Organic and Physical Chemistry Using Chemical Kinetics: Prospects and Developments

ORGANIC AND PHYSICAL CHEMISTRY USING CHEMICAL KINETICS: PROSPECTS AND DEVELOPMENTS

ORGANIC AND PHYSICAL CHEMISTRY USING CHEMICAL KINETICS: PROSPECTS AND DEVELOPMENTS

Y.G. MEDVEDEVSKIKH ARTUR VALENTE ROBERT A. HOWELL AND

G.E. ZAIKOV EDITORS

Nova Science Publishers, Inc. New York

Copyright © 2007 by Nova Science Publishers, Inc.

All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. For permission to use material from this book please contact us: Telephone 631-231-7269; Fax 631-231-8175 Web Site: http://www.novapublishers.com NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material. Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA Organic and physical chemistry using chemical kinetics : prospects and developments / Y.G. Medvedevskikh ... [et al.], editors. p. cm. Includes bibliographical references and index. ISBN-13: 978-1-60692-749-6 1. Chemical kinetics. 2. Chemistry, Organic. 3. Chemistry, Physical and theoretical. I. Medvedevskikh, Y. G. QD502.O74 2007 541'.394--dc22 2007017506

Published by Nova Science Publishers, Inc.

New York

CONTENTS Preface Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

ix Conformation and Deformation of Linear Macromolecules in Concentrated Solutions and Melts in the Self–Avoiding Random Walks Statistics Yu. G. Medvedevskikh

1

Thermodynamics of Osmotic Pressure of Polymeric Solutions Yu. G. Medvedevskikh, L. I. Bazylyak and G. E. Zaikov

23

Generalization of Data Concerning to the Coal Swelling in Organic Solvents and Their Extraction Using the Linear Multiparametric Equations L. I. Bazylyak, D. V. Bryk, R. G. Makitra, R. Ye. Prystansky and G. E. Zaikov

35

New Silazane Oligomers and Polymers with Organic-Inorganic Main Chains: Synthesis, Properties and Application N. Lekishvili, Sh. Samakashvili, G. Lekishvili and G. Zaikov

51

To Question about Influence of Solvent on Interaction Propanethiole by Chlorine Dioxide R. G. Makitra, G. E. Zaikov and I. P. Polyuzhyn

65

Mathematical Modelling of Thermo-Mechanical Destruction of Polypropylene G. M. Danilova-Volkovskaya, E. A. Amineva and B. M. Yazyyev Energy Criterions of Photosynthesis G. А. Коrablev and G. Е. Zaikov

69

73

vi

Contents

Chapter 8

Spatial-Energy Interactions of Free Radicals G. А. Коrablev and G. Е. Zaikov

Chapter 9

Poly(Vinyl Alcohol)[PVA]-Based Polymer Membranes: Synthesis and Applications Silvia Patachia, Artur J. M. Valente, Adina Papancea and Victor M. M. Lobo

Chapter 10

Chapter 11

Chapter 12

Chapter 13

Chapter 14

Chapter 15

Chapter 16

Chapter 17

Chapter 18

Chapter 19

89

103

The Research on the Process of Thermo-Mechanical Destruction in Polypropylene G.M. Danilova-Volkovskaya and E. A. Amineva

167

Zinccontaining Polymer - Inorganic Composite as Vulcanization Active Component for Rubbers of General and Special Assignment V .I. Ovcharov, I. A. Kachkurkina, O. V. Okhtina and B. I. Melnikov

173

Formation of Carbon Nanostructures and Spatial-Energy Stabilization Criterion G. А. Korablev and G. E. Zaikov

187

The Structural Treatment of Limiting Conversion Degree for Solid-State Imidization L. Kh. Naphadzokova, G. V. Kozlov and M. A. Tlenkopachev

201

A Solid-State Imidization and Heterogeneity of Reactive Medium L. Kh. Naphadzokova, G. V. Kozlov and G. E. Zaikov

207

Fractal-Like Kinetics of Reesterification Reaction in Catalyst Presence L. Kh. Naphadzokova, G. V. Kozlov and G. E. Zaikov

217

Description of the Model Reesterification Reaction within the Framework of a Strange Diffusion Concept L. Kh. Naphadzokova, G. V. Kozlov and G. E. Zaikov

225

Estimation of Vapor Liquid Equilibrium of Binary Systems Tert-Butanol+2-Ethyl-1-Hexanol and N-Butanol+2-Ethyl-1-Hexanol Using Artificial Neural Network H. Ghanadzadeh and A. K. Haghi Liquid-Liquid Equilibria of the MME (Methylcyclohexane + Methanol + Ethylbenzene ) System H. Ghanadzadeh and A. K.Haghi Sugar Carbamides J. A. Djamanbaev, J. A. Abdurashitova and G. E. Zaikov

233

243 251

Contents Chapter 20

Index

Impact of Chain-End Structure, Basic Comonomer Incorporation and Pendant Structure on the Stability of Vinylidene Chloride Barrier Polymers Bob A. Howell, Adeyinka O. Odelana and Douglas E. Beyer

vii

257

279

PREFACE If it’s green or wiggly, it’s Biology If it’s stinky, it’s Chemistry If it doesn’t work, it’s physics. (Definitions of sciences on the back of Sasha Zaikova’s sweatshirt High School, Perry, Ohio, U.S.A.)

“Inevitability (verity) is something that nobody knows; the truth everybody knows but each has his or her own truth” Proverb

The word truth is a multi-meaning word which can be applied both to science and life. We will not raise social problems but we will go down to the science, particularly chemical science (organic and physical chemistry). We choose chemical kinetics as a method of research because chemical kinetics is a science about chemical processes, mechanisms of reactions, and about possibilities of directing reactions. Parts of the articles in this volume deal with chemical physics, biochemical physics, and physical organic chemistry. All of these fields of science are interconnected with each other. The authors and editors are all part of an international effort to bring these fields of knowledge to readers around the world. All these efforts are collected at symposia to share and exchange knowledge. Symposium is defined as a convivial meeting, usually following a dinner, for drinking and intellectual conversation. It is derived from ancient Greek word sympósion, which means drinking party, and where ancient philosophers gathered to discuss ideas. It is well-known that the ancient Greek philosopher and scientist Plato loved to attend symposiums very much and he even died during a symposium on his birthday, at the age of 81. These are just fun facts on the background of symposia and none of this concerns the authors and editors of this volume. The papers of this volume focus on the different states of modern chemistry (both reviews and original papers.) Editors and authors will be grateful to the readers for valuable remarks that will be taken into account in further work and research. In the U.S.A., in the times of the Wild West, there was a proverb, stating that “A good word is appreciated, but a good word with a gun behind it is even better.” Interpreting and applying this proverb to modern times and situations, one can say that new hypotheses and

x

Y.G. Medvedevskikh, Artur Valente, Robert A. Howell, et al.

ideas are always appreciated, but new hypotheses and ideas with experimental data and other proof behind them are better. In the words of an engineer-mechanic of the Russian aviation, Vitalii K. Petukhov, said “Try your best to do your best, because bad things will happen on their own” We would like to accept this idea, because our dream is good volume for readers. However, the last decision (the volume is good or bed) will be done by our readers. Editors Prof. Yurii G.Medvedevskikh Branch of L.V.Pisarzhevskii Institute of Physical Chemistry National Academy of Sciences L’viv, Ukraine Dr. Artur Valente, Coimbra University Coimbra, Portugal Prof. Bob Howell Central Michigan University Mount Pleasant, Michigan, USA Prof. Gennady Zaikov N.M.Emanuel Institute of Biochemical Physics Russian Academy of Sciences Moscow, Russia

Chapter 1 - It was proposed a strict statistics of self–avoiding random walks in the d– measured lattice and continuous space for intertwining chains in the concentrated solutions and melts. On the basis of this statistics it was described the thermodynamics of conformation and isothermal and adiabatic deformation of intertwining chains. It has been obtained the equation of conformational state. It was shown, that in the field of chains overlap they are stretched increasing its conformational volume. In this volume there are others chains with the formation of m–ball. Free energy of a chain conformation does not depend upon the fact, if the chains intertwined or they are isolated in the m–ball. Mixing entropy is responsible to the chains interweaving in the m–ball. Dependencies of the conformational radius, free energy and conformation pressure on respective concentration of polymeric chains have been determined. Using the thermodynamics of intertwining polymeric chains of m–ball conformational state and also the laws of isotropic media deformation into linear differential form it were obtained the theoretical expressions for elasticity modules (namely, volumetric volume, Young’s module and shift’s module) and for the main tensions appearing at the equilibrium deformation of the m–ball. Poisson’s coefficient is a function only on the Euclidean’s space and for the real 3–dimensional space is equal to 3/8. It was proposed a simple model explaining the tensile strength of the m–ball by the chains intertwining effect and, thereafter by the loss of the mixing entropy, but not by the chemical bonds breaking.

Preface

xi

Calculations of the elastic properties, the main tensions and tensile strength of natural rubber carried out without using the empirical adjusting parameters are in good agreement with the experimental data. Chapter 2 - It was proposed the analysis of osmotic pressure for diluted, semi–diluted and concentrated polymeric solutions based on the taking into account a free energy of macromolecules conformation as a component of their chemical potential. It was shown, that only into diluted solutions a free energy of macromolecules conformation does not contribute into osmotic pressure and it is described by Vant–Goff’s equation. In a case of semi–diluted and concentrated solutions the contribution of the conformative component of chemical potential of macromolecules into osmotic pressure is dominate. Obtained expressions for the osmotic pressure in a cases of semi–diluted and concentrated solutions are more general than proposed ones in the scaling method and self–consistent field method; generally they are in good agreement with the experimental data and don’t contain the empirical constants. It was discussed the especial role of the critical concentration c* of the polymeric chains intertwining. It was shown, that in this point a free energy of the conformation and also osmotic pressure were determined uniquely, whereas for their derivatives upon the macromolecules concentrations the jump is observed. On the basis of these peculiarities the concentration c* is the critical point of the second order phases transition for the polymeric solutions. This in accordance with the de Clause assumes the Scaling’s ratios application near c*, although does not establish the criteria for the indexes of corresponding power functions estimation. Chapter 3 - Approaches to the consideration of a coal swelling process, which were used up to now and based on the theory of regular solutions, do not give the possibility to generalize quantitatively the experimental data. Adequate relation between the physical– chemical properties of the solvents and the degree of a coal swelling in them can be obtained only with the use of linear multiparametric equations which take into account the effects of the all processes proceeding in the system; besides, the basicity and a molar volume of the liquids are determinative. Such approach is effective at the generalization of data concerning to extraction of a coal. Chapter 4 - On the basis of the diallylsilazanes, α,ω-dihydrideoligoorganosiloxanes and 1,4-bis(dimethylhydridesilyl)benzene, new polyfunctional siliconorganic polymers have been synthesized. General regularities and feasible mechanism of the reaction for obtaining diallylsilazanes have been studied. Based on data of elemental, IR and NMR 1H spectral analysis, the composition and structure of synthesized polymers have been established. The kinetics of polyhydrosailylation reactions has been studied. Quantum-chemical calculations of the model system and data of NMR 1H spectra of the real products of the polyaddition reaction have confirmed probability of passing polyhydrosilylation reaction according to the aforementioned two concurrent directions obtaining both α and β adducts. For the evaluation of relative activity for selected monomers the algebraic-chemical approach has been used. Using Differential Scanning Calorimetric and Roentgen-phase analyses methods it has been established that synthesized polymers are amorphous systems. Thermal (phase) transformation temperatures of synthesized polymers have been determined. Thermooxidation stability of the synthesized polymers has been studied. There was shown that their thermooxidation stability exceeded the analogical characteristic of polyorganocarbosiloxanes.

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Using synthesized diallylsilazanes modification of the properties of some important industrial polymer composites based on phenolformaldehide resins has been carried out. Preliminary investigations showed that synthesized polymers in combination with phenolformaldehyde resins were successfully used as binding-components for polymer/graphite and polymer/carbon black electro-conducting composites. Chapter 6 - There has been provided mathematical description of the processes of thermonuclear destruction in deformed polypropylene melts; the aim was to use the criterion of destruction estimation in modelling and optimising the processing of polypropylene into products. Chapter 7 - The application of methodology of spatial-energy interactions (P-parameter) to main stages of photosynthesis is given. Their energy characteristics are calculated. The values obtained correspond to the reference and experimental data. Chapter 8 - Spatial-energy characteristics of many molecules and free radicals are obtained. The possibilities of applying the P-parameter methodology to structural interactions with free radicals and photosynthesis energetics evaluation are discussed. The satisfactory compliance of calculations with experimental and reference data on main photosynthesis stages is shown. Chapter 10 - There has been investigated the effect of thermo-mechanical impact conditions on destruction kinetics in polypropylene melts. The conditions served as a basis for obtaining quantitative dependencies and mathematical expressions aimed at describing destruction processes. Chapter 11 - In work the synthesis technology of zinccontaining polymer - inorganic composite on the basis of products of secondary raw material processing at joint precipitating with carbamide and formaldehyde (ZnCFO) is described. The structure and properties of ZnCFO are investigated by the differencial-thermal analysis, electronic microscopy and IR-spectroscopy. The ZnCFO action as vulcanization active component of elastomeric compositions on the basis of rubbers of general and special assignment with various vulcanization systems is investigated. The comparative estimation of ZnCFO efficiency depending on type of vulcanization system is given. The ZnCFO influence on character of formed morphological structure of rubbers is determined by the method of percalation analysis. Chapter 12 - Spatial-energy criterion of structure stabilization was obtained. The computation results for a hundred binary systems correspond to the experimental data. The basic regularity of organic cyclic compound formation is given and its application for carbon nanostructures is shown. Chapter 13 - It was shown, that limiting conversion (in the given case - imidization) degree is defined by purely structural parameter – macromolecular coil fraction, subjected evolution (transformation) in chemical reaction course. This fraction can be correctly estimated within the framework of fractal analysis. For this purpose were offered two methods of macromolecular coil fractal dimension calculation, which gave coordinated results. Chapter 14 - It was shown, that the conception of reactive medium heterogeneity is connected with free volume representations, that it was to be expected for diffusioncontrolled solid phase reactions. If free volume microvoids were not connected with one

Preface

xiii

another, then medium is heterogeneous, and in case of formation of percolation network of such microvoids – homogeneous. To obtain such definition is possible only within the framework of the fractal free volume conception. Chapter 15 - It was shown, that the reesterification reaction without catalyst can be described by mean-field approximation, whereas introduction of catalyst (tetrabutoxytitanium) is defined by the appearance of its local fluctuations. This effect results to fractal-like kinetics of reesterification reaction. In this case reesterification reaction is considered as recombination reaction and treated within the framework of scaling approaches. Practical aspect of this study is obvious-homogeneous distribution of catalyst in reactive medium or its biased diffusion allows to decrease reaction duration approximately twofold. Chapter 16 - It is shown, that there is principal difference between the description of generally reagents diffusion and the diffusion defining chemical reaction course. The last process is described within the framework of strange (anomalous) diffusion concept and is controled by active (fractal) reaction duration. The exponent α, defining the value of active duration in comparison with real time, is dependent on reagents structure. Chapter 17 - Vapor-liquid equilibrium (VLE) data are important for designing and modeling of process equipments. Since it is not always possible to carry out experiments at all possible temperatures and pressures, generally thermodynamic models based on equations on state are used for estimation of VLE. In this paper, an alternate tool, i.e. the artificial neural network technique has been applied for estimation of VLE for the binary systems viz. tert-butanol+2-ethyl-1-hexanol and n-butanol+2-ethyl-1-hexanol. The temperature range in which these models are valid is 353.2-458.2K at atmospheric pressure. The average absolute deviation for the temperature output was in range 2-3.3% and for the activity coefficient was less than 0.009%. The results were then compared with experimental data. Chapter 18 - The determination region of solubility of methanol with gasoline of high aromatic content was investigated experimentally at temperature of 288.2 K. A type 1 liquidliquid phase diagram was obtained for this ternary system. These results were correlated simultaneously by the UNIQUAC model. By application of this model and the experimental data the values of the interaction parameters between each pair of components in the system were determined. This revealed that the root mean square deviation (RMSD) between the observed and calculated mole percents was 3.57% for methylcyclohexane + methanol + ethylbenzene. The mutual solubility of methylcyclohexane and ethylbenzene was also demostrated by the addition of methanol at 288.2 K. Chapter 19 - The results of experimental researches on the synthesis of sugars derivatives with glycosylamide and thioamide bonds have been presented in this work. The possibility of using their in the preparative chemistry of sugars, some fields of medicine and agriculture has been shown.

In: Organic and Physical Chemistry Using Chemical Kinetics … ISBN: 978-1-60021-763-0 Editors: Y.G. Medvedevskikh, et al. pp. 1-21 © 2007 Nova Science Publishers, Inc.

Chapter 1

CONFORMATION AND DEFORMATION OF LINEAR MACROMOLECULES IN CONCENTRATED SOLUTIONS AND MELTS IN THE SELF–AVOIDING RANDOM WALKS STATISTICS Yu. G. Medvedevskikh* Physical Chemistry of Combustible Minerals Department; L. M. Lytvynenko Institute of Physical–Organic Chemistry and Carbon Chemistry; National Academy of Sciences of Ukraine

ABSTRACT It was proposed a strict statistics of self–avoiding random walks in the d–measured lattice and continuous space for intertwining chains in the concentrated solutions and melts. On the basis of this statistics it was described the thermodynamics of conformation and isothermal and adiabatic deformation of intertwining chains. It has been obtained the equation of conformational state. It was shown, that in the field of chains overlap they are stretched increasing its conformational volume. In this volume there are others chains with the formation of m–ball. Free energy of a chain conformation does not depend upon the fact, if the chains intertwined or they are isolated in the m–ball. Mixing entropy is responsible to the chains interweaving in the m–ball. Dependencies of the conformational radius, free energy and conformation pressure on respective concentration of polymeric chains have been determined. Using the thermodynamics of intertwining polymeric chains of m–ball conformational state and also the laws of isotropic media deformation into linear differential form it were obtained the theoretical expressions for elasticity modules (namely, volumetric volume, Young’s module and shift’s module) and for the main tensions appearing at the equilibrium deformation of the m–ball. Poisson’s coefficient is a function only on the Euclidean’s space and for the real 3–dimensional space is equal to 3/8. It was proposed a simple model explaining the tensile strength of the m–ball by the chains intertwining effect and, thereafter by the loss of the mixing entropy, but not by the chemical bonds breaking. Calculations of the elastic properties, *

Yu. G. Medvedevskikh: 3a Naukova Str., 79053, Lviv, UKRAINE; e–mail: [email protected]

2

Yu. G. Medvedevskikh the main tensions and tensile strength of natural rubber carried out without using the empirical adjusting parameters are in good agreement with the experimental data.

Key words: intertwining chains, SARW statistics, conformation, polymer chain, random walks, lattice, thermodynamics, modules of elasticity, forces, work..

1. INTRODUCTION Self–avoiding random walks (SARW) statistics has been proposed [1] for single that is for non–interacting between themselves ideal polymeric chains (free–articulated Kuhn’s chains [2]) into ideal solvents, in which the all–possible configurations of the polymeric chain are energetically equal. From this statistics follows, that under the absence of external forces the conformation of a polymeric chain takes the shape of the Flory ball, the most verisimilar radius Rf of which is described by known expression [3, 4]

R f = aN 3 /( d + 2 )

(1)

Here: a is statistical length of the chain’s link; N is number of the links in chain or its length; d is the dimension of the Euclidean’s space. Polymeric chains in the concentrated solutions and melts at molar–volumetric concentration c of the chains more than critical one c* = (NARfd)-1 are intertwined. As a result, from the author’s point of view [3] the chains are squeezed decreasing their conformational volume. Accordingly to the Flory theorem [4] polymeric chains in the melts behave as the single ones with the size R = aN1/2, which is the root–main quadratic radius in the random walks (RW) Gaussian statistics. SARW statistics leads to other result.

2. SARW STATISTICS FOR INTERTWINING CHAINS IN D–DIMENSIONAL LATTICE SPACE Let us introduce the d–dimensional lattice with the cell’s parameter equal to the statistical length a of the chain’s link; let us notify, that Z is number of cells in a space and m chains are represented in it; every chain has the length N. As same as earlier [1], we will disregard the energetic effects considering the all–possible configurations of the chains as equivalent. We appropriate the random chain and notify as ni the numbers of steps of the end of chain random walk along i–directions of d–dimensional lattice. At this,

∑n

i

=N,

i = 1, d

(2)

i

The probability

ω ( n ) that at given ni the end of chain draws si = ni + − ni − efficient

steps is subordinated to Bernoulli’s distribution [1]

Conformation and Deformation of Linear Macromolecules…

⎛1⎞ ω( N ) = ⎜ ⎟ ⎝2⎠

N

∏ {n ! /[( n + s ) / 2 ]! [( n − s ) / 2 ]!} i

i

i

i

3

(3)

i

Change of a sign si in eq. (3) doesn’t change the value

ω ( n ) ; that is why this probability

represents the probability of fact, that the RW trajectory per ni steps along i–directions of the d–dimensional space will be finished in one of the 2d cells M(s), position data of which are given by vectors s = (si), i = 1, d differing only by the signs of own components si. Condition of the self–avoiding RW trajectories absence on the d–dimensional lattice demands the circumstance at which more than one link of the chain can not be stood in every cell. Links of the chain are inseparable; they cannot be divided one from another and located into the cells in random order. Thereby, number of different methods of mN differing links location per Z identical cells under condition that in every cell more than one link of the chain cannot be stood is equal to Z! / (Z – mN)!. By identify of the cells the antecedent probability of fact that the cell will be occupied by presented link equal to 1/Z, and when will be not occupied – then (1 – 1/Z). Consequently, probability ω ( z ) of mN differing links distribution per Z identical cells is determined by Bernoulli’s distribution

Z! ⎛1⎞ ω( z ) = ⎜ ⎟ ( Z − mN )! ⎝ Z ⎠

mN

⎛ 1⎞ ⎜1 − ⎟ ⎝ Z⎠

Z −mN

(4)

Distribution (3) describes the RW trajectory of one random chain whereas the expression (4) assigns the links distribution of all m chains. That is why, the probability ω ( s ) of common event consisting of the fact that the RW trajectory of random chain is also the SARW trajectory and at given Z, n, N and ni will turned out by its own last step in one among 2d equiprobable cells M(s) will be equal to

ω ( s ) = ( ω ( z ))1 / m ω ( n )

(5)

Using the Stirling’s formula under condition Z >> 1, N >> 1, ni >> 1 and factorizations ln(1–1/Z) ≈ –1/Z, ln(1–mN/Z) ≈ –mN/Z, ln(1±si/ni) ≈ ± si/ni–(si/ni)2/2 accordingly to condition si << ni, mN << Z and also assuming N(N–1) ≈ N2, we find the asymptotic (5) with accuracy to the constant multiplier:

⎧ mN 2 1 ⎫ 2 − ∑ si / ni ⎬ , 2 i ⎩ Z ⎭

ω ( s ) ≈ exp⎨−

m ≥1

(6)

As same as earlier [1], let us assume, that the fiducial cells M(s) generally appertain to ellipsoid surface. Then we have [1]

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Yu. G. Medvedevskikh

Z = d d / 2 ∏| si |

(7)

i

Determination (7) means, that the d–dimensional space consisting of Z cells is disposable for any random chain; this demands of their full mixing. Combining the expressions (6) and (7) we will obtain

⎧

ω ( s ) = exp⎨− mN 2 / d d / 2 ∏| si | − ⎩

Function

i

⎫ 1 2 si / ni ⎬ ∑ 2 i ⎭

(8)

ω ( s ) determines the probability that the RW trajectory of the random walk is

simultaneously also by SARW trajectory and by its own last step realizes the state M(s). Hence, it is numerically equal to part of these SARW trajectories among general number (2d)N of RW trajectories which realize the state M(s). Number L(s) of such SARW trajectories determines the thermodynamical probability of the realization M(s):

L( s ) = ( 2d )N ω ( s )

(9)

By summing L(s) upon the all set of possible state of the chain’s end we find general number L of SARW trajectory:

L = ( 2d ) N c( s )

(10)

where

⎧ ⎫ 1 2 c( s ) = ∑ exp⎨− mN 2 / d d / 2 ∏| si | − ∑ si / ni ⎬ 2 i s i ⎩ ⎭

(11)

Then function

w( s ) =

⎧ ⎫ 1 1 2 exp⎨− mN 2 / d d / 2 ∏| si | − ∑ si / ni ⎬ c( s ) 2 i i ⎩ ⎭

(12)

normalized per unity and determines the end of chain distribution upon states M(s) of d– dimensional lattice. It equal to ratio of number L(s) of SARW trajectories realizing the state M(s) to general number L of SARW trajectories: w( s ) = L( s ) / L . In turn, the ratio L/(2d)N equal to part of general number of SARW trajectories among general number of RW trajectories in accordance with the adopted terms [3] is the fatigue function g(N) of the SARW trajectories: g(N) = L/(2d)N = c(s).

Conformation and Deformation of Linear Macromolecules…

5

3. SARW STATISTICS FOR INTERTWINING CHAINS IN CONTINUOUS D–DIMENSIONAL SPACE Let us introduce the variable of displacement xi, which is by semi–axis of conformational ellipsoid; the state M(s) appertains to the surface of this ellipsoid [1]

xi = a | si | d 1/ 2 and parameter

(13)

σ i is a standard deviation of the Gaussian part of the distribution (12)

σ i 2 = a 2 ni d

(14)

In accordance with the expression (2) the following connection is imposed on the values

σi

∑σ

2 i

= a 2 Nd

(15)

i

Since si / ni = xi / σ i , d 2

2

2

d/2

∏| s |= a ∏ x −d

i

i

i

ω( x ) =

the eq. (12) can be re–written as

i

⎧ 1 1 2 2⎫ exp⎨− a d mN 2 / ∏ xi − ∑ xi / σ i ⎬ 2 i c( x ) i ⎩ ⎭

⎧ 1 2 2⎫ c( x ) = ∫ exp⎨− a d mN 2 / ∏ xi − ∑ xi / σ i ⎬dx 2 i i ⎩ ⎭

(16)

(17)

At this, c(x) is d–multiple integral upon all possible values xi, dx =

∏ dx . Since i

i

c( x ) = a d d d / 2 c( s ) we have g(N) = c(x)/addd/2. Integral c(x) can be taken with the adequate accuracy by saddle–point technique [1, 5]. Change of (13) introduces an essential difference between w( s ) and w( x ) : the last determines the probability w( x )dx of fact that the SARW trajectory at given values m, N and

σ i will finished in the elementary volume dx = ∏ dxi lying on the surface of the ellipsoid i

with the semi–axes xi, i = 1,d.

6

Yu. G. Medvedevskikh

4. THERMODYNAMICS OF CONFORMATION AND DEFORMATION OF INTERTWINING CHAINS Maximum w( x ) at given m, N and

σ i determines the most expected or equilibrium

state of the polymeric chain. Semi–axes xi of equilibrium conformational ellipsoid we will found from the condition ∂ ln w( x ) / ∂xi = 0 at xi = X i : 1 /( d + 2 )

⎛ ⎞ X i = σ i ⎜⎜ a d mN 2 / ∏ σ i ⎟⎟ i ⎝ ⎠

(18)

In the absence of external forces the all directions of the end of chain walking are equiprobable accordingly to condition ni = N / d ; so

σ i 2 = σ 02 = a2 N

(19)

Substitution of (19) into (18) makes the semi–axes Xi of equilibrium ellipsoid the same and equal to radius Rm of the conformational sphere; the same distribution density ω ( x ) corresponds to the surface of this conformational sphere:

Rm = aN 3 /( d +2 )m

1 /( d + 2 )

(20)

Expression (20) determines not only the conformational radius of one random chain, but due to the chains intertwining effect also the conformational radius of all m chains. Thereby

Rmd is the conformational volume of m–ball disposable for every among the intertwining chains. As we can see, m–ball is a fractal with two fractal indexes: first is 3/(d+2) and determines the dependence Rm on the chain N, the second is 1/(d+2) and determines the dependence on number of chain in m–ball. We can see from the comparison of (20) and (1), that the conformational radius Rm of m– ball and respectively of any random chain in it is more than the conformational radius Rf of random chain: in m–ball the chains are stretched but are not twisted. The presence of other chains diminishes the number of free cells of d–dimensional lattice accessible for SARW trajectory of presented chains enforcing it to encroach more volume of the space. In the presence of external forces acting along i–axes of the d–dimensional space, σ i ≠ σ 0 and m–ball is deformated into the ellipsoid with semi–axes Xi accordingly to (18). It is convenient to introduce the following variables as a measure of m–ball deformation

Λi = X i / Rm

(21)

Conformation and Deformation of Linear Macromolecules…

7

which characterize the multiplicity of the linear deformation of m–ball along i–direction of a space. Next, let us determine the multiplicity Λv of volumetric deformation via expression

Λv = ∏ X i / Rmd = ∏ Λi i

Λv

(22)

i

Due to (2) [1] at any deformations of the m–ball its conformational volume is decreased: ≤ 1 . The connection equation between Λi corresponds to connection equation (2):

∑Λ

i

i

2

= d / ∏ Λi

(23)

i

In continuous space the thermodynamical probability W ( x ) of the realization of state in which the end of chain is located on the surface of the ellipsoid with the semi–axes Xi is equal to

W ( x ) = Lω ( x )

(24)

As same as for the lattice space, general number L of SARW trajectories in continuous space let us determine in the form (10), that is L ≈ ( 2d ) c( x ) . That is why N

⎧ 1 2 2⎫ W ( x ) ≈ ( 2d ) N exp⎨− a d mN 2 / ∏ xi − ∑ xi / σ i ⎬ 2 i i ⎩ ⎭

(25)

Entropy S of presented conformational state is equal to S = k ln W ( x ) , free energy

F = −TS or F = −kT ln W ( x ) . From (25) follows F = F0 + F ( x ) where

F0 ≈ −kTN ln 2d ≈ −

d kTN 2

⎧ 1 2 2⎫ F ( x ) = kT ⎨a d mN 2 / ∏ xi + ∑ xi / σ i ⎬ 2 i i ⎩ ⎭

(26)

(27)

Thereby, F0 represents by itself a free energy of random walks independent on the conformational state of a chain; F(x) brings a positive contribution into F and the sense of this consists in a fact that the terms F(x) and S(x) represent the limitations imposed on the trajectories of random walk by request of the self–avoiding absence. These limitations form the self–organization effect of the polymeric chain: the conformation of polymeric chain is the statistical form of its self–organization.

8

Yu. G. Medvedevskikh

Since F0 doesn’t depend on the conformational state of a chain we assume that the free energy of a polymeric chain conformation is equal to F = F(x) accordingly to (27). Expression for the free energy of equilibrium conformation of polymeric chain we will obtain by substitution of the values xi = Xi in (27) in accordance with the (18): 2

⎛ d⎞ ⎛R ⎞ Fm = ⎜1 + ⎟kT ⎜⎜ m ⎟⎟ / Λv ⎝ 2 ⎠ ⎝ σ0 ⎠ For non–deformated m–ball we have

⎛ d⎞ ⎛R ⎞ F = ⎜1 + ⎟kT ⎜⎜ m ⎟⎟ ⎝ 2 ⎠ ⎝ σ0 ⎠

(28)

Λv = 1 and

2

0 m

(29)

From this the expression follows for the deformation work ( A = ΔFdef in the system of the mechanics signs) of m–ball into ellipsoid in calculation per one chain

⎛ d⎞ ⎛R ⎞ ΔFdef . = ⎜1 + ⎟kT ⎜⎜ m ⎟⎟ ⎝ 2 ⎠ ⎝ σ0 ⎠ Since

2

⎛ 1 ⎞ ⎜⎜ − 1⎟⎟ ⎝ Λv ⎠

(30)

Λv ≤ 1 , a work of the deformation is positive ΔFdef ≥ 0 , that is realized above the 0

polymeric chain. Let us compare a free energy Fm of the polymeric chain in non–deformated m–ball with a free energy Ff of single deformated polymeric chain [1]

⎛ d⎞ ⎛R F f = ⎜1 + ⎟kT ⎜⎜ f ⎝ 2 ⎠ ⎝ σ0 Here

2

⎞ ⎟⎟ / λv ⎠

(31)

λv is a multiplicity of the volumetric deformation of Flory ball.

Let us assume that the chains in m–ball aren’t intertwined, every among them occupies the isolated volume equal to Rmd/m. Then the multiplicity of the volumetric deformation of Flory ball into m–ball will be equal to

λv = Rm d / mR f d = m −2 /( d +2 )

(32)

We will obtain for the conformation free energy of isolated chain into m–ball

⎛ d⎞ ⎛R F f = ⎜1 + ⎟kT ⎜⎜ f ⎝ 2 ⎠ ⎝ σ0

2

⎞ 2 /( d +2 ) ⎟⎟ m ⎠

(33)

Conformation and Deformation of Linear Macromolecules… that

is

equal

to

Fm0

accordingly

( Rm / σ 0 ) = ( R f / σ 0 ) m 2

2

2 /( d + 2 )

to

(29)

with

taking

into

9 account

that

.

Thereby, free energy of the conformation of single chain into m–ball for intertwining or isolated one from another chains is the same. Free energy of the conformation is not the factor, which facilitates or prohibits the chains intertwining. In the absence of energetic interaction such factor is the entropy of mixing. It can be estimated via the numbers of displacement methods of the all chains links into m–ball with the exception of a displacement links in every chains: (mN)!/(N!)m. From this under the Stirling’s approximation we will obtain the expression for the entropy of mixing ΔS c in calculation per one chain,

ΔSc = kN ln m , and, respectively we will obtain for free energy

ΔFc of mixing ΔFc = −kTN ln m The value

(34)

ΔFc < 0 and can be sufficiently big per absolute value, for instance for melts,

in order to provide the chains intertwining of their mixing in m–ball.

6. EQUATION FOR THE CONFORMATIONAL STATE OF M–BALL Let us determine the pressure P of a conformation via the ordinal thermodynamic ratio (∂F / ∂V )T = − P as a connection measure between the free energy and the volume of conformation. Taking into account the all chains into m–ball, we have F = mFm ,

V = Rmd Λv , that is why P = −m∂Fm / ∂Λv Rmd . By differing the eq. (28) we have 2

⎛ d⎞ ⎛R ⎞ P = ⎜1 + ⎟kT ⎜⎜ m ⎟⎟ m / Rmd Λ2v ⎝ 2 ⎠ ⎝ σ0 ⎠

(35)

By multiplying (35) on V = ( Rm Λv ) 2

d

2

we will obtain the equation of the

conformational state of m–ball:

PV 2 = mkTβ

(36) 2

⎛ d ⎞⎛ R ⎞ β = ⎜1 + ⎟⎜⎜ m ⎟⎟ Rmd ⎝ 2 ⎠⎝ σ 0 ⎠

(37)

10

Yu. G. Medvedevskikh

From the comparison of (35) and (28) it follows, that the pressure of the conformation numerically is equal to the density of free energy of the conformation of m–ball P = mFm/V. That is why we have

FmV = kTβ

(38)

Thereby, the values PV2 and FmV are integrals of the process of equilibrium deformation of m– ball.

7. ADIABATIC EQUATION FOR EQUILIBRIUM DEFORMATION OF M–BALL It is well–known [6, 7], that at the adiabatic deformation of rubber its temperature is increased. The analysis of this phenomenon in the works [6, 7] is not quite correct. That is why let us consider the adiabatic deformation of the m–ball with the use of obtained thermodynamic ratios. For elementary adiabatic process Cv dT = −δA , where Cv is the heat of the m–ball, δA is the elementary work in the systems of the thermodynamics signs. Due to determination of the conformation pressure we can write δA = PdV and, thereby

Cv dT = − PdV

(39)

Using the equation of the conformational state (36) let us divide the variables in (39)

Cv dT / T = −mkβdV / V 2

(40)

Integration of (40) at Cv = const for low–temperature interval in a ranges from V = Rmd and V = Rm Λv and from T0 till T corresponding to the temperatures of the start and the finish d

of the adiabatic process gives

Cv ln

T mkβ = d ( 1 / Λv − 1 ) T0 Rm

(41)

We can see from this, that the adiabatic equation is as follow

{

}

T exp − mkβ / Cv Rmd Λv = const

(42)

In accordance with the experimental data the temperature change at the adiabatic deformation of rubber is slight, that is why it can be assumed that ΔT = T − T0 << T0 ; this permits to re–write (41) with taking into account the expression (37) for

β in following form

Conformation and Deformation of Linear Macromolecules…

11

2

⎛ d ⎞ kT ⎛ R ⎞ ΔT ≈ ⎜1 + ⎟ 0 ⎜⎜ m ⎟⎟ ( 1 / Λv − 1 ) ⎝ 2 ⎠ cv ⎝ σ 0 ⎠

(43)

Here it was assumed that Cv = mcv, where cv is a heat of one chain.

8. EXPRESSION OF THE THERMODYNAMIC FUNCTIONS VIA RELATIVE CONCENTRATION OF MACROMOLECULES In the field of the chains overlapping at c ≥ c = ( N A R f ) *

d

−1

their molar–volumetric

concentration into m–ball and in all volume of the solution or melt is the same:

c = m / N A Rmd . It is more convenient for the melts to use the other determination of concentration since

ρ = mM / N A Rmd , where M is a molar mass of the chain and is experimentally determined by a specific density of the melt. Speculative critical density

ρ * = M / N A R df corresponds

to it. From this follows

ρ / ρ * = c / c* = m 2 /( d +2 )

(44)

The ratio (44) permits to determine the following dependencies, which with the aim of * 1/ 2

the shortness can be represented in the form of the commensurability: Rm ~ ( c / c ) *

*

,

2

Fm ~ c / c and P ~ ( c / c ) .

9. FORCES AND WORK OF THE DEFORMATION Let us introduce one more parameter for characteristics of m–ball deformation with the aim of convenient description of elastic properties of the intertwining chains

ψi = σi / σ0

(45)

Due to the ratio (15) the following connection exists between ψ i

∑ψ

2 i

=d

(46)

i

We determine from the analysis of (18) and (20), and also from the determinations (21) and (22)

12

Yu. G. Medvedevskikh

ψ i = Λi Λv1/ 2

(47)

In the system of the mechanics signs the deformation forces acting on the random chain into m–ball along i–axes of the d–dimensional space are equal to f i = ∂F ( x ) / ∂xi . By differing (27) we will obtain

⎛ 2⎞ f i = kT ⎜⎜ − a d mN 2 / xi ∏ xi + xi / σ i ⎟⎟ i ⎝ ⎠

(48)

However, under the equilibrium deformation in every current conformational state the forces should be equal to zero; just this is expressed via the equilibrium condition ∂F ( x ) / ∂xi = 0 at xi = Xi. Thereby, the substitution of the values xi = Xi into (48) draws fi into zero. That is why the external deformation force along i–direction let us determine as the force, which should be imposed on the non–deformated m–ball with the conformation radius Rm, which is equilibrium with respect to the values σ i = σ 0 in order to transform it into the deformated state of the ellipsoid with the semi–axes Xi equilibrium with respect to the values σ i ≠ σ 0 , i = 1,d. In accordance with this determination in the expression (48) in the second term it is necessary to put

σ i = σ 0 but the values xi to change on Xi accordingly to (18) at

σ i ≠ σ 0 . Making the corresponding substitution we will obtain the following expression for the external main forces of a deformation

(

1 /( d + 2 )

)

⎛R ⎞ ⎛ ⎞ 2 f i = kT ⎜⎜ m2 ⎟⎟ ψ i − 1 / ψ i ⎜⎜ ∏ψ i ⎟⎟ ⎝ i ⎠ ⎝σ0 ⎠

In the adopted systems of signs fi > 0 at the stretching contraction

(ψ i < 1) .

(49)

(ψ i > 1)

and fi < 0 at the

With taking into account the connection (47) the force can be determined via the multiplicities of linear and volumetric deformation of m–ball

(

)

⎛R ⎞ 2 f i = kT ⎜⎜ m2 ⎟⎟ Λi Λv − 1 / Λi Λv ⎝σ0 ⎠

(50)

The work of the deformation A in calculation per one chain into m–ball along the all main directions can be written in accordance with the mechanics rules in form: Xi

A = ∑ ∫ f i dxi i

Rm

(51)

Conformation and Deformation of Linear Macromolecules…

13

Substitution of (49) in (51) with taking into account the connection (47) leads to the expression for A which is identical to the expression (30) for Fdef: A = ΔFdef in the systems of the mechanics signs. The agreement confirms the truth of the determination of external forces of deformation accordingly to (49).

10. ELASTICITY MODULES OF M–BALL Taking into account the big sizes of polymeric chains deformation and their non–linear relation with the tension let us express the relative linear deformation dxi/xi along i–direction of d–dimensional space under the action of all main forces fi, i = 1,d under the approximation of m–ball isotropy via the differential form [8]

Y∂xi / xi = ∂f i / ∏ x j + γ ∑ ∂f j / ∏ xk j ≠i

j ≠i

Here: Y is Young’s module;

(52)

k≠ j

γ is Poisson’s coefficient;

∏x

j

and

j ≠i

∏x

k

are the values of

k≠ j

the sites in d–dimensional space normal to the forces fi and fj correspondly. Let us re–write the (52) relative to Young’s module

Y=

x x ∂f i ∂f i +γ ∑ i j ∏ xi ∂xi j≠i ∏ xi ∂xi xi

2

i

(53)

i

At equilibrium deformation the forces fi are equal to zero, but not their derivatives ∂f i / ∂xi and ∂f i / ∂x j . That is why by differing (48) upon xi and xj and by substituting the equilibrium values xi = Xi into obtained expressions we will obtain

∂f i / ∂xi = 3kT / σ 0 ψ i 2

2

(54)

∂f i / ∂x j = ∂f j / ∂xi = kT / σ 0 ψ iψ j 2

(55)

Derivatives in (54) and (55) have been written in accordance with the determination (48) for one random chain. However, as same as the conformation pressure the elastic properties of the intertwining chains in m–ball need the taking into account the all m chains. That is why by multiplying the right terms of (54) and (55) on m and by substituting the result in (53) we will find 2

⎛R ⎞ d 2 Y = mkT [3 + γ ( d − 1 )]⎜⎜ m ⎟⎟ / Rm Λv ⎝σ0 ⎠

(56)

14

Yu. G. Medvedevskikh

From the comparison of (35) and (56) follows, that the Young’s module of m–ball and the conformation pressure are differed only by the coefficient and

Y=

2[3 + γ ( d − 1 )] P d +2

(57)

In general case of the d–dimensional space the connection between the Young’s module and the pressure is expressed via the volumetric module E = –VdP/dV by ratio [8]

E = Y / d [1 − γ ( d − 1 )]

(58)

From the equation of a state (12) follows

E = 2P

(59)

By comparing the (57) – (59) we will obtain the expression for Poison’s coefficient

γ = ( d + 3 ) /( d + 1 )2

(60)

Thereby, as same as for the random chain [1], the Poison’s coefficient for intertwining chains is determined only by the dimensionality d of the Euclidean’s space an at d = 3 is equal to γ = 3 / 8 . Via the Young’s module and the Poison’s coefficient we find the shift module

μ = Y / 2( 1 + γ )

at d ≥ 2

μ [2]:

(61)

which is also easy expressed via the conformation pressure

μ=

3 + γ ( d −1) P ( d + 2 )( 1 + γ )

(62)

11. MAIN TENSIONS AND THE TENSILE STRENGTH Connection between the tension Gi in planar surface normal to i–direction of the deformation and between its relative value ∂xi / xi also let us write in differential form

∂Gi = Y∂xi / xi

(63)

In general case this equation hasn’t a simple analytical solution, but permits with the use of (23) and (46) easy to obtain the constraint equation between Gi. By acting analogously to the developed algorithm [1], we will obtain

Conformation and Deformation of Linear Macromolecules…

∑G

i

i

(

)

1 2 = − Y 0 1 / Λv − 1 2

15

(64)

Λv = 1 , that is for non–deformated m–ball.

where Y0 = Y at

The sign “minus” signifies, that a sum of the main tensions is subzero (that is negative) at any deformations of m–ball through its volume decreasing. For analytical demonstration of Gi at equilibrium deformation, that is at xi = Xi let us re– write the (63) with taking into account the ratio Y = Y / 0

Λv 2 and substitute in it the

expression ∂ ln xi = ∂ lnψ i − 1 d ln Λv which follows from the connection (47). Then we

2

will obtain 4 / d +2 ⎤ ⎡ ⎛ ⎞ 1 3 ∂Gi = Y ⎢∂ψ i/ ψ i ⎜⎜ ∏ψ i ⎟⎟ − ∂Λv / Λv ⎥ 2 ⎝ i ⎠ ⎥⎦ ⎢⎣ 0

In the starting non–deformated state of m–ball the all

(65)

ψ i = 1 , Λv = 1 and Gi = 0. By

integrating the (65) accordingly to these conditions we will find

(

)

⎤ ⎡1 2 Gi = Y 0 ⎢ 1 / Λv − 1 + I i ⎥ 4 ⎦ ⎣ ψ

i ⎛ ⎞ I i = ∫ ∂ψ i / ψ i ⎜⎜ ∏ψ i ⎟⎟ ⎝ i ⎠ 1

(66)

4 /( d + 2 )

(67)

From this follows, that for the calculation of Ii and respectively Gi the constraint equation (46) between ψ i is insufficiently; additional information about the character of deformation is needed in order to determinate the additional connection between

ψ i . One among the

variants of the Gi calculation is considered in the next chapter. At the m–ball stretching along the i–direction such critical tension is beginning at which m–ball is broken into two parts. Such critical tension Gicr is the numerical estimation of m– ball tensile stretch. Its mechanism likes sufficiently complicating, but we will propose a simple model for the Gicr calculation. Accordingly to this model we assume, that the break of m–ball into two parts at Gicr proceeds at the expense of the chains fraying, that is at the expense of the process inverse to their intertwining, in the issue of which the physical network of the linkings is destroyed. Crosslinking of the chains at rubber vulcanization blocks the chains intertwining and that is why increases the stability of the vulcanized rubber. The chains intertwining in m–ball decreases the entropy of mixing. For non–deformated m–ball the entropy of mixing ΔS c for all m chains determined as

ΔSc = kNm ln m

(68)

16

Yu. G. Medvedevskikh

Let in the deformated m–ball in a moment of break the part of the residual intertwining chains is equal to α . Then the entropy of mixing will be equal to

ΔSc = kNmα ln( mα ) ,

mα > 1

(69)

The break of m–ball we consider as such equilibrium transition at which m–ball with the intertwining parameter α is divided by the plane of fracture into two m/2–balls with the same intertwining parameter. The entropy of mixing into two m/2–balls will be equal to

αm

ΔSc' = kNαm ln( αm / 2 ) ,

2

>1

(70)

The loss of the entropy of mixing at the m–ball braking will be thereafter the work of a break

Δ( ΔS c ) = ΔSc' − ΔSc ;

ΔFbr = −TΔ( ΔS c ) will be

ΔFbr = kTNαm ln 2

(71)

At breaking the m–ball into two parts it can be assumed that

α = 1 / 2 . Then

ΔFbr = ( 1 / 2 )kTNm ln 2

(72)

This work of the break is created by the work of the m–ball deformation at some critical value of the multiplicity of volumetric deformation Λ vcr . That is why by equating a work of the deformation

ΔFdef accordingly (30) multiplied on m– in calculation per all m–ball at

some critical value

Λv to the work of a break ΔFbr accordingly to (72) we will find Λv : cr

2 ⎤ ⎡ 1 ⎛σ0 ⎞ ⎜⎜ ⎟⎟ N ln 2⎥ Λvcr = ⎢1 + ⎥⎦ ⎢⎣ d + 2 ⎝ Rm ⎠

Knowing the

cr

−1

(73)

Λv , we can calculate the tensile strength Gi at the m–ball stretching cr

cr

along the i–direction.

12. CALCULATIONS AND ILLUSTRATIONS For calculations let us consider the real d = 3–dimensional space assuming that among three main tensions fx, fy and fz only one, for example fz is independent variable, that is external force, and fx, and fy are reaction forces on fz. At the isotropy of m–ball the forces and

Conformation and Deformation of Linear Macromolecules…

17

multiplicities of linear deformations along the x and y axes will be equal: f x = f y , In this case the conformational volume of the m–ball shapes the elongated or strangulated ( f z < 0 , Λz < 1) along z–axis the ellipsoid of rotation.

Λx = Λ y .

( f z > 0, Λz > 1)

For the ellipsoid of rotation the general constraint equations (23) and (46) take on the particular form

2Λv + Λz Λv − 3Λz = 0

(74)

2ψ x + ψ z = 3

(75)

2

2

3

2

By assigning the values

Λz as to singular independent variable the values Λv have been

calculated and further Λx = Λ y = ⎛⎜ Λv ⎞⎟ Λ

1/ 2

⎝

z

⎠

.

For the shortness let us confine to the numerical analysis of the isothermal and adiabatic deformation of natural rubber, which at comparatively low chains cross–linking can be described as a melt. For natural rubber – polyisoprene (C5H8)N – the following parameters have been chosen: number–average molar mass of the chain M = 2·106 g/mole and average length of the chain N = 2,9·104; ρ = 0,91·106 g/m3, a = 0,125 nm. On the basis of these parameters ρ* = 1,54·104 g/m3 and ρ/ρ* = 59,1 were determined. The work of the isothermal deformation in units kT has been calculated in accordance with the equation (30) converted to a form

ΔFdef / kT =

5 1/ 5 ⎛ ρ N ⎜⎜ * 2 ⎝ρ

⎞ ⎟⎟(1 / Λv − 1) ⎠

(76)

Results of the calculations are represented on figure 1. Dependence of ΔFdef / kT for one chain of the natural rubber on

Λz is the same as for

the Flory’s ball [1], but numerically exceeds the last in ρ/ρ* times. Let us notify also, that in spite of the “very much” value ΔFdef / kT for one chain in calculation per one link, this magnitude has an order equal to 1. Temperature change at adiabatic deformation of natural rubber was calculated accordingly to eq. (43) which under assumption cv = cv N , where cv = c p is molar heat 0

0

0

of the isoprene carries to

⎛ ρ ⎞ RT ΔT = 5 2 00 N −4 / 5 ⎜⎜ * ⎟⎟(1 / Λv − 1) cp ⎝ρ ⎠

(77)

where R is universal gaseous constant. At the calculation accordingly to (77) it was assumed in accordance with the reference data for the isoprene cp0 =152,3 J/moleK, T0 = 300 K.

18

Yu. G. Medvedevskikh

(

)

(

Figure 1. The work of the natural rubber deformation at its stretching Λz > 1 and squeezing Λz along z axis. Calculation has been done in accordance with the eq. (76) (see the explanations in text). '

'

)

<1

Results of the calculations are represented on figure 2. They are in good agreement with the experimental data [6, 7]. 5

ΔT, K

4 3 2 1 0 0

1

2

3

4

Λz

5

Figure 2. Temperature increasing at adiabatic deformation of natural rubber at its stretching

(

)

(Λz > 1) and

squeezing Λz < 1 along z axis. Calculation has been done in accordance with the eq. (77) (see the explanations in text).

Young’s module has been calculated in accordance with the eq. (56) by taking into account (44) and γ = 3 / 8 :

Conformation and Deformation of Linear Macromolecules…

19

2

⎛ ρ kT Y = 3,75 3 N −8 / 5 ⎜⎜ * a ⎝ρ

⎞ 2 2 ⎟⎟ / Λv = Y 0 / Λv ⎠

(78)

where Y0 = 1,97 MPa is Young’s module of non–deformated rubber at T = 300 K. Results of the calculations are represented on figure 3. For the ellipsoid of rotation Gx = Gy, that is why we can write in accordance with the (66)

(

)

(79)

(

)

(80)

⎡1 ⎤ 2 Gx = Y 0 ⎢ 1 / Λv − 1 + I x ⎥ ⎣4 ⎦ ⎡1 ⎤ 2 Gz = Y 0 ⎢ 1 / Λv − 1 + I z ⎥ ⎣4 ⎦

Due to connection (75) every from integrals Ix and Iz can be balanced to one own variable. In accordance with the (67) and (75) we have ψx

(

/5 I x = ∫ dψ x / ψ 13 3 − 2ψ x x

)

2 2/ 5

(81)

1

Iz = 2

ψz 4/ 5

∫ dψ

z

/ψz

9/ 5

(3 −ψ )

2 4/ 5

(82)

z

1

At this, superior limits of the integration are given by the ratios

ψ x = Λx Λv1 / 2 and

ψ z = Λz Λv1 / 2 following from (47). Results of the calculations accordingly to eq. (79) – (82) at Y0 = 1,97 MPa are represented on figure 4. Needed for the estimation of Gzcr value of critical multiplicity of volumetric deformation

Λv was calculated accordingly to eq. (73) by transforming it to a form cr

⎡ 1 ⎛ ρ* Λvcr = ⎢1 + N 4 / 5 ⎜⎜ ⎝ ρ ⎣ 5

⎤ ⎞ ⎟⎟ ln 2⎥ ⎠ ⎦

As a result, we have obtained

−1

(83)

Λv = 0,103 , respectively Λz = 5,39 , Λx = 0,138 . cr

Gzcr = 48 MPa corresponds to these values.

cr

cr

20

Yu. G. Medvedevskikh

150

Y, MPa 100

50

0 0

1

2

3

Λz

4

5

Figure 3. Dependence of the Young’s module on the multiplicity of linear deformation Λz at stretching and squeezing of natural rubber along z axis. Calculation has been done in accordance with the eq. (78) (see the explanations in text).

50

Gz,Gx, MPa Gz

25

Gx

0

Gz -25

Gx -50 0

1

2

3

4

Λz

5

Figure 4. Dependence of the main tensions Gz and Gx on the multiplicity of linear deformation Λz at stretching and squeezing of natural rubber along z axis. Calculation has been done in accordance with the eq. (79) – (82) (see the explanations in text).

As we can see from the figure 4, calculated dependence of the tension Gz on the multiplicity of natural rubber stretch is in good agreement with the experimental data [6, 7,

Conformation and Deformation of Linear Macromolecules…

21

9]. However, the numerical values Gz and Gzcr are in whole rather higher than the experimental ones. It is connected with fact, that the last represent by themselves not faithful, but conventional tensions and tensile strengths, which were estimated with not taking into account the volumetric deformation of the rubber [6, 7, 9].

CONCLUSION Accordingly to the self–avoiding random walks statistics in the field of the chains intertwining that is in concentrated solutions and melts the polymeric chains are stretched increasing its conformational volume. In this volume other chains are also represented forming the m–ball. Free energy of the chain conformation doesn’t depend on a fact if chains are intertwined or they are isolated in m–ball. The entropy of mixing is responsible for the chains intertwining in m–ball, but not free energy of the chains conformation. Dependencies of the conformational radius, free energy and conformation pressure on relative concentration of the polymeric chains into solution or melt have been determined. Thermodynamical analysis of the isothermal and adiabatic deformation of m–ball has been done. Self–avoiding random walks statistics for intertwining polymeric chains and based on it thermodynamics of their conformational state in m–ball permitted to obtain the theoretical expressions for elasticity modules and main tensions appearing at the equilibrium deformation of m–ball. Calculations on the basis of these theoretical expressions without empirical adjusting parameters are in good agreement with the experimental data.

REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9]

Medvedevskikh Yu. G. // Condensed Matter Physics, 2001, v. 4, № 2 (26), P. P. 209, 219 Kuhn W. Koll. Zs. // 1934, B. 68, S. 2. De Gennes P. G. Scaling Concepts in Polymer Physics // Ithaca: Cornell Univ. Press., 1979. Flory P. J. Statistical Mechanics of Chain Molecules // M.: Myr, 1971. Fedoryuk M. V. Saddle–Point Technique. Moscow, Nauka, 1977, 254 p. (in Russian) Treloar L. The Physics of Rubber Elasticity. Oxford, 1949 Askadskiy A. A. Deformation of Polymers. Moscow, Chimiya, 1973, 448 p. Feynman R., Leighton R., Sands M.. The Feyman Lectures of Physics. // V. 7. Physics of the Continuous Media (Russian translation, Moscow, Mir, 1977), 288 p. Bartenev G. M., Frenkel C. Ya. Physics of Polymers. L.: Chimiya, 1990, 429 p.

In: Organic and Physical Chemistry Using Chemical Kinetics … ISBN: 978-1-60021-763-0 Editors: Y.G. Medvedevskikh, et al. pp. 23-33 © 2007 Nova Science Publishers, Inc.

Chapter 2

THERMODYNAMICS OF OSMOTIC PRESSURE OF POLYMERIC SOLUTIONS Yu. G. Medvedevskikh*1, L. I. Bazylyak1 and G. E. Zaikov*2 1

Physical Chemistry of Combustible Minerals Department L. M. Lytvynenko Institute of Physical–Organic Chemistry and Carbon Chemistry; National Academy of Sciences of Ukraine 2 N. Emmanuel Institute of Biochemical Physics Russian Academy of Sciences

ABSTRACT It was proposed the analysis of osmotic pressure for diluted, semi–diluted and concentrated polymeric solutions based on the taking into account a free energy of macromolecules conformation as a component of their chemical potential. It was shown, that only into diluted solutions a free energy of macromolecules conformation does not contribute into osmotic pressure and it is described by Vant–Goff’s equation. In a case of semi–diluted and concentrated solutions the contribution of the conformative component of chemical potential of macromolecules into osmotic pressure is dominate. Obtained expressions for the osmotic pressure in a cases of semi–diluted and concentrated solutions are more general than proposed ones in the scaling method and self–consistent field method; generally they are in good agreement with the experimental data and don’t contain the empirical constants. It was discussed the especial role of the critical concentration c* of the polymeric chains intertwining. It was shown, that in this point a free energy of the conformation and also osmotic pressure were determined uniquely, whereas for their derivatives upon the macromolecules concentrations the jump is observed. On the basis of these peculiarities the concentration c* is the critical point of the second order phases transition for the polymeric solutions. This in accordance with the de Clause assumes the Scaling’s ratios application near c*, although does not establish the criteria for the indexes of corresponding power functions estimation.

* *

Yu. G. Medvedevskikh; L. I. Bazylyak: 3a Naukova Str., 79053, Lviv, UKRAINE; e–mail: [email protected]; G. E. Zaikov: 4 Kosygin Str., 117977, Moscow, RUSSIA; e–mail: [email protected]

24

Yu. G. Medvedevskikh, L. I. Bazylyak and G. E. Zaikov

Key words: osmotic pressure, polymeric solutions, free energy of conformation.

1. INTRODUCTION Osmose plays an essential role in a wide technological and especially in biological systems represented by solutions of biopolymers. That is why understandable is interest of scientists to the problem of osmotic pressure of polymeric solutions which permits comparatively easy experimentally to determine the advantages and deficiencies of theoretical imaginations about thermodynamical properties of polymeric solutions. Two main approaches for osmotic pressure of polymeric solutions theoretical description can be distinguished. First is Flory–Huggins method [1, 2], which afterwards has been determined as method of self–consistent field. In the initial variant the main attention has been paid into pair–wise interaction in the system “gaped monomeric links – molecules of solvent”. Flory–Huggins parameter χ was a measure of above–said pair–wise interaction and this limited application of presented method by field of concentrated solutions. In subsequent variants such method was extended on individual macromolecules into diluted solutions with taken into account the tie–up of chain links by Gaussian statistics [1]. For description of the osmotic pressure π of polymeric solutions the virial decomposition is used in the Flory–Huggins method

π = RT

c⎛ c⎞ ⎜1 + A ⎟ N⎝ N⎠

(1)

in which c is the molar–volumetric concentration of monomeric links; N is the polymerization degree or length of a chain; A is the second virial coefficient which is the main object of analysis of multiple following variants of Flory–Huggins method. It was discovered, that the expression (1) for the description of π into diluted and semi– diluted solutions required of different values of virial coefficient A. In particular, for the estimation of A in a field of diluted solutions it would be better to accept the whole 3

conformation volume of macromolecule as excluded volume, that is RF , and in the field of semi–diluted solutions – the value a (1 − dχ ) [3] where a is a length of a chain link and 3

R f = aN ν

(2)

is the conformation radius of Flory ball with the index ν = 1/2 or 3/5. Further development of the Flory–Huggins method in direction of taking into account the effects of far interaction, swelling of polymeric ball in “good” solvents [4, 5], difference of free volumes of polymer and solvent [6, 7] leaded to complication of expression for virial coefficient A and to growth of number of parameters needed for its numerical estimation, but weakly reflected on the possibility of equation (1) to describe the osmotic pressure of polymeric solutions in a wide range of concentrations. It was admitted that the best variant for the diluted solutions is the Vant–Goff equation

Thermodynamics of Osmotic Pressure of Polymeric Solutions

π RT

=

c N

25

(3)

and for semi–diluted solutions – Fixman equation [8] or Yamakawa equation [9] differing only by the sense of virial coefficient B

π RT

=

c N

⎡ ⎛ c ⎞⎤ ⎢1 + B⎜ c* ⎟⎥ ⎝ ⎠⎦ ⎣

(4)

here c = N / N A RF is critical concentration of monomeric links corresponding to the start 3

*

of the polymeric balls intertwining. From the point of view [3, 10] the main deficiency of the self–consistent field method is fact, that it does not take into account the fluctuative properties of the polymeric solutions and correlations appearing due to the difference of the energies of pair–wise interaction into system monomeric links – solvent tie–up of links into chain. It is considered that these deficiencies somehow are eliminated by Scaling method [3] which is based on the principle of scaled invariance of polymeric solution properties as function of some characteristic parameters, for example length of chain N, relative concentration c/c* and conformation radius RF of Flory ball. Ideology of method conformably to polymer solutions was appeared from the assumption about the analogy of fluctuative behaviour of polymeric chains in semi– diluted solutions and magnetic in external field near the point of change of phase [11]. Analysis of osmotic pressure of semi–diluted polymeric solutions by Scaling method is based [3] on two positions. Accordingly to the first one it is assumed that the polymeric chain is in “good” solvent for which χ < 1 / 2 . This position is necessary in order to index ν in the expression (2) will be determined by the ratio

ν=

3 (d + 2)

(5)

which is correct for swelling ball and gives the value ν = 3/5, but not ν = 1/2 for d = 3– measured space. The second position assumes that in semi–diluted solutions the polymeric chains are as much strong intertwined that the all thermodynamic values, in particular the osmotic pressure, achieve the limit (at N → ∞) depending only on the concentration of monomeric links, but not on the chain length. The following expression is initial for the determination of osmotic pressure of semi– diluted polymeric solutions accordingly to Scaling method:

π RT

=

c ⎛c⎞ f⎜ ⎟ N ⎝ c* ⎠

(6)

26

Yu. G. Medvedevskikh, L. I. Bazylyak and G. E. Zaikov

in which the dimensionless function f(c/c*) has two asymptotics. It is assumed for the diluted solution (c/c* << 1), that f(c/c*) = 1 or f(c/c*) = 1 + const(c/c*), that leads respectively to the expressions (3) or (4). Power law depentanizer f(c/c*) = const(c/c*)m is postulated for the semi–diluted solution * (c/c >> 1), in which the unknown index m accordingly to the second position of the Scaling method is from independence π on the length of a chain. This leads to the value m = 1/(3ν – 1), that is m = 4/5 for d = 3–dimensional space. That is why the expression (6) is as follow

π RT

= const ⋅ c

or, assuming

π RT

9

4

(7)

ϕ = a 3c as volumetric part of polymer into solution

= const' ⋅ϕ

9

4

(8)

From the point of view [3] the experiments [12] confirm the correctness of the expression (8). However, let note, that the assumption about independence of the osmotic pressure of semi–diluted solutions on the length of a chain is not physically definitely well–founded; per se it is equivalent to position that the system of strongly intertwined chains is thermodynamically equivalent to the system of gaped monomeric links of the same concentration. Therefore, both Flory–Huggins method and Scaling method do not take into account the conformation constituent of free energy of polymeric chains. In presented work the analysis of osmotic pressure of the polymeric solutions has been done with taken into account the thermodynamics of conformation state of macromolecules following from the self–avoiding random walks statistics [13, 14].

2. STARTING POSITIONS The following expression is stringent thermodynamical determination of the osmotic pressure μs

π = − ∫ dμ s / vs

(9)

μs0

in which

μ s 0 and μ s are chemical potentials of the solvent into standard and defined state

respectively and vs its partial–molar volume. It follows from the Gibbs–Durham equation for two–component solution containing ns moles of the solvent and n moles of macromolecules

Thermodynamics of Osmotic Pressure of Polymeric Solutions

dμ s = − where

n dμ ns

27

(10)

μ is the chemical potential of the macromolecules.

Since the polymeric chains unlike to the common molecules possess by free energy of the conformation F (or by negative entropy of conformation which is a measure of polymeric chains self–organization [13]), it should be included as an additional term in usual determination of chemical potential of component of the solution. Hence, we have for the macromolecules

μ = μ 0 + RT ln γc + F

(11)

μ 0 is standard chemical potential of macromolecules; γ is an activity coefficient or

here

coefficient of proportionality between the thermodynamic activity of macromolecules and their molar–volumetric concentration c. Generally, the activity coefficient γ depends on the composition of solution. In the ranges of our narrow purposes of investigations of the macromolecules chemical potential conformation term influence on the osmotic pressure of polymeric solutions we will be neglect by the change of γ lying γ ≅ const in all range of the macromolecules concentrations into solution. This permits to write

dμ = RTd ln c + dF

(12)

Expressions (9) – (12) are initial for analysis of osmotic pressure of macromolecules solution into further presented partial variants.

3. DILUTED SOLUTIONS Let determine the diluted solutions by two conditions

c ≤ c* ,

(13)

ns v s ≅ V

(14)

here:

c* = 1 / N A RF

3

(15)

is critical molar–volumetric concentration of macromolecules into solution corresponding to the start of polymeric chains conformation volumes intertwining; V is general volume of the solution.

28

Yu. G. Medvedevskikh, L. I. Bazylyak and G. E. Zaikov

Accordingly to [13] the conformation radius RF of non–deformated Flory ball is described by the expressions (2) and (5) at d = 3. This dimensionality of real space will be kept further. Free energy F of the conformation in calculation per one mole of macromolecules in general case of diluted solution is equal to [13]

F= here

5 RTN 1 / 5 / λv 2

(16)

λv ≤ 1 is multiplicity of volumetric deformation of Flory ball. In diluted solutions this

multiplicity is function only on the length of a chain and distinction of free energies of the states S1 and S2 of two neighbour monomeric chains. That is why in diluted solutions dF = 0

(17)

It follows that, the determination (9) takes the standard for the diluted solutions form c

n V 0

π = RT ∫ d ln c

(18)

that result (n/V = c) in the Vant–Goff equation

π = RTc

(19)

Hence, in the field of diluted both ideal

(λv = 1) and real (λv < 1) solutions (c ≤ c* ) the

conformation component of the chemical potential of the macromolecules has not an influence on the osmotic pressure, and it is described by Vant–Goff equation.

4. SEMI–DILUTED SOLUTIONS In the given presented case the semi–diluted polymeric solutions determined by the conditions

c ≥ c* ,

(20)

ns v s ≅ V

(21)

The last means that the volumetric part of macromolecules in solution is sufficiently little.

Thermodynamics of Osmotic Pressure of Polymeric Solutions

29

As it follows from [14] in the field of the chains intertwining the molar free energy of the conformation is linear function of relative concentration of macromolecules and is described by the following expression in approximation by deformation of m–ball in real solution

F=

5 ⎛c⎞ RTN 1 / 5 ⎜ * ⎟ 2 ⎝c ⎠

(22)

It follows that

dF =

5 c RTN 1 / 5 d * 2 c

(23)

with taken into account (10), (12), (21) and (23) the determination (9) for osmotic pressure assumes the form c ⎡c n 5 n c⎤ d ln c + N 1 / 5 ∫ d * ⎥ 2 V c ⎦⎥ c* ⎣⎢ 0 V

π = RT ⎢ ∫

(24)

We will obtain after the integration

⎡

⎛ c c* ⎞⎤ − ⎟⎟⎥ , * c ⎠⎦ ⎝c

5 4

π = RTc ⎢1 + N 1 / 5 ⎜⎜ ⎣

c ≥ c*

(25)

The expression (25) is similar to the expression (4) but has more general character: it gives clear and simple determination of virial coefficient B and automatically is transferred into Vant–Goff equation accordingly to condition c = c*. The second term into square brackets (25) points out the relative contribution of the macromolecules conformation free energy into the osmotic pressure. This term is sufficiently

= 4 its part exceeds 80 %. With the c/c* and significant: even at c / c − c / c ≈ 1 and N N increasing this contribution becomes dominant. Accordingly to (19) the osmotic compressibility ∂π / ∂c into diluted solutions does not *

*

1/ 5

depend on the concentration of macromolecules (∂π / ∂c = RT ) ; on the contrary, in semi–

diluted solutions it becomes (as it follows from (25)) as linear function of relative concentration:

c⎞ ⎛ 5 ∂π / ∂c = RT ⎜1 + N 1 / 5 * ⎟ c ⎠ ⎝ 2

(26)

30

Yu. G. Medvedevskikh, L. I. Bazylyak and G. E. Zaikov

5. CONCENTRATED SOLUTIONS Let determine the concentrated polymeric solutions by the conditions

c >> c*

(27)

ns v s < V

(28)

that assumes a great volumetric concentration of macromolecules into solution. Introducing the volumetric part ϕ of macromolecules into solution by the ratio

ϕ = vc

(29)

in which v is partial–molar volume of macromolecules. Attributive expression (9) with taken into account (10), (12) and (23) results in expression (30) by changing the c = ϕ / v ,

c* = ϕ * / v , ns vs = V ( 1 − ϕ ) : ϕ ⎡ ϕ dϕ 5 N 1/ 5 ϕdϕ ⎤ + π = RT ⎢ ∫ ⎥ * ∫ ⎢⎣ 0 v( 1 − ϕ ) 2 ϕ ϕ* v( 1 − ϕ ) ⎥⎦

(30)

In general case v is complicated and independent function on solution composition. However, in narrow purposes of investigations the influence of macromolecules chemical potential conformation component on osmotic pressure we use the approximation v = const . Then after the integration of (30) we will obtain

π =−

RT v

⎡ ⎞⎤ 5 N 1/ 5 ⎛ 1 − ϕ ⎜ ln ( ) 1 ln ϕ − + + ϕ − ϕ * ⎟⎟⎥ , ⎢ * ⎜ * 2 ϕ ⎝ 1−ϕ ⎠⎦ ⎣

ϕ > ϕ*

(31)

It follows that the osmotic compressibility ∂π / ∂c = v∂π / ∂ϕ will be equal to

RT ⎛ 5 1 / 5 ϕ ∂π ⎜1 + N = ϕ* ∂c 1 − ϕ ⎜⎝ 2

⎞ ⎟⎟ , ⎠

ϕ > ϕ*

(32)

Expressions (31) and (32) are more general than the previous ones (25) and (26) and easy transform in them accordingly to condition Taking into account, that

ϕ * ≤ ϕ << 1 .

ϕ * is near to N–4/5 upon order of value, we can assume, that

N 1 / 5 / ϕ * >> 1 . Therefore, under condition ϕ >> ϕ * for concentrated solutions the first additives in (31) and (32) can be neglected and we can obtain

Thermodynamics of Osmotic Pressure of Polymeric Solutions

π =−

5 RT N 1 / 5 [ln(1 − ϕ ) + ϕ ] 2 v ϕ*

31

(33)

∂π 5 N 1/ 5 ϕ = RT * ∂c 2 ϕ 1−ϕ

(34)

This means, that in concentrated solutions π and ∂π / ∂c is wholly determined by the conformation component of chemical potential of macromolecules. Let write other form (33) assigning the condition

ϕ * ≤ ϕ << 1 . Then factorizing

ln(1 − ϕ ) in exponential series we will obtain ⎞ 5 RT N 1 / 5 ⎛ ϕ 2 ϕ 3 ⎜ π= + + ...⎟⎟ * ⎜ 2 v ϕ ⎝ 2 3 ⎠

(35)

As we can see, the eq. (35) is analogue of the scaling expression (8) at evident determination of const’ in the last one. In that way, the thermodynamic approach with the use of conformational term of chemical potential of macromolecules permitted to obtain the expressions for osmotic pressure of semi–diluted and concentrated solutions in more general form than proposed ones in the methods of self–consistent field and scaling. It was shown, that only the osmotic pressure of semi–diluted solutions does not depend on free energy of the macromolecules conformation whereas the contribution of the last one into the osmotic pressure of semi– diluted and concentrated solutions is prelevant.

6. CONCLUSION Let draw attention on the dependence of the osmotic pressure on the length of a chain. If formally to lay that v = vm N , where vm is a partial–molar volume of the chain’s links, then we will obtain

ϕ * = (vm / N A a 3 )N −4 / 5 . Therefore, the expression (33) can be written in the

form

π =−

5 RT N A a 3 [ln(1 − ϕ ) + ϕ ] 2 vm vm

which shows the independence of

(36)

π on N in obvious elevation.

