” 0 42 “SiH2” -588.’) 46 “CON” 0 50 Thiophene -162.6
3 “ACH” 140.1 7 “H20” 472.5 11 “CCOO” -213.7 15 “CNH” -174.2 19 “CCN” 481.7 23 “CC13” -354.6 27 “ACN02” 548.5 31 “DOH” 71.46 35 “Me2SO” 44.58 39 “DMF” 41.7 43 “SiO” 0 47 “OCCOH” 37.54
4 “ACCH2” 365.8 8 “ACOH” -133.1 12 “HCOO” -190.4 16 “(C)3N” -169 20 “COOH” 669.4 24 “CC14” -39.2 28 “CS2” 216.1 32 “I” 53.59 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
1 “CH2” 505.7 5 “OH” 529.0 9 “CH2CO” 128 13 “CH20” 304.1 17 “ACNH2” 0 21 “CCI” 751.9 25 “ACC1” 0 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 172.4 41 “COO” -275.5 45 “CCLF” 0 49 Morpholine 0
2 “CXC” 56.3 6 “CH30H” -340.2 10 T H O ” 0 14 “CNH2” 0 18 ”pyridine” 0 22 “CC12” 67.52 26 “CN02” 0 30 “furfural” 0 34 “C-C” 0 38 “ A C F 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” 23.39 7 “H20” 48.08 11 “CCOO” -110.3 15 “CNH” 0 19 “CCN” 0 23 “CC13” -483.7 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 0 39 “ D M F -268.8 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” 106 8 “ACOH” -155.6 12 “HCOO” 766.0 16 “(C)3N” 0 20 “COOH” 497.5 24 “CC14” 0 28 “CS2” 0 32 “I” 117.0 36 “ACRY” -339.2 40 “CM” 0 44 “NMP” 0 48 “CH2S” 0
543
544
Appendix II
11 “CCOO” 11 “ C C O O 11 “CCOO”
11 “CCOO” 11 “CCOO” 11
“ccoo”
11 “CCOO” 11 “CCOO” 11 “CCOO” 11 “CCOO” 11 “CCOO” 11 “CCOO” 11 “CCOO”
12 “HCOO” 12 “HCOO” 12 “HCOO” 12 “HCOO” 12 “HCOO” 12 “HCOO” 12 “HCOO” 12 “HCOO” 12 “HCOO” 12 “HCOO” 12 “HCOO” 12 “HCOO” 12 “HCOO”
1 “CH2” 114.8 5 “OH” 245.4 9 “CH2CO” 372.2 13 “CH20” -235.7 17 “ACNH2” 475.5 21 “CCI” -34.74 25 “ACCI” 442.4 29 “CH3SH” 0 33 “Br” 18.88 37 “CICC” -275.2 41 “COO” 560.2 45 “CCLF” 0 49 Morpholine 0
2 “C=C” 132.1 6 “CH30H” 249.6 10 “CHO” 185.1 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” 108.9 26 “CN02” -81.13 30 “furfural” 202.3 34 “C-C” 0 38 “ACF’ 0 42 ”SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” 85.84 7 “H20” 200.8 11 “CCOO” 0 15 “CNH” -73.5 19 “CCN” 494.6 23 “CC13” -209.7 27 “ACN02” 0 31 “DOH” -101.7 35 “Me2SO” 52.08 39 “DMF” 85.33 43 “SiO” 0 47 “OCCOH” 151.8
4 “ACCH2” -170 8 “ACOH” -36.72 12 “HCOO” -241.8 16 “(C)3N” -196.7 20 “COOH” 660.2 24 “CC14” 54.47 28 “CS2” 183 32 “I” 148.3 36 “ACRY” -28.61 40 “CF2” 0 44 “NMP’ 0 48 “CH2S” 0
1 “CH2” 329.3 5 “OH” 139.4 9 “CH2CO” 385.4 13 “CH20” -234.0 17 “ACNH2” 0 21 “CCI” 0 25 “ACCI” 24.28 29 “CH3SH” 103.9 33 “Br” 0 37 “CICC” -1 1.4 41 “COO” -122.34 45 “CCLF’ 0 49 Morpholine 0
2 “CXC” 110.4 6 “CH30H” 227.8 10 ‘THO” -236.5 14 “CNH2” 0 18 “pyridine” -233.4 22 “CC12” 0 26 “CN02” 0 30 “furfural” 0 34 “C-C” 0 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” 18.12 7 “H20” 0 11 “CCOO” 1167 15 “CNH” 0 19 “CCN” -47.25 23 “CC13” -126.2 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 0 39 “DMF’ 308.9 43 “SiO” 0 47 “OCCOH” 0
4 ”ACCH2” 428.0 8 “ACOH” 0 12 “HCOO” 0
16 “(C)3N” 0 20 ”COOH” -268. I 24 “CC14” 179.7 28 “CS2” 0 32 ‘‘1’. 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
Appendix I1 ~~
13 “CH20“ 13 “CH20” 13 “CH20” 13 “CH20” 13 “CH20”
13 “CH20” 13 “CH20” 13 “CH20” 13 “CH20” 13 “CH20”
13 “CH20” 13 “CH20” 13 “CH20“
14 “CNH2“ 14 “CNH2” 14 “CNH2”
14 “CNH2” 14 “CNH2” 14 “CNH2” 14 “ C N H 2 14 “CNH2” 14 “CNH2” 14 “CNH2” 14 “CNH2” 14 “CNH2” 14 “CNH2”
1 “CH2” 83.36 5 “OH” 237.7 9 “CH2CO” 191.1 13 “CH20” 0 17 “ACNH2” 0 21 “CC1” 301.1 25 “ACCI” 134.8 29 “CH3SH” -8.538 33 “BT” -202.3 37 “CICC” 240.2 41 “COO” 417 45 “CCLF” 0 49 Morpholine 0
2 “C=C” 26.5 1 6 “CH30H” 238.4 10 T H O ” -7.838 14 “CNH2” -78.36 18 “pyridine” 213.2 22 ”CC12” 137.8 26 “CNO2” 95.18 30 ”furfural” 0 34 “c‘-C” 0 38 “ACF” -273.Y 42 “SiH2” 1338.0 46 “CON” 0 SO Thiophene 0
3 “ACH” 52.13 7 “H20” -314.7 11 “CCOO” 461.3 15 “CNH” 251.5 19 “CCN” -1 8.5 1 23 “CC13” -154.3 27 “ACN02” 0 31 “DOH” -20.11 35 “Me2SO” 128.8 39 “DMF’ 254.8 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” 65.69 8 “ACOH” -178.5 12 “HCOO” 457.3 16 “(C)3N” 5422 20 “COOH” 664.6 24 “CC14” 47.67 28 “CS2” 140.9 32 “I” -149.5 36 “ACRY” 0 40 “CF2” 0 44 “ N M P 0 48 “CH2S“ 0
1 “CH2” -30.48 5 “OH“ -242.8 Y “CH2CO” 0 13 “CH20” 222.1 17 “ACNH2” -200.7 21 “CCI” 0 25 “ACCI” 30.05 29 “CH3SH“ -70.14 33 “BT” 0 37 “CICC” 0 41 “COO” 0 45 “CCLF“ 0 49 Morpholine 0
2 “C=C“ 1.163 6 “CH3OH” 431.7 10 T H O “ 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” 0 26 “CN02“ 0 30 “furfural“ 0 34 c C” 0 38 “‘ACF” 0 42 “SiH2” 464.4 46 “CON” 0 50 Thiophene 0
3 “ACH” 44.85 7 “H20” -330.4 11 “ccoo” 0 15 “CNH” -107.2 19 “CCN” 147. I 23 “CC13” 0 27 “ACNO2” 0 31 “DOH” 0 35 “ M e 2 S O 0 39 “DMF’ -164.0 43 “SiO” 275.9 47 “OCCOH” 0
4 “ACCH2“ -242.8 8 “ACOH” 0 12 “HCOO“ 0 16 “(C)3N” 41.11 20 “COOH”
“
~
0
24 “CC14” -99.81 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
545
546
Appendix II
15 “CNH” 15 “CNH” 15 CN H ‘I
”
15 “CNH” 15 “CNH”
15 “CNH” 15 “CNH”
15 “CNH” 15 “CNH” 15 “CNH” 15 “CNH” 15 “CNH” 15 “CNH”
16 “(C)3N” 16 “(C)3N” 16 “(C)3N” 16 “(C)3N” 16 “(C)3N” 16 “(C)3N” 16 “(C)3N” 16 “(C)3N” 16 “(C)3N” 16 “(C)3N” 16 “(C)3N” 16 “(C)3N” 16 “(C)3N”
1 “CH2” 65.33 5 “OH” -150 9 “CH2CO” 394.6 13 “CH20” -56.08 17 “ACNH2” 0 21 “CCI” 0 25 “ACCl” -18.93 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO” -38.77 45 “ C C L F 0 49 Morpholine 0
2 “C=C” -28.7 6 “CH30H” -370.3 10 “CHO” 0 14 “CNH2” 127.4 18 “pyridine” 0 22 “CC12” 0 26 “CN02” 0 30 “furfural” 0 34 c-C” 0 38 “ACF” 570.0 42 “SiH2” 448.1 46 “CON” 0 SO Thiophene 0
3 “ACH” -22.31 7 “H20” -448.2 11 “CCOO” 136 15 “CNH” 0 19 “CCN” 147.1 23 “CC13” 0 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 0 39 “DMF’ 0 43 ‘ S O ” -1327.0 47 “OCCOH” 0
4 “ACCH2” 223 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” -189.2 20 “COOH” 0 24 “CC14” 71.23 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
1 “CH2” -83.98 5 “OH” 28.6 9 “CH2CO” 225.3 13 “CH20” -194.1 17 “ACNH2” 0 21 “CCI” 0 25 “ACC1” -181.9 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO” 0 45 “CCLF’ 0 49 Morpholine 0
2 ‘‘C=C’’ -25.38 6 “CH30H” -406.8 10 “CHO” 0 14 “CNH2” 38.89 18 “pyridine” 0 22 “CC12” -73.85 26 “CN02” 0 30 “furfural” 0 34 “C-C” 0 38 “ACF’ -196.3 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” -223.9 7 “H20” -598.8 11 “CCOO” 2889 15 “CNH” 865.9 19 “CCN” 0 23 “CC13” -352.9 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 0 39 “ D M F 22.05 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” 109.9 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” -262.0 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CHZS” 0
“
Appendix I1
17 “ACNH2” 17 “ACNH2” 17 “ACNH2” 17 “ACNH2” 17 “ACNH2” 17 “ACNH2” 17 “ACNH2” 17 “ACNH2” 17 “ACNH2” 17 “ACNH2” 17 “ACNH2” 17 “ACNH2” 17 “ACNH2”
1 “CH2” 1139 5 “OH” -17.4 9 “CH2CO” 450.3 13 “CH20” 0 17 “ACNH2” 0 21 “CCI” 287 25 “ACCI” 617.5 29 “CH3SH” 0 33 “Br” 0 37 “ClCC” 0 41 “COO” -89.42 45 “CCLF” 0 49 Morpholine 0
2 “CZC” 2000 6 “CH30H” -118.1 10 “CHO” 0 14 “CNH2” -15.07 18 “pyridine” 89.70 22 “CC12” 0 26 “CN02” 0 30 “furfural” 0 34 ”C-c” 0 38 “ A C F 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH”
