Crystallography of the Polymethylene Chain: An Inquiry into the Structure of Waxes (International Union of Crystallography Monographs on Crystallography)

INTERNATIONAL UNION OF CRYSTALLOGRAPHY BOOK SERIES

IUCr BOOK SERIES COMMITTEE E. N. Baker, New Zealand J. Bernstein, Israel P. Coppens, USA G. R. Desiraju, India E. Dodson, UK A. M. Glazer, UK J. R. Helliwell, UK P. Paufler, Germany H. Schenk (Chairman), The Netherlands IUCr Monographs on Crystallography 1 Accurate molecular structures A. Domenicano, I. Hargittai, editors 2 P.P. Ewald and his dynamical theory of X-ray diffraction D. W. J. Cruickshank, H. J. Juretschke, N. Kato, editors 3 Electron diffraction techniques, Vol. 1 J. M. Cowley, editor 4 Electron diffraction techniques, Vol. 2 J. M. Cowley, editor 5 The Rietveld method R. A. Young, editor 6 Introduction to crystallographic statistics U. Shmueli, G. H. Weiss 7 Crystallographic instrumentation L. A. Aslanov, G. V. Fetisov, G. A. K. Howard 8 Direct phasing in crystallography C. Giacovazzo 9 The weak hydrogen bond G. R. Desiraju, T. Steiner 10 Defect and microstructure analysis by diffraction R. L. Snyder, J. Fiala and H. J. Bunge 11 Dynamical theory of X-ray diffraction A. Authier 12 The chemical bond in inorganic chemistry I. D. Brown 13 Structure determination from powder diffraction data W. I. F. David, K. Shankland, L. B. McCusker, Ch. Baerlocher, editors

14 15 16 17

Polymorphism in molecular crystals J. Bernstein Crystallography of modular materials G. Ferraris, E. Makovicky, S. Merlino Diffuse X-ray scattering and models of disorder T. R. Welberry Crystallography of the polymethylene chain: an inquiry into the structure of waxes D. L. Dorset

IUCr Texts on Crystallography 1 The solid state A. Guinier, R. Julien 4 X-ray charge densities and chemical bonding P. Coppens 5 The basics of crystallography and diffraction, second edition C. Hammond 6 Crystal structure analysis: principles and practice W. Clegg, editor 7 Fundamentals of crystallography, second edition C. Giacovazzo, editor

Crystallography Of The Polymethylene Chain An Inquiry Into The Structure of Waxes DOUGLAS L. DORSET

ExxonMobil Research & Engineering Co. USA

1

3

Great Clarendon Street, Oxford OX2 6DP Oxford University Press is a department of the University of Oxford It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Bangkok Buenos Aires Cape Town Chennai Dar es Salaam Delhi Hong Kong Istanbul Karachi Kolkata Kuala Lumpur Madrid Melbourne Mexico City Mumbai Nairobi São Paulo Shanghai Taipei Tokyo Toronto Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York © Oxford University Press, 2005 The moral rights of the author have been asserted Database right Oxford University Press (maker) First published 2005 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose this same condition on any acquirer A catalogue record for this title is available from the British Library Library of Congress Cataloging-in-Publication Data Dorset, Douglas L., 1942– Crystallography of the polymethylene chain : an inquiry into the structure of waxes / Douglas L. Dorset. p. cm. ISBN 0–19–852908–2 (alk. paper) 1. Waxes. 2. Waxes—Analysis. 3. polymethylene—Structure. I. Title TP670.D67 2004 665
.1—dc22 2004024145 ISBN 0-19-852908-2 (Hbk) 10 9 8 7 6 5 4 3 2 1 Typeset by Newgen Imaging Systems (P) Ltd., Chennai, India Printed and bound in on acid-free paper by Biddles Ltd., King’s Lynn

Preface The problem of multicomponent linear chain assemblies is a ubiquitous one that is certainly encountered in polymer physics but also in the consideration of all lipid arrays, detergents, edible fats, and natural and synthetic waxes. The study of the waxes as a model for the association of linear molecules is the central issue considered in this book, since it has become a particularly fruitful area for detailed study. The molecules themselves are not very complex so that rules for their association in the solid state can be uncovered from the geometric rules governing the assembly of van der Waals surfaces, an important fact was discovered by the great Russian crystallographer, A. I. Kitaigorodskii and published (1955) in his book Organicheskaya Kristallokhimiya, later (1961) translated into English as Organic Chemical Crystallography. This book endeavors to evaluate a model for wax chain assemblies proposed by Le Roux and Loubser (1980), in light of improved analytical techniques for investigating these polydisperse substances. In the spirit of Kitaigorodskii’s work, the crystal structures of pure wax component molecules are reviewed, in order to evaluate what packing arrangements are preferred and what, geometrically, is allowed. The book attempts to give as nearly complete an overview of this structural literature as possible up to April 2004. With the development of electron crystallography (but also improved specimen preparation for X-ray crystallography), wax assemblies have recently been characterized as single crystals. Such studies provide new insights into earlier or concurrent powder diffraction studies and the interpretation of binary phase diagrams, but also rely on spectroscopic results for a most complete description of chain disorder. The relationship between wax and polyethylene structure is also discussed. This book does not intend to be a negative criticism of Le Roux and Loubser’s wax model—nor does it intend to criticize negatively the conceptualization of solid solution stability formulated by Kitaigorodskii. Formulation of such models requires a certain amount of courage, particularly when they are based on scant data from complex systems. It is shown here that, while is much merit in these models, there are also mysteries still to be solved. This book attempts to cover a large literature and undoubtedly overlooks some important studies, mainly due to the insufficiencies of this author’s literature searches. However, one very large literature, the morphological and crystallographic description of high molecular weight linear polyethylene, is only briefly covered in this book. Only the relationship between polymer and wax is explored but not controversial issues such as regularity or irregularity of chain folding upon crystallization of the as-synthesized polymer.

Acknowledgements In a way, this book has been in the works for nearly 35 years, since a review of linear chain structures was included in this author’s Ph.D. thesis. I am grateful to A. Hybl for introducing me to the fascinating structural aspects of linear chain molecules and to D. F. Parsons for suggesting the use of electron diffraction to study such molecules. Such work would have gone nowhere without the invention of critical epitaxial orientation techniques, taught to me by B. Lotz and J. C. Wittmann in Strasbourg, France and by J. R. Fryer in Glasgow, Scotland, with whom I have had a long, productive collaboration. I am quick also to acknowledge, with thanks, the very important collaboration with my friend, Robert G. Snyder (Berkeley, CA) who has demonstrated the unique insights gained by the use of vibrational spectroscopy. (I also am grateful for his writing the first drafts, explaining the use of the technique for the study of linear molecules, which I have adapted for this book.) Other important collaborators include: B. K. Moss, S. Kopp, W. A. Pangborn, J. Hanlon, W. P. Zhang, H. L. Hu (Buffalo, NY), H. Ghiradella, W. F. Tivol, J. N. Turner (Albany, NY), C. J. Gilmore, F. Holland, C. McConnell (Glasgow), J. Jäger, E. Beckmann, F. Zemlin, E. Zeitler (Berlin), M. Rademeyer, G. J. Kruger (Johannesburg), I. Basson (Pretoria), J. L. White (Canberra), B. Annis (Oak Ridge), F. DiSanzo (Clinton, NJ), as well as R. Alamo and L. Mandelkern (Tallahassee). Many thanks to all for their important contributions and discussions. The intense part of preparing this book has encompassed approximately five years. I am grateful for the expertise of M. Tugac and G. Del Bel who made the figures originally published in the literature. Thanks are due to the following publishers for permission to reproduce figures published in their journals: American Association for the Advancement of Science (3.9), American Chemical Society (1.3, 4.2, 5.1, 5.3–6, 5.9, 5.10, 5.13–29, 6.2, 6.4–9, 6.11, 6.12, 10.12, 11.4–6, 11.12–14), American Crystallographic Association (4.3), American Society for Biochemistry and Molecular Biology (7.9, 10.5, 10.7, 10.11), Elsevier Science Publishers (1.4, 7.7, 9.12, 10.6, 10.8), Institute of Physics (11.8), International Union of Crystallography (2.10, 4.7, 5.12), John Wiley and Sons, Inc. (3.13, 9.9), Kluwer Academic Publishers/ Plenum Press (9.5), National Academy of Sciences (4.9, 5.2, 10.9), Oldenbourg Wissenschaftsverlag (5.7, 5.8, 11.1, 11.3, 11.11). E. B. Sirota has kindly given his permission to reproduce Fig. 4.3, R. P. Scaringe to publish Fig. 4.4, W. A. Pangborn to publish Fig. 9.3(b) and R. G. Snyder permission to publish his drawing in Fig. 4.9. Thanks to Helen Ghiradella for the scanning electron micrograph of insect wax streamers in Fig. 9.12(a), also used in the cover art of this book. Molecular packing diagrams in this book were made with software within Tripos SYBYL when the author was at HWI and with Accelrys Cerius2 while at the current position.

ACKNOWLEDGEMENTS

vii

Finally, I am grateful for the following funding sources during my own work in the field: National Institute of General Medical Sciences, National Science Foundation, Margaret L. Wendt Foundation, as well as a consultantship with the (pre-merger) Exxon Research & Engineering Company in Clinton, NY, wherein I was introduced to the world of real waxes. The collaboration with E. B. Sirota, H. E. King, M. M Disko, and R. Fiato is gratefully acknowledged. I am especially grateful to Eric Sirota for his reading of the manuscript and his helpful comments.

This page intentionally left blank

Contents

1

Polydispersity and the paraffin chain—statement of the problem 1.1 1.2

1.3

2

Layer packing of polymethylene chains 2.1 2.2 2.3 2.4

3

Importance Binary solid state of n-paraffins: early descriptions 1.2.1 Polymorphism 1.2.2 Simple phase diagrams 1.2.2.1 Solid solutions 1.2.2.2 Intermediate stages—onset of fractionation 1.2.2.3 Eutectic solids 1.2.3 Stability conditions for binary solid solutions of linear molecules 1.2.4 Experimental variances to Kitaigorodskii’s rules for paraffin solid solutions Summary

The methylene subcell and layer packing—theoretical considerations Observed methylene subcells Layer stacking Summary

Crystal structures and phase transitions of the paraffins 3.1 3.2 3.3 3.4 3.5 3.6 3.7

Introduction Crystal structures of lower chain n-paraffins Triclinic crystal structure of longer even-chain n-paraffins Monoclinic crystal structure of the even-chain n-paraffins Orthorhombic crystal structure of the even-chain n-paraffins “Nematocrystalline” modifications Thermodynamically stable orthorhombic crystal structure of the odd-chain n-paraffins 3.8 Orthorhombic crystal structure of melt-crystallized odd-chain n-paraffins 3.9 Branched n-paraffins 3.10 Aromatic substitution of n-paraffins 3.11 Polyethylene and its alkane models 3.12 Summary

1 1 7 7 8 11 14 14 15 16 18 19 19 23 30 32 33 33 34 37 39 40 45 47 47 49 51 52 56

x

4

5

CONTENTS

Thermotropic disorder in n-paraffin crystals 4.1 Introduction 4.2 Diffraction and microscopical studies of high temperature chain packing 4.3 Vibrational spectroscopic measurements of n-paraffins at high temperature 4.4 Summary Binary and multicomponent solids of n-paraffins 5.1 Introduction 5.2 Solid solutions 5.2.1 Binary combinations 5.2.2 Multicomponent solutions 5.3 Miscibility gap 5.3.1 Binary combinations 5.3.2 Multicomponent combinations 5.4 Eutectic solids—partial co-solubility 5.5 Eutectic solids—no co-solubility 5.6 Effect of chain-folding on phase separation 5.7 Conclusions 5.8 Summary

6

Some functional substitutions in n-paraffins 6.1 6.2 6.3 6.4 6.5 6.6 6.7

7

Introduction Perfluoroalkanes—crystal structure Perfluoroalkanes—binary phases Heteroatoms in chains—crystal structures Heteroatom substitutions—binary phases Unsaturation Summary

Lipid alcohols 7.1 Introduction 7.2 Crystal structure of primary fatty alcohols 7.2.1 Tilted layer polymorphs 7.2.2 Rectangular layer polymorph 7.2.3 Rotator phases 7.3 Crystal structures of other fatty alcohols and thiols 7.4 Binary phase behavior of fatty alcohols 7.5 Crystal structure of cholesterol 7.6 Thermotropic behavior of cholesterol 7.7 Examples of binary phase behavior of cholesterol with simple derivatives 7.8 Summary

57 57 59 68 72 73 73 73 73 85 91 91 101 101 106 106 107 107 109 109 109 113 118 121 121 122 124 124 124 124 125 126 127 129 130 131 132 133

CONTENTS

8

The fatty acids 8.1 8.2

8.3 8.4 8.5

8.6 8.7 8.8

9

Linear fatty acid esters 9.1 9.2 9.3 9.4 9.5 9.6

10

Introduction Pure esters—crystallography Thermotropic behavior of linear fatty acid esters Binary phase behavior of linear fatty acid esters Multicomponent and other natural waxes Summary

The cholesteryl esters 10.1 10.2

10.3 10.4 10.5

11

Introduction Crystal structures of normal chain fatty acids 8.2.1 Even-chain acids 8.2.2 Odd-chain acids 8.2.3 Very short fatty acids 8.2.4 Heteroatom substitution Crystal structure of unsaturated fatty acids Crystal structure of cyclopropane-containing fatty acids Crystal structures of branched-chain fatty acids 8.5.1 Oxygen-substituted fatty acid chains 8.5.2 Methyl-branched chains Thermotropic behavior of fatty acids Binary phase behavior of fatty acids Summary

Introduction Crystal structures 10.2.1 Bilayer packing 10.2.2 Monolayer I packing 10.2.3 Monolayer II packing 10.2.4 Other crystal forms Thermotropic behavior Binary phase behavior Summary

From waxes to polymers—the crystallography of polydisperse arrays 11.1 11.2

Introduction A review of chain packing arrangements for polydisperse assemblies 11.2.1 n-Paraffin solid solutions 11.2.2 Fractionation of n-paraffin solutions—the miscibility gap 11.2.3 Fractionation of n-paraffins—eutectic interactions

xi

135 135 135 136 139 142 142 144 148 149 149 150 153 153 154 155 155 155 163 163 166 170 171 171 171 172 173 174 175 175 178 184

185 185 185 185 188 189

xii

CONTENTS

11.3

11.4 11.5

The crystal structure of waxes 11.3.1 “Typical” lamellar wax structures 11.3.2 From wax to polymer crystal— interlayer bridges What is wax and what is polyethylene? Incentives for future characterization of waxes 11.5.1 Critique of the Le Roux wax model 11.5.2 Directions for future work

189 189 193 200 202 202 203

References

205

Subject Index

227

Compound Index

231

1 Polydispersity and the paraffin chain—statement of the problem

1.1

Importance

Polymethylene chains are ubiquitous structural moieties of a large family of many useful amphiphilic and/or thermoplastic substances. For example, paraffins are important ingredients of petroleum. They form the matrix of separated wax solids and are the combustion standard for diesel fuels. Polymethylene chain synthesis also produces waxes or polyethylenes, the lower molecular weight polymers distinguished from waxes only by synthetic route. The alkane chain can be oxidized to a fatty acid and its esterification to a fatty alcohol produces a major component of plant and animal waxes. Esterification of a fatty acid to cholesterol forms the esters found predominantly in animal fats and (skin, hair) waxes. Esterification of the fatty acid to glycerol forms the glycerolipids, an important component of foodstuffs. Substitution of a phosphate-linked moiety to a diglyceride generates the phospholipids of the cell membrane bilayer. If the carboxylic acid head group of a soap is replaced by another polar function (charged or non-charged) detergents are formed, also of considerable commercial importance. Many chemical compounds incorporating the alkane chain share common features that can be generalized, as can be readily discerned from the crystal structures of these molecules. This is because the polymethylene moiety is often sequestered to well-defined domains of the crystal unit cell so that it can be treated separately as an oligomeric segment of polyethylene. Indeed, the presence of a structurally isolated chain packing itself will determine many of the molecular properties, not only in the crystalline solid but also those of disordered liquid crystalline mesophases at higher temperatures. In the crystalline state, there is often a well-defined methylene subcell for the close packing of these chains within a symmetry group that may be quite different from that of the entire molecular packing in the crystal unit cell. Because of a significant concentration of methylene groups in the molecule, signals from the subcell packing can be easily discerned by various physical measurements. With X-ray diffraction, this dominant chain packing motif was originally exploited to aid solving crystal structures (Vand and Bell, 1951). Fortunately, the number of commonly observed methylene group arrays is small enough so that the first part of determining the layer packing of polymethylene chain derivatives involves subcell