However, for this it was necessary to turn into the parameter vm of the chain’s links, to their tie–up, and the concentration of polymer to express by volumetric part, which is general for the macromolecules and their links. The contrary situation can be observed into diluted solutions: at using the molar–volumetric concentration of links, the Vant–Goff equation in the

32

Yu. G. Medvedevskikh, L. I. Bazylyak and G. E. Zaikov

form (3) indicates on the dependence of π on N, whereas at using the molar–volumetric concentration of macromolecules the same Vant–Goff equation in the form (19), on the contrary, indicates on the independence of π on N. Since the macromolecule (but not its links) is a component of the solution, from the thermodynamic point of view, the expression (19) is more correct form of the Vant–Goff equation writing. Under this connection let mark that the position about an independence of the osmotic pressure of polymeric solutions into concentrated field of the strongly intertwined chains used in the scaling method is successful upon the result (8) in the presented concrete case, but can not be by general principle spreading on the all thermodynamic visualizations of polymeric solutions. For instance, free energy of the macromolecules conformation accordingly to (22) is function not only on the concentration, but also on the length of a chain at any choice of the method for the concentration expression. That fact the scaling method and presented thermodynamic approach from seeming opposite positions lead to practically the same result in the form (8) and (35) can be named as “mysterious incident” if it were not two circumstances. First is exactly free energy of the conformation makes the main contribution into the osmotic pressure of the semi–diluted and concentrated solutions. The second is the peculiarity of the point c = c*. As we can see from the expressions (19) and (25), the osmotic pressure of the solution in the point c = c* has the same value π = RTc independently on the move c → c* from below (c* > c → c*) or from above (c* < c → c*). On the contrary, the osmotic compressibility in the point c = c* has two values: first is ∂π / ∂c = RT at approach zone c → c* from below, the *

⎛ ⎝

second accordingly to (26) ∂π / ∂c = RT ⎜1 +

5 1/ 5 ⎞ N ⎟ at approach zone c → c* from above. 2 ⎠

The reason of this is the analogous behaviour of free energy of the conformation F and its derivative ∂F / ∂c . In accordance with the (16) and (22) in the point c = c* the value

5 RTN 1/ 5 is uniquely independently on a fact from which side to approach into c*. On 2 the contrary, the derivative ∂F / ∂c in the point c = c* has two values: first is ∂F / ∂c = 0 at 5 1/ 5 * move c → c* from below, the second is ∂F / ∂c = RTN / c at move c → c* from 2 above. Hence, in the point c = c* the derivative ∂F / ∂c has a jump, consequence of which is also the jump of ∂π / ∂c . F=

Since free energy of the conformation F = –TS, where S is the entropy of the conformation, it follows, that at given external parameters P and T neither free energy of conformation F nor it’s the first derivative upon temperature S do not change in the point c = c*, testifying only the hump; but their derivatives upon the concentration test the jump. On the basis of these features the point c = c* is the critical one for the change of phase of the second kind for polymeric solutions. In view of this, the analogy between the magnetic behaviour near the critical temperature of the change of phase and polymeric solution behaviour near the critical concentration c = c* of the change of phase noting by Des Cloizeaux [11] permits to use the scaling correlations, however does not determine the criteria of the corresponding power functions [15] indexes estimation.

Thermodynamics of Osmotic Pressure of Polymeric Solutions

33

REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]

[15]

Flory P. J. Principles of Polymer Chemistry // New York: Cornell Univ. Press, 1953, 594 p. Huggins M. L. Physical Chemistry of Polymers // New York: Interscience, 1958, 175 p. De Genes Scaling ideas in Physics of Polymers // Moscow: Myr, 1982, 368 p. Zimm B. H., Stockmayer W. H., Fixman M. Excluded Volume in Polymer Chains // J. Chem. Phys., 1953, 21 (10), p. 1716–1723. Zimm B. H., Stockmayer W. H. Dimensions of Chain Molecules Containing Branches and Rings // J. Chem. Phys., 1949, 17 (3), p. 1301–1314. Prigogine I. The Molecular Theory of Solutions // New York: Interscience, 1959, 479 p. Patterson D. Role of Free Volume Changes in Polymer Solutions Thermodynamics // J. Polym. Sci. C, 1968, 16, p. 3379–3389. Fixman M. // J. Chem. Phys., 1960, 33 (2), p. 370–381. Yamakawa H. // J. Chem. Phys., 1965, 43 (4), p. 1334–1344. Grossberg A. Yu., Khokhlov A. R. Statistical Physics of Macromolecules // Moscow: Nauka, 1989, 344 p. Des Cloizeaux // J. Phys. (France), 1976, 37 (5), p. 431–434. Okano K., Wada E., Taru Y., Hiramatsu H. // Rep. Prog. Polym. Sci. Japan, 17, 141 (1974). Medvedevskikh Yu. G. // Condensed Matter Physics, 2001, v. 4, № 2 (26), p. p. 209, 219. Medvedevskikh Yu. G. Conformation and deformation of linear macromolecules in concentrated solutions and melts in the self–avoiding random walks statistics (see paper in presented book) Marck N. H., Parrinello M. Collective Effects in Solids and Liquids // Adam Hilder Ltd, Bristol, 1982.

In: Organic and Physical Chemistry Using Chemical Kinetics … ISBN: 978-1-60021-763-0 Editors: Y.G. Medvedevskikh, et al. pp. 35-49 © 2007 Nova Science Publishers, Inc.

Chapter 3

GENERALIZATION OF DATA CONCERNING TO THE COAL SWELLING IN ORGANIC SOLVENTS AND THEIR EXTRACTION USING THE LINEAR MULTIPARAMETRIC EQUATIONS L. I. Bazylyak*1, D. V. Bryk*2, R. G. Makitra2, R. Ye. Prystansky1 and G. E. Zaikov*3 1

Physical Chemistry of Combustible Minerals Department; L. M. Lytvynenko Institute of Physical–Organic Chemistry and Carbon Chemistry; National Academy of Sciences of Ukraine 2 Institute of Geology and Geochemistry of Combustible Minerals; National Academy of Sciences of Ukraine 3 N. Emmanuel Institute of Biochemical Physics; Russian Academy of Sciences

ABSTRACT Approaches to the consideration of a coal swelling process, which were used up to now and based on the theory of regular solutions, do not give the possibility to generalize quantitatively the experimental data. Adequate relation between the physical–chemical properties of the solvents and the degree of a coal swelling in them can be obtained only with the use of linear multiparametric equations which take into account the effects of the all processes proceeding in the system; besides, the basicity and a molar volume of the liquids are determinative. Such approach is effective at the generalization of data concerning to extraction of a coal.

Keywords: swelling.

*

L. I. Bazylyak, R. Ye. Prystansky: 3a Naukova Str., 79053, Lviv, UKRAINE; e–mail: [email protected] D. V. Bryk, R. G. Makitra: 3a Naukova Str., 79053, Lviv, UKRAINE; e–mail: [email protected] * G. E. Zaikov: 4 Kosygin Str., 117977, Moscow, RUSSIA; e–mail: [email protected] *

36

L. I. Bazylyak, D. V. Bryk, R. G. Makitra et al.

The action of organic solvents on natural polymers combustible minerals (coal and brown coal or peat) is intensively studied for a long time due to following reasons. Firstly, this is one of the successful method of studying the structure of combustible materials and the second is their technological application for obtaining of a so–called montan–wax or low–molecular liquid extracts which can be transformed into synthetic liquid fuel due to hydration process. Moreover, an interaction of a coal with the solvents is a basis of the coals liquation processes and coals transformation into liquid fuel. The first stage of an interaction in the system “coal–solvent” is a swelling, or an increasing in the volume, as a result of introducing the molecules of a liquid into interstices and directly into the structure of a coal. Depending on the solvent nature and the coal nature, the volume of a coal can increase even in some times, and, respectively the weight growth of investigated sample can be achieved to 100 and more percentages. A review of early works concerning to a coal swelling is represented in [1, 2]. Let us notify, that else in the fifties the coals swelling process was considered as the first degree of their extraction and was connected with physical–chemical interaction of these coals with the solvents [3]. Such process was explained from two points of view, namely: either this process was coursed by adsorption of the liquid into interstices or such process was connected with the change of the cohesion energy of solid and liquid phases of a system. Sanada and co– authors [4 – 6] were taken into account, that the coal is natural three–dimensional polymer and in accordance with the Flory–Huggins’s theory a change of free energy at the coal swelling is conventional sum of the energies of mixing the polymer and solvent and first of all is determined by the disparity of solubility parameters of both components accordingly to Hildebrand parameter δ: ΔG = [ln(1 – Ø2) + χØ22 + Ø2],

(1)

where Ø2 is volumetrical part of netting structure (polymer) in swollen system; and parameter χ indicating the interaction of a polymer with the solvent which is equal to

χ=

β + ( δ 1 − δ 2 )2 V1 RT

(2)

also contains the empirical term β, correction factor, which takes into account the number of branching in the structure of polymer; δ1 and δ2 are Hildebrand’s parameters of solubility for the solvent and polymer and are equal to [(ΔHevapor – RT) / Vm]1/2. After insignificant transformations the Flory–Renner’s equation can be obtained. Such equation helps to calculate the sizes of polymer link between the cross bonds Mc

ρ 2V1Ø21 / 3 , Mc = 2 [ − ln( 1 − Ø2 ) − χØ2 − Ø2 ]

(3)

where ρ2 is the density of a polymer into solution; V1 is molar volume of the solvent. Coefficient χ should be determined empirically for every solvent and, of course, from the concentration dependence of the osmotic pressure and with taken into account a series of

Generalization of Data Concerning to the Coal Swelling…

37

assumptions. In the work Sanada [5] and subsequent works of other authors, the swelling degree in the volumetric parts Q is represented as a function from the δ of solvents. These data in most cases form the parabolic, “belfry”–like curve with a maximum for the solvents, δ2 of which accordingly to a theory of regular solutions is equal to or is near to δ1 of polymer (coal). In reality, it was maintained already in the work [5] that for the coal only approximated dependencies are obtained – a number of experimental data concerning to Q are visibly take one's leaved from the generalizing curve. It was determined in the work [4] at the extraction by solvents in the Soxhlet’s apparatus of vitrain from Yubary field (the content of carbon consists of 85,2 %), that the maximal yields of an extract are observed at their molar volume about 10 cm3/mole (ethylendiamine, dimethylformamide, cyclohexanone 24 – 26 %, acetophenone 35,6 %, pyridine 33,2 %). Such results were explained by the influence of the value of cohesion energy. However, it exists a plenty of exclusions, for example for butanole Vm = 9,5, for which the yield of the extract is only 0,8 %. The explanation of this deviation as a result of the solvent association caused by the presence of hydrogen bond seems unconvincing since under the experiments conditions (the extraction in the Soxhlet’s apparatus, and that is under boiling temperature) the association will be insignificant. It was discovered in the work [6], that the value Mc for japanese coal with the carbon content less than 80 % is unreal low – only 10 (!), next this value is sharply increased and is achieved the maximum Mc = 175 at 85 0C and after that is decreased. Authors starting from following positions explained this fact: firstly, experimental determinations were carried out in pyridine, in which specific interactions can take place and, the second this deviation can be explained by the mistakes at the determination of χ coefficient. The same approach was discussed in the work Kirov and co–authors [7] in detail on example of swelling (and extraction) for three kinds of bituminous Australian coal. These authors confirmed the main observations of Sanada – the swelling degree Q increases from ~ 1,4 in hydrocarbons to ~ 2 in pyridine (δ – 11,0) and again decreases to ~ 1,5 in alcohols. Calculated on this basis value δ of coal increases droningly with increasing the content of carbon from 70 % till 87 % and in a case of more metamorphized coal is sharply decreased again. Data concerning to the extraction of Greta coal are evidence of maximal yield of extract (more than 20 %) under it treatment with ethylendiamine and dimethylformamide (δ – 11,5), however, authors admit a fact that this is a consequence of specific interactions, since in alcohol from the δ of the same order the yield of the extract is only 1 – 2 %. Authors concluded, that although the swelling degree is not directly connected with molecular characteristics of absorbed liquids, however determining factor is their parameter of solubility in spite of the fact that at detailed consideration of the dependencies Q = f(δ) (or f(δ2)) there are a number of deviations (as same as in the work [5]) from the ideal curve for many solvents. It is necessary to notify that although it is hard to estimate the verisimilitude of determined in such a way molecular weights of structural links of a coal between the points of cross bonds, however, in a case of synthetic polymers in a same way determined masses of links visible don’t agree with the values obtained in accordance with others methods. In spite of the indicated lacks, the described above approach is applied to later works concerning to coal swelling and results interpretation. It is necessary to distinguish a plenty of investigations devoted to swelling studies of coal № 6 from Illinois State (standard in USA coal for the carbon–chemical investigations) [8 – 10]. General conclusions are in good agreement with the results of the works [5, 7]. Comparison of swelling degree for different coal in some solvents depending on the content of carbon has been done in the work [11].

38

L. I. Bazylyak, D. V. Bryk, R. G. Makitra et al.

Similar investigation for Siberia Kansk–Achynsk coal was carried out in the works [12, 13]. In both cases, as same as in a work [7], it was proved the dependence of swelling degree of coal on the carbon content in it. That is why logically to assume the possibility of specific interactions also during the swelling process, since the values of parameters of the coal solubility δ2, which are determining accordingly to the Flory–Renner’s equation are differed. It depends on fact if the data for all solvents are taking into account in calculations or such calculations are performed with the exclusion of results for solvents able to be as acceptors of hydrogen bonds (amines, ketones). Different results have been obtained also under application of other methods for calculations, especially of the Van–Krevelen’s method [14]. It is notified in the work [15], that the swelling of some coal does not agree with the thesis of regular solutions theory; that is why, it is not allowed to calculate the parameter χ for them. Authors explain this fact by the presence of oxygen atoms in the investigated coal. But also the molecular weight of separate sections (clusters) between the points of crossing for methylated or acetylated samples of this coal is equal only to 300 – 600 in accordance with the calculations (that is unreal). It is necessary to notify, that the critical analysis of the Flory theory application for the determination of molecular mass and the crossing density of the coal structure has been done in the Painter’s works [16]. Authors assert, that the possible formation of hydrogen bonds between the hydroxy groups of low–metamorphized coal has an important role here; that is why, even a lot of empirical amendments introduction into calculations leads to obtaining the understated values of molecular masses of clusters. Taking into account the above–mentioned lacks many authors concluded that the theory of regular solutions is insufficient for adequate description of the coal swelling process (and also for the extraction process) in different solvents since such theory does not take into account the possible specific solvation of active structures of coal and first of all its heteroatoms [17] especially by formation of hydrogen bonds. With the aim of taking into account the possible acid–base interactions it was proposed by Marzec and co–authors [18, 19] to determine the swelling degree as a function of donor number of DN solvents or as a function of their donor and acceptor numbers disparity accordingly to Gutmann. However, corresponding analysis of data concerning to swelling the slessian bituminous coal showed the following: although between the Q and DN is visible symbasis, however the deviations from the straight line is less than for the function Q = f(δ); but, at the same time it is complicated to confirm about the quantitative description of the process. The same conclusion about only qualitative character of such dependence has been done by authors [13] on example of swelling the brown Kansk–Achynsk coal and some kinds of Donbas coal. Above–mentioned facts and disagreements lead to the conclusions [20] that the sorption of solvents by coal is very complicated process, which covers also the changes under the action of solvent into the coal structure and other possible phenomena. That is why, application for a coal the theories developed for the description of thermodynamically equilibrium process of swelling the simple synthetic polymers is unwarranted first of all due to neglect the existing chemical (specific) solvation interactions. As it was confirmed in many investigations, the swelling Flory–Huggins’s model based on the theory of regular solutions is not sufficiently consistent with the real experimental data. It is caused by a range of simplifying assumptions putted into the base of this model and, first of all, the presence of full isoentalpic mixing (solution) of two phases that is in disagreement with the reality – even

Generalization of Data Concerning to the Coal Swelling…

39

in a case of the polymers which do not contain the donor–acceptor groups into the structure a swelling and solution processes are accompanied with a great enthalpy effect; it is know, that even non–specific solvation is often accompanied by the changes of free energy and enthalpy of the system. And isoentalpy will be not remained in a case of the possible donor–acceptor (acid–base) interaction, which is often observed in a case of synthetic polymers with the content of heteroatoms (polyurethane, nitryle rubbers) and is observed in a case of coal as a result of the presence in it such groups as –OH, –COOH, tertiary atom of nitrogen and ect. Calculations on the basis of the theory of regular solutions for the coal swelling have mostly unsatisfactory generalizing and predicted ability. Thus, our main task was to explain the value of coal swelling as an effect of the sum influence of different properties of penetrating liquids and also to obtain the quantitative picture that is possible starting from the principle of the linearity of free energies. The principle of the linearity of free energies (LFE) is applied in chemistry of solutions over 30 years for quantitative description of the solvents influence on the behavior of dissolved substances (spectral characteristics, constants of the reaction rate). In accordance with this principle general change of free energy of the system consists of the separate inter– independent terms and first of all consists of non–specific and specific solvation and also needed energy for the formation of cavity in the structure of liquid phase with the aim of allocation the exterior molecule introducing there. And only full sum of these all possible energetic effects gives the final (equilibrium) energy of the system [21]:

ΔG = ∑ Δg i

(4)

With taken into account, that the constants of the reaction rates are determined via the equilibrium constants of the activated reactive complex formation, and the last in part depend on the solvation processes, it was proposed by Koppell and Palm [22] the following equation in order to determine the influence of medium properties on the reaction rates of processes proceeding in it:

lg K = a0 +

a1 (n 2 − 1) a2 (ε − 1) + + a3 B + a4 ET (n 2 + 2) (2ε + 1)

(5)

This equation takes into account the influence of the polarization f(n2) and polarity f(ε) of the solvents determining their ability to non–specific solvation and also their basicities B [22] which are accordingly to Koppell–Palm’s quantitatively equal to OH–group displacement absorption band in IR–spectrum of the phenol dissolved in given solvent, and electrophilicity accordingly to Reichardt ET characterizing their ability to introduce into acid–base interactions (specific solvation). Appropriateness of this equation for the generalization of experimental data of the dependencies of reactions rates (and also spectral characteristics of dissolved substances) on physical–chemical characteristics of the solvents has been proved by a number of hundred examples. It was determined by us at the attempts to describe the gasses dissolving processes into liquids with the use of the equation (5) that to obtain of satisfactory results the Koppell– Palm’s equation should be expanded by fifth term, which takes into account the density of the

40

L. I. Bazylyak, D. V. Bryk, R. G. Makitra et al.

energy of solvents cohesion proportional to the squared Hildebrand’s solubility parameter δ2. Due to this fact necessary energy for the formation of cavity for the allocation of the molecule introducing into liquid phase is taking into account:

lg K = a0 + a1 f (n 2 ) + a2 f (ε ) + a3 B + a4 ET + a5δ 2

(6)

Modified equation was turned out effective for the determination of the solvents influence on the equilibrium of such processes as solubility in different media not only of gases, but solids too, the distribution of substances between two phases, resembling equilibrium processes. So, it will be logically to try to use the equation (6) for the swelling processes. As a matter of fact, it was turned out, that with the use of this equation it is possible to determine the quantitative connection between the properties of the solvents and equilibrium swelling degree of a number of polymers, and also of a coal [23 – 25]. In order to achieve the satisfactorily high values of the coefficients of multiple correlations R, it is necessary to exclude from the calculations the data for some quantity (3 – 5) of the solvents. It is hard to explain it. Besides, it was not quite clear the model of the interactions into the system. In a case when the solvation processes are energetically advantageous (∆G < 0) and that is why promote to the swelling process, that is to the solvent penetration into the structure of polymer, then the role of δ2 factor is remained not clear. Such factor characterizes the energy needed for the cavity formation into the structure of the liquid; at the same time, unlike to the evaporation process, under the swelling of substances into liquid the following process takes place: liquid solvent penetrates into the structure of solid polymeric phase mostly as the whole. At the beginning of ninetieth the works of Aminabhavi are appeared [26]. These worked were concerned the polymeric membranes swelling into organic solvents and to diffusion rate D of the liquids into their structure in which these values were considered as dependencies from the molar volume VM of the liquids. Generalizations obtained in [26] are rather unsatisfactory – approximately linear dependencies lgQ or lgD on VM are observed only in the homologic ranges or in the case of similar solvents. But approach must be considered as logical: it is clear, that in a case of bigger sizes of introducing molecule, the last with difficulty will be penetrated into the structure of polymer including the adsorbent interstice. Low generalizing ability of the dependencies presented in the work [26] can be explained by fact that they do not take into account the solvation effects, which promote to liquids penetration. That is why the equation (6) has been expanded by additional term, which takes into account the influence of molar volume of the solvents:

lg Q = a0 + a1 f ( n 2 ) + a2 f ( ε ) + a3 B + a4 ET + a5δ 2 + a6VM

(7)

Such equation under the stipulation that Q is represented not in the volumetric parts accordingly to the Flory–Huggins’s model but in accordance with the interpretation of equilibrium processes in the chemical thermodynamics as a moles of the solvent absorbed by one gram or by one cm3 of polymer was turn out effective under the generalization of data for swelling degree of different synthetic polymers, for example, polyethylene, in different organic solvents depending on their physical–chemical parameters [27]. That’s why, it was necessary to check the possibility of application the equation (7) for the generalization of data

Generalization of Data Concerning to the Coal Swelling…

41

concerning to coal swelling since this equation takes into account the all important possible energetic effects caused by possible donor–acceptor interaction of active groups of the coal with non–inert solvents including the formation of hydrogen bonds; the effects of non– specific coal solvation with solvents which are caused by a presence in it the cyclic aromatic structures as a result of which the visible influence of the ability of some solvents for the polarization can be expected; and also endothermic effects as a result of steric complications of the solvents penetration (VM) and destruction of the liquid phase structure (δ2). Data concerning to a swelling of the most popular coal (namely, coal Illinois № 6) have been taken by us as a main object of our investigations. This coal is the standard object for the carbon–chemical investigations in USA. These data were already analyzed earlier in works [23 – 25] with the aim of their generalization accordingly to equation (6), but obtained results were unsatisfactory. Evidently this was caused by two factors: i) the influence of the molecules sizes of the solvents penetrating into the coal structure (their molar volume) was not taken into account in these works; ii) analyzed starting values of the swelling degree Q were given accordingly to original works [9 – 11] in ml (sometimes in g) of the solvent absorbed by 1 ml or 1 g of coal since the Flory–Huggins’s model has been used by authors (this model uses the volumes of two liquids which are mutually mixed). If to consider the coal swelling process (and generally polymers swelling processes) as thermodynamically equilibrium process then the free energy change at the penetration and at the absorption of a solvent and, respectively, the equilibrium constant of this process, it is preferable to determine the quantity of connected solvent in molar units. In the presented paper we have checked the efficiency of the above–mentioned factors considering studying the swelling process in organic solvents. Illinois coals are low– metamorphized, bituminous and contain 20 – 31 % of volatile substances, are characterized by ash content 8 – 12 % and sulphur content 4 – 7,8 %. Investigated in the work [8] sample was characterized by following composition: C 79,8; H 5,11; N 1,8; Sorg. 2,0 and O 11,2 %. The samples were pulverized from the soluble components with pyridine; after vacuum– drying they were saturated by solvent’s steams till their full saturation at room temperatures in the closed vessels. Authors give the ratio of the weights for swelled samples respectively to the starting W. Generalization of studied data for 10 solvents in accordance with the fifth– parameter equation (6) leads to the expression with unsatisfactory low value of correlation coefficient R = 0,81 [23]. Exclusion from the consideration the most uncoordinated data for dioxane gives the possibility to obtain the fifth–parameter equation with low, but acceptable degree of connection R = 0,941. At the same time, consideration of the molar volume factor and the change of weight parts on the molar ones essentially improve the correlation – for all 10 studied solvents R = 0,940, and after the exclusion the data concerning to cyclohexane for the rest 9 solvents we obtain the equation with high connection degree R = 0,996 [28]. However, there are only two decisive parameters – the basicity which assists to swelling process and the is molar volume, which opposites to this process; taking into account the needed energy and the negotiation of the cohesion forces have only insignificant influence and the exclusion of this parameter from the calculations practically does not worsen the equation

lg Q = −1,96 + ( 0,665 ± 0 ,074 )10 −3 B − ( 4,12 ± 0,58 )10 −3VM ; R = 0,984 and S = 0,030

(8)

42

L. I. Bazylyak, D. V. Bryk, R. G. Makitra et al.

Obtained equations have greater predicted ability comparatively to fifth–parameter equation obtained in the work [23], which does not take into account the factor of molar volume (for nine solvents R is equal to 0,940). The influence of the factor of molar volume is confirmed by fact that between lgQ and VM the neatly marked symbasis is observed, namely: with increasing of VM the value lgQ is decreased. The action of other decisive factor – solvents basicity – is opposite, in other words with the basicity increasing the symbate increasing of lgQ is observed. Evidently, this is caused by the specific solvation of acid centers, which are in the macromolecule of coal and, first of all, of hydroxy groups. Their presence can be assumed taking into account a great number of the oxygen in the Illinois coal. Comparison of these two oppositely directed dependencies leads to the conclusion, that they are mutually compensated. Although these dependencies are only symbate, but the algebraic sum of the influence of these two factors is practically linearly connected with the respective values lgQ [29]. The third factor is more little density of the cohesion energy, which is proportional to needed energy for separation of absorbed molecules from the structure of liquid phase; this factor respectively also decreases the swelling value. However, the influence of this value is insignificant; this fact is confirmed by negligible decreasing of the Q value at its exclusion. The possible processes of non– specific and electrophilic solvation practically do not impact on the value Q. Our considerations about significance of the separate properties of the solvents influence on the swelling degree are confirmed by analogous analysis of data in others works. In the work [10] authors also have been studied the swelling process of the coal Illinois № 6 in the liquid phase. Swelling degree S has been studied by volumetrically as the ratio of volumes of swelling sample to the starting one. Unlike to [8], it was investigated the process in a range of amines including the primary ones, able to the formation of hydrogen bonds and also alcohols. At the generalization of these data in accordance with the fifth–parameter equation without taking into account of VM for the all 17 solvents it was obtained the equation with the low value R = 0,861; but at the use of the sixth parameter equation (7) and after the exclusion of data for isopropanole and dimethylaniline we achieve of high correlation lg Q = −2,91 + ( 0 ,454 ± 1,40 ) f ( n 2 ) + ( 5,73 ± 1,22 ) f ( ε ) + ( 1,43 ± 0 ,37 )10 −3 B − ( 7 ,15 ± 5,26 )10 −3 ET − ( 0 ,722 ± 0,947 )δ 2 − ( 6 ,52 ± 4,54 )10 −3VM

N = 15 , R = 0,981 , S = 0,160

(9)

and after the exclusion of insignificant factors of polarizability and cohesion energy density: lg Q = −2 ,96 + ( 5,67 ± 1,11 ) f ( ε ) + ( 1,5 ± 0 ,30 )10 −3 B − ( 1,47 ± 3,99 )10 −3 ET − ( 4 ,01 ± 2 ,07 )10 −3Vm

R = 0,980 and S = 0,149

(10)

However, the factors of electrophilic solvation and unexpected molar volume have the little influence too. The dependence of lgQ on the solvent property can be satisfactory described by the two–parametric equation too and

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43

lg Q = −4,34 + ( 3,42 ± 0,69 ) f ( ε ) + ( 2,02 ± 0,27 )10 −3 B − ( 0,86 ± 2,55 )10 −3Vm R = 0,968 and S = 0,172

(11)

In this case the basicity and the molar volume of the solvents are decisive factors, the influence of which is oppositely directed. An appearance of the polarity as significant factor is connected with the specific selection of high polar solvents (alcohols, amines). Calculated in accordance with the equation (11) values lgQcalc. and their deviation from the experimental values are represented in Table 1. Accordingly to [9] the swelling process of the Illinois coal № 6 has been carried out principally under other conditions, namely: the samples were previously extracted with pyridine, dried coal was standed till the full saturation with vapors at 100 0C in closed metallic ampoules (with the exception of phenol, investigating temperature of which is 182 0 C). Authors presented the results of investigations as the ratio of swelling W (in percentages) that is the ratio of weights of swelling sample after 1 hour to the dried sample. These data have been previously generalized in the work [24]. Low value R for the all 12 solvents equal to 0,876 after exclusion from the consideration data concerning to the phenol and tetrahydrophurane is increased till 0,972. Essentially better results were obtained with taken into account the molar volume factor. The data concerning to W taken from [9] and calculated on their basis swelling values in moles Q and lgQ are presented in Table 2; the generalization of these data in accordance with the sixth parameter equation (7) leads to higher degree of relationship R = 0,909, and the exclusion from the consideration of one solvent (butylamine) gives the possibility to obtain the equation with satisfactory degree of relationship R = 0,974; an additional exclusion of dimethylformamide gives the equation (11) with R = 0,991. lg Q = −2,61 + (3,50 ± 0,82) f ( n 2 ) + (2,30 ± 0,46) f (ε ) − (0,33 ± 0,14)10 −3 B − (2,37 ± 6,8)10−3 ET + (0,70 ± 0,24)10 −3 δ 2 − (1,5 ± 2,1)10 −3VM

N = 10, R = 0,991 and S = 0,055

(12)

and after the exclusion of insignificant factors lg Q = −2,51 + (2,66 ± 1,20) f ( n 2 ) + (1,80 ± 0,60) f (ε ) − (7,4 ± 5,0)10 −3 ET − (2,8 ± 2,9)10 −3VM

R = 0,964 and S = 0,086

(13)

With the molar volume of the solvents increasing the coal swelling degree is decreased; the same is an effect of the ability to electrophilic solvation. Unlike to both previous cases, the positive influence of the solvents basicity (namely their ability to form the donor–acceptor bonds with acid groups of the coal) here is insignificant evidently as a consequence of especial influence of the conditions of experiment carrying out. Under higher temperatures the hydrogen bonds are easy decomposed. At the same time, the possible positive influence of the factors of non–specific solvation f(n2) and f(ε) is observed. Calculated values lgQ and their discrepancy with the experiment ΔlgQ are presented for the comparison in Table 2.

44

L. I. Bazylyak, D. V. Bryk, R. G. Makitra et al. Table 1. Experimental [10] and calculated in accordance with the equation (10) values of swelling degree of the coal Illinois № 6 №

Solvent

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

2–Picoline Pyridine Butylamine Propylamine Aniline 2–Hexanone Methylaniline Propanol Ethanol Butanole Methanol Dimethylaniline* Isopropanole* Toluene p–Xylene m–Xylene Benzene

S 2,76 2,75 2,64 2,45 1,99 1,98 1,44 1,36 1,34 1,34 1,23 1,10 1,06 1,06 1,06 1,05 1,04

Experiments Qm103 17,84 21,72 16,57 17,62 10,86 8,120 4,052 4,820 5,824 3,715 5,690 0,789 0,784 0,562 0,487 0,407 0,447

lgQm –1,749 –1,663 –1,781 –1,754 –1,964 –2,090 –2,392 –2,317 –2,235 –2,430 –2,245 –3,103 –3,106 –3,250 –3,312 –3,390 –3,350

Calculations lgQm ΔlgQm –1,794 0,045 –1,808 0,145 –1,941 0,160 –1,655 –0,099 –2,205 0,241 –2,312 0,221 –2,037 –0,355 –2,240 –0,077 –2,194 –0,041 –2,242 –0,188 –2,204 –0,041 –– –– –– –– –3,311 0,061 –3,326 0,013 –3,293 –0,097 –3,362 0,012

Note: *data excluded from the calculations.

Both the equilibrium swelling degree and the kinetics of this process depend on the character of the solvent. In the work [10] it has been studied the swelling rate of the coal Illinois № 6 volumetrically in different solvents; on the starting stages it is ordered to the pseudo–first order reactions kinetics as is observed in the case of polymers swelling too. It helped to determine the respective constants rate of the process, which are presented in Table 3. In the work [25] we have generalized these data for 24 solvents with the use of fifth– parameter equation (6). For the all maximal sequence of the data the value of correlation multiple coefficient R was very low and equal to 0,694 and only after the exclusion from the calculation the data for five solvents (that is practically 20 %) it could obtain the satisfactory value of R = 0,957. Additional taking into account the influence of molar volume, that is transition to sixth parameter equation, gives the possibility to obtain the expression with R = 0,883. And in order to obtain the satisfactory correlation it was enough to exclude from the calculations data for only two solvents, namely 2–hexanone (methylbutyl ketone) and triethylamine lg k = 2,20 − ( 2,55 ± 3,84 ) f ( n 2 ) + ( 1,08 ± 4,26 ) f ( ε ) + ( 4,17 ± 1,12 )10 −3 B − ( 71,7 ± 62,5 )10 −3 ET − ( 0,92 ± 2,45 )δ 2 − ( 42,8 ± 9 ,1 )10−3VM

N = 22, R = 0,959 and S = 0,448

(14)

Generalization of Data Concerning to the Coal Swelling…

45

Table 2. Experimental [9] and calculated in accordance with the equation (12) values of “swelling ratio” of soluble part of coal for the coal Illinois № 6 № 1 2 3 4 5 6 7 8 9 10 11 12

Solvent Dimethylformamide N–Methylpirrolodone Dimethylsulphoxide Ethylendiamine Aniline Butylamine* Pyridine Phenol Pipyridine Tetrahydrofuran Toluene Hexane

Experiments W Qm103 6,2 60,54 5,7 37,17 5,5 49,19 4,6 33,24 4,6 34,13 3,8 29,82 3,7 28,67 3,4 22,49 3,0 19,26 2,8 22,97 2,6 16,65 1,6 6,902

lgQm –1,218 –1,430 –1,308 –1,478 –1,467 –1,525 –1,543 –1,648 –1,543 –1,639 –1,779 –2,161

Calculations lgQm –– –1,503 –1,407 –1,466 –1,513 –– –1,475 –1,512 –1,475 –1,615 –1,874 –2,134

ΔlgQm –– 0,073 0,099 –0,012 0,047 –– –0,068 –0,136 –0,068 –0,024 0,095 –0,027

Note: *data excluded from the calculations.

The equation terms characterizing the influence of non–specific solvation and also cohesion energy have a great standard deviations which are more than the absolute values of the coefficients and that is why are evidently insignificant. Checking the value R decreasing at the exclusion of these terms confirmed this assumption and helped to obtain the equation with lesser quantity of significant terms. This equation also adequately characterizes the influence of the solvents properties on the rate of their penetration into the coal structure; besides, the decisive factor in this case as same as in a case of swelling value is the influence of molar volume of the solvents, increasing of which leads to the process rate decreasing.

lg k = 1,12 + ( 4 ,85 ± 0 ,52 )10 −3 B − ( 66,0 ± 19 ,5 )10 −3 ET − ( 42,1 ± 6,2 )10 −3VM R = 0,957 and S = 0,418 (15) Significant factor as same as in a case of swelling degree is the solvents basicity. With the solvents basicity increasing, the process rate is also increased. The less essential is a role the solvents ability to electrophilic solvation; although this factor increases the process rate but it exclusion from the consideration decreases R till 0,928. The value lgQ calculated in accordance with the equation (15) is represented in Table 3. Decisive role of the VM factor during the adsorption process of the solvents by coal is in agreement with the determined in the work [25] proportionality for the alcohols between lgk and steric factor Es of the Hammet–Taft’s equation.

46

L. I. Bazylyak, D. V. Bryk, R. G. Makitra et al. Table 3. Experimental [10] and calculated accordingly to equation (14) values of the logarithms of the constants rate of the coals Illinois № 6 swelling №

Solvent

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Propylamine Butylamine Pyridine 2–Picoline 2–Hexanone∗ Methanol Ethanol Aniline Propanol Butanole Isopropanole Methylaniline Butanole–2 Toluene Isobutanol Dimethylaniline Benzene Pentanol p–Xylene m– Xylene o– Xylene Ethyl benzene Cumene Triethylamine∗

Experiments k105, s–1 1167,0 614,0 316,7 126,7 125,0 53,30 21,30 20,0 10,90 3,84 2,54 2,47 1,32 0,90 0,833 0,59 0,45 0,376 0,375 0,225 0,118 0,113 0,009 0,00038

lgk –1,933 –2,212 –2,499 –2,897 –2,903 –3,273 –3,672 –3,699 –3,963 –4,416 –4,595 –4,607 –4,879 –5,046 –5,079 –5,229 –5,347 –5,425 –5,426 –5,648 –5,928 –5,947 –7,046 –8,420

Calculations lgk –1,679 –2,974 –2,655 –3,124 –– –3,183 –3,624 –3,962 –4,290 –4,926 –4,152 –4,063 –4,694 –5,334 –4,859 –4,578 –4,675 –5,510 –5,924 –5,919 –5,891 –6,032 –6,716 ––

Δlgk –0,254 0,763 0,155 0,226 –– –0,091 –0,048 0,263 0,328 0,511 –0,443 –0,545 –0,185 0,288 –0,220 –0,651 –0,671 0,085 0,498 0,271 –0,037 0,086 –0,330 ––

Note: *data excluded from the calculations.

So, the swelling characteristics of the Illinois coal are determined by total influence of molar volume of liquids and their ability to specific solvation. The same conclusion has been done by authors of the works [30, 31] explaining the adsorption growing by increasing the donor number of the solvents via the formation of hydrogen bond by OH–groups of coal. But these authors have not done respective quantitative generalization giving the possibility on the basis of the linearity of free energies principle adequately to connect the properties of the liquids with their ability to interact with a coal; it was confirmed that the approaches based on the theory of regular solutions equitable only at the consideration of the swelling process in the “inert” (so–called low–basic) solvents, mainly of low–polarity. Correctness of the sixth parameter equation (7) and its simplified forms for the generalization of the swelling data was proved for other coals including the Donbas coal [32] at the parameters B and VM. If to apply the equation (7) to the coal extraction data, then the factor of molar volume VM is insignificant, and the connection between quantities of extracted substance (in g/mole of the solvent) and physical–chemical characteristics can be satisfactorily described by fifth parameter equation (6) or by its simplified forms; in this case possible acid–base interaction is the decisive factor, that is factor B [33 – 35]. This confirmation is in good agreement with the above–said: bigger molecules harder introduce

Generalization of Data Concerning to the Coal Swelling…

47

into the coal structure and after equilibrium state their size does not play the role. Let us notify, that the same approach has the positive results at the data generalization concerning to the solubility of the synthetic low–molecular coal analogous – diphenylolpropane – in 20 solvents. This approach is also applicable for the generalization of data concerning to the coal extraction under sub–critical conditions, but the role of the specific solvation is also insignificant, evidently as a result of its suppression at high temperatures. So, it was discovered the lack of fit the description of the coal swelling process with the use of one–parametric dependencies including those dependencies based on the theory of regular solutions on the solubility parameter of liquids. It was shown, that the quantitative connection between the swelling degree of coal and physical–mechanical properties of the solvents is achieved only on the basis of principle of the linearity of free energy under condition of taking into account the all solvation process. The basicity of the solvents and their molar volume are the factors determining the swelling degree for low–metamorphized coal.

REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]

Kibler M. V. Diejstvije rastvoritieliej na ugli // In book: “Khimiya tviordogo topliva” Moscow, 1951. – v. 1. – p. p. 145 – 267. Keller D. V., Smith C. D. Spontaneous fracture of coal // “Fuel” – 1976. – v. 55. – № 4. – p. p. 272 – 280. Kröger K. Die Steinnohleextraction // “Erdöl und Kohle” – 1956. – Bd.9. – H.7. – s. s. 441 – 446. Sanada Y., Honda H. Solvent extraction of coal // Bull. “Chem. Soe. Japan” – 1962. – v. 35. – № 8. – p. p. 1358 – 1360. Sanada Y., Honda H. Equilibrium swelling of coals in various solvents // “Fuel” – 1966. – v. 45. – № 4. – p. p. 451 – 456. Sanada Y., Honda H. Swelling equilibrium of coals by pyridine // “Fuel” – 1966. – ‘v. 45. – № 4. – p. p. 295 – 300. Kirov N. Y., O’Shea J. N., Sergeant G. D. The determination of solubility parameters of coal // “Fuel” – 1967. – v. 47. – p. p. 415 –424. Green T. K., Kovac J., Larsen J. W. A rapid and convenient method for measuring the swelling of coals // “Fuel” – 1984. – v. 63. – № 7. – p. p. 935 – 938. Mayo F. R., Zevely J. S., Pavelka L. A. Extractions and reactions of coals below 100 о C // “Fuel” – 1988. – v. 67. – № 5. – p. p. 595 – 599. Aida T., Fuku K., Fujii M. et al. Steric requirements for the solvent swelling of Illinois № 6 coal // “Energy and Fuels” – 1991. – v. 5. – № 6. – p. p. 74 – 83. Nelson J. F., Mahajant O. T., Walker P. L. Measurement of swelling of coals in organic liquids // “Fuel” – 1980. – v. 59. – № 12. – p. p. 831–837. Skrypchenko G. B., Khrennikova O. V., Rybakov S. I. // “Khimiya tviordogo topliva” – 1987. – v. 5. – p. p. 23 – 28. Osipov A. M., Bojko Z. V. // “Khimiya tviordogo topliva” – 1987. – v. 3. – p. p. 15 – 18.

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L. I. Bazylyak, D. V. Bryk, R. G. Makitra et al.

[14] Van Krevelen W. Сhemical structure and properties of coal // “Fuel” – 1965. – v. 44. – № 4. – p. p. 229 – 242. [15] Larsen J. W., Shawyer S. Solvent swelling studies // “Energy and Fuels”. – 1990. – v. 4. – № 1. – p. p. 72 – 74. [16] Painter P. C., Graf J., Coleman M. H. Coal solubility and swelling. Parts 1, 2, 3. // “Energy and Fuels” – 1990. – v. 4. – № 4. – p. p. 379 – 397. [17] Weyrich O. R., Larsen J. W. Thermodynamics of hydrogen bonding in coal–derived liquids // “Fuel” – 1983. – v. 62. – № 8. – p. p. 976 – 977. [18] Marzec A., Kisielow W. Mechanism of swelling and extraction and coal structure // “Fuel” – 1983. – v. 62. – № 8. – p. p. 977 – 979. [19] Szeliga J., Marzec A. Swelling of coal in relations to solvent electron–donor numbers // “Fuel” – 1983. – v. 63. – № 10. – p. p. 1229 – 1231. [20] Hsieh S. T., Duda J. L. Probing coal structure with organic vapor sorption // “Fuel” – 1987. – v. 66. – № 2. – p. p. 170 – 178. [21] Mayer U. Eine semiempirische Gleichung zur Beschreibung des Lösungs– mitteleinflusses auf Statik und Kinetik chemischer Reaktionen. Th. 1, 2. // “Monutsh. Chemie” – 1978. – v. 109. – H. 2. – s. s. 421 – 433; H. 4. – s. s. 775 – 790. [22] Koppel I. A., Palm V. A. The influence of the solvent on organic reactivity // In: Advances in Linear Free Energy Relationships. Ed. N. B. Chapman a J. Shorter. London, New York: Plenum Press – 1972. – p. p. 203 – 281. [23] Makitra R. G., Pyrig Ya. M. // “Khimiya tviordogo topliva” – 1988. – v. 6. – p. p. 41 – 45. [24] Makitra R. G., Pyrig Ya. M. // “Khimiya tviordogo topliva” – 1992. – v. 6. – p. p. 11 – 20. [25] Makitra R. G., Pyrig Ya. M., Vasiutyn Ya. M. // “Khimiya tviordogo topliva” – 1995. – v. 3. – p. p. 3 – 13. [26] Aminabhavi T. M., Harogopadd S. B., Khinnavar R. S. et al. Rubber solvent interactions // “Rev. Macromol. Chem. Phys.” – 1991. – v. C 31. – № 4. – p. p. 433 – 497. [27] Makitra R. G., Pyrig Ya. M., Zaglad’ko E. A. // “Plasticheskije massy” – 2001. – v. 3. – p. p. 23 – 27. [28] Makitra R. G., Poliuzhyn I., Prystansky R., Smyrnova O., Rogovyk V., Zaglad’ko O. Zastosuvannya pryncypu linijnosti vilnyh energij shchodo sorbciji ta pronyknennya organichnyh rechovyn // “Praci naukovogo tovarystva im. Shevchenka”. – 2003. – v. 10. – p. p. 152 – 163. [29] Makitra R. G., Prystansky R. // “Khimiya tviordogo topliva” – 2001. – v. 5. – p. 316. [30] Larsen J. W., Green T. K., Kovac J. // “J. Org. Chem.” – 1985. – v. 50. – № 10. – p. p. 4729 – 4735. [31] Hall P. G., Marsh H., Thomas K. M. Solvent induced swelling of coals to study macromolecular structure // “Fuel” – 1988. – v. 67. – № 6. – p. p. 863 – 866. [32] Makitra R. G., Prystansky R. // “Khimiya tviordogo topliva” – 2003. – v. 4. – p. p. 24 – 36. [33] Vasiutyn Ya. M., Makitra R. G., Pyrig Ya. M., Turovsky A. A. // “Khimiya tviordogo topliva” – 1994. – v. 4. – p. p. 66 –73. [34] Makitra R. G., Pyrig Ya. M. // “Khimiya tviordogo topliva” – 1991.– v. 1. – p. p. 67–70.

Generalization of Data Concerning to the Coal Swelling…

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[35] Makitra R. G., Pyrig Ya. M. // “Khimiya tviordogo topliva” – 1993. – v. 3. – p. p. 14 – 18. [36] Makitra R. G., Bryk S. D., Palchykova O. Ya. Doslidzhennya vzajemodiji malometarmophizovanogo vugillya z organichnymy rozchynnykamy (na prykladi diphenilolpropanu) // “Geologiya i geokhimiya goriuchyh kopalyn”. – 2003. – № 3–4. – p. p. 126 – 130.

In: Organic and Physical Chemistry Using Chemical Kinetics … ISBN: 978-1-60021-763-0 Editors: Y.G. Medvedevskikh, et al. pp. 51-64 © 2007 Nova Science Publishers, Inc.

Chapter 4

NEW SILAZANE OLIGOMERS AND POLYMERS WITH ORGANIC-INORGANIC MAIN CHAINS: SYNTHESIS, PROPERTIES AND APPLICATION N. Lekishvili*1, Sh. Samakashvili1, G. Lekishvili1 and G. Zaikov*2 1

I. Javakhishvili Tbilisi State University, Faculty of Exact and Natural Sciences, Scientific Center for Nontraditional Materials; Tbilisi, Georgia 2 N.E. Emanuel Institute of Biochemical Physics of the Academy of Sciences of Russia, Moscow

ABSTRACT On the basis of the diallylsilazanes, α,ω-dihydrideoligoorganosiloxanes and 1,4-bis(dimethylhydridesilyl)benzene, new polyfunctional siliconorganic polymers have been synthesized. General regularities and feasible mechanism of the reaction for obtaining diallylsilazanes have been studied. Based on data of elemental, IR and NMR 1H spectral analysis, the composition and structure of synthesized polymers have been established. The kinetics of polyhydrosailylation reactions has been studied. Quantum-chemical calculations of the model system and data of NMR 1H spectra of the real products of the polyaddition reaction have confirmed probability of passing polyhydrosilylation reaction according to the aforementioned two concurrent directions obtaining both α and β adducts. For the evaluation of relative activity for selected monomers the algebraicchemical approach has been used. Using Differential Scanning Calorimetric and Roentgen-phase analyses methods it has been established that synthesized polymers are amorphous systems. Thermal (phase) transformation temperatures of synthesized polymers have been determined. Thermooxidation stability of the synthesized polymers has been studied. There was shown that their thermooxidation stability exceeded the analogical characteristic of polyorganocarbosiloxanes. Using synthesized diallylsilazanes modification of the properties of some important industrial polymer composites based on phenolformaldehide resins has been carried out. Preliminary investigations showed that synthesized polymers in combination * *

N. Lekishvili: 1, Ilia Chavchavadze ave., 0128 Tbilisi, Georgia, [email protected] G. Zaikov: 119991 Moscow, 5, N.N. Kosigin Street, Russian Federation; [email protected]

52

N. Lekishvili, Sh. Samakashvili, G. Lekishvili et al. with phenolformaldehyde resins were successfully used as binding-components for polymer/graphite and polymer/carbon black electro-conducting composites.

Keywords: diallylsilazane, dihydridsiloxane, polyhydrosilylation, properties, application.

INTRODUCTION The synthesis of silicon-organic monomers and polymers (silazane, siloxane-arylene, carbosilazane, epoxide, etc.) containing aromatic groups with unsaturated radicals of allyl and vinyl types have been attracting particular attention [1-4]. The classical method of polyhydrosilylation revealed new possibilities of obtaining polymers with such a structure. The range of unsaturated monomers used for reaction of polyhydrosilylation increased [4-7]. The use of unsaturated monomers of new type, distinguished from the standard divinyl monomers, required elaboration of a non-traditional approach to this reaction [7]. The other hand, the synthesis of polymers with aforementioned structure is of interest for modification of properties of some important industrial polymers, such as polycarbonate, phenolformaldehide resins, rubbers based on organic and siliconorganic elastomers, etc. [7]. They also may be used in combination with some other organic and element-organic polymers (for example, with polyepoxides) as the substrates for nanohybrides [8, 9].

EXPERIMENTAL Synthesis methods: α,ω-oligodihydridedimethylsiloxanes were synthesized by the methods described in ref [11]. 1,3-tetramethyldisiloxane was obtained by hydrolysis of dimethylchlorinesilane [10]. 1,5-trimethyltriphenyltrisiloxane has been synthesized by reduction of 1,5-dichlorine-1,3,5-trimethyltriphenyltrisiloxane with LiAlH4 [10]. 1,5-tetramethyl-3,3-diphenyltrisiloxane was obtained via interaction of (Me)2SiHCl with diphenylsilandiol [7]. Investigation methods: the IR spectra of all samples were obtained, from KBr pellets, on SPECORD and UR-20 spectrophotometers, while NMR 1H spectra were obtained with AM360 instrument at the operating frequency of 360 MHz. All spectra were obtained using CDCl3 as a solvent and an internal standard. Perkin-Elmer DSC-7 differential scanning calorimeter was used to determine DTA and the thermal (phase) transition temperatures were read at the maximum of the endothermic or exothermic peaks. Heating and cooling scanning rates were 100C/min. The column set comprised 103 and 104 Å Ultrastyragel columns. Wideangle X-ray diffractograms were obtained by DRON-2 instrument. Cu Kα was measured without a filter; the motor angular velocity was ω ≈ 20 / min

New Silazane Oligomers and Polymers with Organic-Inorganic Main Chains…

53

RESULTS AND DISCUSSION We have studied polyhydrosilylation reactions of α,ω-oligodiorganodihydride siloxanes and 1,4-bis(dihydridedimetylsilyl)benzene with dialylsilazanes (DAS) in the presence of Speier’s catalyst (0.1 mole solution of H2PtCl6·6H2O in isopropanol) [3-7] in dry toluene and in mass. The initial diallylsilazanes were synthesized via interaction of industrial organocyclosilazanes (hexametylcyclotrisilazane, methylphenylcyclotrisilazane and methylvinylcyclotrisilazane) with orto-allylphenol (o-AP) and 4-allyl-2-methoxyphenol (Evg.), in the area of Argon being free from oxygen and moisture [6]. The reactions proceeded easily in mass, at 333353K, according to the following scheme [6, 7]:

[CH3(R)SiNH]n+2HO-Ar-CH2-CH=CH2

to > − NH 3

, where R = CH3, CH=CH2, C6H5, Ar = phenylene, methoxiphenylene, n=3. Scheme 1.

The resultant products are slightly viscous, optically transparent (in visual area of the spectra) liquids soluble in ordinary organic solvents (benzene, toluene, acetone, etc.) and practically insoluble in water. The composition and structure of the obtained diallylsilazanes were confirmed based on the data of elemental and IR spectral analysis [6, 7] The maximums of the absorption, related to Si−NH−Si and Si−O−Si, Si−O−C groups (915-925 cm-1, 9901000 cm-1 and 1060-1080 cm-1), also the maximums of the absorption, related to Si−CH3, CH2=CH, Si−C6H5 and benzene ring (1250 cm-1, 1430 cm-1, 1445 cm-1, 1620-1630 cm-1, 1600-1605 cm-1 correspondingly) were found in the IR spectra [6]. It should be noted that the method used for manufacturing diallylsilazanes is accessible (easy of access) and has some of noteworthy positive technological features for a practical viewpoint [6]: • • •

The reaction is carried out without (in the absence) solvents and catalysts; Removal of side products is not difficult; Control of the process is simple due to determination of the gaseus ammonia.

Polyhydrosilylation reactions of 1,4-bis(dimethylhydridesillyl)benzene and α,ω-oligodiorganodihydredesiloxanes with sinthesized dilsilazanes are passing according to the following general scheme:

54

N. Lekishvili, Sh. Samakashvili, G. Lekishvili et al.

CH 3

(CH 2) 3

R

(CH 2) 3

Si R'

CH 3 Rx

Si R'

n

where Rx= O, C6H4, O[Si(CH3 )2 O]m, (m=6,11), CH3(C6H5)SiO, Si(C6H5)2, R = R1= CH3; R= CH3, R1 = CH=CH2, C6H5; R1 = CH3, C6H5; n>>1. Scheme 2.

Preliminarily we had studied the following model system: (CH3)3SiOSi(CH3)2H + DAS. Heating of the corresponding reaction mixture in the temperature range of 60-80 0C, in the absence of the Speier’s catalyst, showed that the polymerization of DAS or other changes of the structures of the initial compounds do not take place. There didn’t observe any changes in the IR, NMR 1H and NMR 13C of initial compounds. Content of the double bond of the allyl group and active Hydrogen did not change either. The process was controlled by determination of active hydrogen in Si−H groups for several times [2, 6]. The influence of the structure of dihydride monomers on the reaction rate, yield and properties of obtained polymers has been studied (table 1, figure 1). Based on kinetic curves (figure 1) of Si−H groups conversion, the reaction rate constants have been determined (table 1). The total reaction order equals to 2. The products of polyhydrosilylation reaction are optically transparent viscous liquids or elastic gums soluble in ordinary organic solvents (toluene, CHCl3, etc.). The composition and structure of produced polysilazanes were established based on the data of the elemental, IR and NMR 1H spectral analyses. In IR spectra there were found the

New Silazane Oligomers and Polymers with Organic-Inorganic Main Chains…

55

maximums of absorption (915-925 cm-1, 990-1000 cm-1, 1020-1060 cm-1, 1250 cm-1, 1410 cm-1, 1430 cm-1, 1445 cm-1, 1600-1605 cm-1), related to Si−NH−Si, Si−O−Si, Si−O−Car , Si−CH2, Si−CH3, Si−C6H5, and benzene link, correspondingly (scheme 5). The data of elemental analysis (for example, Si(I),%, calc./found.=17.01/16.08; Si(VIII),%, calc./found.=17.84/17.09, etc., where the index numbers I and VIII the numbers of polymers in the table 2) corresponded to the structures of the products, obtained in accordance with the reaction scheme 2. One can observe the singlet signals with chemical shifts within the range of δ ≈ 0.03 _ 0.44 ppm for protons in methyl group of ≡Si−CH3 in NMR 1H spectra of the synthesized polymers (there illustrated the data for IV, V and VI - table 2). One can also observe two signals with the center of chemical shifts at1.28 ppm and 1.62 ppm, which correspond to methylene protons in Si_CH2 groups, and multiplet signals with chemical shifts within the range of δ ≈ 6.6 - 7.5 ppm corresponding to protons of phenyl groups in the NMR 1H spectra. There were observed the signals with chemical shifts within the range of δ ≈ 5.1 _ 5.2 ppm corresponding to protons in NH-groups in NMR 1H spectra. The triplet signals with center of chemical shifts at 0.81 ppm correspond to methine protons in Si_ СH(CH3) _ groups [5].

Figure 1. Conversion of Si−H group in time for hydrosilylation reaction of dihydride siloxanes and 1,4bis(dimethylhydridesilyl)benzene with diallylsilazanes: 1.- VII; 2. - VI; 3.- III; 4.- II; 5.- V; 6.- IV (table 1).

The data given above (elemental and spectral analysis and solubility of the resultant products) excludes homopolymerization of diallylsilazanes under the conditions of polyhydrosilylation reaction. To evaluate relative reactivity of dihydridesiloxanes (determination of the rank of their relative reactivity in polyhydrosilylation reaction), algebraic-chemical method, particularly pseudo-ANB-matrices, has been used for the first time for this type reactions. This method is

56

N. Lekishvili, Sh. Samakashvili, G. Lekishvili et al.

a modified version of adjacency matrices [13]. In the context of the aforementioned approach, taking into account the nature (structure) of organic radicals R and R1 at the silicon atoms of the dihydridesiloxanes, it has been established that lg(ΔANB) is efficient topologic index for fixing and investigating QSPR (quantitative structure-property relations) [13]. Corresponding correlation equation has the following form: k=alg(ΔANB)+b , where k is a rate constant for polyhydrosilyation reaction; lg(ΔANB) is a decimal logarithm of the determinant of pseudoANB-matrices; a and b – slope and intercept, which are calculated by method of leastsquares: a=6,792•10-3, b=3,083•10-3. The correlation coefficient r=0.9788 (figure 2).

H

Si

O

Si

H

IV

H

O

Si

Si

O

CH3

C6H5

CH3

CH3

CH3

CH3

Si CH3

The polyaddition reaction rate constants k•10-3, l•mol-1•sec-

12

96.6

0.17

---

333

10

85.5

0.10

2.29

333

12

97.0

0.21

2.78

12

96.4

0.13

4.33

CH3

C6H5

CH3 Si

333

CH3

II

H

ηsp**

CH3

CH3

III

The yield of products of the reactions

dihydridsiloxsanes and 1,4 bis- (dihydridedimethylsillyl)benzine

CH3 I

Reaction temperature,K

#

Duration of reaction, hrs

Table 1. Conditions of hydrosilylation reaction of 1,4-bis(dimethylhydridesillyl)benzine and α,ω-oligodiorganodihydredesiloxanes with diallylsilazanes (DAS)*, the yield and values of specific viscosities of synthesized polymers (in toluene)

O

Si CH3

Si

O 6

H

H

333

CH3

Table 1. (Continued).

Si

H

V

CH3

CH3

CH3 Si

O

C6H5 CH3

H

VII

Si

11

The polyaddition reaction rate constants k•10-3, l•mol-1•sec-

ηsp**

12

91.7

0.22

3.97

333

12

96.2

0.15

2.38

333

12

94.6

0.11

1.54

343

12

93.4

0.12

---

CH3

H

Si

O

Si

333

CH3

C6H5

C6H5 CH3

O

H

Si

O

CH3

Si

H

VI

Si

O

57

CH3

CH3

CH3

The yield of products of the reactions

dihydridsiloxsanes and 1,4 bis- (dihydridedimethylsillyl)benzine

#

Duration of reaction, hrs

Reaction temperature,K

New Silazane Oligomers and Polymers with Organic-Inorganic Main Chains…

H

C8H17 C8H17 CH3 C6H5 CH3 VIII

Si

H

CH3 _

_

O Si C6H5

O Si

H

CH3

_

* CH2=CH CH2 Ar O[(CH3)2SiNH]2(CH3)2SiO_Ar_CH2_ CH=CH2; where Ar= C6H4 (VIII); Ar= CH3OC6H4 (I-VII) (scheme 2); **) 1% solution in toluene.

According to the classic researches, polyhydrosilylation reaction of dihydridesiloxanes with α,ω-divinyloligosiloxanes proceeds according to the general scheme given above (scheme 2) [11]. At the same time, some other modern publications showed that both α and β adducts are obtained (scheme 5) [2-6]. Quantum-chemical calculations of the model system (scheme 5) have confirmed the probability of passing polyhydrosilylation reaction according to mentioned above two concurrent directions.

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N. Lekishvili, Sh. Samakashvili, G. Lekishvili et al.

k10-3 l.mol-1.c-1

4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 4.75

4.8

4.85

4.9

4.95

5

5.1

5.05

Ig(ΔAND) Figure 2. Dependence of value for hydrosilylation reaction rate constants on decimal logarithm of determinant of pseudo-ANB-matrices in the series of α,ω-oligodiorganodihydridesiloxanes (table 1). CH3

CH2

R

Si

CH2 + H

CH

OSi (CH3)3

CH3 CH3 I CH2

CH2

R

CH2

Si

CH3 CH3 II CH2

R

Si

CH3

CH3

CH3

R= CH3O

Si

CH3 Scheme 3.

OSi (CH3)3

CH

CH3 NH

Si

CH3

OSi (CH3)3

New Silazane Oligomers and Polymers with Organic-Inorganic Main Chains…

59

As a method of quantum-chemical calculation, we used AM1 method; MM2 method was applied to perform optimization of geometry of adducts [7]. The calculation of the heat of formation (ΔHform) for the reaction model products showed that formation of α-adduct (I) (ΔHIform = – 1067.77 kJ) is slightly more probable than that of β-adduct (II) (for the product with the structure II, ΔHIIform= – 1055.67 kJ); both I and II products are actually obtained [5]. One can observe the signals with chemical shifts at δ=0.81 and δ=1.62, which correspond to β (II) and α (I) adducts (scheme 4) in NMR 1H spectra of real polysilazanes [5]. In case of the polyhydrosilylation reaction of dihydridesiloxanes with diallylsilazanes (scheme 2) there may also proceed dehydrocondensation reaction (due to the interaction of NH-groups of di- and intermediate oligosilazanes with Si–H groups of dihydridesiloxanes), alongside with the main processes, via obtaining trisilylated nitrogen atom. To determine which process (dehydrocondensation or polyaddition) is more probable, we have calculated basic energetic parameters of model systems, for the products of polyhydrosilylation reaction. As model systems there were selected structures described the actual reaction products [7]:

R'

R'

H3C O

Si H3C

N

Si

CH3

Si

C H2

H C

(III) CH2

CH3

H3C R

,

where R=OCH3, R′=CH3; Scheme 4.

In spite of the fact that formation of model systems containing the trisilylated nitrogen atom is thermodynamically possible (ΔHIIIform.= –928,76 kJ), separation of hydrogen did not take place during the process of polyhydrosylation reaction [6]. At the same time, in IR spectra of actual products of this reaction, the maximum of absorption related to trisilylated nitrogen atoms (950-960cm-1) was not found [6, 7]. Evidently, it is favorable for dihydridesiloxanes to attract terminal allyl groups rather than NH-group bonded to silicon atoms, surrounded with organic radicals under the conditions of polyhydrosilylation reactions. That leads to formation of macromolecules with linear structure (scheme 2) [6]. Using Roentgen-phase (RP) (figures 3) and Differential Scanning Calorimetric (DSC) (figures 4) Analysis Methods, the synthesized polymers have been investigated. It has been established (DSC and RPA methods) that they are amorphous substances. On the DSC-curves (figure 4, a, b and c) endothermic peaks correspond to their glass transition temperature (Tg).

60

N. Lekishvili, Sh. Samakashvili, G. Lekishvili et al. 4.55 Å 7.15 Å

7.15 Å

7.08 Å

1

4.31 Å

4.13 Å

2

3

5

10

15

20

25

2Θ°

Figure 3. Difractograms of polymers: 1.-II; 2. IV; 3.-V (table 1).

a HEAT FLOW (mw)

7.5

1 5

2.5

0 -140.0 -110.0 -80.0

-50.0 -20.0

10.0

Temperature

40.0

( 0C)

70.0

100.0 130.0 160.0

New Silazane Oligomers and Polymers with Organic-Inorganic Main Chains…

61

10

b 7.5

5

2.5

0

-140.0 -110.0

-80.0

-50.0

-20.0

10.0

40.0

70.0

100.0

130.0

160.0

Temperature ( 0 C) 10

HEAT FLOW (mw)

c 7.5

5

2.5

0 -140.0 -110.0

-80.0

-50.0

-20.0

10.0

Temperature

40.0

70.0

100.0

130.0

160.0

( 0 C)

Figure 4. DSC corves of polymers: II (a), VI (b), IV (c) (table 1).

Thermooxidation stability of synthesized polymers (DTA and TGA analyses methods, figures 5) exceeds thermooxidation stability of polydimethylcarbosiloxanes containing terminal functional groups [6]. This fact may be explained by formation of intermediate stable cross-linked macromolecules by interaction of N–H group of polysilazanes with H2N–Si groups of linear oligomers [12] at high temperature (210-2300C, in the open air) (figure 3a,

62

N. Lekishvili, Sh. Samakashvili, G. Lekishvili et al.

curves of DTA, exothermic pick at the 2200C); these oligomers maybe obtained via hydrolysis of Si–NH–Si bonds by air moisture. Intensive thermooxidation destruction of the synthesized polymers proceeds only within the temperature interval of 350-4500C. Based on the TGA curve (figure 5), calculation of the activation energy (Ea) for the basic process of thermooxidation destruction of synthesized polymers, has confirmed the above mentioned supposition. So the value of calculated Ea (64 kJ/mol) exceeds correspond parameter (52-54 kJ/mol) for polydimethylcarbosiloxanes with terminal functional groups [14].

Figure 5. DTA (a) and TGA (b) corves for polymers X (table 1).

Produced diallyllsilazanes and polymers based on them were used for the modification of the properties of some industrial polymer composites based on polymers with functional groups. Some satisfactory results were also obtained by modification of properties of phenolformaldehyde resin (PFR) composites with the synthesized diallylsilazanes (scheme 1). Thas, addition of diallylsilazanes (1-3 mass %) to this composition has improved some of essential characteristics of hardened PFR (table 3). It should be noted that other important physical and mechanical properties of the composites have remained safe (table 3). Besides the aforementioned, preliminary investigations showed that synthesized oligomers and polymers, in combination with phenolformaldehyde resin, were successfully used as binding component for polymer/graphite electro-conducting composites (ECC) [15, 16]. Obtained ECC were recommended for creation of electrode material for electrolytic section and the chemical (fuel) sources of electrical energy (on the basis of analogous material) [16].

New Silazane Oligomers and Polymers with Organic-Inorganic Main Chains…

63

Table 3. Some physical and mechanical properties of the modified phenolformaldehide resin composite

#*

Electrical conductivity, ρ, om.cm

Strength on pressure, σ, MPa

Strength on winding, σ, MPa

I II- 1% III - 1% III - 3%

53,28 49,23 49,63 49,50

21,22 21,22 27,16 56,59

19,80 12,00 18,50 16,90

Specific percussive viscosity, kg. cm/cm2 2,76 2,40 2,45 2,27

IV - 3%

51,67

41,58

26,20

2,75

* I – without modifiers (scheme 1); II – diallylsilazane based on 4-allyl-2-methoxyphenol:hexamethylcyclotrisilazane (2:1); III – diallylsilazane based on 4-allyl-2-methoxyphenol:trimethyltriphenylcyclotrisilazane (2:1); IV – diallylsilazane based on 4-allyl-2-methoxyphenol:hexamethylcyclotetrasilazane (2:1).

ACKNOWLEDGMENT The authors thanks Dr. M. Katsitadze - for the synthesis of 1,3-dimethyl-1,3dioctyledisiloxane and 1,4-bis(dihydridedimetylhyl)benzene, also Prof. Dr. Aneli and Dr. D. Gventsadze - for study of created electro-conducting polymer composites.

REFERENCES [1]

[2]

[3]

[4] [5]

[6]

Silanes and Other Coupling Agents. Edit.: K.I. Mittal. The Fourth International Symposium on Silanes and Other Coupling Agents, MST Conferences, LLC in Orlando, FL, Vol.3. June 11-13, 2003. Kopylov V.M., Koviazina T.G., Buslaeva T.M., Sinicin N.M., Kireev V.V., Gorshkov A.V.. Peculiarity of the Hydrosilylation Reaction of the Polyfunctional Methylvinyland Methylhydrosiloxanes. Zhurnal Obshchei Khimii. (Journal of General Chemistry), 57, 5 1117-1127 (1987) (Rus.); Lekishvili N., Samakashvili Sh., Murachashvili D., Lekishvili G., Gverdtsiteli M.. Oligoepoxysiloxanes with side epoxy groups: synthesis and properties. Chemistry and Industry. (Bulg.). Vol. 77 (2006) (In press). Mukbaniani O.V. and Zaikov G.E. Cyclolinear Organosilicon Copolymers: Synthesis, Properties, Application. Netherlands, Utrecht, VSP (2003). Mukbaniani O., Tatrishvili T., Titvinidze G. Hydrosilylation Reaction of Methylhydridesiloxane to n-Hexene-1. Georgian Chemical Journal. 3, 3 214-215 (2003) (Rus.). Lekishvili N., Samakashvili Sh. Reactions of polyaddition of dihydride siloxanes to diallyl- silazanes: new approaches. Proceedings of Tbilisi State University, 360, 19-23 (2005) (Geo.).

64 [7]

[8] [9]

[10] [11]

[12]

[13] [14]

[15] [16]

N. Lekishvili, Sh. Samakashvili, G. Lekishvili et al. Kopylov V.M., Sokolskaya I.I., Murachashvili D.U., Lekishvili N.G., Khubulava E.I., Zaikov G.E.. New Siliconorganic Modifiers of Rubbers Based on Carbochain Elastomers. Konstruktsii iz Polimernikh Kompozitov, (Constructions from Polymer Composites), 4, 37-48 (2003) (Rus.). Brostow W. The Chain Relaxation Capability. Ch. 5. In performance of Plastics. Ed. W. Brostow, Hanser, Munich-Cincinnati, 2000. Witold Brostow, Wunpen Chonkaew, Haley Hagg and Oscar Olea. V Republican Conference, Chemistry. Abstracts. Georgia, Tbilisi, Georgian Chemical Society. P.41, 2830 October, 2004. Andrianov K.A. Metodi Elementorganicheskogo Sinteza. Kremnii. (Methods of Element Organic Synthesis. Silicon). Mockva, “NAUKA”. 1968 (Rus.). Andrianov K.A., Gavrikova L.A., Rodionova E.F. Investigation of the polyaddition reaction of α,ω-divinylalkyl(aryl)siloxane oligomers with α,ω-dihydroalkyl(aryl)siloxane oligomers. Visokomolekuliarnie soedinenya. (Polymer science) XIII(A), 4 937939 (1971) (Rus.). Lekishvili N.G., Katsitadze M.G., Nakaidze L.I., Khananashvili L.M. Some Kinetically Regularities of Polymerization Condensation Reaction of Organocyclosilazanes with Spacial Groups at Silicon Atoms with Aromatic Dihydroxy compounds. Bulletin of the Academy of Sciences of Georgia. Series of Chemistry. 152, 3 529-531 (1995) (Rus.). Gverdtsiteli M., Gamziani G., Gverdtsiteli I. The Adjacency Matrices of Molecular Graphs and their Modification. Tbilisi University Press. Tbilisi, 1996 (Geo.). N. Lekishvili, M. Kezherashvili, Sh. Samakashvili. Silicon-organic Polymers with Inorganic and Organic-Inorganic Main Chains, Containing Silicon-Nitrogen and Silicon-Oxygen Bonds. Publish Company “UNIVERSALI”. Tbilisi, Georgia, 2006. Aneli J., Khananashvili L., Zaikov G. Structuring and Conductivity of Polymer Composites. Nova Science Publishers, Inc., N.-Y. 1998. Lekishvili N., Gventsadze D., Aneli J., Samakashvili Sh., Khuchua T. Polymer Materials with Specific Properties Based on Secondary Mineral Resources and Petroleum Products. III All-Russian Conference “Physical chemistry of the Processing of Polymers”. Chemical-Technological State University, Ivanovo (Russia), 2006.

In: Organic and Physical Chemistry Using Chemical Kinetics … ISBN: 978-1-60021-763-0 Editors: Y.G. Medvedevskikh, et al. pp. 65-67 © 2007 Nova Science Publishers, Inc.