1 “CH2” -101.6 5 “OH” -132.3 9 “CH2CO” 29.1 13 “CH20” -156.1 17 “ACNH2” 117.4 21 “CCI”
2 “C=C” 47.63 6 “CH30H” -378.2 10 “CHO” 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” -35 1.6 26 “CN02” 0 30 “furfural” 0 34 “C-C” 0 38 “ACF -158.8 42 “SiH2” 0 46 “CON” 0 50 Thiophene -136.6
3 “ACH” 31.87 7 “H20” -332.9 11 “CCOO” 0 15 “CNH” 0 19 “CCN” -169.7 23 “CC13” -1 14.7 27 “ACN02” 2845 31 “DOH” 0 35 “Me2SO” 0 39 “ D M F 0 43 “SiO” 0 47 “OCCOH” 0
247.5 7 “H20” -341.6 11 “CCOO” -294.8 15 “CNH” 0 19 “CCN” -281.6 23 “CC13” 0 27 “ACN02” -139.3 31 “DOH” -136.9 35 “Me2SO” 0 39 “ D M F -334.4 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” 762.8 8 “‘ACOH” -253.1 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” -396.0 24 “CC14” 822 28 “CS2” 0 32 “1” 0 36 “ACRY” 0 40 “CF2” 0 44 “ N M P 0 48 “CH2S” 0
~
18 “pyridine” 18 “pyridine” 18 “pyridine” 18 “pyridine”
18 ”pyridine” 18 “pyridine” 18 “pyridine” 18 “pyridine” 18 “pyridine”
18 “pyridine” I X “pyridine”
I8 “pyridine” I X “pyridine“
0 25 “ACCI” 0 29 “CH3SH” 0 33 “Br” -60.78 37 “CICC” 160.7 41 “COO” 0 45 “CCLF” 0 49 Morpholine 0
4 “ACCH2” 49.8 8 “ACOH” -341.6 12 “HCOO” 554.4 16 “(C)3N” 0 20 “COOH” -153.7 24 “CC14” -205.3 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
547
548
Appendix I1
19 “CCN” 19 “CCN” 19 “CCN” 19 “CCN” 19 “CCN” 19 “CCN” 19 “CCN”
19 “CCN” 19 “CCN” 19 “CCN” 1 Y “CCN”
19 “CCN” 19 “CCN”
20 “COOH” 20 “COOH” 20 “COOH” 20 “COOH” 20 “COOH” 20 “COOH” 20 “COOH” 20 “COOH” 20 TOOH” 20 “COOH” 20 “COOH” 20 “COOH” 20 “COOH”
1 “CH2“ 24.82 5 “OH” 185.4 9 “CH2CO” -2873 13 “CH20” 38.81 17 “ACNH2” 777.4 21 “CCI” 4.933 25 “ACCI“ 4.624 29 “CH3SH” 0.4604 33 “Br” -62.17 37 “CICC” 55.77 41 “COO” 120.3 45 “CCLF” 0 49 Morpholine 0
2 “C=C” 40.62 6 “CH30H” 162.6 10 ‘THO” 0 14 “CNH2” -157.3 18 “pyridine” 134.3 22 “CC12” -152.7 26 “CN02” -515 30 “furfural” 0 34 “C-C” -203 38 ‘*ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” -22.97 7 “H20” 242.8 I 1 “CCOO” -266.6 15 “CNH” -108.5 19 ”CCN” 0 23 “CC13” -15.62 27 “ACN02” 0 31 “DOH” 177.5 35 “Me2SO” 0 39 “DMF’ -151.5 43 “SiO” 0 47 “OCCOH” 16.23
4 “ACCH2”
1 “CH2 315.3 5 “OH” -151 9 “CH2CO” -297.8 13 “CH20” -338.5 17 “ACNH2” 493.8 21 “CCI” 13.41 25 “ACCI” -79 08 29 “CH3SH” 0 33 “Br” -95 37 “ C I C C -11.16 41 “COO” -337 45 “CCLF’ 0 49 Morpholine 0
2 “C=C” 1264 6 “CHSOH” 339.8 10 T H O “ -165.5 14 “CNH2” 0 18 “pyridine” -313.5 22 “CC12” 44.7 26 “CN02” 0 30 “furfural” -208.9 34 “C-C” 0 38 “ A C F 0 42 “S1H2” 0 46 “CON” -322.3 50 Thiophene 0
3 “ACH” 62.32 7 “H20” -66.17 11 “CCOO” -256.3 15 “CNH” 0 19 “CCN” 0 23 “CC13” 39.63 27 “ACN02” 0 31 ”DOH” 0 35 “Me2SO” 463.6 39 ” D M F -228.0 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2”
-138.4 8 “ACOH” 0 12 “HCOO” 99.37 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” -54.86 28 “CS2“ 230.9 32 “I” 0 36 “ACRY“ 81.57 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
89.86 8 “ACOH“ -1 1.0 12 “HCOO” 193.9 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” 183.4 28 “CS2” 0 32 “I” 228.4 36 “ACRY” 0 40 “CF2” 0 44 “NMP“ 0 48 “CH2S” 0
Appendix I1
21 “CCI” 21 “CCI” 21 “CCI” 21 “CCI” 21 “CCI” 21 “CCI” 21 “CCI” 21 “CCL” 21 “CCI” 21 “CCI” 21 “CCI” 21 “CCI” 21 “CCI”
22 “CC12” 22 “CC12” 22 “CC12” 22 “CC12” 22 “CC12” 22 “CC12” 22 “CC12” 22 “CC12” 22 “CC12” 22 “CC12” 22 “CC12” 22 “CC12” 22 “CC12”
549
1 “CH2” 91.46 5 “OH” 562.2 9 “CH2CO” 286.3 13 “CH20” 225.4 17 “ACNH2” 429.7 21 “CCI” 0 25 “ACCI” 153.0 29 “CH3SH“ 59.02 33 “Br” 344.4 37 “CICC” -168.2 41 “COO” 63.61 45 “ C C L F 0 49 Morpholine 0
2 “C=C” 40.25 6 “CH30H” 529 10 ‘ T H O ” 47.51 14 “CNH2” 131.2 18 “pyridine” 0 22 “CC12” 108.3 26 “CN02” 32.73 30 “furfural” 0 34 “C-C” 0 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” 4.68 7 “H20” 698.2 11 “CCOO” 35.38 15 “CNH” 0 19 “CCN” 54.32 23 “CC13” 249.2 27 “ACN02” 86.2 31 “DOH” 0 35 “Me2SO” 0 39 “DMF” 0 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” 122.9 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 519.1 24 “CC14” 62.42 28 “CS2” 450.1 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “ C H 2 S 0
1 “CH2” 34.01 5 “OH” 527.6 9 “CH2CO” 82.86 13 “CH20” -197.7 17 “ACNH2” 0 21 “CCI” -84.53 25 “ACCI” 223.1 29 “CH3SH” 0 33 “Br” 315.9 37 “CICC” -91.8 41 “COO” -96.81 45 “CCLF’ 0 49 Morpholine 0
2 ‘*C=C” -23.5 6 “CH30H” 669.9 10 ‘THO” 190.6 14 “CNH2” 0 18 “pyridine” 587.3 22 “CC12” 0 26 “CN02” 108.9 30 “furfural” 0 34 “C-C” 0 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” 121.3 7 “H20” 708.1 11 “CCOO” -133 15 “CNH” 0 19 “CCN” 258.6 23 “CC13” 0 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 215 39 “DMF” 0 43 ‘ S O ” 0 47 “OCCOH” 361.1
4 “ACCH2” 140.8 8 “ACOH” 0 12 ‘ ~ ~ ~ 0 0 7 3 0 16 “(C)3N” -1 41.4 20 “COOH” 543.3 24 “CC14” 56.33 28 “CS2” 0 32 “I” 177.6 36 “ACRY” 0 40 “CF2” 0 44 “NMP’’ 0 48 “CH2S” 0
550
Appendix I1
23 “CC13” 23 “CC13” 23 “CC13” 23 “CC13” 23 “CC13” 23 “CC13” 23 “CC13” 23 “CC13” 23 “CC13” 23 “CC13” 23 “CC13” 23 “CC13” 23 “CC13”
24 “CC14” 24 “CC14” 24 “CC14” 24 “CC14” 24 “CC14” 24 “CC14” 24 “CC14” 24 “CC14” 24 “CC14” 24 “CC14” 24 “CC14” 24 “CC14” 24 “CC14”
1 “CH2” 36.7 5 “OH” 742.I 9 “CH2CO” 552.1 13 “CH20” -20.93 17 “ACNH2“ 0 21 “CCI” -157.1 25 “ACCI” 191.1 29 “CH3SH” 0 33 “Br” 0 37 ”CICC” 111.2 41 “COO” 255.8 45 “CCLF’ 0 49 Morpholine 0
2 “C=C” 5 1.06 6 “CH30H” 649.1 10 “CHO” 242.8 14 “CNH2” 0 18 “pyridine” 18.98 22 “CC12” 0 26 “CN02” 0 30 “furfural” -64.38 34 “C-C” 0 38 “ACF’ 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH”
288.5 7 “H20” 826.7 11 “CCOO” 176.5 15 “CNH” 0 19 “CCN” 74.04 23 “CC13” 0 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 363.7 39 “DMF” 0 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” 69.9 8 “ACOH” 0 12 “HCOO” 235.6 16 “(C)3N” -293.7 20 “COOH” 504.2 24 “CC14” -30.1 28 ”CS2” 116.6 32 “I” 86.4 36 “ACRY“ 0 40 “CF2” 0 44 “NMP” -35.68 48 “CH2S” 565.9
1 “CH2” -78.45 5 “OH” 856.3 9 “CH2CO” 372 13 “CH20” 113.9 17 “ACNH2” 898.2 21 “CCI” 11.8 25 “ACCI” -75.87 29 “CHSSH” 0 33 “Br” 146.6 37 “CICC” 187.1 41 “COO” 256.5 45 “CCLF’ 0 49 Morpholine 0
2 “C=C” 160.9 6 “CH30H” 709.6 10 T H O ” 0 14 “CNH2” 261.1 18 “pyridine” 368.5 22 “CC12” 17.97 26 “CN02” 490.9 30 “furfural” 546.7 34 “C-C” 0 38 “ACF” 215.2 42 “SiH2” 0 46 “CON” 0 50 Thiophene 108.5
3 “ACH” 4.7 7 “H20” 1201 11 “CCOO” 129.5 15 “CNH” 91.13 19 “CCN” 492 23 “CC13” 51.9 27 “ACNOZ” 534.7 31 “DOH” 0 35 “Me2SO” 337.7 39 “DMF” 498.6 43 “SiO” 233.1 47 “OCCOH” 423.1
4 “ACCHZ” 134.7 8 “ACOH” 10000 12 ”HCOO” 351.9 16 “(C)3N” 316.9 20 “COOH” 63 1 24 “CC14” 0 28 “CS2“ 132.2 32 “I” 247.8 36 “ACRY” 369.5 40 “CF2” 0 44 “NMP’ 0 48 “CH2S” 63.95
Appendix I1
25 “ACCI” 25 “ACCI” 25 “ACCI” 25 “ACCI” 25 “ACCI“ 25 “ACCI”
25 “ACCI” 25 “ACCI” 25 “ACCI” 25 “ACCI” 2.5 “ACCI” 25 “ACCI” 25 “ACCI”
26 “CN02” 26 “CN02” 26 “CN02” 26 “CN02” 26 “CN02” 26 “CN02” 26 “CN02” 26 “CN02” 26 ”CN02” 26 “CN02” 26 “CN02” 26 “CN02” 26 “CN02”