2

POLYDISPERSITY AND THE PARAFFIN CHAIN

identification, usually by some fingerprint procedure. In addition, diffraction spacings at low scattering angle, when compared to the theoretical length of the molecule, determine the tilt of the polymethylene chain axis to the layer plane. For various substances containing alkane chains, the crystal structures of the pure, that is, monodisperse, molecules have been determined in order to provide a static three-dimensional geometrical reference point for understanding their physical properties (Chapman, 1965; Small, 1986; Larsson, 1994). In fact, purity itself might be a precondition for the growth of a particular crystalline polymorph, since the packing of polymethylene chains can be strongly influenced by the small contamination by homologous components (Teare, 1959). For complicated amphiphilic molecules such as the phospholipids, growth of any crystalline form can be frustrated unless the purity of the substance is very high (Albon, 1976). Nevertheless, efforts have been made to grow crystals of representative molecules so that their characteristic layer structures could be determined. The presence of impurities and their effect on crystallization behavior reveals a very important natural property of n-alkane derivatives, too often overlooked in zealous efforts to elucidate their characteristic packing motifs in the solid state. Polymethylene chain materials from biosynthetic or synthetic sources are rarely pure; they are preferentially polydisperse. Even if only one “functional” moiety exists in the linear molecule for some natural products, the material, in a refined or synthesized solid mass, also includes a distribution of chain lengths. Chain unsaturation, functionalization, or branching are other possible variables. The distribution of chain lengths, double bonds, branching, etc. can strongly influence the physical properties of the substance. For example, does a piece of chocolate have the desired “mouth feel,” texture, and flavor release? These properties are determined, to a large degree, by the crystalline polymorphs expressed in solid solutions of triglyceride components of cocoa butter (Matsui, 1988), so that, if one wishes to manufacture candy bars, cheaper synthetic replacements for this hard butter component must mimic closely the physical properties of the natural fat. What stabilizes a certain crystalline polymorph and how readily does it change when the product is stored? Analogous questions can be raised about the formulation of waxes, again if cheaper synthetic ingredients are blended into the more costly natural products, or if synthetic substitutes are sought for natural materials (e.g. spermaceti) from sources that no longer can be exploited legally (Hamilton, 1995). Linear polymers are also polydisperse, complicated by the prospect of chain-folding when the mean molecular weight exceeds a certain value. Historically, polyethylene has often been regarded as a paradigm for other crystalline polymers and has, therefore, been extensively studied to understand various aspects of its crystallization behavior. Explaining the physical properties of such polydisperse linear molecule arrays requires first a study of binary solids. Such investigations constitute the central theme of this book, which describes the crystallography of n-paraffin chains and their simple non-polar and polar derivatives in binary and multicomponent assemblies. Specifically, we shall consider assemblies of the n-paraffins, linear wax esters, fatty acids, fatty alcohols, and the cholesteryl esters, often restricting this

IMPORTANCE

3

description to fully saturated chain substances. (Examples of substances with two (e.g. diglycerides and phospholipids) or three (e.g. triglycerides) polymethylene chains in a single molecule are not described, although analogies between their properties and those of the simpler linear molecules certainly exist. Similarly, other polar derivatives of linear paraffins (e.g. soaps, invert soaps, and detergents) will not be considered here.) In this inquiry, we wish to understand the principles that favor the formation of stable solid solutions and determine the solid state structure itself. When solid solutions are not possible, or when they are metastable, we also wish to uncover the mechanism of phase separation and to determine the structure of the stable fractionated solid. In this book we consider the structure of waxes, not only because they are the simplest place to begin such an investigation but also because of their economic importance. As reviewed by Warth (1947), Hamilton (1995), and others, the first thermoplastic material used by man still has widespread applications to all aspects of daily life and technology. Obviously, candles and polishes come to mind, but the, equally important, presence of wax is exemplified by its further use: in the electrical industry (e.g. insulation of components, weatherproofing), the food industry (coating for washed fruits and vegetables and for cheese, also in packaging) in the production of matches and pyrotechnical devices (anti-moisture and source of flammable carbon), in the manufacture of adhesives (hot melt adhesives as well as the flexing agent for glues and tapes), in the paper industry (sizing of papers, coating for cardboard) for the production of cosmetics (lipsticks, emollients, etc.), as well as the preparation of carbon papers, ribbons, and printing inks. Other uses include the production of crayons. In dentistry, waxes are widely used, for example, for making impressions for casting and for temporary fillings. Batik designs on cloth employ waxes in their production. In sports, waxes are used to produce a gliding surface for skis, not to mention the highly specialized application to cross-country skis to provide adhesion for different snow conditions and temperatures. Wax crystallization can also lead to major industrial problems. For example, crude oils containing a significant n-paraffin component are prone to wax precipitation and this can impede the transport of these fluids through pipelines in cold climates or affect their long-term storage (Won, 1986; Hansen et al., 1988; Pedersen et al., 1989; Holder et al., 1996; Monger-McClure et al., 1999). Although cetane (n-hexadecane) is the combustion standard of diesel fuels, wax crystallization can block fuel filters in cold weather (Coutinho and Ruffier-Méray, 1997; Craig et al., 1998, 1999; Coutinho et al., 2000). In the former case of waxy crudes, a remedy might involve the use of so-called “pour point depressants” to inhibit wax crystallization (Gilby, 1983; Irani et al., 1985). In the latter case, fuel additives (Kern and Dassonville, 1992; Schriver et al., 1996) can reduce crystal size so that they can pass through filter meshes. These additives behave as crystal growth poisons to retard the growth of otherwise favored crystal faces, thus modifying the crystal size and shape. What exactly is a wax? When referring to a class of lipids, waxes can be defined simply as fatty acid esters of long chain or cyclic alcohols (Hawk et al., 1954). This would include: (1) the so-called “true” waxes, that is, the esters of linear fatty

4

POLYDISPERSITY AND THE PARAFFIN CHAIN

alcohols with fatty acids; (2) the cholesteryl esters; (3) esters of Vitamin A; and (4) esters of Vitamin D. However, for natural products, such as plant cuticle waxes, even if category (1) is implied, other ingredients, such as n-paraffins, primary fatty alcohols, free fatty acids, ketones, and secondary alcohols, should also be included (Kreger, 1951). Other waxes such as lanolin from wool fat may contain a large concentration of sterol esters (Larsson, 1994), as do the waxes of skin (Rawlings, 1995). According to Hatt and Lamberton (1956), “a wax is best regarded as a thermoplastic of low mean molecular weight and low mechanical strength.” The material, furthermore, must undergo plastic deformation without disrupting the van der Waals forces that hold component molecules together. Historically, extensive effort has gone into the chemical characterization of various natural waxes. The plant waxes are found in the epicuticle and cuticle of leaves as well as the surface of some fruits (Chibnall et al., 1931, 1934; Kreger, 1951; Kreger and Schamhart, 1956; Vandenburg and Wilder, 1970; Simpson and Miwa, 1977; Reynhardt and Riederer, 1991, 1994; Bianchi, 1995; Merk et al., 1998; Jetter et al., 2000; Meusel et al., 2000). Analyses have also been made of insect waxes (Chibnall et al., 1931; Marshall et al., 1974; Blomquist and Jackson, 1979; Nelson and Blomquist, 1995; Patel et al., 2001), with particular emphasis on bee honeycomb wax (Downing et al., 1961; Tulloch, 1969, 1972; Stransky and Streibl, 1971; Stransky et al., 1971; Tulloch and Hoffmann, 1972; Hepburn, 1986). The diversity of long chain chemical species is as important as the distributions of chain lengths. In some cases, specific structural features (e.g. hollow tubules) are built-up from wax molecules (Marshall et al., 1974). Commercially, the designation, “waxes,” can also signify refined petroleum fractions or a synthetic product. Phenomenologically, materials that melt below 0F (17.8C) are termed oils and those that melt above 100F (37.8C) are termed waxes (Ferris, 1955). The natural source of petroleum has been stated to be prehistoric plant waxes (Kinghorn, 1983). More recently, the thermolytic breakdown of a cuticle aliphatic polymer has been implicated (Tegelaar et al., 1989) as the likely kerogen precursor, especially since defunctionalization of plant wax components does not explain the chain length distributions of petroleum waxes. The most highly crystalline (80–90%) refined paraffin fraction of petroleum wax may contain 80–95% n-alkanes with the rest made up of either branched chains or cycloparaffins (Mazee, 1958a; Tuttle, 1960; Pedersen et al., 1989). Chain lengths range from 18 to 56 carbons. The heavier residual “microcrystalline” fraction from the storage tank bottom (50–60% crystalline) is a hard wax with far fewer linear chain ingredients and with a predominant cycloparaffin fraction. Chain lengths range from 40 to 70 carbons (Pedersen et al., 1989). Synthetic products include those made by the Fischer–Tropsch process (Karrer, 1954; Tuttle, 1960) from carbon monoxide and hydrogen passed over a catalyst (Fe, Co). Depending on catalyst (Le Roux and Dry, 1972) synthetic waxes contain different amounts of methyl branches (Le Roux, 1970). These materials also include higher molecular weight paraffins than are obtained from distillates and they can be oxidized to incorporate fatty acids and their esters (LeRoux, 1979; Reynhardt, 1986).

IMPORTANCE

5

Compositionally, waxes can be defined as an assembly of linear chain molecules, often with a (generally, positively) skewed Gaussian or normal logarithmic distribution of chain lengths, for example, as found for high-wax crude oils (Hatt and Lamberton, 1956; Retief and LeRoux, 1983; Stenger et al., 1984; Tegelaar et al., 1989; Gupta and Severin, 1997; Jayalakshmi et al., 1999; Severin and Gupta, 1999; Dirand et al., 2002). From petroleum and/or synthetic (e.g. Fischer–Tropsch) sources, the waxes often are assemblies of co-soluble linear n-paraffin chains, with branched chain components possible. (An overview of the Fischer–Tropsch process is given by Schulz, 1999.) Sometimes (Altgelt and Boduszynski, 1994) naphthenic components, that is, alkyl chains linked to aromatic or saturated ring moieties, dominate (Srivastava et al., 1992; Musser and Kilpatrick, 1998). From references cited above, for animal and plant sources, the major component is often, but not necessarily, an assembly of linear wax esters, perhaps including some alkanes as well as more complicated long chain diesters. Fossilized mineral waxes will also contain mostly linear esters (Hamilton, 1995). Often these assemblies appear to be a single phase, that is, a solid solution, but evidence can be found for fractionation in some cases. Various crystal forms have been observed in petroleum waxes. Simple solid solutions of n-paraffins can occur as plates or needles. Although branched chain and ring-containing impurities have been identified as ingredients in the needle crystals (Ferris, 1955; Edwards, 1957), it is agreed that the needles are simply plastic plate crystals that are tightly rolled up (Rhodes et al., 1927; Edwards, 1957; Zocher and Machado, 1959). Another form commonly observed is the so-called “mal”-crystal, also including highly branched or ring-containing impurities (Edwards, 1957). A major objective of this volume is to evaluate a model (Le Roux and Loubser, 1980) for a wax crystal structure (Fig. 1.1) that has been accepted by many

A B

C D

Fig. 1.1. Schematic model for a wax proposed by Le Roux and Loubser (1980).

6

POLYDISPERSITY AND THE PARAFFIN CHAIN

researchers, for example, considering the properties of synthetic Fischer–Tropsch aggregates (Basson and Reynhardt, 1992a) or even the wax layer on a plant cuticle (Riederer and Schreiber, 1994). Possible reasons for wax plasticity have been discussed. These include: (1) the sliding of one wax grain with respect to another, perhaps facilitated by a liquid component; (2) the rolling of smaller crystallites between larger ones; and (3) the migration of grain boundaries (Retief and LeRoux, 1983). From existing powder X-ray and nuclear magnetic resonance (NMR) spectroscopic evidence, the assembly might be proposed to contain four zones, since a two-phase model did not effectively explain observed properties. The most crystalline region (A) contains the polymethylene chain packing as found in polyethylene lamellae or orthorhombic paraffin single lamellae. A rigid amorphous region (B) incorporates methyl branches. An interfacial region between the lamellae (C) is also thought to be amorphous with a width depending on the size of the chain length distribution. Solvent or “oil” molecules may be included in this region, according to the model. Finally, a more fluid region (D) contains the volatile lower molecular weight components, thought to be important for modifying the physical properties of the wax. Assessment of such a model requires the investigation of individual waxes, composed of n-paraffins, their branched or ring-containing derivatives, or the linear esters of normal fatty acids, in the most crystalline form that can be grown from them. Structural results from linear waxes will then be compared to the binary phases of cholesteryl esters, as might be found in crystalline fractions of wool wax. This is a complicated co-mixture of sterol and fatty alcohol esters of fatty acids (Warth, 1947). Although the fatty acid chains are often saturated, they may also be multiply branched. Even normal fatty acid esters of cholesterol represent a next level of complication to such linear molecular structures, where the approximate cylindrical symmetry of typical wax molecular components is lost. It will be shown that sterol substitution can include sequestered regions in the unit cell for polymethylene chain packing, a feature common to many lipid crystal structures (Small, 1986). More interesting, the very presence of a methylene subcell packing can also be abolished by just a change of one methylene unit in the attached n-alkyl chain length. The presence of two molecules in the asymmetric unit, instead of the single molecule that is typical of most crystal structures, will also have an impact on the randomized packing of a second ingredient in stable solid solutions. In all of the discussions of waxes in this book, it must be remembered that rules governing the co-solubility or immiscibility of wax components always derive from the underlying solid state structures of their individual pure components. For this reason, considerable effort is made to describe molecular shape and resulting solid state packing characteristics of pure linear molecules, also when functional groups are added to the fundamental polymethylene chain unit. While this book might be regarded as a compendium of polymethylene compound crystal structures, it intends to utilize such geometrical aspects of molecular packing to understand the assembly and stability of polydisperse wax solids.

BINARY SOLID STATE OF n-PARAFFINS

1.2

7

Binary solid state of n-paraffins: early descriptions

1.2.1

Polymorphism

In the discussion of possible layer packing motifs in the crystal structures of polymethylene compounds below, it will be apparent that more than one crystalline form can often (co-)exist for any particular material. The possibility of more than one crystalline form is called polymorphism. The study of polymorphism is integral to understanding the co-solubility of two dimensionally similar molecules in the solid state. In addition to structural probes that will reveal details of molecular packing in all (crystalline) forms, it is also helpful to measure the thermotropic properties of these materials. Consider, therefore, a pure n-alkane chain that has two polymorphic forms A and B. Three types of crystallization behavior can be envisioned, as outlined in Fig. 1.2. The Gibbs free energies of the two polymorphs can be imagined (Schaerer et al., 1956; Sato and Garti, 1988) to cross at a certain temperature T0 (Fig. 1.2(a)). The most stable polymorph will crystallize from the melt at Tm. Transitions of one polymorph to another are reversible in this case and the transition is accordingly termed enantiotropic. In a second case (Fig. 1.2(b)), the Gibbs free energy curves G(A) and G(B) also cross but, at either side of T0, there is an irreversible crystallization of one polymorph to the other. (However the transition at T0 is again enantiotropic.) If temperature T0 lies below the (a)

(b)

B

A A G

G B To

T o


To T

T (c) A Melt

G B

Tm(A) Tm(B) T

Fig. 1.2. Energetics of polymorphic crystallization. Schemes (a) and (b) lead to enantiotropic crystallization whereas (c) leads to monotropic crystallization.