Chapter 5

TO QUESTION ABOUT INFLUENCE OF SOLVENT ON INTERACTION PROPANETHIOLE BY CHLORINE DIOXIDE R. G. Makitra, G. E. Zaikov* and I. P. Polyuzhyn Division of physico-chemistry of fuels of Pisarzhevskij Institute physical chemistry of Ukrainian National Academy of Science , 3A Naukova str., L'viv, Ukraine

The data for influence of solvents on oxidation propanthiole by chlorine dioxide are satisfactorily generalized by means of five parameters equation according to principles of Linear Free Energies Relationships (LFER). An essential role plays the density of media cohesion energy, that bears out radical process nature. Recently the data concerning to interaction of propanthiole with chlorine dioxide in 8 solvents have been published [1]. In this work it was shown, that the dependence of process rate from solvents properties is satisfactory described for seven solvents, after the exclusion of data for ethyl acetate, by the Koppel-Palm four parameters equation (coefficient of multiple correlation R 0,96) at determining role of medium polarity (coefficient of pair correlation between lg(k) and (ε - 1)/(2ε + 1) - r 0.90). Chemical mechanism of the reaction including the formation of ion-radical RS+*Н and radical RS* has been proposed by authors [1]. However, it is known, that in homolytical processes certaine influence on reaction rate has also so-called "cage effect", which is described by density of medium cohesion energy. That was confirmed by generalization of data concerning to influence of solvents upon decomposition rate of benzoyl peroxide [2] or oxidizing processes [3, 4]. That is why the data analysis from work [1] is seemed as expedient by means of five parameter equation:

*

G.E.Zaikov: N.M. Emanuel Institute of Biochemical physics; Russian Academy of Sciences, 4 Kosygin str., Moscow 119991, Russia

66

R. G. Makitra, G. E. Zaikov and I. P. Polyuzhyn

n2 −1 ε −1 + a2 ⋅ + a 3 ⋅ B + a 4 ⋅ ET + a 5 ⋅ δ 2 lg( k ) = a 0 + a1 ⋅ 2 2ε + 1 n +2

(1)

On comparison with known Koppel-Palm equation the equation (1) includes square of Hildebrandt’s solubility parameter δ2 [5], P.219-225. This equation (1) allows with acceptable precision degree to generalize all data from the work [1] (see Table) without necessity of exclusion the data for ethylacetate: lg(k)= 12.57 + (-12.76 ± 9.15)⋅f1(n2) + (23.03 ± 8.02)⋅f2(ε) + (3.72 ± 1.93)⋅10-3⋅B + (-0.67 ± 0.31)⋅ET + (18.04 ± 6.87)⋅10-3⋅δ2 s ± 0.408 N 8 R 0.9638 (2) It is necessary to mark, that as difference to work [1] in presented research for description of electrophilicity more preferable Reichardt parameter (value ET) [2] is applied but not electrophilicity Е offered by Koppel-Palm. As analogy with [1] the exclusion from equation (2) the data for one of solvents - acetone or ethylacetate allows to obtain an equation for lg(k) with R > 0.99. Analysis of meaning for separate parameters of the equation according to [6] by the way of their in turn exclusion shows on only insignificant role of polarizability effects since for the four parameters equation without f1(n2) the correlation coefficient is only insignificantly lesser R 0.9536. The influence of nucleophilic solvation (factor near basicity B in the equation) has relatively low meaning too as at its exclusion value R becomes as 0.9440. In the same time exclusion from the equation any of three rest factors decreases the degree of correlation to not allowed low value R as to 0.919; 0.939; 0.927 relatively. Here the medium polarity has especially significant influence. It is unastonishingly, if one takes into account a high degree of pair correlation between lg(k) and f2(ε) which is equal to 0.901. Values lg(k) calculated by equation (2) are given also in table. In equation (2) significant parameters of "solvation" such as f2(ε) and δ2 have sign "plus". That indicates on preferable solvation of intermediate reactionary complex, which facilitates the reaction runing in result of electrons division. That agrees confirmed with opinion of authors [1] about polar nature of reactive complex. Evidently its formation is limiting stage, because antibatness is observed between lg(k) and ΔG# with high correlation degree as value r is 0.990. Only medium ability to electrophilic solvation ET has a sign "minus", evidently, in consequence of the positive solvation of initial thiol. It is desirable but to note that significant correlation with r 0.916 exists between f2(ε) and ET. Besides, an essential influence is observed of medium cohesion (δ2) since at exclusion of this factor the R value falls to 0.927. That bears out opinion advanced by authors [1] about mainly radical nature of the process. The energetic charactiristics of process such as Е#ACT., ΔН#, ΔG# and ΔS# also can be generalized with acceptable precision by means of five parameters equations. As an example in the table there are given the experimental activation energies (Е#ACT.) and its values calculated by equation (3):

To Question about Influence of Solvent on Interaction Propanethiole…

67

E#АКТ = -51.85 + (-65.14±30.14)⋅f1(n2) + (-125.5±26.4)⋅f2(ε) + (24.90±6.35)⋅10-3⋅B + + (3.70±1.02)⋅ET + (-52.87±22.63)⋅10-3⋅δ2 s ± 1.345 N 8 R 0.9571 (3) Here as well as for lg(k), the exclusion of the most deviating data for one of solvents acetone for ΔG#, heptane or dioxane for Е#ACT and ΔН#, and benzene or heptane for ΔS# allows to receive equations with R > 0.99. For majority of activation descriptors the polarizability as f1(n2) is least meaningful factor exception ΔS# where is δ2 also, as and for lg(k). However its exclusion decreases R from 0.95 to 0.93, that undesirable according to [6]. The exclusion of other parameters from equation is more noticeable. Thus taking into account the cohesion energy density allows essentially to improve upon results of correlation analysis on influence of medium properties on kinetics of oxidation of propanethiole by chlorine dioxide. At the same time a significance of this factor is indirect proof of radical stages in the process. Table. Experimental on [1] and calculated values lg(k) for kinetic of propanthiol oxidation by chlorine dioxide

Solvent

lg(k) experimen t

n-Heptane 1,4- Dioxane Carbon tetrachloride Benzene Diethyl ether Ethylacetate Acetone Acetonitrile

-2.777 -1.444 -1.411 -2.593 -0.086 -1.000 0.583 1.722

computatio n by Eq.(2) -2.773 -1.224 -1.847 -2.353 -0.266 -0.199 0.092 1.689

Е#ACT, ccal/mole experiment computation by Eq. (3) 11.27 11.89 21.00 20.03 6.54 5.14 7.73 9.74 11.54 12.99 13.02 11.91 16.09 15.34 14.74 16.00

REFERENCES [1] [2] [3] [4] [5] [6]

Yakupov M.Z., Lyapina N.K., Shereshovets V.V., Imashev U.B. // Kinetics and catalysis (Rus). 2001. Vol.42. № 5. PP.673-676. Makitra R.G., Pyrih Ya.N.., Havryliv E.M. Depon. In VINITI 1988 № 8418-В-88. Ref. Zh. Khim. 1989. 5Б4128. Kutcher R.V., Vasyutin Ya.M., Makitra R.G., Pyrih Ya.N. // Dokl. Acad. Sci. Ukr.SSR Series "B". 1988. № 6. PP.47-51. Pyrih Ya.N., Makitra R.G., Yatchyshyn Y.Y. // Kinetics and catalysis. (Rus). 1991. Vol.32. № 5. PP.1040-1047. Reichardt Ch. Solvents and Solvent Effects in Organic chemistry. Weinheim: Wiley VCH, 2003. 630 p. Recomendations for Reporting the Results of Correlation Analysis in Chemistry using Regression Analysis // Quant. Struct. Acta Relat. 1985. Vol.4. № 1. P.29.

In: Organic and Physical Chemistry Using Chemical Kinetics … ISBN: 978-1-60021-763-0 Editors: Y.G. Medvedevskikh, et al. pp. 69-72 © 2007 Nova Science Publishers, Inc.

Chapter 6

MATHEMATICAL MODELLING OF THERMOMECHANICAL DESTRUCTION OF POLYPROPYLENE G. M. Danilova-Volkovskaya, E. A. Amineva1 and B. M. Yazyyev2 1

Rostov-on-Don Agricultural Machinery State Academy; 344023, Strana Sovetov Street, 1, Rostov-on-Don. e-mail: [email protected] 2 Ushakov Naval State Academy 353900, Lenin Avenue, 93, Novorossiysk

ABSTRACT There has been provided mathematical description of the processes of thermonuclear destruction in deformed polypropylene melts; the aim was to use the criterion of destruction estimation in modelling and optimising the processing of polypropylene into products.

Keywords: Thermo-mechanical destruction, polypropylene, molecular mass, effective viscosity. During processing polypropylene melts under the action of transverse strain there occur strain-chemical conversions which can result in both decrease and increase in their molecular masses; the mechanical effect on the rapidity and level of the occurring processes is considerably more prominent than the mere contribution of thermal and thermal-oxidative breakdown. These data necessitate studying the process of polymer destruction. For this purpose it would be most effective to apply the criterion of assessment of the intensity with which destructive processes happen in polymer melts. If the destruction is observant from the initial value of molecular mass М0 to a certain finite value М∞, then at point of time t the chain group with molecular mass М0 - Мt (where Мt is the average value of molecular mass at a given point of time) is involved in the process. It is natural to assume that the rate of destruction in a unit time is proportional to the whole

70

G. M. Danilova-Volkovskaya, E. A. Amineva and B. M. Yazyyev

number of breakdowns in macromolecules up to the destruction limit. These assumptions enable us to propose an expression for calculating the rate of destruction process:

d (( M t − M ∞ ) / M t = − Kdt (M t − M ∞ ) / M ∞

,

The integration of this expression results in:

ln

Mt − M∞ = − Kt + e , M∞

(1)

Since at t=0 Мt = M0, then:

С = ln

Mt − M∞ M∞

,

(2)

If we substitute (1) with (2) after some transformations we get:

ln

Mt − M∞ = − Kt , M∞

From here:

М t = ( M 0 − M ∞ )e kt + M ∞ ,

As value М0 - М∞ is constant for the polymer of the given molecular mass, we can designate it as A; after substitution we get:

ln

Mt − M∞ = − Kt M0 − M∞

from here:

М t = A ⋅ e − kt + M ∞ ,

where K is the rate constant depending on the

chemical nature of a polymer and, in particular, on how close macromolecular chains are packed. Each criterion obtained from the given expressions represents a concept of one of the interrelated consequences of thermo-mechanical destruction process: decrease in molecular weight, the number of macromolecular breakdowns, and the approach to the possible level of macromolecular destructions. The merit of the criteria is that their values do not depend on the initial molecular weight [1-3].

Mathematical Modelling of Thermo-Mechanical Destruction of Polypropylene

71

Paper 20 dwells on the ideas allowing us to advance in the quantitative assessment of thermo-mechanic destruction degree. Taking these data as a basis we can propose an expression for calculating the degree of thermo-mechanic destruction in the form of:

ϕ а1 =

1 η 0 − kt ⋅ ⋅e , а ηt

(3)

where a is the constant of proportionality which is equal to 3.105. On the other hand:

ϕ а1 = (η а ,τ 1, 2 ,η 0 , it ) ,

(4)

where ηа is the effective viscosity of a material melt, τ1,2 are transverse strains during processing. Combining the defining parameters of equation (3) and modifying this equation into a dimensionless form, it is possible to demonstrate that criterion φ1а, is the function of only two parameters ηа and τ1,2. Comparing (3) and (4) enables the following expression for the criterion of thermomechanic destruction degree to be proposed:

⎛ τ ⋅t ⎞ ϕ а1 = f ⎜⎜η 0 , 1, 2 ⎟⎟ , ηa ⎠ ⎝

(5)

The direct application of this expression in order to estimate the degree of thermomechanic destruction in connection with polymer processing is hindered because the process rate constant depends on the temperature and intensity of thermo-mechanical impact on a material. Consequently, of significant interest is the issue of selecting an attribute for characterizing the degree of destruction. Most researchers consider it worthwhile to simply use viscosity variable (ηа) or characteristic viscosity variable. Here is proposed the criterion for the rate of thermo-mechanical destruction in the polymeric system Ψ11: −τ 12 ⋅t 1 ⎡η 0 ηa ⎤ Ψ = ⋅⎢ е ⎥, a ⎢⎣η a ⎥⎦ 1 1

where τ12 are strain rate tangents.

(6)

72

G. M. Danilova-Volkovskaya, E. A. Amineva and B. M. Yazyyev

This relation is helpful because it provides an opportunity for the quantitative assessment of polymer thermo-mechanical destruction rate in dependence with the thermo-mechanical impact regime during processing. Analyzing the data obtained when testing the samples of extrusion products made of polypropylene, the conducted research on their molecular-weight properties, and the calculated values of the criterion for the destruction processes rate, we concluded that the processes of attachment and bifurcation correspond to the values of Ψ11 = 1, while the processes of destruction correspond to Ψ11= - 1. Assuming that the effective viscosity in a polypropylene melt is sensitive to changes in molecular mass and in chain-length distribution and taking into consideration the specific character of the thermo-mechanical impact developing during extrusion, it is proposed to calculate the intensity of destruction processes from the latter expression. The advantage of the criterion is that it does not require defining the molecular mass of a polymer. Comparing the values of Ψ11, obtained at testing PP samples processed under various technological regimes and calculated with the aid of a mathematical model allows us to propose applying the criterion to the estimation of physical and chemical transformations occurring in a polymer at modifying the parameters of thermo-mechanical impact. Taking into consideration Ψ11 values, we have found the optimal regime when PP is under extrusion processed into products with improved deformation-strength properties [4].

CONCLUSIONS There has been provided mathematical description of the processes of thermonuclear destruction in deformed polypropylene melts; the aim was to use the criterion of destruction estimation in modelling and optimising the processing of polypropylene into products.

REFERENCES [1] [2] [3] [4]

Olroyd J.G. On the formulation of rheological equation of stat. - Trans. Roy. Soc., 1970, A 200, N 1063, p. 523 -527. De Witt T., Mezner .W. A rheological equation of state which predicts non-Newtonian viscosity, normal stresses and dynamics module. J. Appl.Phys., 1985, v. 26, p. 889-892. Baramboymb I.K. Mechanochemistry of high-molecular substances. – 3rd edition. Moscow. The Chemistry publishing house, 1978, p. 34. Danilova-Volkovskaya G.M. The effect of processing parameters and modifiers on the properties of polypropylene and PP-based composite materials. — Doctoral Thesis, (technical sciences). 2005, p. 273.

In: Organic and Physical Chemistry Using Chemical Kinetics … ISBN: 978-1-60021-763-0 Editors: Y.G. Medvedevskikh, et al. pp. 73-87 © 2007 Nova Science Publishers, Inc.

Chapter 7

ENERGY CRITERIONS OF PHOTOSYNTHESIS G. А. Коrablev*1 and G. Е. Zaikov*2 1

Basic research-educational center of chemical physics and mesoscopy, Udmurt research center, Ural Division, RAS, Izhevsk 2 Institute of biochemical physics after N.M. Emanuel, RAS, 119991, 4 Kosygina St., Russia, Moscow

ABSTRACT The application of methodology of spatial-energy interactions (P-parameter) to main stages of photosynthesis is given. Their energy characteristics are calculated. The values obtained correspond to the reference and experimental data.

Keywords: Spatial-energy parameter, free radicals, structural interactions, photosynthesis.

DESIGNATIONS m1 and m2 ΔU1 and ΔU2 ΔU Z* n* Wi ri ni SEI Р0 РE *

masses of material points (kg); potential energies of material points (J); their resulting (mutual) potential energy of interaction (J); nucleus effective charge (Cl); effective main quantum number; bond energy of electrons on i-orbital (eV); orbital radius of i-orbital (Å); number of electrons on this orbital; spatial-energy interactions; spatial-energy parameter (eVÅ); effective Р-parameter (eV);

G.А. Коrablev: E-mail: [email protected]

74 R Hv N1, N2, … N РС α ρ PS АТP RuDF PGA NADP PGA Е ЕС (eV).

G. А. Коrablev and G. Е. Zaikov dimensional characteristic of atom or chemical bond (Å); light quantum energy (J, eV); number of homogeneous atoms; average repetition factor in the formula (10); structural Р-parameter of complex structure (eV); coefficient of structural interactions, isomorphism (%); degree of structural interaction (%); photosystem (PSI and PSII); adenosine triphosphate; ribulose-diphosphate; 3 phospho-glycerin acid; nicotine-amide-adenine-dinucleotide-phosphate; phosphor-glycerin aldehyde; energy of bond or molecule reduction (eV); resulting energy of bond or reduction for radical groups

INTRODUCTION Photosynthesis – process of converting electromagnetic energy of the sun rays into the energy of chemical bonds of vital organic substances … [1]. It is the only natural process through which the organic world obtains the reserve of free energy and which provides all bio-organisms with chemical energy. From the moment photosynthesis was discovered by D.M. Priestly (1771-1850), the researches passed several important stages. The first works connected with photosynthesis energy refer to 1850-1900 (R. Mayer, D.G. Stocks, J. Sax). The application of physiological concepts – in 1900-1950 (М.S. Tsvet, А.А. Richter, W. Arnold). Further development of bio-physicochemical aspects of synthesis till now resulted in its modern model and clarified the way of carbon during photosynthesis (M. Calvin), concept of two photosystems (R. Emerson), structure of reaction center (I. Deizinhoffer, H. Michel, R. Huber), etc. The basis of photosynthesis – consecutive chain of redox reactions, during which electrons are transferred from donor-reducer to acceptor-oxidizer with the formation of reduced compounds (carbohydrates) and oxygen isolation. It is known that excitation energy for complex organic molecules of chlorophyll type lasts for 10-8-10-9 sec and can be stored only for insignificant fractions of a second. But during photosynthesis the energy of absorbed light quantum is stored for a long period (from several minutes to millions of years). The energy is stored here in molecular as chemical bonds rich with energy in complex organic structures. Therefore photosynthesis energy can be presented based on the analysis of changes in energies of chemical bonds of molecular structures in dynamics of all main types of photosynthesis. This is the aim to use the methodology of spatial-energy interactions (P-parameter) in this paper.

*

G.Е. Zaikov: E-mail: [email protected]

Energy Criterions of Photosynthesis

75

SPATIAL-ENERGY PARAMETER (Р-PARAMETER) Structural and interatomic interactions are sure to have electron nature. Thus the registration of the extent to which electrons fill the atom valence states is the basis of the method of valence bonds in chemistry and is numerically expressed through coulomb electrostatic interaction. Also important are exchange-promotional structural interactions that determine isomorphism, solubility of components in solid, liquid and molecular media [2]. During the interactions of oppositely charged heterogeneous systems the volume energy of interacting structures is compensated to a certain extent thus leading to the decrease in the resultant volume energy. The analysis of different physical and chemical processes allows assuming that in many cases the principle of adding reciprocals of volume energies or kinetic parameters of interacting structures is executed. Some examples: ambipolar diffusion, total rate of topochemical reaction, change in the light velocity when transiting from vacuum into the given medium, resultant constant of chemical reaction rate (initial product – intermediary activated complex – final product). Lagrange equation for relative movement of isolated system of two interacting material points with masses m1 and m2 in coordinate х can be presented as follows:

1 ΔU

≈

1 ΔU 1

+

1 ΔU 2

(1)

where ∆U1 and ∆U2 – potential energies of material points in elementary section of interactions, ΔU - resulting (mutual) potential energy of these interactions. The atom system is formed from oppositely charged masses of nucleus and electrons. In this system energy characteristics of subsystems are the orbital energy of electrons (Wi) and effective energy of nucleus that takes into consideration the screening effects (by Clementi). Therefore, assuming that the resultant interaction energy of the system orbital-nucleus (responsible for interatomic interactions) can be calculated based on the principle of adding reciprocals of some initial energy components, we substantiate the introduction of Pparameter [2] as an averaged energy characteristic of valence orbitals in accordance with the following equations:

1

1

+

=

1

q r Wn Р 2

i

i

Р

E

=

Р r

0

i

i

(2) E

(3)

G. А. Коrablev and G. Е. Zaikov

76

Р

E

1

Р

=

0

(3а)

R

=

1 2

P0

q

q=

Z* n*

+

1 (Wrn) i

(4)

(5)

Here: Wi – bond energy of electrons [3]; ri – orbital radius of i–orbital [4]; ni – number of electrons of the given orbital, Z* and n* – effective charge of nucleus and effective main quantum number [5], R – numerical characteristic of atom (bond). The Р0 value will be called a spatial-energy parameter, and the РE value – effective Р– parameter. Effective РE–parameter has a physical sense of some averaged energy of valence electrons in atom and is measured in energy units, e.g. in electron-volts (eV). The values of Р0- and РE-parameters of some elements calculated based on equations (25) are given in table 1. Table 1. Р-parameters of atoms calculated via the bond energy of electrons

1

Valence electrons 2

W (eV) 3

ri (Å) 4

q2 0 (eVÅ) 5

Р0 (eVÅ) 6

Н

1S1

13.595

0.5295

14.394

4.7985

2P1

11.792

0.596

35.395

5.8680

2P2

11.792

0.596

35.395

10.061

Atom

С

N

2Р1г 2P3г 2S1 2S2 2S1+2P3г 2S1+2P1г 2S2+2P2 2P1 2P2 2P3 2P4г 2P5г 2S1 2S2 2S2+2P3

19.201

0.620

37.240

15.445

0.4875

52.912

25.724 25.724

0.521 0.521

53.283 53.283

4.4044 13.213 9.0209 14.524 22.234 13.425 24.585 6.5916 11.723 15.830 19.193 21.966 10.709 17.833 33.663

R (Å) 7 0.5295 0.46 0.28 R-I=1.36 0.77 0.69 0.77 0.69

Р0/R (eV) 8 9.0624 10.432 17.137 3.525 7.6208 8.5043 13.066 14.581

0.77 0.77 0.77 0.77 0.77 0.70 0.70 0.70 0.55 0.55 0.70 0.70 0.70

11.715 18.862 28.875 17.435 31.929 9.4166 16.747 22.614 34.896 39.938 15.299 25.476 48.09

Energy Criterions of Photosynthesis

77

Table 1. (Continued) Atom

Valence electrons 2P1 2P1 2P1 2P2

W (eV) 17.195

ri (Å) 0.4135

q2 0 (eVÅ) 71.383

Р0 (eVÅ) 4.663

17.195

0.4135

71.383

11.858

2P4

17.195

0.4135

71.383

20.338

2S1 2S2 2S2+2P4

33.859 33.859

0.450 0.450

72.620 72.620

12.594 21.466 41.804

5.3212

1.690

17.406

5.929 8.8456

O

Ca

S

Se

Р

Mg

4S1 4S2 4S2 4S2 3P1 3P2 3P4 3S1 3S2 3S2+3P4 4P1 4P2 4P2 4P2 4P4 4P4 4S1 4S2 4S2+4P4 4S2+4P4 3P1 3P1 3P3 3P3 3S2 3S2+3P3 3S1 3S2

Mn

4S1 4S2 3d1 4S1+3d1 4S2+3d2 4S2+3d5

Na

3S1

Cl

3P1

11.901 11.901 11.904 23.933 23.933

0.808 0.808 0.808 0.723 0.723

48.108 48.108 48.108 64.852 64.852

6.0143 13.740 21.375 13.659 22.565 43.940 8.5811 15.070 15.070 15.070 24.213

10.963

0.909

61.803

22.787

0.775

85.678

10.659

0.9175

38.199

14.642 25.010 49.214 49.214 7.7864

10.659

0.9175

38.199

16.594

18.951

0.803

50.922

6.8859

1.279

17.501

19.050 35.644 5.8568 8.7787

6.7451

1.278

25.118

17.384

0.3885

177.33

4.9552

1.713

10.058

6.4180 10.223 6.5058 12.924 22.774 38.590 4.6034

13.780

0.7235

59.849

8.5461

R (Å) 0.66 RI=1.36 RI=1.40 0.66 0.59 RI=1.36 RI=1.40 0.66 0.59 0.66 0.66 0.66 0.59 1.97 1.97 R2+=1.00 R2+=1.26 1.04 1.04 1.04 1.04

Р0/R (eV) 9.7979 4.755 4.6188 17.967 20.048 8.7191 8.470 30.815 34.471 19.082 32.524 63.339 70.854 3.0096 4.4902 8.8456 7.0203 7.7061 13.215 20.553 13.134

1.04 1.17 1.17 1.6 1.14 1.17 1.6 1.17 1.17 1.17 1.6 1.10 R3-=1.86 1.10 R3-=1.86 1.10 1.10 1.60 1.60 R2+=1.02

42.250 7.3343 12.880 9.4188 13.219 20.710 15.133 12.515 21.376 42.066 30.759 7.0785 РЭ=4.1862 15.085 8.9215 17.318 32.403 3.6618 5.4867 8.6066

1.30 1.30 1.30 1.30 1.30 1.30 1.89 R+I=1.18 R+I=0.98 1.00 R-I=1.81

4.9369 7.8638 5.0043 9.9414 17.518 29.684 2.4357 3.901 4.6973 8.5461 4.7216

G. А. Коrablev and G. Е. Zaikov

78

Table 1. (Continued) Atom

Fe

К

Valence electrons 4S1 3d1 4S1+3d1 4S2+3d1 4S1

W (eV) 7.0256 17.603

4.0130

ri (Å) 1.227 0.364

2.612

q2 0 (eVÅ) 26.572 199.95

10.993

4S2(*)

Р0 (eVÅ) 6.5089 6.2084 12.717 16.664 4.8490 7.2115

R (Å) 1.26

Р0/R (eV) 4.8325

1.26 1.26 2.36 R+I=1.45 2.36 R+I=1.45

10.093 13.226 2.0547 3.344 3.0557 4.9734

Table 2. Structural РС-parameters calculated via the bond energy of electrons Radicals, fragments of molecules

P i'

ОН

Н2О

СН2 СН3 СН Н3О С2Н5 СН2 СН3 СН3 СН СН СО С=О С=О С-О2 С-О2 СО-ОН CH-OH CO-H

P "i (eV)

PC

17.967 9.7979 9.7979 17.967

10.432 9.0624 10.432 17.138

6.5999 4.7080 5.0525 8.7712

O (2P2) O (2P1) O (2P1) O (2P2)

2·9.0624 2·10.432 2·17.138 28.875 31.929 28.875 31.929 28.875 28.875 31.929 31.929 3·17.138 2·31.929 31.929 28.875 31.929 28.875 31.929 31.929 14.581 17.435 28.875 31.929 12.315 11.152 8.4416

17.967 17.967 17.967 2·17.138 2·17.138 2·9.0624 3·17.138 3·9.0624 17.138 9.0624 17.138 17.967 5·17.138 2·9.0624 3·17.138 3·9.0624 10.432 10.432 20.048 20.048 20.048 2·20.048 2·20.048 8.7712 8.7712 9.0624

9.0226 9.6537 11.788 15.674 16.531 11.125 19.696 14.003 10.755 7.059 11.152 13.314 36.590 11.562 18.491 14.684 7.6634 7.8630 12.315 8.4416 9.3252 16.786 17.774 5.1226 4.9159 4.3705

O (2P2) O (2P2) O (2P2) С (2S12P3г) С (2S22P2) С (2S12P3г) С (2S22P2) С (2S12P3г) С (2S12P3г) С (2S22P2) С (2S22P2) O (2P2) С (2S22P2) С (2S22P2) С (2S22P3г) С (2S22P2) С (2S22P3г) С (2S22P2) С (2S22P2) С (2P2) С (2S12P1г) С (2S12P3г) С (2S22P2) С (2S22P2) С (2S22P2) С (2P2)

(eV)

(eV)

Orbitals

Modifying the rules of adding reciprocals of energy characteristics of subsystems as applied to complex structures we can obtain [6] the equation for calculating РС-parameters of complex structure:

Energy Criterions of Photosynthesis

1 Р

⎛ 1 ⎞ ⎛ 1 ⎞ ⎟ +⎜ ⎟ ⎝ NP E ⎠ ⎝ NP E ⎠

=⎜ С

1

+ ...

79

(6)

2

where N1 and N2 – number of homogeneous atoms in subsystems. The calculation results of some complex structures based on equation (6) are given in table 2. The calculations for 21 elements showed that the values of РE-parameters are similar to corresponding values of total energy of valence electrons according to the statistic model of atom. Simple dependence between PE-parameter and electron density at the distance ri can be obtained (according to the statistic model of atom):

β

2/3 i

= A ⋅ P 0 = A Р E , where А-constant

r

(7)

i

When the solution is formed in the places of atom-components contact, the unified electron density has to be established. The dissolving process is accompanied by the redistribution of this density between valence areas of both particles and transition of some electrons from external spheres to the neighboring ones. It is obvious that if electron densities in free atom-components of the solution at the distances of orbital radius ri are similar, the transition processes between boundary atoms of particles are minimal thus favoring the solution formation. Thus the task of evaluating the solubility in many cases comes to comparative evaluation of electron density of valence electrons in free atoms (on averaged orbitals) participating in the solution formation. In this regard the maximum total solubility evaluated through the coefficient of structural interaction and isomorphism α are determined by the state of minimal value that represent relative difference of effective energies of external orbital:

α=

P'o / ri '− P''o / ri '' 100% ; ( P'o / ri '+ P''o / ri '') / 2

' − " α = РС РС 200% ' + Р" РС С

(8)

(9)

Multiple calculations and comparisons with the experiment allowed arranging the unified averaged figure-nomogram of degree of structural interaction and solubility (ρ) dependence upon coefficient α [2].

80

G. А. Коrablev and G. Е. Zaikov

The following spatial-energy principles defining the character of structural spatial-energy interactions were determined: 1. Complete (total-lot) isomorphic interaction takes place at relative difference of Pparameters of valence orbitals of interchanging atoms (within 4-6%). 2. Р-parameter of the smallest value defines the orbital that is mainly responsible for isomorphism. 3. Qualitatively the isomorphism character is defined by geometrical similarity of orbital shapes responsible for isomorphism. At the same time, the more similar are the extensions, trajectories and inclination angles of such orbitals, the more perfect is isomorphism. According to the degree of isomorphic similarity of interchanging structures they can be classified into three types (I, II, III) given for some cases in table 3.

PHOTOSYNTHESIS. INITIAL STAGE Magnesium atom that is four-coordinated with nitrogen atoms is included into chlorophyll in the central cavity of the whole structure. The porphinated chlorophyll ring is located in aqueous medium. Each central Mg atom forming chelate compound has two bonds by donor-acceptor mechanism and two covalence bonds. Two molecules of bacteriochlorophyll are located close to each other (about 3 Å) and form competent-structure – dimer chlorophyll. In the dynamics of structural permutations all four bonds of each Mg atom become equivalent [7]. All this allows assuming that total effective РE-parameter of Mg will be approximately two times greater than from 2S2-orbital (5.4867х2=10.973 eV). At the first stage of photosynthesis in the system of PS-2 dimensional characteristics of hydrogen atom can change in structured water molecules under the radiation with energy hν from boron radius (0.529 Å) to atomic (“metal”) – 0.46 Å, this corresponds to the obtaining of РE-parameter equal 10.432 eV by hydrogen that is similar to РE-parameter of 2Mg. It should be pointed out that general change in the scale of photosynthesis potentials PS-2 approximately equals 1.5 eV, and the difference between the data of Р-parameters of hydrogen atoms equals 1.37 eV. The rest of hydrogen atoms with “boron” РE-parameter equaled to 9.0624 eV have similar values with РE-parameters of 2Р1-orbitals of nitrogen atoms surrounding magnesium. Other data are not less important: initial value of РE-parameter of 2S2-orbital of magnesium atom gives from РE-parameter (table 3) of radical (О-Н) α=8.24 % and ρ ≈ 77-82 %. This ρ value can increase to even 100 % under the light action due to minor changes in dimensional characteristics of atoms-components. Absolute difference of these Р-parameters equals 0.43 eV, thus corresponding to the changes in the scale of potentials during the synthesis of АТP. Total spatial-energy action upon the bond Н-О-Н of magnesium and nitrogen atoms (table 3) results in the possibility of breaking this bond with the isolation of free hydrogen and oxygen atoms.

Table 3. Photosynthesis structural interactions Atoms .molecules. radicals O-P O-P Mg2+-H H2O-CH2 C-O CO-OH CO-H2O CH2-CO2 2Mg-H Mn-H Mn-O Mn-O N-H Mn-OH Mg-(O-H) K+-H Fe-S Na+-H

1 component Orbitals 2Р2 2Р1 3S2 1S1-2Р2 2S1-2Р1 2Р2-2Р2 2S12Р1г-2Р2 2S22Р2-1S1 3S2 (3S2)* 4S13d1 4S13d1 4S23d2 2Р1 4S1 2S2 4S1 4S23d1 3S1

РE. РС (eV) 8.470* 4.6188* 8.6066 11.788 17.435 8.4416 9.3252 16.531 10.973 9.9414 9.9414 17.518 9.4166 4.3969 5.4867 3.344 13.226 3.901

2 component Orbitals 3Р3 3Р1 1S1 2S12P3г-1S1 2Р2 2Р2 -1S1 1S1-2Р2 2S12P3г-2Р2 1S1 1S1 2P1 2P2 1S1 2P1-2S1 2P1-2S1 1S1 2P2 1S1

РE. РС (eV) 8.9215* 4.1862* 9.0624 11.125 17.967 8.7712 9.0226 16.785 10.432 10.432 9.7979 17.967 9.0624 4.7080 5.0575 3.525 13.215 3.525

α (%)

ρ (mol%)

SEI types

5.19 9.83 5.16 5.79 3.01 7.51 2.21 1.53 5.05 4.82 1.45 2.53 3.83 4.75 8.24 5.27 0.08 10.1

100 60-65 100 100 100 90-95 100 100 100 100 100 100 100 100 77-82 100 100 55-60

I I I II I II II, III III I I II II II II, III II I II I

G. А. Коrablev and G. Е. Zaikov

82

This initial process finishes with the participation of manganese-containing system connected with proteins of reaction center PS-2. Structural reconstruction can take place in manganese cluster (two-nucleus or four-nucleus) under the action of radiation [8, 9] from univalent state (4.9369 eV – this is similar to initial values of Mg РE-parameter) to bivalent (9.9414 eV) and further – to quadrivalent state (17.518 eV). All this provides enzymatic action of Mn upon the bond Н-О-Н, both upon oxygen and hydrogen atoms, and hydroxyl group in general. This is confirmed by the approximate equality of РE-parameters of bi- and quadrivalent Mn with РE-parameters of 2Р1 and 2Р2orbitals of oxygen atom (table 3). Thus, all the above interactions and structural re-groupings inducted with light result in the formation of oxidized chlorophyll based on the following reaction [10]: Н2О+2hν→

1 О2+2е-+2Н+ 2

with the isolation of two electrons and two protons. These electrons, broken off from the water, through the chain of “dark” reactions go further to PS-1 that utilizes them in the next photosynthesis stages to reduce NADP+ to NADPN that is carried out also with the help of proton transfer system. For double bond of 2Р1-orbital the carbon atom has РE-parameter – (8.5043 eV) – similar to РE-parameter of hydrogen atom (table 1). Therefore one of the freed hydrogen atoms join the double bond С=С available in NADPN with the formation of single bond with carbon atom [9].

PHOSPHORYLATION It is considered [7,11] that directed transition of protons serves as energy source during phosphorylation. Between the numbers of transported protons and electrons certain stoichiometric relations are revealed. Thus, in the course of electron transfer (along the whole transport system) ATP molecules are formed. Apparently, ATP phosphorylation energy can also be estimated through the system of electron transfer. In particular, electron transfer results in that phosphoric acid molecules present in АТP, NADP and NADPN contain oxygen atoms in the form of О-. Spatial-energy interactions (including isomorphic) are objectively expressed both at similar and opposite electrostatic charge of atoms-components. Such interactions can also take place between two heterogeneous atoms, if only their РE-parameters are roughly equal, and geometric shapes of orbitals are similar or alike. The radiation energy hν in PS-1 promotes, apparently, the changes in dimensional characteristics of phosphorous and oxygen atoms from covalent to anion ones. Therefore, Р0parameters of free phosphorus and oxygen atoms are distributed at the distance of their anion radii 1.86 Å and 1.40 Å, respectively. This similarity of values of their РE-parameters: α=5.19 % for 2Р3-orbitals of phosphorous with 2Р2-orbitals of oxygen (table 3). Such approximate equality of РE-parameters and geometric similarity of shapes of orbitals of atoms-components shows that actual degree of their interaction ρ=100 %, thus

Energy Criterions of Photosynthesis

83

providing the energy of formation of macroenergy bond Р-О. Then bond energy of phosphorous and oxygen atoms from two different molecules of phosphoric acid necessary for structural formation during phosphorylation can be considered phosphorylation energy. To calculate bond energies or energies of molecule reduction during photosynthesis (Е) the technique previously tested [6] for 68 binary and more complicated compounds following the equation was applied:

1 1 = = Е Рс ⎛

1

+

1

N⎞ ⎛ N⎞ ⎜ РE ⎟ ⎜ РE ⎟ ⎝ K⎠ ⎝ K⎠ 1

(10)

2

where N – bond average repetition factor, К – hybridization coefficient that usually equals the number of atom valence electrons registered. The half of internuclear distance (for binary bond) of similar atoms or atomic, covalence or ionic radii (depending upon bond type) can be used as a dimensional characteristic of atoms. The calculations involving anionic distances of atomic orbitals for Р and О atoms were made: 3Р1 (phosphorous)-2Р1 (oxygen) and for 3Р3 (phosphorous)-2Р2 (oxygen). The values of Е obtained appeared to be slightly greater than experimental and reference data (table 4). But actual power physiological processes during photosynthesis have the efficiency below the theoretical, being in some cases about 83% [7]. It is probable that electrostatic component of resulting interactions on anion-anion distances is registered in such a way. In fact, the calculated value 0.83Е practically corresponds to the experimental bond energy values during phosphorylation (first line in table 4) and free energy for АТP in chloroplasts (second line in table 4). The calculations of bond energy based on the same technique but on covalence distances of atoms for free molecule Р…О (sesquialteral bond) and for molecule Р=О in Р4О10 (double bond) are given in table 4 for comparison. Sesquialteral bond was evaluated introducing the coefficient N=1.5 using the average value of oxygen РE-parameter for single and double bonds. It is interesting to point out that calculations of Е based on covalence distances correspond to experimental data without introducing the coefficient 0.83.

ASSIMILATION OF СО2 Binding of СО2 takes place in aqueous medium by the carboxylation reaction of ribulosediphosphate (RuDP) with the formation of 3-phospho-glycerine acid (PGA) – table 5. Water molecule and radical С=О at the distances of molecular interaction have quite similar values of РE-parameters for forming the general structural grouping of dimeric composite type. Total РE-parameter of water molecule and radical С=О nearly equals РE-parameter of СО2 and therefore the molecules of СО2 and Н2О join RuBP with the formation of two radicals СООН в PGA (table 5). In ferment RuDP- carboxylase, Mg atoms and О- ions (5.4867 eV and 4.755 eV) play an active role, their РE-parameters similar to РE-parameter of radical СООН.

Table 4. Bond and reduction energies of molecules during photosynthesis (eV) Atoms, structures, orbitals

1 component

2 component

РE (eV) 2 4.1862 4.1862 8.9215

N/K 3 1/5 1/5 1/5

РE (eV) 4 4.6188 4.755 8.470

N/K 5 1/6 1/6 1/6

Р---О 3S23P3-2S22P4

32.403

1.5/5

70.854 63.339

Р=О 3Р3-2P2 С-Н 2Р2-1S1 Н2О 1S1-2S2 -O-O2P1-2P1 O=O 2P2-2P2 CO2 2P2-2P2 =C=O 2S22P2-2P2 C-O 2P2-2P2 (C=O)-H (2S22P2-2P2)-1S1 -O-H 2P2-1S1 CO-OH (2S22P2-2P2)-(2P21S1) CH2O 2S22P2-1S1-2P2

15.085

2/3

13.066

1 Р-О 3Р1-2Р1 Р-О 3Р2-2Р2

3 component РE (eV) 6

N/K 7

Calculation Е 8 0.400 0.405 0.77

0.83Е 9 0.33 0.34 0.64

Е by [7.8.14]

Notes

-

10 0.340.35 0.670.59 6.14

Free PO molecule

-

6.504

In Р4О10 molecule

3.797

-

3.772

-

2.570

-

2.476

-

-

4.90

-

5.11

2/4

--

-

5.012

-

5.11

2•20.048

2/6

-

-

4.717

-

4.56

2/4

20.048

2/2

-

-

8.8874

-

13.066

1/2

17.967

1/2

-

-

3.782

-

3.688

31.929

2/4

20.048

2/2

9.0624

1/1

4.487

-

4.553

17.967 17.967 8.8874

1/2 1/2 1/1

17.137 9?0624 5.894

1/1 1/1 1/1

-

-

-

-.4.390

-

-

5.894 4.511 3.544

-

-

31.929

1.33/4

2.90624

1/1

20.048

2/2

5.025

-

4.965.07

_ _ -

-

1.5/6 1.5/6

-

-

20.042

2/2

-

-

6.277 6.024 < 6.15> 6.697

1/2

9.0624

1/1

-

-

2•9.0624

1/1

17.967

1/6

-

9.7979

1/1

9.7979

1/1

20.048

2/4

20.048

14.581

2/4

31.929

11 Phosphorylation ÄG of ATP

Decomposition of one molecule

Reduction

Free energy of the formation of one mole

Table 5. Spatial-energy characteristics of СО2 assimilation (eV)

Reaction blocks

PE

RuDF

Mg, RuDFcarboxylase

¾ C = O + H2O 8.4416

+ CO2

9.0226;

17.774;

NADPN, PGA ATP, O2COOH 2X5.1226 ;

PGA ATP Mg 2COH + O2 . . . 2x4.3705; 17.967x2 ;

EC

8.8874

2.570

EC1 =1.401

Calculation: EC2-EC1 =0.37; By [7]: 1 ATP molecule

4.717

3,544 3,544

4.487

5.012

EC3 =2.367

EC2 =1.770

9060

17.967x2

(7.333)

(8.741)

E

CH2O + O2 + . . .

5.025

5.012

EC4 =2.509

EC3-EC1 ~ 0.97 EC3-EC2 ~ 0.60 3 ATP molecule (1.06 eV) 2 ATP molecule

Notes: РE – initial values of РE-parameters, for Мg (5.4867), Mg2+ (8.6066), for О- (4.755; 4.6188) Е – bond or reduction energy ЕС – resulting bond or reduction energy for groups of radicals or fragments: 1/ЕС=1/Е1+1/Е2+…

86

G. А. Коrablev and G. Е. Zaikov

A great difference in the number of atoms of interacting structures proves that carboxylase can play only a fermentative role, “tuned” to obtain this final product (СООН). The further complicated way of СО2 assimilation to form СН2О flows through series of intermediate compounds and reactions (Calvin cycle). Let us show some results of calculations of total spatial-energy assimilation processes of СО2. When СО2 is reduced to the level of its structural formation in СН2О, the chemical bonds are reconstructed on all stages of the cycle. Therefore, the additional activation energy from ATP and NADPN is required. It is also obvious that power consumption should be rationally calculated taking into account the reconstruction processes of chemical bonds, i.e. via the values of bond energy – for binary structures, and reduction energy – for more complex molecules and radicals (Е). Thus we calculated the value E based on equation (10) for several compounds and radicals during photosynthesis – tables 4 and 5. For radical – С =О the calculations were made in two possible variants of activity of valence orbitals of carbon atoms. The compliance of calculated Е values with reference data [12,13] was in the range of 5% for all bonds of covalence type without introducing the coefficient 0.83. The main part of light energy is stored by a plant on the reduction stage to PGA. At the same time, 4.56 eV (per molecule) are spent – [12.13]. Our calculations give the reduction energy of radical СОН equal to 4.487 eV. Free energy for the formation of one mole of СН2О based on reference data [7,12, etc] is 4.96-5.07 eV. The calculations following the method of Р-parameter evaluate this energy as 5.025 eV. Н In molecule О=С–Н the average repetition factor for carbon atom bond was taken as equal to (2+1+1)/3=1.33. Applying the approved approach to calculate the resulting bond energy (or the reduction energy) of structural subsystems for each stage, the values of these energies were calculated (table 5) – ЕС. It is known [7] that the cycle moving energy to PGA can be 1.06 eV due to three ATP molecules (per one СО2 molecule), one ATP molecule is consumed in the cycle to PGA. Following our data, the cycle moving energy (ΔЕС) equals the difference of ЕС values for the corresponding stages: 1) stage СО2 – FGAК: ΔЕС=1.770-1.401=0.369 eV Phosphorylation energy of one ATP molecule = 0.34-0.35 eV 2) stage СО2 – FGA: ΔЕС=2.367-1.401=0.966 eV Phosphorylation energy of three ATP molecules: 0.34х3=1.02 eV Thus Р-parameter gives the satisfactory characteristics of energetics of the СО2 assimilation cycle main stages. Photorespiration reaction is as if “competitive” to the СО2 assimilation reaction. Also here it is possible to reveal similar values of РE-parameters of interacting radicals С=О and НСОН with РE-parameters of oxygen atoms. As in assimilation reaction the ferment RuDP- carboxylase “is tuned” for the formation of final product СООН. Other ferments can participate in photosynthesis and photorespiration, for example, the substitution of Mg atoms for Fe atoms results in the formation of cytochromes, in which РEparameter of two-valence iron (РE=10.093 eV) is an active spatial-energy component of photosynthesis structural interactions. Therefore, iron-sulfur proteins – ferrdoxins executing

Energy Criterions of Photosynthesis

87

various transport functions connected with ATP synthesis are initial and secondary acceptors of electrons in the system PSI.

CONCLUSION In this approach we give quantitative and semi-quantitative evaluation of spatial-energy interactions at main stages of complicated biophysical process of photosynthesis based on the utilization of initial atomic characteristics. The analysis of results after the application of Рparameter methodology shows that they correspond to reference data both in the direction and energetics of these processes.

REFERENCES [1] [2] [3] [4] [5] [6]

[7] [8] [9] [10] [11] [12] [13] [14]

Big medical encyclopedia. М.Т.26.1985.560 p. Korablev G.A. Spatial-Energy Principles of Complex Structures Formation. Netherlands. Brill Academic Publishers and VSP. 2005, 426p. (Monograph). Fischer C.F. Average-Energy of Configuration Hartree-Fock Results for the Atoms Helium to Radon.//Atomic Data.-1972. -№ 4. -p. 301-399. Waber J.T.. Cromer D.T. Orbital Radii of Atoms and Ions//J. Chem. Phys -1965. -V 42. -№12. -p. 4116-4123. Clementi E.. Raimondi D.L. Atomic Screening constants from S.C.F. Functions. 1.//J.Chem. Phys.-1963. -v.38. -№11. -p. 2686-2689. Korablev G.A.. Zaikov G.E. Energy of chemical bond and spatial-energy principles of hybridization of atom orbitalls.//J. of Applied Polymer Science. USA. 2006. V.101.n3.P.2101-2107. Photosynthesis/Edited by Govingi. М.:Mir, V.1-1987, 728p; V.2-1987, 460p. P. Clayton. Photosynthesis. Physical mechanisms and chemical models. М.:Mir-1984, 350p. S.A. Schukarev. Inorganic chemistry. V.2-1974, 382p. D. Hall, K. Rao. Photosynthesis. М.:Mir, 1983. J. Edwards, D. Walker. Photosynthesis of С3 and С4-plants: Mechanisms and regulation. М.: 1986. Encyclopedia in physics. М.: 1966, V.5, 576p. Kamen M.D. Primary processes in photosynthesis. L. 1963. Break-off energy of chemical bonds. Potentials of ionization and affinity to electron / Edited by V.I. Kondratjev. М.:Nauka, 1974, 351p.

In: Organic and Physical Chemistry Using Chemical Kinetics … ISBN: 978-1-60021-763-0 Editors: Y.G. Medvedevskikh, et al. pp. 89-101 © 2007 Nova Science Publishers, Inc.

Chapter 8

SPATIAL-ENERGY INTERACTIONS OF FREE RADICALS G. А. Коrablev*1 and G. Е. Zaikov*2 1

Basic research-educational center of chemical physics and mesoscopy, Udmurt research center, Ural Division, RAS, Izhevsk 2 Institute of biochemical physics after N.M. Emanuel, RAS, 119991, 4 Kosygina St.; Russia, Moscow

ABSTRACT Spatial-energy characteristics of many molecules and free radicals are obtained. The possibilities of applying the P-parameter methodology to structural interactions with free radicals and photosynthesis energetics evaluation are discussed. The satisfactory compliance of calculations with experimental and reference data on main photosynthesis stages is shown.

Keywords: Spatial-energy parameter, free radicals, structural interactions, photosynthesis.

DESIGNATIONS m1 and m2 а Δх ΔU1 and ΔU2 ΔU Z* n* * *

masses of material points (kg); their acceleration (m/s2); coordinate (m); potential energies of material points (J); their resulting (mutual) potential energy of interaction (J); nucleus effective charge (Cl); effective main quantum number;

G.А. Коrablev: E-mail: [email protected] G.Е. Zaikov: E-mail: [email protected]

G. А. Коrablev and G. Е. Zaikov

90 Wi ri ni SEI Р0 РE R N1, N2, … РС Ψ α ρ

bond energy of electrons on i-orbital (eV); orbital radius of i-orbital (Å); number of electrons on this orbital; spatial-energy interactions; spatial-energy parameter (eVÅ); effective Р-parameter (eV); dimensional characteristic of atom or chemical bond (Å); number of homogeneous atoms; Р-parameter of complex structure (eV); Ψ-function; coefficient of structural interactions, isomorphism (%); degree of structural interaction (%).

INTRODUCTION Free radicals are the atom groups or molecule fragments having unpaired electrons. Most of them are unstable with high reactivity. Interacting between themselves and with other molecules they produce new compounds that continue chemical reactions based on chain principle – similar to neutrons in chain nuclear reactions. In many cases such processes are the main reason of pathologic condition of living systems [1]. Therefore the problem of searching “retardants” for these chain reactions of free radicals is critical. For instance, it is known that sulfur-containing amino acid (cysteine) “attracts” unpaired electrons of protein [2,3]. Similar properties are reported about selenium, the element of the same subgroup VI-а of the System as sulfur [4]. It is found out that the number of unpaired electrons in dry bio-objects (after their production) decreases when introducing nitric oxide or increasing the moisture content. On the contrary, the role of oxygen atoms (also the element of VI-а subgroup of the System) is often expressed as the role of an accelerator of irreversible reactions of free radicals. Free radicals (including oxygen) demonstrate specific influence in complicated biophysicochemical processes of photosynthesis. Fundamental regularities of reactions with free radicals were found by I.I. Semenov and his disciples. Important contribution to solving the problem of free radical participation in biological processes was made by N.M. Emmanuel, А.G. Gurvich, B.N. Tarusov, L.А. Bluemenfeld, G.М. Frank, W. Gordy, B. Commoner, M.J. Calvin and others. It seems interesting to find a functional dependence and directedness of free-radical processes with initial energy and dimensional characteristics of their atomscomponents. In this paper we are attempting to explain such processes applying the methodology of spatial-energy notions (P-parameter).

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91

METHODOLOGY SUBSTANTIATION Comparing multiple regularities of physical and chemical processes we can assume that in many cases the principle of adding reciprocals of volume energies or kinetic parameters of interacting structures is implemented. Some examples: ambipolar diffusion, total rate of topochemical reaction, change in the light velocity when transiting from vacuum into the given medium, resulting constant of chemical reaction rate (initial product – intermediary activated complex – final product). Lagrange equation for relative movement of isolated system of two interacting material points with masses m1 and m2 in coordinate х with acceleration α can be presented as follows:

1 ≈ − ΔU 1 /( m 1 aΔx) + 1 /( m 2 aΔx)

1 or:

ΔU

≈

1

ΔU 1

+

1

ΔU 2

(1)

where ∆U1 and ∆U2 – potential energies of material points in elementary section of interactions, ΔU - resulting (mutual) potential energy of these interactions. The atom system is formed from oppositely charged masses of nucleus and electrons. In this system energy characteristics of subsystems are the orbital energy of electrons (Wi) and effective energy of nucleus that takes into consideration the screening effects (by Clementi). Therefore, assuming that the resultant interaction energy of the system orbital-nucleus (responsible for interatomic interactions) can be calculated based on the principle of adding reciprocals of some initial energy components, we substantiate the introduction of Pparameter [5] as an averaged energy characteristic of valence orbitals in accordance with the following equations:

1

1

+

=

1

q r Wn Р 2

i

i

Р

E

Р r

=

i

0

(2) E

(3)

i

1

=

1 2

P0

q

q=

Z* n*

+

1 (Wrn) i

(4)

(5)

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92

Here: Wi – bond energy of electrons [6]; ri – orbital radius of i–orbital [7]; ni – number of electrons of the given orbital, Z* and n* – effective charge of nucleus and effective main quantum number [8]. The Р0 value will be called a spatial-energy parameter, and the РE value – effective Р– parameter. Effective РE–parameter has a physical sense of some averaged energy of valence electrons in atom and is measured in energy units, e.g. in electron-volts (eV). Based on the results [5] the values of РE-parameters numerically equal (within 2%) total energy of valence electrons (U) by the atom statistic model. Using the well-known ratio between electron density (β) and inneratomic potential by the atom statistic model, we can obtain the direct dependence of РE-parameter upon the electron density at the distance ri from the nucleus:

β

2 i

3

= A P0 =

r

AP

E

where А – constant

i

Validity of this equation was confirmed when calculating the electron density using Clementi’s wave functions and comparing it with electron density value calculated via РEparameter value. Besides the modules of maximum values of ψ-function radial part were compared with Р0-parameter values, and the line dependence between these values was found. Using some properties of wave function for P-parameter, the wave equation of P-parameter was obtained. Based on calculations and comparisons two principles of adding spatial-energy criterions depending upon wave properties of P-parameter and systemic character of interactions and charges of particles were substantiated: 1. Interaction of oppositely-charged (heterogeneous) systems consisting of I, II, III, ... atom sorts is satisfactorily described by the principle of adding corresponding energy reciprocals by equations (2-5) (this corresponds to the minimum of weakening oscillations taking place in antiphase); 2. During the interaction of similarly-charged (homogeneous) subsystems the principle of algebraic adding of their P-parameters is realized based on the following equations:

m Σ Р0= P'0+ P'0' +...+ P0m i =1

(6)

∑ РE =

∑ Р0 R

(7)

where R –dimensional characteristic of atom (or chemical bond). This principle corresponds to the maximum of oscillation intensification taking place in the phase. Modifying the rule of adding energy reciprocals of subsystems as applied to complex structures we can obtain the equation for calculating РС-parameter of complex structure:

Spatial-Energy Interactions of Free Radicals

1 ⎛ 1 ⎞ ⎛ 1 ⎞ ⎟ +⎜ ⎟ + ... =⎜ Pc ⎜⎝ NPE ⎟⎠1 ⎜⎝ NPE ⎟⎠ 2

93

(8)

where N1 and N2 – number of homogeneous atoms in subsystems. During the formation of solution and other structural interactions the same electron density must be formed in the areas of contact of atoms-components. This process is accompanied by the redistribution of electron density between valence zones of both particles and transition of a part of electrons from some outer spheres into neighboring ones. Apparently, spanning electrons of atoms do not participate in such an exchange. Apparently, with the closeness of electron densities in free atoms-components, the transition processes between boundary atoms of particles will be minimum, thus favoring the formation of new structure. So, the evaluation of the degree of structural interactions in many cases comes to the comparative evaluation of electron density of valence electrons in free atoms (on averaged orbitals) participating in the process. The less is the difference (Р'0/r'i – P"0/r"i), the more favorable is the formation of a new structure or solid solution from energy point. In this connection the maximum total solubility evaluated through the coefficient of structural interaction α is defined by the condition of minimum value of α that represents a relative value of effective energies of outer orbitals of interacting subsystems:

P 'o / ri '− P ''o / ri '' α= 100% ( P 'o / ri '+ P ''o / ri '') / 2

' − Р" РС С 200% (9a) α = ' + Р" РС С

(9)

The nomogram of dependence of structural interaction degree (ρ) upon the coefficient α, unified for a broad range of structures was designed based on all the data obtained. Figure 1 shows the nomogram obtained using РE-parameters calculated via the bond energy of electrons (wi) for structural interactions of isomorphic type. Following this methodology the mutual solubility of atoms-components was evaluated in many (over a thousand) simple and complex systems. The calculation results agree with reference and experimental data. Isomorphism as a phenomenon is used to be applied to crystalline structures. Apparently, analogous processes can also take place between molecular compounds where their role and significance are no less than of purely coulomb interactions. In complex organic structures the main role can be performed by separate “blocks” or fragments. Therefore the task is to identify these fragments and evaluate their spatial-energy parameters. According to wave properties of Р-parameter, total Р-parameter of each fragment has to found based on the principle of adding reciprocals of initial P-parameters of all the atoms. The resultant Р-parameter of fragment block or all the structure is calculated following the rule of algebraic adding of P-parameters of fragments constituting them. The role of fragments can be performed by valence-active radicals, e.g. СН, СН2, (ОН)-, NO, NO2, (SO4)2-, etc. In complex structures this carbon atom usually has not one, but two or three side bonds. The priority significance when calculating based on the principle of adding

G. А. Коrablev and G. Е. Zaikov

94

reciprocals of P-parameters have those bonds, for which the condition of interference minimum is better executed. Therefore first the fragments of bond С-Н (for СН, СН2, СН3 …) are calculated, and then separately the fragments N-R, where R-binding radicals (e.g. – for the bond C-N).

Figure 1. Nomogram.

Apparently, spatial-energy interactions (SEI) based on equalization of electron densities of valence orbitals of atoms-components have in nature the same universal significance as purely electrostatic coulomb interactions, but they supplement each other. Isomorphism known from the time of E. Micherlikh (1820) and D.I. Mendeleev (1856) is only a particular manifestation of this overall natural phenomenon. The quantitative side of evaluating isomorphic replacements of components, both in complex and simple systems, can be rationally placed in the frameworks of P-parameter methodology. The problem of evaluating the degree of structural SEI for molecular and organic structures is more complicated. The methodology for calculating P-parameters of molecules, structures and their fragments are successfully implemented [5]. But such structures and their fragments are not often completely isomorphous to each other. Nevertheless SEI proceeds between them, its degree can be evaluated only semi-quantitatively or qualitatively. All systems can be split into three types based on their isomorphous similarity: I Systems mainly isomorphous to each other – the systems with almost the same number of heterogeneous atoms and summarily similar geometric shapes of interacting orbitals. II Systems with limited isomorphous similarity – the systems that: 1. either differ in the number of heterogeneous atoms but have summarily similar geometric shapes of interacting orbitals;

Spatial-Energy Interactions of Free Radicals

95

2. or definitely differ by geometric shape of orbitals but have the same number of interacting dissimilar atoms. III Systems without isomorphous similarity – the systems that considerably differ both in number of dissimilar atoms and geometric shape of their orbitals. Then, taking into account some experimental data, all types of SEI can be approximately classified as follows: Systems I 1. α < (0-6)%; ρ = 100 %. Complete 100% isomorphism, complete isomorphous replacement of atoms-components; 2. 6 % < α < (25-30)%; ρ = 98 – (0-3) %. Either broad or limited isomorphism as shown in nomogram 1; 3. α > (25-30) %; no SEI Systems II 1. α < (0-6)%; a. а) Reconstruction of chemical bonds, can be accompanied with the formation of a new compound; b. b) Breaking of chemical bonds can be accompanied with the separation of a fragment from the initial structure, but without joining or replacing. 2. 6 % < α < (25-30)%; A limited internal reconstruction of chemical bonds without the formation of a new compound and replacements is possible. 3. α > (20-30) %; no SEI Systems III 1. α < (0-6)%; a. а) Limited change in the type of chemical bonds of the given fragment, internal regrouping, without breaking from the main part of the molecule and replacements is possible; b. b) Some dimensional characteristics of the bond can change; 2. 6 % < α < (25-30)%; A very limited internal regrouping of atoms; 3. α > (25-30) %; no SEI. Nomogram № 1 is made for isomorphous interactions, i.e. for such structures or subsystems with the same number of dissimilar atoms and approximate geometric resemblance of interacting atomic orbitals.

G. А. Коrablev and G. Е. Zaikov

96

In all other cases the calculated values of α and ρ refer only to the given type of interactions, nomogram of which is not yet existing, and all the comparisons are merely assumptions of qualitative or semi-quantitative character. But if taking into account the universality of spatial-energy interactions in nature, this evaluation can be significant for analyzing structural rearrangements in complex biophysicochemical processes (this will be further shown on the example of photosynthesis). Enzymatic systems can greatly contribute to the correlation of the degree of structural correlations. In this model the enzyme role is as follows: active parts of its structure (fragments, atoms, ions) the РE-parameter value equal to the РE-parameter of the reaction final product. I.e. the enzyme is structurally “tuned” via ПЭВ to obtaining the reaction final product, but will not join it due to imperfect isomorphism of its structure (in accordance with III).

CALCULATIONS AND COMPARISONS Based on equations (2-5) with initial data calculated with quantum-mechanical techniques [6-8], the values of Р0-parameters of the majority of elements being tabulated constant values for each valence atom orbital were calculated. Mainly covalent radii were applied as a dimensional characteristic for calculating РE-parameter – by main type of chemical bond of interactions considered (table 1). For hydrogen atom also the value of Bohr radius and value of atomic (“metal”) radius were applied. In some cases the calculations of P-parameters are given considering the possibility of hybridization of atom orbitals (marked with “Г”) – following the methodology discussed before [9]. Besides we took into account the bond repetition factor for carbon and oxygen atoms. In the course of calculations for potassium atom – element of group IV of large period in the System the possibility of the influence of internal d-orbitals was considered. For several elements the values of РE-parameters were calculated using ionic radii whose values are given in column 7. All the values of atomic, covalent and ionic radii are basically taken by BelovBokiy, but crystalline ionic radii – by Batsanov [10]. Table 1. Р-parameters of atoms calculated via bond energy of electrons Atom 1 Н

Valence electrons 2

1S

1

W (eV) 3

13.595

ri (Å) 4

0.5295

q2 0 (eVÅ) 5

14.394

Р0 (eVÅ) 6

4.7985

R (Å) 7 0.5295 0.46 0.28 R-I=1.36

Р0/R (eV) 8 9.0624 10.432 17.137 3.525

Spatial-Energy Interactions of Free Radicals

97

Table 1. (Continued) Atom

С

N

1

Valence electrons

W (eV)

ri (Å)

q2 0 (eVÅ)

Р0 (eVÅ)

R (Å)

Р0/R (eV)

2P1

11.792

0.596

35.395

5.8680

2P2

11.792

0.596

35.395

10.061

0.77 0.69 0.77 0.69

7.6208 8.5043 13.066 14.581

0.77 0.77 0.77 0.77 0.77 0.70 0.70 0.70 0.55 0.55 0.70 0.70 0.70 7 0.66 RI=1.36 RI=1.40 0.66 0.59 RI=1.36 RI=1.40 0.66 0.59 0.66 0.66 0.66 0.59 1.97 1.97 R2+=1.00 R2+=1.26 1.04 1.04 1.04 1.04

11.715 18.862 28.875 17.435 31.929 9.4166 16.747 22.614 34.896 39.938 15.299 25.476 48.09 8 9.7979 4.755 4.6188 17.967 20.048 8.7191 8.470 30.815 34.471 19.082 32.524 63.339 70.854 3.0096 4.4902 8.8456 7.0203 7.7061 13.215 20.553 13.134

1.04 1.17 1.17 1.6 1.14 1.17 1.6 1.17 1.17 1.17 1.6

42.250 7.3343 12.880 9.4188 13.219 20.710 15.133 12.515 21.376 42.066 30.759

2Р1г 2P3г 2S1 2S2 2S1+2P3г 2S1+2P1г 2S2+2P2 2P1 2P2 2P3 2P4г 2P5г 2S1 2S2 2S2+2P3 2 2P1 2P1 2P1 2P2

19.201

0.620

37.240

15.445

0.4875

52.912

25.724 25.724

0.521 0.521

53.283 53.283

3 17.195

4 0.4135

5 71.383

4.4044 13.213 9.0209 14.524 22.234 13.425 24.585 6.5916 11.723 15.830 19.193 21.966 10.709 17.833 33.663 6 4.663

17.195

0.4135

71.383

11.858

2P4

17.195

0.4135

71.383

20.338

2S1 2S2 2S2+2P4

33.859 33.859

0.450 0.450

72.620 72.620

12.594 21.466 41.804

5.3212

1.690

17.406

5.929 8.8456

O

Ca

S

Se

4S1 4S2 4S2 4S2 3P1 3P2 3P4 3S1 3S2 3S2+3P4 4P1 4P2 4P2 4P2 4P4 4P4 4S1 4S2 4S2+4P4 4S2+4P4

11.901 11.901 11.904 23.933 23.933

0.808 0.808 0.808 0.723 0.723

48.108 48.108 48.108 64.852 64.852

10.963

0.909

61.803

22.787

0.775

85.678

6.0143 13.740 21.375 13.659 22.565 43.940 8.5811 15.070 15.070 15.070 24.213 14.642 25.010 49.214 49.214

G. А. Коrablev and G. Е. Zaikov

98

Table 1. (Continued)

Atom

Р

Mg

Mn

Valence electrons

W (eV)

ri (Å)

q2 0 (eVÅ)

Р0 (eVÅ)

R (Å)

Р0/R (eV)

3P1 3P1 3P3 3P3 3S2 3S2+3P3 3S1 3S2

10.659

0.9175

38.199

7.7864

10.659

0.9175

38.199

16.594

18.951

0.803

50.922

6.8859

1.279

17.501

19.050 35.644 5.8568 8.7787

4S1 4S2 3d1 4S1+3d1 4S2+3d2 4S2+3d5 3S1

6.7451

1.278

25.118

17.384

0.3885

177.33

4.9552

1.713

10.058

4.6034

3P1

13.780

0.7235

59.849

8.5461

2 4S1 3d1 4S1+3d1 4S2+3d1 4S1

3 7.0256 17.603

4 1.227 0.364

5 26.572 199.95

6 6.5089 6.2084 12.717 16.664 4.8490

1.10 R3-=1.86 1.10 R3-=1.86 1.10 1.10 1.60 1.60 R2+=1.02 1.30 1.30 1.30 1.30 1.30 1.30 1.89 R+I=1.18 R+I=0.98 1.00 R-I=1.81 7 1.26

7.0785 РE=4.1862 15.085 8.9215 17.318 32.403 3.6618 5.4867 8.6066 4.9369 7.8638 5.0043 9.9414 17.518 29.684 2.4357 3.901 4.6973 8.5461 4.7216 8 4.8325

1.26 1.26 2.36 R+I=1.45 2.36 R+I=1.45

10.093 13.226 2.0547 3.344 3.0557 4.9734

6.4180 10.223 6.5058 12.924 22.774 38.590

Na Cl 1 Fe

К

4S2(*)

4.0130

2.612

10.993

7.2115

Table 2 contains the computational results of structural РС-parameters of free radicals by the equation (8). The calculations are made for those radicals forming protein and aminoacid molecules (СН, СН2, СН3, NH2, etc), as well as for free radicals being formed during radiolysis and dissociation of water molecules (Н, ОН, Н3О, НО2). The comparison of РС-parameter values of free radicals obtained with carbon, sulfur, selenium and oxygen atoms was carried out in supposition of paired interactions by all possible variants – based on the equation (9). It should be specifically stressed that here we have the calculations of РE-parameters and structural interactions of practically all possible values of initial dimensional characteristics of atoms. In the norm of stable bonds without external interactions covalent bonds are the most probable in organic molecular structures. The other options of SEI given in tables 1-3 correspond to such possible structural regrouping when due to some reasons their dimensional characteristics vary from covalent to atomic or even ionic. The results of such calculations of coefficient α and degree of structural interactions (ρ) are given in table 3, when analyzing it the following conclusions and comparisons can be made: 1. Valence orbitals of sulfur and selenium atoms have quite similar values of Pparameters as well as the degrees of structural interactions (ρ). On the contrary, РE-parameters

Spatial-Energy Interactions of Free Radicals

99

of oxygen atoms sufficiently differ from such values thus resulting, in many cases, in the opposite results in chemical activity of its atoms. 2. Degree of structural interactions of sulfur and selenium atoms with radicals СН3, NH2,H3O equals 100%. But with radicals СН and СН2 it equals zero or is insignificant – in the range of 0 – 47%. It should be mentioned that structural interactions of the same elements with basic carbon chain of polymeric biomolecules cannot result in their breaking-in since the corresponding values of α for the interactions of Se-C and S-C exceeds 30%, thus ρ=0 in these cases. Atoms of S and Se can sufficiently structurally influence fragments of СН3 that are frequently located on the ends of hydrocarbon chains or in the form of free radicals. The data given confirm high reactivity of sulfur and selenium atoms as retardants of chain reactions of free radicals as elements “drawing back” unpaired valence electrons of free radicals, but at the same time preserving the basic structure of hydrocarbon chain. 3. Interactions of oxygen atoms result in α > 30% and ρ=0 with structures NH2, H3O and – with radicals СН and СН3 based on С atom (2S22P2). But for radical СН2 on the same base of carbon ρ=75-80 %, and for radical СН3 based on С atom (2S12P3г) – α=2,87 % and ρ=100 %. It is also important to add that in contrast to S and Se, atomic structures of oxygen and carbon have great values of РE-parameters and produce SEI at ρ=100 %. All this means that 1) degree and character of structural SEI of oxygen are ambiguous and considerably differ from the elements of selenium and sulfur; 2) oxygen atoms have potential possibilities for decomposing some molecular structures of bio-objects initiating the further free-radical process. 4. Water molecules (Н2О) produce ρ=100% with free radicals СН2, Н and ОН, this proves the possibility of decreasing the number unpaired electrons in dry bio-objects with their humidity decrease. In this approach the mechanism of radical Н3О formation during water dissociation can be apparently explained according to SEI (table 3). Hydrogen being released during dissociation by equation Н2О Н+ + ОН¯ further completely interacts with water molecules (as they have ρ=100%): Н+ + Н2О Н3О+. Table 2. Structural РС-parameters calculated via bond energy of electrons Radicals, fragments of molecules ОН

Н2О

СН2 СН3

Pi'

(eV)

17.967 9.7979 9.7979 17.967 2·9.0624 2·10.432 2·17.138 28.875 31.929 28.875 31.929 28.875

P "i (eV)

PC

10.432 9.0624 10.432 17.138 17.967 17.967 17.967 2·17.138 2·17.138 2·9.0624 3·17.138 3·9.0624

6.5999 4.7080 5.0525 8.7712 9.0226 9.6537 11.788 15.674 16.531 11.125 19.696 14.003

(eV)

Orbitals O (2P2) O (2P1) O (2P1) O (2P2) O (2P2) O (2P2) O (2P2) С (2S12P3г) С (2S22P2) С (2S12P3г) С (2S22P2) С (2S12P3г)

G. А. Коrablev and G. Е. Zaikov

100

Table 2. (Continued) Radicals, fragments of molecules СН NH NH2 Н3О Н2О–Н НО2 С2Н5 NO СН2 СН3 СН3 СН СН СО С=О С=О СО-Н2 С-О2 С-О2 СО-ОН NO CH-OH CO-H Se-H S-H Se-H S-H СО-СН3 SO2 SeO2

Pi'

(eV)

28.875 31.929 31.929 22.296 22.296 22.296 22.296 3·17.138 9.0226 17.138 2·31.929 22.296 31.929 28.875 31.929 28.875 31.929 31.929 14.581 17.435 12.315 28.875 31.929 12.315 22.614 11.152 8.4416 12.880 13.215 12.880 13.215 12.315 20.533 20.710

P "i (eV)

PC

17.138 9.0624 17.138 9.064 17.138 2·9.0624 2·17.138 17.967 9.0624 2·17.967 5·17.138 17.967 2·9.0624 3·17.138 3·9.0624 10.432 10.432 20.048 20.048 20.048 2·9.0624 2·20.048 2·20.048 8.7712 17.967 8.7712 9.0624 9.0624 9.0624 17.137 17.137 8.7712 2·20.048 2·20.048

10.755 7.059 11.152 6.4370 12.019 9.9980 13.509 13.314 4.5212 11.604 36.590 9.9495 11.562 18.491 14.684 7.6634 7.8630 12.315 8.4416 9.3252 7.3330 16.786 17.774 5.1226 10.012 4.9159 4.3705 5.3194 5.3758 7.3533 7.4615 5.1226 13.579 13.656

(eV)

Orbitals С (2S12P3г) С (2S22P2) С (2S22P2) N(2P3) N(2P3) N(2P3) N(2P3) O (2P2) O (2P2) O (2P2) С (2S22P2) N(2P3) С (2S22P2) С (2S22P3г) С (2S22P2) С (2S22P3г) С (2S22P2) С (2S22P2) С (2P2) С (2S12P1г) С (2S22P2) С (2S12P3г) С (2S22P2) С (2S22P2) N(2P3) С (2S22P2) С (2P2) Se (4P2) S (3P2) Se (4P2) S (3P2) С (2S22P2) S (3P2) Se (4P4)

GENERAL CONCLUSIONS 1. Oxygen and its systemic fragments initiate free-radical processes normally producing the rational balance with all forms of active protection of macromolecules from them; in particular, atoms of sulfur and selenium can be applied for that. 2. Spatial-energy characteristics of different valency for sulfur and selenium define the possibility of formation of such structures with these elements that possess multipronged physical and chemical properties from poisons to oxidants. 3. Methodology of spatial-energy parameter helps not only to explain experimentally determined dependencies of interactions of these elements with free radicals, but also provides practical solution for searching new reagents with given properties.

Spatial-Energy Interactions of Free Radicals

101

Table 3. Evaluation of the degree of structural interactions (ρ) Atoms, molecules, radicals 1 Se–CH3 S–CH3 О–CH3 Se–C О-С О-С S–C O-H O-H2 O-H H2O-H H2O-OH OH-H Se-CH3 Se–H3O S–H3O O–H3O O-CH2 O-CH Se-NH2 S-NH2 O-NH2 O-CH3 S-CH3 O-S О–CH2 Se–CН S–CН Se–CН2 S–CН2 Se–CН2 S–CН2 Se–CН S–CН

1 component Orbitals РE , РС (eV) 2 3 4Р4 20.710 3Р4 20.553 2Р4 30.815 4Р4 20.710 2Р4 30.815 2Р2 17.967 3Р4 20.533 2Р2 17.967 2Р2 17.967 2Р1 9.7979 1S1-2Р2 9.0226 2Р2-1S1 8.7712 4Р2 13.219 4Р2 12.880 4Р2 12.880 3Р2 13.215 2Р2 17.967 2Р2 17.967 2Р1 9.7979 4Р2 12.880 3Р2 13.215 2Р2 17.967 2Р2 17.967 3Р2 13.215 2Р2 20.048 2Р2 17.967 4Р4 20.710 3Р4 20.553 4Р4 20.710 3Р4 20.553 4Р2 12.880 3Р2 13.215 4Р2 12.880 3Р2 13.115

2 component Orbitals РE , Р С (eV) 4 5 2S22P2-1S1 19.696 2S22P2 19.696 2S22P2 19.696 2S22P2 31.929 2S22P2 31.929 2S12P1 г 17.435 2S22P2 31.929 1S1 17.138 1S1 9.0624 1S1 9.0624 1S1 9.0624 1S1 9.0624 2S12P3 г-1S1 14.003 1S1-2P2 13.314 1S1-2P2 13.314 1S1-2P2 13.314 1S1-2P2 13.314 2S22P2-1S1 16.531 2S22P2-1S1 7.059 2P3-1S1 13.625 2P3 13.625 2P3 13.625 2S12P3 18.491 2S1P3 г-1S1 14.003 3Р4 20.533 2S12P3г-1S1 11.125 2S22P2-1S1 11.152 2S22P2 11.152 2S22P2 16.531 2S22P2 16.531 2S22P2 11.562 2S22P2 11.562 2S22P2 11.152 2S22P2 11.152

α (%)

6 5.02 4.16 44 42.6 3.55 3.01 43.4 4.72 0.88 7.80 0.40 2.83 3.27 5.76 2.56 0.75 29.7 8.33 32.15 5.62 3.06 27.5 2.87 5.76 2.39 34 60 59.3 22.4 21.7 10.8 13.3 14.4 16.9

ρ (mol%) 7 100 100 0 0 100 100 0 100 100 84-88 100 100 100 100 100 100 0 75-80 0 100 100 0 100 100 100 0 0 0 2-5 2.5-5.5 7 47-52 30-35 23-28

Assumed SEI type 8 III, 1 III, 1 III, 3 I, 3 I, 1 I, 1 I, 1 II, 1 II, 1 II, 1 II, 1 II, 1 II, 1 III, 1 III, 1 III, 1 III, 3 III, 2 III, 3, II, 3 III, 1 III, 1 III, 3 III, 1 III, 1 I, 1 II, 3, III, 3 III, 3 III, 3 III, 3 III, 3 III, 2 III, 2 III, 2 III, 2

REFERENCES [1] [2] [3]

[4]

А.G. Golubev. Biochemistry of life extending // Success in gerontology-2003Iss.12,p.57-76. P.A. Alexander. Nuclear radiation and life. Translated from English. М.: 1959. Brack C.,Bechter-Thuring E and Labuhn M. N-acetylrysteine clows down ageing and increases the life span of Drosophila melanogaster//Cell Mol. Life Sci.-1977 vol 53/P960-966. Beziepkin V.G., Sirota N.P. and Gaziev A.L. The prolongation of survival in mice by dictary antioxidants depends on their age by the start of feeding this diet//Mech. Ageing Dev.-1996.-vol 92.-P.227-234.