1 “CH2” 106.8 5 “OH” 325.7 9 “CH2CO” 518.4 13 “CH20” -25.15 17 “ACNH2“ 334.9 21 “CCI” -129.7 25 “ACCI” 0 29 “CHSSH” 0 33 “Br” 593.4 37 “CICC” 0 41 “COO” -71.18 45 “ C C L F 0 49 Morpholine 0
2 “C=C” 70.32 6 “CH30H” 612.8 10 “CHO” 0 14 “CNH2” 108.5 18 “pyridine” 0 22 “CC12” -8.309 26 “CN02” 132.7 30 “furfural” 0 34 “C-C” 0 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” -97.27 7 “H20” -274.5 11 “CCOO” -171.1 1.5 “CNH” 102.2 19 “CCN” 363.5 23 “CC13” 4.2266 27 “ACNO2” 2213 31 “DOH” 0 35 “Me2SO” 0 39 “DMF” 0 43 “SiO” 0 47 “OCCOH” 434.1
4 “ACCH2” 402.5 8 “ACOH” 622.3 12 “HCOO” 383.3 16 “(C)3N” 2951 20 “COOH” 993.4 24 “CC14” 248.4 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” -209.7 48 “CH2S” 0
1 “CH2” -32.69 5 “OH” 261.6 9 “CH2CO” -142.6 13 “CH20” -94.49 17 “ACNH2” 0 21 “CCI” 113 25 ”ACCI” 132.9 29 “CH3SH” 0 33 “Br” 10.17 37 “ C I C C 10.76 41 “COO” 248.4 45 “CCLF” -218.9 49 Morpholine 0
2 “C=C” -1.996 6 “CH30H” 252.6 10 T H O ” 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” -9.639 26 “CN02” 0 30 “furfural” 0 34 “C-C” -27.7 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 SO Thiophene 4.565
3 “ACH” 10.38 7 “H20” 417.9 11 “CCOO” 129.3 15 “CNH” 0 19 “CCN” ,2827 23 “CC13” 0 27 “ACN02” 533.2 31 “DOH” 139.8 35 “Me2SO” 0 39 “DMF” -223.1 43 “SiO” 0 47 “OCCOH”
4 “ACCH2” -97.05 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” -34.68 28 “CS2” 320.2 32 “I” 304.3 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
n
551
552
Appendix II
27 “ACN02” 27 “ACN02” 27 “ACN02” 27 “ACN02” 27 “ACNO2” 27 “ACN02” 27 “ACN02” 27 “ACN02” 27 “ACN02” 27 “ACNO2” 27 “ACN02” 27 “ACN02” 27 “ACNO2”
28 “CS2” 28 “CS2” 28 “CS2” 28 “CS2” 28 “CS2” 28 “CS2” 28 “CS2” 28 “CS2” 28 “CS2” 28 “CS2” 28 “CS2” 28 “CS2” 28 “CS2”
1 “CH2” 5541 5 “OH” 561.6 9 “CH2CO” 0 13 “CH20” 0 17 “ACNH2” 134.9 21 “CCI” 0 25 “ACCI” 0 29 “CH3SH” 0 33 “Br” 0 37 “CICC’ 0 41 “COO” 0 45 “CCLF” 0 49 Morpholine 0
2 “C=C”
1 “CH2” -52.65 5 “OH“ 609.8 9 “CH2CO” 303.7 13 “CH20” 112.4 17 “ACNH2” 0 21 “CCI” -73.09 25 “ACCI” 0 29 “CH3SH” 0 33 “Br” 0 37 “CICC -47.37 41 “COO” 469.8 45 “CCLF’ 0 49 Morpholine 0
2 “C=C’ 16.62 6 “CH30H” 914.2 10 ‘THO” 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12”
18 “pyridine” 0 22 “CC12” 0 26 “CN02” -85.12 30 “furfural” 0 34 “C-C”
3 “ACH” 1824 7 “H20” 360.7 11 “CCOO” 0 15 “CNH” 0 19 “CCN” 0 23 “CC13” 0 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO”
0
0
0
6 “CH30H” 0 10 “CHO” 0 14 “CNH2” 0
38 0 42 0 46 0 50 0
“ACF”
39 “DMF” 0
“SiH2”
43 “SiO” 0
“CON”
47 “OCCOH” 0
4 “ACCH2” -127.8 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0
20 “COOH” 0 24 “CC14” 514.6 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
Thiophene
0
26 “CN02” 277.8 30 “furfural” 0
34 “ C - c 0 38 “ A C F 0 42 “SiH2” 0
46 “CON” 0 50 Thiophene 0
3 ‘*ACH” 21.5 7 “H20” 1081 11 “CCOO” 243.8 15 “CNH” 0
19 “CCN” 335.7 23 “CC13” -26.06 27 “ACN02” 0
31 “DOH” 0
35 “Me2SO” 0
39 “ D M F 0 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” 40.68 8 “ACOH” 1421 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” 40.71 28 “CS2” 0 32 “I” 292.7 36 “ACRY” 0 40 “CF2” 0
44 “NMP” 0 48 “CH2S” 0
Appendix I1
-7.481 5 “OH” 461.6 9 “CH2CO” 160.6 13 “CH20” 63.71 17 “ACNH2” 0 21 “CCI” -27.94 25 “ACCl” 0 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO’ 0 45 “CCLF” 0 49 Morpholine 0
2 “C=C“ 0 6 “CH30H” 448.6 10 ‘ T H O ” 0 14 “CNH2” 106.7 18 “pyridine” 0 22 “CC12” 0 26 “CN02” 0 30 “furfural” 0 34 “C-C” 0 38 ”ACF” 0 42 “SiH2” 0 46 “CON” 0 SO Thiophene 0
3 “ACH” 28.41 7 “H20” 0 11 “CCOO” 0 15 “CNH” 0 19 “CCN” 161.0 23 “CC13” 0 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 31.66 39 “DMF” 78.92 43 “SiO” 0 47 “OCCOH’ 0
4 “ACCH2” 19.56 8 “ACOH” 0 12 “HCOO” 201.5 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” 0 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 1004 48 “CH2S” -18.27
1 “CH2” -25.31 5 “OH” 521.6 9 “CH2CO” 317.5 13 “CH20” -87.31 17 “ACNH2” 0 21 “CCI” 0 25 “ACCI” 0 29 “CH3SH” 0 33 “Br” 0 37 “ C l C C 0 41 “COO” 43.37 45 “ C C L F 0 49 Morpholine 0
2 “C=C” 82.64 6 “CH30H” 0 10 T H O ” 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” 0 26 “CNO2” 0 30 “furfural” 0 34 ”C-c” 0 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” 157.3 7 “H20” 23.48 11 “CCOO“ -146.3 15 “CNH” 0 19 “CCN” 0 23 “CC13” 48.48 27 “ACN02” 0 31 “DOH” 0 35 “Me2S.O” 0 39 “ D M F 0 43 “SiO” 0 47 “OCCOH” 0
4 ‘;9CCH2” 128.8 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 570.6 24 “CC14” -133.2 28 “CSY 0 32 “I” 0 36 “ACRY” 0 40 “CM” 0 44 “NMP” 0 48 “CH2S” 0
1 “CH2”
29 “CH3SH” 29 “CH3SH” 29 “CH3SH” 29 “CH3SH” 29 “CH3SH” 29 “CH3SH” 29 “CH3SH” 29 “CH3SH” 29 “CH3SH” 29 “CH3SH” 29 “CH3SH” 29 “CH3SH” 29 “CH3SH”
30 “furfural” 30 “furfural”
30 “furfural” 30 “furfural”
30 “furfural” 30 “furfural”
30 “furfural” 30 “furfural” 30 “furfural” 30 “furfural” 30 ”furfural” 30 “furfural” 30 “furlural”
553
554
Appendix II ~~
31 “DOH” 31 “DOH” 31 “DOH” 31 “DOH” 31 “DOH” 31 “DOH” 31 “DOH” 31 “DOH” 31 “DOH” 31 “DOH” 31 “DOH” 31 “DOH” 31 “DOH”
32 “1” 32 “I” 32 “I” 32 “I” 32 “I” 32 “I” 32 “I” 32 “I” 32 “I” 32 “I” 32 “I” 32 “I”
32 “I”
~
~
29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO” 347.8 45 “ C C L F 0 49 Morpholine 0
2 “C=C” 0 6 “CH30H” 240.8 10 “CHO” 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” 0 26 “CN02” 481.3 30 “furfural” 0 34 “C-C” 0 38 “ACF“ 0 42 “SiH2” 0 46 “CON” 0 SO Thiophene 0
3 “ACH” 221.4 7 “H20” -137.4 11 “CCOO” 152 15 “CNH” 0 19 “CCN” 169.6 23 “CC13” 0 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 417.2 39 “ D M F 302.2 43 “SiO” 0 47 “OCCOH” -353.5
4 “ACCH2” 150.6 8 “ACOH” 838.4 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” 0 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” -262.0 48 “CH2S” 0
1 “CH2” 128 5 “OH S01.3 9 “CH2CO” 138 13 “CH20” 476.6 17 “ACNH2” 0 21 “CCI” 0 25 “ACCI” 0 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO” 68.55 45 “CCLF” 0 49 Morpholine 0
2 “C=C” 0 6 “CH30H” 431.3 10 ‘ T H O ” 245.9 14 “CNH2” 0 18 “pyridine” 0 22 ”CC12” 40.82 26 “CN02” 64.28 30 “furfural” 0 34 “C-C” 0 38 “ACF’ 0 42 “SiH2” 0 46 “CON” 0 SO Thiophene 0
3 “ACH” 58.68 7 “H20” 0 11 “CCOO” 2 1.92 15 “CNH” 0 19 “CCN” 0 23 “CC13” 21.76 27 “ACN02” 2448 31 “DOH” 0 35 “Me2SO” 0 39 “DMF’ 0 43 “SiO” 0 47 “OCCOH” 0
4 “ACCHZ” 26.4 1 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 616.6 24 “CC14” 48.49 28 “CS2” -27.45 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP’ 0 48 “CHZS” 0
1 “CH2” 139.9 5 “OH” 267.6 9 “CH2CO” 135.4 13 “CH20” 9.207 17 “ACNH2” 192.3 21 “CCI” 0 25 “ACCI” 0
Appendix I I
33 “Br” 33 “Br” 33 “Br” 33 “Br” 33 “Br” 33 “Br“ 33 “Br”
33 “Br” 33 “Br” 33 “Br” 33 “Br” 33 “Br” 33 “Br”
34 “C-C”
34 “C-c” 34 “C-C” 34 “C-C’ 34 C- C” “
34 “C-C“ 34 “C-C” 34 “C-C” 34 “C-C” 34 “C-C“ 34 ”C-c“
34 “C-C” 34 “C-C”
1 “CH2” -31.52 5 “OH” 72 1.9 9 “CH2CO” -142.6 13 “CH20’ 736.4 17 “ACNH2” 0 21 “CCI” -262.3 25 “ACCI” -185.3 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO” -195.1 45 “CCLF” 0 49 Morpholine 0