8

POLYDISPERSITY AND THE PARAFFIN CHAIN

melting point of the highest melting form, then polymorph B will crystallize from the melt. If T0  Tm, either A or B can crystallize. Usually, below some temperature T0
, polymorph A preferentially converts to B from the melt. On the other hand, when crystallized below T0
from solution, either A or B can form. When G(A) and G(B) do not cross (Fig. 1.2(c)), either crystal form can be observed in the crystallized melt. The melting process is unidirectional, that is, monotropic. 1.2.2

Simple phase diagrams

The description of n-paraffin binary solids by phase diagrams and diffraction measurements was already well-established when Mnyukh published a review of binary paraffin solids in 1960. The binary phase diagrams, determined from cooling curves of co-melted ingredients sampled at various concentrations, were interpreted with measurements of lamellar layer thicknesses, the so-called “long spacing” in powder X-ray diffraction patterns. Nowadays, thermal changes to a substance, or a combination of several substances, are only rarely followed by cooling curves, that require measuring temperature change at a constant rate with a thermocouple dipped into the bulk (see Mazee, 1957). The differential scanning calorimeter (DSC) conveniently measures transition temperatures for small (ca. 1 mg) samples. One of the first observations to be made for (enantiotropic) phase changes for many organic substances is that they may not be entirely reversible, that there may be a slight undercooling of the specimen before it recrystallizes from the melt. Sometimes the undercooling can be enhanced kinetically by a larger cooling rate, that is, the transitions do not strictly conform to equilibrium conditions. At low DSC scan rates, reversible behavior can also be observed (Fig. 1.3). Phase transitions in organic substances can be further classified phenomenologically. First-order transitions are strictly isothermal, whereas so-called “higher-order” transitions occur over a somewhat extended temperature range.

0.5 mW

Heat

Exo Endo Cool 40

60

80 T (°C)

100

120

Fig. 1.3. Nearly reversible crystallization of low molecular weight linear polyethylene at 5C min1. (Dorset, D. L. (1989) Bridged lamellae: crystal structure(s) of low molecular weight linear polyethylene. Macromolecules 32, 162–166.)

BINARY SOLID STATE OF n-PARAFFINS

9

Efforts have been made to categorize several types of non-first-order melting processes in organics (Westrum and McCullough, 1963). As can be seen from the tails in DSC melting peaks or a plot of Cp versus T, transitions of many polymethylene compounds are not isothermal. This is because the entropy of melting (S  H/T) consists of positional, orientational, configurational, etc. processes for disordering such flexible molecules (Ubbelohde, 1978). Although breaks in the Cp versus T plot, calculated from DSC scans, could detect phase transitions much as cooling curves were once evaluated, the endothermic transitions themselves are mostly used to plot the phase diagrams of binary combinations, or, alternatively, peak positions for lower temperature transitions combined with the return of highest temperature transition to baseline (Smith and Pennings, 1974). A simple quantitative method has been suggested for creating such phase diagrams, based on “shape factors” for the transition endotherms (Courchinoux et al., 1988). For single transition peak, for example, observed for a cholesteryl linoleate sample (Fig. 1.4(a)), three temperatures can be defined: To, the onset; Ts, the peak, and Tf, the final. (The first and third represent the intersects of the tangent lines for the respective curve rise and fall respect to the plot baseline.) From these identified temperature points, “shape-factors” are defined, viz.: Ts  Ts  To; Tf  Tf  To. For complex peaks, additional points of this kind can be identified (Fig. 1.4(c)–(d)). To plot a phase diagram, three temperature values are used from these measurements: To, Ts  Ts, and Tf  Tf. An example of such an analysis was the construction of the peritectic phase diagram of cholesteryl linoleate with cholesteryl oleate (Dorset, 1990a). Thermal measurements, by themselves, are often insufficient for complete characterization of a phase diagram (Turner, 1971; Rajabalee et al., 1999a). Independent structural probes, such as powder X-ray diffraction, are often utilized to define concentration/temperature domains where the same crystalline phase would be found. To visualize simple binary phase diagrams, it is often sufficient to plot peak temperatures. While this ignores the actual liquidus and solidus curves for solid solutions, by merely considering a mean of the two, such a plot can be compared, at any temperature to the average of: x(S) B 

ea  1 , ea  eb

for the solidus

and b (S) x(L) xB , B  e

for the liquidus

(This approach is followed for drawing phase and interpreting phase diagrams in this book.) Quantities are defined:

冤

ea,b  exp 

HA,B 1  1 R T TA,B

冢

冣冥

where HA,B and TA,B are the transition enthalpies and temperatures for pure components A and B, respectively. These relationships are based on Raoult’s law of ideal solutions (Lee, 1977). Deviations are a sign of nonideality.

10

POLYDISPERSITY AND THE PARAFFIN CHAIN (b)

(a) To

Exo

Tf

Endo

Ts 0

10

20

30

(c)

40

50

60

0

10

20

30

Ts 10

20

30

40

60

T s

T
s

0

50

To Tf T
f

(d)

T o
To Tf

40

50

Ts 60

0

10

20

0

10

20

30

40

50

60

30 40 T (°C)

50

60

(f)

(e)

0

10

20

30 40 T (°C)

50

60

Fig. 1.4. Examples of “shape factors” from DSC scans of cholesteryl ester binary solids. The dotted curves reveal the monotropic nature of mesoforms that are observed only when cooling from the melt. (Dorset, D. L. (1990) Binary phase behavior of cholesteryl oleate with cholesteryl linoleate. Biochim. Biophys. Acta 1046, 57–63.)

For fractionated systems, the liquidus curve can be compared to: ln xA 

冢

HA 1  1 R T TA

冣

which is the Schroeder–Van Laar equation. For nonideal interactions, phenomenological equations have proposed to account for an observed nonzero heat of mixing. One model that has been used for wax precipitation (Won, 1986; Hansen et al., 1988) has included activity coefficients where mole fractions are replaced by activities such that ai  xi␥i, where ␥i is the activity coefficient. Another approach is the Bragg–

BINARY SOLID STATE OF n-PARAFFINS

11

Williams equation (see Lee, 1977; Tenchov, 1985), where an interaction term, ␳o, determines the deviation of an ideal liquidus temperature T ideal from its observed value T, that is: ␳o(1  xA)2/HA  (T/T ideal)  1 Experimental deviations on either side of the ideal liquidus curve can be interpreted in terms of preferred cross- or self-interactions of component molecular species (Lee, 1977; Tenchov, 1985). An alternative lattice model for nonideal systems has been formulated by Flory (1953). As pointed out by Pitzer (1995), the description of nonideal interactions is still somewhat qualitative. For eutectic phase diagrams, Tammann (1925) had shown that the isothermal dwell time observed in cooling curves correspond to the crystallization of the eutectic solid. These dwell times increase in length as one approaches the eutectic point. The observed “halt period” is proportional to the heat content of the eutectic solid. In DSC measurements, the transition enthalpy of the lower melting component can, similarly, be plotted against molar concentration to locate the eutectic point. This technique has been applied to seek compound formation in polymer–solvent gels (Guenet and McKenna, 1988), as it has been applied to lipid eutectics (Galanti and Porter, 1972; Griffen and Porter, 1973). A simple experimental overview of these observations will serve as an introduction to the subject as applied to wax assemblies. Review articles can be cited (Mnyukh, 1960; Turner, 1971; Dirand et al., 2002) for further reading. As will be shown below, there are numerous intermediate stages between perfectly miscible and totally immiscible binary solids. Basically, phase diagrams begin with stable solid solutions where the components can substitute for one another in the solid. A miscibility gap can occur (Fig. 1.5(a)) where microphase separation begins. As the miscibility gap region approaches the two-phase region of the solid solution, the latter interaction becomes nonideal (Fig. 1.5(b)). Finally, the miscibility gap can be thought to intersect the solid solution region to begin eutectic relationships between solid solutions (Fig. 1.5(c)). As the materials become more and more dissimilar the separation is absolute so that the eutectic exists between two pure forms (Fig. 1.5(d)). These principles are discussed in textbooks on physical chemistry (e.g. Levine, 1995) or on phase diagrams themselves (Gordon, 1968; Kitaigorodsky, 1984). 1.2.2.1 Solid solutions Solid solutions contain nonidentical chain lengths (molecular volumes), packing in a common lamella (average unit cell). When the chain length difference is not great (e.g. solids formed from co-melts of n-C32H66 with n-C34H70), then, in terms of melting temperature, the solutions are nearly ideal over all concentrations. Cooling curves measuring the change in temperature (T) with time (t) at constant pressure can be used to plot the characteristic temperature–composition binary phase diagram of a solid solution (Mazee, 1957). The time required to cool the binary combination of alkanes varies according to the amount of heat q lost from the system so that the slope dT/dt is, to a first approximation, inversely proportional to the isobaric heat

12

POLYDISPERSITY AND THE PARAFFIN CHAIN

(a)

s

Liquid

Temperature

(b)

Liquidu

Liquid

+ solid Solidus

Solid Solution 2 phases

100% A

100% B Composition

(c)

(d)

Temperature

Liquid

Solid A + liquid

Solid B + liquid

Solid A + solid B (eutectic) A

B

100% A

Composition

100% B

Fig. 1.5. Succession of phase diagrams accompanying a loss of co-solubility. (a) Solid solution with miscibility gap; (b) non-ideal solid solution; (c) eutectic relationship between solid solutions. (The miscibility gap can be imagined to intersect the solid solution transition curves.) (d) Eutectic relationship between immiscible components.

capacity of the substance at a given temperature, that is, Cp  dqp/dT (Levine, 1995). Phase changes are located by breaks in the cooling curves, that is, where the slope changes. For ideal solid solutions, the freezing point of the lower melting substance can be actually raised by adding different amounts of the higher melting substance. Above the liquidus boundary (Fig. 1.5(a)) a single liquid solution is found and below the solidus boundary a single solid solution is found. Between the two curves, a mixture of two phases is encountered, comprising both liquid and solid solutions. Powder X-ray diffraction data (Fig. 1.6) were utilized to test the continuity of the lamellar layer thickness measured directly at low angle. A continuously smooth linear variation of this layer thickness is expected to link a lamellar spacing, for example, in powder diffraction patterns for the two pure components according to Vegard’s law (Vegard and Dale, 1928). Vegard’s law states that the change in unit cell volume should be linear with the change in composition for an ideal solid solution. For the n-paraffins, since the lateral spacing of chains in a layer can be almost invariant with composition (see below), the volume change is expressed directly as an average

BINARY SOLID STATE OF n-PARAFFINS

100

13

Powder diffraction Radiation used = X-ray Wavelength = 1.5418 c33001

__ticks __simul

Subcell reflections 80

60

“Lamellar” reflections

40

20

0 0

5

10

15

20 25 30 Diffraction angle

Single crystal diffraction Radiation used = Electron Wavelength = 0.0251 c33004 Zone = [1 0 0] n = 0 0.4

35

40

45

50

Single crystal diffraction Radiation used = Electron Wavelength = 0.0251 c33005 Zone = [1 1 0] n = 0 0.4

01l

0.2

0.2 hhl

020 0.0

0.0

–0.2

–0.2

–0.4

–0.4 –0.4 –0.2

0.0

0.2

0.4

–0.4 –0.2

0.0

0.2

0.4

Fig. 1.6. Hypothetical powder X-ray diffraction pattern from n-tritriacontane (top) compared to electron diffraction patterns from the same material (bottom).

change in combined chain length in a lamella. (However, slight variations can be measured in the lateral spacings, Retief et al., 1985.) Actually, in many measurements of paraffin binary solid solutions, this so-called lamellar spacing often lies somewhat above the ideal line defined by Vegard’s law (i.e. the line that connects the values for the pure components). This deviation was thought to indicate the dominance of the longer chain ingredient in the layer when its concentration was large

14

POLYDISPERSITY AND THE PARAFFIN CHAIN

(Mnyukh, 1960). Alternatively, electron diffraction patterns from epitaxially oriented layers can provide the same parameters, with the additional benefit that they are single crystal patterns with no peak overlap (Fig. 1.6). 1.2.2.2 Intermediate stages—onset of fractionation When the solid solution formed by two materials just begins to become unstable, a careful determination of a phase diagram reveals a miscibility gap at low temperature where the single solid solution begins to separate into two solid solutions. Metallurgists often refer to this region as one where an ordering process takes place (Guy and Hren, 1973). The binodal phase boundary delineating this two-phase region can be imagined to move toward the solidus curve of the solid solution (e.g. as the volumetric difference between molecules increases), until it intersects it. At the final point, a eutectic phase diagram is formed from the interaction of solid solutions (see below). Experimental examples of this gradual fractionation process for binary n-paraffin solids will be shown in later chapters. For this series of phase diagrams, it is assumed that the concentration-dependent transition curves for the solid solution portion are nonideal, that is, there is a minimum to the solidus curve at some intermediate temperature (Fig. 1.5(b)). If the solid solution transitions are more ideal as they are intersected by the miscibility gap, a peritectic phase relationship results. 1.2.2.3 Eutectic solids When a paraffin chain length difference is great enough (e.g. C21H44 with C31H64) or when two different crystalline forms interact (e.g. C20H42 with C30H62), the two components will be totally immiscible in the solid state (Mnyukh, 1960). Before this extreme difference in chain lengths is reached, solid solutions can fractionate (e.g. n-C30H62 with n-C40H82). In addition to the slope changes in cooling curves, there will also be a halt or plateau with zero slope, as a eutectic solid forms (Mazee, 1957). The duration of the arrest plateau is related to the amount of eutectic solid separating from the cooled melt (Tammann, 1925) and hence, the amount of heat required to melt this solid. In the binary phase diagram of the completely fractionated system, the freezing point of either pure component is lowered as the other added to it. Above the liquidus boundary, the melt of the co-miscible components, a liquid solution, is observed. Between the liquidus and the isothermal solidus curve, pure solid exists in equilibrium with the liquid solution, and below the solidus, the two components coexist as two phases in the solid form. The minimum melting point where the liquidus and solidus join, is called the eutectic point. Following Tammann’s (1925) observation of arrest duration, the eutectic point can also be found by plotting enthalpy (H) of the eutectic solid to melt transition against molar concentration (Galanti and Porter, 1972; Griffen and Porter, 1973). Eutectics may be formed from solid solutions, or they may express the total immiscibility of the two components. Both cases (Fig. 1.5(c),(d)) are relevant to the study of n-paraffins.