102 [5]

G. А. Коrablev and G. Е. Zaikov

Korablev G.A. Spatial-Energy Principles of Complex Structures Formation, Netherlands, Brill Academic Publishers and VSP, 2005,426p. (Monograph). [6] Fischer C.F. Average-Energy of Configuration Hartree-Fock Results for the Atoms Helium to Radon.//Atomic Data,-1972, -№ 4, -p. 301-399. [7] Waber J.T., Cromer D.T. Orbital Radii of Atoms and Ions//J. Chem. Phys -1965, -V 42, -№12, -p. 4116-4123. [8] Clementi E., Raimondi D.L. Atomic Screening constants from S.C.F. Functions, 1.//J.Chem. Phys.-1963, -v.38, -№11, -p. 2686-2689. [9] Korablev G.A., Zaikov G.E. Energy of chemical bond and spatial-energy principles of hybridization of atom orbitalls.//J. of Applied Polymer Science. V.101,n.3,Aug.5,2006,p.2101-2107. [10] S.S. Batsanov. Structural chemistry. Facts and dependencies. М.:MSU-2000,292p.

In: Organic and Physical Chemistry Using Chemical Kinetics … ISBN: 978-1-60021-763-0 Editors: Y.G. Medvedevskikh, et al. pp. 103-166 © 2007 Nova Science Publishers, Inc.

Chapter 9

POLY (VINYL ALCOHOL)[PVA]-BASED POLYMER MEMBRANES: SYNTHESIS AND APPLICATIONS Silvia Patachia,a Artur J. M. Valente,b Adina Papanceaa and Victor M. M. Lobob a

Department of Chemistry, “Transilvania” University of Brasov, 29 Eroilor Street, 500036 Brasov, Romania. b Department of Chemistry, University of Coimbra, 3004-535 Coimbra, Portugal

1. INTRODUCTION Poly(vinyl alcohol) (PVA) is a polymer of great interest because of its many desirable characteristics specifically for various pharmaceutical, biomedical, and separation applications. PVA has a relatively simple chemical structure with a pendant hydroxyl group (figure 1a). The monomer, vinyl alcohol, does not exist in a stable form, rearranging to its tautomer, acetaldehyde. Therefore, PVA is produced by the polymerization of vinyl acetate to poly(vinyl acetate) (PVAc) followed by the hydrolysis to PVA (figure 2). Once the hydrolysis reaction is not complete, there are PVA with different degrees of hydrolysis (figure 1b). For practical purposes, PVA is always a co-polymer of vinyl alcohol and vinyl acetate [1].

H2C

CH OH a.

Figure 1. Continued.

n+m

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H2C

CH OH

CH2

CH O

n

C

O

CH3

m

b. Figure 1. Molecular strucuture of PVA fully hydrolyzed (a) and partially hydrolyzed (b).

n H2C

initiator

CH

*

CH2

CH

*

O

OCOCH3

Vinyl acetate

COCH3

n

Poly(vinyl acetate) a.

*

CH2

CH

*

+ n CH3OH

O COCH3

n

NaOH

*

CH2

CH

*

OH

n

Poly(vinyl alcohol)

Methanol

+

Poly(vinyl acetate)

n CH3OCOCH3 Methyl acetate b. Figure 2. Polymerization of vinyl acetate (a) and hydrolysis of PVAc to PVA (b).

PVA must be cross-linked in order to be useful for a wide variety of applications. A hydrogel can be described as a hydrophilic, cross-linked polymer, which can sorbe a great amount of water by swelling, without being soluble in water. Other specific features of hydrogels are their soft elastic properties, and their good mechanical stability, independent of the shape (rods, membranes, microspheres, etc.). PVA can be prepared by chemical or physical cross-linking; general methods for chemical cross-linking are the use of chemical cross-linkers or the use of electron beams or γ-

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radiation, whilst the most common method to produce physical cross-linking PVA is the socalled “freezing-thawing” process. PVA can be cross-linked [2] using cross-linking agents such as glutaraldehyde, acetaldehyde, etc. When these cross-linking processes are used in the presence of sulfuric acid, acetic acid, or methanol, acetal bridges form between the pendant hydroxyl groups of the PVA chains. As with any cross-linking compound, however, residual amounts are present in the PVA gel matrix; furthermore, other compounds such as initiators and stabilisers will reamin after synthesis. To use these gels for pharmaceutical or biomedical applications, we will have to extract all residues from the gel matrix. This is an extremely undesirable timeconsuming extraction process; also, if the process is not 100 % efficient and the residue is not completely removed, the gel will not be acceptable for biomedical or pharmaceutical applications. Other methods of chemical cross-linking include the use of electron beam or γirradiation. These methods have advantages over the use of chemical cross-linking agents as they do not leave behind toxic, elutable compounds. The minimum gelation dose of γ-rays (from 60Co sources) depends on the degree of polymerisation and the concentration of polymer in solution [3]. The effect of irradiation dose on the physical properties of PVA fibers, hydrogels and films irradiated in water is reported in [4-6]. The third mechanism of hydrogel preparation involves “physical” crosslinking due to crystallite formation [7]. This method addresses toxicity issues because it does not require the presence of a cross-linking agent (figure 3). Such physically cross-linked gels also exhibit higher mechanical strength than PVA gels crosslinked by chemical or irradiative techniques because the mechanical load can be distributed along the crystallites of the three-dimensional structure [1]. Some characteristics of these “physically” crosslinked PVA gels include a high degree of swelling in water, a rubbery and elastic nature, and high mechanical strength. In addition, the properties of the gel may depend on the molecular weight of the polymer, the concentration of the aqueous PVA solution, the temperature and time of freezing and thawing, and the number of freezing/thawing cycles [8-10].

Figure 3. Schematic representation of PVA gels formed by freezing/thawing process.

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PVA hydrogels have been used for numerous biomedical and pharmaceutical applications. PVA hydrogels are non-toxic, non-carcinogenic, show bioadhesive characteristics, and they are easily processed. The safety of PVA is based on the fact that the acute oral toxicity of PVA is very low, with LD50s (the amount of a material, given all at once, which causes the death – lethal dose - of 50 % of a group of test animals) in the range of 15-20 g/kg; when orally administered PVA is very poorly absorbed from the gastrointestinal tract; PVA does not accumulate in the body when administered orally; PVA is not mutagenic or clastogenic; and the no-observed adverse-effect level (NOAEL) of orally administered PVA in male and female rats were 5000 mg/kg body weight/day in the 90-day dietary study and 5000 mg/kg body weight/day in the two-generation reproduction study, which was the highest dose tested [11]. Furthermore, PVA gels exhibit a high degree of swelling in water and a rubbery and elastic nature. For all these features PVA is an excellent biomaterial. In fact, PVA is capable of simulating natural tissue and can be readily accepted into the body. PVA gels have been used for contact lenses, the lining for artificial organs, and drug-delivery applications. Recently, intelligent hydrogels have been used to produce micro- and nano-fabricated devices that seek to develop a platform of well controlled functions in the micro- and nano-level. For example, polymer surfaces in contact with biological fluids, cells, or cellular components can be tailored to provide specific recognition properties or to resist binding depending on the intended applications. Another recent application of PVA is related with the development of biomimetic methods to build biohybrid systems or even biomimetic materials for drug delivery, drug targeting, and tissue engineering devices. Besides all these applications, PVA is an important gel in different enginnering and industrial fields. For example, in the U.S.A., the majority of PVA is used in the textile industry as a sizing and finishing agent. PVA can also be incorporated into a water-soluble fabric in the manufacture of degradable protective apparel, laundry bags for hospitals rags, sponges, sheets, covers, as well as physiological hygiene products. PVA is also widely used in the manufacture of paper products. As with textiles, PVA is applied as a sizing and coating agent. It provides stiffness to these products making it useful in tube winding, carton sealing and board lamination. PVA is used as a thickening agent for latex paint and common house hold white glue or in other adhesive mixtures such as remoistenable labels and seals, as well as gypsum-based cements such that used for ceramic tiles. PVA is relatively insoluble in organic solvents and its solubility in aqueous solutions is adaptable to its necessary application [11]. The US Food and Drug Administration (FDA) allows PVA for use as an indirect food additive in products which are in contact with food [11]. For example, under 21 CFR 73.1, PVA is approved as a diluent in color additive mixtures for coloring shell eggs and under 21 CFR 349.12, PVA is approved as an ophthalmic demulcent at 0.1–4.0 %. Other applications of PVA are in areas of water and wastewater treatment (extraction, ultra-filtration, ion-exchange materials, etc.), catalysis, separation, etc. As an industrial and commercial product, PVA is valued for its solubility and biodegradability, which contributes to its very low environmental impact. Several microorganisms ubiquitous in artificial and natural environments — such as septic systems, landfills, compost and soil — have been identified and they are able to degrade PVA through enzymatic processes. Membranes have gained an important place in chemical technology and are used in a broad range of applications. The key property that is exploited is the ability of a membrane to

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control the permeation rate of a chemical species through the membrane. In controlled drug delivery, the goal is to moderate the permeation rate of a drug from a reservoir to the body. In separation applications, the goal is to allow one component of a mixture to permeate the membrane freely, while hindering permeation of other components. The objective of this chapter is to give an overview of the developments in synthesis and applications of PVA-based membranes in the last years.

2. SEPARATIONS BY MEMBRANAR PROCESSES 2.1. Pervaporation Processes Pervaporation, in its simplest form, is an energy efficient combination of membrane permeation and evaporation. Pervaporation involves the separation of two or more components across a membrane by differing rates of diffusion through a thin polymer and an evaporative phase change comparable to a simple flash step. A concentrate and vapour pressure gradient is used to allow one component to preferentially permeate across the membrane. A vacuum applied to the permeate side is coupled with the immediate condensation of the permeated vapors. Pervaporation is typically suited to separating a minor component of a liquid mixture, thus high selectivity through the membrane is essential. Despite concentrated efforts to innovate polymer type and tailor polymer structure to improve separation properties, current polymeric membrane materials commonly suffer from the inherent drawback of tradeoff effect between permeability and selectivity, which means that membranes more permeable are generally less selective and vice versa. Pervaporation (PV) is considered to be a promising alternative to conventional energy intensive technologies like extractive or azeotropic distillation in liquid mixtures’ separation for being economical, safe and ecofriendly. PV can be considered the so-called ‘clean technology’, especially well-suited for the treatment of volatile organic compounds. The separation of compounds using pervaporation methods can be classified into three major fields viz. (i) dehydration of aqueous–organic mixtures [12], (ii) removal of trace volatile organic compounds from aqueous solution [13] and (iii) separation of organic–organic solvent mixtures [14]. The hydrophilic membranes were the first ones to have found an industrial application for organic solvent dehydration by PV [15]. Very recently, B. Smita et al. [16] reported that some restrictions for a variety of membranes for their application are still encountered, suggesting potential routes to overcome these drawbacks as, for example, the development of appropriate membrane material (flux and selectivity of a membrane are deciding factors in pervaporation mass transport; therefore, development of a new polymer material is a key research area in membrane technology. The aim in the development of new pervaporation membranes is either to increase the flux, keeping the selectivity constant or aiming for higher selectivities at constant flux, or both. In order to achieve such goals, the use of PVA as component of copolymers, blends, or composites membranes for pervaporation has been used.

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2.1.1. Pervaporation of Phenol/Water Using pervaporation through PVA membranes, J. W. Rhim et al. [17] have studied the separation of water-phenol mixtures. The pervaporation separation of water-phenol mixtures was carried out using poly(vinyl alcohol) (PVA) cross-linked membranes with low molecular weight poly(acrylic acid) (PAA), at 30, 40, and 50 °C. They have used pervaporation because the separation rate is higher (for liquid organic mixtures) in pervaporation than in reverse osmosis. A separation factor of the mixture, α, is calculated using α = ( Ywater / Yphenol ) / (Xwater / Xphenol ) where X is the weight fraction of permeate and Y, the weight fraction of feed. A very high separation factor has been obtained in phenol dehydration by using pervaporation process and PVA/PAA as membranes. The membrane composition and the process characteristics are presented in table 1. Table 1. Characteristics of the separation process by pervaporation function of the membrane composition and structure, composition of feed mixture and temperature [18] Membrane composition PVA/PAA 80/20

Composition of liquid mixture phenol/water

80/20

Permeation rate / / (g m-2 h-1)

T / ºC

Separation factor

50

30

3580*

* Ref. 17.

Conclusion: the separation factor increases by increasing the cross-linker, and decreases by increasing the temperature.

2.1.2. Isopropanol/Water Separation The selective separation of water from aqueous solutions of isopropanol or the dehydration of isopropanol can be carried out with different membranes, which contain polar groups, either in the backbone or as pendent moieties. For the dehydration of such a mixture, poly(vinyl alcohol) (PVA) and PVA-based membranes have been used extensively. PVA is the primary material from which the commercial membranes are fabricated and has been studied intensively for pervaporation because of its excellent film forming, high hydrophilicity due to –OH groups as pendant moieties, and chemical-resistant properties. On the contrary, PVA has poor stability at higher water concentrations, and hence selectivity decreases remarkably. The use of conjugated polymer as membranes to separate various liquid mixtures has been reported in the literature [19,20]. From those, polyaniline (PANi) is one of the most interesting and studied conjugated polymers. Polyaniline is usually prepared by direct oxidative polymerization of aniline in the presence of a chemical oxidant, or by electrochemical polymerization on different electrode materials [21,22]. The possible interconversions between different oxidation states and protonated and depronated states [23], figure 4, make this material remarkable for different purposes. Under most conditions, PANi

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acts as a passive material, but electrolysis or exposure to acidic aqueous solutions gives rise to conductive materials. In fact, the susceptibility of PANi protonation-deprotonation is an important property once it makes possible to control the electrical conductivity of polyaniline, being possible to obtain changes of more than two orders of magnitude in the electrical conductivity [24]. Both synthesis and characterization of PANi have been reviewed by different authors [21-23]. These reviews deal with chemical, electrochemical and gas-phase preparations, polymerization mechanisms, physicochemical and electrochemical properties, redox mechanisms, theoretical studies, and applications of the polymer. Interest in polyaniline (PANi), as a material for membrane separations, stems for its high selectivity toward liquids since most liquids are in the size regime of 0.2–1 nm. Another advantage is that PANi has the ability to be tailored after its synthesis through doping/undoping processes. Since there is a tremendous driving force for adding protonic dopants to the imine nitrogens in the PANi backbone [20], the polymer chains are readily pushed apart by the incoming dopants. Thus, doping would induce morphological changes in the polymer resulting in varying permselectivities. Besides such morphological changes, the undoped and doped forms of PANi exhibit different characteristics. For instance, the undoped form of PANI is hydrophobic, while the doped form is hydrophilic [25,26]. Hence, doped PANi preferentially permeates water over the organics, such as isopropanol. The abovementioned advantages are considered to search for novel membranes containing PANi nanoparticles dispersed in the PVA matrix. The synthesis of a novel hybrid nanocomposite membrane by in situ polymerization of aniline in the PVA matrix in acidic media is described in the Ref. 27. Aniline monomer was introduced into the PVA matrix and by carrying in situ polymerization outside the mesopores of the polymer matrix, a nanocomposite structure was formed. The organic phase extends along the channels to the openings in the nanocomposite structure due to strong interactions between the nanoparticle formed and the continuously polymerized PANi nanoparticles. This hybrid polymer shows lower swelling degree and higher water selectivity (about five-folds) compared to the plain poly(vinyl alcohol). M. Sairam et al. [28], taking on the basis of the cited PANi nanoparticles dispersed in the PVA matrix, suggests the incorporation of TiO2 filler-coated with polyaniline (emeraldine state) salt nanoparticles in PVA. PVA contains a large number of hydroxyl groups which can effectively inhibit the aggregation of TiO2 nanoparticles by the organic surface modification and help to keep the TiO2 particles well dispersed in the aqueous PVA solution at the nanoscale for dehydration of iso-propanol. In order to control the dispersion of TiO2 fillers and to adjust the permselectivity, the PV membranes formed have been crosslinked chemically with glutaraldehyde. With this modification of TiO2 nanoparticles, it is expected that strong interfacial bond, viz., Ti–O–C be formed on the surface of TiO2 nanoparticle, anchors PVA molecules to the surface of TiO2 nanoparticles such that surfaces of TiO2 nanoparticles will be wrapped with the layer of PVA polymer. It is known [29] that there are number of Ti–OH groups that will cover the surface regions of TiO2 nanoparticles. When PVA chain segments are adsorbed onto the surface of TiO2 nanoparticle, Ti–OH groups on the surface of TiO2 nanoparticles will react with the hydroxyl groups linking to the PVA chains. Dehydration and condensation reactions can occur between both the hydroxyl groups.

N

N

N

N

(PNA)

4H+ + 2eHN

HN

X-

XNH

NH

acid (H+X-) (EM)

oxidation

base (NaOH)

reduction

HN

HN

HN

N

(LM)

NH

NH

reduction

NH

N N

solvent (NMP) 1st acid-base cycle

N

as-cast EM film NH

(NA) N

Figure 4. Interconversions among the various intrinsic oxidation states and protonated/deprotonated states in polyaniline.

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Another approach to enhance separation performance of membrane for dehydration of isopropanol is the modification of PVA membranes in gaseous plasma [30]. The modification of membrane properties in nitrogen plasma environment lead to increase in selectivity by about 1477 at 25 °C; such increase in the selectivity is justified by an increase of crosslinking on membrane surface provoked by plasma treatment. The same authors reported the possibilities of using a membrane made by PVA modified by LiCl, whose surface has been modified by exposure to low-pressure nitrogen plasma [31]. The best results have been obtained for 0.05 wt% of LiCl in PVA membrane at 25 ºC (selectivity 14 and flux 250 g m-2h-1). Hybrid membranes composed of poly(vinyl alcohol) (PVA) and tetraethylorthosilicate (TEOS), synthetised via hydrolysis and a co-condensation reaction for the pervaporation separation of water-isopropanol mixtures has also been reported [32]. These hybrid membranes show a significant improvement in the membrane performance for water– isopropanol mixture separation. The separation factor increased drastically upon increasing the crosslinking (TEOS) density due to a reduction of free volume and increased chain stiffness. However, the separation factor decreased drastically when PVA was crosslinked with the highest amount of TEOS (mass ratio of TEOS to PVA is 2:1). The highest separation selectivity is found to be 900 for PVA:TEOS (1.5:1 w/w) at 30°C. For all membranes, the selectivity decreased drastically up to 20 mass % of water in the feed and then remained almost constant beyond 20 mass %, signifying that the separation selectivity is much influenced at lower composition of water in the feed. Recently, a new effective membrane for different organic solvents dehydration by pervaporation has been reported. Novel hydrophylic polymer membranes based on crosslinked poly(allylamine hydrochloride) (PAA.HCl)-PVA have been developed [33]. The crosslinking agent was GA. The role of the PVA into the membrane is to increase its flexibility and the stability. But the increasing of the PVA ratio, determines the decreasing of the water selective amine hydrochloride functional groups amount and as consequence, the rate of water intake by the membrane decreases. So, for different specific applications the optimization of the PAA.HCl/PVA ratio in the formulation is essential. Also, the amount of GA and curing temperature has to be optimized to obtain the desired membrane properties. The characteristics of the iso-propanol (IPA) dehydration process, by using the pervaporation technique, are presented in the table 2. Table 2. The characteristics of the iso-propanol (IPA) dehydration process, by using pervaporation technique, through (PAA.HCl)-PVA membrane Composition of the membrane PAA.HCl/PVA/GA 60/35/5

* Ref. 33.

Composition of liquid mixture IPA-water (wt%)

85/15

Water flux / / (kgm-2h-1)

T / ºC

Separation factor

3.14

70

2930

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2.1.3. Pervaporation Ethanol/Water Alcohol is a clean energy source that can be produced by the fermentation of biomass. However, it needs to be highly concentrated. In general, aqueous alcohol solutions are concentrated by distillation, but an azeotrope (96.5 wt% ethanol) prevents further separated by distillation. Pervaporation, a membrane separation technique, can be used for separation of these azeotropes: pervaporation is a promising membrane technique for the separation of organic liquid mixtures such as azeotropic mixtures [34] or close-boiling point mixtures. The synthesis of novel organic-inorganic hybrid membranes via hybridization between organic and inorganic materials using the sol-gel reaction is reported elsewhere [35]. It is well-known that poly(vinyl alcohol) (PVA) membranes are highly water permselective for aqueous ethanol solutions during PV. However, the swelling of the PVA membrane in an aqueous ethanol solution results in both an increase in solubility and diffusivity of ethanol, and consequently lowers the water permselectivity [36]. The control of membrane swelling has been attempted by cross-linking, surface modification, and annealing methods. However, it is difficult to effectively control the swelling of the membrane. An attempt to improve and to control the swelling is done by using mixtures of PVA and tetraethoxysilane (TEOS), as an inorganic component, in order to obtain PVA/TEOS hybrid membranes prepared by sol-gel reaction. The addition of TEOS into the PVA membrane decreases the swelling of the membrane and improves the water permselectivity of the PVA/TEOS hybrid membrane. T. Uragami et al. also studied the effect of the annealing process to PVA/TEOS hybrid membranes. They found that the separation factor H2O/EtOH increases from 329 to 893 (with the same permeation rate) when PVA/TEOS (TEOS content 25 %) membranes are submitted from an annealing process at 160 ºC during 8 hours to 130 ºC during 24 hours. In a previous section, the effect of plasma on PVA surface for pervaporation processes was also mentioned. In fact, plasma treatment is a surface-modification method to control the hydrophilicity–hydrophobicity balance of polymer materials in order to optimize their properties in various domains, such as adhesion, biocompatibility and membrane-separation techniques. Non-porous PVA membranes were prepared by the cast-evaporating method and covered with an allyl alcohol or acrylic acid plasma-polymerized layer; the effect of plasma treatment on the increase of PVA membrane surface hydrophobicity was checked [37].The allyl alcohol plasma layer was weakly crosslinked, in contrast to the acrylic acid layer. The best results for the dehydration of ethanol were obtained using allyl alcohol treatment. The selectivity of treated membrane (H2O wt% in the pervaporate in the range 83–92 and a water selectivity, αH2O , of 250 at 25 ºC) is higher than that of the non-treated one (αH2O = 19) as well as that of the acrylic acid treated membrane (αH2O = 22). PVA dense membranes treated by acrylic acid (Acr.Ac) plasma were obtained by A. Essamri et al. [38]. These membranes were used for dehydration of the EtOH-H2O mixtures by pervaporation. The behaviour of these films on ethanol-water pervaporation has increased performances after plasma treatment. This means an increase of the flux (J) and water selectivity (β) for the modified membrane – due to the surface properties modification by plasma treatment – comparing to the untreated membrane. Conclusion: using plasma treatment, a good ratio between flux and selectivity could be obtained. Also, different other techniques for obtaining PVA/PAcr.Ac blends were reported [3956]:

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1. mixing of PVA and PAcr.Ac. aqueous solutions, solvent evaporation and thermal treatment of the resulted film; 2. mixing of PVA and PAcr.Ac. aqueous solutions with curing agents solutions, solvent casting and thermal treatment of the resulted film; 3. repetitive cycles of freezing and thawing of the aqueous solutions of polymer mixture, in the presence or the absence of the curing initiators; 4. UV irradiation either of the aqueous solutions of polymers mixtures in the presence of photoinitiators and curing agents, or of the PVA hydrogels swelled with acrylic acid; 5. acrylic acid polymerization in the matrix of PVA, in the presence of curing agents and initiators; 6. sedimentation polymerization of acrylic acid in the presence of PVA solution, crosslinking agent and initiator; 7. swelling of PAcr.Ac dried hydrogels with an aqueous solution of PVA and application of the freezing and thawing technique. Changes in blends’ properties were obtained through different ways: by changing the polymer mixing ratios; by using a small amount of acids that are catalysts for esterification reactions; by changing the crosslinking degree of the polymers. PVA and PAcr.Ac. are compatible polymers on the whole range of composition [40-45]. These blends are homogeneous and the films are transparent evidencing a good clarity [43,57] or semitransparency [43]. However a heterogeneous IPN [45] was obtained by acrylic acid polymerization in a PVA matrix. The blends could exhibit different morphologies: continuous or microporous [46]. The blend crystalinity degree decreases with increasing the PAcr.Ac content up to 50 wt%, from 26 % to 2 %, and then remains constant [42]. The blends are water insoluble [47]. They can swell in different solvents: water, acetone, aqueous solutions of acids and alkalis [47]. The swelling ratios increase with increasing the PAcr.Ac content in IPNs [45,48]. It was pointed out that the swelling degree evidenced a strongly decrease as the PAcr.Ac content in membrane decreases to 20% [49]. The technique of obtaining blends influences their swelling ratios by inducing different crosslinking degrees. For example, increasing the number of freezing-thawing cycles leads to a swelling ratio significant decrease [50]. In general, the swelling ratios increase with the increasing the temperature up to 40 ºC [45]. The dependence of swelling ratios on temperature shows a different function of the blend composition. So, interpenetrating polymer networks (IPNs) with a weight ratio of vinyl alcohol residue in PVA to acrylic acid monomer 4:6 exhibit positive swelling changes with temperature but IPNs 6:4 evidence negative swelling ones [48]. pH strongly influences the swelling behavior of the blends. For example, the difference of the swelling ratio of IPN 4:6 between pH=4 and pH=7 is 2.0 [48]. Membranes of PVA/PAcr.Ac blends evidence a selective permeability against different components of a liquid mixture. So, they may be used for the ethanol dehydration by pervaporation technique. Table 3 presents a summary of the published results.

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These blends show good mechanical properties. The presence of PVA in the blend improves the mechanical properties. Hydrogels have a significant mechanical strength and elasticity [42]. The tensile strengths are larger than those of crosslinked PVA membranes and show a maximum value at about 0.7 wt% glutaric dialdehyde (GA) [46]. Full-IPNs have higher compressional strength (2929 g load for 50 % compression) than the corresponding semi-IPNs (1883 g load for 50 % compression) [42]. These membranes can swell in water and different aqueous solutions evidencing the following aspects: • • •

the presence of PAAm affects in a positive way the swelling; the swelling in water increases with temperature (positive thermosensitivity); -swelling in the water/ethanol mixture increases linearly with the water content.

Because of membrane preferential swelling in different aqueous solutions, it may be recommended for use in separation processes by pervaporation. The PVA/PAAm IPN membranes were found to have pervaporation separation factors ranging from 45 to 4100 and permeation rates of about 0.06-0.1 kg m-2 h-1, for 95 % ethanol aqueous solution, at 75 ºC [46]. For a concentration of 10 wt% ethanol, the permeation rates were as large as 9 kg m-2 h-1 and the separation factors were about 20 [46]. Recently, a new effective membrane for dehydration of different organic solvents by pervaporation has been reported. Novel hydrophylic polymer membranes based on crosslinked poly(allylamine hydrochloride) (PAA.HCl)-PVA have been developed [33]. The crosslinking agent was glutaraldehyde (GA). The role of PVA into the membrane is to increase its flexibility and the stability. But the increasing of PVA percentage, determines the decreasing of the water selective aminehydrochloride functional groups amount and as consequence, the rate of water intake by the membrane decreases. So, for different specific applications, the optimization of the PAA.HCl/PVA ratio in the formulation is essential. Also, the amount of GA and curing temperature has to be optimized to obtain the desired membrane properties. The characteristics of the ethanol dehydration process, by the pervaporation technique, are presented in table 4. Polymers, such as polysaccharides (cellulose and chitosan (CS)) show a stronger affinity to water; hence their copolymers, blends or composites have been widely investigated for pervaporative (PV) separation of EtOH/H2O mixtures [58-60]. Chitosan is generally preferred due to its high abundance, natural occurrence, hydrophilicity, chemical resistance, adequate mechanical strength, good membrane forming properties and ease of processing. PV performance of EtOH/H2O mixtures through the surface crosslinked CS composite membranes exhibit a high selectivity value but a low permeation flux [61]. The PV membranes of derivatives of CS obtained by chemical modification have also been widely studied [62,63].

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Table 3. Characteristics of the separation process by pervaporation function of the membrane composition and structure, composition of feed mixture and temperature [18,43,46] Composition of the membrane PVA/PAcr.Ac 50/50 IPN 30/70 IPN 50/50 IPN 70/30 IPN 90/10 IPN 80/20

Composition of liquid mixture ethanol-water 95.6/4.4 10/90 85/15 10/90 85/15 10/90 85/15 10/90 85/15 95.6/4.4 90/10 80/20 50/50

95/5

Permeation rate / / (g m-2 h-1)

T/ ºC

Separation factor

260

50

5000 750 3800 360 2700 110 2000 90 9 30 27 60 65 125 120 550

50

50 12 0.8 15 0.85 15 1.0 18 3.0 39 14000 5800 9000 2800 1500

50 50 50 60 75 60 75 60 75 75 60

Permeate activation energy Ea / (kJ mol-1) -

30.5 30.9 38.9 -

260 150

Table 4. Dehydration of ethanol, using membranes PAA.HCl (60 wt%)–PVA (35 wt%–GA (5 wt%) (aprox. 60μm thick) [33] Feed concentration / (wt%)

T / ºC

Water flux / (kg m-2 h-1)

Selectivity

85

70

2.00

450

95

70

0.47

3953

B.-B. Li et al. [64] have studied the separation of EtOH-H2O solutions by pervaporation (PV) using chitosan (CS), poly (vinyl alcohol)-poly(acrylonitrile) (PVA–PAN) and chitosanpoly(vinyl alcohol)/poly(acrylonitrile) (CS–PVA/PAN) composite membranes. It was found that the separation factor of the CS–PVA/PAN composite membrane increased with an increase of PVA concentration in the CS–PVA polymer from 0 to 40 wt%. With an increase in the membrane thickness from 12 to 18 µm, the separation factor of the CS–PVA/PAN composite membrane increased and the permeation flux decreased. With an increase of ethanol–water solution temperature, the separation factor of the CS membrane decreased and the permeation flux of the CS membrane increased while the separation factor and the permeation flux of PVA/PAN and CS–PVA/PAN composite membranes increased.

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Sodium alginate (SA), which is one of the polysaccharides extracted from seaweed, has shown excellent water solubility [65], but the mechanical weakness of SA membranes has been a drawback as a pervaporation membrane material. The use of SA–PVA blended membranes prepared by physical mixing of components, in different ratios, for pervaporation dehydration is reported elsewhere [66,67]. Taking on the basis of SA-PVA membranes, Dong et al. [68] studied the PVA–SA hollow-fiber composite membranes for organic dehydration by pervaporation. In particular, a polysulfone hollow-fiber membrane is coated by a PVA-SA blended solution. The founded optimal process of preparing membranes is as follows: 80 wt% PVA and 20 wt % SA are blended, and the casting solution of the PVA–SA blend with a concentration of 2 wt % is obtained by dissolving the blend in water; then the blend solution is cast onto the PS hollow-fiber membrane, and the composite membrane is crosslinked with 1.5 wt% maleic acid and 0.05 wt% H2SO4 in ethanol solvent for 8 h. For isoproanol, n-butanol, tert-butanol and ethanol aqueous solutions, as the alcohol concentration is 90 wt% at 45 ºC, higher separation factors and permeation fluxes of crosslinked PVA–SA blended membranes are obtained: 1727, 414 g m-2 h-1; 606, 585 g m-2 h-1; 725, 370 g m-2 h-1 and 384, 384 g m-2 h-1, respectively. This shows that these blended membranes have the potential to be used in industry. 2.1.7. Acetic Acid/Water Separation by Pervaporation Poly(vinyl alcohol) and polyacrylamide (PAAM) blends, obtained by the different methods described above, can also be used for acetic acid dehydration, due to its capacity to swell in mixtures of acetic acid/water. Swelling in water/acetic acid mixture shows a maximum of swelling shifting to higher temperatures when higher acetic acid concentrations increase (from 20 ºC for 50 % acetic acid to 40 ºC for 70 %). Water is preferentially sorbed by membranes, but much less from water-acetic acid mixtures than from ethanol/water mixtures [46]. Table 5 presents the characteristics of the pervaporation process. Table 5. Characteristics of the separation process by pervaporation according to membrane composition and structure, composition of feed mixture and temperature [18,52] Compositi-on of the membrane PVA/PAcr.Ac

Composition of liquid mixture

Permeation rate / / (g m-2 h-1)

T / ºC

Separation factor

75/25

Acetic acidwater

5.6

30

795

90/10

A recent paper [69] presents a new type of PVA hybrid membrane prepared by hydrolysis followed by condensation of a PVA and a tetraethylorthosilicate (TEOS) mixture, which shows a significant performace in water-acetic acid mixture separation. The highest separation selectivity (1116) with a flux of 3.33×10-2 kg m-2 h-1 at 30 ºC for 10% mass of water in the feed has ben obtained by using the membrane containing 1:2 mass ratio of PVA and TEOS. The performance of these membranes was explained on the basis of a reduction of free volume and a decrease of the hydrophylic character owning to the formation of

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covalently bonded crosslinks. Significant lower apparent activation energy values have been obtained for water permeation comparatively to these of acetic acid permeation. The close values obtained for activation energy for total permeation and water permeation signify that the coupled transport is minimal due to the selective nature of membranes. The equal magnitude of activation energy for water permeation and activation energy for water diffusion indicates that both diffusion and permeation contribute almost equally to the PV process. The Langmuir mode of sorption dominates the process for all types of studied membranes. Another recent work presents the possibility to use a membrane made by PVA-gacrylonitrile (AN) to separate acetic acid/water mixtures by pervaporation [70]. The best separation factor (14.6) has been obtained by using PVA-g-AN (52 %) membrane, at 30ºC, 90 % acetic acid in the feed. The permeation rate was 0.09 kg m-2 h-1.

2.1.5. Separation Caprolactam (CPL)/Water Mixtures by Pervaporation Caprolactam (CPL) is the monomer of Nylon-6, extensively used in high quality Nylon-6 fibers and resin obtaining. Worldwild capacities reached above 4.5 million metric tones in 2005. A CPL dehydration study has been performed by pervaporation, using PVA crosslinked membranes (with GA as crosslinker agent and heat treatment of the membrane) [71]. In spite of the excellent dehydration performance for CPL/water mixtures exhibited by PVA crosslinked membranes (total permeation flux by 800 g m-2 h-1 and separation factor by 575, for PVA membrane crosslinked with 0.5 wt% GA, at 323 K and 50 wt% CPL in the feed), the authors recommended the use of a composite membrane with an active layer made by PVA, due to the poor durability and mechanical strength of the studied membrane. 2.1.6. Separation of Fluoroethanol/Water Mixtures by Pervaporation 2,2,2,-trifluoroalcohol (TFEA) is used for obtaining 2,2,2-trifluoroethyl methacrylate (TFEMA), necessary for preparation of functional water repellent paints and optical fiber coating agents. TFEMA can be manufactured by esterification of TFEA and methacrylic acid (MA) in the presence of an acid catalyst, at 70 ºC. To obtain a higher conversion rate it is necessary to remove the water from the system, avoiding the formation of the thermodynamic equillibrium composition. To attain this goal, a pervaporation technique has been proposed, using a PVA composite membrane, made by casting of a mixture of PVA aqueous solution and a GA one on a polyethersulfone (PES) porous support, solvent evaporation and thermic curing [72]. Excellent dehydration performance has been obtained (separation factor 320 and permeation flux 1.5 kg m-2 h-1, for 90 wt% TFEA in the feed and 80 ºC). 2.1.7. Separation of Methacrylic Acid/Water Mixtures by Pervaporation A PVA composite membrane, made by casting of a mixture of PVA aqueous solution and a GA one on a polyethersulfone (PES) porous support, solvent evaporation and thermic curing, has been used to attain this aim [72]. Excellent dehydration performance has been obtained (separation factor 740 and permeation flux 2.3 kg m-2 h-1, for 90 wt% TFEA in the feed, and 80 ºC). 2.1.8. Water Desalination PVA/Poly(ethylene glycol) (PEG) membranes crosslinked by aldehydes and sodium salts were used in water desalination by pervaporation. The desalination of 8 % NaCl solution by

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pervaporation at 55 ºC and 5.00 kPa (downstream pressure) resulted in a single stage salt rejection of 99% and the water flux of 14 kg h-1 [73].

2.1.9. Dehydration of Methanol by Pervaporation Another important application of membrane-based pervaporation is a well-established and commercially exploited method for the dehydration of organic solvents; in particular the dehydration of alcohols is done with the help of high permselective (hydrophilic) poly(vinyl alcohol)/polyacrylonitrile (PVA/PAN) thin film composite membranes, under the trade name of “GFT- Gesellshaft Fur Trenntechnik” membranes. One of the key successes of PV is that, if suitable membranes can be produced with a high permeability and a good selectivity to water, it is possible to achieve an excellent separation, particularly at the azeotropic composition. However, more number of novel polymeric membranes are needed for a successful operation of the process in view of the fact that PV is environmentally cleaner than the conventional distillation; moreover, this process is energy intensive. Consequently the success of any membrane depends on a high flux, a good separation factor (selectivity) and a long-term stability as well as a favourable mechanical strength to withstand the cyclic modes of PV operating conditions, as described before. Also, membranes from blends of PVA/Poly(acrylic acid) [PAcr.Ac.] show a selective permeability against different components of a liquid mixture. This property of membranes makes them useful for the separation of components from liquid mixtures by the pervaporation method, i.e., for methanol dehydration. Recently, a novel hydrophylic polymer membrane based on poly(allylamine hydrochloride) (PAA.HCl)/PVA, crosslinked with GA, has been also tested for methanol dehydration by pervaporation technique [33]. Even if the reported results show a small selectivity of the last type of membrane, the blend’s composition, the curing degree and the process conditions (temperature, feed concentration, etc.) could be used to obtain a better separation of methanol. Table 6 presents a summary of the published results. Table 6. Characteristics of the separation process by pervaporation according to membrane composition and structure, composition of feed mixture and temperature [18] Composition of the membrane

Composition of liquid mixture

PVA/PAcr.Ac: 80/20

Methanolwater

PAA.HCl/PVA/ GA 60/35/5

Methanolwater (%wt.)

70/30 90/10 95/5 86.5/1 3.5

Permeation rate / / (g m-2 h-1) 70 340 109 33 1800

T / ºC

Separation factor

Ref.

50 70 70 70 60

55 28 465 2650 23

42

33

2.1.10. Dehydration of Acetone by Pervaporation Novel hydrophilic polymer membranes based on crosslinked poly(allylamine hydrochloride) (PAA.HCl)-PVA have been developed in order to dehydrate different organic compounds by pervaporation [33]. The characteristics of the acetone dehydration process,

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using a pervaporation technique, are presented in the table 7. The high selectivity of the membrane should be noted. The selectivity and flux characteristics of these membranes are excellent compared with most of the known membranes. Table 7. Dehydration of acetone, using membranes PAA.HCl (60%wt.)-PVA (35%wt.-GA(5%wt.) (aprox. 60μm thick) [33] Feed concentration / (% wt.) 86

T / ºC 50

Water flux / (kg m-2 h-1) 1.80

Selectivity 2270

2.1.11. Pervaporation of Ethanol/Toluene PVA-PAcr.Ac. membranes have been tested also for ethanol separation from ethanol/toluene mixture, by using pervaporation technique. The reported data concerning the separation process characteristics are presented in table 8. Table 8. Characteristics of the separation process by pervaporation according to membrane composition and structure, composition of feed mixture and temperature [18, 40] Composition of the membrane PVA/PAcr.Ac 10/90

Composition of liquid mixture Ethanol/toluene

Permeation rate / / (g m-2 h-1)

T / ºC

Separation factor

25-480

30

300-80

10-90% ethanol

2.1.12. Pervaporation of Ethanol/Benzene PVA-PAcr.Ac.blends membranes are suitable also for separation of components in ethanol/benzene mixtures. Reported data are presented in table 9. 2.1.13. Pervaporation of Methanol/Toluene Methanol/toluene mixtures could be separated by pervaporation technique using PVA/PAcr.Ac. blend membranes. Reported data are presented in table 10. Table 9. Characteristics of the separation process by pervaporation according to membrane composition and structure, composition of feed mixture and temperature [18,46] Composition of the membrane PVA/PAcr.Ac

Composition of liquid mixture ethanol/benzene

Permeation rate/ / (g m-2 h-1)

T / ºC

Separation factor

Permeate activation energy Ea / (kJ mol-1)

20/80

10/90

30

50

110

19.2

SIPN

90/10

560

30/70

10/90

12

SIPN

90/10

460

30/70

10/90

6

SIPN

90/10

360

3.5 50

650

27.6

1.9 50

1100 53

31.4

120

Silvia Patachia, Artur J.M. Valente, Adina Papancea et al. Table 10. Characteristics of the separation process by pervaporation according to membrane composition and structure, composition of feed mixture and temperature [18,40] Composition of the membrane PVA/PAcr.Ac 10/90

Composition of liquid mixture methanol/toluene 10/90 30/70

Permeation rate/ / (g m-2 h-1)

T / ºC

Separation factor

120 265

30 30

460 50

2.1.14. Separation Methyltertbutyl Ether (MTBE)/Methanol Mixtures by Pervaporation MTBE is a well known enhancer of the number of octanes in gasoline and as excellent oxygentated fuel additives that decrease carbon monoxide emissions. Therefore, MTBE has been one of the fastest growing chemicals of the past decade. MTBE is produced by reacting methanol with isobutylene from mixed-C4 stream liquid phase over a strong acid ionexchange resin as catalyst. An excess of methanol is used in order to improve the reaction conversion. This excess has to be separated from the final product. The pervaporation technique, more energy efficient and with lower cost process, has been proposed as alternative to distillation [74]. A membrane prepared by PVA blending with PAcr.Ac. in aqueous solution, casting, solvent evaporation and then crosslinking by heat treatment (at 150 ºC), has been used. The obtained results show that the prepared membranes are methanol selective, but the performance of these membranes (separation factor=30, for PVA/Pacr.Ac.=80/20, 5 wt% methanol in the feed, 25 ºC) is lower than those reported by J.W. Rhim and Y.K. Kim [75] (separation factor 1250 for PVA/Pacr.Ac.=75/25, 20 wt% methanol in the feed, 30 ºC). The authors suggested that a combination of pervaporation with a conventional separation technique such as a hybrid distillation-pervaporation system could be useful economically to break the azeotropy. 2.1.15. Pervaporation of Benzene/Cyclohexane The separation of benzene/cyclohexane mixtures is one of the most important and most difficult processes. Cyclohexane is produced by catalytic hydrogenation of benzene. The unreacted benzene in the effluent stream must be removed for pure cyclohexane recovery. Separation of benzene and cyclohexane is difficult because they have close boiling points (difference only 0.6 K) and close molecular sizes [76]. It is generally thought that separating benzene/cyclohexane mixtures is mainly governed by solubility selectivity due to the interaction between benzene molecule and membrane. Hence, increasing benzene solubility in the membrane is essential to obtain high permselectivity toward benzene. Poly(vinyl alcohol) (PVA) is polar and hydrophilic, and is an ideal membrane material to separate benzene/cyclohexane mixtures [77]. The selection of PVA is also due to its economical cost, commercial availability and good membrane-forming properties. F. Peng et al. report [78] the synthesis of poly(vinyl alcohol) membranes incorporating crystalline flake graphite (CG-PVA membranes). These blends take advantage of structure of graphite being similar to that of benzene favouring, in this way, the adsorption and packing of benzene on graphite surface and, consequently, increase the selectivity. A CG-PVA membrane exhibits a higher

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separation factor of 100.1 with a flux of 90.7 g m-2 h-1 at 323 K for benzene/cyclohexane (50/50, w/w) mixtures, showing that the incorporation of graphite into the PVA matrix interfered the polymer chain packing and enhanced effectively fractional free volume, and thus favourable for components diffusing through the membrane. Another interesting approach reported by the some authors [79] is to perform pervaporation of benzene/cyclohexane by using β-cyclodextrin (β-CD)-filled cross-linked poly(vinyl alcohol) (PVA) membranes (β-CD/PVA/GA). In the present case, the very important properties of the β-CD are used to increase the perselectivity toward benzene. The permeation flux of βCD/PVA/GA membranes increased when the β-CD content was 0–8 wt%, but permeation flux decreased slightly when the β-CD content was 8–20 wt%. The separation factor towards benzene increased when β-CD content was in the range 0–10 wt% and decreased slightly when the β-CD content was 10–20 wt%. Compared with the β-CDfree PVA/GA membrane, the separation factor of the β-CD/PVA/GA membrane for benzene to cyclohexane considerably increased from 16.7 to 27.0, and the permeation flux of benzene increased from 23.1 to 30.9 g m-2 h-1 for benzene/cyclohexane (50/50, wt) mixtures at 323 K. To solve the tradeoff between permeability and selectivity of polymeric membranes, organic-inorganic hybrid membranes composed of poly(vinyl alcohol) (PVA) and -glycidyl oxypropyl trimethoxysilane (GPTMS) were prepared by an in situ sol-gel approach for pervaporative separation of benzene/ cyclohexane mixtures [80]. The permeation flux of benzene increased from 20.3 g m-2 h-1 for pure PVA membrane to 137.1 g m-2 h-1 for PVAGPTMS membrane with 28 wt % GPTMS content, while the separation factor increased from 9.6 to 46.9, simultaneously. The enhanced and unusual pervaporation properties were attributed to the increase in the size and number of both network pores and aggregate pores, and the elongation of the length of the diffusion path in PVA-GPTMS hybrid membranes. Another hybrid membrane was prepared by filling carbon graphite (CG) into poly (vinyl alcohol) (PVA) and chitosan (CS) blending mixture [81]. This blend membrane shows homogenous distribution of graphite particles, considerable alteration of hydrogen bonding interaction, remarkable decrease of crystallinity degree, dramatic enhancement of mechanical properties and significant increase of free volume in CG-PVA/CS, which may contribute for improving the separation performance of the membranes by the synergistic effect of blending and filling. Comparing the performance of this blend with that used for PVA and PVA/chitosan membranes, for C6H6/C6H12 separation, that new hybrid membrane exhibits a highest separation factor of 59.8 with a permeation flux of 124.2 g m-2 h-1 at 323 K, 1 kPa.

2.1.17. Separation Cyclohexene/Cyclohexan Mixtures by Pervaporation Solid PVA-Co2+ composite asymetric membranes have been prepared starting from PVA and two different salts: Co(NO3)2 and Co(CH3COO)2, respectively, in order to separate cyclohexene/cyclohexan mixtures. A facititated transport mechanism has been evidenced, due to the capacity of Co2+ ions to coordinate the olefin molecules [82]. The authors reported stronger complexation of Co2+ ions with cyclohexene in the case of PVA/ Co(CH3COO)2 mixtures then in the case of PVA/ Co(NO3)2 mixtures. It was found that for a concentration ratio of ([Co2+]/[OH]) by 0.75 mol/mol, the permeation flux of PVA membrane containing Co2+ increases 2-3 times and the separation factor increses 50 times compared with pure PVA membrane.

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2.1.17. Fusel Oil Components Separation One of the main products of sugar manufacturing is molasses, which contains approximately 50% sucrose and 50% other components (water, various other organic components and inorganic salts). Because of its high sucrose content, a substantial portion of the molasses is used for the production of ethyl alcohol through fermentation. The byproducts of the fermentation broths, more volatile than the alcohol, are mainly aldehydes with acetaldehyde being the principal component. The aldehyde is removed, as a distillation head product. The other by-product of the distillation step, the bottom product, is fusel oil. It is composed of several alcohols, primarily C3, C4 and C5 aliphatic alcohols. The separation of its components, using pervaporation technique and PVA/PAcr.Ac. blend as membrane has been reported [55]. The characteristics of the pervaporation process are presented in table 11. Table 11. Characteristics of the separation process by pervaporation according to membrane composition and structure, composition of feed mixture and temperature [18,55] Composition of the membrane PVA/PAcr.Ac 90/10

Composition of liquid mixture: fusel oil

Permeation rate/ / (g m-2 h-1)

T / ºC

Separation factor

5000

60

10

Alcohols mixture with 10-30 % of water

Permeate activation energy Ea / (kJ mol-1) 49.4-41.7 (water) 60.8-55.7 (EtOH)

2.2. Separation by Evapomeation Evapomeation is a new membrane-separation technique for liquids mixtures, which eliminates some disadvantages of the pervaporation technique such as the decreasing of membrane permselectivity, due to its swelling by the direct contact with the feed solution. In evapomeation technique the membrane is not in direct contact with the feed solution, only with the solution’s vapors. In this way the swelling of the membrane could be suppressed and consequently, the permeation rates in evapomeation are smaller than those in pervaporation, but the separation factor is greater [83]. The differences between the pervaporation and evapomeation processes may be seen in figure 5.

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Figure 5. Schematic presentation of the pervaporation and evapomeation processes.

2.2.1. Isomers Separation by Evapomeation Separation of n-propanol from a mixture of n-propanol (n-PrOH) and i-propanol (iPrOH) Taking into account the capacity of cyclodextrins (CD-s) to entrap a large number of organic and inorganic molecules, due to their hydrophobic cavity, β-CD has been introduced into PVA in order to obtain a good separation of isomer mixtures. Two methods for obtaining PVA/(β-cyclodextrins) (β-CD) blends have been reported: I.

membranes were prepared by casting the solution (4%) of PVA (PD=1650; saponification degree = 99.7 %) and β-CD in DMSO at 25 ºC and solvent evaporation at 80 ºC [83,84]; II. by casting the aqueous solution of PVA (Mn=125,000), β-CD and 0.1% glutaraldehyde and water evaporation at room temperature in a vacuum oven for 24 h [85]. PVA and β-CD evidenced a good compatibility and produce transparent blend films [84]. The blend membranes are permselective for different organic isomers. So, these could be used for the separation of n-propanol from a mixture of n-propanol (n-PrOH) and i-propanol (i-PrOH) [84] and the separation of p-xylene from a p-xylene and o-xylene mixture [35]. It was evidenced that, in both cases, the separation was better by applying the evapomeation technique than that of the pervaporation. It was observed that the n-PrOH concentration in the permeate through the CD/PVA membrane by pervaporation was approximately same as that in the feed solution, namely, the PrOH isomers could hardly be separated through these membranes by pervaporation. The nPrOH concentration in the permeate obtained by evapomeation was higher than that in the

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feed solution, evidencing a higher permeation of the CD/PVA membrane for n-PrOH compared to i-PrOH. The same situation was evidenced in the case of xylene isomers separation. The evapomeation is more efficient than that of pervaporation [83]. The n-PrOH concentration in the permeate and the normalized permeation rate increased with the increasing CD content in the CD/PVA membrane. The addition of CD in the PVA membrane determined the increasing of the swelling degree and preferential sorption of nPrOH and p-xylene, due to the fact that the affinity of CD for these isomers was stronger than that for i-PrOH and o-xylene respectively [84]. The influence of the CD content in the membrane and the n-PrOH respectively p-xylene content in the feed mixture on the separation factors and sorption and diffusion selectivities of the CD/PVA membranes for the n-PrOH/I-PrOH and p-xylene and o-xylene mixtures by evapomeation are presented in tables 12 and 13. Table 12. Separation factors and sorption and diffusion selectivities of the CD/PVA and PVA membrane for the n-PrOH/i-PrOH (50/50 w/w) mixture and p-xylene and o-xylene (10/90 w/w) mixture by evapomeation versus the CD content [18, 83, 84] CD content / / wt%

Separation of n-PrOH/i-PrOH (50/50 w/w) mixture αsorp. αdiff. αsep.

Separation of p-xylene and oxylene (10/90 w/w) mixture αsep. αsorp. αdiff.

0

2.01

1.89

1.06

1.72

0.53

3.27

20

-

-

-

1.19

0.94

1.27

30

-

-

-

2.93

1.08

2.74

40

2.61

2.07

1.26

3.93

0.78

5.04

Table 13. Separation factors and sorption and diffusion selectivities of the CD/PVA (CD content: 40 wt %) membrane for the n-PrOH/I-PrOH mixture and p-xylene and oxylene mixture by evapomeation versus the n-PrOH and respectively p-xylene, concentration in the feed [83,84] Content of feed / / wt% n-PrOH p-xylene 10 -

αsep.

αsorp.

αdiff.

15.2

3.68

4.14

50 -

10 30

2.61 3.93 3.26

2.07 0.78 1.86

1.26 5.04 1.75

-

50 70 90

1.86 1.99 0.63

1.06 1.48 1.03

1.75 1.34 0.61

It may be seen that a very high separation factor of organic liquid isomers through polymer membranes has been obtained for PrOH isomers [84].

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A similar situation is reported for the separation of xylene isomers [83]. These results show the CD/PVA membranes are good candidates for isomers separation from organic liquid mixtures by evapomeation. PVA/CD hydrogels swell in water. The swellability of PVA/CD hydrogels is marginally higher than that of the PVA gel, indicating that the crosslink density is higher in the PVA/CD system than in the PVA gel. The higher crosslink density may be an additional factor in retarding the migration of the drug in the presence of CD.

2.3. Separation by Pertraction Pertraction is a continuous membrane-based extraction process, which has been proposed for, e.g., removing metal and organic pollutants from waste water treatment [86] and for concentrating valuable components from complex broths in bioproduction [87] as a consequence of solvent extraction. In this technology, the membrane contactor combines two functions, i.e., separation and extraction. It generally consists of a hydrophobic liquid phase so that the extraction and stripping of the solutes occurs in a three-phase system with two liquid/liquid interfaces. To this purpose, different techniques, such as impregnation of a microfiltration membrane by a circulating hydrophobic phase, supported liquid membrane and hydrophobic membrane, have been applied [88]. A very effective way to improve the pertraction performances in permeability and selectivity is to incorporate extractants into the hydrophobic phase, which react with a given solute reversibly and selectively. S. Touil et al. [88] have reported the efficiency of membranes of cyclodextrin (CD)containing PVA membranes (with CD covently grafted to the polymer chain) for the geometrical xylene isomer discrimination using the pertraction (combination of separation and extraction) technique. They found that in the presence of CD-containing membranes permeability coefficients of xylene isomers are higher when compared to control PVA membrane. It is also reported that α-CD is more effective to selectively extract the xylene isomers than β-CD. Flux observed for pertraction of single isomers and of the o-/p- binary mixtures was in the same order as the binding constants to α-CD i.e.p-xylene > m-xylene > oxylene. The fabricated membranes exhibit a p-xylene selectivity for low p-xylene feed mole fraction (<70%) and a o-xylene selectivity for higher p-xylene feed mole fraction. The pxylene enrichment factor observed at 10% p-xylene in the feed equal to 6, is the higher value ever reported for the separation of xylene isomers using CD containing membranes. The effect of way how CD, in particular α-CD, is introduced in PVA membranes is analysed in ref. 89. Physical trapping give rise to materials with an incorporation rate of 80 and 90% from the starting CD, whereas covalent attachment was quantitative. In both cases, however, it is found a high discrimination of p-and m-xylene over o-xylene.

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2.4. Separation by Membrane Extraction The development of membranes for, e.g., removing metal and organic pollutants from wastewater treatment [86, 90] and for concentrating valuable components from complex broths in bioproduction [87] is an attractive area. Due to its structure and possibility to form complexes or inclusion compounds with different organic or inorganic substances, PVA hydrogels could be used to retain Cu(II) ions from waste waters (at pH values higher than 8). A green complex PVA-Cu (II) is obtained. The following equation of reaction could describe the PVA-Cu (II) complex formation:

CH CH 2 OH

CH

2

CH2

CH OH

2+ Cu

+ OH CH CH 2

OH

H

H

CH O

O

CH

CH

2

2

CH CH 2

Cu

2

CH

O

CH O

CH CH 2

CH

CH

H

H

2

This complex could be further used in S2- ions retaining from wastewaters. Sulphide ions react with copper ions from the PVA matrix, leading to nanoparticles of CuS entrapped in the hydrogel. PVA-Cu (II) green hydrogel becomes black as it can be seen in figure 6. The repartition constant of Cu (II) ions between the PVA cryogel and water has been determined as 13.45. The repartition constant of sulphide ions between the PVA-Cu(II) complex and water is very close of the first value, due to the high affinity S2- to Cu2+ [92]. PVA hydrogel membranes obtained by freezing and thawing method could also retain iodine, in the presence of iodide ions. Red or blue complexes are formed in function of iodine concentration. A high repartition coefficient of iodine between cryogel and water has been obtained. They are dependent on the iodine concentration, evidencing a high level of interaction between PVA and iodine/iodide complex (K= 175 for 10-3 I2/I- aqueous solution and K= 455 for 3. 10-3 I2/I- aqueous solution) [93]. Taking into account that the iodine extraction from an aqueous solution is generally done by using very toxic and environmentaly dangerous organic solvents, such as CCl4, CHCl3, extraction of iodine with PVA hydrogel, non-toxic and biodegradable, could be a good candidate for “clean” technologies. CH2 CH CH

H

H

O

O

CH CH

2

CH CH

Cu

2 O

O

H

H

CH 2

CH 2 + 2

CH CH

2

S

2-

CH

CH

2

OH

CH OH

CuS OH

OH

CH CH 2

CH CH 2

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a.

b. Figure 6. Photographic aspect of PVA-Cu (II) complex (a) and PVA-Cu(II)-CuS composite [91].

Another important task in environmental protection is nowadays the effective decontamination of medical wastewaters. The development of new medicines for the treatment of oncologic and chronic diseases brings with it the need to efficiently decontaminate media containing these medicines. The existing methods are intensely energy consuming or environmentally non-friendly (e.g., the use of ion exchangers with amine groups). In the photodynamic therapy of cancer, for example, macrocyclic tetrapyrrholic compounds named porphyrins are used. Porphyrin-containing wastewaters can negatively affect the aquatic ecosystems (plants and fish population), even in very small concentrations. Recent studies present a method adequate for the advanced purification of medical wastewaters containing such porphyrins [94]. The method consists of the retention by sorption of the porphyrins on poly (vinyl alcohol) (PVA) hydrogels. Poly (vinyl alcohol) (PVA) is selected as the polymer of choice for the purification of industrial and medical wastewaters due to its capacity to form physically crosslinked hydrogels with the advantages of non-toxic, non-carcinogenic and biodegradable properties.

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Some authors consider that poly(vinyl alcohol) hydrogels represent an efficient and environmentally viable alternative advanced purification method for porphyrin-containing medical wastewaters. Many efforts to improve the efficiency and the selectivity of membrane processes are based on molecular recognition properties. The incorporation of cyclodextrins in polymeric membranes will improve affinity and selectivity properties of those membranes due to the possible formation of host-guest complexes by supramolecular interactions. Cyclodextrins (CD) are cyclic oligosacharides having 6, 7, 8 or more glucose unities [95] called α-, β- and γ-CD, respectively. These compounds show a large number of applications once they exhibit complex formation with organic molecules, they are excellent models of enzymes which led to their use as catalysts, both in enzymatic and nonenzymatic reactions, and they are natural products and readily available. For these reasons, we can find applications of these compounds in analytical chemistry [96], drug carrier systems [97], etc. Cyclodextrins are water soluble macrocycles shaped like a rigid, truncated cone with a hydrophilic external surface and a relative non-polar cavity [98]. In fact, the cavity is lined by hydrogen atoms and glycosidic oxygen bridges. The non-bonding electron pairs of the glycosidic oxygen bridges are directed toward the inside of the cavity, producing a high electron density and lending it some Lewis base character. As a result of this special arrangement of the functional groups in the CD molecules, the cavity is relatively hydrophobic compared to water while the external faces are hydrophilic. These hydrophobic cavities provide an enormous host potential for molecular ability to form inclusion complexes with a large variety of organic and inorganic compounds in different solvents (including water) [99-101]. The selectivity originated from the different binding constants to CD depends on the size and shape of guest molecules. This fitting effect has been successfully exploited for separation of positional isomers and enantiomers in such techniques as HPLC and capillary electrophoresis [102,103]. It appears from literature that CD-containing membranes have been mainly based on the immobilization onto hydrophilic polymers acting as a barrier for hydrophobic compounds and thereby limiting their non selective diffusion [83,104,105]. Poly(vinyl alcohol) (PVA) seems to be one of the most efficient polymer matrix for CDcontaining membranes owing to its ability to form free-standing films and its hydrophilic character due to the presence of hydroxyl groups. In these membrane materials CDs have been either trapped in PVA [83,84] or covalently linked to the chain [106]. Retaining of different ions from solutions is a very important target for wastewaters purification and for recovery of different ionic expensive species from solutions. PVA is a non-ionic polymer, but it could be blended with ionic or ionizable polymers and it could be copolymerized or grafted, giving materials that exhibit ion-exchange capacity. So, the PVA/poly(sodium styrene sulphonate) [PSSNa] blend was obtained by casting aqueous solution of polymers mixture (PVA with Mw= 124,000-186,000 and HD=99% and PSSNa with Mw= 70,000). The resulted films were crosslinked with 1,2-dibromethane in gaseous phase. A semi-interpenetrating network (SIPN) in which polyelectrolyte (PSSNa) chains are trapped inside a based PVA network was obtained [44]. A totally miscible blend with a very good film clarity and high mechanical resistance [44] resulted. The membrane evidenced ion exchange capacity that depends on: crosslinking time (tc) and the membrane composition. This capacity increases with the time of crosslinking from 0,8 to 2,0 meq/g after tc= 2 respectively 12 h. The best result for ion exchange capacity was

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obtained for membranes with 45% PSSNa content. The membrane kept about 60% of the initial exchange capacity after more than 2 years [44]. The blends swelling ratio in pure water is shown as a decreasing function of crosslinking time [44]. The membrane, initial supple (tc<2 h) becomes stiff and brittle after a longer crosslinking time (tc =8 h). The PVA/PSSNa membranes evidence a high permselectivity, comparable with the one of commercial ion exchange membrane as it can see in table 14, where were presented the permeability coefficient (P) and the ratio P to D (diffusion coefficient) that express the effect of porosity and of the electrolyte exclusion. Table 14. Diffusion of sodium chloride at 25 ºC through a PVA/PSSNa membrane* (Na+ form) [18, 44] C / (mol L-1)

0.01

0.1

1

P / (cm2 s-1)

1.91×10-7

7.06×10-7

2.50×10-6

P/D

0.013

0.047

0.167

*Capacity: cp=0.98 meq/g. Swelling ratio:τg=0.47. Thickness of dry and swollen sample: 140 and 200μm.

Also, the PVA/Poly(1,1 Dimethylenepiperidinium chloride) (PDMeDMPCl) blend membrane evidenced ion exchange capacity that increased with the time of crosslinking (tc) from 0,92 to 1,2 meq/g after tc= 15min respectively 120 min and showed a maximum capacity value, function of the weight fraction of PDMeDMPCl at 0.45 [44]. These membranes kept about 50% of the initial exchange capacity after more than 2 years. The PVA/PDMeDMPCl blend membranes evidenced a lower permselectivity than PVA/PSSNa membranes, probably because of a possible phases’ separation during the solvent evaporation, as it can see from table 15 [44]. Table 15. Diffusion of sodium chloride at 25 ºC through a PVA/PDMeDMPCl membrane* (Cl- form) [18,44]

*

C / (mol L-1)

0.01

0.1

1

P / (cm2 s-1)

2.38×10-6

6.31×10-6

7.17×10-6

P/D

0.16

0.42

0.48

Capacity: cp=0.83 meq/g. Swelling ratio:τg=0.67. Thicknesses of dry and swollen sample: 80 and 150μm.

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The PVA/PAcr. Ac. blends may also act like an ion exchange membranes if they are treated with 1,2-dibromoethane in gas phase. The average capacity of ion exchange is 6 mequivalent /g and depends on the weight fraction of the crosslinkable polymer [44]. Biosorption or bioaccumulation, the process of passive cations binding by dead or living biomass, represents a potentially consecutive way of removing toxic metals from industrial wastewaters. Biosorption could be employed most effectively in a concentration range below 100 mg L-1, where other techniques are inactive or too expensive. Metal ion binding during biosorption processes has been found to involve a complex mechanism, such as ion-exchange, complexation, electrostatic attraction or micro precipitation. There have been some indications that ion-exchange plays an important role in metal sorption by algal biomass. Although numerous papers on the metal–microorganism interactions are available in the literature, still large uncertainties exist. Biosorbents are complex and variable materials. The composition of cell wall, to which metal ions are bound, depends not only on biosorbent species, but also on environmental conditions of its growth. Recent studies confirmed that Azolla Caroliniana Wild fern, which is known as an effective bioacumulator in living state, is effective also in dry state (higher than 91% for Cr (III) ions retention) [107]. The dried fern particles have been also treated with nitric acid aiming to eliminate of cations initially present in the fern’s body and to enhance its bioaccumulation capacity, but no important modification has been evidenced by this treatment [108]. The use of Azolla Caroliniana dry fern in water depollution avoids the problems of plant acclimatization in different climate conditions or polluted water characteristics and the water re-pollution by toxics delivery from died fern maintained in water. The insertion of dried fern in a polymeric matrix avoids the fern particles mechanical degrading and permits the bioaccumulating material regeneration and it is reworking, determining the effectiveness of this advanced cleaning wastewater. Taking into account the non-toxicity and biodegradability of PVA, this depollution method is an ecological one.

2.5. Separation by Ultrafiltration Ultrafiltration (UF) is a membrane separation technique used to separate extremely small particles and dissolved molecules in fluids, using suction or pressure. In membrane separation systems, liquid containing two or more components comes into contact with a membrane that permits some components (for example, water in the fluid) to pass through the membrane (the permeate), while other components cannot pass through it (the retentate). The physical and chemical nature of the membrane (e.g., pore size and pore distribution) affect the separation of the liquid and its components. The primary basis for separation is molecular size (normally higher than 15-200 Å), although other factors such as molecule shape and charge can also play a role. Molecules larger than the membrane pores (0.001 to 0.1 μm) will be retained at the surface of the membrane (not in the polymer matrix as they are retained in microporous membranes) and concentrated during the ultrafiltration process. Compared to non-membrane processes (chromatography, dialysis, solvent extraction, or centrifugation), ultrafiltration is far gentler to the molecules being processed, does not require

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an organic extraction which may denature labile proteins, maintains the ionic and pH milieu, is fast and relatively inexpensive, can be performed at low temperatures (for example, in the cold room), and is very efficient and can simultaneously concentrate and purify molecules. The retention properties of ultrafiltration membranes are expressed as Molecular Weight Cutoff (MWCO). This value refers to the approximate molecular weight (MW) of a dilute globular solute (i.e., a typical protein) which is 90% retained by the membrane. However, a molecule’s shape can have a direct effect on its retention by a membrane. For example, linear molecules like DNA may find their way through pores that will retain a globular species of the same molecular weight. There are three generic applications for ultrafiltration. a) Concentration: ultrafiltration is a very convenient method for the concentration of dilute protein or DNA/RNA samples. It is gentle (does not shear DNA as large as 100 Kb or cause loss of enzymatic activity in proteins) and is very efficient (usually over 90% recovery). b) Desalting and Buffer Exchange (Diafiltration): ultrafiltration provides a very convenient and efficient way to remove or exchange salts, remove detergents, separate free from bound molecules, remove low molecular weight materials, or rapidly change the ionic or pH environment. c) Fractionation: ultrafiltration will not accomplish a sharp separation of two molecules with similar molecular weights. The molecules to be separated should differ by at least one order of magnitude (10×) in size for effective separation. Fractionation using ultrafiltration is effective in applications such as the preparation of protein-free filtrates, separation of unbound or unincorporated label from DNA and protein samples, and the purification of PCR products from synthesis reactions. Ultrafiltration (UF) is an important component in wastewater treatment and in food industry [109,110]. With increasing concerns and regulations in environment as well as in food safety, the process of ultrafiltration has become more critical, whereby new technology development to provide faster and more efficient water treatment is not only necessary but also urgent. Currently, conventional polymeric UF membranes are prepared mainly by the phase immersion process, typically generating an asymmetric porous structure with two major limitations: (1) relatively low porosity and (2) fairly broad pore-size distribution [111,112]. As a result, these membranes suffer two deficiencies: low flux rate due to the low porosity (i.e., limited permeability) and high fouling rate due to the asymmetric pore-size distribution having small pores on the surface [113]. In fact, the main problem with UF, however, is the flux decline caused by the irreversible adsorption of foulants onto the surface or even inside the pores of the membrane. Solute adsorption often involves hydrophobic interactions—hydrophobic membranes have a high tendency to foul in water treatments. However, many hydrophobic membranes remain the most useful media for ultrafiltration due to their superior performance in terms of mechanical, chemical and thermal stability. One approach to reduce fouling is using hydrophilic polymers, such as cellulose acetate (CA). Although CA membranes have outstanding properties in reducing membrane fouling, they lack long-term chemical, thermal and biological stability. Therefore, much research has focused on the development of good hydrophilic UF membranes using a high hydrophilic polymer. To avoid, or diminish the fouling process, a blend of PVA with cellulose (CELL) has been obtained by spin coated of the PVA (M=50 000; 99% hydrolysis degree) / glutaraldehyde (GA) solution (corresponding to 0.005 or 0.01 moles of GA/ mole of PVA

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repeat unit) mixture onto the regenerated cellulose membranes (M=10 000) [114]. A composite structure has been obtained. This hydrogel coating may penetrate the larger pores of the cellulose membrane and can exclude protein from entering them (100% protein retention). So, the hydrogel coating reduces the irreversible fouling of the cellulosic surface. Relative water fluxes varied from 97.4 to 46.8 % as the thickness of the coating under hydrostatic pressure varied from 0.8 to 5.2 μm. This blend is recommended as thin-gel composite membranes for bovine serum albumin ultra-filtration [114]. Polyvinyl alcohol (PVA) polymer is an attractive material to be developed as a new type of UF membrane with good anti-fouling characteristics. PVA membranes have a high level of mechanical strength, low fouling potential, longterm thermal resistance and pH stability. It has also been shown that PVA has good resistantce to most solvents besides strong polar solvents such as water, dimethyl acetamide, and N-methyl-2- pyrrolidone. Many studies relative to PVA-based membrane materials focused on modifying commercial membranes to improve their anti-fouling performance [115,116]. For example, Na and Liu [117] reported that a PVA-based composite UF membrane could improve membrane hydrophilicity and its anti-fouling performance. The anti-fouling PVA composite membranes were dynamically prepared with an aqueous solution containing PVA, crosslinking agents and additives passed through porous substrate membranes such as polyacrylonitrile, polyvinylidene fluoride and Nylon. X. Wang et al. [118] reported a new type of ultrafiltration membrane based on a different type of nanostructured porous support—electrospun nanofibrous scaffold in conjunction with a very thin layer of hydrogel coating to minimize fouling. Both the nanofibrous mid-layer support and the top coating layer were manufactured from crosslinked hydrophilic poly(vinyl alcohol) (PVA), where the degree of hydrolysis and the molecular weight of PVA were simultaneously adjusted to partially optimize the filtration performance and the mechanical durability. In that study PVA is the base material for fabrication of both the porous nanofibrous mid-layer support and the non-porous top coating layer. PVA is often used in ultrafiltration because of its superb hydrophilicity, biocompatibility, chemical and thermal stability. However, as PVA is water-soluble, it must be crosslinked to form water-resistant articles. PVA can be crosslinked through the reaction with hydroxyl groups using a wide range of chemicals [119,120]. X. Wang et al. synthesised a new high flux ultrafiltration nanofibrous composite membrane containing a crosslinked PVA electrospun scaffold and a PVA hydrogel coating. The crosslinked electrospun scaffold using 96% hydrolyzed PVA with high molecular weight (85 000–124 000 g/mol) exhibits the best overall mechanical performance with high tensile, strength and elongation. The crosslinking reaction only resulted in a minor shrinkage in volume (<5%) in the electrospun scaffold, whereby the resulting porosity was relatively high (>80%). The PVA coating layer on the electrospun scaffold was crosslinked by using GA at varying concentrations. Although the PVA hydrogel coating layer is macroscopically non-porous, it acts microscopically as a mesh of hydrophilic chains connected by crosslinking points. The mesh size can be controlled by the degree of crosslinking in the hydrogel and the best permeation rate and filtration efficiency is achieved by using the GA/PVA repeat unit ratio of 0.06 to crosslink the top PVA layer. The ultrafiltration test indicates that the flux rate of PVA

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nanofibrous composite membranes is at least several times better than those of existing thin film composite membranes [121-123], where its performance can be further optimized by reducing the top layer thickness or changing the layer composition. Another way of using PVA for UF membranes is by modifying PVA by controlling hydroxyl groups. In this way the pore structure can be easily adjusted by the method phase inversion. Otherwise, once PVA is a water –soluble polymer it is difficult to form porous UF membranes with an ideal morphological structure by the method of wet phase inversion directly when water is used as a coagulation bath. Acetalization of PVA is commercially used in the modification of PVA [124]. In general, formaldehyde, acetaldehyde and butyraldehyde have been used in acetalization of PVA. However, the hydrolyzing temperature of poly(vinyl formal) and poly(vinyl butyral) is higher than their deformation temperature. The hydrolysis and crosslinking for both poly(vinyl formal) and poly(vinyl butyral) membranes are difficult to perform directly below their deformation temperature. The crosslinking of the acetalized PVA with glutaraldehyde is easy to carry out without damaging the membrane shape and structure. In the Ref. 124 a number of hydrophilic UF membranes using the acetalized PVA is presented. The UF permeation tests were carried out using bovine serum albumin (BVA) solution as the feed instead of water. The modified PVA membrane exhibits a high level of water permeation along with good retention of BSA. It was found that the modified PVA UF membranes are hydrophilic and showed a good tendency dramatically to relieve protein fouling, thereby providing a better alternative to commercial UF membranes.