174.6 6 “CH3OH” 494.7 10 T H O ” 0 14 “CNH2” 0 18 “pyridine” 42.71 22 “CC12” -174.5 26 “CNO2” 125.3 30 “furfural” 0 34 “C-C” 0 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
1 “CH2” -72.88 5 “OH” 68.95 9 “CH2CO” 443.6 13 “CH20” 0 17 “ACNH2” 0 21 “CCI” 0 25 “ACCI” 0 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 2073 41 “COO” 0 45 “CCLF’ 0 49 Morpholine 0
2 “C=C” 41.38 6 “CH30H” 0 10 T H O ” 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” 0 26 “CN02” 174.4 30 “furfural” 0 34 “C-C” 0 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” -154.2 7 “H20” 0 11 “CCOO” 24.37 15 “ C N H 0 19 “CCN” 136.9 23 “CC13” 0 27 “ACNO2” 4288 31 “DOH” 0 35 “Me2SO” 32.9 39 “DMF” 0 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” 1112 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 5256 24 “CC14” 77.55 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
3 “ACH” 0 7 “H20” 0 11 “CCOO” 0 15 “CNH” 0 19 “CCN” 329.1 23 “CC13” 0 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 0 39 “DMF” -1 19.8 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” 0 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14’ 0 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
555
0 .‘H0330., LP 0 ,,0!S.7 Eb PO8‘8‘ m a . , 6s 0 L.OSzaVIV..SE 0 ‘‘Hoa.. 1E 0 ,,ZON3V7:.LZ 0 .‘€I3377 EZ IE‘ZP,,N33.. 61 0 ,,HN3,, Sl SSLI “0033.>11 9‘9% uOZHv L 9‘EZluH3V>*E
L.OSZaVInSE “OSZaINY,, SE
“OSZaVIn SE ‘.OSZaPlY,>SE ‘,OSZaVI.? SE ..oszaPl3. SE “OSZ~PlY.> SE ‘.OSZawV,>SE ,.oszaVIY,, SE .,oszawY.>SE “OSZaVIn SE ..OSZaVIY,. SE
.,OSZW.7 SE
Appendix 11
37 “ClCC” 37 “ClCC” 37 “ClCC” 37 “CICC” 37 “CICC” 37 “CICC” 37 “CICC” 37 “CICC” 37 “CICC” 37 “CICC” 37 “ClCC” 37 “CICC” 37 “CICC”
38 “ACF“ 38 “ACF’ 38 “ACF“ 38 “ACF’ 38 “ACF” 38 “ACF” 38 “ A C F 38 “ACF” 38 “ACF” 38 “ACF” 38 “ACF” 38 “ACF’ 38 “ACF’
1 “CH2” 47.41 5 “OH” 738.9 9 “CH2CO” 40.9 13 “CH20” -217.9 17 “ACNH2” 0 21 “CCl” 383.2 25 “ACCl” 0 29 “CH3SH” 0 33 “Br” 0 37 “ClCC” 0 41 “COO” 730.8 45 “CCLF” 0 49 Morpholine 0
2 “C=C” 124.2 6 “CH30H” 528 10 “CHO” 183.8 14 “CNH2” 0 18 “pyridine” 281.6 22 “CC12” 301.9 26 “CN02” 379.4 30 “furfural” 0 34 “C-C” 631.5 38 “ACF’ 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” 395.8 7 “H20” 0 11 “CCOO” 611.3 15 “CNH” 0 19 “CCN” 335.2 23 “CC13” -149.8 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 0 39 “DMF” 255 43 ‘ S O ” 0 47 “OCCOH” 0
4 “ACCH2” 419.1 8 “ACOH” 0 12 “HCOO” 134.5 16 “(C)3N” 0 20 “COOH” 898.2 24 “CC14” -134.2 28 “CS2” 167.9 32 “I” 0 36 “ACRY” 837.2 40 “CF2” 0 44 “NMP” 26.35 48 “CH2S” 2429
1 “CH2” -5.132 5 “OH” 649.7 9 “CH2CO” 0 13 “CH20” 167.3 17 “ACNH2” 0 21 “CCI” 0 25 “ACCI” 0 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO” 0 45 “CCLF” 0 49 Morpholine 0
2 ‘‘CXC“ -131.7 6 “CH30H” 645.9 10 “CHO” 0 14 “CNH2” 0 18 “pyridine” 159.8 22 “CC12” 0 26 “CN02” 0 30 “furfural” 0 34 c-C” 0 38 “ACF” 0 42 ”SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” -237.2 7 “H20” 0 11 “CCOO” 0 15 “CNH” -1 98.8 19 “CCN” 0 23 “CC13” 0 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 0 39 “DMF” 0 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” -157.3 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 116.5 20 “COOH” 0 24 “CC14” -124.6 28 “CS2” 0 32 “1” 0 36 “ACRY” 0 40 “CF2” -117.2 44 “NMP” 0 48 “CH2S” 0
‘I
557
558
Appendix II
39 “DMF’ 39 “DMF” 39 “ D M F 39 “DMF” 39 “DMF” 39 “DMF” 39 “ D M F 39 “DMF” 39 “DMF” 39 “DMF’ 39 “DMF’ 39 “DMF’ 39 “DMF”
40 “CF2” 40 “CF2” 40 “CF2” 40 “CF2” 40 “CF2” 40 “CF2” 40 “CF2” 40 “CF2” 40 “CF2” 40 “CF2”
40 “CF2” 40 “CF2” 40 “CF2”
1 “CH2” -3 1.95 5 “OH” 64.16 9 “CH2CO” 97.04 13 “CH20” -158.2 17 “ACNH2” 343.7 21 “CCI” 0 25 “ACCI” 0 29 “CH3SH” -7 1 33 “Br” 0 37 “CICC” -137.7 41 “COO” 72.31 45 “ C C L F 0 49 Morpholine 0
2 “C=C” 249 6 “CH3OH” 172.2 10 “CHO” 13.89 14 “CNH2” 49.7 18 “pyridine” 0 22 “CC12” 0 26 “CNO2” 223.6 30 “furfural” 0 34 “C-C” 6.699 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” -133.9 7 “H20” -287.1 11 “CCOO” -82.12 15 “CNH” 0 19 “CCN” 150.6 23 “CC13” 0 27 “ACNO2” 0 31 “DOH” -191.7 35 “Me2SO” 136.6 39 “DMF’ 0 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2”
1 “CH2” 147.3 5 “OH” 0 9 “CH2CO” 0 13 “CH20” 0 17 “ACNH2” 0 21 “CC1” 0 25 “ACCI” 0 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO” 0 45 “CCLF’ 111.8 49 Morpholine 0
2 “C=C” 62.4 6 “CH3OH” 0 10 “CHO” 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” 0 26 “CN02” 0 30 “furfural” 0 34 “C-C” 0 38 “ A C F 185.6 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” 140.6 7 “H20” 0 11 “CCOO” 0 15 “CNH” 0 19 “CCN” 0 23 “CC13” 0 27 “ACNO2” 0 31 “DOH” 0 35 “Me2SO” 0 39 “DMF’ 55.8 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” 0 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” 0 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
-240.2 8 “ACOH” 0 12 “HCOO” -116.7 16 “(C)3N” -185.2 20 “COOH” -97.77 24 “CC14” -186.7 28 “CS2” 0 32 “I” 0 36 “ACRY” 5.15 40 “CF2” -5.579 44 “NMP” 0 48 “CH2S” 0
Appendix II ~ _ _ _ _ _ _
41 “COO” 41 “COO” 41 “COO” 41 “COO” 41 “COO” 41 “COO” 41 “COO” 41 “COO” 41 “COO” 41 “COO” 41 “COO” 41 “COO” 41 “COO”
42 “SiH2” 42 “SiH2” 42 “SiH2” 42 “S1H2” 42 “SiH2” 42 “SiH2” 42 “SiH2” 42 “SiH2” 42 “SiH2” 42 “SiH2” 42 “SiH2” 42 “SiH2“ 42 “SiH2”
1 “CH2” 529 5 “OH 88.63 9 “CH2CO” 123.4 13 ”CH20’‘ -247.8 17 “ACNH2” -22.1 21 “CCI” 182.2 25 “ACCI” 956.1 29 “CH3SH” 0 33 “Br” 627.7 37 “CICC” -198 41 “COO” 0 45 “CCLF” 0 49 Morpholine 0
2 “C=C” 1397 6 “CH30H” 171 10 T H O ” 577.5 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” 305.4 26 “CN02” -124.7 30 “furfural” -64.28 34 “C-C” 0 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” 317.6 7 “H20” 284.4 11 “CCOO” -234.9 15 “CNH” 284.5 19 “CCN” -61.6 23 “CC13” -1 93 27 “ACN02” 0 31 “DOH” -264.3 35 “Me2SO” -29.34 39 “DMF’ -2X.65 43 “ S O ” 0 47 “OCCOH” 122.4
4 “ACCH2” 615.8 8 “ACOH” -167.3 12 “HCOO” 145.4 16 “(C)3N” 0 20 “COOH” 1179 24 “CC14” 335.7 28 “CS2” 885.5 32 “I” 288.1 36 “ACRY” -53.91 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
1 “CH2” -34.36 5 “OH” 1913 9 “CH2CO” 992.4 13 “CH20” 448.5 17 “ACNH2“ 0 21 “CCI” 0 25 “ACCI” 0 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO” 0 45 “ C C L F 0 49 Morpholine 0
2 “c‘=C” 0 6 “CH30H” 0 10 T H O ” 0 14 “CNH2” 961.8 18 ”pyridine” 0 22 “CC12” 0 26 “CN02” 0 30 “furfural” 0 34 “C-C” 0 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” 787.9 7 “H20” 180.2 11 “CCOO” 0 15 “CNH” 1464 19 “CCN” 0 23 “CC13” 0 27 “ACN02” 0 31 “DOH“ 0 35 “Me2SO“ 0 39 “DMF” 0 43 “SiO” -2 166 47 “OCCOH” 0
4 “ACCH2” 0 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” 0 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP“ 0 48 “CH2S” 0
559
560
Appendix II
43 “SiO” 43 “SiO” 43 “SiO” 43 “SiO” 43 “SiO” 43 “SiO” 43 “SiO” 43 “SiO” 43 “SiO” 43 “SiO” 43 “SiO” 43 “SiO” 43 “SiO”
1 “CH2” 110.2 5 “OH” 0 9 “CH2CO” 0 13 “CH20” 0