BINARY SOLID STATE OF n-PARAFFINS

15

Low-angle diffraction in the powder X-ray patterns from such solids indicates the presence of two independent spacings (and their higher orders) which are constant over varying concentration. This implies that the two components exist as separate crystalline blocks within the solid phase. No information about the structural interface between these components is given, however. For fractionated solids of two immiscible cholesteryl esters, Hsu and Johnson (1974) proposed that the crystallites should coexist as some sort of “mechanical mixture.” Textbooks on metallurgical phase diagrams (Gordon, 1968), on the other hand, indicate that eutectic solids can be much more highly ordered, for example, as lamellar structures, with possibilities for epitaxial relationships to occur across the crystallite boundaries in the fractionated solid (Kerr and Lewis, 1971). The analogous case will be shown for phase-separated linear chain combinations, and is anticipated by light microscopic observations on certain organic eutectics (Podolinskii, 1980; Podolinskii et al., 1987). 1.2.3

Stability conditions for binary solid solutions of linear molecules

Based on numerous experimental observations on binary solids formed from n-paraffins, Kitaigorodskii (1961) formulated two rules to predict the stability of solid solutions. The first condition is volumetric and states that the non-overlap volume  between two components of a solid solution must be minimal. If the overlapping volume for the two components is r, then the quantity e  1  /r must be typically greater than or equal to ~0.8. This rule seems to be valid for a variety of molecular shapes involved in solid solutions (Kitaigorodsky, 1984). That the individual component molecules have similar shapes and sizes is directly implied. Continuous solid solutions, therefore, would not exhibit any significant lattice distortion. In terms of volumetric difference, Kravchenko (1946) observed for paraffins with one carbon difference, stable solid solutions were found when the main chain lengths were greater than 16 carbons. Partial miscibility was found for chain lengths between 7 and 17 carbons and no miscibility was found when the mean chain length was less than 8 carbons. For a chain length difference of two carbons, the respective values were: fully miscible, nC  33; partially miscible 34  nC  13; immiscible nC  14. When nC  4, the respective values are: nC  67; 68  nC  27; nC  28. The second condition for a stable solid solution was once thought to be influenced by space group symmetry. If molecules A are added to a crystal of molecules B, the average symmetry of the solvent crystal B must remain the same or be lowered by the addition of the second component. According to Kitaigorodskii (1961, 1984), the solid solution cannot have higher symmetry than either of the pure components. If the molecules of the host crystal are chiral, then the symmetry cannot be changed. If the host crystals contain molecules that either have a mirror plane or a center of inversion, then the symmetry can be lowered by adding a chiral A molecule. There are other cases where the symmetry would not be lowered if the A molecules were added. For example, a centrosymmetric B crystal, where the molecules include the inversion center, can be substituted by A with mm symmetry, if the two possible molecular polarities are equally occupied in the cell to produce an average inversion

16

POLYDISPERSITY AND THE PARAFFIN CHAIN

center. Conversely, if B molecules have mirror symmetry, centrosymmetric A molecules can be statistically packed to simulate the host mirror operation. For a solid solution to be continuous, Kitaigorodskii (1961) states further that the symmetries of arrays of A in B must be the same as those of B in A. Dissimilarity implies a discontinuity in solubility. Hence the same space group must be expressed, on average, over the whole concentration range if the molecules are not asymmetric or if both are asymmetric. If only one molecule is asymmetric, then the retention of symmetry or its lowering will take place, respectively, at either extreme of the concentration range. However, it might happen that the addition of the first few asymmetric molecules to the symmetric lattice will lower its symmetry to form a continuous average symmetry over all concentrations. In this case there is also a continuity of solid solutions, but this also implies that there are no geometrical difficulties in passing from one crystal form to the other. When these principles are applied to the n-paraffins, the following rules were observed (Mnyukh, 1960): Continuous solid solutions were possible only when the two ingredients have the same methylene subcell packing. The two pure materials should also have the same layer packing—that is, oblique layers with tilted chains cannot form solid solutions with rectangular layers of untilted chains. 1.2.4

Experimental variances to Kitaigorodskii’s rules for paraffin solid solutions

While the above guidelines appeared to apply for many binary combinations of paraffin chains, there were certain experimental discrepancies noted in early work. For example, a binary phase diagram was constructed for n-C35H72/n-C36H74, in which it appeared that the solid solubility was continuous over all concentrations (Mazee, 1958b). Since the shorter odd-chain paraffin should pack preferentially in an orthorhombic unit cell and the even-chain should crystallize as a monoclinic structure, it was thought that the two chains would be incompatible, despite the difference in chain length of just one methylene unit (Mnyukh, 1960). Later, in a qualitative study of the n-C20H42/n-C22H46 binaries by single crystal X-ray diffraction (Lüth et al., 1974), the P1 space group symmetry of the pure components was found to transform to the higher orthorhombic space group A21am when the concentration of the second component approached 10 mol%. Similar observations had been made much earlier (Piper et al., 1931). Also, Teare (1959) had shown how the monoclinic form of n-C36H74 would transform to a higher-symmetry orthorhombic unit cell with small amounts of impurity (presumably also a solid solution). Mazee (1958b) claimed that only one molecule of n-C35H72 in a cluster of 250 chains of n-C36H74 was required to change the solid solution structure from monoclinic to orthorhombic. In fact, accumulated evidence from many binary systems (Gerson and Nyburg, 1994; Jouti et al., 1995a,b; Achour-Boudjema et al., 1996; Achour et al., 1998; Nouar et al., 1997a,b,1998a,b; Ghogomu et al., 1998; Metivaud et al., 1998; Provost et al., 1998; Rajabalee et al., 1999a,b) concludes that there is no continuous solid solubility of any alkane pair at low temperature. Reasons for these deviations from Kitaigorodskii’s

BINARY SOLID STATE OF n-PARAFFINS

17

(1961) rules will be given below. (They have also been discussed by Turner, 1971.) In any case, solid solubility of two materials is also structurally relevant, since co-solubility demonstrates a close similarity of molecular shape and size. In fact, this point underscores one of the major structural applications of binary phase diagrams in this book. Powder X-ray data (Fig. 1.6) do not provide nearly all of the crystallographic information necessary for the characterization of binary solids. Because of the one long unit cell axis, it can be very difficult to index, and thus interpret, these patterns (Dirand et al., 2002). With electron diffraction measurements on oriented preparations (Fig. 1.6), it is now possible to observe multicomponent linear chain solids as single crystals, especially in the microcrystalline state (Dorset, 1995a). This has done much to revise some of the generalizations made earlier for bulk samples. (The extra information provided by electron diffraction observations is exploited extensively in this book.) Electron diffraction has been criticized (Chevallier et al., 1999), for example, “. . . the samples that were obtained by evaporation of dilute solution onto carbon-film-covered electron microscope grids probably do not correspond to the natural and real state of these waxes and petroleum products.” However, if the whole multicomponent chain assembly has been deposited onto the grid surface, and adequate care has been taken to stabilize shorter chain components that they may not volatilize under high vacuum, it is difficult to imagine why single crystal structural information should be inferior to the admitted limitations of powder diffraction measurements. Again, the primary distinction to be made between the techniques is that powder X-ray diffraction is a bulk measurement whereas electron diffraction probes local environments. There are strengths and weaknesses inherent to either investigation. As will be demonstrated in this book, electron diffraction has opened up the study of polydisperse arrays as single crystals, yielding unambiguous crystallographic data and even permitting crystal structure determination of waxes. This revolutionary development in crystallography depends on the optimal preparation of oriented samples by epitaxial co-crystallizations, developed by Wittmann and Lotz (1990). The rules originally postulated for stability of solid solutions are actually those dictated by equilibrium thermodynamics rather than the actual observation of longlived metastable states. Linear molecules are polymorphic, as also recognized by Kitaigorodskii (1961), so that it may be that the thermodynamically most stable polymorphs of pure components are not the ones involved in the formation of continuous solid solutions. The symmetry rules for solid solution formation also do not necessarily correspond to the crystal structures of the pure materials. Very little structural information was given in the early literature about the mechanism for phase separation. However, aged binary compositions (18–72 mol%) of n-C30H62 with n-C35H72 were found to contain superlattice reflections, indicating a fractionation process. Combinations of the two ingredients were proposed for a series of superstructures (Mazee, 1958b) but the single crystal structure was solved only recently after the investigation of oriented microcrystalline samples. In addition to addressing the problem of co-solubility in the solid state, therefore, the structures

18

POLYDISPERSITY AND THE PARAFFIN CHAIN

of fractionated combinations will also be shown to comprise a sequence of crystal structure types. Finally, the structural rules derived from single crystal observations of binary solids are quite relevant to the stability or fractionation of multicomponent mixtures. The existence of pseudo-components, proposed to explain deposition of paraffins from crude petroleum (Hansen et al., 1988), where a cluster of chains can mimic a pure paraffin, will also be demonstrated, facilitating the conceptualization of these phenomena by binary phase diagrams. Recent studies of paraffin precipitation at the cloud point indicate that, although this temperature is determined mainly by heavier paraffin ingredients in crude petroleum, the actual crystallization of multicomponent combinations can be very complicated, involving the formation of multiple solid phases, as discussed by Coutinho and Ruffier-Méray (1997). These authors cited “azeotrope-type” interactions between paraffin pairs, referring to the pseudocomponent concept.

1.3 1.

Summary

It will be assumed that the molecular principles responsible for the formation of polydisperse solids will continuously refer to the solid state structures (including polymorphic forms) of pure components. Further justification for this assumption will be given in the next chapter. 2. A conceptual model has been proposed by LeRoux to facilitate the understanding of polydisperse chain arrays in waxes. This model includes: (1) a stabilized crystalline region of linear chains; (2) a rigid amorphous region enclosing methyl branches; (3) an isolated interlayer region where solvent or “oil” molecules can be trapped; and (4) a separate fluid phase. 3. Based on binary phase diagrams and powder X-ray diffraction data, Kitaigorodskii proposed rules for the stabilization of binary linear chain solid solutions. These include: (1) a symmetric component, where the average crystal structure symmetry of the binary solution cannot be greater than that of its components; and (2) a volumetric (length) component where the volumetric dissimilarity between molecules cannot be very large. 4. Experimental results can be cited that challenge Kitaigorodskii’s symmetry rules for the stabilization of continuous solid solutions.

2 Layer packing of polymethylene chains

2.1

The methylene subcell and layer packing—theoretical considerations

The polymethylene chain –(CH2)n–, as found in the n-paraffins or their derivatives, commonly packs in sequestered layers, so that the methylene repeat (c0  2.55 Å) will have a crystalline “subcell” of its own. In a survey of the literature, Kitaigorodskii (1961) discussed how the melting points of all aliphatic compounds converge to a single value as the polymethylene chain repeat n becomes large. The efficient packing of this hydrophobic entity is of considerable importance energetically for the layer packing stability of polymethylene chain compounds in the crystalline state. Since the molecules are linear, it is obvious that their most efficient clustering would align their axes parallel to one another to maximize their intermolecular contacts within a two-dimensional layer. It might be possible to determine the close packing of such molecules via a phenomenological Lennard–Jones nonbonded potential energy function:   Arn  Brm (see Pertsin and Kitaigorodsky, 1987), where the reciprocal exponent for the interatomic distance r in the repulsive term is n  12, and in the attractive term it is m  6. (A good overview of methods for modeling intermolecular energy is given by Moelwyn-Hughes, 1965.) Typically, sums are made over all nonchemically bonded interatomic contacts. Empirical values are assumed for A and B, including the interaction of the various atomic species, that have been derived from model compounds so that they match experimental measurements. Sometimes an exponential function is used for the repulsive term (e.g. Williams, 1969). However, for the close packing of organic molecules, the interacting molecules can, to a very good approximation, be modeled by hard repulsive atomic van der Waals surfaces so that their close packing would be dictated by a systematic insertion of protrusions into depressions, to minimize the empty space within the unit cell (Kitaigorodskii, 1961). This so-called “hard sphere potential” relies on the boundaries defined by van der Waals surfaces, defined independently by Pauling and Kitaigorodskii, and reviewed recently by Zefirov (1997). For polymethylene chains, individual atomic van der Waals surfaces (Fig. 2.1) were assumed to be generated by the radii, RC  1.9 Å, and RH  1.35 Å. (The latter hydrogen radius was somewhat higher than the value RH  1.17 Å, normally found in X-ray crystal structures, and was adjusted to force the packing density of lateral interactions to correspond to experimental values. For end-group interactions, the smaller value was

20

LAYER PACKING OF POLYMETHYLENE CHAINS

Fig. 2.1. van der Waals surface of an n-paraffin molecule. 10 Å

Fig. 2.2. Dislocation of adjacent paraffin chains, illustrating how an oblique layer can form from a rectangular layer.

used.) For the close packing of infinite chains, the projected geometry (Fig. 2.2) was consulted for two interacting untilted chains in a rectangular layer, and one was translated with respect to another to minimize the empty space between the two molecules. Second, the possibility of oblique or tilted layers was considered by sliding two parallel chains along c0 so that van der Waals protrusions would seek indentations along the chain (e.g. between the methylene units). Such intermolecular interactions are demonstrated by the example in Fig. 2.3. For projections of untilted layers, two close packing arrangements could be found for chains with parallel carbon–carbon zigzag planes, termed tM and tT, and another was found for chains where these planes were nearly perpendicular to each other,

THE METHYLENE SUBCELL AND LAYER PACKING (a)

21

(b)

Fig. 2.3. Close packing of paraffin molecules:(a) van der Waals surfaces; (b) skeletal representation.

termed tO. In terms of van der Waals surfaces, the type of interactions is illustrated in Fig. 2.4. Corresponding to the efficient packing of general shapes (Kitaigorodskii, 1957a), the first two layers could be generated by two separate translation operations, while the latter would be generated by the interaction of a 21 axis perpendicular to the translational operation t. The two-dimensional layer cell lengths were therefore determined to be: M: a0  4.2 Å b0  4.4 Å ␥0  111 T: a0  4.3 Å b0  4.5 Å ␥0  103 O: a0  4.96 Å b0  7.40 Å ␥0  90 For layers M and O, it is possible to have a close packing arrangement when the methylene groups are on the same level. For the T layer, the methylene repeats of adjacent chains should be translated with respect to one another by c0/2. Theoretical methylene subcells could be generated from these two-dimensional arrays, therefore, if the possibility of oblique layer packing was also considered (Kitaigorodskii, 1957b, 1961). Such tilted chain layers are important when the number of methylene repeats is finite. For these arrays, a general symbol can be given G(m, n) where G  M, T, or O and m and n represent relative translational slips along parallel chains. The quantities m or n can either be integral or half translations of the chain repeat, that is, c0( 2.54 Å) or c0/2, respectively. Resultant chain tilts affect either the a0 or b0 axes, or both. Again the principle of close packing is obeyed, requiring that protrusions fit into hollows.

22

LAYER PACKING OF POLYMETHYLENE CHAINS

a




b

Fig. 2.4. Efficient packing of paraffin chains in a layer with symmetry 21t (see Kitaigorodskii, 1961). Table 2.1 The Kitaigorodskii layers Subcell

Layer

Layer cell dimensions (Å)

H O

H(0, 0) O(0, 0) O(0, 2) O( 1, 0) O( 1, 1) M(0, 0) M( 1, 0) M(0, 1) T( 12, 0) T(21, 1) T(12, 1)

a  4.8 a  4.96, b  7.42, ␥  90 a  4.96, b  9.0, ␥  90 a  5.57, b  7.42, ␥  90 a  5.57, b  7.85, ␥  81.5, 98.5 a  4.2, b  4.4, ␥  111 a  4.9, b  4.4, ␥  107 a  4.2, b  5.1, ␥  107 a  4.3, b  4.5, ␥  103 a  4.3, b  5.2, ␥  109

M

T

Possible chain packing arrays derived from theoretical constructions are as follows: T Subcell Layers. An easily achieved layer packing occurs when the chains along 1 the a0 direction are shifted by c0/2 to produce the two options: T[ 2 , 0]. Predicted subcell dimensions from these constructs are given in Table 2.1. The observed unit cell dimensions for the [0 0 1] projection are also given. Two other possibilities: T[ 12 , 1]are also considered. The basic subcell dimensions are: a  4.3, b  4.5, c  2.54 Å, ␣  90, ␤  107, ␥  103.

OBSERVED METHYLENE SUBCELLS

23

M Subcell Layers. A number of options are available. In addition to the rectangular layer M[0, 0], the oblique arrays: M[1, 0], M[1 , 0], M[0, 1], and M[0, 1 ] can also be formed. Representative dimensions of subcell and layer unit cell are given in Table 2.1. The subcell dimensions are: a  4.2, b  4.4, c  2.54 Å, ␥  111. O Subcell Layers. In addition to the rectangular layer already discussed, that is, O[0, 0], a number of oblique layers can also be formed. These include the following possibilities: O[0, 2], O[ 1, 0], O[0, 1], and O[ 1, 1]. Cell dimensions are listed in Table 2.1. The subcell dimensions are: a  4.96, b  7.40, c  2.54 Å.