3. OTHER DOMAINS OF MEMBRANES APPLICATION 3.1. Fuel Cells Ion conducting polymers containing strong acidic groups (e.g., sulfonic acid) are of interest for a broad range of applications, such as biosensors, chemical sensors, catalysts, actuators, ion-exchange membranes and polymer electrolyte membrane (PEM) fuel cells [125-127]. PEM fuel cells, in particular, are being investigated as replacements to current power sources used in transportation and portable electronics [128]. In this application, the ion conducting polymer or PEM serves as both a cell separator, separating the anode from the cathode, and an electrolyte, conducting protons from the anode to the cathode. Although there are a number of advantages to PEM fuel cells (e.g., renewable fuels, environmentally benign, high efficiencies), there are also a number of key shortcomings with current PEMs that hinder fuel cell efficiency. These shortcomings include low proton conductivity at higher temperatures, poor water management and high fuel crossover. Fuel crossover is a main concern as it applies to the methanol fuel-based PEM fuel cell (also known as the direct methanol fuel cell (DMFC)). Direct-methanol fuel cells (DMFCs) have attracted considerable attention for certain mobile and portable applications, because of their high specific energy density, low poison emissions, easy fuel handling, and miniaturization [129,130]. However, the methanol permeation through electrolyte membranes (usually called methanol cross-over) in DMFCs still is one of the critical problems hindering the commercialization [131,132]. Nafion®, a

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poly-(perfluorosulfonic acid) membrane, is the major membrane used in polymer electrolyte membrane fuel cells (PEMFCs) presently. However, Nafion® membrane has a poor barrier property to methanol crossover (high methanol permeability). The methanol crossover to cathode not only reduces fuel efficiency, but also increases the overpotential of the cathode, thus resulting in lower cell performance [133]. The reason is known to be originated from protonic drag of methanol and diffusion through the hydrophilic channels within the membrane. Therefore, the effective methods for reducing methanol cross-over are to decrease the average diameter of ion-rich hydrophilic domains and increase the hydrophobicity of membrane surface. To date, much effort has been undertaken to develop new alternatives. For example, sulfonated aromatic polymers, i.e., polymers with the sulfonic acid groups directly attached to the main chain or carrying short pendant side chains with terminal sulfonic acid units, attract increasing interest because of their chemical and thermal stability, and the ease of the sulfonation procedure. Some of the proposed polymers are sulfonated polysulfone (SPSU) [134] sulfonated poly(phenylene oxide) (SPPO) [135] sulfonated poly-(ether ether ketone) (SPEEK) [136] poly(phenylquinoxaline) (PPQ) [137] and poly(benzeneimidazole) (PBI) [138]. Poly(2-acrylamido-2-methyl-1-propanesulfonic acid)(PAMPS) was found to show higher proton conductivity than partially hydrated Nafion due to the sulfonic acid groups in its chemical structure [139]; consequently it can be chosen as a component for a new protonconducting electrolyte membrane [140]. However, PAMPS, shows also some limitations as, for example, is highly water-soluble. Another key factor for the development of protonconducting polymer electrolyte membranes is the water swelling. Extreme swelling causes a loss of the dimensional stability, while low swelling reduces proton conductivity because of low water absorption of the membranes. Cross-linking is an efficient means to limit the swelling, also yielding the dimensional and thermal stability of the membranes. [141-143]. Another consideration is alcohol cross-leaking, which is a key issue in the practical use of DMFC, but it can be controlled effectively by adjusting the cross-linking density of the prepared membranes. [144]. J. Qiao et al. [144] have synthesised a family of conducting polymer membranes of chemically modified poly(vinyl alcohol) - poly(2-acrylamido-2methyl-1-propanesulfonic acid) (PVAPAMPS) prepared on the basis of a new concept of binary chemical cross-linking. It has been demonstrated that the excessive swelling of pristine PVA-PAMPS can be well controlled by chemical cross-linking using nbutylaldehyde/terephthalaldehyde, n-hexylaldehyde/terephthalaldehyde, and noctylaldehyde/terephthalaldehyde as binary cross-linking agents. By changing the spacer length of the auxiliary crosslinkers, PVA-PAMPS membranes produce promising swelling characteristics and very good mechanical properties and flexibilities. The type and the amount of water absorbed by the chemically cross-linked PVA-PAMPS polymer blends are dependent not only on the sulfonic acid amount, but also on the spacer length of the CH2 chain in the auxiliary crosslinkers and the cross-linker composition. The membranes show a larger sorption of nonfreezing water relative to freezing water. For a PVA-PAMPS of 1:1.5 in mass, with O5T5 as a binary cross-linking agent, a proton conductivity of 0.12 S cm- 1 at 25 °C and of 0.098 S cm-1 at 5 °C is reported. The same authors [145] have mofidied PVAPAMPS polymer blends by introducing a further polymer, the poly(vinylpyrrolidone) (PVP). The proton conductive polymer membranes PVA–PAMPS–PVP has the best proton conductivity of 0.088 S cm-1, at 25 ºC, for a polymer composition PVA:PAMPS:PVP of

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1:1:0.5 in mass, which is comparable to commercially available Nafion117, and a methanol permeability of 6.1×10-7 cm2 s-1, one third of Nafion 117 methanol permeability (1.7×10-6 cm2 s-1 [146]), at room temperature. The use of a modified PVA membrane as a proton-exchange membrane is reported in the Ref. 147. The chemical structure of poly(vinyl alcohol) membranes is modified via sulfonation, using sulfophthalic acid (sPTA) as a sulfonating agent. The ion-exchange capacity (IEC), water uptake, methanol permeability and proton conductivity properties are evaluated for a set of sulfonated PVA membranes, with a variety of degrees of substitutions. The permeability of methanol and proton conductivity of these polymers are compared with those of Nafion115. The values of methanol permeability and proton conductivity obtained are 18.0 × 10-7 cm2 s-1 and 0.112 S cm-1 respectively. Methanol permeability values of the membranes treated with 10% sPTA, at different cross-linking times, are around 5 × 10-7 cm2 s-1, and proton conductivity values of the sulfonated PVA membranes ranged between 0.024 and 0.035 S cm-1. The effect of annealing temperatures (65 – 250 ºC) and blend composition of Nafion® 117, solution-cast Nafion®, poly(vinyl alcohol) (PVA) and Nafion®/PVAblend membranes for application to the direct methanol fuel cell is reported in [148]. These authors have found that a Nafion®/PVAblend membrane at 5 wt% PVA (annealed at 230 ºC) show a similar proton conductivity of that found to Nafion® 117, but with a three times lower methanol permeability compared to Nafion® 117. They also found that for Nafion®/PVA (50 wt% PVA) blend membranes, the methanol permeability decreases by approximately one order of magnitude, whilst the proton conductivity remained relatively constant, with increasing annealing temperature. The Nafion®/PVA blend membrane at 5 wt% PVA and 230 ◦C annealing temperature had a similar proton conductivity, but three times lower methanol permeability compared to unannealed Nafion® 117 (benchmark in PEM fuel cells).

3.2. Sensors The sensitivity of hydrogels to a large number of physical factors like temperature [149], electrical voltage [150], pH [151-153], concentration of organic compounds in water [154], and salt concentration [155] make them promising materials for a broad range of applications as microsensors [156] and microactuators [154] in MEMS devices. The following principles for the pH value detection are used in sensors based on the swelling behavior of hydrogels: changes of the holographic diffraction wavelength in optical Bragg grating sensors [157], shifts of the resonance frequency of a quartz crystal microbalance in microgravimetric sensors [158], a bending of micromechanical bilayer cantilevers [153], as well as a deflection of silicon membranes in piezoresistive pressure sensors [159]. The swelling ability of pH-sensitive hydrogels depends on the functional acidic or basic groups at the polymer back- bone. Due to the dissociation of these groups and the influx of counterions, the concentration of ions in the hydrogel is higher than in the surrounding solution. This causes a difference in osmotic pressure and results in a solution flux into the hydrogel and, consequently, a swelling. The interaction and repulsion of charges along the polymer chain also lead to an increased swelling. Equilibrium of ionic gels occurs when the elastic restoring force of the polymer network balances the osmotic forces. During the

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swelling process hydroxide ions are transported into the neutral gel, while during the shrinkage protons diffuse into the gel and neutralize the negative charged acidic carboxylate groups. This ion diffusional flux induces an electrical potential difference that drives the electromigration of the ions in the direction opposite to that of the diffusion. In so called “Donnan equilibrium” the diffusional flux of the ions in one direction is equal to the electromigrational flux in the opposite direction, resulting in a net zero mass transport and a net zero charge transport. The change of the electrical potential at the gel– solution interface is a function of the pH value of the surrounding solution. A Nernst–Planck equation coupled with the Poisson and the mechanical equilibrium equations can be used to describe the gel swelling/deswelling process [160]. Because the gel response is typically diffusion driven, the time response of the volume change approximately follows the square of the sample dimension. Scaling to micro-dimensions enhances the time response. Consequently, a reduction of the sample size improves the sensor performance. G. Gerlach et al. discuss the influence of the preparation conditions of hydrogel (poly(vinyl alcohol)/poly(acrylic acid) blend films on the sensitivity and response time of the chemical and pH sensors [161]. These authors have used swelling degree hydrogel properties as chemo-mechanical transducers for pH value variation. The hydrogel swelling leads to a bending of a thin silicon membrane and, by this, to an electrical output voltage of the sensor chip. The influence of the gel swelling/deswelling kinetics on the response time and longterm signal stability of proposed pH sensors leads to a signal drift. Such drift depends on the pH value of the ambient solution and is caused by the slow continuous change of the electrical potential at the gel–solution interface. The influence of previous gel swelling states can be minimized by a prolonged rinsing in de-ionized water after every measurement at high pH values. It is described that measurements in solutions with pH < 3 and large pH changes should be avoided in order to maintain sufficient sensor sensitivity for a long time. In order to achieve high signal reproducibility of pH sensors, a compensation of previous output signal values should be used. Due to the chemical interactions between PVA and boric acid that lead to directly proportionally of the swollen hydrogel shrinking and the boric acid concentration, a sensor for this acid, difficult to determine by classical titration because of its weakness, has been proposed [162]. The development and applications of optical chemical sensors have grown rapidly. Among all sensors, optical pH sensors have received the most attention because of the importance of pH measurement in various scientific research and practical applications [163]. Optical pH sensors are based on pH-dependent changes of the absorbance or luminescence of certain indicator molecules immobilized on/in certain solid substrates. The immobilization of pH indicators to solid substrates is a key step in the development of optical pH sensors. Till now, there are three widely used methods for immobilization of pH indicators namely, adsorption or impregnation; covalent binding and entrapment. The adsorption and entrapment methods are relatively easy, but the leaking out of the indicators is a serious problem. The covalent binding method is relatively complicated and time-consuming, but very reliable since the indicators is not likely to leak out [164]. There have been many reports in which the immobilization method was covalent binding. In fact, many pH indicators used in above reports own at least one active amino or carboxyl group so that they can be covalently bound relatively easily to a solid substrate [165,166]. Kostov et al. had discussed the immobilizing process of Congo red, neutral red and phenol

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red to an activated diacetylcellulose membrane, and found that the indicator of phenol red was difficult to be immobilized via their method because of no active amino [167]. On the other hand, three factors that impact on the longterm stability should be considered, namely, the pH indicators themselves, the substrates and the linking bonds between the indicators and substrates. The commonly used ester linkage and acid-amide linkage are not very stable in acidic or alkaline aqueous conditions. Polymeric pH indicators, phenolphthalein-formaldehyde (PPF) and o-cresolphthaleinformaldehyde (CPF) were synthesized with phenolphthalein and o-cresolphthalein reacted by formaldehyde under alkaline conditions, respectively. They can be immobilized in hydrolyzed cellulose diacetate membranes (HCDA) mainly due to macromolecular entrapment, and can be covalently bound to poly(vinyl alcohol) (PVA) via the considerable newly produced hydroxylmethyl groups [168,169]. Phenol red (phenolsulfonphthalein) and its derivatives are commonly used for pH determination. Phenol red immobilized PVA membrane for an optical pH sensor is developed based on the same approach, since the molecular structure of phenol red is similar to that of phenolphthalein. Phenol red was first reacted with the formaldehyde to produce hydroxymethyl groups, and then it was attached to PVA membrane via the hydroxymethyl groups. The changes of spectra characteristics after immobilization, the ionic strength effects, response time, reproducibility and long-term stability of the sensor membrane are discussed by Z. Liu et al. [170]. Sol–gel-based biosensors have attracted an enormous scientific attention is the last decades [171-179]. Despite the volume of the published work, inherent drawbacks associated with the nature and the synthetic routes followed for the preparation of such gels still exist. These include cracking of the films, high concentration of methanol/ ethanol in the resulted sol, and the most important point regarding the development of amperometric-based biosensors, the lack of conductivity. Constantinos G. Tsiafoulis et al. report the electrochemical behaviour of a composite film based on ferrocene intercalated V2O5.nH2O xerogel (FeCp2–VXG) with photocrosslinkable polyvinyl alcohol with styrylpyridinium residues (PVA–SbQ), in order to be used as an electrocatalyst and host protein platform to develop an amperometric biosensor. PVA–SbQ has been extensively used as a matrix for the immobilization of proteins [180183]. The hydrophilicity of the polymer matrix, the mild conditions that are used during the immobilization and photopolymerization procedure make PVA–SbQ an effective support material for the immobilization of proteins. Using glucose oxidase as a model enzyme, prospects of GOx–PVA–SbQ/FeCp2–VXG modified electrodes for further biosensor work in terms of working stability and storage stability, dynamic range, compatibility to proteins, applicability to near neutral pH, permeability and electrocatalytic activity are evaluated. Comparing with other xerogel based architectures, vanadium pentoxide xerogel shows to be superior in terms of conductivity and compatibility to enzymes. The proposed electrocatalyst provides about 20% increase of the sensitivity compared with the pure mediator, is compatible with biomolecules and its applicability over the useful pH range for most of the (bio)sensors applications indicates promise for further use. Low-cost, disposable, SiO2/Si3N4 chemical field effect transistor (ChemFET) microsensors have been fabricated for pH measurements and adapted to biochemical applications by using polyvinyl alcohol (PVA) enzymatic layers deposited and patterned

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either by dip-coating, or spin-coating and photolithographic techniques. Both processes have been compared for the development and optimization of a creatinine-sensitive enzymatic field effect transistor (Creatinine-EnFET). The Creatinine-EnFET has been characterized by linear detection properties (sensitivity around 30 mV/pCreatinine) on the [10–1 000 μmol L−1] concentration range.(Creatinine-EnFET) [184]. Chronic end-stage kidney failure affects many patients in the world. Since its development in the 1960s, kidney dialysis has allowed a great number of patients to survive. So far, these techniques, and haemodialysis in particular, have been under constant development so that the quality of health care and the patients’ life expectancy can be improved. To go further, dialysis efficiency must be known precisely, requiring a continuous monitoring of different chemical species concentrations into the blood: urea, creatinine as well as the H+, K+ and Na+ ions. Creatinine is the end product of creatine metabolism in mammalian cells. Therefore, it is an important diagnostic substance in biological fluids. Creatinine can be used for the diagnosis of renal, thyroid and muscle function. It plays a major role in treatment with external dialysis. Normal range for plasma creatinine is 35–140 μmol L−1. However it can reach concentrations higher than 1000 μmol L−1 in the case of kidney dysfunction. Thus, creatinine detection has to be developed in the [10 – 1000 μmol L−1] concentration range for haemodialysis applications. A highly sensitive amperometric biosensor for glutamate has been fabricated by immobilizing enzyme in a photo-crosslinkable polymer, polyvinyl alcohol bearing a styrylpyridinium (PVA-SbQ), membrane on a palladium deposited screen-printed carbon electrode is reported in Ref. 181. The polymer was previously reported to be suitable for fabrication of a thin enzyme membrane (about 1 mm thick) [185]. Enzyme can be immobilized in the PVA-SbQ matrix with high surface density and retain their functional characteristics to a large extent for several months upon repetition of wetting and drying [186]. Moreover, enzymes can be immobilized in this polymer using photolithography techniques [187], which can be adapted to mass production using ordinary screen printing or semiconductor-fabrication processes on a planar electrode [188]. Strong electrochemical interference from oxidizable species, such as ascorbic acid and uric acid, in the biological samples exposes a serious problem for the practical operation of amperometric biosensors with a working potential of 0.4 V or higher [189]. For example, electrochemical oxidation of ascorbic acid (AA) generates the dehydroascorbic acid (DAA), with the loss of two electrons and the consequent loss of hydrogen ions. One way to solve this problem is to modify the electrode surface with a permselective membrane. A variety of polymer membranes have been reported to be useful for eliminating interferents [190-192]. These polymers show permselective properties based on size exclusion (e.g. poly-l-lysine and poly (4-stryenesulfonate) membrane) and/or charge interaction between solutes and the membrane (e.g., Nafion). Biosensors fabricated on the Nafion and polyion-modified palladium strips are reported by C.-J. Yuan [193]. They found that Nafion membrane is capable of eliminating the electrochemical interferences of oxidative species (ascorbic acid and uric acid) on the enzyme electrode. Furthermore, it can restricting the oxidized anionic interferent to adhere on its surface, thereby the fouling of the electrode was avoided. Notably, the stability of the proposed PVA-SbQ/GOD planar electrode is superior to the most commercially available membrane-covered electrodes which have a use life of about ten days only. Compared to the conventional three-dimensional electrodes the proposed planar electrode exhibits a similar

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long-term stability, but is smaller, more responsive and more versatile. The manufacturing processes used in the semiconductor industry can be adapted to produce these electrodes at a unit cost that is low enough to ensure cost-effectiveness. The blend of PVA with PEG- modified glucose oxidase could be used as glucose sensor characterized by the linearity of calibration curve in the range of concentration by 5 × 10-5 - 5 × 10-3 mol glucose L-1 [194].

3.3. Biochemical/Medical Applications In the recent years, the scientists’ position concerning the diseases treatments was completely changed. No longer is the treatment of specific diseases, such as diabetes, asthma, cardiac problems, osteoporosis, cancer etc. based only on conventional pharmaceutical formulation. Biology and medicine are being to reduce the problems of disease to problems of molecular science, and are creating new opportunities for treating and curing disease. Such advances are closely related with advances in biomaterials and are leading to a variety of approaches for relieving suffering and prolonging life [195]. An exponential increase of the biomaterials application could be noted in the last years. R. Langer and N.A. Peppas reported the main domains of biomaterials application that could be schematically represented in figure 7.

Figure 7. Repartition of the main domains of biomaterials applications.

The suitable materials for the above mentioned domains are polymers, metals and ceramics. Among these, polymers play an important role. Even the polymers have a lot of remarkable properties that could be used in biomaterials design, the interaction between these artificial materials and tissues and blood could create serious medical problems such as clot formation, activating of platelets, and occlusion of tubes for dialysis or vascular grafts. In the last few years, novel techniques of synthesis have been used to correlate desirable chemical, physical and biological properties of biomaterials. One of the widely used categories of polymers for biomaterials design is that of homo-or copolymers, which could generate hydrogels. Hydrogels are three-dimensional polymer networks that could swell in water without dissolution and that, due to their high water content and rubbery nature, are very similar to natural tissues and could be considered

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biocompatible. Also, hydrogels may provide desirable protection for drugs, peptides and proteins from the potentially harsh environment in vicinity of the release site. Hydrogels could be also excellent candidates as biorecognizable biomaterials that could be used as bioadhesive systems, as targetable carriers of bioactive agents or as conjugates with desirable biological properties. PVA is a well known polymer with large possibilities to be used as biomaterial, due to its non-toxicity, biocompatibility, non-carcinogenity, capability to react with other compounds and to be blend with a lot of polymers, changing its initial neutral network with positively or negatively charged one. Also, by modifying their initial structural characteristics such as molecular weight, hydrolysis degree, OH groups tacticity, some of PVA properties could be modified, such as mechanical and thermal resistance, water solubility, and chemical stability. Also their capability to be crosslinked by chemical or physical routs, to be blended with different polymers or copolymers, to be graft or copolymerize with different chemical partners lead to obtaining of intelligent hydrogels those stimuli-responsive properties could be relatively easy to tailor. Also, PVA hydrogels evidenced a very good behaviour in contact with skin and other tissues, mucosa, or blood. PVA exhibits a bioadhesive nature, shape-memory properties, avoid the protein adsorption onto the gel surface and is biocompatible. Recent reports [1,196] showed that PVA hydrogels are used as blood-compatible material, as contact lenses, as membranes for plasmapheresis, as artificial skin, as vocal cord reconstruction, as articular cartilage, in controlled drug delivery as neutral non-biodegradable matrix (in human body conditions), but more recent studies evidenced that by blending, by grafting or by copolymerization, by crosslinking by different methods, PVA-based hydrogels could be use also as temperature, pH, electrolyte-sensitive biomaterials. Polyvinyl alcohol (PVA), which is a water soluble polyhidroxy polymer, is one of the widely used synthetic polymers for a variety of medical applications [197] because of easy preparation, excellent chemical resistance, and physical properties. [198] But it has poor stability in water because of its highly hydrophilic character. Therefore, to overcome this problem PVA should be insolubilized by copolymerization [43], grafting [199], crosslinking [200], and blending [201]. These processes may lead a decrease in the hydrophilic character of PVA. Because of this reason these processes should be carried out in the presence of hydrophilic polymers. Poly(vinyl pyrrolidone), PVP, is one of the hydrophilic, biocompatible polymer and it is used in many biomedical applications [202] and separation processes to increase the hydrophilic character of the blended polymeric materials [203,204]. An important factor in the development of new materials based on polymeric blends is the miscibility between the polymers in the mixture, because the degree of miscibility is directly related to the final properties of polymeric blends [205]. A very complete study, effect of pH, concentration of SA, PVA/PVP ratio and the temperature on the SA release, concerning the controlled delivery of SA from PVA/PVP membranes is given in the Ref. 206. Four main conclusion arise from this study: a) the presence of PVP increased the released amount of SA; suitable PVA/PVP ratio was found to be as 60/40 (v/v) for PVA/PVP membranes; b) the release percentage of SA through PVA/PVP membranes and swelling degrees of the PVP-40 membranes increase with an increase in the pH of donor solution; the pH of the acceptor solution do not affect much the transfer of SA through PVP-40 membranes; c) grafting of PVA with VP is more effective than blending with PVP for the release of SA; and d) the increase in the temperature increase

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the transfer of SA; the release percentage for SA is found being 57.5 % and 66.6 % at 32 ºC and 37 ºC, respectively. Delivery of hydrophilic molecules such as proteins and DNA for therapeutic application is generally considered a great challenge [207,208], because these molecules are rapidly degraded by enzymes found under in vivo conditions both intracellularly at the site of application as well as in the general circulation, causing low bioavailabilities and requiring frequent injections [209]. Nanoscale carriers such as nanoparticles and nanocomplexes have reached increasing attention, since they can be administered by various routes, including the intravenous and intranasal routes [210,211]. Controlled and sustained release of these drug candidates can be accomplished using microspheres and implants from biodegradable polymers [207,212]. The classic copolyesters of lactic and glycolic acid (PLGA) are not ideal for protein and DNA delivery since inactivation and uncontrolled release is a consequence of poor compatibility between lipophilic polymers and hydrophilic drug candidates [213,214]. This is especially the case for DNA, where the complexation capabilities and protecting abilities of the carrier substance are very important. M. Wittmar et al. [215] selected PVA, once it is biocompatible and can be eliminated from the body by renal excretion [216,217]. To this polymer backbone, amine groups were covalently coupled in a polymer-analogous reaction using carbonyl diimidazole (CDI) to introduce cationic charges under physiological conditions [218,219]. This modification affects the colloidal stability of carrier systems by imparting positive surface charges on one hand [220] and increasing the protein or DNA loading by electrostatic interactions on the other hand [221,222]. As the secondary and tertiary amino-groups functions possess lower cytotoxicity, diamines, and PVA were coupled via the hydrolytically stable urethane bond [223]. The resulting PVA can be used in different ratios to complex DNA. K.S. Oh et al. [224] have used PVA-containing matrices as temperature sensitive drug delivery systems. Their approach is based on the fact that the constant release is not the only way to accomplish the maximum drug effect and the minimum side effects and the assumption used for constant release rate sometimes fails its validity for physiological conditions. Such difficulty can be overcome by technology that senses environmental stimuli and appropriately controls the drug-release rate. Stimuli-sensitive polymers undergo phase transition in response to changes in, for example, pH, temperature, or the metabolites [225227]. Especially, polymer materials with temperature-induced swelling transitions resulting from both polymer–water and polymer–polymer interactions have been reported [228]. K.S. Oh et al. have prepared a novel polymer complex gel composed of F-68 (Pluronic, poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) triblock copolymer) and poly vinyl alcohol (PVA). The polymer complex gel if formed by intra/intermolecular interactions via hydrogen bonding in water. For the application as a temperature-sensitive delivery system of acetoaminophen, F-68/PVA complex gel is prepared with a form of polymeric bead encapsulated by poly(lactide-co-glycolide)(PLGA) membrane and pulsatile release of acetoaminophne, used as model drug, pattern is observed in response to pulsatile change of temperature between 35 ºC and 40 ºC. A new material with good antithrombogenic properties, suitable as biomedical material which assures the endothelialization of the inner surface of a polyurethane tube to imitate the inner wall of a natural blood vessel has been synthesized by blending PVA with poly(carbonate urethane)(PCU) [229].

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This blend was obtained by polymers mixture extrusion and extraction with the azeotropic mixture of hexane/ethanol, and modifying the obtained polymer surface by coupling of 4-isocyanato butanoic acid methyl ester (as a spacer molecule) to PVA blend, saponification of methyl ester groups and coupling of 4-amino-TEMPO (2,2,6,6tetramethylpiperidine-1-oxyl) [229]. Generally is difficult to delimitate the medical or pharmaceutical application of PVA hydrogels as gel matrix, micro spheres, aerosols or membranes. Taking into account the consensual accept of the membrane concept, we could consider as application in membrane form transerdmal patches, wound dressing, materials for tissue engineering, thin coatings with imprintig gels for molecular recognition, biomembranes in artificial organs, haemodialysis.

3.3.1. Transdermal Patches The most common form of drug delivery is via the oral route. Although this has the notable advantage of easy administration, it also has significant drawbacks namely poor bioavailability due to hepatic metabolism and the tendency to produce rapid blood level spikes (both high and low), leading to a need for high or frequent dosing, which can be both cost prohibitive and inconvenient. Another method utilized in drug delivery is the systems that deliver the drugs through the skin into the bloodstream, making them easy to administer. In transdermal drug delivery, improved bioavailability, more uniform plasma levels, longer duration of action resulting in a reduction in dosing frequency, reduced side effects and improved therapy due to maintenance of plasma levels up to the end of the dosing interval, and patient compliance could be possible. Transdermal patch technology represents an important area of biomaterials, due to its non-invasive character, ease to use, and a relatively high bioavailability. Generally, these patches could deliver drugs from one to seven days. Currently, 11 drugs, or drugs combinations are delivery through body via this method [195]. Nowadays, scientists are exploring various physical forces to enhance the transport through the skin to expend the number of drugs being delivery such as electricity, (iontophoresis, electroporation) or ultrasounds. Drug delivery to the skin has been traditionally designed for dermatological drugs to treat skin diseases or for disinfection of the skin itself. In recent years, a transdermal route has been considered as a possible site for the systemic delivery of drugs. The possible benefits of transdermal drug delivery include that drugs can be delivered for a long duration at a constant rate, that drug delivery can be easily interrupted on demand by simply removing the devices, and that drugs can bypass hepatic first-pass metabolism. Furthermore, because of their high water content, swollen hydrogels can provide a better filling for the skin in comparison to conventional ointments and patches. Versatile hydrogels-based devices for transdermal delivery have been proposed [230]. Recently, porphyrins have been applied to cancer photodynamic therapy (also known as photochemotherapy), a method based on applying a porphyrinic compound onto the tumour and then irradiating with a light source. The porphyrin acts as a photosensitiser, transferring its energy to the oxygen found in tumoral tissue, generating singlet (radicalic) oxygen, which has the ability to oxidize tumour cells and also induce cell death (apoptosis). To stabilize and to assure a convenient delivery of porphyrins their entrapment in a hydrogel matrix has been proposed. Different porphyrins (figure 8), water soluble (5,10,15,20-tetra-sulphonato-phenyl

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porphyrin, TSPP) and water insoluble (5,10,15,20-tetra-pyridil porphyrin, TPyP, and 5,10,15,20-tetra-phenyl porphyrin, TPP)) have been immobilized in PVA cryogel matrix.

TPyP: R=-C5NH4 ; TPP: R=-C6H5 ;TSPP: R= -C6H4-SO3-Na+ Figure 8. Structure of the porphyrins TPyP, TPP and TSPP.

The porphyrins structure and the PVA molecular weight determine differences in the porphyrins sorption onto the PVA hydrogels, as it can be seen in figure 9 [231].

Figure 9. Comparison between the sorption degree of porphyrins on the PVA hydrogel, as function of PVA molecular weight and porphyrin type.

One can conclude that PVA hydrogels represent an efficient encapsulation vehicle for the studied porphyrins, both water soluble and non-water soluble. Their biocompatible, biodegradable, non-toxic, and non-carcinogenic nature makes them especially effective for pharmaceutical applications, but also for environmental uses, such as advanced wastewater

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decontamination. Hydrogels prepared from high molecular mass PVA have a better sorption profile for porphyrins, and are better suited for the preparation of controlled-release vehicles. Also, PVA has a number of desirable characteristics that make it a good bioadhesive polymer. It has mechanical strenght, high elasticity, and swells upon immersion in water.Crosslinked PVA has been proposed as drug delivery carriers. In these gels the drug is able to be released fast or slowly due to the gel’s high or low swelling ratio upon immersion in water. Previous studies by Morimoto et al. [232] have shown that several drugs such as indomethacin, glucose, insulin, heparin, and albumin can be released from crosslinked PVA gels. PVA properties depend upon the degrees of polymerization and hydrolysis. The solubility of PVA in water increases greatly as its degree of hydrolysis increases. Properties such as water solubility, high tensile strength and tack make PVA useful as an adhesive with fully hydrolyzed grades of PVA being water-resistant adhesives. PVA cryogel maximum adhesion has been achieved after two freezing/thawing cycles, saples prepared by three and four cycles still exhibit adhesive characteristics. The mucoadhesive and drugs release (i.e., theophyline and oxprenolol hydrochloride) behavior could be adjusted by degree of crystalinity which depend on the number of freezing/thawing cycles.

3.3.2. PVA Based Materials as Wound Dressing The current generation of medical dressing differs from their predecessors primarily because they are based on non traditional polymers in this area. In creating new wound coverings, instead of cellulose stock, other natural and synthetic polymers are being increasingly used. One of them is PVA, because of its exceptional properties. Also, an important change in dressing form should be noted: in many cases, preference is given to granulated sorbents, hydrogels, films and sponges [233]. Applied to wounds, burns or surgical incisions, hydrogel materials cover the injured parts of skin (wounds) and promote healing and skin growth. There are two ways of wound treatment: under dry or wet conditions. In the former gauze is applied to the skin, the latter calls for the use of hydrogels. Since many agree that wounds heal faster in a wet environment, hydrocolloid type materials mixed with gelatin, hydrophobic polymers and water have been developed and already see practical use. However, these materials are mechanically weak and require periodic change, and the residue must be removed by washing with physiological salt solution. This process determines exfoliation of the new skin and delays healing. Also the removing of the dressing induces pain. To avoid all these drawbacks new wound dressing materials have been tested. So, PEO/PVA hydrogel, crosslinked by electron beams, has been synthesized and tested as dressing on animals wounds. Wounds dressed with a hydrogel healed almost completely within 14 days, while those using gauze were only half-healed within that time. Clinical tests confirmed the safety and effects of this product [234]. The main features for a hydrogel dressing are the following: to protect injured skin and keep it appropriately moist to accelerate the healing process; to absorb liquids exuded by the body; to prevent infection from external bacilli; to be non-toxic, non-irritant and noncarcinogenic; to be soft and high adhering to the skin; to have mechanical resitance; to have high permeability; to resist to sterilizing process; to remove without pain; to be transparent to allow observation of the healing process.

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(b)

Figure 10. Hydrogel membrane (a) and their application as wound dressing (b).

New generation of therapeutic coverings have to be characterized also by the ability to exercise a biologically active effect on wound. Incorporation of one or more drugs in the polymeric matrix that acts as a vehicle with controlled delivery capacity makes the new dressings able to exert anesthetizing, antimicrobial or combined effect. Also, the immobilization of proteolytic enzymes and an antimicrobial on a polymer substrate helps by decreasing the cleansing and healing time, especially in the purulent wounds treatment [235]. Table 16. Some exemples of systems used as new wound dressings Polymer system/ drug PVA/ proteolytic enzyme protease C/ polyhexamethyleneguanidine salt (PHMG) (antimicrobial factor (AM)) a/-PHMG (C)= PHMG hydrochloride; b/-PHMG (P)=PHMG phosphate

Properties -PHMG influences the viscosity of the initial PVA solution (a higher decrease has been observed in case (a) then in case (b)) -(a) and (b) determines the decreasing of the activation energy of viscous flow -additive adding (sodium tetraborat as crosslinking agent) determines the increasing of the spinning PVA solution -the porous structure of the film and the repartition of the complex is influenced by the type of AM

Ref. 233

PVA film/ Sodium tetraborate/ Proteolytic enzyme Protease C (Pr)+ polyhexamethyleneguanidine hydrochloride [PHMG], as antimicrobial (AM)

-biological active material -increases the AM desorption rateby 1.5-4.5 times For PHMG with M, 10000, total desorption of AM from the film could be obtained

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PVA film/ Sodium alginate/ Proteolytic enzyme Protease C (Pr)+ polyhexamethyleneguanidine hydrochloride [PHMG], as antimicrobial (AM)

-biological active material -decreases the rate of inactivation of Pr by 2 times -decrease the amount of desorbed AM by 10 times, giving the film self-disinfecting properties.

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Polymer system/ drug PVA film/ Sodium alginate (Alg)/ Proteolytic enzyme Protease C (Pr)+, a cationic polymeric antimicrobial (AM=Metacid) PVA film/ Tetraborate (TB)/ Proteolytic enzyme Protease C (Pr)+, a cationic polymeric antimicrobial (AM=Metacid) PVA film/ Sodium alginate/ Proteolytic enzyme Protease C (Pr)+, a cationic polymeric antimicrobial (AM=Fogucid) PVA film/ Tetraborate (TB)/ Proteolytic enzyme Protease C (Pr)+, a cationic polymeric antimicrobial (AM=Fogucid)

PVA/β-CD/salicylic acid

PEO/PVA PVA hydrogel UV crosslinked/ nitric oxide

acrylamide-functionalized nondegradable poly(vinyl alcohol) (PVA), UV- photocrosslinked

Properties -AM-s are derivatives of PMGH obtained by neutralization with HCl (Metacid) and H3PO4 (Fogucid) -The interactions between AM-s and PVA determine the modifying of the composite film morphology and as consequence the modifying of the water and water vapors sorption (Metacid increases the films water sorption and Fogucid decreases it). -The films swelling capacity influence the AM-s delivery: Fogucid is desorbed more rapidly than Metacid. -Incorporation of additives also influence the AM-s desorption from the composite films: In both cases, the AM-s desorption is more difficult, due to the diffusion hindrances caused by the increasing of the diffusing particles as a result of formation of a complex, in the case of Alg., and caused by the intermolecular crosslinks, in case of TB. -The vapors water sorption rate gradually increases in time for pure PVA films and decreases as absolute values by comparing to PVA pure films when Alg or TB are added; a more important decrease could be obtained when AM with higher molecular weight is added. -β-CD forms inclusion complexes with different water soluble substances i.e. salicylic acid - The drug release from the PVA/β-CD gel is nearly proportional to time -wound dressing NO release from NO-modified hydrogel occur over a time period up to 48 h., and there were no associated decrease in fibroblasts growth or viability in vitro associated with NO hydrogels. Exogeneous NO released from hydrogels wound dressing has potential to modulate healing. -As the PVA content increased from 10% to 20%, protein flux decreased, with no trypsin inhibitor (TI) permeating through 20% PVA hydrogels; -Further increase in model drug release was achieved by incorporating hydrophilic PVA fillers into the hydrogel. As filler molecular weight increased, TI flux increased. - Release studies conducted using growth factor in vehicles with hydrophilic filler showed sustained release of platelet-derived growth factor (PDGF-β,β) for up to 3 days compared with less than 24 hours in the controls. In vitro bioactivity was demonstrated by doubling of normal human dermal fibroblast numbers when exposed to growth factor–loaded vehicle compared to control.

Ref. 235

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3.3. Materials for Tissue Engineering There are three ways in which materials have been shown to be useful in tissue engineering: • • •

the materials able to induce cellular migration or tissue recognition; the materials are used to encapsulate cells and act as an immunoisolation barrier; the materials are used as matrix to support cell growth and cell organization.

Some reports showed that PVA-base hydrogels could be used in all the above mentioned ways. So, poly(vinyl alcohol) (PVA), physically crosslinked by repeated freeze-thawing cycles of polymer aqueous solutions, is widely employed to make hydrogels for biomedical applications. To increase the similarity between hydrogels and natural tissues and to obtain “polymeric hybrid tissues”, 3T3 cells have been incorporated, from a mouse fibroblast cell line, into PVA hydrogels obtained by one freeze-thawing cycle using as a solvent complete culture medium [239]. Hydrogels were also made using eight freeze-thawing cycles from PVA solutions prepared using as a solvent either complete culture medium or water. Cell adhesion experiments were performed by seeding 3T3 and human umbilical vein endothelial cells (HUVEC) on to the hydrogel surface. The obtained results show that PVA is not cytotoxic. Although PVA hydrogel surface characteristics do not seem to favor the adhesion of substrate-dependent cells, encouraging results were obtained with the 3T3 cells incorporation. DMA analysis indicates that the networks prepared by eight freeze-thawing cycles possess a mechanical consistency comparable, even slightly better, than the ones prepared by only one freeze-thawing cycle and used for the cell incorporation studies. Esmaiel Jabbari and Saeed Karbasi [240] noted that fibroblast cells seeded on N-vinyl pyrrolidone (NVP)-grafted PVA hydrogel, by using γ-radiation, had an extended oval morphology while those seeded on Acr.Ac.-grafted PVA had a rounded spherical morphology. These results support the use of NVP for grafting PVA to increase swelling and improve cell viability [240]. In order to achieve the firm fixation of the artificial cornea to host tissues, composites of collagen-immobilized poly(vinyl alcohol) hydrogel with hydroxyapatite were synthesized by a hydroxyapatite particles kneading method. The preparation method, characterization, and the results of corneal cell adhesion and proliferation on the composite material were studied. PVA-COL-HAp composites were successfully synthesized. A micro-porous structure of the PVA-COL-HAp could be introduced by hydrochloric acid treatment and the porosity could be controlled by the pH of the hydrochloric acid solution, the treatment time, and the crystallinity of the HAp particles. Chick embryonic keratocyto-like cells were well attached and proliferated on the PVA-COL-HAp composites. This material showed potential for keratoprosthesis application. Further study such as a long-term animal study is now required [241]. PVA/collagen substrate has been succesfull used also for osteoblasts grow [1]. Prosthesis, made by a composite body comprising polyvinyl alcohol hydrogel and ceramic or metallic porous body, has been proposed for a damaged bone, an artificial articular cartilage or an artificial intervertebral disc repairing. With this prosthesis, PVA hydrogel enhances lubrication and shock absorbing functions, and the porous body allows the ingrowth

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and ossification of the bone tissue of a living body therein to affinitively connect said hydrogel to the bones of the living body [242]. Nowadays the importance of knee meniscal function is recognized. The treatment for meniscus injury has been changing from resection to repair. However, depending on the type of injury, meniscectomy cannot be avoided. In consideration of the prognosis in such patients, artificial meniscus using polyvinyl alcohol-hydrogel (PVA-H) with high water content has been developed and performed an animal experiment as preliminary study. In the experiment using rabbits, the lateral meniscus was replaced with an artificial meniscus in one knee side and lateral meniscectomy was performed in another knee side of each rabbit. In the knees treated by artificial meniscus replacement, regressive changes were initially observed but did not progress after a certain period, and the articular cartilage state was good even after 1 year. In addition, neither wear nor breakage of PVA-H was observed. These results suggest that artificial meniscus using PVA-H with high water content compensates for meniscus function and is clinically applicable. However, for clinical application some problems such as fixation method, tolerance of PVA-H, remain to be solved [243,244]. To assess further the use of polyvinyl alcohol-hydrogel (PVA-H) artificial meniscus, some mechanical tests about PVA-H and animal experiment have been performed. In mechanical tests, it was found that a high water content PVA-H showed viscoelastic behavior similar to that of human meniscus. Moreover, the frictional coefficient of PVA-H against natural articular cartilage was also effective. In the animal experiment using rabbits, the lateral meniscus was replaced with an artificial meniscus in one knee side and lateral meniscectomy was performed in another knee side of each rabbit. In the results, the articular cartilage state of knee joint implanted PVA-H meniscus was good even after 2 years, while osteoarthrosis (OA) change progressed in meniscectomy knee joint. In addition, neither wear nor breakage of PVA-H was observed. These results proved that an artificial meniscus using a high water content PVA-H can compensate for meniscal function and might be clinically applicable [245,246]. The main disadvantage of hydrogels is their poor mechanical properties after swelling. In order to eliminate the disadvantage, hydrogels can be modified by physical blending [247,248] or/and chemical modification by grafting [249-251], crosslinking method [252254] and semi-interpenetrating or interpenetrating polymer networks [255,256]. In order to overcome this difficulties, blends of PVA and chitosan have good mechanical properties and the applications of these blends have been reported [257,258] Chitosan (poly-β(1,4)-dglucosamine), a cationic polysaccharide, is obtained by alkaline deacetylation of chitin, the principal exoskeletal component in crustaceans. As the combination of properties of chitosan such as water binding capacity, fat binding capacity, bioactivity, biodegradability, nontoxicity, biocompatibility, and antifungal activity, chitosan and its modified analogs have shown many applications in medicine, cosmetics, agriculture, biochemical separation systems, tissue engineering, biomaterials and drug controlled release systems [259-263]. Yang et al. [264] reported the preparation of PVA/chitosan blended membranes in various ratios and treated with formaldehyde. They were interested in studying the effect of chitosan content on the transport and equilibrium properties of membranes with of creatinine, uric acid and vitamin B12. 5-Fluorouracil (5-FU) is an antineoplastic agent that usually arrests tumor cells at the G1S phase of the cell cycle and the choice in the treatment of carcinoma of colon or rectum; it is also used in the treatment of precancerous dermatoses, especially actinic keratosis for which

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is the treatment of choice if the lesions are multiple [265]. The cytotoxic anticancer drug often causes severe side effects because it does not act selectively on the target. In order to control the release rate of 5-FU, chitosan/ PVA blended hydrogel membranes can be used as the protective drug coatings. It was found that the water content and water vapour transmission rates on the blended hydrogel membrane increased with increasing chitosan content. In antibacterial assessment, the antibacterial activity of all chitosan/PVA blended hydrogel membranes is similar. The viable cell number of aurococcus on the various chitosan/PVA blended hydrogel membranes is about (2.5 ±0.5)×107 cells/mL. The authors show that permeability of solutes such as creatinine, 5-FU and vitamin B12 through chitosan/PVA blended hydrogel membranes increase linearly with chitosan content in the blended hydrogel membranes, whereas there is a sharp change of permeability of uric acid through the chitosan/ PVA blended hydrogel membrane when the chitosan content is changed from 60 to 80% in the blended hydrogel membrane.

3.3.4. Biomembranes in Artificial Organs Hydrogel hybrid-type organs designed for implantation consists of living cells surrounded by suitable membranes. The living cells such as Langerhans islets, hepatoma (Hep G2), hepatocytes, etc, secreste specific compounds in response to the changes in body fluids. These systems work as a self-controlling bioreactor. The main point in design of an artificial organ is the choice of the suitable material and the preparation technique for membrane obtaining. The main requirements for the membrane are: • • • • •

permeabilty against water, oxygen and nutrients; permeability for specific secretations of living cells; impermeability to components of the immune system; resistance to the biodegradability in the body conditions; non-adhesive for proteins (avoiding their deposition)

Artificial organs could be obtained by two main techniques: 1. microencapsulation of a small amount of living cells in microcapsules that will be injected into the organism; 2. design of a masive container with semipermeable membrane walls that contain a high number of living cells and that could be implanted in the peritoneal cavity acting as a substitute of the damaged organ [266]. The principle of a bioartificial pancreas design is presented in figure 11.

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Figure 11. Scheme of a bioartificial pancreas surrounded by a hydrogel membrane [266].

Some methods used for artificial organs design are presented in table 17. Table 17. Design of some artificial organs Matrix

Crosslinker

poly(allyl amine) and PVA as extracellular matrices

-

crosslinked alginate covered by a PVA membrane

-alginate is crosslinked by Ca2+ions and PVA is crosslinked by GA

Entrapped cells hepatocytes encapsulated in Ba-alginate capsules Langerhans islets

alginate matrix covered with PMMA membrane

Langerhans islets

semipermeable membrane

pancreatic islet tissue

Applications

Ref.

-bio-artificial liver (BAL) that exhibit good metabolic functions such as albumin synthesis and ammonia removal -bio-artificial pancreas -this procedure caused denaturation of cellular proteins

267

-The shell has been deposit by interfacial precipitation -The cells are not damaged by this procedure and have a long term of survival - The development of the bioartificial pancreas for treatment of human diabetes

266

266

268,269

As it could be seen from the table 17, some methods of membranes obtaining could damage the living cells. The problems under study, related with artificial organs design are not only the obtaining of the suitable membrane, but also the possibilities of providing the suitable living conditions for the cells, avoiding their damage caused by the products of their methabolism.

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A lot of reports dials with biomembranes application in artificial kidney and pancrease achieving and with haemodialysis problems [270-272] because hydrogels have the ability to swell in water and retain a significant fraction of water within its structure without dissolving and they have physical properties similar to those of human tissues and possesses excellent tissue compatibility. Poly(vinyl alcohol) membranes satisfy the basic requirements for a bioartificial pancreas: good permeability for glucose, insulin and albumin but the passage of immunoglobulin G was completely prevented [273]. Furthermore, islets cultured in the PVA tubular membranes can perform their function of secreting insulin after 30 days in the static incubation study and rapidly releasing insulin through the membranes in response to changes in concentrations of glucose in the dynamic perifusion experiment [274]. Experimental data shown in Ref. 275 obtained from in vivo transplantation studies confirm that islets entrapped by the PVA tubular membrane chamber could change the glucose level in diabetic rats. When the m-2 [385] type of PVA chamber was implanted into streptozotocin induced diabetic rats, nonfasting blood glucose levels dropped from 500 ± 35 mg dL-1 to the lowest value (210 ± 22 mg dL-1). Furthermore, the performance of the bioartificial pancreas can be enhanced by the increased numbers of implanted chambers. If three m-2 chambers were implanted, nonfasting blood glucose levels in the diabetic rats decreased to 130–160 mg dL-1 and such a low blood glucose value was maintained for 1 month. This indicates that implanting three m-2 chambers in the diabetic rats could provide improved permeability of insulin to normalize blood glucose levels and improved survival of islets from the immune system of the recipient. Therefore, this membrane provides adequate performance for secretory products in an application as a synthetic extracellular matrix for a bioartificial pancreas.

3.4. Catalysis Membrane reactors have found utility in a broad range of applications including biochemical, chemical, environmental, and petrochemical systems. The variety of membrane separation processes, the novel characteristics of membrane structures, and the geometrical advantages offered by the membrane modules have been employed to enhance and assist reaction schemes to attain higher performance levels compared to conventional approaches. In these, membranes in a reactor existing as membrane laminates or physically separated membranes with a fluid phase between them, can provide particular combinations for functions, such as separation of products from the reaction mixture, separation of a reactant from a mixed stream for introduction into the reactor, controlled addition of one reactant or two reactants, segregation of a catalyst (and cofactor) in a reactor, immobilization of a catalyst in (or on) a membrane. Membranes can act as both catalyst and reactor; membranes perform a wide variety of functions, often more than one function in a given context. Membranes in a reactor can be employed to introduce/separate/purify reactants and products, to provide the surface for reactions, to provide a structure for the reaction medium, or to retain specific catalysts [276]. Membranes can be used as a matrix for immobilization of a catalyst. Four basic types of catalysts are relevant: (a) enzymes and (b) whole cells for biocatalysis; (c) oxides and (d) metals for nonbiological synthesis. Biocatalysts will be considered first since their immobilization in (or on) the membrane was explored much earlier. Five techniques have been studied in varying degrees. They are (1) enzyme contained in the spongy fiber matrix;

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(2) enzyme immobilized on the membrane surface by gel polarization; (3) enzyme adsorbed on the membrane surface; (4) enzyme immobilized in the membrane pores by covalent bonding; (5) enzyme immobilized in the membrane during membrane formation by the phase inversion process of membrane making. Membranes can also be used as a reactor where catalysts are used frequently. The membrane may physically segregate the catalyst in the reactor, or have the catalyst immobilized in the porous/microporous structure or on the membrane surface. The membrane having the catalyst immobilized in/on it acts almost in the same way as a catalyst particle in a reactor does, except that separation of the product(s) takes place, in addition, through the membrane to the permeate side. All such configurations involve the bulk flow of the reaction mixture along the reactor length while diffusion of the reactants/products takes place generally in a perpendicular direction to/from the porous/microporous catalyst. PVA/chitosan blend membranes can be applied for the synthesis of monoglyceride, when used as a membrane enzyme reactor [277]. Lipases can catalyze hydrolysis of esters, synthesis of esters, trans-esterification, and synthesis of some polymers. They have been applied in many fields including the food industry, fine chemistry, and the pharmaceutical industry. The low stability of native lipases makes them unsuitable for industrial applications. In order to use them more economically and efficiently, their operational stability can be improved by immobilization. Numerous efforts have been focused on the preparation of lipases in immobilized forms involving a variety of both support materials and immobilization methods [278]. It was reported that PEGylated lipase entrapped in PVA cryogel could be conveniently used in organic solvent biocatalysis [279]. This method for enzyme immobilization is more convenient in comparison to other types of immobilization that take advantage of enzyme covalent linkage to insoluble matrix, since the chemical step which is time consuming and harmful to enzyme activity is avoided. The application of this catalytic system to the hydrolysis of acetoxycoumarins demonstrated the feasibility of proposed method in the hydrolysis products of pharmaceutical interest and to obtain regioselective enrichment of one of the two monodeacetylated derivatives. Monoglyceride (MG) is one of the most important emulsifiers in food and pharmaceutical industries [280]. MG is industrially produced by trans-esterification of fats and oils at high temperature with alkaline catalyst. The synthesis of MG by hydrolysis or glycerolysis of triglyceride (TG) with immobilized lipase attracted attention recently, because it has mild reaction conditions and avoids formation of side products. Silica and celite are often used as immobilization carriers [281]. But the immobilized lipase particles are difficult to reuse due to adsorption of glycerol on this carriers [282]. PVA/chitosan composite membrane reactor can be used for enzymatic processing of fats and oils. The immobilized activity of lipase was 2.64 IU/cm2 with a recovery of 24%. The membrane reactor was used in a two-phase system reaction to synthesize monoglyceride (MG) by hydrolysis of palm oil, which was reused for at least nine batches with yield of 32–50%. J. Xu et al. [283] have shown that immobilization of enzymes can be done using a specially designed composite membrane with a porous hydrophobic layer and a hydrophilic ultrafiltration layer. A polytetrafluoroethylene (PTFE) membrane with micrometer pores as an excellent hydrophobic support for immobilization was employed for the porous hydrophobic layer, and a biocompatible material of polyvinyl alcohol (PVA) which provided a favourable environment to retain the lipase activity was used to prepare the hydrophilic

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ultrafiltration layer. Enzyme molecules are adsorbed in pores of the hydrophobic layer and deposited on the interface between the hydrophilic layer and the hydrophobic layer by filtration. The PTFE layer supplied a large hydrophobic interface area to immobilize lipases which is beneficial for lipase activation [284]. The ultrafiltration PVA layer played a key role in controlling the enzyme loading and preventing enzymes from being dissolved into the aqueous phase. Furthermore, the mass-transfer resistance of water and water-solubility products through the hydrophilic membrane is lower than that through the hydrophobic dense cortical layer of an asymmetric membrane, which could reduce the negative effect of diffusion and product inhibition. A composite membrane with a porous PTFE layer and an ultrafiltration PVA layer demonstrated high efficiency in immobilizing Candida rugosa lipase. The immobilized enzyme membranes were used in a biphasic membrane reactor (BMR) for the hydrolysis of olive oil. The optimum enzyme loading per unit membrane area is 0.042 mg-protein cm-2. In the BMR, lipases on the surface of the membrane were removed by the flow of organic phase, but the flow of the organic phase does not decrease the activity of biocatalytic membranes. The lipase immobilized at the interface of the PTFE membrane and PVA layer are stable. The maximum reaction rate per unit of membrane area (9.25 μmol h-1 cm-2) is be higher than the value reported in the literature [285] (2.18 μmol h-1 cm-2) and [286] (1.77 μmol h-1 cm-2). The immobilized lipase membrane in the BMR shows high activity for more than 30 h of reaction, with little change in the activity. One of the extensively used synthetic polymers used as a support for immobilization of biocatalysts is polyacrylamide (PAAm) [287,288]. The major advantage is that it can be polymerized either chemically or by using radiation. Advantages of γ-ray polymerization against chemical polymerization is that the polymerization can be carried out even under frozen conditions thus allowing the matrix to be molded to any form such as beads or membranes [289-291]. However one of the major drawbacks of this polymer especially in a membranous form is its brittleness. PVA has also been extensively used for immobilization of biocatalysts in a membranous form. As compared to PAAm, PVA is more hydrophilic and having adhesive property with better tensile strength in dry conditions. But it has high swelling index and dissolves readily in water when not cross-linked. PVA can be cross-linked using a variety of reagents including γ-rays. PVA/acrylamide blend membranes prepared on cheese cloth support by γ-irradiation induced free radical polymerization can be used for urease entrapment. The enzyme urease is entrapped in the membrane during polymerization process and using glutaraldehyde as crosslinking agent. The main advantage of this blend to this process is that it can be reused a number of times without significant loss of urease activity [292]. But, glutaraldehyde (GA) is a well-known toxic reagent and its presence in the PVA matrix as residuals unremoved by washing procedures could damage the organism tissues. P.A. Ramires and E. Milella [293] proposed a technique of PVA/hyaluronic acid and PVAgellan membranes crosslinking, by using GA in vapors state. They evaluated the harmful effects of GA residuals released from the membranes by the cytotoxicity and cytocompatibility in vitro tests, based on the cell culture method. The results showed that these materials have no toxic effects: they do not affect viability and proliferation nor exert damages on mithocondrial and lysosomal functions. The use of GA in vapor phase as

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crosslinking agent of natural and artificial polymer blends is demonstrated to be an effective way to avoid the presence of toxic residuals into materials [293].

3.5. PVA and PVA Derivatives-Based Membranes as Vapors and Gas Barrier PVA films have high water-vapor permeability (water-vapor-transmission coefficient PH2O is 270 g 0.1 mm/10 h m2 cm-Hg) [294] that increases rapidly with relative humidity and with decrease in the hydrolysis degree. PVA films have also a low gas permeability coefficient: PH2 = 6.6 × 10-13 mL cm/(cm2 s cm-Hg); PO2= 6.24 × 10-17 mL cm/(cm2 s cm-Hg); PF2 < -13 10 mL cm/(cm2 s cm-Hg); PN2 = 10-11 mL cm/(cm2 s cm-Hg); PCO2 = 10-13 mL cm/(cm2 s cm-Hg) [294]. The gas permeability increases with increase the relative humidity, with decrease hydrolysis degree of PVA, with increase temperature, and tends to decrease sharply as the degree of crystallinity increases. The decrease in crystallinity and the decrease in Tg would be expected to increase the gas permeability. Because of its low gas permeability, PVA has excellent flavour-retaining properties [18]. Physical crosslinked PVA cryogel is considered to have a good permeability for oxygen that is a desirable property for biomaterials [1]. Sometimes, in different systems, the oxygen presence is undesirable because of its reactivity and tendency to oxidize the contact materials that leads to corrosion of metallic materials or depreciation of food quality. Also oxygen could inhibit different chemical reactions or could interfere in different analysis (RES, polaroghaphy, etc.). Due to these practical aims, membranes with low oxygen permeability have been developed. Some of them are PVA, PVA blends or their derivative membranes, due to the PVA excellent oxygen barrier properties [18]. One of the PVA derivatives extensively used in this field is ethylene-vinyl alcohol copolymer (EVOH). Their blends with different polyolefins are also effective as oxigen barrier materials. Blend film oxygen permeability is influenced by the film composition and morphology. Generally, a heterogeneous structure, containing orientated fibrils and lamellae of EVOH evidences lower oxygen permeability than that emphasized by a more homogeneous morphology with finer dispersed particles (table 13 [295]). The O2 permeability of the blends obtained in the batch mixer decreases (from 59.1 to 47.7 mm cm3/m2 day-1 atm-1 for EVOH / PPlv and from 53.6 to 43.3 mm cm3/m2 day-1 atm-1 for EVOH/ PPhv) with the increasing of EVOH content from 12.5 to 25 vol%. The permeability for the extruded films was lower that those of the pressed films (22.1 mm-1 cm3/m2 day-1 atm-1 for 10 vol. % EVOH). Dry EVOH/PP-g-maleic mldehyde (MAH) blend, obtained by moulded injection also evidenced good barrier properties for toluene. This property is improved by increasing EVOH concentration which determines both size and deformation of the minor phase increase, indicating that the laminar structure becomes more pronounced [296]. But even the laminar structure is maximized a moulded injection sample is not likely to reach a permeability as low as expected for a multilayered system [296].

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Oxygen and toluene permeability of the blend film decreases as a nonlinear function with increasing the EVOH content, as it may be seen in table 19.

PPLv / (%)

PPhv / (%)

PP-g-MAH (%)

Remarks

HDPE / (%)

P O2 / / cm3 mm/ (m2 day-1 atm-1)

EVOH / (%)

Fibrils and lamellae

Fine dispersed particles

Morphology

Table 18. Influence of the films “composition and of the blend morphology on the films” permeability to O2 [295]

1225 1225 >25

-

X

-

-

58-80

Permeability independent of EVOH conc.

-

-

X

-

65-230

Permeability independent of EVOH conc.

-

-

X

-

>65

<12 <12 10 10 10 20 20

20

X 10 90 80 80 60

X 80 -

10 -

<65 <70 22-25 22.1 23.1-25.5 12.4 51.6

20

-

60

-

20

9.5

-interface between large particles of EVOH and PP can run from one side to the other of the film, created voids increasing the permeability. -smaller EVOH particles . -lover level of voids -draw ratio=3.4 -draw ratio=2.8 -draw ratio=2.8-8.7 -draw ratio=3.4 -draw ratio=3.4 -poor adhesion between PP and HDPE interfaces. -draw ratio=3.2 -lamellae coexists with fibrils

HDPE= high density polyethylene; PPLv= polypropylene with low viscosity; PPhv= polypropylene with high viscosity; PP-g-MAH= polypropylene graft maleic aldehyde.

Table 19. Oxigen and toluene permeability of melt-blended EVOH-Nylon 6(L), measured at 30 ºC [297] EVOH/Nylon 6(L) 100/0 75/25 50/50 25/75 0/100

P(oxygen)×1013 cm3 cm s-1 cm-2 cm-Hg-1 0.31 0.57 1.63 4.87 13.79

P (toluene) g mm m-2 24h-1 0.08 0.10 0.14 0.23 0.29

The EVOH-COOH compatibilizer use determines the increasing of the blend film oxygen permeability that becomes two orders of magnitude higher than that of a coextruded film with the same percentage of EVOH [298]. That means that EVOH-COOH acts that an interfacial agent. Excessive emission of CO2 has caused the most dramatic increase in global atmospheric temperature. So many countries’ governments and researchers pay much attention to how to predict, control and reduce the amount of CO2, emission. Compared to the absorption and

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adsorption techniques, membrane processes can be operated continuously and require less energy for the separation or purification. However, commercial polymer membranes cannot achieve both enough high selectivity and permeability to meet these needs. L. Xu et al. [299] have shown that polyvinylidene fluoride (PVDF)-PVA hydrogel membranes contained sodium carbonate solution and immobilized carbonic anhydrase can be used for removing CO2 in air. Hydrogel membranes are particularly attractive because of high permeability and separation factor [300], and good stability for CO2/N2 separation [299]. PVDF hollow fiber membrane modified by alkali was coated by PVA hydrogel on its surface and PVDF-PVA hydrogel membranes show better hydrophilic performance. For carbonate hydrogel (sodium carbonate concentration of 3.7 %) membrane, CO2, concentration from 1.3 % to 0.6 % in feed gas could be decreased to 0.9-0.4 % at the outlet at 25 °C. PVA/CELL blend could be also used to obtain the membranes with a low permeability for CO2 [301]. In the last years, the replacement of gasoline with other new fuels became a priority because of unavoidable depletion of natural petroleum sources. The methanol/gasoline fuel has been proved to be one of the best replacements for gasoline because of its low cost, high efficiency and low air pollution. Because of the corrosive character of methanol, the metal vials for storing fuels have to be changed. Polyolefins such as high density polyethylene (HDPE) have been considered as a potential material for methanol/gasoline fuel storrage because of their low cost, lightweight, easy design and processing, recyclability, safety, high chemical resistance to corrosion, and flexibility. An important draw back of the HDPE use for this purpose is its poor permeation resistance to hydrocarbon solvents, such as gasoline. Escaping of the gasoline vapor into the atmosphere could determine serious environmental pollution. Many efforts have been directed to finding methods that could reduce the HDPE permeability. One of them is HDPE blending with polymers such as polyamide (PA) or PVA with low permeability for hydrocarbons. To overcome the incompatibility between the nonpolar and polar polymers, a compatibilizer has to be present in these blends. The high permeation resistance of the polymeric blend against the hydrocarbons depends on the blend composition but also on the obtaining technique. So, multi-layer co-extrusion of PE, compatibilizer precursor (CP) and PA, laminar blend blow molding of PE, CP and PA blends, laminar blend blow molding of PE and modified PA (MPA) have been applied for low permeation materials obtaining. Because PA and CP did not sufficiently increase the HDPE permeation resistance, PVA has been introduced in the blend because of its recognized high barrier qualities. Good methanol/gasoline fuel permeation resistance together with clearly defined MPAPVA and MPA laminar structures were found in containers blow-molded from PE/PMPAPVA and PE/MPA blends, respectively, with an optimum CP of about 20 wt% [302].

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4. CONCLUSION In the recent years, many researchers have devoted attention to the development of membrane science and technology. Different important types of membranes, such as these for: nanofiltration, ultrafiltration, microfiltration, separation of gases and inorganic membranes, facilitated or liquid membranes, catalytic and conducting membranes, and their applications and processes, such as wastewater purification and bio-processing have been developed [303]. In fact, almost 40 % of the sales from membrane production market are for purifying wastewaters. Poly(vinyl alcohol) (PVA) has been characterized on many levels and examined for numerous applications. It is a polymer of great interest because of its relatively simple structure, easy processing, and potential use in biomedical and pharmaceutical fields. The possibilities to control the PVA’s biodegradability make from PVA a friendly polymer. Also the large possibilities to modify and control the PVA properties starting from synthesis process (such as molar mass, hydrolysis degree, OH groups repartition on the polymeric chain, tacticity) and also from its capability to react with a lot of reagents leading to polymer analogous compounds or to be cross-linked by chemical or physical ways make from PVA a versatile product. Also its capacity to be blend with other polymers or to be copolymerized with different co-monomers or to be doped with organic or inorganic compounds or to encapsulate drugs or enzymes enlarges the possibilities of PVA-based materials use. PVA capability of film formation, its mechanical resistance, high optical properties and the capacity of its hydrogels to swell in water and the hydrogels high sensitivity to the environmental alterations could characterize PVA as an intelligent material with special properties that could be tailored in function of the use interest. Hydrogel membranes fulfill many of the important conditions for most of abovementioned application fields. Therefore, we have focused our paper on the applications of PVA-based membranes in areas such as for separation membranar processes, fuel cells, sensors, biochemical/medical applications, catalyst or PVA derivatives membranes as gas and vapor barriers. However, PVA is also extensively used in other different forms, such as gel matrices, micro and nano spheres, aerosols, aqueous solution, films, powder etc. Although some of the different types of PVA gels have been referred in chapter 3.3, it still remains much more to say. This clearly proves that PVA is an old, yet new polymer or, in other words, an old polymer with a promising future, due to its capacity to respond to all the actual society priorities: clean technologies, non-toxicity, biocompatibility, biodegradability, intelligent materials.

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In: Organic and Physical Chemistry Using Chemical Kinetics … ISBN: 978-1-60021-763-0 Editors: Y.G. Medvedevskikh, et al. pp. 167-171 © 2007 Nova Science Publishers, Inc.

Chapter 10

THE RESEARCH ON THE PROCESS OF THERMOMECHANICAL DESTRUCTION IN POLYPROPYLENE G. M. Danilova-Volkovskaya1 and E. A. Amineva2 1

Rostov-on-Don Agricultural Machinery State Academy 344023, Strana Sovetov Street, 1, Rostov-on-Don. e-mail: [email protected] 2 Ushakov Naval State Academy 353900, Lenin Avenue, 93, Novorossiysk

ABSTRACT There has been investigated the effect of thermo-mechanical impact conditions on destruction kinetics in polypropylene melts. The conditions served as a basis for obtaining quantitative dependencies and mathematical expressions aimed at describing destruction processes.

Keywords: polypropylene, mechanical destruction, oxidation rate, hydroperoxides. The research on the processes of mechanical destruction in deformed polypropylene (PP) melts was conducted with the aid of stable radical (tripentachlorphenylmethyl) consumption. There was defined the dependence of radical generation rate on shear rate. At low values γ it is approximate to linear. The rate of thermal priming of radicals at 220 °С equals Vi = 2.10 -7 mole/kg.sec. The contribution of mechanical priming to the dependence of radical generation rate becomes predominant as early as at γ =0,01 sec -1. The temperature dependence of radical generation rate in the Arrhenius coordinates at

&

γ& =0,76 sec -1 has an extreme character (figure 1), passing the minimum at 200°С. The low

temperature part of the curve corresponds to negative activation energy which manifests the predominance of mechanical priming process in this region. In the high-temperature region

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thermal priming is substantially observed, activation energy in this part of the curve is positive. Obviously, the area of minimal priming rates is optimal for processing since here mechanical priming is not prominent any more, while thermal priming has not reached great values yet. Under real processing conditions the position of the minimum at the temperature dependence of priming rate can change due to the presence of oxygen. However, the temperature defined in the current paper can be regarded as a starting point for searching optimal temperature conditions. At the initial period of mechanical destruction in a polypropylene melt in inert atmosphere the concentration of macromolecules increases (figure 2). The dependence of destruction rate (Vi ) on temperature is linear in the Arrhenius coordinates. After a certain

Figure 1. The temperature dependence of radical generation rate at γ& =0,76 sec -1.

Figure 2. The kinetics of changes in the concentration of PP macromolecules at thermo-mechanical impact:11800C, 2-2000C, 3-2300C.

The Research on the Process of Thermo-Mechanical Destruction in Polypropylene 169 period of thermo-mechanical impact (about 10 minutes) the concentration of macromolecules −4

falls to a certain value (23.10 mole/kg), it doesn’t change further. Oxidation decomposition of deformed isotactic PP manifests a number of noticeable properties: With the growth of deformation degree λ in polymer samples, the periods of oxidation induction τ dramatically increase, τ is exponentially dependent on λ:

τ = τ 0 exp(aλ ) ,

(1)

where τ0 and a depend on oxygen pressure. Oxygen uptake is described by a kinetic law:

[O2 ] = Ф2 (t −τ )2 ,

(2)

i.e. after induction period τ oxidation of an oriented polymer remains a chain degeneratebranch process with quadratic breakdown of kinetic chains. The law holds true only after oxygen uptake equaling 2 . 10-2 mole/kg. Orientation also influences initial oxidation rates, i.e. parameter Ф depends on λ but it does not affect further stages, maximum oxidation rates don’t depend on λ at all. Upon annealing the difference in the values of τ disappears. The behaviour of chain-length distribution is non-characteristic: during thermal-oxidative degradation of isotropic PP films the degradation shifts towards decrease in molecular mass, while during oxidation in deformed films it shifts towards increase in molecular mass. It means that with oxidation in isotropic samples in the induction period the destruction of molecules prevails. On the other hand, with oxidation in deformed samples attachement and cross-linking dominate. A third peculiarity of oxidation in deformed PP is a dramatic decrease in the escape of hydroperoxide, the main branching component. Hydroperoxide escape а sharply drops with the growth of λ (figure 3), in accordance with equation

a = a 0 exp (− b λ ) ,

(3)

It implies that in deformed PP — unlike with oxidation of most isotropic non-deformed polymers — oxygen changes into products other than peroxides (alcohols, ethers, ketones, etc.). This effect is not due to deformation impact on hydroperoxide stability: rate constants of thermal decomposition of hydroperoxide in PP are the same for both isotropic and deformed samples. Moreover, even at 20°С, when hydroperoxide is stable, its escape during radiationinduced oxidation sharply drops with the growth of λ. At deformation there is no more than a slight change in degree of PP crystallization, at annealing there is even an increase. Because oxidation is localized in the amorphous phase, it was logical to expect that at annealing the induction period should grow and oxidation rate

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should drop proportionally to degree of crystallization. Both of these suggestions fail; therefore, the increase in thermo-oxidation stability in deformed PP is not connected with changes in degree of crystallization.

Figure 3.The kinetics of oxygen uptake by deformed PP samples at deformation degree: λ:

= 0 (1), λ =

4,5 (2); λ = 7 (3); λ = 9 (4). Neither is it connected with oxygen solubility and diffusion, since oxygen solubility in deformed polymers decreases by 5-10 times, and diffusion coefficient lessens significantly. Oxidation kinetics of oriented PP was measured under conditions of external priming. The parameter specifying the oxidability of a polymer is slightly dependent on deformation. For instance, at 200°С it only decreases by 1.5 times with λ changing from 0 to 10. This unambiguously clarifies that the main reason for increase in thermal-oxidative stability of deformed PP is a sharp drop in the escape of a branching agent (hydroperoxide), i.e. a decrease in hydroperoxide escape. This conclusion is consistent with experimental observations: in the induction period chains are not initiated; after the induction period oxygen uptake occurs, but hydroperoxide does not form, i.e. kinetic chains are missing. Oxygen is consumed only in priming events, but the escape of radicals is insignificant and oxygen uptake in a chain reaction is negligibly small. In priming events internal interaction of radicals prevails, which provides for recombination, cross-linking and shift of chain-length distribution towards greater masses. The nature of these interactions has not been explicitly defined, it could be explained by disproportionation [1]. This accounts for low values of hydroperoxide escape, formation of cross-links and alcohol groups during initial periods of deformed PP oxidation. Chain decomposition of hydroperoxide, formed by means of valence transfer along the molecule, is considered to be another reason for decrease in hydroperoxide escape. Thus, slowdown in valence transfer rate and a dramatic decrease in the escape of radicals during priming lead to depression of the oxidation process and to the lessening of branching agent escape. Oriented deformation behaves like substances decomposing hydroperoxide without formation of radicals, i.e. it is a means of “stabilisation in absence of a stabilser”. The conducted investigations and the obtained quantitative dependencies and expressions were used for developing a method of criterial assessment of the degree of thermo-

The Research on the Process of Thermo-Mechanical Destruction in Polypropylene 171 mechanical destruction in PP melts during processing under the conditions of intensive shear deformations[2]

Figure 4.The kinetics of hydroperoxide formation in PP samples at deformation degree: λ = 0 (1), λ = 4,5 (2); λ = 7 (3); λ = 9 (4).

CONCLUSIONS There has been investigated the effect of thermo-mechanical impact conditions on destruction kinetics in polypropylene melts. The conditions served as a basis for obtaining quantitative dependencies and mathematical expressions aimed at describing destruction processes.

REFERENCES [1] [2]

Baramboymb I.K. Mechanochemistry of high-molecular substances. – 3rd edition. Moscow. The Chemistry publishing house, 1978, p. 34. Danilova-Volkovskaya G.M. The effect of processing parameters and modifiers on the properties of polypropylene and PP-based composite materials. — Doctoral Thesis (technical sciences). 2005, p. 273.