17 0 21 0 25 0 29 0 33 0 37 0 41 0 45 0 49 0
“ACNH2” “CCI” “ACCI” “CH3SH”
2 “C=C” 0 6 “CH30H” 0 10 “CHO” 0 14 “CNH2” -125.2 18 “pyridine” 0 22 “CC12” 0 26 “CN02” 0 30 “furfural”
3 “ACH” 234.4 7 “H20” 0 11 “CCOO” 0 15 “CNH” 1604 19 “CCN” 0 23 “CC13” 0 27 “ACN02” 0 31 “DOH” 0 35 “ M e 2 S O 0 39 “DMF” 0 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2”
4 “ACCH2” 6.214 8 “ACOH” -234.7 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH”
38 “ACF” 0 42 “SiH2”
3 “ACH” -23.88 7 “H20” 832.2 11 “CCOO” 0 15 “CNH” 0 19 “CCN” 0 23 “CC13” -1 96.2 27 “ACN02” 0 31 “DOH” 262 35 “Me2SO” 0 39 “DMF’ 0 43 “SiO”
0
0
0
0
“Br”
“CICC”
34 “C-c” 0 38 “ACF’ 0
“COO” “CCLF” Morpholine
42 “SiH2” 745.3 46 “CON” 0 50 Thiophene 0
0
8 “ACOH” 0
12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14 70.81 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 ~ ~ 2 ’ 7 0 44 “ N M P 0 48 “CH2S” 0
1 “CH2” 13.89 5 “OH” 796.9 9 “CH2CO” 0 13 “CH20” 0 17 “ACNH2”
2 ‘‘C=C’’ -16.11 6 “CH30H” 0 10 “CHO” 0 14 “CNH2”
0
0
21 “CCI” 0 25 “ACCI” 161.5 29 “CH3SH” -274.1 33 “Br” 0 37 “CICC -66.31 41 “COO” 0 45 “ C C L F
22 0 26 0 30 0 34
46 “ C O N
47 “OCCOH”
48 “CH2S”
44 “ N M P
0
0
0
0
44 “NMP”
49 Morpholine 0
50 Thiophene 0
44 “NMP’ 44 “NMP’ 44 “NMP” 44 “NMP” 44 “NMP” 44 “NMP” 44 “NMP’ 44 “NMP’ 44 “ N M P 44 “NMP” 44 “NMP”
0
18 “pyridine” “CC12” “CN02”
“furfural” “C-C”
0
0
24 “CC14” 0
28 0 32 0 36 0 40 0 44
“CS2” “I”
“ACRY” “CF2” “NMP”
Appendix II
45 “CCLF’ 45 “CCLF” 45 “CCLF” 45 “CCLF” 45 “CCLF’ 45 “CCLF” 45 “CCLF” 45 “ C C L F 45 “CCLF” 45 “CCLF” 45 “CCLF’ 45 “CCLF” 45 “CCLF’
46 ‘TON” 46 “CON” 46 “CON” 46 “CON” 46 “CON” 46 “CON” 46 “CON” 46 “CON” 46 “CON” 46 “CON” 46 “CON” 46 “CON” 46 “CON”
1 “CH2” 30.74 5 “OH” 794.4 9 “CH2CO” 0 13 “CH20” 0 17 “ACNH2” 0 21 “CCI” 0 25 “ACCI” 0 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO” 0 45 “CCLF’ 0 49 Morpholine 0
2 ‘‘C=C’’ 0 6 “CH30H” 762.7 10 “CHO” 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” 0 26 “CN02“ 844 30 “furfural” 0 34 “C-c” 0 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” 167.9 7 “H20” 0 11 “CCOO” 0 15 “CNH” 0 19 “CCN” 0 23 “CC13” 0 27 “ACNO2” 0 31 “DOH” 0 35 “Me2SO” 0 39 “DMF” 0 43 ‘ S O ” 0 47 “OCCOH” 0
4 “ACCH2” 0 8 “‘ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” 0 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” -32.17 44 “NMP” 0 48 “CH2S” 0
1 “CH2” 27.97 5 “OH” 394.8 9 “CH2CO” 0 13 “CH20” 0 17 “ACNH2” 0 21 “CCl” 0 25 “ACCI” 0 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO” 0 4s “ C C L F 0 49 Morpholine 0
2 ‘‘C=C’’ 9.755 6 “CH30H” 0 10 “CHO” 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” 0 26 “CN02” 0 30 “furfural” 0 34 “C-C” 0 38 “ACF” 0 42 “SiH2”
3 “ACH” 0 7 “H20” -509.3 11 “CCOO” 0 15 “CNH” 0 19 “CCN” 0 23 “CC13” 0 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 0 39 “DMF” 0 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” 0 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” -70.25 24 “CC14” 0 28 “CS2” 0 32 ‘*I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
0
46 “CON” 0 50 Thiophene 0
561
562
Appendix I1
47 “OCCOH” 47 “OCCOH” 47 “OCCOH” 47 “OCCOH” 47 “OCCOH” 47 “OCCOH” 47 “OCCOH” 47 “OCCOH” 47 “OCCOH” 47 “OCCOH” 47 “OCCOH” 47 “OCCOH” 47 “OCCOH”
48 “CH2S” 48 “CH2S” 48 “CH2S” 48 “CH2S” 48 “CH2S” 48 “CH2S” 48 “CH2S” 48 “CH2S” 48 “CH2S” 48 “CH2S” 48 “CH2S” 48 “CH2S” 48 “CH2S”
1 “CH2” -11.92 5 “OH” 517.5 9 “CH2CO” 156.4 13 “CH20” 0 17 “ACNH2” 0 21 “CCI” 0 2.5 “ACCI” 7.082 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO” 101.2 45 “ C C L F 0 49 Morpholine 0
2 “C=C” 132.4 6 “CH30H” 0 10 T H O ” 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” -I 94.7 26 “CN02” 0 30 “furfural” 0 34 “C-C” 0 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” -86.88 7 “H20” -205.7 11 “CCOO” -3.444 15 “CNH” 0 19 “CCN” 119.2 23 “CC13” 0 21 “ACN02” 0 31 “DOH” 515.8 35 “Me2SO” 0 39 “DMF” 0 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” -19.45 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” 3.163 28 “CS2” 0 32 “I” 0 36 “ACRY“ 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
1 “CH2” 39.93 5 “OH” 0 9 “CH2CO” 0 13 “CH20” 0 17 “ACNH2” 0 21 “CCI” 0 25 “ACCI” 0 29 “CH3SH” 6.971 33 “Br” 0 37 “CICC” 148.9 41 “COO” 0 4.5 “CCLF” 0 49 Morpholine 0
2 “C=C” 543.6 6 “CH30H” 420 10 “CHO” 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” 0 26 “CN02” 0 30 “furfural” 0 34 “C-C” 0 38 “ACF“ 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” 0 7 “H20” 0 11 “CCOO” 0 1.5 “CNH” 0 19 “CCN” 0 23 “CC13” -363.1 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO”
4 “ACCH2” 0 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” -11.3 28 “CS2” 0 32 “I” 0 36 *‘ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
a
39 “DMF” 0 43 “SiO” 0 47 “OCCOH” 0
Appendix II ~~
-~
49 Morpholine -61.2 49 Morpholine 49 Morpholine 49 Morpholine 49 Morpholine 49 Morpholine 49 Morpholine 49 Morpholine 45, Morphoiine 49 Morpholine 49 Morpholine 49 Morpholine 49 Morpholine
50 Thiophene 50 Thiophene 50 Thiophene
50 Thiophene
SO Thiophene SO Thiophene 50 Thiophene
SO Thiophene SO Thiophene
SO Thiophene SO Thiophene
SO Thiophene
SO Thioohene
I ”CH2” -23.61 5 “OH” -61.20 9 “CHZCO” 0 13 “CH20” 0 17 “ACNHZ” 0 21 “CCI” 0 25 “ACCI” O 29 “CH3SH” 0 33 “Br” O 37 “CICC” 0 41 “COO” 0 45 “CCLF” 0 49 Morpholine 0
2 ”C=C“ 161 I 6 “CH’3OH” -89 24 10 T H O “ 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12“ 0 26 “CN02” 0 30 “lurfural” 0 34 “C-C” 0 38 ”ACF” 0 42 ”SiH2“ 0 46 “CON“ 0 SO Thiophcnc 0
3 “ACH” 142.9 7 “H20” -384.3 I I “CCOO” 0 1.5 “CNH’’ 0 19 “CCN” 0 23 “CC13” 0 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 0 39 “DMF” 0 43 “ S i O 0 47 “OCCOH” 0
4 “ACCH2” 274. I 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” 0 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “ N M P 0 48 “CH2S” 0
1 “CH2” -8.479 5 “OH” 682.5 9 “CH2CO” 278.8 13 “CH20” 0 17 “ACNH2” 0 21 “CCI” O 25 “ACCI” 0 29 “CH3SH” O 33 “Br” 0 37 “ClCC” 0 41 “COO” 0 45 “CCLF’ 0 49 Morpholine 0
2 “C=C“ 0 6 “CH70H” 597 8 10 T H O ” 0 I4 “CNH2” 0 18 “pyridine” 221 4 22 “CC12” 0 26 “CN02“ 176 3 30 “furfural” 0 34 “C-C” 0 38 “ACF” 0 42 “SiH2” 0 46 “CON“ 0 SO ’I’hiophene 0
3 “ACH” 23.93 7 “H20” 0 11 “CCOO” 0 15 “CNH” 0 19 “CCN” 0 23 “CC13” 0 27 “ACN02” 0 31 ”DOH” 0 35 “Me2SO” 0 39 “DMF” 0 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” 2.845 8 “ACOH” 810.5 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” -79.34 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “ N M P 0 48 “CH2S”
Note all group-interaction parameters that do not exist are set to zero. Interactions between the same group are equal to zero.
0
563
Reactivity in Molecular Crystals Edited by Yuli Ohashi Copyright @ K d a o r h a Ltd .Tokyo. 1999
Appendix I11 Table 1: Trivalent phosphorus antioxidants. Structure
CAS registrv number
Trade names
126523-78-41
TNPP
689.1
131570-04-41
Phosphite 168
646.9
(.?806-.?4-6]