2.2

Observed methylene subcells

When the theoretical polymethylene chain layers and subcells were originally formulated, only a few quantitative crystal structures of molecules containing polymethylene chains had been determined, against which the predictions could be compared. The methylene subcell is an important concept in the crystallography of such materials; a number have been observed, including the three generated by Kitaigorodskii (1961). In fact, two, T and O, are observed quite frequently. Later, Segerman (1965) was able to predict other subcells, in addition to the ones formulated by Kitaigorodskii. Within 17 years of the 1961 English translation of Kitaigorodskii’s monograph, a comprehensive review of these subcells was published, based on numerous lipid crystal structures (Abrahamsson et al., 1978). These are reviewed below. O⊥ subcell. This methylene chain packing, shown in Fig. 2.5, is equivalent to Kitaigorodskii’s O subcell, with representative experimental dimensions: as  4.970, bs  7.478, and cs  2.549 Å, with a cross-sectional area 18.58 Å2, for each chain. This subcell contains four –CH2– groups related by symmetry Pbnm. Both the rectangular layer and a number of oblique layers (e.g. O[0, 2] and O[ 1, 0]) have been observed for n-alkanes and their simple derivatives. Fractional coordinates for the unique methylene unit are:

C(1) H(1) H(2)

x/a

y/b

z/c

0.065 0.049 0.273

0.038 0.179 0.010

0.25 0.25 0.25

(Note that the accepted assignment of axes for this subcell can differ. For example, when applied to polyethylene, the above as- and bs-axes are transposed to give space group Pnam.) O⊥ ’ subcell. For the frequently observed O⊥ subcell, all chains have a common orientation when projected down the 5 Å axis. In a variant form (Fig. 2.5), chains are related by a mirror in this projection. Experimental cell constants are: as  7.43,

24

LAYER PACKING OF POLYMETHYLENE CHAINS

1 4

3 4

1 4

3 4

b9s

1 4

1 4

3 4

3 4

bs

1 4

1 4

3 4

1 4

a9s 3 4

as 1 4

T||

3 4 1 4

1 4 3 4

3 4

1 4

1 4

1 4

3 4

bs 3 4 1 4

as

3 4

1 4

1 4

as

3 4

3 4

O⊥

3 4

1 4

bs

1 4 3 4

3 4

M||

3 4

O9⊥ 1 2

1 2

bs

1 2 1 2

1 2

bs 1 2

1 2

as O||

1 2

as O9||

Fig. 2.5. Commonly observed methylene subcells.

OBSERVED METHYLENE SUBCELLS

25

bs  5.01, cs  2.54 Å, again in space group Pbnm. The cross-sectional area of an individual chain is therefore 18.61 Å2. Fractional atomic coordinates are: x/a C(1) H(1) H(2)

0.029 0.025 0.163

y/b

z/c

0.071 0.254 0.086

0.25 0.25 0.25

T subcell. This subcell (Fig. 2.5), where all chain axes are parallel, identical to Kitaigorodskii’s T, has typical cell dimensions: as  4.285, bs  5.414, cs  2.539 Å, ␣s  80.99, ␤s  112.2, ␥s  121.78, with some variation allowed. The crosssectional area per chain is 18.23 Å2. Two methylene groups are contained in the unit cell. Fractional atomic coordinates for each group in space group P1 are: x/a C(1) H(1) H(2)

0.062 0.353 0.056

y/b

z/c

0.089 0.216 0.216

0.25 0.25 0.25

(These coordinates are defined with respect to axes as*, bs*, perpendicular to cs.) Segermann (1965) has postulated that this triclinic subcell is actually a monoclinic packing, deformed by shearing, since there is so much experimental variation of cell constants. Using a monoclinic transformation of the data given by Vand and Bell (1951) for the triclinic subcell, he proposed a B2/m cell with dimensions: as  8.156, bs  5.121, cs  2.45 Å, ␤s  112.1. The carbon atom coordinate for the asymmetric unit was transformed from (0.0395, 0.6021, 0.1991) in the triclinic cell (Vand and Bell, 1951) to (0.2813, 0.1021, 0.000) in the monoclinic cell. M subcell. The M subcell formulated by Kitaigorodskii (1961) (Fig. 2.5) has been observed experimentally but not so frequently as O⊥ or T . Typical cell dimensions for the parallel chain packing are: as  4.30, bs  4.74, cs  2.54 Å, ␥s  110.9, that is, a chain cross-section of 19.04 Å2. Fractional atomic coordinates in space group P21/m (c- axis unique) are: x/a C(1) H(1) H(2)

0.000 0.203 0.203

y/b

z/c

0.087 0.275 0.144

0.25 0.25 0.25

In addition to these, there are a number of other methylene chain packing forms: O subcell. This orthorhombic parallel chain packing (Fig. 2.5) crystallizes in space group B2212, with cell constants: as  8.150, bs  9.224, cs  2.551 Å. The

26

LAYER PACKING OF POLYMETHYLENE CHAINS

cross-sectional area per chain is 18.77 Å2. Although it has been observed, fractional coordinates are based on calculation, not experimental measurement:

C(1) H(1) H(2)

x/a

y/b

z/c

0.185 0.085 0.285

0.295 0.358 0.358

0.000 0.000 0.000

Originally, this subcell had been defined in space group P21212 with two unique methylene groups in the unit cell (carbon positions: 0.315, 0.205, 0.000; 0.315, 0.295, 0.500). Primitive cell constants were taken to be: a  8.15, b  9.21, c  2.55 Å (Sydow, 1958). O
 subcell. Another orthorhombic parallel chain packing (Fig. 2.5) crystallizes in space group Pma2. Cell constants are: as  7.93, bs  4.74, cs  2.53 Å, with a chain cross-section: 18.79 Å2. Fractional atomic coordinates are:

C(1) H(1) H(2)

x/a

y/b

z/c

0.250 0.147 0.353

0.015 0.138 0.138

0.500 0.500 0.500

This was originally defined in space group P2122 with a second unique methylene carbon at (0.25, 0.170, 0.00) (Abrahamsson and Ryderstedt-Nahringbauer, 1962). Hexagonal subcell. A rotationally distorted chain packing can occur in many polymethylene chain compounds and is often called the “rotator” or ␣-phase. Kitaigorodskii (1961) termed it H[0, 0] (Fig. 2.6) and calculated a trigonal cell constant: as  4.80 Å. Although the designation presumed rectangular chain layers

Fig. 2.6. Average representation of the hexagonal methylene subcell.

OBSERVED METHYLENE SUBCELLS

27

Fig. 2.7. Hybrid HS1 methylene subcell.

it can also occur in some oblique layers. Larsson (1967) prepared samples of n-nonadecane with this subcell. The unit cell constants in a centered orthorhombic layer were: as  4.79, bs  8.30 Å, true hexagonal symmetry was found in each layer of the crystal structure. Chain rotation is only a phenomenological description of the average disorder based on the symmetry of the diffraction patterns. Postulates of the true, non-disordered, chain packing will be given in a later chapter. Hybrid subcells and nonparallel chain packing. In addition, two hybrid subcells have been identified. One that is relevant to chain packing in phospholipids and cholesteryl esters has been termed HS1 and has the unusual feature of individual chains with both perpendicular and parallel packing to their nearest neighbors. As determined earlier by electron diffraction measurements (Dorset, 1976a) (Fig. 2.7), the cell constants of HS1, shown in Fig. (c), are: as  7.76, bs  10.03, cs  2.54 Å. In projection, the plane group symmetry is pgg. Another hybrid, the HS2 subcell, has been described (Abrahamsson et al., 1978). So far we have considered only the possibility of parallel chain axes in a layer. Segermann (1965) also found that molecular axes in neighboring sheets of parallel chains could be crossed with respect to each other, and, accordingly, derived 12 subcells for this chain packing that, for example, had been identified experimentally for tetradecanamide (Turner and Lingafelter, 1955) and potassium caprate (Vand et al., 1949). Information about subcell packing can also be determined from powder X-ray patterns (see Fig. 1.6). A powder diffraction pattern from polymethylene chain materials contains two regions where information about the layer packing can be determined. As stated in Chapter 1, the low-angle “lamellar” reflections determine the lamellar thickness. At high diffraction angle, strong reflections due to the methylene subcell are observed. Larsson (1966) has listed the dhkl values for strong reflections in this region, used as a “fingerprint” to identify the subcell type.

28

LAYER PACKING OF POLYMETHYLENE CHAINS

Hexagonal (H): Triclinic parallel (T ) Orthorhombic perpendicular (O⊥ ) (O⊥
) Monoclinic parallel (M ) Orthorhombic parallel (O) (O
)

4.15 Å 4.6, 3.8 Å 4.20, 3.80 Å 4.27, 3.97, 3.71 Å 4.57, 4.35, 3.85 Å 4.61, 4.12, 3.75 Å 4.71, 4.05, 3.78 Å

In the low-angle region, a so-called “long spacing” or “lamellar spacing,” is measured. (For an orthorhombic unit cell, this would represent the actual c-axis length, this axis, by convention, assigned to the longest unit cell dimensions for long chain molecular and polymer crystals. For monoclinic or triclinic unit cells, the distance will correspond to d001.) For a homologous series of polymethylene compounds crystallizing with the same layer packing, that is, an all-even or all-odd chain-length series differing by –(CH2)2– increments, a plot of lamellar spacing versus number of chain carbons will determine the tilt of the chain axes to the lamellar end surface. The plot finds the length difference per increment of the tilted chain subcell along cs (Chapman, 1965). From this observation, the chain tilt angle, ␦, is calculated: sin ␦ 

increment of [CH2]2 2.55 Å

Inspection of the intensity distribution of low-angle reflections provides other clues about the type of layer packing. For example, if the overall intensity falloff of the lamellar reflections is approximately Gaussian, with the strongest intensity at the (001) reflection, all layers are equivalent in this direction, even if the unit cell comprises a bilayer. If the intensities alternate between strong and weak, with the weak reflections occurring at even orders (e.g. (002), . . .), then the bilayer contains alternate layers, for example, related by a mirror symmetry element perpendicular to the layer stacking direction. (Examples are the fatty acids, to be shown later.) Substitution of a polymethylene chain by a ketone or ester linkage can also affect the intensity distribution for the (00l) reflections (Kreger, 1951; Chapman, 1965). Subcell identification can also be made with single crystal electron diffraction patterns. A gallery of representative patterns is shown in Fig. 2.8. Such patterns are obtained when the crystalline sample is oriented with the linear chain axes parallel to the electron beam. (Visualization of “pure” subcell patterns in a fortunate accident of diffraction of coherent electron radiation from elastically bent crystalline layers when projecting down a long unit cell axis (see Dorset, 1983, 1995a).) If the chain tilt of the unknown structure cannot be determined approximately from the spacing of reflection rows in transmission patterns from untilted layers another technique, known as reflection high-energy electron diffraction (RHEED) is useful. This surface grazing incidence diffraction technique finds the diffraction from outer chain methylene repeats from a thin film on a polished metal stub (Fig. 2.9). The spacing

OBSERVED METHYLENE SUBCELLS (a)

(b)

(d)

29

(c)

(e)

Fig. 2.8. Characteristic electron diffraction patterns from methylene subcells in a projection down the chain axes. (a) H; (b) O⊥ ; (c) T ; (d) M ; (e) HS1.

Fig. 2.9. RHEED pattern from a rectangular paraffin layer.

between the second and fourth orders can be compared to the spacing of an untilted methylene chain repeat (2.55 Å) to obtain this average tilt value (Karle and Brockway, 1947). Returning to transmission electron diffraction allows setting the goniometer tilt angle for an in-plane rotational search for patterns from a projection down the chain axes (Fig. 2.8).

30

2.3

LAYER PACKING OF POLYMETHYLENE CHAINS

Layer Stacking

Stacking of finite polymethylene chain layers to form a three-dimensional crystal can also be predicted from the repulsive “hard-sphere” van der Waals model, where protrusions from terminal groups in a new layer are to fit into the surface intermolecular depressions left in the already-formed underlayer. Since the relative number of intermolecular contacts across individual layers is far less than the numerous lateral contacts within a single layer, it can be readily understood that this stacking of chain lamellae contributes only a minor part of the total internal crystalline energy. It also explains why crystals of polymethylene compounds are often thin laths or lozenges. The relationship between the methylene subcell packing and the layer stacking of chains is illustrated in Fig. 2.10. Specific experimental examples of the theoretical predictions below are given in Chapter 3. Odd-chain n-paraffins have mm symmetry, including a mirror symmetry element through the center of the molecule, normal to its axis. O[0, 0] rectangular layers are anticipated because one of the mirrors is expected to be retained in the threedimensional crystal (Kitaigorodskii, 1961). In his analysis of indentations on the methyl plane surface for a single rectangular layer, Kitaigorodskii (1961) found two likely nucleation sites for the next chain layer. If the layers individually have mirror symmetry, there is no such thing as right- and left-handed layers, so they are identical. (a)

O

b

O bs

cs

c

a as

(b)

cs

c

Fig. 2.10. (a) Relation between a methylene subcell and layer stacking for a hypothetical orthorhombic paraffin (Dorset, D. L. (1980) Electron diffraction intensities from bent molecular organic crystals. Acta Crystall A36, 592–600); (b) fit of van der Waals surfaces for chains interacting across a lamellar boundary.

LAYER STACKING

31

The only variables, therefore, are the distances between the layers, determined by the methyl–methyl contacts of apposing layers, and the displacement of adjacent layers with respect to their surfaces. In this model study, the van der Waals radii RC  1.9 Å and RH  1.2 Å were assumed. Nucleated by one set of intermolecular depressions on the underlayer, a new layer will grow so that a ⬇ 5.0, b ⬇ 7.4, c  6.3 2.54 (n  1) Å with four molecules in the unit cell. The resultant space group would be Pbcm. The second predicted layer sequence produces very similar unit cell dimensions in space group Pnam, again with four molecules in the unit cell. Even-chain paraffins have 2/m ⬅ 1 molecular symmetry. The unit cell should retain a center of symmetry only, permitting the formation of either rectangular or oblique layers, even if the subcell is O⊥. Using arguments similar to those for the odd-chain paraffins, an orthorhombic unit cell would be formed from stacking rectangular layers, with cell constants: a 艑 5.0, b 艑 7.4, c  6.6 2.54 (n  1) Å, anticipating space group Pbca. Monoclinic crystal structures of the even-chain alkanes, retaining the 21-axis of a single layer can be built-up by stacking O[0, 2] or O[1, 0] layers. Again, similar considerations of fitting chain-end protrusions from one layer into depressions on the surface of the underlayer are taken into account. The actual monoclinic form of n-paraffins (see below) involves the O[1, 0] sequence has predicted cell constants: a 艑 5.6, b 艑 7.4, d001  1.13 (n  1) 2.4 Å, where the 21 axis is parallel to the b unit cell edge. The ␤-angle in space group P21/c is near 117. Since the unit cell volume is slightly less than that of the orthorhombic form, it is understandable that this should also be the lowest energy polymorph. The sequence of O[0, 2] layers is found for other polymethylene chain derivatives, for example, fatty acids. One of the consequences of the stacking of oblique O[1, 0] layers is a form of disorder called polytypism. (This is distinguished from polymorphism, which characterizes the chain packing within a layer. Polytypism describes the stacking of layers.) When this occurs, the tilt of adjacent chain layers can be mirrored with respect to each other to form an average structure actually with an orthorhombic unit cell, even though the constituent layers are still oblique. The reason for polytypism is the relatively small energetic contribution of end-plane interactions in the growth of crystals, so that the nucleation of adjacent layers with the same tilt or with mirrored tilt values would have comparable energies. Energy calculations of Boistelle and Aquilano (1977) predicted the nucleation of such polytypes. Of the other two subcells derived by Kitaigorodskii (1961) only the T packing is relevant to the n-alkanes. A polymorph based on this subcell is found for the shorter even-chain compounds (see below) because the triclinic structure in space group P1 will retain the molecular center of symmetry. After a rather complicated analysis, Kitaigorodskii (1961) concluded that T[12 , 0]was the preferred layer stacking for forming the crystal structure. Attempts to predict the packing of n-alkane chains ab initio with atom–atom potential functions has been less than successful when only static molecules were considered (Van de Streek et al., 2002). It was required that thermal motion should be included into a molecular dynamics calculation to produce an accurate model for

32

LAYER PACKING OF POLYMETHYLENE CHAINS

the triclinic chain packing of even-chain n-paraffins. However, the triclinic unit cell is predicted as the most stable one for all chain lengths through polyethylene. In other words, structures were more successfully predicted with the original hard sphere potentials than by more sophisticated potential function formulations. Predictions of layer packing motifs have been made for other organic materials (Scaringe, 1991), as well as a specific model for the H-subcell (Scaringe, 1992) to be shown in Chapter 4. Finally, if a polymethylene chain is derivativized by some sort of “functional group,” it is often found that simple methylene subcells and layer packings are conserved, even if more than one polymethylene chain is attached to the other group. As shown in a review of phospholipid crystal structures (Pascher et al., 1992), the most important consideration for lamellar packing is the relative cross-sectional areas occupied by the substituent groups. (For amphipathic materials, this pendant group is often sequestered to a separate thin layer in the unit cell.) Chain packing will compensate for this “head-group” cross-section, matching it as close as possible by allowed chain axis tilt, or even interdigitation of apposing (tilted or untilted) chain axes in a layer, if the head-group cross-section is rather large. Only rarely will the methylene subcell be an unusual one. Some variation is allowed for the lateral subcell axial dimensions and, with the other mechanisms (chain tilt and interdigitation) for matching the substituent group cross-sectional area, the common subcells will satisfy geometric demands.