In: Organic and Physical Chemistry Using Chemical Kinetics … ISBN: 978-1-60021-763-0 Editors: Y.G. Medvedevskikh, et al. pp. 173-185 © 2007 Nova Science Publishers, Inc.

Chapter 11

ZINCCONTAINING POLYMER - INORGANIC COMPOSITE AS VULCANIZATION ACTIVE COMPONENT FOR RUBBERS OF GENERAL AND SPECIAL ASSIGNMENT V. I. Ovcharov, I. A. Kachkurkina, O. V. Okhtina and B. I. Melnikov Ukrainian State Chemical-Technological University, Dnepropetrovsk, Ukraine; [email protected]

ABSTRACT In work the synthesis technology of zinccontaining polymer - inorganic composite on the basis of products of secondary raw material processing at joint precipitating with carbamide and formaldehyde (ZnCFO) is described. The structure and properties of ZnCFO are investigated by the differencial-thermal analysis, electronic microscopy and IR-spectroscopy. The ZnCFO action as vulcanization active component of elastomeric compositions on the basis of rubbers of general and special assignment with various vulcanization systems is investigated. The comparative estimation of ZnCFO efficiency depending on type of vulcanization system is given. The ZnCFO influence on character of formed morphological structure of rubbers is determined by the method of percalation analysis.

Key words: Polymer-inorganic composite; Vulcanization active component; Elastomeric composition; Vulcanization; Morphological structure; Physical-mechanical properties.

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INTRODUCTION Despite of 150-year's history of vulcanization process, it is impossible to consider that fundamental and applied researches in direction of vulcanization systems perfection are completed. For today one of the ways of rubbers properties improvement is the synthesis and application of the new chemicals-additives, including, vulcanization active, that is connected, first of all, with reduction of global stocks of zinc ores as basic raw material for reception of traditional activator - zinc oxide. Besides, modern increase of industrial potential and the accumulation of big quantity wastes derivate the problems of ecological character, which require the emergency decision. Therefore creation of resourcesaving technologies of the new compounds reception from products of secondary raw material processing has paramount importance.

EXPERIMENTAL Taking into account above told, in the work the efficiency of zinccontaining carbamideformaldehyde composite (ZnCFО) as vulcanization active component of various vulcanization systems for rubbers of general and special assignment is investigated for the first time. The technological circuit of ZnCFО synthesis is developed in the Ukrainian State Chemical-Technological University. ZnCFО is the product of reaction of carbamide and formaldehyde polycondensation in zinc salts solution at recycling of metalcontaining wastes of chemical manufactures. The material base of ZnCFО manufacture are fulfilled catalysts, solutions from zincing and others zinccontaining wastes of various origin. The maximal degree of zinc extraction (φ Zn2+) = 95-98 % and mass ratio of zinc hydroxide to carbamide-formaldehyde component in composite (mZn(OH)2 : mCFО) = 1:0,7-1 is achieved at the observance of the following technological parameters: temperature (Т) = 2535 0С; concentration of zinc salts in solution (с Zn2+) = 150-170 g/l; pH of zinc salts solution = 2; pH of the reactionary mix at complete precipitating Zn2+ = 7-8; pH of the reactionary mix at polycondensation = 3-5; mole ratio of carbamide to formaldehyde (nC : nF) = 1:1 [1,2].

Figure 1. EM micrographs of the ZnO (a) and ZnCFO (b) particles (increase in 10000 times)

Zinccontaining Polymer - Inorganic Composite as Vulcanization…

175

The electronic microscopy method on the EM-125 (fig. 1) for definition of ZnCFО particles size and characteristic of its surface was applied. Known zinc oxide was chosen as the object of comparison. The electronic photos of powders testify, that new composite and zinc oxide have external similarity under the form of particles, wide range on dispersiveness (0,4-6,0 microns for zinc oxide, fig. 1a; 0,3-6,0 microns for ZnCFО, fig. 1b) also contain as crystal as amorphous phases in their structure. 0 0

810 C

a)

0

450 C-460 C

exo

20

0

endo

40

Zn(OH)2 CF ZnCF 0

0

200

b)

180 C

100

170 C -

0

0

80

90 C-100 C

60

400

600

800

0

t, C

1000

m, % 0

Zn(OH)2 CF ZnCF

10

20

30

40

50 200

400

600

800

0

t, C

1000

Figure 2. Results of derivatographic researches of Zn(OH)2, CFO and ZnCFO: a – DTA curves, b – TG curves

The definition of thermal stability of inorganic zinccontaining (Zn(OH)2), organic carbamide-formaldehyde (CFO) components and ZnCFО composite was carried out by the method of differencial-thermal analysis on the derivatograph "Q-1500 D" of F. Paulik, J.

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Paulik, L. Erdey system in the temperature range 20-1000 0C at heating rate 10 0C/min and mass of samples 200 mg. DTA and TG curves of researched products are given on fig. 2. How it is shown, endothermic peak on DTA curve of Zn(OH)2 and greatest loss of weight at t ≈ 150 – 160 0C are caused by transition of hydroxide in oxide. DTA curves of CFO and ZnCFО have external similarity on character of the thermal effects, however, for ZnCFО the shift of maximum in range of lower temperatures is observed. So, peaks at t ≈ 90 – 100 0C are caused by loss of atmospheric moisture containing in samples. Endothermic maximum and greatest loss of weight (≈ 35 %) in temperature range 260 – 270 0C characterize the beginning of CFO thermodestruction, and secondary exothermic peak at t ≈ 560 0C is caused by the subsequent decomposition of sample. Unlike CFO on DTA curve of ZnCFО the first endothermic maximum is observed at t ≈ 170 – 180 0C, and secondary exothermic - at t ≈ 450 – 460 0C, describing decomposition of organic component. The occurrence of new endothermic peak in range t ≈ 810 0C testifies about expansion of temperature range of ZnCFО destruction process in comparison with CFO, because the temperature interval of weight loss for CFO is 260 – 560 0C, and for ZnCFО - 170 – 810 0C, and ZnCFО has extremely greater rest of weight. It is necessary to note, that ZnCFО at thermal action is decomposed not achieving a melting point, that was confirmed by the method of definition of melting temperature in capillary [3,4]. During experiment the intensive escape of gas and change of sample colour from white to grey at temperatures 170 0C and 220 0C, appropriating to first endothermic peak on DTA curve, were visually observed.

110

T, %

Zn(OH) 2 CFO ZnCFO

2360

100 1384 90 80 70

1640 1550

60 50 1120

40

3350 30 20 10 400

800

1200

1600

2000

2400

2800

3200

3600

v, cm

4000

-1

Figure 3. IR-spectrums of absorption of ZnCFO and its inorganic (Zn(OH)2) and organic (CFO) parts

The study of ZnCFО also was carried out by the method of IR-spectroscopy on spectrometer UR-20. For detection of possible chemical bonds between inorganic and organic components in ZnCFО the spectras of Zn(OH)2, CFО and ZnCFО were studied (fig. 3) . As it is shown, IR-spectrum of ZnCFО repeats the characteristic absorption bands of CFО at 3350, 1640 and 1550 cm-1, caused by presence of secondary amide group [5], at the same time the

Zinccontaining Polymer - Inorganic Composite as Vulcanization…

177 H

R2C

N

group, is intensity of absorption band in range 2340-2360 cm-1, identifying considerably decreased [6]. In comparison with IR-spectrum of Zn(OH)2 on ZnCFО spectrum the intensity of characteristic absorption band at 1384 cm-1 is decreased. The distinctive feature of ZnCFО spectrum is the presence of absorption band at 1120 cm-1, which probably corresponds to bonds (for example, coordination) between inorganic and organic components of the composite. It is possible to assume, that the coordination bonds in the composite arise H R2C

N

group and zinc in Zn(OH)2. between nitrogen atom of The researches of ZnCFО compatibility with the matrix of isoprene rubber in plasticorder "Brabender" PLE 6511 have shown, that the disperse process of composite is accompanied by lower power consumption and its best compatibility in comparison with zinc oxide (fig. 4). The absence of ZnCFО particles as extraneous impurities in rubber mix also was visually observed, while the zinc oxide particles were well appreciable [7]. ZnCFO ZnO

MV, N*m 70

65

60

55

50

45 0,0

2,5

5,0

7,5

activator, phr. Figure 4. Rheological properties of the modeling unfilled rubber mixes on the basis of isoprene rubber with a various type and contents of sulfur vulcanization activators

That is, the given results of experimental researches have confirmed composite, chemically connected structure of ZnCFО with presence of functionally active groups, which due to the organic-inorganic nature has certain relationship with a rubber matrix, is easy dispersed and combined with its. An estimation of ZnCFО efficiency as vulcanization active component was carried out in modelling unfilled elastomeric compositions on the basis of isoprene, butadiene-nitrile, chloroprene and butyl rubbers of sulphur, thiuram, peroxide, metaloxide and resin vulcanization systems.

1 The researches were carried out by the professor E. Djagarova at University of Chemical Technology and Metallurgy (Sofia, Bulgaria)

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The rubber compounds were mixed in a laboratory internal mixer, the tests of elastomeric compositions were carried out according to working techniques and requirements of state accepted standard [8,9].

RESULTS AND DISCUSSION The influence of ZnCFО concentration (3,0; 5,0; 7,0 phr) on formation of properties complex of the unfilled rubber mixes and their vulcanizates on the basis of isoprene rubber of the following recipe, phr: isoprene rubber - 100,0; sulfur - 1,0; di - (2-benzothiazolyl) disulfide - 0,6; N, N'-diphenylguanidine - 3,0; stearic acid - 1,0, was carried out in comparison with the known activator - zinc oxide (5,0 phr). The analysis of Rheometer data of sulfur vulcanization process of elastomeric compositions at 1550C (fig. 5) shows, that on crosslink density and cure rate, about what the constants of speed in the main period (k2) testify, they surpass the control composition with 5,0 phr of zinc oxide. Improvement of the complex of elastic - strong parameters of rubbers with ZnCFО as at normal test conditions, and after thermal air aging (tab. 1), probably, is caused by influence of the new activator on vulcanization network character. So, the percent part of polysulfide bonds (C-Sx-C) and amount of sulfur atoms appropriating to one crosslink (S atoms/crosslink) in vulcanizates with ZnCFО are decreased, the percent part of disulfide bonds (C-S2-C) is increased (fig. 62). M, dN*m 20 18

4 3 2

16

1

14 12 10 8 6 4 0

5

10

15

20

25

t,m in

30

Figur 5. Rheometer data of sulfur vulcanization process of modeling unfilled elastomeric compositions on the basis of isoprene rubber at 1550C with ZnCFO as the activator: 1 – ZnO – 5,0 phr., k2 = 0,47 min-1; 2 - ZnCFO – 3,0 phr., k2 = 0,51 min-1; 3 - ZnO – 5,0 phr., k2 = 0,58 min-1; 4 - ZnO – 7,0 phr., k2 = 0,69 min-1

2 The researches were carried out by the professor W. M. Rzymski at Technical University (Lodz, Poland).

Zinccontaining Polymer - Inorganic Composite as Vulcanization…

179

Table 1 Properties of the modeling unfilled vulcanizates on the basis of isoprene rubber, containing various concentration of the ZnCFO activator

Parameter

ZnO 5,0 phr. 10,0/9,0* 27,0/20,5 890/735 39/28 38/35 62/60

300% Modulus, MPa Tensile strength, MPa Elongation at break, % Tear strength, kN/m Shore A hardness Elasticity, %

Activator type ZnCFO 3,0 phr. 5,0 phr. 10,0/9,0 11,0/10,0 26,0/22,4 28,5/22,8 830/750 835/750 41/38 43/39 40/36 42/38 66/64 69/65

7,0 phr. 10,0/9,0 20,6/19,4 835/730 40/32 42/38 68/64

The note: * - in the denominator the parameter value after thermal aging of the sample at 1000C×24 hrs is given

ZnO as activator of sulfur vulcanizat ion system S

atoms

/ crosslink = 7,6

70% 26% 4% ZnCFO as activator of sulfur vulcanization system S

atoms

/ crosslink = 7, 3

68% 28 % 4% Figure 6. Influence of activator type on vulcanization network character of the elastomeric compositions: - % part of C – Sx – C bonds; - % part of C – S2 – C bonds; - % part of C – S – C bonds.

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That is, the analysis of the received results, has shown an opportunity of equal-mass replacement of the traditional activator - zinc oxide on the new polymer - inorganic composite (5,0 phr) at maintenance of a high activation level of sulfur vulcanization process of rubber mixes on the basis of diene isoprene rubber and improvement of the physical-mechanical properties complex of their vulcanizates. sulfur vulcanization system ZnO 5,0 phr.;

M, dN*m

=0,29 min

-1

ZnO 3,0 phr.;

ZnCF

3,0 phr.;

2

=0,22 min

-1

ZnCF

5,0 phr.;

=0,25 min 2

-1

=0,29 min

-1

ZnCF

30

2

thiuram vulcanization system

7,0 phr.;

2

M, dN*m 24

24

2

=0,33 min

-1

ZnCF

3,0 phr.;

=0,41 min

-1

2

Zn

5,0 phr.;

=0,56 min 2

-1

Zn

7,0 phr.;

=0,58 min

-1

2

18

18

12 12

6

6

0

5

10

15

20

25

0

30

5

10

15

20

25

30 t, min

t, min

peroxide vulcanization system ZnO 3,0 phr.; M, dN*m 28

=0,11 min

-1

2

-1

ZnCF

3,0 phr.;

2

=0,08 min

ZnCF

5,0 phr.;

2

ZnCF

7,0 phr.;

2

-1

=0,12 min

-1

=0,13 min

24 20 16 12 8 4 0

5

10

15

20

25

30

t, min

Figure 7. Cure curves of vulcanization process of modeling unfilled elastomeric compositions on the basis of nitrile-butadiene rubber at 1550C with various vulcanization systems.

Zinccontaining Polymer - Inorganic Composite as Vulcanization…

181

It is known, that zinc oxide is not only activator of sulfur vulcanization of diene rubbers, but also component of others vulcanization systems, therefore the further research of the ZnCFО efficiency was carried out in elastomeric compositions on the basis of polar butadiene nitrile rubber of general and special assignment of sulfur, thiuram and peroxide vulcanization. Influence of the ZnCFО contents (3,0; 5,0; 7,0 phr) on crosslink kinetics of the modelling unfilled rubber mixes from NBR-26 of sulfur, thiuram and peroxide vulcanization of recipe, phr: NBR-26 - 100,0; sulfur - 1,5; 2-mercaptobenzthiazole - 0,8; stearic acid – 1,5; tetramethylthiuramdisulfide - 3,0; peroximon F-40 - 3,0, is possible to estimate on the data of fig. 7. As it is shown, the increase of ZnCFО concentration results in increase of the maximum torque and, accordingly, crosslink degree of elastomeric compositions, decrease of optimum cure time, that, in turn, causes increase of cure rate, confirmed by counted constants of speed in the main period (k2). The analysis of vulcanizates physical-mechanical properties testifies, that with the increase of ZnCFО contents increase the tensile strength, hardness, resilience; elongation at break and residual deformation at compression on 20 %. That is, ZnCFО is effective component of given vulcanization systems, as at equal-mass replacement of known zinc oxide (5,0 phr) the cure rate, the concentration of crosslink bonds are increased and general properties complex of rubber mixes and their vulcanizates is improved. M, dN*m 75

ZnCF ZnCF ZnCF

60

3,0 phr.; 5,0 phr.; 7,0 phr.

45

ZnO 3,0 phr.; ZnO 5,0 phr.; ZnO 7,0 phr.

30

15

0

5

10

15

t, min Figure 8. Cure curves of metaloxide vulcanization process of modeling unfilled elastomeric compositions on the basis of chloroprene rubber at 1550C with various type and contents of vulcanization agents

The comparative estimation of efficiency of zinc oxide and ZnCFО similar concentrations (3,0; 5,0; 7,0 phr) as the agents of metaloxide vulcanization system was carried out on example of modelling unfilled elastomeric compositions from chloroprene rubber of recipe, phr: chloroprene rubber - 100,0; magnesium oxide - 7,0. Kinetic curves of rubber mixes curing process at 1550C are shown on fig. 8. The analysis of the submitted data testifies, that at increase of zinc oxide contents vulcanization kinetics is changed as follows: the scorch time and optimum cure time are decreased, the cure rate is increase. Vulcanization

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process of rubber mixes at ZnCFО presence proceeds similarly, however, they surpass on 1522 % compositions with zinc oxide on crosslink degree parameter. The estimation of elastic strong properties of rubbers in vulcanization optimum has shown, that ZnCFО provides them higher parameters level and resistance to thermal air aging (tab. 2). Table 2. Properties of modeling unfilled elastomeric compositions on the basis of chloroprene rubber in vulcanization optimum Parameter

Contents of ZnO, phr

Contents of ZnO, phr

3,0

5,0

7,0

3,0

5,0

7,0

Tensile strength, MPa, unaged samples

22,2

25,5

28,3

24,1

26,3

28,9

0

17,8

20,4

22,6

19,5

21,3

23,4

0

16,2

18,6

20,7

17,6

19,5

21,3

120 С×12 hrs 120 С×24 hrs Tear strength, kN/m unaged samples

32

37

38

33

37

39

0

23

26

27

26

29

31

0

27

31

33

29

33

35

120 С×12 hrs 120 С×24 hrs

For continuation of research of ZnCFО efficiency in structure of various vulcanization systems its was entered into the rubber mix on the basis of butyl rubber of resin vulcanization of following recipe, phr: butyl rubber-1675 - 100,0; amberol ST-137 - 5,0; stearic acid - 3,0, at equal-mass replacement of zinc oxide (3,0 phr). The influence of ZnCFО on kinetics of resin vulcanization at 1600C is shown in a fig. 9, which analysis testifies, that in comparison with control mix the researched composition is characterized by decrease of crosslink degree, preservation of scorch time and reduction of optimum cure time, causing increase of cure rate. I.e., at ZnCFО use as a component of resin vulcanization the acceleration of formation process of crosslinking network with low density of crosslink bonds is observed which explains the unsatisfactory level of physical-mechanical parameters of rubber. The ZnCFО negative influence on properties of elastomeric compositions of resin vulcanization is caused by interaction between the vulcanization agent (phenol-formaldehyde resin on the basis of poctylphenol – ST-137) and ZnCFО, that results in desactivation of resin as crosslinking agent of resin vulcanization system.

Zinccontaining Polymer - Inorganic Composite as Vulcanization…

183

M , dN*m ZnO - 3,0 phr. 24 22

ZnCF

- 3,0 phr.

20 18 16 14 12 0

10

20

30

40

50

t, m in

60

Figure 9. Vulcanization kinetics of modeling unfilled elastomeric compositions on the basis of butyl rubber of resin vulcanization at 1600C with ZnO or ZnCFO

Thus, from the analysis of results of experimental researches on estimation of ZnCFО vulcanization activity in comparison with zinc oxide in structure of various vulcanization systems (VS) follows, that its efficiency decreases in line (fig. 10): sulfur VS > thiuram VS > metaloxide VS > peroxide VS > resin VS % 40 35 30 25 20 15 10 5 0

sulfur VS

thiuram VS

metaloxide VS

peroxide VS

Figure 10. Change of elastomeric compositions properties (%) with various vulcanization systems at ZnCFO presence (in comparison with ZnO): - crosslink degree (∆М, dN·m); - tear strength (В, кN/m).

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Taking into account the ZnCFО positive influence on formation of the complex of the physical-mechanical characteristics of vulcanizates on the basis of various rubbers and theoretical preconditions about interrelation "recipe - structure - property", it was interested to define the morphology features of elastomeric compositions. With this purpose the percalation method of the analysis by the rheometer data of rubber mixes was used [10]. According to the theory of interrelation "recipe - structure - property" the maximum level of the physical-mechanical characteristics of elastomeric compositions is realized at condition of heterogeneous structure formation with the minimal particles size of heterophase (r - value, opposite to tangent of the corner of kinetics curve inclination) and its optimum contents. The analysis of data submitted on the fig. 11 shows, that replacement of zinc oxide on ZnCFО composite in various vulcanization systems for rubbers of general and special assignment influences on morphological structure of compositions, reducing the particles size of heterophase and providing thus high complex of the elastic-strong properties of vulcanizates. It is necessary to note, that at increase of the ZnCFО contents from 5,0 up to 7,0 phr parameter r essentially does not change and keeps the minimal value. I.e., the best complex of properties have the compositions with ZnCFО, in which the morphology with the minimal particles size of heterophase is formed at its contents ≈5,0 phr. The given statement is coordinated with the results of physical-mechanical tests of vulcanizates, received by experimental method. isoprene rubber of sulfur vulcanization nitrile-butadiene rubber of sulfur vulcanization nitrile-butadiene rubber of thiuram vulcanization nitrile-butadiene rubber of peroxide vulcanization chloroprene rubber of metaloxide vulcanization

r

isoprene rubber of sulfur vulcanization nitrile-butadiene rubber of sulfur vulcanization nitrile-butadiene rubber of thiuram vulcanization nitrile-butadiene rubber of peroxide vulcanization chloroprene rubber of metaloxide vulcanization

r 0,40

0,40

0,36

0,36

0,32

0,32

0,28

0,28

0,24

0,24

0,20

0,20

0,16

0,16

0,12

0,12

0,08

0,08

0,04

0,04

0,00

0,00 0

1

2

3

4

5

6

7

0

1

2

3

4

contents of ZnO, phr

a)

5

6

7

contents of ZnCFO, phr

b)

Figure 11. Dependence of particles size of heterophase of modeling unfilled compositions on the basis of various rubbers with different vulcanization systems from the ZnO (a) or ZnCFO (b) contents

It is possible to explain the decrease of ZnCFО efficiency as component of various vulcanization systems for rubbers of general and special assignment in the earlier submitted line (fig. 10) also by character of formed morphology of compositions. So, at use of ZnCFО as the activator of sulfur vulcanization the structure of rubbers with the minimal value of parameter r is formed, and at transition from sulfur to peroxide vulcanization of elastomeric compositions the particles size of heterophase is increased (fig. 11 b).

Zinccontaining Polymer - Inorganic Composite as Vulcanization…

185

CONCLUSION Generalizing results of researches of the ZnCFО efficiency as the component of various vulcanization systems for rubbers of general and special assignment, it is possible to make the following conclusions: 1. ZnCFО is the chemically connected composite with presence of functionally active groups, which due to the organic-inorganic nature, is easy dispersed and combined with rubber matrix; 2. ZnCFО is the effective vulcanization active component of the sulfur, thiuram, peroxide and metaloxide vulcanization systems for isoprene, nitrile-butadiene and chloroprene rubbers; at the same time it is not effective in resin vulcanization system for butyl rubber. On a degree of positive influence on the properties of elastomeric compositions vulcanization systems with ZnCFО are arranged in a line: sulfur VS > thiuram VS > metaloxide VS > peroxide VS; 3. ZnCFО at the contents ≈5,0 phr promotes to formation of morphological structure of compositions with the minimal particles size of heterophase, that is realized in the improvement of physical-mechanical properties of rubbers.

REFERENCES [1] [2] [3] [4]

[5] [6] [7]

[8] [9] [10]

Melnikov B.I., Perekhrest O.A., Demidov D.V., Machula S.L. // Khimichna Promislovist Ukraini. 2000. N 3. P. 32-35. Kachkurkina I.A., Ovcharov V.I., Okhtina O.V. // Voprosi Khimii i Khim. Tekhnologii. 2005. N 5. P. 134-139. Uendland U. Termicheskie metodi analyza. Mir, Moskva, 1978. P. 526. Ćwiczenia laboratoryjne z chemii I technologii polimerów / Pod red. Ireny Słowikowskiej. Ofycyna Wydawnicza Politechniki Warszawskiej, Warszawa, 1997. P. 244. Kalinina L.S. Kachestvenniy analyz polimerov. Khimiya, Moskva, 1975. P. 248. Gordon A., Ford R. Sputnik khimika. Mir, Moskva, 1976. P. 541. E. Djagarova, D. Jeveleva, Z. Zdravkov. Une possibilité d’élargir l’information obtenne par le plasticorder Brabender // J. of the Univ. of Chem. Technology and Metallurgy. 2002. V. 37. N 3. P. 71-78. Averko-Antonovich I.U., Bikmullin R.T. Metodi issledovaniya strukturi I svoystv polimerov. Kazan. Gos. Tekh. Univ., Kazan, 2002. P. 604. Laboratorniy praktikum po tekhnologii rezini. Osnovnie svoystva rezin i metodi ih opredeleniya. Khimiya, Moskva, 1976. P. 240. N.M. Gavriluk // Khimichna Promislovist Ukraini. 1996. N 4. P. 37-41.

In: Organic and Physical Chemistry Using Chemical Kinetics … ISBN: 978-1-60021-763-0 Editors: Y.G. Medvedevskikh, et al. pp. 187-199 © 2007 Nova Science Publishers, Inc.

Chapter 12

FORMATION OF CARBON NANOSTRUCTURES AND SPATIAL-ENERGY STABILIZATION CRITERION G. А. Korablev* and G. E. Zaikov* Basic research-educational center of chemical physics and mesoscopy, Udmurt research center, Ural Division, RAS, Izhevsk Institute of biochemical physics after N.M. Emanuel, 119991, 4 Kosygina St., RAS, Russia, Moscow

ABSTRACT Spatial-energy criterion of structure stabilization was obtained. The computation results for a hundred binary systems correspond to the experimental data. The basic regularity of organic cyclic compound formation is given and its application for carbon nanostructures is shown.

Keywords: spatial-energy parameter, compound stabilization, carbon nanostructures.

INTRODUCTION The problem of a priory assessment of stable structure formation is one of the main problems of chemical physics and material science. Its solution, in turn, is directly linked with the regularities of isomorphism, solubility and phase-formation in general. Surely, such problems can be cardinally solved only based on fundamental principles defining the system of physical and chemical criteria of a substance and quantum-mechanical concepts of physics and chemistry of a solid suit it.

* *

G.А. Korablev: E-mail: [email protected] G.E. Zaikov: E-mail: [email protected]

G. А. Korablev and G. E. Zaikov

188

But many computations of phase-formation based on the application of pseudo-potential, quantum-mechanical techniques, statistic-thermodynamic theories are carried out now only for comparatively small number of systems, for instance [1-3]. A lot of papers dedicated to the phenomenon of isomorphic replacement, arrangement of an adequate model of solids, energy theories of solid solutions, for instance [4-7]. But for the majority of actual systems many problems of theoretical and prognostic assessment of phase-formation, solubility and stable phase formation are still unsolved. This paper is developing the method where complex initial characteristics of an atom are used as a criterion of structure stabilization.

SPATIAL-ENERGY PARAMETER (Р-PARAMETER) The introduction of Р-parameter as a criterion of structural interactions is based on the assumption that the resulting energy in the system: orbital-nucleus, immediately responsible for inter-atomic interactions, can be calculated based on the principle of adding reverse values of some primary atom characteristics in initial state [8]. In this model Р0-parameter is a tabulated constant spatial-energy characteristics of each orbital of an atom. The criterion

Р

E

=

Р r

0

has a physical sense of some averaged energy of valence

i

electrons in the atom at a distance ri from the nucleus. The reliability of initial equations and regulations was proved with numerous calculations and comparisons. In particular, it was shown [8] that РE-parameter numerically equals the energy of valence electrons in a statistical atom model and is a direct characteristic of electron density in the atom at the given distance from the nucleus. Spatial-energy principles of isomorphic replacement were found: 1. Complete (100%) isomorphic replacement at approximate equality of P-parameters of valence orbitals of interchangeable atoms:

Р

' E

≈ РE "

2. Р-parameters of atom valence orbital with the least value determine the orbital that is mainly responsible for isomorphism and structural interactions. But isomorphism is a particular case of phase-formation. Therefore, when we take its ratios as a basis and take coordination into account it can be assumed that the following condition has to be performed for atoms of a stable homogeneous crystalline structure:

Р К

'

or:

≈ Р К

"

E

1

⎛ Р0 N ⎜⎜ ⎝ Kr

E

(1)

2

⎞ ⎛ Р0 N ⎟⎟ ≈ ⎜⎜ ⎠ ⎝ Kr 1

⎞ ⎟⎟ ⎠

2

;

Р1 ≈ Р 2

(2)

Formation of Carbon Nanostructures and Spatial-Energy Stabilization Criterion

where:

Р

E

=

РN 0

r

189

, К – coordination number of atoms, r – dimensional bond

characteristic of the given atom, N – number of homogeneous atoms in the compound formula. Based on the physical sense of РE-parameter the given condition (2) is the condition of equality of effective values of structure atom orbitals (in the assumption of paired inter-atom interaction). In a more complicated case when the central atom (A1) has heterogeneous surroundings consisting of atoms (А2, В, С) at different inter-nuclear distances, the condition of stable structure formation looks as follows: '' ''' ' N P0 N 1 N = P 0 + P 0 N 2 + P 0 3 + ... Kr К 1 r1 К 2 r 2 К 3 r 3

(3)

Here, the left-hand part of equation refers to the central atom, and the right-hand part of the equation refers to the atoms surrounding it. Let us apply the correlations (2, 3) to some types of crystalline structures using tabulated values of Р0-parameters calculated and given in [8]. At the same time, for structures with basic ionic and metallic bond the values of Р0-parameters calculated via the atom ionization energy (Е) were used – table 1.

CRYSTALS WITH BASIC IONIC BOND Equation (2) contains the value of actual dimensional bond characteristic of the given atom in the structure. In crystals with basic ionic bond, the ion radius can be applied as such dimensional bond characteristic (with a certain approximation), i.e. the stabilization condition for such structures is as follows:

N 1 Р '0 N 2 Р "0 ⎛ Р E ⎞ ⎛ Р E ⎞ ≈ ;⎜ ⎟ ≈ ⎜ ⎟ ; Р1 ≈ Р 2 К 1 r к К 2 r а ⎝ К ⎠1 ⎝ К ⎠2

(4)

where rk – cation radius, ra – anion radius. Table 2 contains the results of some calculations following the equation (4) for several structures, such as NaCl. In all calculations mainly the ion radii by Belov-Bokiy (first line) and partly – Goldschmidt and Poling (second line) were used. Comparisons of such calculative parameters (РE/К) of structure atoms (7th and 8th columns) prove the equality of these values with the precision of up to 25%. To determine the structure type from equation (4) it is necessary to calculate the ratio of coordination number of cation and anion (K1/K2) and taking into consideration the ratio of cation and anion radii values (in the model of rigid spheres), the structure itself can be determined.

Table 1. Р–parameters of some atoms calculated via the ionization energy

Atom Н

С

N

O F Cl Br I Na Al Fe (II) Fe (III)

Σ Р0

Рi =

ΣР 0 ri

(Å)

q2 (eVÅ)

Р0 (eVÅ)

13.595 11.260 24.383 47.860

0.5295 0.596 0.596 0.620

14.394 35.395 35.395 37.243

4.7985 5.641 10.302 16.515

4.7985

(eV) 9.0624

2s1

64.480

0.620

37.243

19.281

51.739

86.810

2p1 2p1 2p1 2s1 2s1 2p1 2p1 2p1 3p1 4p1 5p1 3s1 3p1 3s1 3s1 4s1 4s1 3d1

14.54 29.60 47.426 77.472 97.89 13.618 35.118 17.423 12.268 11.84 10.451 5.138 5.986 18.829 28.440 7.893 16.183 30.64

0.488 0.487 0.487 0.521 0.521 0.414 0.414 0.360 0.728 0.851 1.044 1.713 1.311 1.044 1.044 1.227 1.227 0.365

52.912 52.912 52.912 53.283 53.283 71.380 71.380 94.641 59.842 73.346 77.65 10.058 26.44 27.119 27.119 26.57 26.57 199.95

6.257 11.329 16.078 22.966 26.012 5.225 12.079 5.882 8.125 8.859 9.567 4.694 6.055 11.396 14.173 7.098 11.369 10.564

6.257 17.586 33.664 56.63 82.642 5.225 17.304 5.882 8.125 8.859 9.567 4.694

12.822 36.111 68.984 108.69 158.62 12.621 41.797 16.389 11.161 10.410 9.1638 2.7402

31.624

23.939

18.462

15.046

29.026

23.656

Valence orbitals

Е (eV)

1s1 2p1 2p1 2s1

ri

(eVÅ)

ri (Å)

Рi =

ΣР0 ri

Note

1.36

(eV) 3.528

for Н-

2.60 0.20

19.900 258.7

for С4for С4+

1.48

22.746

for N3-

0.15 1.36 1.36 1.345 1.81 1.96 2.20 0.98

550.9 3.8419 12.724 4.3774 4.4890 4.5199 4.3486 4.7898

for N5+ for Ofor О2-

Formation of Carbon Nanostructures and Spatial-Energy Stabilization Criterion

191

Table 2. Spatial-energy criterion of stable phase formation in the structures of Na-Cl type Atom

Structure

Orbital

Po (eVÅ)

К

ri (Å)

Р'e/к1

F

М'F

2р1 2s1

5.882 6.432

6 6

1.33 1.33 1.36

0.737 0.806 0.786

Cl

M'Cl

3р1

8.125

6

1.81

0.748

Br

М'Br

4р1

8.859

6

1.96

0.753

J

М'J

5р1

9.567

6

2.20 2.16

0.725 0.740

Li

LiГ

2s1

3.487

6

0.68 0.78

0.855 0.740

Nа

NaГ

3s1

4.694

6

0.98

0.798

К

КГ

4s1

5.06

6

1.65

0.634

Rb

RbГ

5s1

5.728

6

1.49

0.641

Сs

CsF

6s1

6.106

6

1.05

0.617

0.788

H

М'Н

1s1

4.794

6

1.36

0.588

0.798-0.617

Sr0,ВаО

2Р2

17.304

6

MgO,CaO

2р2+2р2

22.653

6

1.36 1.32 1.36 1.32

2.121 2.185 2.776 2.860

Bа

BаО,ВаS

6s2

16.172

6

1.38

2.190

2.195 2.412 2.533 3.298 2.120 1.894

Sr

SrO

5s2

17.367

6

1.20

2.412

2.185

4s2

15.803

6

1.04

2.0ЗЗ

2.776

1.06

2.485

2.664

3s2

15.436

6

0.74

3.477

2.860

0.78

3.298

2.78

1.82

1.894

2.195

1.74

1.981

2.195

1.82

2.664

3.298

O

Са Mg

СаO СаS MgO MgS ВаS

3p2

20.682

6

МgS

S

CaS

3р2 +3р2

29.092

6

SrS Eu Ti

Р''e/к2

0.798-0.617

0.806-0.725

1.74

2.78

2.485

1.82

2.664

2.412

EuO

6s2

18.978

6

1.24

2.551

2.776

TiO

Зd

9.483

6

0.78

2.026

2.121

2

Nomenclature: М' – metal of 1st group (Li, Na, K, Rb, Сs); Г – halogen; M'' – metal of 2nd group (Mg, Ca, Sr, Ba).

CRYSTALS WITH IONIC-COVALENT AND METALLIC BONDS. INTERMETALLIDES Numerous and various structures belong to these classes of compounds, moreover, a lot of them are practicable. Compounds of metals with each other belong to intermetallic compounds in the narrow sense. However, the distinct border between them cannot be made as there is no such border

192

G.А. Korablev and G.E. Zaikov

between metals and non-metals, and their properties frequently change considerably depending upon the composition and temperature. I.e. rational theory of phrase stability has to be the same for different types of structures. When we apply the initial model to double compounds with ionic-covalent and metallic bonds, the calculations were made based on the equation (2) for 45 binary structures in the assumption of paired inter-atomic interaction. The results of some of them are given in table 3. Analogous calculations were made for dozens of crystalline structures of penetration – metal carbides and hydrocarbides (only some of them are given in table 4). In all these cases the relative difference of values of P-parameters of interacting systems can be considered the stability criterion – (coefficient α) based on the following equation:

α

E

=

Р − Р ⋅ 100% (Р 2+ Р1) 2 2

1

(5)

On the results of all these calculations it can be concluded: stable structures are formed if αST<(25-30)%.

Formation of Carbon Nanostructures After different allotropic modifications of carbon nanostructures (fullerenes, tubules) have been discovered, a lot of papers dedicated to the investigations of such materials, for instance [9-15] were published, determined by the perspectives of their vast application in different fields of material science. However, a strictly defined model of such system formation does not currently exist. To further study the problem of nanostructure phase-formation the methodology of Р-parameter is applied in this paper. The main conditions of stability of these structures formulated based on modeling the compositions of over thirty carbon clusters are given [9]: 1. Stable carbon clusters look like polyhedrons where each carbon atom is threecoordinated. 2. More stable carbopolyhedrons containing only 5- and 6-term cycles. 3. 5-term cycles in polyhedrons – isolated. 4. Carbopolyhedron shape is similar to spherical. 5. In polyhedrons – even number of apexes, 12 pentagons and any number of hexagons. Let us show some possible explanations of such experimental data based on the application of spatial-energy concepts. As before we will consider the approximate equality of effective energies of interacting subsystems as the main condition for the formation of stable structure based on the following equation:

Formation of Carbon Nanostructures and Spatial-Energy Stabilization Criterion

⎛ Р0 ⎞ ⎛ Р0 ⎞ ⎜ ⎟ ≈⎜ ⎟ ; Р1 ≈ Р 2 ⎝ КR ⎠1 ⎝ КR ⎠ 2

193

(2а)

where К – coordination number, R – bond dimensional characteristic, N – number of homogeneous atoms in the structure. At the same time, the phase-formation stability criterion (coefficient α) is the relative difference of parameters Р1 and Р2 that is calculated following the equation (5) and is αST<(20-25)%. During the interactions of similar orbitals of homogeneous atoms Р '0 = Р "0 . When N1=N2 –

K 1 R1 ≈ K 2 R 2

(6)

Let us consider these initial notions as applicable to certain allotropic carbon modifications using dimensional characteristics and values of Р-parameters that are given in [8] and table 1. 1. Diamond. Modification of structure where К1=4, К2=4;

Р '0 = Р"0 ,

R1=R2, Р1=Р2

and α=0. This is absolute bond stability. 2. Non-diamond carbon modification for which

R

4+ 2

Р '0 = Р"0 ,

К1=1; R1=0,77Å; К2=4;

= 0.2Å , α=3.82%. Absolute stability due to ionic-covalent bond.

3. Graphite.

Р '0 = Р"0 , К1=К2=3, R1=R2, α=0 – absolute bond stability.

4. Chains of hydrocarbon atoms consisting of the series of homogeneous fragments with similar values of P-parameters. 5. Cyclic organic compounds as a basic variant of carbon nanostructures. Apparently, not only inner-atom hybridization of valence orbitals of carbon atom takes place in cyclic structures, but also total hybridization of all cycle atoms. And not only the distance between the nearest similar atoms by bond length (d) is the basic dimensional characteristic, but also the distance to geometric center of cycle interacting atoms (Д) as the geometric center of total electron density of all hybridized cycle atoms. Then the basic stabilization equation for each cycle atom will take into account the average energy of hybridized cycle atoms:

Table 3. Spatial-energy criterion of stabilization of crystalline structures

Atom

Structures

1 As Fe

2 As2Fe As2Fe AgSb AgAs AgCd AgAs

Ag (I) As (I) Ag Ag (I) Pt (II) Sb (I) As (III) Al (III) Au (I) Al (I) Pt (II) Al (III) Se (II) As (III) Zn (III) Au Au

Structure type

Orbitals

∑P

' 0

К

R

' И

R'

P

'

( Å) 8 1.48

(eV) 9 3.698 3.846 0.529

12

1.44 1.48

0.411 0.462

7.108

2

1.44

4.936

5S1 6S2

7.108 24.043

12 12

1.38

1.572 1.452

ZnS W W CaF2 CaF2 ZnS ZnS

5P1 4P3 3S2+3P1 6S1 3P1 6S2 3S2+3P1 4P2

8.742 37.448 31.624 8.909 6.055 24.043 31.624 22.614

12 4 8 8 4 8 4 4

ZnS

4P3

39.448

AsSn

NaCl

4P3

AuCd AuSb Au2Pb

Mg Cu Mg

Ag2S Ag2O Ag3Pt Ag3Pt AuSb AgSb AlAs AlAu4 AlAu4 Al2Pt Al2Pt Al2Se3 Al2Se3 AsJn AsGa

(eVÅ) 5 8.210 18.462

6 3 6

5S1

7.108

12

Mg

4P1

8.210

Cu2O

5S1

Cu Cu Mg

3 FeS2 FeS2

4

Mg

4S2

( Å) 7 0.8 1.13

1.13

1.61 1.49 1.44 1.43 1.38 1.43 1.6

0.452 14.282 2.764 3.092 2.180 2.178 11.057 10.609

4

1.48

6.663

40.749

4

1.66

6.137

6S1

8.909

12

1.44

0.516

6S1

8.909

12

1.44

1.032

0.69

"

P

(eV) 10 3.846 3.698 0.452 0.462 0.446 0.524 0.411 3.996 4.164 1.452 1.572 0.516 0.411 13.87 3.092 2.764 2.178 2.180 10.608 11.057 6.137 6.776 6.617 6.663 0.446 0.452 1.045

Table 3. (Continued).

Atom

Structures

1 K Bi

2 Bi2K Bi2K CuCd3 AgCd3 AgZn3 NiMo NiMo LiAg LiAg CdSe CdS CdTe PtGa2 SnNi3 SnNi3 TiCu3 TiCu3 PtMg7 PtMg7 Sb3Cu10 Sb3Cu10 Ga2S3 Ga2S3 GeS2 GeS2 Ni2Al3 Ni2Al3 Cu3Se2 Cu3Se2

Cd (I) Ag (II) Ni (II) Mo (II) Li Ag (I) Cd (II) Pt (VI) Ni (II) Sn (IV) Ti (IV) Cu (I) Pt (V) Mg Sb (III) Cu (I) Ga (III) S (II) Ge (IV) S (II) Ni (II) Al Se (II) Cu (I)

Structure type 3 Cu2Mg Cu2Mg Mg Mg Mg

Orbitals

∑P

4 4S1 6P1

(eVÅ) 5 5.060 12.971

6 12 12

8.349

1

5S

2

9

' 0

К

R

'

И

R'

P

'

1.28

(eV) 9 0.634 0.594

12

1.56

1.338

36.965 18.838 20.872 3.487 7.108

12 12 12 8 8

1.44 1.24 1.39 1.44

2.139 1.266 1.252 0.641 0.617

( Å) 7 1.33

( Å) 8

W W

5S +4d 4S2 5S2 2S1 5S1

ZnS

5S1+4d1

16.671

4

1.56

2.672

CaF2 SnNi3 SnNi3

6S2+5d4 4S2 5P2+5S2 4S2+3d1 4S1 6S2+5d3 3S2 5P3 4S1 4S2+4P1 3P2 4P2+4S2 3P2 4S2+3d2 3S2+3P1 4P2 4S1

136.65 18.838 69.505 46.839 13.165 96.496 15.436 41.870 7.081 37.678 20.682 61.176 20.682 28.765 31.624 22.614 13.165

8 12 12 12 12 12 12 12 12 4 2.667 4 2 8 12 6 8

1.38 1.24 1.58 1.46 1.28 1.38 1.60 1.61

12.377 3.798 3.666 2.673 2.571 5.827 5.628 6.502 6.02 13.456 12.783 11.003 11.364 5.799 5.529 3.906 3.857

Mg

0.68

1.39 1.82 1.39 1.82 1.24 1.43 1.93 1.28

"

P

(eV) 10 0.594 0.634 1.221 1.266 2.302 1.252 1.266 0.617 0.641 2.929 2.840 2.915 13.554 3.666 3.798 2.571 2.673 5.628 5.827 6.02 6.502 12.783 13.456 11.364 11.003 5.529 5.799 3.857 3.906

Table 4. Spatial-energy criterion of carbide and hydride formation Atom

Structure

Orbitals

Р0 (eVÅ)

К

Ri(Å)

[(N/P0)/(KRi)]1

C

carbides

2Р2 + 2P2

51.739

6

2.6

3.317

α-Fе

FеС cementite

4S2

18.462

6

0.6

3.846

3.317

α-Fe

FеС

4S2

18.462

6

0.6

2.885

3.317

Тi (II)

TiС

4S2

17.026

6

0.76

3.639

3.317

V(II)

VC

4S2

17.162

6

0.72

3.973

3.317

Cr(II)

CrC

4S2

18.869

6

0.83

3.769

3.317

Zr(II)

ZrC

5S2

18.547

6

0.925

3.342

3.317

Нf(II)

HfO

6S2

19.826

6

0.963

3.432

3.317

W(II)

WC

6S2

23.344

8

0.956

3.052

3.317

Ce(II)

CеC

6S2

23.4778

6

1.125

3.478

3.317

Nb(II)

NbC

5S1 + 4d1

16.669

6

0.62

3.429

3.317

SC(II)

ScC

4S2

16.599

6

0.912

3.033

3.317

Mn(II)

МnС

4S2

18.025

6

0.91

3.301

3.317

Ti(I)

TiH

4S1

6.795

14

0.841

0.578

0.588

Ti (II)

TiH2

4S2

17.026

12

0.76

1.819

1.613

H

TiH2

1S1

4.794

4

1.36

1.763

1.619

1

3.487

6

0.66

0.655

0.882

4.794

6

1.36

0.682

0.655

Li

LiH

2S

H

LiH

1S1

[(N/P0)/(KRi)]2

Formation of Carbon Nanostructures and Spatial-Energy Stabilization Criterion

197

"

⎛ ∑ P0 ⎞ ≈ ⎛ ∑ P0 ⎞ ; ' ≈ " ⎟ P P ⎟ ⎜ ⎜ Кd КД ⎠ ⎝ ⎝ ⎠ '

i

(7)

i

where ΣР0=Р0N; N – number of homogeneous atoms, Р0 – parameter of one cycle atom, К – coordination number relatively to geometric center of cycle atoms. Since in these cases К=N, the following simple correlation appears:

P '0 ≈ P "0 ; d Д

Р

' E

≈

Р

"

(8)

E

During the interactions of similar orbitals of homogeneous atoms

d≈Д

Р '0 ≈ Р"0 , then: (8а)

Equation (8) reflects a simple regularity of stabilization of cyclic structures: In cyclic structures the main condition of their stability is an approximate equality of effective interaction energies of atoms along all bond directions. The corresponding geometric comparison of cyclic structures consisting of 3, 4, 5 and 6 atoms results in the conclusion that only in 6-term cycle (hexagon) the bond length (d) equals the length to geometric center of atoms (Д). d=Д Such calculation of α following the equation analogous to (5), gives for hexagon α=0 and absolute bond stability. And for pentagon d≈1.17Д and the value of α=16%, i.e. this is the relative stability of the structure being formed. For the other cases α>25% - structures are not stable. Therefore hexagons play the main role in nanostructure formation and pentagons are additional substructures, spatially limited with hexagons. Based on stabilization equation hexagons can be arranged into symmetrically located conglomerates consisting only of 3 or 7 hexahedrons. A conglomerate of three hexagons contains one central atom and 12 atoms around it. A conglomerate of seven hexahedrons comprises 12 external and 12 internal (common) atoms. In these two cases geometric centers of hybridized molecular orbitals of each hexahedron are equidistant from such nearest centers of a conglomerate. This, apparently, explains the experimental fact that polyhedrons of carbon clusters represent an icosahedron – 12-apex crystalline structure each apex of which is connected with five other apexes. Following such a model, for instance, clusterС60 can be formed of two structures 3 hexagons in each and two structures 7 hexagons in each (2х3+2х7=20) plus 12 pentagons between them located separately and acting as a binding formation. It is assumed [12] that defectless carbon nanotubes (NТ) are formed as a result of rolling the bands of flat atomic graphite net. The graphite has a lamellar structure, each layer of

198

G.А. Korablev and G.E. Zaikov

which is composed of hexagonal cells. Under the center of hexagon of one layer there is an apex of hexagon of next layer. Such a transition from graphite plane to nanotube should be accompanied by the change of coordination numbers of carbon atoms. Coordination numbers are 3 and 12 – for some atoms, and 3 and 2 – for other atoms. All this can be found in accordance with the stabilization formula based on the given pattern. Examples: From equation (2а) we have:

К1 ≈ R2 К 2 R1

Then: 1. For graphite

2. For ionic-covalent bond

3. For ionic-ionic bond:

К К К К К К

1 2 И К

4+ И 4− И

R ≈ 1.675Å ≈ 2 : 1 R 0.77Å 0.77 Å = R = ≈ 4 :1 0 . 2 Å R 2.60Å ≈R = ≈ 13 : 1 0 . 2 Å R

=

2

1

К

И

4−

И 4+ И

These are 13 atoms of hexagons, the central atom of which has the coordination of 12 atoms. The process of rolling flat carbon systems into NT is, apparently, determined by polarizing effects of cation-anion interactions resulting in statistic polarization of bonds in a molecule and shifting of electron density of orbitals in the direction of more electronegative atoms. Thus, the spatial-energy notions given allow characterizing in general the directedness of the process of carbon nanosystem formation.

GENERAL CONCLUSIONS 1. The introduction of spatial-energy criterion of structure stabilization is substantiated. 2. The application of this criterion to cyclic systems on the example of carbon nanostructure formation is given.

REFERENCES [1] [2]

[3] [4]

W. Harrison. Electron structure and properties of solids: Physics of chemical bond. / vol.1, — М: Mir, 1983, — 381 p. A.Yu. Zakharov, V.V. Lebedev. To the theory of reconstruction processes in multicomponent condensed systems. // Electron structure and properties of refractory compounds, alloys and metals. / Proceedings of IAM NAS of Ukraine, 2004, p. 13-21. J. Slater. Methods of self-coordinated field for molecules and solids. — М: 1978, 662 p. V.S. Urusov. Energy crystal-chemistry. М: Nauka, 1975,—335 p.

Formation of Carbon Nanostructures and Spatial-Energy Stabilization Criterion [5]

[6] [7] [8] [9]

[10] [11] [12] [13] [14] [15]

199

Кirkova E., Djarova M., Donkova B. Inclusion of isomorphous impurities during crystallization from solutions, Progress in Crystal Growth and Characterization of Materials, Volume 32, Issues 1-3, 1996, Pages 111-134. S.S. Batsanov. Structural chemistry. Facts and dependences. М: МSU, 2000, 292 p. M.A. Shumilov. On conditions of unlimited mutual solubility of metals in solid state. // News of HEI, Ferrous metallurgy. – 2001, №10, p.19-21. Korablev G.A. Spatial-Energy Principles of Complex Structures Formation, Leiden, the Netherlands, Brill Academic Publishers and VSP, 2005, 426 pages (Monograph). V.I. Sokolov, I.V. Stankevich. Fullerenes – new allotropic forms of carbon: structure, electron structure and chemical properties. // Success in chemistry, 1993, v.62, №5, p.455-473. A.L. Ivanovsky. Quantum chemistry in material science. Nanotubular forms of substance. Ekaterinburg, UrD RAS, 199 , 176 p. A.E. Alexeensky, M.V. Baidakova, A.Ya. Vul, V.I. Siklitsky. Structure of diamond nanocluster. // PТТ, 199 , v.41, №4, p. 740-743. Yu.E. Lozovik, A.M. Popov. Formation and growth nanostructures – fullerenes, nanoparticles, nanotubes. // Success in physical science, 1997, v.167, №7, p.751-774. A.V. Eletsky. Carbon nanotubes. // Success in physical science, 1997, v.167, №9, p. 945-972. A.L. Kolesnikov, A.E. Romanov. On discminary approach for describing fullerene structure. // PТТ, 1998, v.40, №6, p. 1178-1180. S.M. Dunaevsky, M.N. Rozova, N.A. Klenkova. Electron structure of graphite nanotubes. // PТТ, 1997, v.39, №6, p. 1118-1121.

In: Organic and Physical Chemistry Using Chemical Kinetics … ISBN: 978-1-60021-763-0 Editors: Y.G. Medvedevskikh, et al. pp. 201-206 © 2007 Nova Science Publishers, Inc.

Chapter 13

THE STRUCTURAL TREATMENT OF LIMITING CONVERSION DEGREE FOR SOLID-STATE IMIDIZATION L. Kh. Naphadzokova, G. V. Kozlov and M. A. Tlenkopachev1 Kabardino-Balkarian State University, Chernishevsky st. 173, Nalchik-360004, Russian Federation 1 National University of Mexico, Mexico

ABSTRACT It was shown, that limiting conversion (in the given case - imidization) degree is defined by purely structural parameter – macromolecular coil fraction, subjected evolution (transformation) in chemical reaction course. This fraction can be correctly estimated within the framework of fractal analysis. For this purpose were offered two methods of macromolecular coil fractal dimension calculation, which gave coordinated results.

Keywords: polyamides; solid-state; polymerization; nanocomposites; FTIR; catalysis.

INTRODUCTION The authors [1] studied kinetics of poly (amic acid) (PAA) solid-state imidization both in the presence of nanofiller (layered silicate Na+-montmorillonite) and without it. It was found, that temperature imidization Ti raising in range 423-523 K and nanofiller contents Wc increase in range 0-7 phr result to essential imidization kinetics changes expressed by two aspects: by essential increase of reaction rate (reaction rate constant of first order k1 increases about on two order) and by raising of conversion (imidization) limiting degree Qlim: from about 0,25 for imidization reaction without filler at Ti=423 K up to 1,0 at Na+-montmorillonite content 7

202

L. Kh. Naphadzokova, G. V. Kozlov and M. A. Tlenkopachev

phr and Ti=523 K. Let’s mark too, that all kinetic curves conversion degree-reaction duration Q(t) have typical shape of curves with autodeceleration characteristic for fractal reactions, i.e., either fractal objects reactions, or reactions in fractal spaces [2]. Differently speaking, indicated reaction aspects in sufficient degree have general character. If for the first effect (k1 increase) the authors [1] offered probable chemical treatment considering nanofiller as catalyst, then the second effect (Qlim raising) did not obtain explanation, although its theoretical and practical significance is obvious. Therefore the purpose of the present paper is structural treatment of limiting conversion degree in solid-state imidization process based on the general principles of fractal analysis.

EXPERIMENTAL The kinetics of PAA, synthesized from 4,4/-oxydianiline and pyromellitic dianhydride, solid-state imidization both in filler absence and with addition of 2 phr Na+-montmorillonite was studied [1]. The nanofiller was treated by solution of P-phenylenediamine in HCl and then washed by de-ionized water to ensure a complete removal of chloride ions. The conversion (imidization) degree Q was determined as a function of reaction duration t with the aid of Fourier transformation of IR-spectra bands 726 and 1014 cm-1. The samples for FTIR study were obtained by spin-coating of PAA/Na+-montmorillonite mixture solution in N,N-dimethylacetamide on KBr disks, which then were dried in vacuum for 48 h at 303 K. It was shown, that the used in paper [1] method gives exfoliated nanocomposites. The other details of nanocomposites polyimid/Na+-montmorillonite synthesis and study in paper [1] were adduced. The solid-state imidization process was made at four temperatures Ti: 423, 473, 503 and 523 K.

RESULTS AND DISCUSSION It is known [3], that macromolecular coil in various polymer’s states (solution, melt, solid phase) represents fractal object characterized by fractal (Hausdorff) dimension Df. Specific feature of fractal objects is distribution of their mass in the space: the density ρ of such object changes at its radius R variation as follows [4]:

⎛R⎞ ρ = ρ dens ⎜ ⎟ ⎝a⎠

D f −d

,

(1)

where ρdens is density of material, which consists of fractal object in dense packing assumption, a is lower linear scale of object fractal behavior, d is dimension of Euclidean space, in which is fractal considered (it is obvious, that in our case d=3). From the equation (1) ρ decrease at Df reduction follows, as always Df
The Structural Treatment of Limiting Conversion Degree…

203

densely-packed region is formed, where chemical reactions proceeding is impossible. Proceeding from that, it is possible to confirm, that for a chemical reaction only the part of macromolecular coil is accessible, which is the larger, the smaller its fractal dimension Df. In the leaking coil case (Df≤1,5 [3]) both low- and high-molecular substances can pass freely through it and this assumes, that in such case the value Q=1,0. At Df=2,5 chemical reaction ceases and gelation process [5] begins. This means, that at reaching Df=2,5 Q=0. The indicated estimations allow to write the fractional exponent ν for chemical reactions similarly to the definition, accepted in paper [6]:

ν = D f − ( D f gel − 1) = D f − 1,5 , where

D f gel

(2)

is the value Df at gelation, equal to 2,5.

Let’s remind, that according [7] the value ν characterizes system states fraction, un changing in its evolution process. In case of chemical reactions generally and imidization process particularly this assumes, that the value ν characterizes macromolecular coil part inaccessible for chemical transformations. Then the accessible for such transformations coil part β is determined as follows [8]:

β = 1 − ν = 2,5 − D f

.

(3)

Proceeding from the said above, it’s possible to define the limiting conversion degree Qlim by the following identity [8]:

Qlim = β .

(4)

Therefore, the estimation Qlim problem brings to the question of fractal dimension Df determination. At present two methods of indicated dimension determination one exist. First method consists of using of chemical reactions fractal kinetics general relationship [9]:

Q~t

( 3− D f ) / 2

,

(5)

where Q is conversion degree, t is reaction duration. Plotting of the dependences Q(t) in log-log coordinates allows to determine the value Df according to the slope of these dependences in their linearity case. In figure 1 the mentioned dependences for process of PAA imidization without filler are shown. As can be seen, these dependences are linear, that allows to make estimation Df by the indicated method.

204

L. Kh. Naphadzokova, G. V. Kozlov and M. A. Tlenkopachev

Figure 1. The dependences of imidization degree Q on reaction duration t in log-log co-ordinates for PAA imidization process at temperatures: 423 (1), 473 (2), 503 (3) and 523 K (4).

As it is shown in paper [1], imidization process corresponds to the first order reactions. For such reaction it can be written [10]:

dQ = k1 (1 − Q) , dt

(6)

where k1 is the first order reaction rate constant. Differentiating the relationship (5) by t and equaling the derivatives dQ/dt in (5) and (6), let’s obtain the equation, which can be considered as the second method [10] of the estimation Df:

t

( D f −1) / 2

=

C , k1 (1 − Q)

(7)

where C is constant determined from boundary conditions and in the imidization process case equal to 0,25 min-1 and the values k1 were adduced in paper [1]. In figure 2 the comparison of dimensions Df calculated by two methods ( D f and 1

D f2

respectively) is shown. As can be seen, both these methods given close values Df and therefore further their average magnitude will be used, i.e., Df=( D f + D f )/2. 1

2

Further parameters β can be made estimated according to the equation (3) and compared with the limited conversion degree Qlim, obtained experimentally [1]. Such comparison for PAA imidization process without filler and in the presence of 2 phr Na+-montmorillonite at

The Structural Treatment of Limiting Conversion Degree…

205

four indicated above temperatures of imidization in figure 3 is shown. Good enough correspondence of theory and experiment (their average discrepancy is equal to ~12%) was obtained, that confirms the offered treatment correctness.

Figure 2. The comparison of macromolecular coil fractal

D f1

and

D f2

calculated according to the

relationships (5) and (7), respectively, for PAA imidization process without filler (1) and in the presence of 2 phr Na+-montmorillonite (2).

Figure 3. The dependence of limiting imidization degree Qlim on parameter β value for PAA imidization process without filler (1) and in the presence of 2 phr Na+-montmorillonite (2).

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CONCLUSIONS Therefore, the results obtained in the present paper assume, that limiting conversion (in given case-imidization) degree is defined by purely structural parameter – macromolecular coil fraction, subjected to the evolution (transformation) in chemical reaction course. This fraction can be correctly estimated within the framework of fractal analysis. For this purpose two methods of macromolecular coil fractal dimension calculation have been offered, which give co-ordinates results.

REFERENCES [1] [2] [3] [4] [5] [6] [7] [8]

Tyan HL, Liu YC, Wei KH. Polymer. 1999; 40: 4877-4886. Kozlov GV, Zaikov GE. J. Balkan Tribolog. Assoc. 2004; 10: 1-30. Baranov VG, Frenkel SYa, Brestkin YuV. Doklady AN SSSR. 1986; 290: 369-372. Brady RM, Ball RC. Nature. 1984; 309: 225-229. Kozlov GV, Shustov GB, Zaikov GE. J. Balkan Tribolog. Assoc. 2003; 9: 467-514. Kozlov GV, Batyrova HM, Zaikov GE. J. Appl. Polymer Sci. 2003; 89: 1764-1767. Nigmatullin RR. Teoretich. I Matematich. Fizika. 1992; 90: 354-367. Kozlov GV, Shustov GB. In book: Proceeding of International Seminar “Fractal and Applied Synergetics. FIPS-01”. 2001. MSOU, Moscow, p. 155-157. [9] Novikov VU, Kozlov GV. Uspekhi Khimii. 2000; 69: 378-399. [10] Kozlov GV, Zaikov GE. Teoretich. Osnovy Khimichesk. Tekhnologii. 2003; 37: 555557.

In: Organic and Physical Chemistry Using Chemical Kinetics … ISBN: 978-1-60021-763-0 Editors: Y.G. Medvedevskikh, et al. pp. 207-215 © 2007 Nova Science Publishers, Inc.

Chapter 14

A SOLID-STATE IMIDIZATION AND HETEROGENEITY OF REACTIVE MEDIUM L. Kh. Naphadzokova1, G. V. Kozlov1 and G. E. Zaikov2 1

Kabardino-Balkarian State University, 360004, Russia, Nalchik, Chernishevsky st., 173 2. Institute of Biochemical Physics, Russian Academy of Sciences, 119991, Russia, Moscow, Kosygin st., 4

ABSTRACT It was shown, that the conception of reactive medium heterogeneity is connected with free volume representations, that it was to be expected for diffusion-controlled solid phase reactions. If free volume microvoids were not connected with one another, then medium is heterogeneous, and in case of formation of percolation network of such microvoids – homogeneous. To obtain such definition is possible only within the framework of the fractal free volume conception.

Keywords: Imidization, nanofiller, reactive medium, heterogeneity, fractal free volume.

INTRODUCTION The authors [1] studied kinetics of poly (amic acid) (PAA) solid phase imidization in the presence of nanofiller (Na+-montmorillonite) and in its absence. It was found out, that the kinetic curves conversion (imidization) degree Q versus reaction duration t were have typical for polymerization reactions shape with autodeceleration showing imidization rate reduction as time is passing. As it is known [2], such curves Q(t) are specific for reaction passing in heterogeneous medium and are described by the simple relationship:

k ~ t −h ,

(1)

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were k is the reaction rate, h is the heterogeneity exponent (0
EXPERIMENTAL The kinetics of solid state imidization of PAA, synthesized from 4,4/-oxydianiline and pylomellitic dianhydride, both without filler and with addition of 2 and 5 weight % Na+montmorillonite [1]. The nanofiller is processed by solution of P-phenylenediamine in HCl and then washed with de-ionized water to ensure a complete removal of chloride ions. The conversion (imidization) degree Q was determined as a function of reaction duration t with the aim of Fourier transformation of IR-spectra bands 726 and 1014 cm-1. The samples for IR studies were prepared by spin-coating of mixture PAA/Na+-montmorillonite solution in N,Ndimethylacetamide on KBr disks. Then the KBr disks were dried in vacuum at 303 K for 48 h. It was shown, that the used in paper [1] method gives exfoliated nanocomposites. The other details of polyimide/Na+-montmorillonite nanocomposites synthesis and studies in paper [1] were cited. The solid state imidization process was made at four temperatures Ti: 423, 473, 503 and 523 K.

RESULTS AND DISCUSSION The solid phase imidization process in the most simple and general form can be represented as follows [3]: A+A → inert product,

(1)

where A is reagent, which in considered case is PAA. The type (1) reaction can be described by the following scaling relationship for diffusioncontrolled reactions [3]:

ρ A ~ t − ds / 2 ,

(2)

where ρA is concentration of nonreacted reagent A, which further was accepted equal to (1Q), ds is spectral dimension of reactive medium. In figure 1 the dependence ρA(t) in double logarithmic coordinates, corresponding to the relationship (2), for solid state imidization reaction without filler at the four mentioned above imidization temperatures Ti are shown. As can be seen, the received dependences are linear and according to their slope the value ds can be obtained. The Ti increase in the range 423-523

A Solid-State Imidization and Heterogeneity of Reactive Medium

209

K results to substantial growth of reactive medium connectivity degree characterized by dimension ds: from 0,42 up to 1,68. Let’s mention, that such ds increase occurs without reactive mixture composition change. This means, that the energetic restrictions result to the appearance of fractal space, in which instead of value ds effective spectral dimension

d s′

must be use, reflecting the existence of the mentioned above restrictions and connected with ds by the equation [2]:

d s′ = β d s ,

(3)

where β is parameter, characterizing a distribution of reagent “jumps” (motion) times.

Figure 1. The dependences ρA=(1-Q) on t in log-log coordinates, corresponding to the relationship (2), for PAA solid state imidization without filler at temperatures: 423 (1), 473 (2), 503 (3) and 523 K (4).

In its turn, the values

d s′ = 2(1 − h) .

d s′

and h are connected with one another by the equation [2]: (4)

In figure 2 the dependence h(Ti) is shown, from which follows rapid decrease h or increase of homogeneity of reactive medium at Ti raising. At Ti≈540 K exponent h=0, i.e., reactive medium becomes homogeneous. The authors [1] have show that the melting temperature Tm for studied polyimides is about equal to 800 K. On the basis of the known law of two-thirds

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L. Kh. Naphadzokova, G. V. Kozlov and G. E. Zaikov

Tg Tm

=

2 , 3

(5)

the polyimide glass transition temperature Tg can be estimated as equal to ~533 K. Differently speaking, as it was expected [4], reactive medium in case of solid state imidization becomes homogeneous (Euclidean) at glass transition. The shape of the curve h(Ti), adduced in figure 2, i.e., h goes to zero at temperature raising, assumes, that the fractallike effects, namely,

d s′

variation, are connected with energetic disorder [2]. In such case the

energetic state of polymer structure can be characterized by excess energy localization regions dimension Df [5]. The value Df can be estimated according to the following equation [6]:

Df =

4πTi ln(1 / f g )Tg

,

(6)

where fg is relative fluctuational free volume, for determination of which the following method is used. Firstly the relative fraction of local order region (clusters) ϕcl was estimated according to the percolation equation [4]:

ϕ cl = 0,03(1 − k )(Tg − Ti ) 0,55 ,

(7)

where k is crystallinity degree, which is equal to ~0,2 [1]. Further fraction of loosely-packed matrix of polymer structure ϕl.m. [4] was estimated:

ϕ l .m. = 1 − ϕ cl − k ,

(8)

and then the value fg was determined as follows [7]:

f g = 0,113ϕ l .m. .

(9)

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211

Figure 2. The dependence of heterogeneity exponent h of reactive medium on imidization temperature Ti for PAA solid state imidization at Na+-montmorillonite contents Wc: 0 (1), 2 (2) and 5 (3) weight %.

In figure 3 the dependence h(Df) is adduced, from which follows the expected result: a polymer structure energetic excitation degree raising, due to thermal energy “pumping” at Ti increase, results to h reduction. At Df≈6,3 the reactive medium becomes homogeneous (h=0). Therefore, the data of figures 2 and 3 give the answer to the question, at what conditions h=0, i.e., when the reactive medium becomes homogeneous. Nevertheless, the physics of this process remains vague. The glass transition gives singularities neither in fg behaviour, nor in Df behaviour. Therefore for explanation of heterogeneous↔homogeneous medium transition let’s use representations of the conception of fractal (local) free volume

f gfr

[6]. According

to this conception free volume microvoid is necessary to simulate not by three-dimensional sphere, as it was accepted in classical polymer physics [8], but by Df-dimensional sphere. In this case between fg and

fg

where

fr

⎛ Vh fr = f g ⎜⎜ ⎝ Vh

Vh fr

f gfr

the following relationship [6] was obtained:

⎞ ⎟⎟ , ⎠

(10)

and Vh are volumes of free volume microvoid in case of its simulation by Df- and

three-dimensional sphere, respectively. The value Vh can be estimated as follows [6]:

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L. Kh. Naphadzokova, G. V. Kozlov and G. E. Zaikov

V

1/ 3 h

⎛ T − Ti = ⎜⎜ m ⎝ Tm

⎞ ⎟⎟ ⎠

−ν

,

(11)

where percolation index ν was accepted equal to 0,85 [6].

Figure 3. The dependence of heterogeneity exponent h of reactive medium on excess energy localization regions dimension Df for PAA solid state imidization. The notation is the same, that in figure 2.

Further from geometrical considerations in assumption of three-dimensional microvoid of free volume its radius rh can be estimated and then

Vh fr can be calculated according to the

equation [6]:

π f rh f = . ( D f / 2)! D /2

Vh

fr

D

In figure 4 dependence h(

(12)

f gfr )is

adduced where the value

f gfr

was calculated

according to the equations (10)-(12). As follows from the data of this figure, the value h=0 or reactive medium homogeneity at value

f gfr

speaking, at

f gfr =0,34 is achieved. Let’s recollect, that the mentioned

corresponds to percolation threshold for overlapping spheres [6]. Differently

f gfr =0,34 fluctuational free volume microvoids, simulated by Df-dimensional

sphere, form continuous percolation network or continuous diffusion channels. Therefore,

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213

between heterogeneous and homogeneous reactive medium, at any rate, in case of solid state imidization, quantitative difference exists. For heterogeneous reactive medium dehydration product (water molecule), which is in free volume microvoid, forces to expect the opening of overlapping it neighboring microvoid, after that it makes “jump” from the first to the second and further the process repeates. For homogeneous reactive medium such process of “expectation” is not required by virtue of the existence of through percolation channels of free volume. Let’s mark, that the mentioned processes of “jumps” are realized on local level.

Figure 4. The dependence of heterogeneity exponent h of reactive medium on relative fractal volume

f gfr

for PAA solid state imidization. The notation is the same, that in figure 2.

And lastly, in figure 5 the dependence of coefficient β in the equation (3) on adduced. Again the value β reaches it limiting magnitude β=1 (i.e., The relationship between β and

β = 2,94 f gfr .

f gfr

f gfr

is

d s′ = d s ) at f gfr =0,34.

is given by the simple empirical equation:

(13)

The plot of figure 5 demonstrates, that the energetic restriction, defining transition from ds to

d s′ , is the necessity of “jumps” of reaction products or reagents between free volume

microvoids. It is clear, that the Ti raising decrease “jump” expectation time and the formation of through percolation channels of free volume microvoids cancels these restrictions.

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Figure 5. The dependence of the coefficient β in the equation (3) on relative fractal free volume

f gfr

for

PAA solid state imidization. The notation is the same, that in figure 2.

CONCLUSIONS Therefore, the results of the present paper showed, that the notion of reactive medium heterogeneity connected with free volume representations, that was expected for diffusioncontrolled solid phase reactions. If free volume microvoids were not connected with one another, then medium is heterogeneous, and in case of formation of overlapping percolation network of such microvoids – homogeneous. To obtain such definition is possible only within the framework of the fractal free volume conception.

REFERENCES [1] [2] [3] [4] [5] [6]

Tyan H.-L., Liu Y.-C., Wei K.-H. Polymer, 1999, v. 40, №11, p. 4877-4886. Kopelman R. In book: Fractals in Physics. Eds. Pietronero L., Tosatti E. Moscow, Mir, 1988, p. 524-527. Meakin P., Stanley H.E. J. Phys. A, 1984, v. 17, №1, p. L173-L177. Kozlov G.V., Novikov V.U. Uspekhi Fizichesk. Nauk, 2001, v. 171, №7, p. 717-764. Balankin A.S. Synergetics of Deformable Body. Moscow, Ministry Defence SSSR Publ., 1991, 404 p. Kozlov G.V., Sanditov D.S., Lipatiov Yu.S. In book: Achievements in Polymer Physics and Chemistry Field. Ed. Zaikov G.E. a.a. Moscow, Khimiya, 2004, p. 412-474.

A Solid-State Imidization and Heterogeneity of Reactive Medium [7] [8]

215

Belousov V.N., Beloshenko V.A., Kozlov G.V., Lipatiov Yu.S. Ukrainskii Khimich. Zhurnal, 1996, v. 62, №1, p. 62-65. Sanditov D.S., Bartenv G.M. Physical Properties of Disordered Structures. Novosibirsk, Nauka, 1982, 256 p.

In: Organic and Physical Chemistry Using Chemical Kinetics … ISBN: 978-1-60021-763-0 Editors: Y.G. Medvedevskikh, et al. pp. 217-223 © 2007 Nova Science Publishers, Inc.

Chapter 15

FRACTAL-LIKE KINETICS OF REESTERIFICATION REACTION IN CATALYST PRESENCE L. Kh. Naphadzokova1, G. V. Kozlov1 and G. E. Zaikov2 1

Kabardino-Balkarian State University, 360004, Russia, Nalchik, Chernishevsky st., 173 2 Institute of Biochemical Physics, RAS, 119991, Russia, Moscow, Kosygin st., 4

ABSTRACT It was shown, that the reesterification reaction without catalyst can be described by mean-field approximation, whereas introduction of catalyst (tetrabutoxytitanium) is defined by the appearance of its local fluctuations. This effect results to fractal-like kinetics of reesterification reaction. In this case reesterification reaction is considered as recombination reaction and treated within the framework of scaling approaches. Practical aspect of this study is obvious-homogeneous distribution of catalyst in reactive medium or its biased diffusion allows to decrease reaction duration approximately twofold.

Keywords: reesterification, kinetics, catalyst, diffusion, scaling, mean-field approximation.