Weston 618
733.0
126741-53-71
Ultranox 626
604.7
Sandostab P-EPQ Irgafos P-EPQ
M,
1035.4
566
Appendix III
Table 2: Major commercial hindered amine stabilizers. Structure
k>."CHzf,.
HN$&H21
CAS registry number
Trade names
M,
152829-07-91
Tinuvin 770
480.1
(82451-48-71
Cyasorb UV-3346
1600 (average)
[63843-89-01
Tinuvin 144
685.0
[64022-57-71
Mark LA 55
608.9
[81406-61-31
Hostavin TMN 20
350.6
[61269-61-23
Spinuvex A-36
[420.7]
11
Appendix 111
567
Table 3: Major commercial hindered phenolic antioxidants. Structure
Chemical name
lb,, HO
\
CHzCHzCOCHz
C
CAS registry Trade names number
M,
tetrakis [methylene [6683-19-8] (3.S-di-terr-butyl-4hydroxyhydrocinnamate)] methane
Irganox 1010
1177.7
2.2'methylenehis(4-methyM-terthutylphenol)
Cyanox 2246
340.5
[119-47-1]
[41484-35-9] lrganox 1035 642.0
9
2,6-di-tert-butyl4-methylphenol
[128-37-0]
Butylated hydroxytoluene ( B W
220.4
[1843-0.?-4]
Topanol CA
544.8
[2082-79-31
Irganox 1076 530.9
C"3
H,C-CH-CH
N J - 1.6-hexame thylene-bis-3(3,s-di-tcrt-butyl4-hy droxypheny l) propionamide
568
Appendix 111
Table 3: (continued) Structure
Hpc3H%\
Chemical name
/ F H \ / OH
CAS registry Trade names number
4,4'-Butylidenebis- [85-60.91 (6-rert-butyl-3me thylphenol)
Santowhite powder
[40601-76-1] Cyanox 1790
M,
382.6
699.9
[27676-62-61 Good-rite 31 14 784.1
R = -CH
[341.?7-09-21 Good-rite 3125 1042.4
[1709-70-21
4,4'-711iobis(2-fert- 196-69-51 HO$
S
q OH
but yl-5-methylphenol)
Ethanox 330 Irganox 1330
775.2
Santonox R
358.0
Reactivity in Molecular Crystals Edited by Yuli Ohashi Copyright @ K d a o r h a Ltd .Tokyo. 1999
Subject Index
ABS plastics 27.317 Activity 82 Activity coefficient 82,93,276 - Combinatorial contribution 95 - Estimation methods 94 - Free volume contribution 95 - Molar 86 - Molecular structures 375 - Residual contribution 95 - Volume fraction 86 - Weight fraction 86 Additive Degradation 370 High molecular mixtures 466 Identity 359 Ionogenic 50 List of 405 Migration rates from polyolefins 452 Reference compound 462 Uselevel 359 Used in plastics 48,380 Adhesive 405 Aging effect 457 Aldol condensation 413 Aliphatic diamines 331 - Chemical stability 332 - Reaction with olive oil 332 - SFC/FID analysis 332 Amino resins 34 Amorphous polymer structure, generation of 142 Analysis - GUMS 415 - Sensory 415 - Mixture of migrants 465 Analytical methods - Calibration 308 - Calibration graph 326 - CEN standard format 311,317 - Chemical derivation 326,329,333 - Confidence bounds 309 - Confirmation 310,318,327,336 - Cost efficiency 313 - Development 306 - Generally agreed methods 313,315 - In-house validation 313 Limit of detection 308,318,325,334 - Micro-disitillation 329 - Practicality 313 ~
Pre-validation 306.313 Precision 308 - Procedures 462 - QM-method 306 Regression line 326 - SML-method 306,317 - Solutions of the diffusion equation 6 - Stability check 310.333 Standard addition procedure 326. - Standard error of estimate 308 - Standard error of procedure 308 - Validation of 302 - Workability 310 - Test report 312 Antiacids 63 Antioxidant 54 - Chain-breaking 55 - Hydroperoxide decomposing 57 Ap-values 456 Aroma barrier 424 Arrhenius equation 248 Atactic 18 -
-
~
~
BADGE 13,319 Barrer’s equation 213 Barrier - Functional 113,438,466 - Layer 407 BCR project ‘Monomers’ 315 BgVV 291,317,319,337 Bifunctional monomers 319,331. Binding agent 43 - Inmolten form 43 - Formation by chemical reaction 43 - Microcrystalline wax 44 - Plastic dispersion 44 - Solution 43 Bisphenol A diglycidyl ether - Confirmation 321 - Ethanolysis products 320,325 - Half-life time 321 - Hydrolysis products 320,325 - Massspectrum 323 - QMmethod 321 - Selective MS-MS analysis, 324 - SMLmethod 321 Blooming 54
570
Subject Index
Carcinogens 365,366 Catalyst 16.405 Cavity, in polymer (see “Holes” in polymers) Carbonyl compounds - a$ unsaturated 414 Cellulose, regenerated 41 CEN TCl94/SC1 313,315 Chain - Branching 18 - Configuration 18 Chapman-Enskog equation 159 Chemical potential 79 - Excess 83 Chromatography - Gas(GC) 410 - High performance liquid (HPLC) 457 Coating, temperature resistant 45 Code of Federal Regulations 359,365 Compliance testing 292,300,334 Compositional analysis of plastics 292,341 Condensation process 21 1 Consumption factor (CF) 362 Convection 183 Copolymer 12 - Block 12 - Graft 12 - Ethylene 23 Council of Europe 406 Crank-Nicholson discretization scheme 223 Crosslinker 14 Crystalline polymer 20, 127. 142, 153
Daily diet 361 Daily intake 361 - Acceptable (ADI) 362,400 - Estimate 362 - Tolerable (TDI) 400 Degradation process, - Melt degradation 53 - Photo-oxidation 53 - Thermal degradation 53 - Thermal oxidation 53 Degradation products 5 Dehydrating agent, for PET 64 Delaney Clause 365 Density of polymers 20 Desorption - Counter current column, in a 409 - CUNeS 270 Detection limit 400 Diameter of molecules 255 Diels-Alder condensation 411 Dietary cocentration 362,365.366 - Predictable 364 - Upper-bound 365 Diethyleneglycol 335 Diffusion - Activated process 130
Activated zone 128 From an infinite thick layer 192-194 - One sided from an infinitely thin layer 192 - Resistance to 217 - Two sided from a finitely thick layer 195 - Two sided from an infinitely thin layer 191 Diffusion activation energy 128, 132 - Intermolecular 129 - Intramolecular 129 - Reference 448 Diffusional jump 128, 145 - Back 144 - Frequency 131 - Length 131.140 Diffusion coefficient - Adjustable coefficients 130, 133,136 - Alkanes in polyethylene 173 - Alkanes. self-diffusion 178 - Calculated versus experiment 146,151, 154 - Dependence from molecular weight 450 - Effective 289 - Einstein equation 1413 - Estimation 256,374,435 - Inaer 171 - lntradiffusion 172 - Mutual 170. 172.177 - Organic compounds in LDPE 265 - Paraffins in paraffin 176 - Plastic specific parameter-values in polyolefins 448 - Polyolefins 451 - Rates 131,147 - Refined equation for 448 - Self-diffusion 133. 134. 139 - Solvent dependence 283,421 - Styrene i n polystyrene 436 - Tracer 172.179 - Upper bond value 446 - Upperlimit 435 - Water,in 1x0 - Zero penetrant concentration, at 138 Diffusion coefficient models - Ab initio 125. 141,147 - Atomistic 126 - Classical approach 126, 152 - Computational approach 141,152 - Correlative 133, 135 - First principles 126, 132, 141 - Free-volume 133. 152 - General equation for plastics 175 - Heuristic 125,447 - Limm and Hollifield 447 - Liquids 176 - Microscopic 126, 130, 140 - Molecular 128 - Molecular dynamics 141,145,153 - Molecular statistical 129,137 - Pace and Datyner 131 - Reference equation 172 -
-