2.4 1.

2.

3.

4.

Summary Using a hard sphere potential to simulate the van der Waals packing, Kitaigorodskii accurately predicted the most commonly encountered methylene “subcells” in crystalline polymethylene chain layers. While there are several more subcell packing arrays observed in the crystal structures of materials containing polymethylene chains, these occur much less frequently than the three derived theoretically. In addition to the lateral packing of methylene groups within a layer, chain tilt is also important. For a given methylene subcell only certain chain tilts are permitted. These have been enumerated by Kitaigorodskii. Layer packing of chains is partially dependent upon the relative importance of “end-group packing” effects, compared energetically to the methylene subcell packing. Molecular point-group symmetry elements, such as centers of symmetry and mirror planes, can be preserved in the crystal structures, that is, included as elements of the space group symmetry. Polymorphism includes the differences of methylene chain packing as well as the layer tilt, while polytypism considers only different possible stacking sequences of chain layers.

3 Crystal structures and phase transitions of the paraffins

3.1

Introduction

The layer packing and methylene subcells of polymethylene chains were introduced in the previous chapter. In this chapter, the known crystal structures of the n-paraffins will be discussed in some detail. The structural basis for polymorphism associated with thermotropic transitions is also given. Crystal growth is thus justified from preferred assembly of chains in oblique and rectangular layers at various temperatures and for various chain lengths. The thermodynamically stable crystal structures of n-paraffins, n-CmH2m 2, can be reviewed as follows (Asbach and Kilian, 1970): For the odd-chain paraffins in the range 11  m  43, the chains pack in an orthorhombic unit cell. Following principles of organic chemical crystallography (Kitaigorodskii, 1961), the perpendicular mirror plane in the molecular point group is utilized by the space group symmetry. Even-chain paraffins where m  24 are preferentially triclinic. Those in the range 26  m  38 are monoclinic in the lowest energy crystal form, while those with m 40 are orthorhombic. The triclinic and monoclinic structures preserve the molecular center of inversion (Kitaigorodskii, 1961). Depending on purity or crystallization conditions, an orthorhombic form can also be expressed by the 26  m  38 even-chain series. The interconversion of crystal polymorphs can be understood (Mnyukh, 1963) by comparing packing energies of chain stems (nC • ) to those of the chain ends (): U  nC •  . The chain cross-sectional areas for the various subcells are 18.56. Å2 (O⊥), 18.73 Å2 (T ), and 19.70 Å2 (H) so that  (O⊥)   (T ). However, the chain-end packing energies lie in the sequence (T)  (Mo)  (O), where Mo is a monoclinic structure utilizing the O⊥ subcell. The advantage of the triclinic end plane packing over that of the monoclinic is diminished, per even-chain carbon atom, according to: ne  (M0  T)/(T  0) , so that U(T) 艑 U(MO) in the region 24  nC  26. Using a similar relationship, the triclinic to orthorhombic transition occurs at chain lengths greater than 26 carbons. Typical numerical values (Mnyukh, 1963) are: T  2.98 kcal mol1; o  1.03 kcal mol1; T  1.77 kcal mol1; o  1.84 kcal mol1. By inserting a vacancy, an impurity will disrupt the efficient triclinic end plane packing, and the layer will revert to a rectangular packing.

34

CRYSTAL STRUCTURES AND PHASE TRANSITIONS

To introduce the influence of temperature changes, the odd-chain paraffins are stated by Asbach and Kilian (1970) to transform from an orthorhombic structure into the so-called hexagonal “rotator” phase. This is somewhat of an over-simplification. Four stable forms of n-C33H68 have been described (Piesczek et al., 1974; Ewen et al., 1980). The lower temperature orthorhombic structure is stated to transform to two higher-energy monoclinic polymorphs before the rotator phase is formed. Similar intermediate forms have been observed calorimetrically by Takamizawa et al. (1982). Asbach and Kilian (1970) partitioned the even-chain alkanes that form a lowtemperature monoclinic polymorph into two classes. In one chain-length range, 26  m  32, a direct transition from the monoclinic crystal to the rotator phase occurs, as also observed by Takamizawa et al. (1982). Unit cell dimensions have been given for the sequence of polymorphs (Asano and Abe, 1984; Asano et al., 1996). Also consistent with the observations of Sullivan (1974), n-paraffins in the range 34  m  38 encounter an intermediate orthorhombic structure before the rotator phase is reached. Some alteration of this scheme might be necessary for highly purified materials, since, for example, a higher-temperature monoclinic form is claimed for n-C36H74 (Takamizawa et al., 1982). In this and following sections, the known crystal structures of the n-paraffins will be discussed in some detail, referring also to the preferred space groups predicted by Kitaigorodskii (1961).

3.2

Crystal structures of lower chain n-paraffins

In this and following sections, the known crystal structures of the n-paraffins will be compared to the preferred space groups predicted by Kitaigorodskii (1961). It is, first of all, interesting to determine if the chain packing features found for longer paraffins are preserved when lower chain length n-alkanes are crystallized from the liquid state. The even-chain n-alkanes are easiest to describe systematically even though crystal structures of lowest carbon number chains are not representative of the longerchain structures. For ethane, there may be as many as three polymorphs for this hydrocarbon (Braam and Vos, 1980). The structures are of little use for the general understanding of long chain packing; n-butane also packs with nonparallel chains (Fig. 3.1) in space group P21/c (Boese et al., 1999). Neutron diffraction studies also indicate polymorphic behavior (Refson and Pawley, 1986), where only the lowest temperature form packing with nearly parallel chains. Metastable and plastic crystal forms pack with chain axes crossed by nearly 90. Regular chain packing in even-chains begins with n-hexane (Fig. 3.2(a)) and continues via n-octane (Fig. 3.2(b)) (Norman and Mathiesen, 1961a,b; Boese et al., 1999) and n-decane (Fig. 3.2(c)) (Bond and Davies, 2002), through n-C24H50 (see next section) to form a homologous structural series. The space group is P1 with one molecule in the unit cell. Chain axes lie parallel to one another. Earlier, from powder X-ray data, Norman and Mathiesen (1972) had established that the lower even-chain

CRYSTAL STRUCTURES OF LOWER CHAIN n -PARAFFINS

35

(b) (a)

(c)

Fig. 3.1. Crystal structure of n-butane.

(a)

(b)

(c)

Fig. 3.2. Regular packing of short even-chain n-paraffins. (a) n-hexane; (b) n-octane; (c) n-decane.

36

CRYSTAL STRUCTURES AND PHASE TRANSITIONS

Fig. 3.3. Crystal structure of propane. (a)

(b)

Fig. 3.4. Crystal packing of n-pentane.

n-paraffins through n-hexadecane are isostructural, in accord with current quantitative single crystal results. The odd-chain n-paraffins exhibit less regular packing behavior for shortest chain lengths. This can be illustrated quite simply by a two-dimensional analysis of packing efficiency utilizing a polygonal outline of the molecular shape and then considering the efficient arrangements of these shapes into a closely tiled motif. The crystal structure of propane (Boese et al., 1999) in Fig. 3.3 is highly unusual, crystallizing in space group P21/n where a  4.15, b  12.61, c  6.98 Å, ␤  91.28. Comparing the intermolecular gaps in the propane layer packing to those in ethane or n-butane (Thalladi and Boese, 2000), explains why this n-alkane has the lowest melting point of all n-alkanes, that is, due to an inherently lower packing coefficient. The molecular outline is pentagonal. As is well-known, there are no efficient crystallographic tiling motifs for five-sided polygons that retain the underlying point group symmetry.

TRICLINIC CRYSTAL STRUCTURE

37

(a)

(b)

Fig. 3.5. Parallel chain packing of odd-chain n-paraffins: (a) n-heptane; (b) n-nonane.

The crystal structure of n-pentane (Norman and Mathiesen, 1964; Boese et al., 1999) is orthorhombic, Pbcn, where a  4.13, b  9.02, c  14.82 Å. Again (Fig. 3.4) the chains do not pack in a parallel arrangement. True parallel chain packing in odd-chain paraffins begins with n-heptane, which, with n-nonane, has a triclinic structure (Boese et al., 1999), space group P1 , with two molecules in the unit cell (Fig. 3.5). The orthorhombic structure predicted by Kitaigorodskii (1961) begins with n-C11H24 (Norman and Mathiesen, 1972).

3.3

Triclinic crystal structure of longer even-chain n-paraffins n-CmH2m 2, m  24

Two crystal structures have been determined for even n-paraffins in the triclinic space group P1 . The molecular packing of n-octadecane, n-C18H38, (Fig. 3.6) was re-determined (Nyburg and Lüth, 1972) from previously reported data (Hayashida, 1962). Cell constants of this crystalline form had been reported earlier (Müller and Lonsdale, 1948). In the most recent determination, they are: a  4.285, b  4.820, c  24.898 Å, ␣  85.15, ␤  67.8, ␥  72.70. The homologous structure of n-eicosane, n-C20H42 (Nyburg and Gerson, 1992), with cell constants: a  4.293, b  4.84, c  27.35 Å, ␣  85.3, ␤  68.2, ␥  72.6, is very similar in appearance except that, in the second structure, the molecule is rotated 180 around its long axis to preserve a favorable end-plane packing. The series of triclinic structures continues up to n-C24H50, a chain length limit where other polymorphs are metastable (see below). Gerson and Nyburg (1994) reported twinned crystals for n-tetracosane, despite numerous attempts to grow the untwinned form. Nevertheless, the crystal structure was solved and shown to be the expected triclinic chain

38

CRYSTAL STRUCTURES AND PHASE TRANSITIONS

Fig. 3.6. Crystal structure of n-octadecane.

packing that is isostructural with the shorter homologs. (This chain packing is equivalent to the so-called “Tp” structure cited by Metivaud et al., 1998 and Rajabalee et al., 1999a,b.) The relationship between these longer triclinic structures and the ones determined earlier by Norman and Mathiesen has also been established (Nyburg and Potworowski, 1973). Using an orthonormal axis system (x along the unit cell a-axis, z along the c*-axis), the coordinates of the chain directions in the cell could be established so that the vector from the midpoint of the C(1)–C(2) bond to the (0, 0, 1⁄2) point of the unit cell could be defined. An analogy was found for a homologous series of n-paraffins with this structure, where the proportionality of chain lengths could be used to scale cell dimensions. In all comparisons to other chain lengths, relatively stable values: a  4.285, b  4.820 Å, ␥  72.0 were observed (also true for the triclinic structures of Boese et al., 1999) so that the values of c and the other two unit cell angles were the principle variables. A transformation matrix between the unit cell axes of the two longer structures and the shorter n-alkanes was found, after which it was shown that the crystal structure of, for example, n-C6H14 could be predicted quite accurately from that of n-C18H38 (Nyburg and Potworowski, 1973), and, later, the cell constants of the complete triclinic series from n-C10H22 to n-C16H34 (Nyburg et al., 1976). Lamellar spacings could be predicted (Broadhurst, 1962) by the equation d(001)  1.219m 1.28 Å. Alternatively, Nyburg and Potworowski (1973) found: d(001) 1.200m 1.44 Å. In the crystal structure of n-octadecane, Abrahamsson et al. (1978) found the most perfect expression of the T methylene subcell, also predicted by Kitaigorodskii (1961) (see Chapter 2). In their discussion of the triclinic paraffin structures, on the other hand, Nyburg and Gerson (1992) refer to the B2/m monoclinic subcell structure proposed by Segermann (1965). An orthorhombic form proposed by Vainshtein et al. (1958) for n-C18H38 must have utilized data from an impure sample, so that a solid solution structure was characterized instead (see Chapter 5). It is also possible to account for the crystal habit by a periodic bond chain model, accounting for the most favorable attachment energies between molecules within the unit cell (Hartman, 1963). Using such an approach for the triclinic form of evenparaffins, Clydesdale and Roberts (1991), as well as Liu and Bennema (1994), were able to predict the major crystal faces quite accurately.

MONOCLINIC CRYSTAL STRUCTURE

(a)

39

(b)

Fig. 3.7. Oblique layer chain packing of even-chain n-paraffins: (a) monoclinic n-hexatriacontane; (b) polytypic n-octacosane.

3.4

Monoclinic crystal structure of the even-chain n-paraffins

The parent X-ray structure for this polymorphic form is that of n-hexatriacontane, n-C36H74 (Shearer and Vand, 1956). The cell constants in space group P21/a are: a  5.57, b  7.42, c  48.35 Å, ␤  119.1, with two molecules in the unit cell. The methylene subcell is O⊥ with as  4.945, bs  7.42, cs  2.546 Å. Hence, the layer packing (Fig. 3.7(a)) is just the O[1, 0] structure predicted by Kitaigorodskii (1961) (see Chapter 2). The chains are inclined to the normal to the basal plane around the bs subcell axis by 27. The crystals of this form are flat lozenges with the largest face being (001). The acute angle between the boundary {110} faces is about 75. This polymorphic form had also been described previously by Schoon (1939) for n-C30H62. Reflection high-energy electron diffraction measurements (Thiessen and Schoon, 1937; Schoon, 1938) of large well-formed crystals revealed the direction of chain tilt within the lozenge habit (i.e. the long diagonal axis is the axis of chain tilt). (Three other minor oblique forms of n-C36H74, corresponding to Kitaigorodskii layers have been reviewed recently by Kubota et al., 2004.) A systematic view of the polymorph packing was presented by Nyburg and Potworowski (1973). Using an analysis similar to that for the triclinic polymorph, these authors were able to predict the c-spacings and ␤-angles for monoclinic homologs from n-C26H54 to n-C38H78, to tabulate the d(001) lamellar spacings. Starting with d(001)  42.25 Å for n-C36H74, the other values for homologs in the series can be obtained by adding or subtracting 2.26(m/2) (Å). With a

40

CRYSTAL STRUCTURES AND PHASE TRANSITIONS

periodic-bond-chain model to predict crystal growth, the crystal habit of the monoclinic crystal can be explained (Liu and Bennema, 1993). An ordered polytypic expression of this polymorph was described by Boistelle et al. (1976). Orthorhombic cell constants for n-C36H74 in space group Pbca were measured to be a  7.42, b  5.59, c  84.5 Å, Z  4. The crystals of this paraffin were not sufficiently good for data collection so those from the shorter chain homolog, n-C28H58, (c  66.50 Å) were used instead. Comparing the unit cell short axis spacings to those of the orthorhombic perpendicular subcell axes, the layer structure must be Kitaigorodskii’s O[1, 0] layer as was indeed verified by the quantitative crystal structure analysis (Fig. 3.7(b)). The energetic possibilities for the occurrence of such polytypes or non-180 rotational twins across the (001) planes were considered by Boistelle and Aquilano (1977) and compared to experimental observations of crystal growth.