INTRODUCTION Saturated complex polyesters, particularly, poly (butylene terephthalate) (PBT) are used as engineering thermoplastics possesing good thermo – and wearstability, excellent moulding. These properties also allow to use them as matrix material for polymer composites [1]. One of the perspective ways of search of effective catalysts for such systems is kinetic study of the reesterification model reaction, performed in the presence of various catalysts and comparison it with the results of the similar reaction without catalyst. Clarification on the example of model system of the most effective catalysts list allows to use them for obtaining both filled and nonfilled PBT and compare catalytic activity of various catalysts. The purpose of the

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present paper is the comparative analysis of reesterification reactions without and in the presence of tetrabutoxytitanium (TBT) within the framework of modern physical concepts [24].

EXPERIMENTAL The reesterification model reaction kinetics of methylbenzoate by heptanole-1 in catalyst (TBT) presence and without it was studied at 443 K on the gas chromatograph «Biokhrom» using diphenyloxide according to the earlier described method [5] as an internal standard. The rate constant k1 was calculated according to the equation of irreversible reaction of the first order. TBT of mark «tch», is used which was distiled in vacuum, three times selecting fraction with boiling temperature Tb=430-432 K at pressure 1,33 Gpa [6]. Obtaited by such method fraction was preserved under molecular sieve 4 A. For kinetic studies four-neck retort was scavenged by argon and poured methylbenzoate and heptanole-1 into it. After immersion of the retort into preliminary heated up to 443 K silicone oil, TBT was introduced. Catalyst concentration made into reactionary mixture 0,10 mol.% in calculation on reagent, taken in deficiency. Every definite time intervals probes were taken by a calibrated syringe through self-covered membrane. The taken reactive mixture was cooled by injecting in preliminary weighted amount of standard solution. The taken probes were analyzed on gas chromatograph as described above with using helium as gas-carrier [5].

RESULTS AND DISCUSSION In figure 1 the kinetic curves of reesterification reactions without catalyst and in the presence of TBT are shown. The attention is draw by itself both quantitative and qualitative differences of these Q(t) curves. The quantitative difference is expressed by much faster growth Q at t increase due to catalyst presence that was expected. The qualitative change is reflected in the Q(t) curve form change. If in the absence of TBT linear dependence was obtained, which indicates on the reaction proceeding in Euclidean (homogeneous) space [7], then in TBT presence a typical curvilinear Q(t) dependence was obtained with reaction rate dQ / dt decrease with t increase. Such reactions are typical for heterogeneous (fractal) mediums [8] owing to which they are called fractal-like. The dependence

dQ / dt

this case is described by the relationship [8]:

dQ −h ~t , dt

(1)

on t in

Fractal-Like Kinetics of Reesterification Reaction in Catalyst Presence

219

where h is the heterogeneity medium exponent, which varies within the limits 0
Figure 1. The kinetic curves conversion degree time (Q-t) for reesterification reaction without catalyst (1) and in TBT presence (2).

Let’s consider the reasons of reesterification reaction fractal-like kinetics in TBT presence. This reaction can be described in general form as recombination reaction of reagents A and B [4]: A+B → inert product.

(2)

Within the framework of the mean-field theory the reagent A concentration decay ρA=ρB is given by the equation [4]:

ρA ~

1 , k1t

(3)

where k1 is reaction rate constant. In figure 2 the comparison of calculated according to the relationship (3) and determined experimentally functions ρA(t) is adduced, where ρA is determined as (1-Q). As can be seen, for the reesterification reaction without catalyst ρA decay as t increase is excellently described within the framework of the mean-field theory, whereas in TBT presence ρA decay is much slower, than it was predicted by the relationship (3). As it was known [4], the last effect is due

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to local fluctuations of reagents distributions and in this case the function ρA(t) is given as follows:

ρ A (t ) ~ t − α

(4)

ρ A (t ) ~ exp(− At α )

(5)

and

for short and long reaction times, respectively. In the relationships (4) and (5) the exponent α is defined by space dimension d, in which a reaction proceeds, A is constant.

Figure 2. The dependences of reagent A concentration decay ρA on reaction duration t for reesterification reaction without catalyst (1, 3) and in TBT presence (2, 4).

For recombination reaction described by the equation (2), can be written [4]:

α=

d . 4

(6)

Let’s note three important aspects followed from the model [4] application for description of reesterification reaction. At first as reesterification reactions with TBT and in it absence proceed in identical conditions, then from the comparison of figure 1 kinetic curves follows, that the reaction fractal-like behaviour in TBT presence is due to local fluctuations of catalyst distribution in reactive medium. Secondly the division of reaction duration into short and long

Fractal-Like Kinetics of Reesterification Reaction in Catalyst Presence

221

times is connected with reagents and catalyst diffusion. At local fluctuations presence small enough regions by size ξ exist, where positive or negative TBT fluctuations are large enough. If we obtain characteristic scale of time tξ, which is required for passing of diffusible particle the distance ξ, then the condition ttξ – long times. And, thirdly, the equation (6) gives the value of exponent α for free diffusion of reagents. In case of biased (with preferential orientation) diffusion the value α is determined as follows [4]:

α=

d +1 , 4

(7)

i.e., for three-dimensional space in case of biased diffusion α=1. In this case the scaling approach [4] gives the relationship (4), analogous to the equation (3). This correspondence is confirmed by the figure data. Therefore, the present result allows to make a conclusion, that the intensive stirring of reactive medium results to reagents biased diffusion (namely, methylbenzoate and heptanole-1), but TBT diffusion remains unbiased.

Figure 3. The dependences of reagent A concentration decay ρA on reaction duration t in log-log coordinates for reesterification reaction in TBT presence.

In figure 3 the dependence ρA(t) in log-log coordinates, corresponding to the relationship (4), for the reesterification reaction in TBT presence is adduced. As can be seen, this dependence breaks down into two linear parts with different slopes. For the first part (t<90 min.) the slope is equal to ~0,75, i.e., corresponded to the equation (6) for reaction proceeding in three-dimensional Euclidean space (d=3). For the second part (t>90 min.) the slope is equal to ~3, i.e., not corresponded to possible value of this exponent for recombination reaction or other analogous reactions, for which the value α is limited from above by the value 1,5 [2-4, 9]. This means, that for the considered reesterification reaction times smaller of 90 min. it’s necessary to identify as short times, i.e., on this temporal interval reactive particles concentration decay controls by local fluctuations of TBT distribution, and times equal or

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larger that 90 min. – to long times, where TBT is homogeneously distributed. This means, that in the last case the function ρA(t) should be described by the relationship (5). Actually, adduced in figure 4 the dependence ρA on td/4 in log coordinates is linear, that confirms the assumption made above.

Figure 4. The dependences of reagent A concentration decay ρA on parameter td/4 (d=3) in log coordinates in the case of long times for reesterification reaction in TBT presence.

CONCLUSIONS Therefore, the reesterification reaction without catalyst can be described by mean-field approximation, whereas introduction of catalyst (TBT) is defined by the appearance of its local fluctuations. This effect results to fractal-like kinetics of reesterification reaction. In this case reesterification reaction is considered as recombination reaction and treated within the framework of scaling approaches. Practical aspect of this study is obvious-homogeneous distribution of catalyst in reactive medium or its biased diffusion allows to decrease reaction duration approximately twofold.

REFERENCES [1] [2] [3] [4] [5] [6]

Chen J.-H., An Y.U., Kim S. J., Im S. Polymer, 2003, v. 44, №23, p. 5655-5661. Grassberger P., Procaccia I. J. Chem. Phys., 1982, v. 77, №12, p. 6281-6284. Meakin P., Stanley H.E. J. Phys. A, 1984, v. 17, №1, p. L173-L177. Kang K., Redner S. Phys. Rev. Lett., 1984, v. 52, №12, p. 955-958. Naphadzokova L.Kh., Vasnev V.A., Tarasov A.I. Plast. Massy, 2001, №3, p. 39-41. Cullinane N.M., Chard S.J., Price G.F., Millward B.B., Langlois G. J. Appl. Chem., 1951, v. 1, №3, p. 400-406.

Fractal-Like Kinetics of Reesterification Reaction in Catalyst Presence [7] [8] [9]

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Kozlov G.V., Zaikov G.E. Teoretich. Osnovy Khimich. Tekhnologii, 2003 v. 37, №5, p. 555-557. Anacker L.W., Kopelmam R. J. Chem. Phys., 1984, v. 81, №12, p. 6402-6403. Redner S., Kang K. J. Phys. A, 1984, v. 17, №2, p. L451-L455.

In: Organic and Physical Chemistry Using Chemical Kinetics … ISBN: 978-1-60021-763-0 Editors: Y.G. Medvedevskikh, et al. pp. 225-231 © 2007 Nova Science Publishers, Inc.

Chapter 16

DESCRIPTION OF THE MODEL REESTERIFICATION REACTION WITHIN THE FRAMEWORK OF A STRANGE DIFFUSION CONCEPT L. Kh. Naphadzokova1, G. V. Kozlov1 and G. E. Zaikov2 1

Kabardino-Balkarian State University, 360004, Russia, Nalchik, Chernishevsky st., 173 2 Institute of Biochemical Physics, RAS, 119991, Russia, Moscow, Kosygin st., 4

ABSTRACT It is shown, that there is principal difference between the description of generally reagents diffusion and the diffusion defining chemical reaction course. The last process is described within the framework of strange (anomalous) diffusion concept and is controled by active (fractal) reaction duration. The exponent α, defining the value of active duration in comparison with real time, is dependent on reagents structure.

Keywords: esterification, kinetics, catalysis, diffusion, microstructure.

INTRODUCTION One of the perspective ways of search of effective inorganic filler-catalysists for complex polyesters is kinetic study of the reesterification model reaction, performed in the presence of various inorganic compounds [1]. Such method allows to use the obtained results in the synthesis process of the filled complex polyesters [2]. Synthesis processes in common case can be considered as a complex system of selforganization, developing during time, that results to formation of time-dependent fractal structures [3]. In such reactions the important role is played by diffusive processes, which in the considered case have very specific nature. This specificity is due to the fact, that in chemical reactions not all reagents contacts occur with proper for reaction’s product

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formation orientation of reacting molecules. This aspect of reaction is accounted for by steric factor p (p≤1) [4]. Variation p can result to the change of a diffusion type, reaction’s product structure and, as consequence, to the rate of chemical reaction change. This question can be explained by a simple example. As it is known [5], characteristic size r(t) of a region, which can be visited by the reagent molecule during time t, is equal to:

r (t ) ~ t 1 /( 2 + θ ) ,

(1)

where θ is connectivity index of reactive medium. For the case of classical Gaussian diffusion θ=0 and, believing r(t)=2 and t=4 relative units, the equality within the framework of the relationship (1) will be obtained. Such equality assumes p=1, i.e., each contact of reagents molecules results to reaction product formation. Let’s assume, that the value p decreases up to 0,05, i.e., only one from 20 contacts of reagents molecules forms a new chemical species. This means the increase t in 20 times and then at r(t)=2 and t=80 relative units from the relationship (1) will be obtained θ=4,33. Since θ is connected with dimension of walk trajectory of reagents molecules dw by the simple equation [5]:

dw = 2 + θ ,

(2)

then θ increase results to dw raising, i.e., slows down the chemical interaction process. In its turn, the value dw is connected with Hurst exponent H by the equation [5]:

dw =

1 H

.

(3)

The change θ from 0 up to 4,33 results to raising dw from 2 (Brownian motion) up to dw=6,33 according to the equation (2) and to H reduction from 0,5 up to 0,158 according to the equation (3). As it is known [5], subdiffusive (slow) transport processes correspond to the value 0≤H≤0,5 and classical Gaussian diffusion – H=0,5. Therefore, the decrease p from 1,0 up to 0,05 results to the qualitative change of diffusion type too: it changes from Gaussian classical to anomalous (strange). Let’s note, that the mentioned transition can occur without changing of general diffusive processes in reactive medium too, since it is due to «rejection» of all diffusive phenomena, not resulting to the chemical reaction, i.e., to formation of new chemical substance. Proceeding from the said above, the purpose of the present paper is to study diffusive processes influence within the framework of the offered treatment on main characteristics of reesterification model reaction.

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227

EXPERIMENTAL The kinetics of reesterification model reaction of methylbenzoate by heptanole-1 in mica presence was studied at 443 K. Mica catalytic activity was determined on the observed rate constant of the first order k1 at the twentieth multiple of heptanole-1 excess and mica contents 30 mass.% in calculation on the methylbenzoate [2]. The reesterification kinetics was studied on the gas chromatograph «Biokhrom» with using as the internal standard diphenyloxide according to the earlier described method [1]. The rate constant k1 was calculated according to the equation of irreversible reaction of the first order. The mica «Flagopit» with polydispersity 0,749 and average probable particles size 0,23×10-6 m is used. The initial mica (conditional designation NMM) and also mica chemically modified by sodium hydroxide (SMM) and sulphur acid (AMM) were applied.

RESULTS AND DISCUSSION Earlier it was shown [6], that for reaction of type A+B → inert products

(4)

the scaling relationship is true:

ρA ~ t D/4 ,

(5)

where ρA is concentration of «surviving» in the reaction process particles, t is reaction duration, D is dimension controlling the reaction course. In case of reaction course in the Euclidean spaces the value D is equal to the dimension of this space d and for fractal spaces D is accepted equal to spectral dimension ds [6]. By plotting ρA=(1-Q) (where Q is conversion degree) as a function of t in log-log coordinates the value D from the slope of these plots can be determined. It was found, that the mentioned plots fall apart on two linear parts: at t<100 min with small slope and at t>100 min the slope essentially increases. In this case the value ds varies within the limits 0,069-3,06. Since the considered reactions are proceed in Euclidean space, that is pointed by a linearity of kinetic curves Q-t, this means, that the reesterefication reaction proceeds in specific medium with Euclidean dimension d, but with connectivity degree, characterized by spectral dimension ds, typical for fractal spaces [5]. The authors [5] have formulated fractional equation of transport processes, having the following form:

∂ α ψ ∂ 2β = ( Bψ ) , ∂t α ∂r 2β

(6)

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L. Kh. Naphadzokova, G. V. Kozlov and G. E. Zaikov

where ψ=ψ(t,r) is distribution function of particles,

∂ 2β ∂r 2β

is Laplacian operator in d-

dimensional Euclidean space and B is relation of transport generalized coefficient and d. The introduction of fractional derivatives

∂ α ∂t α

allows to account for the effects of memory

(α) and nonlocality (β) in context of common mathematical formalism [5]. The introduction of fractional derivative

∂ α ∂t α

in the kinetic equation (6) allows to account for random

walks in fractal time (RWFT) – «temporal component» of strange dynamical processes in turbulent mediums [5]. The absence of any noticeable jumps in particles behavior serves as the distinctive feature of RWFT; in this case root-mean-square displacement 〈r2(t)〉 increases with t as tα. The parameter α has sense of fractal dimension of «active» time, in which real walks of particles look as random process; interval of active time is proportional to tα [5]. In its turn, the exponent 2β in the equation (6) accounts for instantaneous jumps of particles (Levy «flights») from the one region of turbulence in to another. The existence of turbulence zones in reesterification reaction follows with the necessity from intensive stirring of reactive medium as by virtue of inert gas passing, as owing to mechanical stirring. Therefore, exponents relation α/β gives relation of RWFT contact frequencies and Levy «flights». The value β in the first approximation can be adopted as constant and then relation α/β will be inversed proportional to waiting time of chemical reaction realization. Depending on concrete value α persistent (superdiffusive, 1<α≤2) and antipersistent (subdiffusive, 0≤α<1) processes are distinguished. In case of antipersistent processes active time represents itself Cantor’s set (0≤α<1), consisting breakings in any point of t ray. Breakings corresponded to those time moments, in which particle at a regular time «sticks» in turbulent field. On the contrary, persistent processes assume a faster course (1<α≤2) of active time in comparison with real time t [5]. The value α/β can be determined according to the relationship [5]:

α ds = β d

.

(7)

We assume that the dependence of Q on active time tα should be linear and namely according to these considerations choose the value β=0,25. Constructed by the indicated method the dependence at t=60 and 300 min in figure 1 is adduced. As can be seen, it is approximately linear and passed through coordinates origin. Attention is attracted by the fact, that active time tα is much smaller (in 50-150 times) than real time t. Although this difference is due to the above made value β choice and, consequently, α, it imagines close to reality. So, for reesterification in the presence of NMM and SMM the value Q≈0,20 is achieved during 300 min, whereas in other polycondensation reactions at analogous conditions synthesis is practically completed during 20 min [7], i.e., it proceeds approximately in 60 times faster. Analytically the relationship Q(tα) for reesterification reaction can be expressed as follows: Q=0,108tα.

(8)

Description of the Model Reesterification Reaction…

229

Further let’s consider the question, which parameters define the value α and, hence, the active time value tα. As it is known [5], the relation α/β is connected with exponent μ at t in the generalized transport equation as follows:

α = μ. β

(9)

Figure 1. The dependence of conversion degree Q at t=60 and 300 min on active time tα for reesterification reaction without mica (1) and in presence NMM (2), SMM (3), AMM (4).

In its turn, μ and Hurst exponent H are connected between themselves like this [5]: μ=2H.

(10)

At definite conditions the value H is defined by dimension Df (Euclidean or fractal) of reaction product (heptylbenzoate molecule) only [8]:

H = 2 − Df

.

(11)

The combination of the equations (9)-(11) allows to obtain the simple theoretical relationship between α and Df (at condition β=0,25):

α = 0,5(2 − D f ) .

(12)

The value of dimension Df can be determined with the aid of the following equation [9]:

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L. Kh. Naphadzokova, G. V. Kozlov and G. E. Zaikov

t

( D f −1) / 2

=

c1 , k1 (1 − Q)

(13)

where c1 is constant estimated from boundary conditions and accepted in the present paper equal to 8×10-4 c-1. The value Df characterizes reagents (methylbenzoata and heptanole-1) and the final product of reesterification reaction (heptylbenzoate) structure. It is found, that Df variation makes 1,48-1,96. In figure 2 the comparison of value α, calculated according to the equations (9) and (12), as the function of Df is adduced. As it is expected, α increase at Df reduction is observed and also a good correspondence of calculation according to the two mentioned equations. This means, that the value α and, hence, reaction active time tα, is defined by reagents structure in the reesterification reaction process. The data of figure 2 demonstrate, that at the present choice β=0,25 in reesterification reaction course only antipersistent (subdiffusive) transport processes are possible (α=1 is achieved for low-molecular substances with Df=0 only), i.e., active time is always smaller than real time. This indicates on the important role of Levy «flights» in strange diffusion type definition.

Figure 2. The dependence of exponent α, calculated according to the equations (9) (points) and (12) (solid line), on reagents molecules dimension Df for reesterification reaction. The legend is the same, as in figure 1.

CONCLUSIONS Therefore, the results of the present paper have shown, that there is the principal difference between the description of generally reagents diffusion and the diffusion defining chemical reaction course. The last process is described within the framework of strange

Description of the Model Reesterification Reaction…

231

(anomalous) diffusion concept and is controlled by active (fractal) reaction duration. The exponent α, defining the value of active duration in comparison with real time, is dependent on reagents structure.

REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9]

Naphadzokova L.Kh., Vasnev V.A., Tarasov A.I. Plast. Massy, 2001, №3, p. 39-41. Vasnev V.A., Naphadzokova L.Kh., Tarasov A.I., Vinogradova S.V., Lependina O.L. Soed. A, 2000, v. 42, №12, p. 2065-2071. Karmanov A.P., Matveev D.V., Monakov Yu.B. Doklady RAN, 2001, v. 380, №5, p. 635-638. Barns F.S. Biofizika, 1996, v. 41, №4, p. 790-802. Zelenyi L.M., Milovanov A.V. Uspekhi Fizichesk. Nauk, 2004, v. 174, №8, p. 809-852. Meakin P., Stanley H.E. J. Phys. A, 1984, v. 17, №1, p. L173-L177. Korshak V.V., Vinogradova S.V. Nonequilibrium Polycondensation. (Rus.), Moscow, Nauka, 1972, 695 p. Feder E. Fractals, New York, Plenum Press, 1989, 242 p. Kozlov G.V., Bejev A.A., Lipatov Yu.S. J. Appl. Polymer Sci., 2004, v. 92, №4, p. 2558-2568.

In: Organic and Physical Chemistry Using Chemical Kinetics … ISBN: 978-1-60021-763-0 Editors: Y.G. Medvedevskikh, et al. pp. 233-242 © 2007 Nova Science Publishers, Inc.

Chapter 17

ESTIMATION OF VAPOR LIQUID EQUILIBRIUM OF BINARY SYSTEMS TERT-BUTANOL+2-ETHYL-1HEXANOL AND N-BUTANOL+2-ETHYL-1-HEXANOL USING ARTIFICIAL NEURAL NETWORK H. Ghanadzadeh and A. K. Haghi* The University of Guilan, P. O. Box 3756, Rasht, Iran

ABSTRACT Vapor-liquid equilibrium (VLE) data are important for designing and modeling of process equipments. Since it is not always possible to carry out experiments at all possible temperatures and pressures, generally thermodynamic models based on equations on state are used for estimation of VLE. In this paper, an alternate tool, i.e. the artificial neural network technique has been applied for estimation of VLE for the binary systems viz. tert-butanol+2-ethyl-1-hexanol and n-butanol+2-ethyl-1-hexanol. The temperature range in which these models are valid is 353.2-458.2K at atmospheric pressure. The average absolute deviation for the temperature output was in range 2-3.3% and for the activity coefficient was less than 0.009%. The results were then compared with experimental data.

Keywords: VLE data; Binary system; artificial neural network.

1. INTRODUCTION The precise vapor-liquid equilibrium (VLE) data of binary mixtures like alcohol-alcohol are important to design many chemical processes and separation operations. The VLE investigations of binary systems have been the subject of much interest in recent years[1-9].

*

A.K. Haghi: Corresponding author e-mail: [email protected]

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Conventional method of estimating the VLE is based on equations of state (EOS). These EOS although derived from strong theoretical principles and involve a number of adjustable parameters in terms of binary interaction parameters, as well as parameters in mixing rule equations. Furthermore, the binary interaction parameters that are functions of both temperature and composition need to be calculated at every temperature at which the VLE is required. The iterative method of estimation of VLE using EOS makes it unsuitable for real time control. The development of numerical tools, such as neural networks, has paved the way for alternative methods to estimate the VLE [10–14]. It has attracted considerable interest because of its ability to capture with relative ease the non-linear relationship between the independent and dependent variables. Several authors have reported application of ANN for estimation of thermodynamic properties such as estimation of viscosity, density, vapor pressure, compressibility factor and VLE. A ANN model for estimation of vapor pressure from aerosol composition, relative humidity and temperature has been reported by Potuchuti and Wexler [15]. Chouai et al. [16] have used a ANN model for estimating the compressibility factor for the liquid and vapor phase as a function of temperature and pressure for several refrigerants. ANN has also been used for estimating the shape factors as a function of temperature and density for a number of refrigerants that can be used in the extended corresponding state model [17,18]. Lagier and Richon [19] have used ANN model for estimation of compressibility factor and density as a function of pressure and temperature for some refrigerants. Although a number of papers have been published with experimental data for vapor liquid equilibrium for various systems and estimation of VLE using conventional thermodynamic models, not many have used this technique for estimating the VLE. A ANN based group contribution method for estimation of liquid phase activity coefficient have been suggested by Petersen et al. [10] that can be used for estimation of VLE. A multilayer perceptron with a single hidden layer has been used by Guimaraes and McGreavy [11] for estimating the VLE of benzene–hexane system. Sharma et al. [12] have used the multi-layer perceptron model to estimate the VLE for the methane–ethane and ammonia–water systems. They have also highlighted the advantage of ANN over conventional EOS for estimating the VLE systems containing polar compounds. Ganguly [13] on the other hand, has used the radial basis function to estimate the VLE for several binary and ternary systems. Urata et al. [14] have estimated the VLE using two multi-layer perceptrons. The input parameters for the first ANN are normal boiling point divided by molecular weight, density and dipole moment for both the components and the output is a negative or positive sign. The second ANN has an extra input of mole fraction of one of the components in the liquid phase in addition to the inputs of the first ANN. The output from the second ANN is logarithm of the activity coefficient for that component. Using the logarithmic activity coefficients, vapor liquid composition and equilibrium temperature were estimated. Mohanty [15] has used a single multilayer perceptron for estimating the VLE of carbon dioxide–difluoromethane system. In this paper, attempt has been made to use ANN for estimating the VLE for the systems tert-butanol+2-ethyl-1-hexanol and n-butanol+2-ethyl-1-hexanol.In the next section, the theory of ANN has been explained and the type of ANN which is used for estimating the VLE has been defined. In section 3, the data inputs to the network has been shown at atmospheric pressure and in temperature range of 353.2-458.2 K within the results and in section 4, the outputs of ANN has been compared with experimental results.

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2. ARTIFICIAL NEURAL NETWORK THEORY The driving force behind the development of the ANN models is the biological neural network, a complex structure, which is the information processing system for a living being. Thus ANN mimics a human brain for solving complex problems, which may be otherwise difficult to solve using available mathematical techniques. The advantage of using a ANN model is that it does not require any other data except the input and output data. Once the model has been adequately trained, the input data is sufficient to estimate the output. The other advantage is a single model can be used to get multiple outputs. From its initiation in the early forties till today there are hundreds of ANN architecture developed, however, there are a few such as multi-layer perceptron and radial basis function that are more popular and find wide applications. Details have been dealt with elsewhere [21,22], therefore only a brief description of multilayer perceptron neural network that belongs to the feed forward neural network architecture in general has been described.

2.1. The Multi-Layer Perceptron (MLP) Network This type of network is composed of an input layer, an output layer and one or more hidden layers (figure 1). Bias term in each layer is analogous to the constant term of any polynomial. The number of neurons in the input and the output layer depends on the respective number of input and output parameters taken into consideration. However, the hidden layer may contain zero or more neurons. All the layers are interconnected as shown in the figure and the strength of these interconnections is determined by the weights associated with them. The output from a neuron in the hidden layer is the transformation of the weighted sum of output from the input layers and is given as (1)

(1) The output from the neuron in the output layer is the transformation of the weighted sum of output from the hidden layer and is given as (2)

(2) where pi is the ith output from the input layer, zj is the jth output from the hidden layer wij is the weight in the first layer connecting neuron i in the input layer to neuron j in the hidden layer, w˜ kj is the weight in the second layer connecting neuron j in the hidden layer to the neuron k in the output layer and g and ˜g are the transformation functions. The transformation function is usually a sigmoid function with the most common being (3) ,

(3)

236

H. Ghanadzadeh and A. K. Haghi The other commonly used function is (4),

(4) One of the reasons for using these transformation functions is the ease of evaluating the derivatives that is required for minimization of the error function.

q1

z0

qr

1

r

1

2

Output layer

z1

Hidden layer

Bias=1

Bias=1 p0

z0

n

1

Input layer

d p1

pd

Figure 1. Multilayer perception with one hidden layer.

3. NEURAL NETWORK MODEL The neural network model for the two binary systems viz. tert-butanol+2-ethyl-1-hexanol and n-butanol+2-ethyl-1-hexanol is based on the experimental data reported by Ghanadzadeh et al. [23]. The summary of the data is shown in tables 1 and 2. All neural networks take numeric input and produce numeric output. The transformation function of a neuron is typically chosen so that it can accept input in any range, and produce output in a strictly limited range. Although the input can be in any range, there is a saturation effect so that the unit is only sensitive to inputs within a fairly limited range. Numeric values have to be scaled into a range that is appropriate for the network. The three input parameters to the multi-layer perceptron are the atmospheric pressure and the mole fraction of liquid(X1) and vapor (Y1) phases. The output parameter is the boiling temperature.

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Table 1. The experimental data of VLE for 2-ethyl hexanol+TBA [23] T (K) 459.7900 445.5325 436.1964 428.8066 422.7940 388.2300 380.5000 372.1293

X1 0.0000 0.0050 0.0100 0.0150 0.0199 0.0899 0.1599 0.2299

Y1 0.0008 0.2984 0.4755 0.5892 0.6667 0.9200 0.9542 0.9666

T (K) 368.9010 366.7212 363.8160 361.6598 360.6300 359.5657 357.0900 355.5700

X1 0.3000 0.4399 0.5100 0.6499 0.7200 0.7899 0.8599 0.9300

Y1 0.9730 0.9797 0.9819 0.9858 0.9877 0.9899 0.9925 0.9957

Table 2. The experimental data of VLE for 2-ethyl hexanol+NBA [23] T (K) 458.15 452.6213 444.5697 441.3355 418.6233 409.6233 405.6594

X1 0.0000 0.0049 0.0112 0.0200 0.0900 0.1685 0.2300

Y1 0.0008 0.2994 0.3245 0.398 0.7289 0.8125 0.8480

T (K) 402.8900 400.9500 399.5000 398.2821 396.1976 393.3350 392.0000

X1 0.3000 0.3400 0.4400 0.5100 0.6500 0.8600 0.9270

Y1 0.8703 0.8845 0.9110 0.9234 0.9235 0.9576 0.9768

At first, this network has been learned by the experimental inputs and output. During the training period, optimizing the weights minimizes the error between the experimental and estimated boiling temperature. The derivatives of the error function with respect to the weights are estimated using the error back propagation technique, in which the error in the output layer is propagated backwards to estimate the derivatives in the lower layer [21]. The minimization of the error function is then carried out using the gradient descent method in which the weights are moved in the direction of negative gradient. Varying the number of neurons in the hidden layer carries out training. The model with the minimum number of neurons in the hidden layer that gives the desired accuracy is selected. A single hidden layer was found to be sufficient for all the three cases.

4. RESULTS AND DISCUSSION Two neural networks have been used in this research. In the first network, the ANN input data is the mole fractions of liquid and vapor phases and the output is the activity coefficient of binary system. The experimental data and the estimated results of the activity coefficient are given in tables 3 and 4.

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Table 3. experimental and estimated of the activity coefficient for 2-ethyl hexanol+TBA Experimental ANN Experimental ANN Experimental 4.7600 2.2834 2.1000 1.7121 1.2698 1.2800

ANN 4.7603 2.2528 2.2482 1.9400 1.2747 1.2753

Experimental 1.0000 1.1700 1.1900 1.3000 2.0600 2.7300

ANN 0.9980 1.1523 1.1965 1.3000 2.0603 2.7305

Table 4. experimental and estimated of the activity coefficient for 2-ethyl hexanol+NBA Experimental ANN Experimental ANN Experimental 4.5500 3.5700 2.8200 1.7700 1.3500 1.1220 1.0000 1.0000

ANN 4.5515 3.5767 2.8208 1.7724 1.3501 1.1220 1.0003 1.0000

Experimental 1.0000 1.1500 1.2499 1.4101 1.690 2.8200 3.5201 4.3000

ANN 0.9985 1.1471 1.2506 1.4101 1.6903 2.8204 3.9100 4.2982

6.00 Exp Exp ANN ANN

activity coefficient

5.00

4.00

3.00

2.00

1.00

0.00 0.00

0.20

0.40

0.60

mole fraction of TBA

Figure 2. the activity coefficient of 2-ethyl hexanol+TBA.

0.80

1.00

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239

In the figures 2 and 3, the experimental data and the ANN output have been compared. Then, the activity coefficients, which are output of the first network together with the atmospheric pressure, mole fraction of liquid and vapor phases, are given to the second network. After the learning and training of ANN the output, which is temperature, generated. Now, we can compare the experimental data with the output of ANN. Figures 4 and 5 show this comparison. The output data of model is given in the tables 5 and 6. The average absolute deviation for the temperature output was in range of 2-3.3% and for the activity coefficient was less than 0.009%. If more experimental data are available for the present system, the model could be improved to be applicable for a much wider range.

5.00 EXp Exp ANN ANN

4.50

activity coefficient

4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00 0.00

0.20

0.40

0.60

0.80

mole fraction of NBA

Figure 3. the activity coefficient of 2-ethyl hexanol+NBA. 480 exp

460

ANN

temperature/K

440 420 400 380 360 340 320 300 0.00

0.20

0.40

0.60

X or Y

0.80

1.00

1.00

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H. Ghanadzadeh and A. K. Haghi

Figure 4. Boiling temperature diagram (T) for the system of 2-ethyl-l-hexanol + TBA.

490

exp

Temperature /K

470

ANN

450 430 410 390 370 350 0.00

0.20

0.40

0.60

0.80

1.00

X or Y Figure 5. Boiling temperature diagram (T) for the system of 2-ethyl-l-hexanol + NBA.

Table 5. boiling temperatures of 2-ethyl-l-hexanol + TBA T (K) 459.5798 453.2555 441.3895 432.5254 425.7604 406.7601 385.5020

X1 0.0000 0.0025 0.0075 0.0125 0.0175 0.0549 0.1249

Y1 0.0005 0.1496 0.3870 0.5323 0.6280 0.7934 0.9371

T (K) 375.9545 370.7535 367.3869 365.4056 363.5585 361.0082 359.5574

X1 0.1949 0.2650 0.3700 0.4749 0.5799 0.7199 0.9676

Y1 0.9604 0.9698 0.9764 0.9808 0.9839 0.9879 0.9937

Table 6. boiling temperatures of 2-ethyl-l-hexanol + NBA T (K) 458.0382 453.2278 447.3343 441.5815 4426.1870 411.9936 406.1795

X1 0.0000 0.0024 0.0080 0.0156 0.0550 0.1293 0.1993

Y1 0.0007 0.1501 0.3120 0.3613 0.5635 0.7707 0.8110

T (K) 403.7110 401.6450 400.0036 398.3105 396.9314 394.6240 392.6627

X1 0.2650 0.3200 0.3900 0.4750 0.5800 0.7550 0.8935

Y1 0.8398 0.8774 0.8978 0.9172 0.9234 0.9401 0.9668

5. CONCLUSION Development of ANN model for estimating VLE is less cumbersome than methods based on EOS. It does not require parameters such as the critical properties of the components or the

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binary interaction parameters, nor the mixing rules as required by conventional methods. Binary interaction parameters may not be linearly related to the temperature and hence assumption of linear relation may lead to erroneous results. Once the ANN model is trained estimation of VLE is a one step process. This considerably saves computational time. Hence, it may be highly suitable to use it in place of conventional methods for real time process control. Since ANN works like a black box, it can be applied to any type of binary mixture for which the VLE data is available irrespective of the type of the system. However, the major disadvantage of this technique is that it can be used only in the range in which it has been trained, as it is empirical in nature. In this work, artificial neural network models have been developed for the binary systems, tert-butanol+2-ethyl-1-hexanol and n-butanol+2-ethyl-1hexanol, to estimate the vapor liquid equilibrium in the temperature range of 353.2–458.2K and the atmospheric pressure. The weights have been optimized so as to minimize the error between the estimated and experimental VLE. The weights for the models have been tabulated for all the binary systems that can be used for predicting the VLE at any temperature. The models were able to estimate the vapor liquid equilibrium satisfactorily. The percent deviation in estimating the vapor phase mole fraction was found to be similar to experimental data in ANN model. The average absolute deviation for the boiling temperature was in range of 2-3.3% and for the activity coefficient was less than 0.009%.The weights thus optimized during the training period can be used in ANN models for predicting the VLE of the binary systems at the boiling temperature in the range considered in this paper.

REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]

H. Artigas, C. Lafuente, M.C. Lopez, F.M. Royo, J.S. Urieta, Fluid Phase Equilib. 134 (1997) 163. H. Artigas, C. Lafuente, S. Martin, J. Minones Jr., F.M. Royo, Fluid Phase Equilib. 192 (2001) 49. A. Rodriguez, J. Canosa, A. Domenguez, J. Tojo, Fluid Phase Equilib.198 (2002) 95. J. Seo, J. Canosa, J. Lee, H. Kim, Fluid Phase Equilib.172 (2000)211. E. Vecher, A. Vicent, R. Gonzales, A. Marteniz, Fluid Phase Equilib.227 (2005) 239. J.B. Monton, R. Munyoz, M.C. Burguet, J. de la Torre, Fluid Phase Equilib. 227 (2005) 19. P. Oracz, M. Goral, G. Wilczek Vera, S. Warycha, Fluid Phase Equilib. 126 (1996) 71. T. Hiaki, M. Nanao, S. Urata, J. Murata, Fluid Phase Equilib. 194 (2002) 969. M.C. Lliuta, I. Lliuta, F. Lavachi, Chem. Eng. Sci. 55 (2000) 2813. R. Petersen, A. Fredenslund, P. Rasmussen, Comput. Chem. Eng. 18(1994) s63–s67. P.R.B. Guimaraes, C. McGreavy, Comput. Chem. Eng. 19 (S1)(1995) 741–746. R. Sharma, D. Singhal, R. Ghosh, A. Dwivedi, Comput. Chem. Eng. 23 (1999) 385– 390. S. Ganguly, Comput. Chem. Eng. 27 (2003) 1445–1454. S. Urata, A. Takada, J. Murata, T. Hiaki, A. Sekiya, Fluid Phase Equilib. 199 (2002) 63–78. Mohanty, S., Int. J. Refrigeration, in press. W. Potukuchi, A.S. Wexler, Atmospheric Environ. 31(1997) 741–753.

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A. Chouai, S. Laugier, D. Richon, Fluid Phase Equilib. 199 (2002) 53–62. G. Scalabrin, L. Piazza, D. Richon, Fluid Phase Equilib. 199 (2002)33–51. G. Scalabrin, L. Piazza, G. Cristofoli, Int. J. hermophys. 23 (2002)57–75. S. Laugier, D. Richon, Fluid Phase Equilib. 210 (2003) 247–255. C.M. Bishop, Rev. Sci. Instrum. 65 (1994) 1803–1832. C.M. Bishop, Neural Networks for Pattern Recognition, Oxford University Press, Oxford, 1995. [23] H. Ghanadzadeh, A. Ghanadzadeh, R. Sariri and A. Boshra, Fluid Phase Equilib. 233(2005) 123-128.

In: Organic and Physical Chemistry Using Chemical Kinetics … ISBN: 978-1-60021-763-0 Editors: Y.G. Medvedevskikh, et al. pp. 243-250 © 2007 Nova Science Publishers, Inc.

Chapter 18

LIQUID-LIQUID EQUILIBRIA OF THE MME (METHYLCYCLOHEXANE + METHANOL + ETHYLBENZENE ) SYSTEM H. Ghanadzadeh and A. K.Haghi* The university of Guilan, P O. Box 3756, Rasht, Iran P.O .Box 3756 Rasht, Iran

ABSTRACT The determination region of solubility of methanol with gasoline of high aromatic content was investigated experimentally at temperature of 288.2 K. A type 1 liquid-liquid phase diagram was obtained for this ternary system. These results were correlated simultaneously by the UNIQUAC model. By application of this model and the experimental data the values of the interaction parameters between each pair of components in the system were determined. This revealed that the root mean square deviation (RMSD) between the observed and calculated mole percents was 3.57% for methylcyclohexane + methanol + ethylbenzene. The mutual solubility of methylcyclohexane and ethylbenzene was also demostrated by the addition of methanol at 288.2 K.

Keywords: liquid-liquid equilibria; phase equilibria; plait point; ternary system; UNIQUAC model.

1. INTRODUCTION The precise liquid-liquid equilibria (LLE) data is necessary to rational design of many chemical processes and optimize extraction processes. Many researchers have investigated various kinds of multi-component systems in order to understand and provide further *

A.K.Haghi: Corresponding author e-mail: [email protected]

244

H. Ghanadzadeh and A. K. Haghi

information about the phase behavior and the thermodynamic properties of such systems [18]. In order to be able to predict LLE in multi-component systems an adequate equilibrium model. Earlier researchers reported the correlation of LLE systems with the solution model of the UNIQUAC [9-10]. This model could depends on optimized interaction parameters between each pair of components in the system, which can be carried out by experiments.By optimizing the interaction parameter, the UNIQUAC equation can be best fitted to the experimental composition. In recent years, there has been increasing attraction in adding a range of oxygenated compounds, mainly alcohols and ethers, to gasoline due to their octane enhancing [11]. Also, by using oxygenated compounds instead of Lead in the gasoline the levels of contamination can be remarkably reduced. In some countries, the oxygenated compounds such as, methyl tert-butyl ether (MTBE), tert-amyl methyl ether (TAME) and ter-amyl alcohol (TAOH) have been used. Methanol is one of the most appropriated oxygenated compounds for this purpose because of its physical-chemical properties. Methanol can be easily produced from a variety of organic materials [12], petroleum, and coal. However, phase separation and the high vapor pressure of methanol in gasoline had been a restriction for achieving a wide application. Therefore, thermodynamic studies and the precise liquid-liquid equilibria data for methanol and representative compounds of the gasoline is necessary in order to the determine region of solubility of methanol and plait point of the interest system. Recently, Trejo et al. [13] have reported liquid-liquid equilibria measurements for methanol and representative compounds of the gasoline, and their investigation were somehow important in gasoline reformation with methanol. However, the present study is an effort to show experimentally that methanol can be used as an appropriate oxygenated compound in gasoline formulations. In view of this, the investigation included, the liquidliquid phase equilibria data for three different ternary systems: methylcyclohexane + methanol +ethyl benzene at 288.2 K. Where the paraffin is methylcyclohexane a representative component of the gasoline, methanol, is the oxygenated compound, and the aromatic hydrocarbons are benzene, ethyl benzene. A high aromatic gasoline (35.4 vol % aromatic, 60.4 vol % saturates, and 4.2 vol % olefins) having density of 0.738 gr/ml was used in this study. The UNIQUAC model was used to correlate the experimental liquid-liquid equilibria data. However, the values for the interaction parameters were observed for the UNIQUAC model. The influence of aromatic compounds on mutual solubility of methylcyclohexane and methanol was also investigated at 288.2 K.

2. EXPERIMENTAL 2.1. Materials Methanol, toluene, methylcyclohexane and ethylbenzene were obtained from Merck at a purity of about 99.5 % and were used without further purification. The purity of these materials was checked by gas chromatography.

Liquid-Liquid Equilibria of the MME…

245

2.2. Apparatus and Procedure The liquid-liquid phase equilibria measurements under ambient pressure and temperature (288.2 K) were carried out using an apparatus of a 300 ml glass cell. The temperature of the cell was controlled by a water jacket and measured with a copper-constantan thermocouple and was estimated to be accurate within ± 0.1 K. A series of liquid-liquid equilibria measurements were performed by changing the composition of the mixture. The prepared mixtures were placed in the extraction vessel, and stirred for 2 h and then left to settle for 4 h. Samples were taken by a syringe (Gaschromatographic’s Hamilton 0.4 μL) from both the upper (methylcyclohexane) phase and lower layers (aromatic phase). Both phases were analyzed using Konik gas chromatography (GC) equipped with a thermal conductivity detector (TCD) and Shimadzu C-R2AX integrator. A 2 m × 2 mm column was used to separate the components

2.3. The UNIQUAC Model At liquid-liquid equilibrium, the composition of the two phases (refined phase and extracted phase ) can be determined from the following equations (γixi ) 1= (γixi ) 2

(1)

Σ xi1 = Σ xi2 =1

(2)

Here γi1 and γi2 are the corresponding activity coefficients of component i in phase 1 and 2, xi1, and xi2 are the mole fraction of components i in the system and in phase 1 and 2 respectively. The interaction parameters between methylcyclohexane , methanol and ethyl benzene are used to estimate the activity coefficients from the UNIQUAC groups. Eqs. (1) and (2) are solved for the mole fraction (x) of component i in the two liquid phase.The UNIQUAC model (universal quasi –chemical model) is given by Abrams and prausnitz [8] as c c θi Φi z c gE c = ∑xi ln( ) + ∑qi xi ln( ) − ∑qi xi ln(∑θ jτ ji ) RT i=1 xi 2 i=1 Φi i=1 j =1

(3)

or lnγi = lnγic+ lnγiR

(4)

where

⎛Φ ln γ ic = ln ⎜⎜ i ⎝ xi

⎞ z ⎛θ ⎟⎟ + q i ln ⎜⎜ i ⎠ 2 ⎝ Φi

⎞ φ ⎟⎟ + ιι − i xi ⎠

c

∑xι j =1

j j

(5)

246

H. Ghanadzadeh and A. K. Haghi ⎡ ⎛ ⎜ ⎢ c ⎜ θ τ c ⎛ ⎞ ⎢ j ij ln γ i R = qi ⎢1 − ln ⎜ ∑ θ jτ ji ⎟ − ∑ ⎜ c ⎜ ⎟ ⎢ ⎝ j =1 ⎠ j =1⎜ ∑ θ k τ kj ⎜ ⎢ ⎝ k =1 ⎣

⎞⎤ ⎟⎥ ⎟⎥ ⎟⎥ ⎟⎥ ⎟⎥ ⎠⎦

(6 )

Here, γic is combinatorial parte of the activity coefficient, and γiR the residual part of the activity coefficient. The variable τij the adjustable parameter in the UNIQUAC equation and xi the equilibrium mole fraction of component i. The parameter Фi ( segment fraction ) and θi ( area fraction ) are given by the following equation:

Φ

=

i

x i ri

∑

x i ri

i=1

θ

i

=

x i ri

ij

(8 )

c

∑

i=1

τ

(7 )

c

xiq

i

( u ij − u ⎛ = exp ⎜⎜ − RT ⎝

jj

⎞ ⎟ ⎟ ⎠

(9 )

The parameter uij characterizes the interaction energy between compounds i and j and uij equals uji.

⎛ z⎞ ⎟ (ri − q i ) − (ri − 1 ) ⎝2⎠

ιi = ⎜

(10 )

where z=10, is lattice coordination number, ri the number of segments per molecule, and qi the relative surface area per molecule.

3. RESULTS AND DISCUSSION Figures 1 compare graphically the observed and calculated phase behavior (liquid-liquid equilibria data) for three ternary system: methylcyclohexane +methanol + ethylbenzene) at temperature of 288.2 K.

Liquid-Liquid Equilibria of the MME…

247

toluene 0.5

0.5

0.6

EXP Uniquac

0.4

0.7

0.3

0.8

0.2

0.9

0.1

1.0

0.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

methanol

0.9

1.0

methylcyclohexane

Figure 1. Experimental (⎯) and predicted UNIQUAC (---) LLE data at 288.2 K.

The liquid-liquid phase diagrams exhibit type 1 systems and as expected for these type of systems, the diagrams present plait point (where the two phases in equilibrium become experimentally miscible). Due to the variation of tie-line, the measuring of plait point is slightly difficult. Meanwhile, the value of the plait point is important and it is a necessary value to define the interval of solubility that present in components of a system. On other hand, this point can define the appropriate quantity of oxygenated compound that can be added to gasoline without phase separation. In view of the above, the plait points were determined using a graphic method [14]. The values of the plait point for these systems are presented in table 3 Table 1. The UNIQUAC binary interaction parameters (u12 and u21) optimized for the system methylcyclohexane + methanol + ethylbenzene Components Methylcyclohexane methanol ethylbenzene

Methylcyclohexane 0.000 -112.337 9.17

methanol 425.760 0.000 135.369

ethylbenzene 32.675 -54.406 0.000

Table 2. The UNIQUAC structural parameters Components Ethybenzene Methylcyclohexane methanol

r 4.600 4.640 1.4311

q 3.510 3.550 1.4720

Table 3. Experimental and predicted values of the plait point and the percentage of relative error Components Methylcyclohexane-methanolethylbenzene

Experimental 0.5996

Uniquac 0.6480

Relative error % 0.917

248

H. Ghanadzadeh and A. K. Haghi

As it can be observed from figure 1, the ternary systems present a small region of partial miscibility that limited by the plait point. This reveals that, methanol is totally miscible with the gasoline in a wide interval. As illustrated in figure 1 and indicated in table 4. it is evident that despite the representative compounds of the gasoline, the region of completely miscibility and also the plait point values are nearly the same and independent of the type of aromatic hydrocarbon. This provides an advantage as it can define the appropriate quantity of oxygenated compound (methanol) that can be added to the gasoline. The UNIQUAC model was successfully used to correlate the experimental liquid-liquid equilibria data. As it can be seen from figure 1, the predicted tie lines (dashed lines) are in good agreement with the experimental data (solid lines). In other words, the UNIQUAC equations adequately fit the experimental data for this multi-component system. The optimum UNIQUAC interaction parameters uij between methylcyclohexane, methanol, and ethylbenzene were determined using the observed liquid-liquid data, where the interaction parameters describe the interaction energy between molecules i and j or between each pair of compounds. Table 4 show the calculated value of the UNIQUAC binary interaction parameters for the mixture methanol + ethylbenzene using universal values for the UNIQUAC structural parameters. The equilibrium model was optimized using an objective function, which was developed by Sørensen [15]. Table 4. Experimental and predicted LLE for the ternary system (methycyclohexane + methanol + ethylbenzene) at 288.2 K Methylcyclohexane (upper phase) Mole fraction Mole fraction methanol methylcyclohexane Exp. Uniquac Exp. Uniquac 0.8224 0.8386 0.1270 0.8810 0.7262 0.7600 0.1970 0.8659 0.6565 0.7229 0.2600 0.8360 0.5845 0.6621 0.3290 0.8040 0.5122 0.5586 0.3998 0.7699 0.4167 0.4049 0.4999 0.7070 0.3269 0.2801 0.5996 0.6480 RMSD% 4.83 4.40

Ethylbenzene (lower phase) Mole fraction methylcyclohexane Exp. Uniquac 0.2407 0.1102 0.2115 0.1181 0.1925 0.1371 0.1740 0.1591 0.1438 0.1851 0.1211 0.2328 0.1047 0.2801 2.40

Mole fraction methanol Exp. 0.8698 0.8360 0.7930 0.7675 0.7420 0.7040 0.5996

Uniquac 0.8810 0.8659 0.8360 0.8040 0.7699 0.7070 0.6480 2.67

Moreover, the objective function obtained by minimizing the square of the difference between the mole fractions calculated by UNIQUAC model and the experimental data. Furthermore, he UNIQUAC structural parameters r and q were carried out from group contribution data that has been previously reported [14-15]. The values of r and q used in the UNIQUAC equation are presented in table 4. The goodness of fit, between the observed and calculated mole fractions, was calculated in terms RMSD [1]. The RMSD values were calculated according to the equation of percentage root mean square deviations (RMSD%): ⎡ 3 2 n ⎢ ∑∑ RMSD % = 100 ∑ ⎢ i j k ⎢ ⎢ ⎣

(xi,exp − xi,calc) ⎤⎥ 2 j

6n

⎥ ⎥ ⎥ ⎦

(1)

Liquid-Liquid Equilibria of the MME…

249

Mole fraction of ethyle benzane

where n is the number of tie-lines, xexp indicates the experimental mole fraction, xcalc is the calculated mole fraction, and the subscript i indexes components, j phases and k = 1,2,…n ( tie-lines ). The average (RMSD%) between the observed and calculated mole percents with a reasonable error was 3.57% methylcyclohexane + methanol + ethylbenzene (see table 4). The percentage of relative error between the experimental and predicted values of the plait point for these systems have been also compiled in table 4. The experimental result shows that the existence of aromatic compound(ethylbenzene) in gasoline increases the solubility of methanol in methylcyclohexane. 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0.00

0.20

0.40

0.60

0.80

1.00

Mole fraction of methanol Figure 2. 1.00 0.90

Separation factor

0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 0.1

0.15

0.2

0.25

0.3

mole fraction of methanol in mch phase

Figure 3.

0.35

250

H. Ghanadzadeh and A. K. Haghi

4. CONCLUSION An experimental investigation of equilibrium behavior of the systems composed of methylcyclohexane + ethylbenzene + methanol was carried out at 288.2 K. The liquid-liquid phase diagrams exhibit type 1 systems and indicate that methanol is totally miscible with the gasoline in a wide interval. Therefore, methanol may be considered as a good candied in gasoline formulations for vehicular fuels. The optimum UNIQUAC interaction parameters between methyl cyclohexane, methanol and ethylbenzene were determined using the experimental liquid-liquid data. The average RMSD value between the observed and calculated mole percents with a reasonable error for these system were methylcyclohexane + methanol + ethylbenzene. in the UNIQUAC model.

REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]

[11] [12]

[13] [14]

[15] [16] [17]

H. Ghanadzadeh, A.Ghanadzadeh, Fluid Phase Equilibria, 202 (2002) 339. H. Ghanadzadeh, A.Ghanadzadeh, J. Chem. Thermodyn, 35 (2003) 1393-1401. A. Arce, A. Blanco, J, Martinez-Ageitos, I. Vidal, Fluid Phase Equilibria, 109 (1995) 291. M. J. Fernandez-Torres, V. Gomis-Yagues, M. Ramos-Nofuentes, F. Ruiz-Bevia, Fluid Phase Equilibria, 164 (1999) 267. J. A. Alkandary, A. S. Aljimaz, M. S. Fandary, M. A. Fahim, Fluid Phase Equilibria, 187-188 (2001) 131. N. Pesche, S. I. Sandler, J. Chem. Eng. Data, 40 (1995) 315. B. Wisniewska-goclowska, S. K. Malanowski, Fluid Phase Equilibria, 180 (2001) 103. J. F. Fabries, J.L. Gustin, H. Renon, Chem. Eng. Data , 22 (1977), 303-308 D. S. Abrams, J. M. Prausnitz, AICHE J. 21 (1975) 116. J. M. Prausnitz, T. F. Anderson, E. A. Grens, C. A. Eckert, r. Hsien, J. P. Oconnell, “Computer Calculations for Multicomponent Vapor-Liquid and Liquid-Liquid Equilibria”, Prentice-Hall, Inc, Englewood, (1980). H. Higashiuchi, Y. Sakuragi, Y. Arai, and M. Nagatani, Fluid Phase Equilibria, 58 (1990) 147. E.Velo Garcia, “Cinetica equilibria y transport de materia en la hidratacion catalitica directa de isobuteno a tert-butanol”. Ph.D. Thesis, Universitat Politecnica de catalunya Barcelona, Spain (1992) B. E. Garcia-Flores, G. Galicia-Aguilar, R. Eustaquio-Rincon, A. Trejo, Fluid Phase Equilibria, 185 (2001) 275. H.Ghanadzadeh, “Eleccion de disolventes selectivos para la extraccion en fase liquida de alcoholes C4 (ABE) a partir de biomasa. Ph.D. Thesis, Universitat Politecnica de Catalunya Barcelona, Spain (1993). J. M. Sorensen, “Correlation of liquid-liquid equilibrium data” Ph.D. Thesis, Technical University of Denmark, Lyngby, Denmark, (1980). N. Pesche, S. I. Sandler, J. Chem. Eng. Data, 40 (1995) 315. Helinger, S. I. Sandler, J. Chem. Eng. data, 40 (1995) 321.

In: Organic and Physical Chemistry Using Chemical Kinetics … ISBN: 978-1-60021-763-0 Editors: Y.G. Medvedevskikh, et al. pp. 251-255 © 2007 Nova Science Publishers, Inc.

Chapter 19

SUGAR CARBAMIDES J. A. Djamanbaev1, J. A. Abdurashitova and G. E. Zaikov2 1

Institute of Chemistry and Chemical Technology, Kyrgyz Academy of Sciences, 256 a, Chui Prospect, Bishkek 720071, Kyrgyzstan, e-mail: [email protected] 2 N.M. Emanuel Institute of Biochemical Physics, Russian Academy of Sciences, 4 Kosygin Str., Moscow 119334, Russia; E-mail: [email protected]

ABSTRACT The results of experimental researches on the synthesis of sugars derivatives with glycosylamide and thioamide bonds have been presented in this work. The possibility of using their in the preparative chemistry of sugars, some fields of medicine and agriculture has been shown.

Keywords: monosaccharides, glycosylisotiocyanates, glycosyltiocyanates, glycosylureas, glycosylnitrozometylureas.

The study of the reactions with the participation of glycosyl bonds is important not only for the theory of carbohydrates structure and reactional ability of carbohydrates. They represent a significant interest and solution for a number of important problems of organic, bioorganic chemistry, and molecular biology, fermentative catalysis, since the glycosyl bond is one of the most important structural elements of many biologically active compounds. The bioorganic chemistry laboratory of the Institute of Chemistry and Chemical Technology under the National Academy of Science of the Kyrgyz Republic is conducting studies in the area of kinetics, mechanisms of catalysis of carbohydrate reactions and development of new methods of synthesis of the physiologically active compounds with the N-glycosylamide bonds (derivatives of the sugar carbamides) for their application in medicine and other industries. Among the practically important properties of this type of derivatives of the sugar carbamides is the high hydrolytic stability as compared to the simple N-glycosides of alkyl(aryl)amines. Chemical connection of sugars with the unprotected hydrocsyl groups with the biologically active compounds at the account of stable N-

252

J. A. Djamanbaev, J. A. Abdurashitova and G. E. Zaikov

glycosylamide bonds will lead to the growth of solution in water, decrease of toxic and change of selective action of the preparations [1, 2]. Two bases approaches are used in the synthesis of sugar carbamides: direct interaction of carbohydrates with carbamides and their analogs in the conditions of acid catalysis (a) and interaction of acetylation N-glycosylisothiocyanates with amines (b) or interaction of acetylation N-glycosylamines with arylisothiocyanates (c) [3]. OH O OH

OH

+

H 2N

OH

NHR

NHR

O

+

OH

H 2O

a)

OH

OAc O OAc

N=C=O + H2N

NH C

OH

O

OH

OAc O OAc

C

H

OH O

+

R/

OAc

NH C

H N

R/ b)

O

OAc OAc OAc O OAc

OAc OAc

OAc OAc O

NH2 + C6H5NCO

OAc

NH C O

H N

C6H5

c)

OAc OAc

The first direct approach requires a long stand of the reaction mixture under high temperature. In the crystal form the product could be receive only after the fermentative splitting of un-reacted glucose. In the further studies [4-6] the direct method was somewhere improved and applied to other mono- and disaccharides, however, there were no principal changes in the synthesis methods. The second approach - amination glycosylisothiocyanates was suggested by E. Fisher [3,7]. The method was widely used in the synthesis of analogs of glycoproteins and nucleosides of pirimidine and geterocyclic derivatives of the carbohydrates [7-8]. The version of the isothiocyanates method of E. Fisher is based on the interaction between alkyl- and arylisothiocyanates with glycosylamines, produced, for example, though hydrogenezation glycosylazids [3]. These methods have many stages and require preliminary protection of the OH-groups, followed by the removal of protective functions. The advantages of E. Fisher,s method include its universality - the ability to introduce ureido (thioureido) fragments in any position of the carbohydrate ring with the presence of amino group in this position. The works of [9, 10] suggest a simplified isothiocyanates synthesis of glycosylureas. According to this method, in the beginning they receive anomerical mixture of Nalkylglycosylamines, conduct the condensation with isocyanates and receive anomerical mixture of N-alkylglycosylamines, conduct the condensation with isocyanates and receive anomerical mixture of N-alkylglycopyranosylthioureas. After the processing of this mixture with the ant acid the β-anomer of N-alkyl-N/-glycopyranosylthiourea is separated.

Sugar Carbamides OH O OH

OH

OH O

NH2R/

NHR/

OH

OH

253 OH O

RNCO

OH OH O

C

NHR

O OH

OH

H+

NH

OH OH

OH

R/

R/ N

OH OH

C

NHR

O OH

The authors suggest a new more effective method of synthesis of N-glycosylcarbamides with the use of N-arylglycozides [11, 12]. The kinetic studies have shown that the replacement of the glycosyl hydrocsyl by N-arylaglycon leads to the growth of the reaction properties of C1 in the reactions of nucleophilic addition and replacement, easing introduction of aglycons with small basic in the conditions of acid catalysis. OH O

OH O OH

OH

+ NH2C6H4R

OH

- H2O

OH

NHC6H4R/ +

OH OH

NH2CONHR//

-NH2C6H4R/

OH OH O HN

C

NH

R//

O

OH OH OH /

R =H, CH3 , ì -NO2, ï

C

O OH

R//=H, CH3, C2H5, C3H7, C4H9, C6H5, C6H4OCH3

To receive N-glycosylureas on the reaction of N-transglycosylation, it is enough to heat the mixture of ureido derivatives and N-arylglycozides for a short period (10-30 min.) in an alcohol environment with some small addition of mineral acid until the mixture becomes homogenous. The scheme shows that arylamine plays the role of nucleophilic catalyst reaction of direct condensation of monosaccharide with the ureido derivatives. That is why in order to simplify the synthesis of N-glycosylureas, one can go without N-arylglycozid and instead use the catalyst additions of arylamine [13, 14]. When using the small basic m-nitroanilin as a catalyst, β-anomerical forms of glucopyranosylureas are mostly formed. The stability of N-glycosylamid bond allows to recommend these fragments as a connecting bridge between sugars and biologically active compounds for the receiving sugar derivatives as drugs. The use of sugar carbamides is limited mostly to N-glycosylureas, which are recommended for technical reasons. Currently, a more important tendency is developing which leads to their applications in the area of medical-biological problems. The sugar derivatives with N-nitrozo-N-alkylcarbamide fragments deserve a special attention due to their important role in the chemical therapy of the cancer diseases [15, 16].

254

J. A. Djamanbaev, J. A. Abdurashitova and G. E. Zaikov

The interest to compounds of this class arouse after the discovering of high antileucemia activity of 1-methyl-1-nitrozourea [15]. Methods of synthesis of N-nitrozocarbamide fragments in the carbohydrate rings were worked out to get select acting antitumour remedies [17, 18, 19, 20]. Comparative methods of pharmaco-toxicological research help to ascertain [2, 19] that adding of N-nitrozo-N-metylurea on the glycosyl center leads to the sharp lowering of toxic activity of the antitumour preparation and to changing of spectrum of its activity to a number of experimental swelling models. It is shown, that toxic and selective actions of carbohydrate analogs of nitrozometylurea depend on the monosaccharide carrier of the cytosine agent. N-nitrozo derivatives of N-glycosylureas attract attention to them not only as perspective antitumour preparations also as compounds with high reactional ability on the bases of which new methods of the carbohydrate derivative synthesis can be developed. The authors in their works [21, 22] show that N-nitrozo derivative of carbohydrates can easily come into the reaction of substitution on carbonil group of N-aglicon witch the help of interaction of amines witch the development of sugar carbohydrate derivatives. OH O OH

NH C

N(NO)CH3

OH O

NH2R

NH C

OH

O

H N

R + CH3OH + N2

O

OH

OH

OH

OH

The described reaction opens great possibilities for the synthesis of different Nglycosylation derivatives witch carbamide bridges including such derivatives of sugar, the synthesis of which by methods of direct interaction of nucleophilic agents with a glycoside center, turns out to be difficult for poor reactional ability of the attack amino group. The example of it can be shown by reaction of N-glycosylation semicarbazids [22]. OH O OH

NH C

N(NO)CH3

OH O

NH2-NH2

OH

O

OH

NH C O

H N

NH2 + CH3OH + N2

OH OH

OH

The developed method of getting of glycosylation semicarbazids with N-glycosyl bond and the final reactional amino group opens wide possibilities in the chemistry of semicarbazid derivatives.

REFERENCES [1] [2] [3]

V. A. Afanasjev, J. A. Djamanbaev, G.E. Zaikov // Progress in chemistry. V. 51. 1982. p.661. J. A. Djamanbaev, L. A. Ostrovskaja, V. A. Afanasjev // Chemical therapy of suellings in the USSR. Issue 52. 1988. p. 145. J. Goodman. Adv. Carbohydrate Chem.V.13. 198. p. 215.

Sugar Carbamides [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]

[20] [21] [22]

255

Benn M.N., Jones A.S. J. Chem. Soc. V.82. 1960. p. 3837. Badawi E. Jones A.S. Staseg M. Tetrahedron. 1966. p.281. N. G. Shkantova, M. I. Dudkin, S.E. Grinshpun // J. Life of applied chemistry. V. 40. 1967. p. 164. Zbigniew by ,Witczak J. Adv. Carbohydrate Chem. and biochem. V.44. 1986. p. 91. Djamandaev J.A., Abdurashitova J.A., Sarimzakova R. K., Dermugin V.S.//Vestnic KNU.-Bishkek.-2003.-Ser. 3.-V.-1.-p. 123. Tsujihara K., Ozeki M., Morikawa T., Arai Y. Chem. pharm. Bull. V. 29. 1981. p. 2509. Tsujihara K., Ozeki M., Morikawa T.,Kawamori M., Akaike Y., Arai Y.// J. Med. Chem. V. 25. 1982. p. 441. V. A. Afanasjev, J. A. Djamanbaev // Proceeding of the Academy of sciences of Kyrg SSR. № 2. 1973. p. 64. V. A. Afanasjev, J. A. Djamanbaev // Chemistry of natural compounds. № 2. 1974. p. 176. V. A. Afanasjev, J. A. Djamanbaev // Proceeding of the Academy of sciences of Kyrg SSR. № 2. 1982. p. 43. V. A. Afanasjev, J. A. Djamanbaev, E. I. Kurmanalieva / Author, certificate USSR. № 772101. 1980. N. M. Amanual, D.B. Korman, L. A. Ostrovskaja, L. B. Gorbacheva, N.P. Dementjeva. Nitrozoalkylureas – a new class of antisuellig means. M: Science. 1977. 320 p. Schein P.S., Heal J., Gveen D., Wolley P.V. Fudman. Cancer Chemotherapy. (Basel). 1978. B. 64. Suami T., Machinami T. Bull. Chem. Soc. Japan. V. 43. 1970. p. 2953. Panasci L.C., Fox P.A., Schein P.S. Cancer. Res. v. 37. 1974. p. 3321. N. M. Amanual, D.B. Korman, L. A. Ostrovskaja. From the collection of conferences. Actual problems of the swelling experimental chemical therapy. Chernogolovka. 1980. p. 126. V. A. Afanasjev, J. A. Djamanbaev . Patent of the USA. № 4.656.259. 1987. J. A. Djamanbaev, V. A. Afanasjev, Z. А. Djamanbaeva / Collection. Carbohydrates and carbohydrate plants of Kyrgyzstan. Publishing house: Ilim. Frunze. 1984. p. 3. J. A. Djamanbaev, Z. А. Djamanbaeva, V. A. Afanasjev. Rospatent. № 2027721. 1995.

In: Organic and Physical Chemistry Using Chemical Kinetics … ISBN: 978-1-60021-763-0 Editors: Y.G. Medvedevskikh, et al. pp. 257-277 © 2007 Nova Science Publishers, Inc.

Chapter 20

IMPACT OF CHAIN-END STRUCTURE, BASIC COMONOMER INCORPORATION AND PENDANT STRUCTURE ON THE STABILITY OF VINYLIDENE CHLORIDE BARRIER POLYMERS Bob A. Howell*, Adeyinka O. Odelana and Douglas E. Beyer Center for Applications in Polymer Science Central Michigan University

INTRODUCTION Vinylidene chloride copolymers occupy a place of prominence in the barrier plastic packaging industry. The homopolymer, poly(vinylidene chloride) (PVDC), is not commercially important because it undergoes catastrophic decomposition at its melt temperature. Rather, it is the copolymers with vinyl chloride, alkyl acrylates, acrylonitrile, and alkyl methacrylates that are commercially viable.[1-8] The vinylidene chloride copolymers contain low levels of unsaturation due to thermal dehydrochlorination during polymerization. Copolymerization with one or more comonomers (≤ 15 wt %) decreases melt temperature and increases solubility. Often one copolymer is introduced to improve processability or solubility of the polymer, while another is introduced to provide specific use properties. A vinylidene chloride (VDC) copolymer containing high VDC content acts as excellent barrier to the transport of small molecules, principally oxygen, (to prevent food spoilage) as well as excellent barrier to the transport of flavor and aroma constituents (to prevent flavor scalping on the store shelf).[9-11] These copolymers occupy a place of prominence in the barrier plastics packaging industry. They have been used as wraps for meat and diary products, and as components of rigid multilayer structures such as bottles, jars, tubs, etc. Packages are important for good appearance, taste and shelf life. Modern packaging *

Bob A. Howell: Mt. Pleasant, MI 48859-0001; [email protected]

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represents a sophisticated technology rooted deeply in fundamental polymer science. Plastics represent a large percentage of new packaging materials. Plastics have many advantages over conventional packaging materials for many applications. These advantages include: • • • •

Plastics can be used over a wide range of temperature. Some plastics, principally VDC copolymers, provide an excellent barrier to the transport of small molecules such as oxygen, water, and carbon dioxide. Providing good moisture barrier thus preventing dehydration of food items. Providing an aroma barrier to help retain flavor in foods and to prevent the absorption of undesirable flavors or aroma.

Copolymerization results in regular structure, high density, and high crystallinity. These polymers are generally free of the defect sites characteristic of similar vinyl polymers, i.e., they are regular head- to-tail, unbranched and highly crystalline polymers. While these outstanding characteristics have made them commercial successes, high VDC content copolymers undergo thermally-induced degradative dehydrochlorination at process temperatures. The thermal instability of VDC and its copolymers has been of interest for several decades.[12,13] The dehydrochlorination occurs at modest temperatures (120 – 200 °C) and is a typical chain process involving initiation, propagation, and termination phases (figure 1), often enhanced by defects in the polymer mainchain.[14-16] Defect structures, arising from internal unsaturation (allylic dichloromethylene groups), serve as initiation sites for the degradation.[17] Sequential dehydrohalogenation can lead to the formation of conjugated polyene sequences along the polymer mainchain.

Figure 1. Hydrogen Chloride Evolution for the Thermal Degradation of a Typical Vinylidene Chloride Polymer.

This is the primary degradation process accompanying processing of the polymer. The early stage of the dehydrochlorination process is uncomplicated by interfering processes. The only product observed by evolved gas analysis is hydrogen chloride (scheme 1). The sample

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weight loss is directly reflective of the extent of degradation.[18, 19] Hence, the degradation of vinylidene polymers presents an ideal reaction that can be studied using thermogravimetric techniques.[20, 21]

CH2

Fast

CCl2

CH

n

CCl n

+

n HCl

Scheme 1. The Principal Step Involved in the Thermal Degradation of Vinylidene Chloride Polymers.

These copolymers must, therefore, be processed with care at relatively low temperatures (150 – 170 °C) in specially designed equipment. If appreciable, the degradation can lead to discoloration of the materials thereby making them unsuitable for packaging.

Scheme 2. Mode of Degradation of Vinylidene Chloride Polymers.

Thermal homolysis of an allylic carbon – chlorine bond generates a tight carbon, chlorine radical pair. The chlorine atom abstracts an adjacent hydrogen atom to extend the unsaturation by one unit. Allylic dichloromethylene units are regenerated in the polymer mainchain and serve as initiation sites for degradation and so propagate the dehydrochlorination reaction (scheme 2).[14] Another consequence of this degradation is the evolution of hydrogen chloride. The vinylidene chloride repeat unit loses a mole of hydrogen chloride which can react with the walls of process equipment, commonly stainless steel, to form iron(III) chloride which is a strong Lewis acid catalyst, strong enough to promote further dehydrohalogenation of the vinylidene repeat units at process temperatures (120 – 200 °C). Hence, this problem must be overcome or at least controlled to permit the commercial

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exploitation of these materials. One way is to scavenge the hydrogen chloride as it is formed during thermal degradation. This will prevent reaction with the walls of the processing equipment and the subsequent formation of metal halides. Attempts to stabilize VDC systems have often resulted in decreased stability as a result of E2 elimination reactions which introduce initiation sites (unsaturation) for the thermal degradation. Presently, passive bases such as magnesium oxide, or tetrasodium pyrophosphate which are capable of absorbing hydrogen chloride, are introduced into the polymer melt during processing to partially overcome this problem.[22] However, the presence of these inorganic bases may negatively impact clarity of finished items, particularly for film applications. For this reason organic bases which would be compatible with the polymer, and would effectively absorb evolved hydrogen chloride, and would not actively promote the dehydrochlorination reaction have been sought.[23] Amines, even highly hindered amines, have been found to be too basic to function as satisfactory stabilizing additives.[24,25] In this case, an amine has been incorporated as a comonomer into a vinylidene chloride copolymer. Vinylidene chloride copolymers containing a constant five mole percent methyl acrylate and small but varying amounts (0.1 – 3.0 mole percent) of 4-vinylpyridine have been subjected to thermogravimetry to assess thermal stability. In addition, some limited studies of the impact of initiator used for polymerization and the nature of acrylate comonomer on the thermal stability of vinylidene chloride polymers have been initiated using thermogravimetric techniques.

RESULTS AND DISCUSSION The thermal degradation of the vinylidene chloride /methyl acrylate copolymer at modest temperatures (120 – 200 °C) corresponds to the first order loss of hydrogen chloride from the vinylidene chloride repeat units in the polymer. Since hydrogen chloride has been shown to be the only volatile product of the degradation at these temperatures, the degradation reaction can be easily studied by thermogravimetry.[14-16, 18-21] Hence, the rate of change of sample mass is a measure of the rate of degradation. It has also been found that the thermal degradation is a typical chain process involving initiation, propagation, and termination phases (figure 2), often enhanced by defects in the polymer mainchain.[14] The degradation becomes prominent in the vicinity of 190 °C and occurs smoothly to reflect the loss of one mole of hydrogen chloride from each vinylidene chloride repeat unit in the polymer chain (figure 2). Both initiation and propagation phases of degradation are obvious in the plot of weight loss versus time (figure 2). However, this becomes more apparent in the plot of ln{(w∞- wo) / w∞ - wt)} versus time (figure 3) , where w∞ is the weight of the sample at infinite time (t∞) taken as that weight which would remain after 37.62% of the initial vinylidene chloride component weight had been lost (corresponding to the loss of one mole of hydrogen chloride from the vinylidene chloride repeat units in the polymer); wt is the sample weight at any time, t, during the experiment; and wo is the sample weight at time zero (to), i.e., the time at which the first point was recorded.

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Figure 2. Degradation of a Vinylidene Chloride/Methyl Acrylate (Five Mole percent)/ 4-Vinylpyridine (0.1 Mole Percent) Terpolymer at 170 °C.