Subject Index Semi-predictive 133 Vrentas and Duda 134,139,152 Diffusion equation 221 - Boundary conditions 222,232 - Comparison of solutions 197 - Cylindrical coordinates 234 - Discretized 228 - Initial condition 221 - Spherical coordinates 234 - Two dimensional 235 Diffusion in polymerlliquid systems 199-208 - General solution of equation 201,206 - Influence of food 208 - Simplified solution 206 - Simplified solution for infinite thickness of polymer 207 - Solution based on error function 201 Diffusion, types - Anomalous 127,149 - Fickian 127, 138 Directive - Ceramic 398 - Framework 394.396,419 - MEG and DEG 405 - Migration tests, for 394 - Monomers 394 - Nitrosamines, draft 405 - Regenerated cellulose film 398 - Vinylchloride 405 Dirichlet boundary conditions 222,228
Regenerated cellulose film 398,405 European project - AIR2-CT93-1014 344 - FAIR-CT984318 347 - SMT4-CT9C2129 353 Euler forward-difference scheme 222 EVA-copolymers 23 EVOH-copolymers 23 Evaporation process 211 Excess functions 96 Extraction 287 - Organic solvents, with 409 - Techniques 409
-
-
-
Eigenmodes 226 Einstein-Smoluchowski equation 159 Elastomers 19 Electrolytic conductivity 253 Energy - Activation, for diffusion 128, 129, 131, 169 - Cohesive, density 90 - Density of interaction 165 - Molar interaction 90 Enthalpy 79 Excess, of mixing 95 - Mixing, of 81 Entropy 79 - Excess, of mixing 95 Epichlorohydrin 328 - Hydrolysis 330 - Half-life time 331 Micro-distillation 329 Epoxy coating 319 Epoxy lacquer 328 Equilibrium conditions 288 Equilibrium state 80 Error function 193 EU Directive 90/128/EEC 291,300,313.445 - 94162lEEC 336 Ceramics 398 - Framework 396 ~
~
~
~
571
Fat simulant - ~ ~ 3 04027 - Oliveoil 402 - Sunfloweroil 402 Fat test 402 - Alternative 404 FDA 337 - Consumption factor 338 - Dietary intake 338 - Threshold-of-Regulation 337,341 Fick’s second law 187,367 - Polymerlfood system 368 Flux 184 - Divergence 186 Flow temperature 19 Food - Classification 360 - Conditions of use 361 - Distribution factor 362,364 - Exposure to packaging 7,363 - Polarity 420 - Purity 396 - Quality 3 - Testing protocols for packaging 361 Food packaging legislation 291 Food simulants 290,361 - Chemical reaction with migrants 333 - Ethanol 290 - Iso-octane 290 - Olive oil 292. - Solubility in polymer 290 - Triglycerides 290.333, - Volatile solvents 290 Free energy 79 - Excess 83 Free enthalpy 79 Free radical 11,66 Free-volume, in polymers 95. 134, 138. 143,152 - Diffusion models 133, 139. Functional barrier plastics 338 - Acryliclayer 343 Barrier properties 343 - Black box approach 340 - Corelayer 340 - Efficiency 339 ~
572
Subject Index
Lag time 339,343 Mathematical model 339 - Model contaminants 340 - Multi-layer structure 339,343 - On paper and board, 343 - Permeation 338,343 - PVDClayer 343 - QM/SML relationship 340 - Recycling specific substances 340 - Surrogates 340 - Test procedures 339 -
Plastic and simulant. between 456 - Sources 4 Internal energy 79 Isotactic 18 Lacquer 43 Coating 319 Lagrange interpolating condition 232 Leaks in package (see pores) Legislation - European Community 7 - Plastics 7 Lennard-Jones temperature 255 -
-
Gas - Ideallaw 84 - Perfect 80 Gas permeability measurement - By sorption 250 - Permeation in a gas stream 251 - Permeation in a sealed container 250 Gibbs free energy (see free enthalpy) Glass transition temperature, of polymer 19,20, 126 Glassy polymers 127, 141 - Diffusion in 136 Global odor 426 Global sensory analysis 409 Group - Contribution 89 - Contribution method 90 - Functional 89 Hagen-Poiseuille equation 253 HAS-photoantioxidants 59,465 Heat - Conduction of 184. 187 - Equation 190 - Solution in polymer 25 - Stabilizers 62 Henry’s - Constant 87 - Law 81,240 Hildebrand correction 166 HIPS-polymers 27 Holes in polymers 133. 138,143 - Affinity and saturation constants. of Homologous series 88. 161 Hydrogen bond 17 Hydroperoxides 59
137
Inhibitor 15 Initiator 14 Ink 405 - Off-odor 426 Ionomer 26 Interaction 4 - Packaging and food, between 407 - Polymers and foodstuffs, between 445
Mass Balance 202,432,434 - Molecular relative 89 - Transfer categories to food 371 - Transfer coefficient 370 - Transfer from liquid (food) into polymer 202 - Transfer from polymer into liquid (food) 203 - Transfer, influence of diffusion in food 208 - Transport 4 Mass spectrometer 410 - Electro-spray-ionization(ESI) or API ion source 462 Mathematical modeling 292.337, Microcrystalline waxes 44 Micro-distillation 329 Migrants - Acrylonitrile 291 - Analytical procedures 300 - Bisphenol A 291,325 - Butadiene 291 - Diffusion 289 - Ethylenediamine 291 - Molecular weight 287 - 1-Octene 291 - Specific migrant 306 - Vinylchloride 291 - Volatility 292 - Volatilization. 319 MIGRATEST Lite 468 Migration 4 - Additives to foods, of 373.378,453,459 - Alternative test 296,404 - Amount to food 383 - Analytical determination 296 - Antioxidant. of 366,369 - Area-related QM 293,322,328 - BHT from polyolefins 369 - Categories 370 - Carcinogenic monomers, of 393 - Control factors 287 - Control methodologies 291 - Data, calculated and experimental 375.378, 454 - Decision tree 372 - Dimensionless curve 296 - Direct measurement 296 -
Subject Index Effect of flavor components 371 Enhanced by full immersion 456 - Equilibrium 293 - Estimation 432 - Food and food simulating solvent, to 369 - Frompolymer 289 Indirect assessment 292 - Intopolymer 289 - High temperature 371 - Level 366 Limits 291 - Limits, regulatory 435 - Low temperature, at 370 Mass balance 293 - Maximumamount 207 - Migration potential 292 Modeling 7.8,374,375 - More severe test 296,297 - Nitrosamines in rubber 405 - Overall 402,404 - Pitfalls 457 - Plastic constituents 287 - Polymedfood system 367 - Polymer additives. of 369 - Prediction, 294.368 - QM 291.300.316.334 - Ratc 9 - Rates. for additives from polyolefins 452 Semi-direct test 297 - Specific 402 - Study 370 - Styrene 370 Swelling, with 218 - Test, accelerated 441 - Test, conditions 403 Test principles 287 - Testing 7 - Total mass transfer 292 - Toxicological parameters 291 Viny! chloride 405 - Worst case 370 - Worst case, estimate 374 Migration modeling - Laminate, polymeric glues, varnish 467 - Software 468 Mixt boundary conditions 231 Modern food packaging applications 336 Monoethyleneglycol 335 Monomer 1 0 , l l - Residual 407
-
-
573
Solution of the diffusion equation 6. 137
-
-
-
-
~
-
-
-
~
Nernst diffusion layer 209 Nernst's law 81 Nucleation - Heterogeneous 21 - Homogeneous 21 Numerical instability 224 Numerical mathematics 466 Numerical methods
Odor compounds Identification 411 - Separation 411 Odor threshold 407,409,413 - Absolute 410,415 - Determination 414 - Relative 422 Off-flavors 7,407 - Overlapping 409 - Styrene 442 Off-odors 407 - Coatedpapers 411 - PE.in 413 - Sources 407 Oil absorption 463 Olefin oxidation products 414 Olfactometer 420 Optimization criteria 4 Organoleptic characteristic 396 Overall migration fat test 297 - Accelerated test 298 - Analytical tolerance 297 - CENstandards 297 - High temperature fat test 299 - Majorproblems 297 - Rapid extraction test 298 - Substitute fat test 299 -