3.5

Orthorhombic crystal structure of the even-chain n-paraffins

The X-ray crystal of n-C36H74 in its orthorhombic form was determined by Teare (1959). Cell constants were found to be: a  7.42, b  4.96, c  95.14 Å, with four molecules in the unit cell (i.e. two layers). Lozenges grown from petroleum ether solution were found to express the (001) face while the boundary {110} faces intersect at a 67.5 acute angle (Dawson and Vand, 1951; Anderson and Dawson, 1953). From systematic absences in the diffraction pattern, two possible space groups could be chosen: Pca21 or Pcam. The former was preferred because it led to a simple chain packing arrangement. (Kitaigorodskii (1961) had proposed space group Pbca for this polymorph.) The crystal structure is represented in Fig. 3.8. A systematic analysis of the even-chain orthorhombic structures (Nyburg (a)

(b)

Fig. 3.8. Crystal structure of orthorhombic n-hexatriacontane.

ORTHORHOMBIC CRYSTAL STRUCTURE OF THE EVEN-CHAIN

41

(b)

a

(a)

b

(020)

(200)

(110)

+10

Sin x

I110 ≈ I200 > I020 > I210 (110) (200) (210)

(020)

0

−10 0

1.0

2.0

3.0

4.0

−1 d *(nm )

Fig. 3.9. (a) Single layer of orthorhombic n-hexatriacontane, bright-field electron micrograph revealing bend contours. The lateral crystal dimension is approximately 10 m; (b) highresolution lattice image of n-hexatriacontane layer revealing chain positions. (Zemlin, F., Reuber, E., Beckmann, E., Zeitler, E., and Dorset, D. L. (1985) Molecular resolution electron micrographs of monolamellar paraffin crystals. Science 229, 461–462.)

and Potworowski, 1973) predicts a layer packing d(002)  1.27 m 1.84 Å. (The actual cell length is twice this distance since there are two lamellar layers in the unit cell.) This polymorph is equivalent to the so-called “Op” structure cited by Rajabalee et al. (1999b). The layer habit of this polymorph can be readily observed from low magnification electron micrographs of monolayer crystals (Fig. 3.9(a)). Multilamellar crystals in this orientation mainly produce electron diffraction patterns expressing single layer contributions (Dorset, 1976b), due to diffraction incoherence induced by elastic crystal bending (Dorset, 1980; Moss and Dorset, 1983). This intensity distribution, apparently originating from a single layer, was originally observed by Garrido and Hengstenberg (1932). The rectangular layer packing was described qualitatively by reflection and transmission electron diffraction (Thiessen and Schoon, 1937; Brummage, 1946). In addition to the most recent electron diffraction determination

42

CRYSTAL STRUCTURES AND PHASE TRANSITIONS

of the chain layer packing (Dorset, 1976b), previous descriptions of the orthorhombic layers based on electron data had been given by Cowley et al. (1951) and Vainshtein et al. (1958). High-resolution electron micrographs have been recorded by Zemlin et al. (1985) that depict directly the chain packing in a rectangular layer (Fig. 3.9(b)). For electron diffraction studies of solution-crystallized samples, only the methylene subcell packing can be observed, since the chains are more or less perpendicular to the layer plane. Fortunately, epitaxial orientation techniques, such as those developed by Wittmann and Lotz (1990), nucleate the chain axes in an orientation parallel, rather than perpendicular, to the underlying substrate, so that the projection onto the chains is available for data collection. Such oriented growth exploits the eutectic phase diagram between the polymethylene chain compound and the diluent, the former being a minor ingredient. The diluent crystallizes first and preferred orientation of the linear molecule is achieved by lattice matching at the crystal interface. A variety of diluents are available (Wittmann and Lotz, 1990). For example, a preferred orientation of paraffin on ␤-naphthol had been noted in passing by Zocher and Machado (1959). If the co-crystallization is carried out from a cooled co-melt of the two materials, the diluent can often be removed later by sublimation in high vacuum (e.g. if the nucleating surface is the naphthalene (001) crystal face), or by flotation on a water surface (e.g. if the nucleating surface is the benzoic acid (001) crystal face). The molecular interaction has been discussed in terms of a binary eutectic phase diagram (Dorset et al., 1989). Deposition onto a nucleating layer is also possible from the vapor phase where the linear chain molecule is deposited onto a substrate (e.g. potassium hydrogen phthalate) that is subsequently removed by flotation on water. Inorganic salt substrates (e.g. KCl, KBr) can also be employed (Ueda, 1986, 1987) but they must first be cleaned by outgassing the freshly cleaved crystal face by heating in the vacuum chamber before deposition of the linear chain. The inorganic substrates are quite good for nucleating fluorocarbons but, because of their high symmetry, at least two equivalent orientations of the linear chains occur in the overlayer. Lower symmetry organic substrates promote anisotropic growth of overlayers, extending in one orientation for several micrometers. Interestingly, the crystal surfaces of n-paraffins, etc. can also serve as nucleation substrates for chains deposited from the vapor phase. This has been employed by Wittmann and Lotz (1985) as a “decoration” technique to probe crystal surface order. Lath-like crystals are epitaxially oriented on, for example, benzoic acid to provide a [1 0 0] projection of the unit cell (Fig. 3.10). From electron diffraction intensities, the crystal structure can be verified (Moss et al., 1984; Dorset and Zemlin, 1990). The 0kᐉ pattern in Fig. 3.11(a) can be interpreted qualitatively to give the basic crystal structure. Comparing the spacing of inner lamellar 00ᐉ reflections to the c* position of the most intense 01ᐉ reflections (see Fig. 3.11(c)), the indices of these intense spots are related to the carbon chain length m in a lamella, where ᐉ  m, m 2 for these two 01ᐉ reflections. Tilting the structure around the chain axes by 33 gives the hhᐉ pattern (Fig. 3.11(b)). High-resolution micrographs of the epitaxially oriented paraffin (Dorset and Zemlin, 1990) reveals the lamellar structure

ORTHORHOMBIC CRYSTAL STRUCTURE OF THE EVEN-CHAIN

43

Fig. 3.10. Lath-like crystals of epitaxially nucleated n-hexatriacontane.

(a)

(c)

b ••

• ••

•• ••

••

•• ••

••

= m, m + 2

•• •

c = 2m + 2, 2m + 4

••

(d)

(b)

(e)

Fig. 3.11. Epitaxially nucleated n-hexatriacontane. (a) 0kᐉ electron diffraction pattern; (b) hhᐉ electron diffraction pattern; (c) schematic 0kᐉ pattern showing relation between reflection indices and carbon number m in chain (n-CmH2m 2); (d) high-resolution electron micrograph of the epitaxially oriented paraffin; (e) optical transform of (d).

44

CRYSTAL STRUCTURES AND PHASE TRANSITIONS

(a)

(b)

Fig. 3.12. (a) Sectorization of n-C82H166; (b) direct visualizations of sectors as electron microscope lattice images.

(Fig. 3.11(d)) also via its optical transform (Fig. 3.11(e)). Total replacement of the hydrogens by deuterium also makes no difference to the crystal structure (Dorset, 1991a), although, presumably, the cell constants for the perdeuterated form should be slightly smaller (Lacks, 1995). Crystallization of this orthorhombic form has been extensively studied. Its layer morphology can be understood from preferred “attachment energies” of the long chains (Boistelle and Aquilano, 1978). In fact, the lateral packing of chains has been shown to amount to 96% of the total internal energy of the crystal (Lundager Madsen and Boistelle, 1976), accounting for the slowest crystal growth along [0 0 1]. Although the monoclinic form of even-chain paraffins has been found to be thermodynamically preferred for chain lengths from m  26 to 38 (Asbach and Kilian, 1970), there are numerous observations of a stable orthorhombic form, either when these are crystallized rapidly from dilute solution, or from the melt, as thin layers (Dorset, 1980). In fact, n-C24H50 has been crystallized in this rectangular layer form. Crystallization of even-chain paraffins onto an epitaxial substrate also favors this polymorph, even for the shorter chain lengths (Dorset, 1990b). While it is true that the orthorhombic polymorph appears to be expressed preferentially for the longer chain even n-paraffins—for example, single layers from n-C82H166 (Dorset, 1986), there is a subtle change in crystal morphology, most noticeable for chain lengths near n-C50H102 and larger while the chains are still extended in the lamellae. As noted in bright-field electron micrographs of lamellae nucleated from hot solvent (Fig. 3.12(a)), the crystals are sectorized so that striations occur along 130 in {110} sectors. That is to say, the original lamellar habit, grown from solution, was not planar in suspension but actually some sort of

“NEMATOCRYSTALLINE” MODIFICATIONS

45

three-dimensional twin. Since the twins are fourfold, a nonplanar diagonal packing in the orthorhombic perpendicular methylene subcell is suggested, perhaps one from the group of O[ 1, 1] layers suggested by Kitaigorodskii (1961). High resolution electron microscopy (Dorset et al., 1990) of such twinned structures (Fig. 3.12(b)) reveals an alternation of oblique and rectangular chain packings, again similar to the collapse of polyethylene lamellae (Revol and Manley, 1986), even though the chains are unfolded. (In the chain-folded polymer, or chain-folded n-paraffins, the striations run along <130> in {110} sectors.) For some reason, this observed sectorization of n-paraffins is largely ignored by polymer physicists, perhaps because the chainfolding origin of sectorization in polymers was often assumed to be true without proof. In a consideration of possible energetically favored chain attachments to a lamellar monolayer, Boistelle and Lundager Madsen (1978) predicted that polymethylene chains might be nucleated lengthwise to the (001) face in an epitaxial orientation, in addition to the usual nucleation of the next chain layer, growing into another lamella. This prediction was realized by Wittmann and Lotz (1985) who, as mentioned above, used the microcrystalline overgrowth as an anisotropic probe of crystal surfaces. When applied to the sectorized n-paraffin layers above, only weak indications of preferred orientation of the crystallites within sectors was found (Dorset et al., 1990), despite the overwhelming preference for a single orientation of decorating crystallites observed on the surface of the chain-folded polymer within a single-fold sector (see below).

3.6

“Nematocrystalline” modifications

Epitaxial orientation of longer chain n-paraffins (e.g. n-C50H102, n-C60H122) on organic substrates is very difficult to achieve when these were crystallized from a co-melt with an appropriate diluent (e.g. benzoic acid). When the material was crystallized from the vapor phase onto a substrate such as potassium hydrogen phthalate (Zhang and Dorset, 1990), lamellae were not found in the epitaxially oriented mass, after removal of the nucleating substrate. Electron diffraction patterns very much resembled those from epitaxially oriented polyethylene. Upon annealing the solid in the presence of the substrate, a nascent lamellar structure emerged (Fig. 3.13) and, eventually, after observing a number of intermediate patterns, those from the well-formed lamellae were observed. Model calculations indicate that the initial nucleation, by analogy to mesophases, must have been a “nematically” disordered packing of the long chains, however with a highly ordered methylene subcell packing (Fig. 3.13). We term this disorder “nematocrystalline.” During annealing, allowing the chains to reptate toward a final, stable, lamellar form, intermediates would be found where bridging molecules across the nascent lamellae would constrain the gap to some integral multiple of the cs/2 spacing of the O⊥ subcell. When these bridging molecules are entirely transferred to respective lamellae, the interlamellar gap can then jump to a

46

CRYSTAL STRUCTURES AND PHASE TRANSITIONS (a) b*

(011)s (l = 17) ×

c* (002)s (l = 34)

c

(b)

b

b* l =15

l =17 c*

∆z

l = 32 l = 34

l =17

l = 34

Fig. 3.13. Model of lamellar growth from nematocrystalline form of a paraffin. (a) Initially crystallized solid has no layer structure so that its diffraction pattern resembles that from chain-folded polyethylene; (b) Upon annealing, layers begin to form, leading to 00ᐉ low-angle lamellar reflections. However, if the gap distance z is still an integral multiple of the zigzag chain repeat cs/2, the strong 01ᐉ “polyethylene” reflections are singlets. When a true lamellar packing forms, the gap distance is no longer an integral multiple of cs/2. Hence the intense 01ᐉ reflections are split into doublets. (Zhang, W. P. and Dorset, D. L. (1990) Phase transformation and structure of n-C50H102/n-C60H122 solid solutions formed from the vapor phase. J. Polym. Sci. Part B. Polym. Phys. 28, 1223–1232.)

nonintegral value, causing the 01ᐉ “polyethylene” reflections to split. By vibrational spectroscopy, this nematocrystalline chain packing has also been observed for shorter paraffins (n-C21H44, n-C36H74) and a low molecular weight polyethylene deposited from the vapor phase onto a cold surface (Hagemann et al., 1987).

ORTHORHOMBIC CRYSTAL STRUCTURE OF ODD-CHAIN

47

(a)

(b)

Fig. 3.14. Low-energy A-form of tricosane.

3.7

Thermodynamically stable orthorhombic crystal structure of the odd-chain n-paraffins

The crystal structure of n-tricosane, n-C23H48, (Fig. 3.14) was originally reported by Smith (1953). Orthorhombic cell constants are: a  4.970, b  7.478, c  62.31 Å and the space group was found to be Pbcm, the structure favored by Kitaigorodskii (1961). As listed by Nyburg and Potworowski (1973), the layer spacing d(002) can be predicted from 1.273m 1.875 Å. The methylene subcell is O⊥. Fractional coordinates for the first two carbons are (0.1931, 0.03362, 0.02525) and (0.3123, 0.1162, 0.0457). This packing was also found for the lowest temperature form of n-C33H68 (Piesczek et al., 1974). The untilted chain layer had been characterized previously by reflection high-energy electron diffraction (Thiessen and Schoon, 1937) as well as transmission diffraction (Garrido and Hengstenberg, 1932). (This packing form has been termed “Oi” by Rajabalee et al., 1999a.)

3.8

Orthorhombic crystal structure of melt-crystallized odd-chain n-paraffins

Crystallization from the melt can induce a higher energy B-polymorph to crystallize. Piesczek et al. (1974) stated that the first transition from the n-C33H68 A to B polymorphs crystallized a monoclinic chain packing in space group Aa where the monoclinic ␤-angle was very close to 90 (a  7.57, b  4.98, c  87.94 Å, ␤  91.2). In studies of epitaxially oriented odd-chain paraffins (Hu et al., 1989; Dorset and Zhang, 1991), this polymorph was found also to be orthorhombic in space

48

CRYSTAL STRUCTURES AND PHASE TRANSITIONS

(a)

(b)

Fig. 3.15. Higher-energy B-form of tritriacontane. (a)

(b)

Fig. 3.16. Proposed monoclinic B-form of n-heptacosane.

group A21am (similar to the solid solution structure reported by Lüth et al., 1974). For n-C33H68 in this space group: a  7.50, b  4.96, c  87.94 Å. The crystal structure, determined from the three-dimensional electron diffraction intensity data (Dorset, 1999a), is represented in Fig. 3.15. The chain packing also has been identified for certain paraffin solid solutions (Gerson and Nyburg, 1994). Prediction of layer spacing is very closely approximated by the equation given (Nyburg and Potworwski, 1973) for the lower energy A-form in space group Pbcm. Again the same indexing scheme used above for even-chain orthorhombic n-paraffins can predict the crystal structure qualitatively from the 01ᐉ patterns (Fig. 3.11) applies to this space group. A monoclinic crystal structure in Aa was justified (Rajabalee et al., 2002) by a Rietveld refinement of X-ray powder data from n-C27H56, obtained at 325 K. Unit cell parameters are: a  7.538, b  4.973, c  72.60 Å, ␤  91.32 (Fig. 3.16). (It has been termed “Mdci” by these authors (Rajabalee et al. (1999a,b) and is equivalent to the ␤1 and ␤2 forms cited by other authors.)