0.07

ln(W ∞-W o /W ∞-W t)

0.06 0.05 0.04 0.03 0.02 0.01 0 0

500

1000

1500

2000

2500

Time (sec) Figure 3. Thermal Degradation of a Vinylidene Chloride/Methyl Acrylate (Five Mole Percent)/ 4Vinylpyridine (0.1 Mole Percent) Terpolymer at 170 °C.

The initiation degradation reaction is apparent in the initial portion of the weight loss versus time plot while the propagation reaction is dominant at long reaction time. Thus rate constants for both processes may be extracted from the data presented in this plot. Data from the appropriate portions of this plot are replotted in figures 4 and 5. Figure 4 represents a plot of ln mass change versus time for the early portion of the degradation in which initiation is occurring. An excellent linear plot is obtained for which the slope reflects the rate constant, ki, for the initiation of degradation. Similarly, the corresponding plot (figure 5) of data at long reaction time allows the extraction of kp, the rate constant for propagation of the degradation

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ln (w∞ - wo/w∞ -

reaction. Multiple determinations were carried out at three different temperatures to obtain reliable rate constants for the determination of activation parameters. In all cases excellent reproducibility was observed. The rate constants for the degradation at 170, 180, and 190 °C are tabulated in table 1.

Figure 4. Initiation Rate Constant (ki) for the Thermal Degradation of a Vinylidene Chloride/Methyl Acrylate (Five Mole Percent)/ 4-Vinylpyridine (0.1 Mole Percent) Terpolymer at 170 °C.

Figure 5. Propagation Rate Constant (kp) for the Thermal Degradation of a Vinylidene Chloride/Methyl Acrylate (Five Mole Percent)/ 4-Vinylpyridine (0.1 Mole Percent) Terpolymer at 170 °C.

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Table 1. Rate Constants for the Thermal Degradation of Vinylidene Chloride/Methyl Acrylate (Five Mole Percent)/4-Vinylpyridine (Variable Content) Terpolymers. 4-Vinylpyridine (Mole %) 0 0 0 0.1 0.1 0.1 0.3 0.3 0.3 0.5 0.5 0.5 1

ki x 105 (sec-1)a,c 1.54 ± 0.02 3.31 ± 0.03 6.27 ± 0.02 1.86 ± 0.01 3.65 ± 0.05 6.62 ± 0.01 20.2 ± 0.10 30.3 ± 0.10 38.8 ± 0.10 46.4 ± 0.30 57.1 ± 0.10 65.5 ± 0.20

kp x 105 (sec-1)b,c 2.07 ± 0.04 4.27 ± 0.01 8.97 ± 0.02 2.26 ± 0.01 4.76 ± 0.01 9.28 ± 0.01 25.3 ± 0.20 32.1 ± 0.10 44.8 ± 0.40 54.6 ± 0.10 62.3 ± 0.10 72.9 ± 0.11 204.0 ± 3.00

Temperature (°C) 170 180 190 170 180 190 170 180 190 170 180 190 170

a. Rate constant for the initiation of degradation. b. Rate constant for the propagation of degradation. c. Average of three determinations accompanied by the average deviation.

It may be noted that the rate constants for degradation of the vinylidene chloride/methyl acrylate (five mole percent) copolymer containing no 4-vinylpyridine (ki = 1.54 x 10-5 sec-1 ; kp -5 -1 -5 -1 = 2.07 x 10 sec ) are virtually identical to those previously reported; (ki = 1.55 x 10 sec ; kp -5 -1 = 2.09 x 10 sec ).[1] To demonstrate the impact of the increasing incorporation of 4-vinylpyridine into the polymer in a consistent manner, data from table 1 reflecting degradation at a single temperature (170 °C) are collected in table 2. Table 2. Rate Constants for the Thermal Degradation of Vinylidene Chloride/Methyl Acrylate (Five Mole Percent)/ 4-Vinylpyridine (Variable Content) Terpolymers at 170 °C 4-Vinylpyridine (Mole %) 0 0.1

ki x 105 (sec-1)a,c 1.54 ± 0.02 1.86 ± 0.01

kp x 105 (sec-1)b,c 2.07 ± 0.04 2.26 ± 0.01

0.3

20.15 ± 0.10

25.25 ± 0.2

0.5 1

46.44 ± 0.3 -

54.60 ± 0.10 240.03 ± 3.00

a. Rate constant for the initiation of degradation. b. Rate constant for the propagation of degradation. c. Average of three determinations accompanied by the average deviation.

The initiation and propagation rate constants for the degradation of the 4-vinylpyridine copolymers obtained at several temperatures may be used to determine both the activation

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energy (Ea) and the enthalpy of activation (ΔH‡) for the two processes. This is illustrated for the determination of the Arrhenius activation energy for the initiation of degradation of a vinylidene chloride/methyl acrylate (five mole percent)/4-vinylpyridine (0.1 mole percent) copolymer. A plot of ln ki versus 1/T for the reaction is shown in figure 8. The slope of this plot is given by -13037 and is equal to - Ea/R where R, the gas constant, is 1.9872 cal/mol·deg. The value of the Arrhenius activation energy, Ea, for the initiation process is then equal to - (-13037) x (1.9872 cal/mol·deg), i.e., 25.91 kcal/mol. Similarly, from a plot of ln (k/T) versus 1/T, the enthalpy of activation for each process may be obtained. This is also illustrated for the determination of the activation enthalpy for the propagation of degradation of a vinylidene chloride/methyl acrylate (five mole percent)/4vinylpyridine (0.1 mole percent) copolymer in figure 7. The slope of the plot of ln (kp/T) versus 1/T (figure 7) is given by -ΔH‡/R and the enthalpy of activation, ΔH‡, for the propagation reaction is calculated to be equal to 27.92 kcal/mol. The activation parameters for both the initiation and propagation reactions are recorded in table 3.

Figure 6. Arrhenius Activation Energy for the Initiation of Degradation of a Vinylidene Chloride/ Methyl Acrylate (Five Mole percent)/ 4-Vinylpyridine (0.1 Mole Percent) Terpolymer.

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Figure 7. Activation Enthalpy for Propagation of the Thermal Degradation of a Vinylidene Chloride/ Methyl Acrylate (Five Mole Percent)/ 4-Vinylpyridine (0.1 Mole Percent) Terpolymer.

Table 3. Activation Parameters for the Initiation and Propagation Reactions for the Thermal Degradation of Vinylidene Chloride/ Methyl Acrylate (Five Mole Percent)/ 4Vinylpyridine (Variable Content) Terpolymers. 4-Vinylpyridine (Mole %) 0 0 0.1 0.1 0.3 0.3 0.5 0.5

Enthalpy of Activation, ΔH‡, (kcal/mol)a 27.76 29.01 25.01 27.92 10.78 12.43 4.96 6.17

Arrhenius Activation Energy, Ea, (kcal/mol)a 28.66 29.91 25.91 28.82 11.68 13.33 5.86 7.07

Entropy of Activation, ΔS‡, (cal/mol·deg; 190°C)b -9.42 -7.7 -12.35 -8.86 -25.9 -24.26 -31.73 -30.53

Process Initiation Propagation Initiation Propagation Initiation Propagation Initiation Propagation

a. Based on the uncertainty in the values for rate constants and the temperature control (± 0.02 ºC) possible with the TGA unit, the estimated uncertainty in activation values is less than 0.1 kcal/mol. b. Calculated from the expression: ΔS±/R = ln k-23.760 – ln T – ΔH‡/RT.

The degradation onset and the temperatures of maximum degradation were determined from the derivative plot of weight loss versus temperature (as illustrated in figure 8) and are displayed in table 4. A composite plot for the degradation of the 4-vinylpyridine containing polymers is displayed in figure 9.

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Figure 8. Derivative Plot of Weight Loss versus Temperature for the Thermal Degradation of a Vinylidene Chloride/Methyl Acrylate (Five Mole Percent) / 4-Vinylpyridine (0.5 Mole Percent) Terpolymer at 170 °C.

Table 4. Thermal Degradation of Vinylidene Chloride /Methyl Acrylate (Five Mole Percent) / 4-Vinylpyridine (Variable Content) Terpolymers. 4Vinylpyridine (Mole %) 0 0.1 0.3 0.5

Degradation Onset a (°C) 202 200 194 184

Temperature of Maximum Degradation Rate. b (°C) 241 231 222 215

a. Extrapolated onset temperatures from the derivative plot of weight loss versus temperature; the reproducibility for multiple determinations is ± 0.2 ºC. b. Maximum in the derivative plot of weight loss versus temperature; the reproducibility for multiple determinations is ± 0.1 ºC.

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Figure 9. Composite Plot of Weight Loss versus Temperature (°C) for the Thermal Degradation of Vinylidene Chloride/ Methyl Acrylate (Five Mole Percent)/ 4-Vinylpyridine (Variable Content) Terpolymers.

From a composite plot of weight loss versus temperature (°C) for the thermal degradation of vinylidene chloride/methyl acrylate (five mole percent) /4-vinylpyridine (variable content) terpolymers shown in figure 9, it is observed that the incorporation of low levels of 4vinylpyridine (0.1-3 mole percent) into the copolymer has a great impact on stability. All vinylpyridine copolymers are less stable than the standard vinylidene chloride/methyl acrylate polymer containing no 4-vinylpyridine. The instability increases as the mole percent of the 4vinylpyridine in the polymer increases. The polymer containing 3% 4-vinylpyridine is dramatically less stable. These qualitative observations are also supported by the rate constants presented in table 1 and the activation parameters recorded in table 3. Both the initiation and the propagation rate constants for the degradation of the polymers increase as the levels of 4-vinylpyridine in the copolymer increase. Similar conclusions can be drawn from a consideration of the temperatures for the onset of degradation compiled in table 4. The extrapolated onset temperatures decrease as the mole percent of the 4-vinylpyridine increases. The copolymer containing three mole percent 4-vinylpyridine has an extrapolated onset temperature for degradation of approximately 130 °C! These results are fully consistant with the conclusions from an NMR study of thermal aging of these polymers.[26] The stability of vinylidene chloride copolymers generated using different polymerization initiators has also been examined. The two common types of initiators for radical polymerization are azo compounds and peroxides. A common azo initiator is azoisobutronitrile or AIBN. The initiation of vinylidene chloride polymerization using AIBN is illustrated in scheme 3.

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Scheme 3. Initiation of Vinylidene Chloride Polymerization Using AIBN as Initiator.

It can be seen that the initiator fragment to chain end linkage is a carbon-carbon bond. In contrast for initiation using a peroxide the initiator fragment to chain end linkage is a carbonoxygen bond (see scheme 4).

Scheme 4. Initiation of Vinylidene Chloride Polymerization Using Di-t- butyl Peroxide (TBPO) as Initiator.

It has sometimes been observed that vinylidene chloride polymers generated using peroxide initiators are less stable than similar polymers generated using azo initiators. What is the origin of this difference in stability? Could it arise as a consequence of differences in chain-end structure? To explore this possibility the thermal stability of two polymers generated using azo initiators (similar in structure to AIBN) and another produced using di-tbutylperoxide (TBPO) as initiator has been examined using thermogravimetry. A direct comparison of the thermal degradation characteristic of these polymers is provided in figure 10.

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Figure 10. Composite Plot of Weight Loss versus Temperature (°C) for the Thermal Degradation of Vinylidene Chloride/ Methyl Acrylate (Five Mole Percent) Copolymers Generated Using Different Initiators.

This comparison suggests that there is little difference in the thermal stability of the three polymers. This is supported by the extrapolated onset temperatures (see table 5) for the degradation obtained from the derivative plots of weight loss versus temperature. Table 5. Thermal Stability of Vinylidene Chloride /Methyl Acrylate (Five Mole Percent) Copolymers Generated Using Different Initiators

Initiator Type Azo Azo Peroxide (TBPO)

Initiation Temperature (°C) 34 86 86

Degradation Onset (°C)a 208 202 202

Temperature of Maximum Degradation Rate. (°C)b 234 238 237

a. Extrapolated onset temperatures from the derivative plot of weight loss versus temperature; the reproducibility for multiple determinations is ± 0.2 ºC. b. Maximum in the derivative plot of weight loss versus temperature; the reproducibility for multiple determinations is ± 0.1 ºC.

The onset temperature for degradation is virtually identical for the three polymers. This would suggest that any thermal instability observed for vinylidene chloride polymers generated using peroxide initiators must arise elsewhere, perhaps from residual initiator in the finished polymer.

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It has been suggested that vinylidene chloride copolymers containing alkyl pendants display stability greater than that of the corresponding polymer with no alkyl side-groups.[27] The pendant alkyl groups presumably serve as sources of hydrogen atoms which may be abstracted by reactive species (chlorine atoms, carbon radicals) formed by degradation along the mainchain. This has been tested for with vinylidene chloride/ butyl acrylate copolymers.[20] A most probable mode of stabilization is outlined in scheme 5. Chlorine atoms formed from thermolysis of a carbon-chlorine bond may abstract a hydrogen atom from the alkyl pendant rather than the mainchain which would introduce unsaturation. The most probable hydrogen atom to be abstracted is that adjacent to the oxygen atom since the resulting carbon radical would be conjugatively stabilized. It was shown that this process was not competitive with hydrogen abstraction from the mainchain.[20] Figure 11 presents a direct comparison of the thermal degradation characteristics of these polymers. The fate of the radicals formed in the potential stabilization process is illustrated in scheme 6.

Scheme 5. Proposed Mode of Stabilization of Vinylidene Chloride Copolymers Containing Pendant Butyl Ester Groups.

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Scheme 6. Proposed Fates of Radicals Formed by Butyl Ester Sidechain Scavenging of Chlorine Atoms Generated During the Degradative Dehydrochlorination of Vinylidene Chloride/ Butyl Acrylate Copolymers.

In this instance the thermal stability of vinylidene chloride /alkyl acrylate copolymers in which the alkyl groups are isomeric butyl units has been examined by thermogravimetry. The butyl ester comonomers incorporated are shown below (scheme 7).

Scheme 7. Structures of Butyl Ester Comonomers Incorporated Into Vinylidene Chloride Polymers.

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A composite plot of weight loss versus temperature for the degradation of vinylidene chloride copolymers containing five mole percent of an isomeric butyl acrylate comonomer is displayed in figure 11. From this plot it is apparent that there is little difference in the degradation behavior of these polymers. This is even more apparent from the degradation onset data presented in table 6. As may be seen the onset temperature for degradation is essentially identical independent of the nature of the butyl group. This is somewhat surprising, particularly for the case of the sec-butyl ester. The potential stabilization as a consequence of the presence of the sec-butyl acrylate comonomer is illustrated in scheme 8. As shown in this scheme, the radical formed by hydrogen atom abstraction would be both fully substituted and alpha to oxygen, and therefore, should be considerably more stable than the corresponding radicals formed in the case of the other esters.

Figure 11. Composite Plot of Weight Loss versus Temperature (°C) for the Thermal Stability of Vinylidene Chloride / Butyl Acrylate Ester (Five Mole Percent) Copolymers.

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Figure 12. Composite Plot of Weight Loss versus Temperature (°C) for Vinylidene Chloride/ Butyl Acrylate Ester (Five Mole Percent) Copolymers and for Comparison a Vinylidene Chloride/ Methyl Acrylate (Five Mole Percent) Copolymer.

A composite plot of weight loss versus temperature for vinylidene chloride/ butyl acrylate ester (five mole percent) copolymers and for comparison a vinylidene chloride/methyl acrylate (five mole percent) copolymer is displayed in figure 12. The figure shows that the stability of the copolymers containing butyl acrylate was no greater than that of the polymer containing methyl acrylate as comonomer. This observation is supported by the extrapolated onset temperatures (see table 6) for the degradation obtained from the derivative plots of weight loss versus temperature. Table 6. Thermal Stability of Vinylidene Chloride/ Butyl Acrylate Ester (Five Mole Percent) Copolymers and a Vinylidene Chloride/ Methyl Acrylate (Five Mole Percent) Copolymer

VDC Copolymer

Degradation Onset (°C)

VDC / MA VDC / BA VDC / IBA VDC / SBA

200 204 205 207

Temperature of Maximum Degradation Rate(°C) 241 241 244 243

a. Extrapolated onset temperatures from the derivative plot of weight loss versus temperature; the reproducibility for multiple determinations is ± 0.2° C. b. Maximum in the derivative plot of weight loss versus temperature; the reproducibility for multiple determinations is ± 0.1° C.

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Scheme 8. Possible Mode of Stabilization of a Vinylidene Chloride Copolymer Containing Pendant secButyl Ester Groups.

From the data presented here it is clear that little stabilization is provided by the presence of pendant buytl groups of any structure despite the fact that abstractable hydrogen atoms, particularly in the case of the sec-butyl acrylate copolymer, are available. This stands in contrast to an earlier observation that the presence of aliphatic pendant groups afforded stability for vinylidene chloride copolymers.[43] It may be that the size of the pendant groups in this case is too small, i.e., that the availability of abstractable hydrogen atoms is not great. Further work will be required to resolve this issue. Both methyl acrylate and butyl acrylate have been used to prepare vinylidene chloride copolymers with sufficient stability to permit thermal processing. The presence of alkyl acrylate units in the polymer mainchain limits the size of vinylidene chloride sequences and thus the propagation of degradative dehydrochlorination. More importantly it lowers the melt

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temperature such that processing can be accomplished at a temperature at which thermal dehydrochlorination is not prominent. In an attempt to determine whether or not one comonomer is more suitable for the purpose of generating relatively stable vinylidene chloride copolymers, copolymers containing five mole percent methyl acrylate, butyl acrylate, and 2.5 mole percent of each methyl acrylate and butyl acrylate have been investigated using thermogravimetry. A composite plot of weight loss versus temperature for the degradation of the three polymers is shown in figure 13.

Figure 13. Thermal Degradation of Vinylidene Chloride/ Alkyl Acrylate Copolymers.

It is apparent that there is little difference in the stability of the three polymers. This is supported by the degradation onset data presented in table 7. The onset temperature for degradation is virtually identical for the three polymers. Based upon this very limited exploration it would appear that the presence of either monomer in the copolymer has effectively the same impact on stability. Table 7. Thermal Stability of VDC/ Alkyl Acrylate (Five Mole Percent) Copolymers

VDC Copolymer VDC / MA VDC/BA VDC / MA / BA

Degradation Onset (°C)a 200 204 204

Temperature of Maximum Degradation Rate. (°C)b 241 241 240

a. Extrapolated onset temperatures from the derivative plot of weight loss versus temperature; the reproducibility for multiple determinations is ± 0.2 °C. b. Maximum in the derivative plot of weight loss versus temperature; the reproducibility for multiple determinations is ± 0.1 °C.

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CONCLUSION The kinetics of the thermally-induced degradative dehydrochlorination of vinylidene chloride copolymers are well suited for study using thermogravimetry. The degradation corresponds to a well defined process – the first order elimination of hydrogen chloride- such that the mass loss as a function of time provides a direct reflection of the extent of degradation. Degradation may be studied in two ways; degradation as a function of temperature (dynamic) and degradation at constant temperature as a finction of time (isothermal). Initiation and propagation rate constants of the dehydrochlorination reaction can be obtained from isothermal thermogravimetric data. For the dynamic method, samples were subjected to increasing temperature at a rate of 5 °C/min. over a range of 25 to 350 °C. Polymers containing even small levels of 4-vinylpyridine undergo facile thermally-promoted degradative dehydrochlorination. All the polymers containing 4-vinylpyridine are less stable than the standard vinylidene chloride/methyl acrylate (five mole percent) copolymer. The polymer containing three mole percent 4-vinylpyridine is dramatically less stable with degradation onset at about 130 °C. This demonstrates that the pyridine moiety is sufficiently basic so as to actively strip hydrogen chloride from vinylidene chloride units, promoting E2 elimination in vinylidene sequences to generate initiation sites (internal unsaturation; allylic dichloromethylene units) for the thermal dehydrochlorination reaction. Limited studies suggest that the nature of the initiator, azo versus peroxide, used for the preparation of vinylidene chloride copolymers has little influence on the stability of the resulting polymers. The nature of the comonomer incorporated, methyl versus butyl acrylate, also seems to have little impact on the stability of the copolymers generated. The incorporation of isomeric butyl acrylate esters into vinylidene chloride copolymers also displays little impact on the stability of the resulting polymer, beyond that obtained by incorporation of any comonomer, independent of butyl structure.

REFERENCES [1]

[2] [3] [4] [5] [6] [7] [8] [9]

R.A. Wessling, D.S. Gibbs, P.T. Delassus, B.E. Obi, and B.A. Howell, Kirk-Othmer Encyclopedia of Chemical Technology, John Wiley and Sons, 2nd Edition, New York, NY, (1997), Vol 24, pp. 883-923. P.T. Delassus, J. Vinyl Tech., 3, 240, (1981), and references cited therein. P.T. Delassus, K.L. Wallace and H.J. Townsend, Polym. Prepr., 26, 116, (1985). G. Talamini and E.Peggion, in “Vinyl Polymerization”, G.E. Ham, Ed., Part 1, Vol. 1, Dekker, New York, (1967), Chapter 5. A.L. Logothetis, J. Polym. Sci., Polym. Chem. Ed., 17, 2541, (1979). G.M. Burnett, R.A. Haldon and J.N. Hay, Eur. Polym. J., 4, 83, (1968). R.A. Wessling, “Polyvinylidene Chloride”, Gordon and Breach, New York, (1977). D.S. Gibbs, R.A. Wessling, “Kirk- Othmer: Encyclopedia of Chemical Technology, John Wiley and Sons, 3rd Edition, New York, NY, (1983), Vol 23, pp. 764-798. G. Strandburg, P.T. Delassus and B.A. Howell, in S.J. Risch and J.H. Hotckiss, (Eds), Food and Packaging Interactions II, ACS Symposium Series, No. 473, Washington, D.C. (1991), Ch. 12.

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[10] P.T Delassus, W.E. Brown and B.A. Howell, in A.L. Brody and K.S. Marsh (Eds) Encyclopedia of Packaging Technology, John Wiley and Sons, 2nd Edition, New York, NY, (1997), pp. 958 -961. [11] P.T. Delassus, G. Strandburg, and B.A. Howell, Tappi J., 71, 177, (1988). [12] R.F. Boyer, J. Phys. Coll. Chem., 51, 80, (1947). [13] L.A. Matheson and R.F. Boyer, Ind. Eng. Chem., 44, 867, (1952). [14] B.A. Howell, J. Polym. Sci., Polym. Chem. Ed., 25, 1681, (1987). [15] B.A. Howell, P.T. Delassus, J. Polym. Sci., Polym .Chem. Ed., 25, 1697, (1987). [16] S.Collins, K. Yoda, N. Anazawa and C. Brikinshaw, Polym. Degrad. Stab., 66, 87, (1999). [17] B.A. Howell and P.B. Smith, J. Polym. Sci., Polym. Chem. Ed., 26, 1287, (1988). [18] B.A. Howell and M. Liu, Thermochim. Acta, 243, 169, (1994). [19] B.A. Howell and C.V. Rajaram, J. Therm. Anal., 40, 575, (1993). [20] B.A. Howell, Z. Ahmed and S.I. Ahmed, Thermochim. Acta, 357/8, 103, (2000) and previous papers in the series. [21] B.A. Howell, B.S. Warner, C.V. Rajaram, Z. Ahmed and S.I. Ahmed, Polym. Adv. Technol., 5, 485, (1994). [22] B.A. Howell and B.B.S. Sastry, “Degradation of Vinylidene Chloride / Methyl Acrylate Copolymers in the Presence of Phosphines”, Proceedings, 22nd North American Thermal Analysis Society Meeting, pp. 122- 127, (1993). [23] B.A. Howell and H. Liu, Thermochim. Acta, 212, 1, (1992). [24] B.A. Howell and F.M. Uhl, Thermochim. Acta, 357,113, (2000). [25] A.Velazquez and W.H. Starnes, Jr., Polym. Prepr., 32 (3), 197, (1991). [26] B.A. Howell and P.B. Smith, J. Therm. Anal Cal., 83, 71, (2006). [27] Dolezel, M. Pegoraro and E. Beati, Eur. Polym. J., 6, 1411 (1970).

INDEX A accelerator, 90 access, 53, 202 acclimatization, 130 accuracy, 3, 5, 237 acetic acid, 105, 116, 117 acetone, 53, 66, 67, 113, 118, 119 acetophenone, 37 acid, 38, 39, 42, 43, 46, 74, 82, 84, 112, 116, 117, 120, 133, 134, 135, 136, 137, 138, 141, 142, 146, 147, 153, 178, 181, 182, 201, 207, 227, 252, 253, 259 acrylate, 260, 263, 264, 267, 270, 271, 272, 273, 274, 276 acrylic acid, 108, 112, 113, 118, 136 acrylonitrile, 115, 117, 257 actinic keratosis, 148 activation, 62, 66, 67, 86, 115, 117, 119, 122, 145, 153, 167, 180, 262, 264, 265, 267 activation energy, 62, 86, 115, 117, 119, 122, 145, 167, 264 activation enthalpy, 264 activation parameters, 262, 264, 267 active radicals, 93 actuators, 133 additives, 30, 120, 132, 146, 174, 260 adenine, 74 adenosine, 74 adenosine triphosphate, 74 adhesion, 112, 144, 147, 155 adhesives, 144 adiabatic, x, 1, 10, 17, 18, 21 adsorption, 36, 45, 46, 120, 131, 136, 140, 152, 156 aerosols, 142, 157 age, ix, 101 ageing, 101

agent, 105, 106, 111, 113, 114, 117, 134, 135, 145, 148, 153, 154, 155, 170, 182, 254 aggregation, 109 aging, 178, 182 agriculture, xiii, 148, 251 AIBN, 267, 268 air pollution, 156 albumin, 144, 150, 151 alcohol(s), 37, 42, 43, 45, 103, 108, 109, 111, 112, 113, 115, 116, 118, 120, 121, 122, 127, 128, 132, 134, 135, 136, 137, 140, 141, 146, 147, 151, 154, 157, 158, 160, 169, 170, 233, 244, 253 aldehydes, 117, 122 algorithm, 14 alkyl methacrylates, 257 alloys, 200 allylamine, 111, 114, 118, 150 alternative(s), 107, 120, 128, 133, 134, 234 amendments, 38 amines, 38, 42, 43, 251, 252, 254, 260 amino acid, 90 amino-groups, 141 ammonia, 53, 150, 234 amorphous phases, 175 anhydrase, 156 aniline, 108, 109 animals, 106, 144 anion, 82, 84, 191, 199 annealing, 112, 135, 169 anticancer drug, 149 apoptosis, 143 apparel, 106 applied research, 174 aqueous solutions, 106, 108, 109, 113, 114, 116, 147 argon, 218 aromatic compounds, 244 aromatic hydrocarbons, 244 articular cartilage, 140, 147, 148 ascorbic acid, 138

280

Index

ash, 41 assessment, 69, 70, 71, 149, 171, 187, 188 assignment, xii, 173, 174, 181, 184, 185 assimilation, 85, 86 assumptions, 37, 38, 70, 95 asthma, 139 asymptotics, 26 atmospheric pressure, xiii, 233, 234, 236, 239, 241 atomic orbitals, 84, 95 atoms, 38, 56, 59, 74, 76, 78, 79, 81, 82, 84, 86, 90, 92, 93, 94, 95, 96, 98, 99, 100, 178, 188, 189, 190, 191, 197, 198, 199, 270, 274 ATP, 82, 83, 86, 87 attachment, 72, 125 attention, 24, 31, 52, 133, 136, 137, 141, 152, 155, 157, 218, 253, 254 autodeceleration, 202, 207 availability, 120, 274

B barriers, 157 basicity, xi, 35, 41, 42, 43, 45, 47, 66 beams, 105, 144 behavior, 39, 113, 135, 144, 148, 202, 228, 244, 246, 250, 272 bending, 135, 136 benign, 133 benzene, xi, 46, 51, 53, 55, 63, 67, 119, 120, 121, 234, 244, 245 benzoyl peroxide, 65 binding, xii, 52, 62, 93, 106, 125, 128, 130, 136, 148, 199 bioaccumulation, 130 bioavailability, 142 biocatalysts, 153 biocompatibility, 112, 132, 140, 148, 157 biodegradability, 106, 130, 148, 149, 157 biological processes, 90 biological stability, 131 biological systems, 24 biologically active compounds, 251, 253 biomass, 112, 130 biomaterials, 139, 140, 142, 148, 154 biomedical applications, 105, 140, 147 biomolecules, 98, 137 biosensors, 133, 137, 138 biosorption, 130 blend films, 123, 136 blends, 107, 112, 113, 114, 116, 118, 119, 120, 123, 129, 130, 134, 140, 148, 154, 156, 158 blocks, 15, 93 blood, 138, 139, 140, 142, 151 bloodstream, 142

body fluid, 149 body weight, 106 bonding, 48, 121, 128, 141 bonds, xiii, 36, 37, 43, 62, 74, 75, 81, 86, 93, 98, 137, 177, 178, 179, 181, 182, 192, 199, 251 boric acid, 136, 162 branching, 36, 169, 170 breakdown, 69, 169 Brownian motion, 226 Bulgaria, 177 butadiene, 177, 180, 181, 185 butyl ether, 244 by-products, 122

C Ca2+, 150 calibration, 139 cancer, 127, 139, 142, 253 candidates, 125, 140, 141 capillary, 128, 176 carbamide, xii, 173, 174, 175, 254 carbides, 196 carbohydrate(s), 74, 251, 252, 254, 255 carbon, xii, 37, 41, 52, 74, 82, 86, 93, 96, 98, 99, 120, 121, 138, 187, 193, 197, 198, 199, 200, 234, 258, 259, 268, 270 carbon atoms, 86, 199 carbon dioxide, 234, 258 carbon monoxide, 120 carbon nanotubes, 199 carcinoma, 148 carrier, 128, 141, 218, 254 cartilage, 148 cast, 112, 116, 135 casting, 113, 116, 117, 120, 123, 128 catalysis, 67, 106, 201, 225, 251, 252, 253 catalyst(s), xiii, 53, 54, 113, 117, 120, 128, 133, 151, 152, 157, 174, 202, 217, 218, 219, 220, 222, 253, 259 catalytic activity, 217, 227 catalytic hydrogenation, 120 catalytic system, 152 cation, 191, 199 cell, 2, 3, 130, 133, 134, 135, 143, 147, 148, 153, 245 cell adhesion, 147 cell culture, 153 cell culture method, 153 cell cycle, 148 cell death, 143 cell growth, 147 cell line, 147 cell organization, 147

Index cellulose, 114, 131, 132, 137, 144 cellulose diacetate, 137 ceramic(s), 106, 139, 147 certificate, 255 chains conformation, 21 channels, 109, 134, 212, 213 characteristic viscosity, 71 chemical bonds, x, 1, 74, 86, 87, 95, 176 chemical energy, 74 chemical interaction, 36, 136, 226 chemical kinetics, ix chemical properties, xi, 35, 100, 200, 244 chemical reactions, 90, 154, 203, 225 chemical stability, 140 chitin, 148 chlorine, 65, 67, 259, 270 chlorophyll, 74, 81 chromatography, 130, 244, 245 chronic diseases, 127 circulation, 141 classes, 192 clean energy, 112 clean technology, 107 cleaning, 130 clusters, 38, 197, 199, 210 C-N, 93 CO2, 80, 83, 155, 156 coagulation, 133 coal, xi, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 244 coatings, 142, 149 cohesion, 36, 37, 40, 41, 42, 45, 65, 66, 67 collagen, 147 colon, 148 combined effect, 145 compatibility, 123, 137, 141, 151, 177 compensation, 136 compliance, xii, 86, 89, 142 complications, 41 components, xiii, 3, 36, 41, 75, 79, 81, 82, 90, 91, 93, 94, 95, 106, 107, 113, 116, 118, 119, 121, 122, 125, 126, 130, 149, 175, 176, 234, 240, 243, 244, 245, 247, 249, 257 composites, xii, 52, 62, 107, 114, 147, 158 composition, xi, 27, 30, 41, 51, 53, 55, 62, 108, 111, 113, 115, 116, 117, 118, 119, 120, 122, 128, 130, 133, 134, 135, 154, 155, 156, 173, 178, 182, 192, 209, 234, 244, 245 compost, 106 compounds, 54, 64, 74, 82, 86, 90, 93, 105, 107, 126, 127, 128, 140, 149, 157, 174, 192, 200, 225, 234, 244, 246, 248, 251, 254, 255, 267 compressibility, 29, 30, 32, 234

281

computation, xii, 67, 187 concentration, x, xi, 1, 2, 11, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 36, 105, 114, 115, 116, 118, 119, 121, 123, 124, 126, 130, 131, 135, 136, 137, 138, 139, 140, 154, 156, 168, 169, 174, 178, 179, 181, 208, 218, 219, 220, 221, 222, 227 conception, xii, 207, 211, 214 concrete, 32, 228 condensation, 107, 109, 111, 116, 252, 253 conducting polymer composites, 63 conductivity, 63, 109, 133, 134, 135, 137, 245 Congress, iv connectivity, 209, 226, 227 constant rate, 142 consumption, 86, 167, 177 contamination, 244 control, 107, 109, 112, 125, 146, 149, 155, 157, 178, 182, 234, 265 conversion, xii, 54, 117, 120, 201, 202, 203, 204, 206, 207, 208, 219, 227, 229 conversion rate, 117 cooling, 52 copolymers, 107, 114, 140, 257, 258, 259, 260, 264, 267, 270, 271, 272, 273, 274, 276 copper, 126, 245 cornea, 147 correlation(s), 25, 32, 40, 41, 42, 44, 56, 65, 66, 67, 95, 189, 198, 244 correlation analysis, 67 correlation coefficient, 41, 56, 66 corrosion, 154, 156 cosmetics, 148 coupling, 142 covalent bond, 98, 152, 197, 199 covalent bonding, 152 creatine, 138 creatinine, 138, 148, 149 critical analysis, 38 critical density, 11 critical value, 16 crystalline, 93, 96, 120, 188, 189, 192, 194, 199, 258 crystallinity, 121, 147, 154, 210, 258 crystallites, 105 crystallization, 169, 200 crystals, 191 culture, 147 curing, 111, 113, 114, 117, 118, 139, 181 curing process, 181 cycles, 105, 113, 144, 147, 197 cyclodextrins, 123, 128 cyclohexanone, 37 cytocompatibility, 153 cytosine, 254

282

Index

cytotoxicity, 141, 153

D data analysis, 65 death, 106 decay, 219, 220, 221, 222 decomposition, 24, 65, 169, 170, 176, 257 defects, 258, 260 deficiency, 25, 218 definition, xiii, 175, 203, 207, 214, 230 deformation, x, 1, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 28, 33, 72, 133, 154, 169, 170, 171, 181 degenerate, 169 degradation, 169, 258, 259, 260, 261, 263, 264, 265, 267, 269, 270, 272, 273, 275, 276 degradation process, 258 degree of crystallinity, 154 dehydrate, 118 dehydration, 107, 108, 109, 111, 112, 113, 114, 116, 117, 118, 213, 258 dehydrochlorination, 257, 258, 259, 274, 276 dehydrocondensation, 59 delivery, 106, 130, 140, 141, 142, 143, 145, 146 demand, 142 demulcent, 106 denaturation, 150 Denmark, 250 density, 6, 9, 11, 36, 38, 39, 42, 65, 79, 92, 93, 111, 125, 134, 138, 178, 182, 202, 234, 244, 258 dependent variable, 234 deposition, 149 depreciation, 154 depression, 170 derivatives, xi, xiii, 23, 32, 114, 137, 146, 152, 154, 157, 204, 228, 236, 237, 251, 252, 253, 254 dermatoses, 148 desorption, 145, 146 destruction, xii, 41, 62, 69, 70, 71, 72, 167, 168, 169, 171, 176 destruction processes, xii, 71, 72, 167, 171 destructive process, 69 detection, 135, 138, 176 detergents, 131 deviation, xiii, 37, 43, 233, 239, 241, 243, 263 diabetes, 139, 150 dialysis, 130, 138, 139 diamines, 141 diet, 101 differential scanning, 52 differential scanning calorimeter, 52 diffraction, 135

diffusion, xii, xiii, 40, 75, 91, 107, 117, 121, 124, 128, 129, 134, 136, 146, 152, 153, 170, 207, 208, 212, 214, 217, 221, 222, 225, 226, 230 diffusivity, 112 diluent, 106 dimensionality, 14, 28 dimer, 81 dimethylformamide, 37, 43 diphenylolpropane, 47 dipole moment, 234 discrimination, 125 disinfection, 142 disorder, 210 dispersion, 109 displacement, 5, 9, 39, 228 dissociation, 98, 99, 135 distillation, 107, 112, 118, 120, 122 distribution, xiii, 2, 3, 4, 5, 6, 40, 72, 121, 130, 131, 169, 170, 202, 209, 217, 220, 221, 222, 228 distribution function, 228 division, 66, 220 DMA analysis, 147 DNA, 131, 141 dopants, 109 doping, 109 dosing, 142 double bonds, 84 double logarithmic coordinates, 208 dream, x dressing material, 144 dressings, 145 Drosophila, 101 drug delivery, 106, 107, 140, 141, 142, 144 drug delivery systems, 141 drug release, 146 drugs, 140, 142, 144, 145, 157, 253 drying, 41, 138 DSC, 52, 59, 61 DTA curve, 175, 176 durability, 117, 132 duration, xiii, 142, 202, 203, 204, 207, 208, 217, 220, 221, 222, 225, 227, 231

E Education, 161 effective spectral dimension, 209 effluent, 120 elaboration, 52 elasticity, x, 1, 2, 21, 114, 144 elastomers, 52 electrical conductivity, 109 electricity, 142 electrocatalyst, 137

Index electrodes, 137, 138 electrolysis, 109 electrolyte, 129, 133, 134, 140 electromagnetic, 74 electromigration, 136 electron(s), 48, 66, 73, 74, 75, 76, 78, 79, 81, 82, 87, 90, 91, 92, 93, 94, 96, 97, 98, 99, 105, 128, 138, 144, 188, 198, 199, 200 electron density, 79, 92, 93, 128, 188, 198, 199 electron pairs, 128 electrophoresis, 128 electroporation, 142 electrostatic interactions, 141 elongation, 121, 132, 181 emission, 155 enantiomers, 128 encapsulation, 144, 164 endothelial cells, 147 endothermic, 41, 52, 59, 176 energetic excitation, 211 energetic parameters, 59 energy, x, xi, xii, 1, 8, 9, 21, 23, 28, 32, 36, 37, 39, 40, 41, 42, 45, 62, 65, 67, 73, 74, 75, 76, 78, 79, 81, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 96, 99, 100, 101, 107, 117, 118, 120, 127, 133, 143, 156, 168, 187, 188, 189, 190, 191, 194, 196, 197, 198, 199, 210, 212, 246, 248, 264 energy characteristics, xii, 73, 75, 78, 85, 89, 91, 100, 188 energy density, 42, 67, 133 energy parameters, 93 England, 158 enthalpy of activation, 264 entrapment, 136, 137, 143, 153 entropy, x, 1, 9, 15, 16, 21, 27, 32 environment, 111, 131, 140, 144, 152, 253 environmental conditions, 130 environmental impact, 106 environmental protection, 127 environmental stimuli, 141 enzymatic activity, 131 enzyme immobilization, 152 enzymes, 128, 137, 138, 141, 151, 152, 157 epoxy groups, 63 equality, 81, 82, 188, 189, 191, 197, 198, 226 equating, 16 equilibrium, x, xiii, 1, 6, 8, 10, 12, 13, 15, 16, 21, 38, 39, 40, 41, 44, 47, 136, 148, 233, 234, 241, 244, 245, 246, 247, 248, 250 equipment, 259 ester, 137, 142, 271, 272, 273 estimating, 234, 240 ethanol, 112, 113, 114, 115, 116, 119, 137, 142, 244

283

ethers, 169, 244 ethyl acetate, 65 ethyl alcohol, 122 ethylene, 117, 141, 154 ethylene glycol, 117 ethylene oxide, 141 Euclidean space, 202, 221, 227, 228 evaporation, 40, 107, 113, 117, 120, 123, 129 evolution, xii, 201, 203, 206, 259 excitation, 74 exclusion, 38, 41, 42, 43, 44, 45, 65, 66, 67, 129, 138 excretion, 141 exercise, 145 exothermic peaks, 52 exploitation, 260 exposure, 109, 111 extracellular matrix, 151 extraction, xi, 35, 36, 37, 38, 46, 47, 48, 105, 106, 125, 126, 130, 142, 174, 243, 245, 262 extraction process, 38, 105, 125, 243 extrusion, 71, 72, 142, 156

F fabric, 106 fabrication, 132, 138 family, 134 fat, 148 fatigue, 4 FDA, 106 FEMA, 117 fermentation, 112, 122 fermentation broth, 122 fibers, 105, 117 fibroblasts, 146 fillers, 109, 146 film(s), 105, 108, 112, 113, 118, 128, 133, 137, 144, 145, 146, 154, 155, 157, 169, 260 film formation, 157 filtration, 106, 132, 153 fish, 127 fixation, 147, 148 flavor, 257, 258 flexibility, 111, 114, 156 Flory theory, 38 fluctuations, xiii, 217, 220, 221, 222 fluid, 130, 151 food, 106, 131, 152, 154, 257, 258 food industry, 131, 152 food safety, 131 Ford, 185 formaldehyde, xii, 133, 137, 148, 173, 174, 175, 182 fouling, 131, 132, 133, 138 fractal analysis, xii, 201, 202, 206

284

Index

fractal dimension, 203, 228 fractal kinetics, 203 fractal objects, 202 fractal space, 202, 209, 227 fractal structure, 225 France, 33 free energy, x, xi, 1, 7, 8, 9, 21, 23, 24, 26, 27, 28, 29, 31, 32, 36, 39, 41, 47, 74, 84 free radicals, xii, 73, 89, 90, 98, 99, 100 free volume, xii, 24, 111, 116, 121, 207, 210, 211, 212, 213, 214 freezing, 105, 113, 126, 134, 144 FTIR, 201, 202 fuel, 36, 62, 120, 133, 135, 156, 157 fuel efficiency, 134 fullerene, 200

G gas phase, 130 gases, 40, 157 gasoline, xiii, 120, 156, 243, 244, 247, 248, 249, 250 gastrointestinal tract, 106 gel, 105, 106, 112, 125, 132, 136, 137, 140, 141, 142, 144, 146, 152, 157 gelation, 105, 203 generalization, xi, 35, 39, 40, 41, 42, 43, 46, 47, 65 generation, 106, 144, 145, 167, 168 Georgia, 51, 64 gerontology, 101 glass, 59, 210, 211, 245 glass transition, 59, 210, 211 glass transition temperature, 59, 210 glucose, 128, 137, 139, 144, 151, 252 glucose oxidase, 137, 139 glutamate, 138 glycerin, 74 glycerol, 152 glycoproteins, 252 glycoside, 254 glycosylation, 254 goals, 107 government, 155 grades, 144 graphite, xii, 52, 62, 120, 121, 199, 200 grouping, 84 groups, 38, 39, 41, 42, 43, 46, 52, 53, 54, 55, 59, 61, 62, 74, 85, 90, 108, 109, 111, 114, 127, 128, 133, 134, 135, 137, 140, 141, 142, 157, 170, 177, 185, 245, 251, 258, 270, 271, 274 growth, 24, 36, 130, 144, 146, 169, 200, 209, 218, 252, 253 growth factor, 146

H halogen, 192 hardness, 179, 181 harmful effects, 153 HDPE, 155, 156 healing, 144, 145, 146 health, 138 health care, 138 heat, 10, 11, 17, 59, 117, 120, 253 heating, 176 heating rate, 176 helium, 218 hepatocytes, 149, 150 hepatoma, 149 heptane, 67 heterogeneity, xii, 207, 208, 211, 212, 213, 214, 219 heterogeneous systems, 75 hexane, 142, 234 high density polyethylene, 155, 156 hip, 208, 227 homogeneity, 209, 212 homopolymerization, 55 Honda, 47 hospitals, 106 host, 128, 137, 147 host tissue, 147 human brain, 235 humidity, 99, 154, 234 hybrid, 109, 111, 112, 116, 120, 121, 147, 149 hybridization, 82, 87, 96, 101, 112, 198 hydrocarbons, 37, 156 hydrogels, 104, 105, 106, 113, 125, 126, 127, 128, 135, 140, 142, 143, 144, 146, 147, 148, 151, 157, 160, 164 hydrogen, 37, 38, 41, 42, 43, 46, 48, 54, 59, 81, 82, 96, 121, 128, 138, 141, 258, 259, 260, 270, 272, 274, 276 hydrogen abstraction, 270 hydrogen atoms, 81, 82, 128, 270, 274 hydrogen bonds, 38, 41, 42, 43 hydrogen chloride, 258, 259, 260, 276 hydrolysis, 52, 62, 103, 104, 111, 116, 131, 132, 133, 140, 144, 152, 153, 154, 157 hydrolytic stability, 251 hydroperoxides, 167 hydrophilicity, 108, 112, 114, 132, 137 hydrophobic interactions, 131 hydrophobicity, 112, 134 hydrosilylation, 55, 56, 58 hydroxide, 136, 174, 176 hydroxyapatite, 147 hydroxyl, 81, 103, 105, 109, 128, 132, 133

Index hydroxyl groups, 105, 109, 128, 132, 133 hygiene, 106

I identity, 203 imidization, xii, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214 immersion, 131, 144, 218 immobilization, 128, 136, 137, 145, 151, 152, 153 immune system, 149, 151 immunoglobulin, 151 implants, 141 impregnation, 125, 136 impurities, 177, 200 in situ, 109, 121 in vitro, 146, 153 in vivo, 141, 151 inclusion, 126, 128, 146 incompatibility, 156 independence, 26, 31, 32 independent variable, 16, 17 index numbers, 55 indicators, 136, 137 indomethacin, 144 induction peroid, 169, 170 industrial application, 107, 152 industry, 106, 116, 139, 152, 257 infection, 144 infinite, 260 information processing, 235 inhibition, 153 inhibitor, 146 initial state, 188 initiation, 235, 258, 259, 260, 261, 263, 264, 267, 268, 276 injections, 141 input, 234, 235, 236, 237 insertion, 130 instability, 258, 267, 269 insulin, 144, 151 integration, 19, 29, 30, 70 intensity, 69, 71, 72, 177 interaction(s), xii, xiii, 9, 24, 25, 36, 37, 38, 39, 40, 41, 46, 48, 52, 53, 59, 61, 65, 73, 74, 75, 79, 80, 81, 82, 84, 87, 89, 90, 91, 92, 93, 94, 95, 96, 98, 100, 120, 121, 126, 128, 130, 135, 138, 139, 141, 146, 170, 182, 188, 189, 192, 197, 198, 199, 234, 240, 243, 244, 245, 246, 247, 248, 250, 252, 254 interface, 136, 153, 155 interference, 93, 138 intermetallic compounds, 192 intermolecular interactions, 141 internal reconstruction, 95

285

interpretation, 37, 40 interval, 10, 62, 142, 176, 221, 228, 247, 248, 250 inversion, 133 iodine, 126 ion exchangers, 127 ionization, 87, 189, 190 ions, 84, 95, 121, 126, 128, 130, 135, 136, 138, 202, 208 IR, xi, xii, 39, 51, 52, 53, 54, 55, 59, 173, 176, 202, 208 Iran, 233, 243 iron, 86, 259 irradiation, 105, 153 irreversible aggregation, 202 IR-spectra, 52, 53, 55, 59, 202, 208 IR-spectroscopy, xii, 173, 176 isobutylene, 120 isolation, 74, 81 isomers, 123, 124, 125, 128 isoprene, 17, 177, 178, 179, 180, 185 isothermal, x, 1, 17, 21, 276 isotropic media, x, 1

J Japan, 33, 47, 255

K K+, 80, 138 KBr, 52, 202, 208 ketones, 38, 169 kidney, 138, 151 kidney dialysis, 138 kidney failure, 138 kinetic curves, 54, 202, 207, 208, 218, 219, 220, 227 kinetic parameters, 75, 91 kinetic studies, 218, 253 kinetics, ix, xi, xii, xiii, 44, 51, 67, 136, 167, 168, 170, 171, 181, 182, 183, 184, 201, 202, 207, 208, 217, 218, 219, 222, 225, 227, 251, 276 knees, 148 Kyrgyzstan, 251, 255

L lamellae, 154, 155 laminar, 154, 156 lamination, 106 landfills, 106 lateral meniscus, 148 laws, x, 1 learning, 239 lending, 128 lesions, 149

286

Index

life expectancy, 138 life span, 101 linear dependence, 218 linear function, 28, 29 linear macromolecule, 33 linear molecules, 131 linkage, 137, 152, 268 links, 2, 3, 9, 24, 25, 26, 31, 37, 170 lipase(s), 152, 153 liquid interfaces, 125 liquid phase, xiii, 36, 39, 40, 41, 42, 120, 125, 234, 243, 244, 245, 247, 250 liquids, xi, 35, 37, 39, 40, 41, 46, 47, 48, 53, 54, 109, 122, 144 liver, 150 living conditions, 150 local order, 210 localization, 210, 212 location, 3 low temperatures, 131, 259 low-molecular substances, 230 LTD, 158 luminescence, 136 lying, 5, 27 lysine, 138

M macromolecular chains, 70 macromolecular coil, xii, 201, 202, 203, 205, 206 macromolecular coil fractal dimension, xii, 201, 206 macromolecules, xi, 23, 24, 26, 27, 28, 29, 30, 31, 32, 59, 61, 70, 100, 168, 169 magnesium, 81, 181, 260 mammalian cells, 138 management, 133 manganese, 81 manufacturing, 53, 122, 139 market, 157 mass loss, 276 matrix, 105, 109, 113, 121, 126, 130, 137, 138, 140, 142, 143, 145, 147, 150, 151, 152, 153, 177, 185, 210, 217 mean-field theory, 219 measurement, 136 meat, 257 mechanical properties, 47, 114, 121, 134, 148, 173 media, 40, 65, 75, 109, 127, 131 medicine, x, xii, xiii, 139, 148, 157, 251 melt(s), 1, 2, 9, 11, 17, 21, 33, 69, 71, 72, 155, 167, 168, 171, 202, 257, 260, 274 melting, 176, 209 melting temperature, 176, 209 membrane separation processes, 151

membranes, 104, 107, 108, 109, 111, 112, 114, 115, 116, 117, 118, 119, 120, 121, 123, 124, 125, 126, 128, 129, 130, 131, 132, 133, 134, 135, 137, 138, 140, 142, 148, 149, 150, 151, 152, 153, 154, 156, 157 memory, 228 Mendeleev, 94 metabolism, 138, 142 metabolites, 141 metal carbides, 192 metallurgy, 200 metals, 139, 151, 192, 200 methacrylic acid, 117 methane, 234 methanol, xiii, 105, 118, 120, 133, 135, 137, 156, 243, 244, 245, 246, 247, 248, 249, 250 Mexico, 201 Mg2+, 80, 85 mice, 101 micrometer, 152 microorganism, 130 microscopy, xii, 173, 175 microspheres, 104, 141 microstructure, 225 microvoid, 211, 212, 213 migration, 125, 147 minerals, 36 miniaturization, 133 missions, 120 mixing, x, 1, 4, 9, 15, 16, 21, 36, 38, 113, 116, 234, 240 model system, xi, 51, 54, 57, 59, 217 modeling, xiii, 177, 178, 179, 180, 181, 182, 183, 184, 197, 233 models, xiii, 87, 128, 233, 234, 235, 241, 254 modules, x, 1, 2, 21, 92, 151 moisture, 53, 62, 90, 176, 258 moisture content, 90 molar volume, xi, 26, 30, 31, 35, 36, 37, 40, 41, 42, 43, 44, 45, 46, 47 molasses, 122 mole, xiii, 17, 28, 37, 46, 53, 67, 83, 86, 125, 131, 167, 169, 174, 234, 236, 237, 239, 241, 243, 245, 246, 248, 249, 250, 259, 260, 263, 264, 267, 272, 273, 275, 276 molecular biology, 251 molecular mass, 38, 69, 70, 72, 144, 169 molecular orbitals, 199 molecular structure, 74, 98, 99, 137 molecular weight, 37, 38, 70, 105, 108, 131, 132, 140, 143, 146, 234 molecules, xii, 24, 27, 36, 41, 42, 46, 74, 78, 80, 81, 82, 83, 84, 86, 89, 90, 94, 98, 99, 100, 101, 109,

Index 121, 123, 128, 130, 131, 136, 141, 153, 169, 200, 226, 230, 248, 257, 258 monomer(s), xi, 51, 52, 54, 103, 109, 113, 117, 157, 275 monosaccharide, 253, 254 Moon, 159, 161, 165 morphology, 146, 147, 154, 155, 184 motion, 209 moulding, 217 movement, 75, 91 mucosa, 140 multi-component systems, 243 multiplicity, 7, 8, 16, 19, 20, 21, 28 multiplier, 3

N Na+, 80, 129, 138, 143, 201, 202, 204, 205, 207, 208, 211 NaCl, 117, 191, 194 nanocomposites, 201, 202, 208 nanoparticles, 109, 126, 141, 200 nanostructures, xii, 187, 193, 198, 200 nanotube(s), 199, 200 natural environment, 106 natural polymers, 36 neglect, 27, 38 negotiation, 41 Netherlands, 63, 87, 101, 200 network, xiii, 15, 121, 128, 135, 140, 178, 179, 182, 207, 212, 214, 234, 235, 236, 237, 239 neural network(s), xiii, 233, 234, 235, 236, 237, 241 Neural Network Model, 236 neurons, 235, 237 neutrons, 90 nicotine, 74 nitric acid, 130 nitric oxide, 90, 146 nitrile rubber, 181 nitrogen, 39, 59, 81, 111, 177 NMR, xi, 51, 52, 54, 55, 59, 267 nonlocality, 228 non-metals, 192 nontoxicity, 148 North America, 277 nucleus, 73, 75, 76, 81, 89, 91, 92, 188 numerical analysis, 17 numerical tool, 234 nutrients, 149

O observations, 37, 170, 267 occlusion, 139

287

octane, 244 OH-groups, 252 oil(s), 122, 152, 218 olefins, 244 oligomers, 61, 62, 64 olive oil, 153 operator, 228 optical chemical sensors, 136 optical fiber, 117 optical properties, 157 optimization, 59, 111, 114, 138 ores, 174 organ, 149 organic compounds, 107, 118, 135, 198 organic polymers, 52 organic solvent(s), 36, 40, 41, 53, 54, 106, 107, 111, 114, 118, 126, 152 organism, 149, 153 organization, 7, 27 orientation, 221, 226 oscillation, 92 osmosis, 108 osmotic pressure, xi, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 36, 135 ossification, 148 osteoporosis, 139 output, xiii, 136, 233, 234, 235, 236, 237, 239 oxidability, 170 oxidation, 65, 67, 108, 110, 138, 167, 169, 170 oxidation rate, 167, 169, 170 oxides, 151 oxygen, 38, 42, 53, 74, 81, 82, 84, 86, 90, 96, 98, 99, 128, 143, 149, 154, 155, 168, 169, 170, 257, 258, 268, 270, 272

P PAA, 108, 111, 114, 115, 118, 119, 201, 202, 203, 204, 205, 207, 208, 209, 211, 212, 213, 214 packaging, 257, 259 pain, 144, 145 paints, 117 palladium, 138 palm oil, 152 PAN, 115, 118 pancreas, 149, 150, 151 parameter, xii, 2, 5, 11, 16, 24, 31, 36, 37, 38, 40, 41, 42, 43, 44, 46, 47, 62, 65, 66, 73, 74, 75, 76, 79, 81, 82, 84, 86, 87, 89, 90, 91, 92, 93, 94, 95, 96, 98, 100, 169, 170, 179, 182, 184, 187, 188, 189, 197, 198, 201, 205, 206, 209, 222, 228, 236, 244, 246 particles, 79, 92, 93, 109, 121, 130, 146, 147, 152, 154, 155, 174, 175, 177, 184, 185, 221, 227, 228

288

Index

passive, 109, 130, 260 PCR, 131 peat, 36 peptides, 140 perception, 236 percolation, xiii, 207, 210, 212, 213, 214 peritoneal cavity, 149 permeability, 107, 113, 118, 121, 125, 129, 131, 134, 135, 137, 145, 149, 151, 154, 155, 156 permeation, 107, 112, 114, 115, 116, 117, 121, 122, 124, 132, 133, 156 permit, 259, 274 peroxide, 177, 181, 183, 184, 185, 268, 269, 276 pH, 113, 126, 131, 132, 135, 136, 137, 140, 141, 147, 174 phase inversion, 133, 152 phenol, 39, 43, 108, 136, 137, 182 phenolphthalein, 137 philosophers, ix phosphorous, 82, 84 phosphorus, 82 phosphorylation, 82, 84 photolithography, 138 photopolymerization, 137 photosynthesis, xii, 73, 74, 81, 82, 83, 84, 86, 87, 89, 90, 95 physical and mechanical properties, 62, 63 physical chemistry, ix, 65 physical properties, 105, 140, 151 physical-mechanical properties, 180, 181, 185 physics, ix, 65, 73, 87, 89, 187, 211 plants, 87, 127, 255 plasma, 111, 112, 138, 142 plasma levels, 142 plasmapheresis, 140 plastics, 257, 258 platelets, 139 Plato, ix PMMA, 150 poison, 133 Poland, 178 polar groups, 108 polarity, 39, 43, 46, 65, 66 polarizability, 42, 66, 67 polarization, 39, 41, 152, 199 pollutants, 125, 126 pollution, 130, 156 poly(vinylpyrrolidone), 134 polyacrylamide, 116, 153 polyamides, 201 polycarbonate, 52 polycondensation, 174, 228 polydispersity, 227

polyesters, 217, 225 polyimide(s), 208, 209, 210 polyisoprene, 17 polymer(s), xi, xii, 2, 24, 25, 26, 31, 36, 37, 39, 40, 41, 44, 51, 52, 54, 55, 56, 59, 60, 61, 62, 69, 70, 71, 72, 103, 104, 105, 106, 107, 108, 109, 111, 112, 113, 114, 115, 118, 121, 124, 125, 127, 128, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 141, 142, 144, 145, 147, 148, 152, 153, 154, 156, 157, 158, 169, 170, 173, 180, 202, 210, 211, 217, 257, 258, 259, 260, 263, 265, 267, 269, 270, 272, 273, 274, 275, 276 polymer blends, 134, 154 polymer chains, 109 polymer composites, xii, 51, 62, 217 polymer destruction, 69 polymer materials, 112, 141 polymer matrix, 109, 128, 130, 137 polymer melts, 69 polymer mixing, 113 polymer networks, 113, 140, 148 polymer solutions, 25 polymer structure, 107, 210, 211 polymeric blends, 140 polymeric chains, x, xi, 1, 2, 13, 21, 23, 25, 26, 27 polymeric materials, 140 polymeric membranes, 40, 118, 121, 128 polymerization, 24, 54, 103, 108, 109, 113, 144, 153, 201, 207, 257, 260, 267 polymerization mechanism, 109 polymerization process, 153 polyolefins, 154 polyorganocarbosiloxanes, xi, 51 polypropylene, xii, 69, 71, 72, 155, 167, 168, 171 polyurethane, 39, 142 polyvinyl alcohol, 137, 138, 147, 148, 152 poor, 108, 117, 133, 134, 140, 141, 142, 148, 155, 156, 254 population, 127 porosity, 129, 131, 132, 147 porphyrins, 127, 142, 143, 144, 160 Portugal, x, 103 potassium, 96 potential energy, 73, 75, 89, 91 power, xi, 23, 32, 84, 86, 133, 177 precipitation, 130, 150 preference, 144 pressure, x, xi, 1, 9, 10, 13, 14, 21, 23, 31, 63, 107, 111, 118, 130, 132, 135, 169, 218, 234, 244, 245 priming, 167, 170 probability, xi, 2, 3, 4, 5, 7, 51, 57 process control, 241 production, 90, 122, 138, 157

Index prognosis, 148 proliferation, 147, 153 propagation, 237, 258, 260, 261, 263, 264, 267, 274, 276 proportionality, 27, 45, 71 propylene, 141 prosthesis, 147, 165 proteins, 81, 87, 131, 137, 140, 141, 149, 150 proteolytic enzyme, 145 protons, 55, 81, 82, 133, 136 PTFE, 152 pure water, 129 purification, 127, 128, 131, 156, 157, 244 PVA, vi, 103, 104, 105, 106, 107, 108, 109, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 156, 157, 160, 162 PVA films, 146, 154 PVAc, 103, 104 PVP, 134, 140 pyromellitic dianhydride, 202 pyrophosphate, 260

Q qualitative differences, 218 quartz, 135

R radiation, 81, 82, 101, 105, 147, 153, 169 radical polymerization, 153, 267 radius, x, 1, 2, 6, 12, 21, 24, 25, 28, 73, 76, 79, 81, 90, 91, 96, 191, 202, 212 random walk, x, 1, 2, 4, 7, 21, 26, 33, 228 range, xiii, 24, 27, 38, 42, 52, 54, 55, 86, 93, 98, 106, 112, 113, 121, 130, 132, 133, 135, 137, 138, 139, 151, 175, 176, 177, 201, 208, 233, 234, 236, 239, 241, 244, 258, 276 reactant(s), 151, 152 reaction center, 74, 81 reaction medium, 151 reaction order, 54 reaction rate, 39, 54, 56, 57, 58, 65, 75, 91, 153, 201, 204, 208, 218, 219 reaction rate constants, 54, 56, 57, 58 reaction time, 220, 221, 261 reactivity, 48, 56, 90, 98, 154 reagents, xiii, 100, 153, 157, 202, 213, 219, 220, 221, 225, 226, 230 real time, xiii, 225, 228, 230, 231, 234, 241 reality, 37, 38, 228

289

reception, 174 recognition, 106, 128, 142, 147 recombination, xiii, 170, 217, 219, 220, 221, 222 reconstruction, 81, 86, 140, 200 recovery, 120, 128, 131, 152 rectum, 148 recycling, 174 redistribution, 79, 93 reduction, 52, 74, 82, 83, 85, 86, 111, 116, 136, 142, 174, 182, 202, 207, 211, 226, 230 reflection, 276 refractory, 200 regenerated cellulose, 132 regeneration, 130 regulation(s), 87, 131, 188 rejection, 118, 226 relationship(s), 43, 177, 203, 204, 205, 207, 208, 209, 211, 213, 218, 219, 220, 221, 226, 228, 229, 234 reliability, 188 repair, 148 replacement, 95, 148, 156, 180, 181, 182, 184, 188, 253 reproduction, 106 Republican, 64 resection, 148 residuals, 153 residues, 105, 137 resilience, 181 resins, xii, 51, 52 resistance, 114, 128, 140, 149, 153, 156, 157, 182 response time, 136, 137 retention, 127, 130, 131, 132, 133 rings, 254 RNA, 131 rods, 104 rolling, 199 Romania, 103, 160 room temperature, 41, 123, 135 root-mean-square, 228 rubber(s), xi, xii, 2, 10, 15, 17, 18, 19, 20, 21, 39, 52, 173, 174, 177, 178, 179, 180, 181, 182, 183, 184, 185 rubber compounds, 178 Russia, x, 23, 35, 51, 64, 65, 73, 89, 187, 207, 217, 225, 251

S safety, 106, 144, 156 sales, 157 salt(s), 109, 117, 118, 121, 122, 131, 135, 144, 145, 174

290

Index

sample, 36, 41, 42, 43, 129, 136, 154, 176, 179, 258, 260 saturation, 41, 43, 236 scaling, xi, xiii, 23, 31, 32, 208, 217, 221, 222, 227 scaling approach, xiii, 217, 221, 222 scaling relations, 208, 227 search, 109, 217, 225 searching, 90, 100, 168 second virial coefficient, 24 sedimentation, 113 seeding, 147 segregation, 151 selecting, 71, 218 selectivity, 107, 108, 109, 111, 112, 114, 116, 118, 119, 120, 121, 125, 128, 156 selenium, 90, 98, 99, 100 self-control, 149 self-organization, 225 semiconductor, 138, 139 sensitivity, 135, 136, 137, 138, 157 sensors, 133, 135, 136, 137, 157 separation, 42, 59, 95, 103, 106, 107, 108, 111, 112, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 128, 129, 130, 131, 140, 148, 151, 152, 156, 157, 161, 233, 244, 247 series, 31, 36, 58, 86, 198, 245, 277 serum, 132, 133 serum albumin, 132, 133 shape, 2, 94, 104, 128, 130, 131, 133, 140, 197, 202, 207, 208, 210, 234 shape-memory, 140 shear, 131, 167, 171 shear deformation, 171 shock, 147 Si3N4, 137 Siberia, 38 side effects, 141, 142, 149 sign(s), 3, 8, 10, 12, 13, 15, 66, 234 signals, 55, 59 silicon, 52, 56, 59, 135, 136 similarity, 79, 82, 94, 147, 175, 176 simulation, 211 SiO2, 137 sites, 13, 258, 259, 276 skin, 140, 142, 144 skin diseases, 142 social problems, ix society, 157 sodium, 117, 128, 129, 145, 156, 227 sodium hydroxide, 227 soil, 106 sol-gel, 112, 121 solid phase, xii, 202, 207, 208, 214

solid solutions, 188 solid state, 200, 208, 209, 210, 211, 212, 213, 214 solubility, xiii, 36, 37, 38, 40, 47, 48, 55, 66, 75, 79, 93, 106, 112, 116, 120, 140, 144, 153, 170, 187, 188, 200, 243, 244, 247, 249, 257 solvation, 38, 39, 40, 41, 42, 43, 45, 46, 47, 66 solvents, xi, 2, 24, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 53, 65, 66, 67, 113, 128, 132, 156 sorption, 38, 48, 117, 124, 127, 130, 134, 143, 144, 146 Spain, 250 species, 107, 128, 130, 131, 138, 226, 270 specificity, 225 spectral dimension, 208, 227 spectrum, 39, 176, 254 speed, 178, 181 spin, 131, 138, 202, 208 stability, xi, 15, 51, 61, 104, 108, 111, 114, 118, 132, 134, 136, 137, 138, 140, 141, 152, 156, 169, 170, 192, 197, 198, 253, 260, 267, 268, 270, 273, 274, 275, 276 stabilization, xii, 187, 188, 191, 194, 198, 199, 270, 272, 274 stages, xii, 44, 67, 73, 74, 82, 86, 87, 89, 169, 252 standard deviation, 5, 45 statistics, x, 1, 2, 21, 24, 26, 33 steel, 259 stock, 144 storage, 137 strain, 69, 71 strength, xi, 2, 72, 105, 114, 117, 118, 132, 137, 179, 182, 183, 235 stretching, 12, 15, 16, 18, 20 strong interaction, 109 structural characteristics, 140 structural formation, 82, 86 structure formation, 184, 187, 189 styrene, 128 substitution, 8, 12, 70, 86, 254 substrates, 52, 136, 137 sucrose, 122 suffering, 139 sugar, 122, 251, 252, 253, 254 sulfur, 87, 90, 98, 99, 100, 177, 178, 180, 181, 183, 184, 185 sulfuric acid, 105 sulphur, 41, 177, 227 Sun, 159, 160, 165 supported liquid membrane, 125 suppression, 47 surface area, 246 surface modification, 109, 112 surface properties, 112

Index surface region, 109 survival, 101, 150, 151 susceptibility, 109 swelling, xi, 24, 25, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 104, 105, 106, 109, 112, 113, 114, 116, 122, 124, 129, 134, 135, 136, 141, 144, 146, 147, 148, 153, 254, 255 swelling process(es), xi, 35, 36, 38, 40, 41, 42, 43, 46, 47, 136 synergistic effect, 121 synthesis, xii, xiii, 52, 63, 74, 81, 87, 105, 107, 109, 112, 120, 131, 139, 150, 151, 152, 157, 173, 174, 202, 208, 225, 228, 251, 252, 253, 254 synthetic polymers, 37, 38, 40, 140, 144, 153 systems, xi, xii, xiii, 10, 12, 13, 51, 59, 90, 92, 93, 94, 95, 106, 128, 130, 140, 141, 142, 145, 148, 149, 151, 154, 173, 174, 177, 180, 181, 182, 183, 184, 185, 187, 188, 192, 199, 200, 217, 233, 234, 236, 241, 244, 247, 248, 249, 250, 260

T tacticity, 140, 157 technology, xii, 106, 107, 125, 131, 141, 142, 157, 173, 258 temperature, xiii, 10, 32, 37, 43, 54, 56, 57, 61, 71, 105, 108, 111, 113, 114, 115, 116, 118, 119, 120, 122, 133, 135, 140, 141, 152, 154, 155, 167, 168, 169, 174, 176, 192, 201, 210, 211, 218, 233, 234, 236, 237, 239, 240, 241, 243, 245, 246, 252, 257, 258, 263, 265, 266, 267, 269, 272, 273, 275, 276 temperature dependence, 167, 168 tensile strength, x, 1, 16, 21, 114, 144, 153, 181 tension, 13, 14, 15, 21 TEOS, 111, 112, 116 tetraethoxysilane, 112 textiles, 106 TGA, 61, 62, 265 theory, xi, 35, 36, 37, 38, 46, 47, 184, 192, 200, 205, 234, 251 therapy, 127, 142, 253, 254, 255 thermal aging, 179, 267 thermal analysis, xii, 173, 175 thermal decomposition, 169 thermal degradation, 260, 267, 268, 270 thermal energy, 211 thermal resistance, 132, 140 thermal stability, 131, 132, 134, 175, 260, 268, 269, 271 thermal treatment, 113 thermodestruction, 176 thermodynamic properties, 234, 244 thermodynamics, x, 1, 2, 10, 21, 26, 40 thermogravimetric technique, 259, 260

291

thermogravimetry, 260, 268, 271, 275, 276 thermolysis, 270 thermooxidation, xi, 51, 61 thermoplastics, 217 three-dimensional space, 221 threshold, 212 thyroid, 138 time, 36, 38, 40, 41, 43, 55, 56, 57, 59, 66, 67, 69, 79, 86, 94, 98, 105, 128, 129, 136, 144, 145, 146, 147, 152, 174, 176, 181, 182, 185, 189, 197, 207, 213, 218, 219, 221, 225, 228, 229, 230, 241, 260, 261, 276 tissue, 106, 142, 143, 147, 148, 150, 151 toluene, 53, 54, 56, 57, 119, 120, 154, 155, 244 total energy, 78, 92 toxic effect, 153 toxic metals, 130 toxicity, 105, 106, 130, 140, 157 trade, 118 training, 237, 239, 241 trajectory, 3, 4, 5, 6, 226 transformation(s), xi, xii, 36, 51, 70, 72, 201, 202, 203, 206, 208, 235, 236 transistor, 137 transition(s), xi, 16, 23, 44, 52, 79, 82, 93, 141, 176, 184, 199, 210, 211, 213, 226 transition temperature, 52 translation, 21 transmission, 149, 154 transplantation, 151 transport, 82, 87, 107, 117, 121, 136, 142, 148, 226, 227, 228, 229, 230, 250, 257, 258 transport processes, 226, 227, 230 transportation, 133 trifluoroethyl methacrylate, 117 trypsin, 146 tumor, 148 tumor cells, 148 turbulence, 228

U UK, 166 Ukraine, x, 1, 23, 35, 65, 173, 200 uncertainty, 265 uniform, 142 UNIQUAC, xiii, 243, 244, 245, 246, 247, 248, 250 unit cost, 139 United States, 165 universality, 95, 252 urea, 138 urethane, 141, 142 uric acid, 138, 148, 149 USSR, 254, 255

292

Index

UV, 113, 146 UV irradiation, 113

vulcanization, xii, 15, 173, 174, 177, 178, 179, 180, 181, 182, 183, 184, 185

V

W

vacuum, 41, 75, 91, 107, 123, 202, 208, 218 valence, 75, 76, 78, 79, 82, 86, 91, 92, 93, 94, 96, 98, 170, 188, 198 validity, 141 values, xii, xiii, 5, 8, 10, 12, 13, 17, 19, 21, 24, 25, 32, 37, 38, 40, 41, 42, 43, 44, 45, 46, 56, 66, 67, 70, 71, 72, 73, 76, 78, 81, 82, 84, 85, 86, 92, 95, 96, 98, 99, 117, 126, 135, 136, 146, 167, 168, 169, 170, 188, 189, 191, 192, 197, 198, 204, 209, 236, 243, 244, 247, 248, 249, 265 vanadium, 137 vanadium pentoxide, 137 vapor, 48, 153, 154, 156, 157, 233, 234, 236, 237, 239, 241, 244 variable(s), 5, 6, 10, 19, 71, 130, 246, 267 variation, 136, 202, 210, 230, 247 vehicles, 144, 146 vein, 147 velocity, 52, 75, 91 vessels, 41 vinyl chloride, 257 vinylidene chloride, 257, 259, 260, 263, 264, 267, 268, 269, 270, 271, 272, 273, 274, 276 viscosity, 63, 69, 71, 72, 145, 155, 234 visual area, 53 vitamin B1, 148, 149 vitamin B12, 148, 149 volatile substances, 41 vulcanizates, 178, 179, 180, 181, 184

walking, 6 washing procedures, 153 wastewater, 106, 125, 126, 130, 131, 144, 157, 160 wastewater treatment, 106, 126, 131 water absorption, 134 water diffusion, 117 water evaporation, 123 water sorption, 146 water vapor, 146 weakness, 116, 136 wear, 148 weight loss, 176, 259, 260, 261, 265, 266, 267, 269, 272, 273, 275 weight ratio, 113 wetting, 138 writing, 32

Y yield, 37, 54, 56, 57, 152

Z zinc, 174, 175, 177, 178, 180, 181, 182, 183, 184 zinc oxide, 174, 175, 177, 178, 180, 181, 182, 183, 184 ZnO, 174, 178, 179, 182, 183, 184