Packaging - Conditions of use and testing 361 - History 411 - Minimization 4 - Requirements 4 Packaging waste 336 Partition - Effects 370 - Function, translational 167 - Multilayer structure 467 - LDPE/octanol 278 - Octanollwater 278 Partition coefficient 5, 82, 89, 209.288.370,375, 420.433 - Aqueous ethanol 280 - Aromas in polyolefiniwater systems 279 - Estimation 100,111,114 - Estimation using Unifac 100 - LDPEkleaning agents 281 - LDPE/ethanol (methanol) 265 - LDPEkkin creme 281 - Non-ideal solutions 84 - Polymedliquid 199 - PS/milk 280 - Solvents/food 421 PBT plastics 30 Permeability 240 - Coefficient 240,242-246.257
574
Subject Index
Coefficients in laminates 284 Coefficients in LDPE 263 - Convertion factors 241 - Measurement 252 - Package 248 - Parameters 247 - Solvent dependence 277 - Total package 248 - Tube 251 Permeation 4.7 - In a gas stream 251 - In a sealed container 250 - Steady state 240 - Through a membrane 240 - Time dependence 250 Peroxides 15 PET plastics 30 Phenol - hindered 66 - Polynuclear 70 Phosphites 57 Photoantioxidant 59 Phthalates 52 Plastics 1 - Degradation 53 - Processing 49 - Processing stabilizers 57 Plastic dispersions 44 Plastics directive 291,300,315 Polyamide 31,331 Polybutene-1 25 Polybutylene terephthalate 30 Polycarbonate 31,325 Polycrystallinity 20 Polyester - Thermoplastic 30 - Unsaturated 35 Polyethylene 21 Polyethylene terephthalate 30,335.338 Polyisobutene 25 Polymer 17 - Crystallisation 20 - Distribution of different chain length 19 - Orientedstate lY - Primarystructure 17 Polymer, biodegradable 41 - Polysaccharides 41 - Polyesters 42 Polymer, containing fluoride 33 Polymer reaction 13 Polymer swelling 290 Polymerization 11 - Addition 11 - Condensation 12 - Ionicaddition 11 Polymethylmethacrylate 32 Poly(4-methylpentene-l ) (P4MPl) 25 Polyoxymethylene 33 Polyolefines 290 Polypropylene 23 -
Polystyrene 26 - Volatile substances 428 Polysulfone 33 Polyurethane - Crosslinked 36 - Foam 37 - Linear 36 Polyvinylchloride 28 Polyvinylether 34 Polyvinylidenechloride 29 Pores in package 253 Potential energy constant 255 Pouch method 273 Practical Guide 445 Principle - Additive 89 - Inertness, of 396 Product 4 Propylenediamine 333 Protection of public health 365 QM/SML ratio 293 Diffusion model 294 - Influence of layer thickness 293,295 - Influence of partition coefficient 293,295 - Influence of polymer type 294 Quality I - Assurance 4 - Preservation 2 - Reduction 420 - Requirements 3 Quantity - Extensive 79 - Intensive 79 - Maximum permitted (QM) 445 - Specific 79,88 Quinone methode 68 -
Radical former 16 Raoult's law 80,276 Rate - Chemical reaction 187,218 - Constant, reaction 370 - Penetration 421 Ratio food volume to polymer volume 367 Raw material - Fossil 10 - Renewable 10 - Residual 407 Recommendation 393 Recycled material 405 Recycling plastics 7.337 - BgVVstatement 337 - Challenge test 344 - Cleansing efficiency 344 - Closed-loop 344 - Contaminants 337 - Direct food contact 337
Subject Index ILSI guidelines 344 Migration model 347 - Post consumer PET 344 Recycling process 345 - Safety/quality assurance 338 Solid-phase condensation 345 Surrogates 344 Reference collection 320 Reference compound class 161 Refillable plastic bottle. 349 Compliance testing 350,353 - Inertness test 350 - Misuse 350 - PET 349 - Re-migration 350 Regulation 365 - Food contact materials 445 - Harmonizing law 393 Residue limit 400 Resolution Colorants 406 Ink.draft 406 Ion exchange resins 406 - Paper and board. draft 406 - Polymerisation aids 406 - Varnishes 406 Restriction criterion 306.308.316.325.335 Retention indices - Method 90 - Molecular 111 Retention time 412.415 Rubbery polymer 126. 144 Diffusion in 128 -
-
-
-
-
-
-
-
Sackur-Tetrode equation 167 Safety margin 4,446 SAN plastics 27,317 SBpolymer 27 Scalping 4 Scavenger, acid 63 Scientific Committee for Food (SCF) 396 Selective ion monitoring (SIM) 412 Selective methods 462 Sensorial evaluation, global 410 Sensory - Methods 7 - Specific descriptors 408 - Threshold 416.420 Self-diffusion - Gas 168.170 Liquids 177 Separation chromatographic 462 Shelf-life 2,439.440 Silicone, starting material 40 Simulants for migration tests 404 SML/QM correspondence 445 Sniffing 410, 414 Solubility 420,423425 - Coefficient 87,240,255 -
575
Hansen parameter 93 Parameter 91-93 Solution - Athermal 83 - Ideal 80.276 - Non-ideal 84 - Regular 83,91 - Regular, theory 90,96 Sorption - Constant (see solubility coefficient) - Curves 270 - Modeldual 270 - Penetrant 136 - Theory 137 Specific migration 297 Specific migration limit (SML) 400,291,300, 3 16,334 Stabilizer - Heat, for PVC 62 - Hindered amine (HAS), for heat 465 - Organotin 75 Standard - chemical potential 80 - pressure 79 Standard methods 313 - BADGE 3,319 - Carbonyl chloride 325 - CEN ENV 13130 standards 314 - Epichlorohydrin 328 - Ethylenediamine 331 - Hexamethylenediamine 331 - Vinylchloride 314 Standardization 404 Starting material 11 Steam distillation 409 Stochastic process 132, 140, 149 Stokes-Einstein equation 160, 175 Storage - Temperature 420 - Time 420 Siructure - Data of polymers 126 - Increment 89,111 Styrene copolymer 27 Suhstitution tests. conditions 403 Surface to volume ratio 329 Symbol, for - Labelling 396 - Material 396 Syndiotactic 18 Synoptic document 400 Swelling front 218 -
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Taste - Description 409 - Ethylbenzene 430 - Styrene 430 - Threshold 421 Temperature
576
Subject Index
Reference 167 Standard 167 Test liquid - Ethanol 402 - Isooctane 402 - Media 403 Thermal conductance 183 Thermoplastics 10 Thermoset 18,34 Threshold - Absolute 420 - Air, in 414 - Concentration 438 - Level 424, - Limits 409 - Relative 422,423 - Relative, of odor and taste 422 Threshold of regulation 7,365,366 Time lag 215-217 Time steps 225 Toxic effect - Acute 365 - Chronic 365 - Noncarcinogenic 365 Toxicity testing 401 - Long term 365,401 - Mutagenesis studies 401 - Short term 365 - 90-daystudy 401 Transamidation 333 Transport - Energy 183 - Momentum 183 - Process 183 Trouton’s rule 166
Valence bond 17 - Primary 17 - Secondary 17 Validation 302,334 - Alternative approach 313,334 - Collaborative trial 302,313 - Critical difference 305.318 - Inter-laboratory study 303 - I S 0 5725,303 - Performance characteristics 302 - Probability level 305 - Reduced test scheme 334 - Repeatability r 303,308,334 - Reproducibility R 303 - Statistical tools 303 - Validation parameters 302 - Variance 304 Van der Waals forces 17 Vapor pressure - Estimation 112 - Saturated 80 Viscosity 183 Volume - Fraction 86 - Polymermolar 87 - Reference 167 W-values 112.116 Weight fraction 85 Worst case scenario 292,347,446
UNIFAC 90 - Calculations for liquids 99
Ziegler-Natta catalysts
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Calculations for polymers 97 Limitations 109 UVabsorber 61
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