BRANCHED n -PARAFFINS

3.9

49

Branched n-paraffins

Methyl branching can occur in a fraction of the long chains in many waxes and also polyethylene. Nevertheless, quantitative structural information about branched chain alkanes is scant. It is well-known that certain types of branches, such as ketone oxygens, can be accommodated into the crystalline lattices of n-paraffins, and, indeed, have been used, via dielectric relaxation, as probes of phase transitions (Oldham and Ubbelohde, 1940; Strobl et al., 1978). The crystal structure of 12-tricosanone (Fig. 3.17) was solved from powder X-ray data in space group Pcam, with cell constants: a  7.55, b  4.90, c  62.3 Å, Z  4 (Malta et al., 1974). This is the same crystal packing found by Smith (1953) for the low temperature A-polymorph of odd-chain n-paraffins (interposing the a-and b-axes to define the equivalent space group). At low concentrations, the presence of the ketone does not disturb the typical odd-chain n-paraffin chain packing (Oldham and Ubbelohde, 1940; Strobl et al., 1978). Electron diffraction measurements were also made on palmitone, 16-hentriacontanone (Zhang and Dorset, 1989), after the molecule was epitaxially oriented on potassium hydrogen phthalate or KCl. Again an orthorhombic structure was found with cell constants: a  7.56, b  4.93, c  82.8 Å. The space group is A21am (Dorset, 1995a), corresponding to the higher energy B-form of the odd-chain alkanes. It is interesting to note that the position of the ketone oxygen can be predicted by the intensity profile of low-angle “lamellar” reflections (Kreger, 1951). When the group occurs at 1/p of the chain length then the pth diffraction order will be weak or absent. On the other hand, methyl branches are not so easily accommodated into the alkane chain packing. The static defect energy is estimated to be somewhere between 5.5 and 12.9 kcal mol1 for insertion of a methyl group into an orthorhombic chain packing (Farmer and Eby, 1979). Since terminal halogen (I, Br) groups can closely mimic the van der Waals radius of a methyl group (Pauling, 1960), the crystal (a)

(b)

Fig. 3.17. Crystal structure of 12-tricosanone.

50

CRYSTAL STRUCTURES AND PHASE TRANSITIONS (a)

(b)

Fig. 3.18. Crystal structure of 1-iodo-3-methyl-tricosane.

structure of chiral 1-iodo-3-methyltricosane was carried out (Abrahamsson et al., 1968) to investigate the packing of branched chain paraffins. This compound crystallizes in space group P212121 with cell constants: a  5.57, b  7.59, c  62.14 Å, where Z  4. From its crystal structure (Fig. 3.18), it is found that the lamellar surface is now serrated with a complicated arrangement of head to tail molecular packing. Conformational twists are also needed to minimize the void volume at the layer surfaces. Despite these complications, the overall layer packing is still the O[1, 0] type predicted by Kitaigorodskii (1961), the methylene subcell packing being O⊥. The molecules, therefore, pack in interdigitated layers. Interdigitation, as well as the chain tilt, are devices polymethylene chains can use to equalize the cross-sectional area of the methylene subcell packing with the packing of the interlamellar interface, as will be shown in Chapter 8 for the branched chain fatty acids. Partial interdigitation of apposing layer surfaces is anticipated in the electron diffraction analyses of four racemic methyl-branched n-paraffins to obscure the true lamellar boundary, viz. 3-methyl-branched tritriacontane and tetratriacontane and 4- and 5-methyl branched derivatives of the latter alkane (Dorset, 2000c). When epitaxially crystallized on benzoic acid, their metastable crystal structures include rectangular layers. Crystal structure analyses, therefore, indicate a partial penetration of chains from one lamella to another. On standing for five months, the 3-methyl-branched alkanes were found to begin transformation to a more ordered superlattice structure. Electron diffraction studies on solution-crystallized 1-methyl pentacosane indicate that the layers pack in a rotator phase at room temperature and in rectangular layers

AROMATIC SUBSTITUTION OF n -PARAFFINS

51

with the O⊥ methylene subcell at very low temperatures. No studies have been carried out on epitaxially oriented samples. Highly branched chains such as squalene (Ernst and Fuhrhop, 1979) contain no regular subcell; nor is there a real layer arrangement for the molecular packing.

3.10

Aromatic substitution of n-paraffins

To anticipate the interaction of “naphthenic” components in certain waxes, the crystal structure of a phenyl-substituted n-alkane, 1-phenyl decane, was determined recently (Merz, 2002). (The previous model for naphthenic packing was rather primitive, regarding a stacking of molecular disks, Ebert et al., 1983.) As shown in Fig. 3.19, the crystal structure (space group P212121, a  5.14, b  8.91, c  31.69 Å) is typical for polymethylene chain substitutions where the chain packing crosssection must accommodate for the surface area bulk of the heterogroup layer. This compensation occurs (as shown for the branched chain material above), by choice of methylene subcell, chain tilt and the possibility of chain interdigitation. In this example, the polymethylene subcell is O⊥. (A preliminary electron and powder X-ray diffraction study of 1-nonadecyl cyclohexane indicates a similar packing arrangement. The O⊥ subcell is included into an O(0, 2) layer. Unit cell dimensions are a  35.73, b  5.08, c  18.09 Å, ␤  129.94. Direct methods analyses of the h0ᐉ data support the interdigitated layer packing.) This packing arrangement is also adopted by certain non-ionic detergents, for example, 1-decyl-␣-D-glucoside (Moews and Knox, 1976). Even highly branched chains substituted with a ring moiety, for example, 11-cis-retinal, adopt a layer packing separating the two unlike molecular moieties (Gilardi et al., 1972). Obviously, in multicomponent solids, there is no possibility for such molecules to be co-soluble with crystalline unbranched n-paraffins. A metastable mesophase with layer spacing d  22.4 Å was identified when 1-nonadecyl cyclohexane was cooled from the melt (Sirota et al., 2000).

Fig. 3.19. Crystal structure of 1-phenyl decane.

52

3.11

CRYSTAL STRUCTURES AND PHASE TRANSITIONS

Polyethylene and its alkane models

Theoretically, alkane chain lengths can extend to infinity. As the number of methylene units becomes large, the linear polymer, polyethylene, is formed. Its crystal structure was originally described by Bunn (1939), and the so-called stem packing of the polymethylene chains is just the O⊥ methylene subcell described in Chapter 2. However, the real polymer is not monodisperse, that is, the ratio of the weight average molecular weight to the number average molecular weight is never 1.0, although it can be made to be very small, for example, 1.1. A three-dimensional single crystal structure determination of the infinite chain-folded polymer was made from electron diffraction data (Hu and Dorset, 1989) by direct methods (Dorset, 1991b). The electron diffraction data had been collected from both crystals grown by self-seeding and also those epitaxially oriented on organic substrates. The orthorhombic space group again is Pnam with a  7.48, b  4.97, c  2.55 Å. The analysis, based on 50 independent reflections, clearly shows the O⊥ subcell packing of orthorhombic n-paraffins (Fig. 3.20). An equivalent result was obtained when 28 unique powder X-ray data (Kawaguchi et al., 1979) were assigned crystallographic phases by direct (a)

(b)

Fig. 3.20. Crystal structure of polyethylene. (a) [0 0 1] potential map; (b) [1 0 0] potential map.

POLYETHYLENE AND ITS ALKANE MODELS

53

Fig. 3.21. Electron micrograph of chain-folded polyethylene single crystals revealing sectorization.

methods (Dorset, 1997a). Earlier, the same three-dimensional subcell packing of a paraffin wax had been described from texture electron diffraction intensity data (Vainshtein and Pinsker, 1950). In the literature, much has been made of the difference between chain “setting angle” (i.e. the angle of the chain plane to the subcell bc face) in n-paraffins and polyethylene (Kawaguchi et al., 1979) but there seems to be insufficient systematic experimental reason to claim any difference. (By electron diffraction, detection of subtle differences is frustrated by multiple scattering perturbations to the intensities, Dorset and Moss, 1983.) Chain-folded crystals of the “infinite” length polymer grow in suspension by self-seeding in a three-dimensional lamellar habit and, when they are dried on a flat substrate, collapse to form pleats in so-called fold sectors, these pleats (Fig. 3.21) running along the <13 0> direction (Bassett et al., 1959, 1963; Niegisch and Swan, 1960; Reneker and Geil, 1960; Basset and Keller, 1961, 1962; Boudet, 1984). By high-resolution electron microscopy and electron microdiffraction, it was shown that the pleats alternate between a rectangular and an oblique chain packing (Revol and Manley, 1986). There has been considerable controversy over the existence of regular chain folds in each sector and, indeed, it has been postulated that the regular fold geometry on the crystal surface is responsible for the sectorization of the lamellae when they collapse. Decoration experiments (Wittmann and Lotz, 1985) indicate that the folds do seem to have a common direction in a sector, although the distribution of orientations also seems to be somewhat splayed. Ideally, the crystal packing of polyethylene could be explored further if the chain lengths of monodisperse paraffins could be made long enough. This was initially attempted in Sweden with n-hectane, n-C100H202 (Ställberg et al., 1952), leading to the characterization of screw dislocation growth in the electron microscope (Dawson, 1952). This chain length was not sufficient to induce folds. Longer chain n-paraffins do fold, however (Ungar et al., 1985) with the onset of this behavior

54

CRYSTAL STRUCTURES AND PHASE TRANSITIONS

Fig. 3.22. Chain-folded crystal of n-C168H338.

commencing near n-C150H302, where the crystallization of extended or folded chains also depends on the growth conditions. Low magnification diffraction-contrast chain-folded crystals of n-C168H358 resemble those of chain-folded polyethylene (Fig. 3.22). Isothermal lamellar thickening is noted during solution growth, a phenomenon not observed for polyethylene (Organ and Keller, 1987). If the crystals of, say, n-C198H398, are prepared as chain-extended lamellae, the polymethylene chain decoration of Wittmann and Lotz (1985) will resemble that obtained for ordinary n-paraffins (i.e. with no surface evidence for sectorization). On the other hand, if the chains are folded, the decoration resembles that for sectorized polyethylene (Organ and Keller, 1987). Formation of chain folds depends on the degree of undercooling when these materials are crystallized from solution. A near integral relation between non-folded and folded “stem” lengths is noted (Ungar et al., 1988). This indicates that the chain folds are tight and reentry is adjacent. Integral folds are thermodynamically favored. Increased concentration of the paraffin in solution can retard growth of extended chain polymorphs by self-poisoning of a growing crystal face by a folded chain (Ungar and Organ, 1990). Melt crystallization can produce chain-folded lamellae with disordered surfaces (Ungar and Keller, 1986) while crystallization from solution produces sharp folds with a lamellar spacing of a near integral fraction of the extended chain length (Ungar et al., 1988). No single crystal structure has been reported for chain-folded n-paraffins. Another possible model for chain-folded polyethylene has been the cycloalkanes. An initial crystal structure attempting to discern the geometry of the chain fold was that of cyclotetratriacontane (CH2)34 (Kay and Newman, 1968). The molecules pack in space group P1 (a  8.172, b  5.470, c  18.91 Å, ␣  87.30, ␤  95.17, ␥  106.17), with the methylene units packing in the T subcell. Although the

POLYETHYLENE AND ITS ALKANE MODELS

55

Fig. 3.23. Crystal structure of cyclotetratriacontane.

chain-fold geometry was well-resolved, the application to a regular polyethylene model was questionable because the carbon zigzag chain planes are all parallel in the cycloalkane structure while those of the polymer are perpendicular to one another (Fig. 3.23). The crystal structure of the homolog (CH2)36 was also determined (Trzbiatowski et al., 1982) (space group: Aa, a  10.33, b  8.24, c  42.2 Å, ␤  107.1), but, although the fold connectivity to the stem regions is somewhat different in this monoclinic structure, the chain planes are still parallel to one another. This crystal structure can persist for perimeters up to 72 carbons. Electron diffraction experiments were carried out for synthetic cycloalkanes with larger perimeters (Lieser et al., 1988; Dorset and Hsu, 1989). For (CH2)48 crystallized from solution, the first example of Kitaigorodskii’s M(0, 0) layer packing is observed, that is, the M methylene subcell in a rectangular layer. The larger (CH2)72 will crystallize as the T subcell from solution but will form the O⊥ packing when epitaxially oriented from the melt. The same orthorhombic chain packing of polyethylene is found for (CH2)96 oriented from the melt, while an oblique packing probably crystallizes from solution. Finally, when the chain perimeter is expanded to (CH2)120, the orthorhombic perpendicular (O⊥) chain packing is crystallized from solution. Polymethylene decoration again reveals a motif very similar to the chain-folded n-paraffins or polyethylene (Tsuji and Ihn, 1995). A monoclinic form can also be crystallized. The fold region of this cycloalkane in its orthorhombic form is more ordered than that of the infinite polymer but less ordered than the folds found for its monoclinic polymorph. The above experiments on chain-folded n-paraffins and large perimeter cycloalkanes suggest that there can be an interplay between chain folding and the stem packing, particularly when the stem lengths are somewhat short. Unfortunately, no single crystal structure has been reported for large perimeter cycloalkanes. Much more can be said about the structure of polydisperse low molecular weight linear polyethylene, since its crystal structure has been determined recently by electron crystallography (Dorset, 1999b). This topic will be addressed in Chapter 11 since the structure is closely related to a certain class of paraffin waxes.

56

3.12 1.

CRYSTAL STRUCTURES AND PHASE TRANSITIONS

Summary

The documented crystal structures of n-paraffins in their various polymorphs validate predicted packing motifs discussed in the previous chapter. 2. Non-lamellar intermediates have been identified for long, chain-extended, n-paraffins under certain growth conditions. 3. Chain branching can be accommodated within a polymethylene chain region as long as the branch size is not too large. For example, a ketone carbonyl oxygen can pack within the subcell region. Methyl branches, on the other hand, are not included in these crystalline regions. 4. Derivativization of an alkane chain of a simple head group, for example, phenyl substitution, introduces the principles of heterogeneous layer packing. The methylene subcell and hetero-layer must accommodate one another by mechanisms such as: choice of subcell, chain tilt, and (sometimes) chain interdigitation. Similar packing principles are found for amphiphilic molecules with n-alkyl chains. 5. Chain folding affects the nature of polymethylene layer packing. The folded region can behave like a head group in its effect on chain layer packing.

4 Thermotropic disorder in n-paraffin crystals

4.1

Introduction

It was shown in the previous chapter that n-paraffins crystallize in a number of polymorphic and polytypic forms. Typical DSC (differential scanning calorimeter) scans for even- and odd-chain n-paraffins (Fig. 4.1) include small endothermic transitions at low temperature due to the change in crystalline polymorph. For certain paraffin chain lengths (e.g. 38 carbons for even-chains), a higher temperature transition from the crystalline state into the rotator phase occurs, followed by the melt. Dependence of polymorphic transition and melting temperatures on paraffin chain length has been extensively studied. All polymethylene compounds, even derivativized ones, converge to a common melting point as the chain length becomes very long (Hatt and Lamberton, 1956; Kitaigorodskii, 1961). That similar phase transitions follow smooth curves when plotted against chain length was shown originally by Schaerer et al. (1956). For the odd-chain paraffins, the orthorhombic layer packing persists to low chain lengths to give a continuous phase transition curve. Even chains crystallize in several polymorphic forms, causing breaks to occur in the transition curves. As discussed in previous chapters, even–odd effects in melting temperature are due to symmetrically favored crystalline packing, that is, a rectangular layer packing, for example, odd-chain members, accommodating a molecular mirror plane, and a tilted layer packing for the other even-chain members, expressing the molecular inversion center (see Broadhurst, 1962). The even–odd effect, therefore, expresses the energetic differences of the respective layer stackings. The transition and melting temperatures for the n-alkanes, along with respective transition enthalpies, have been summarized by Small (1986) and others. For the orthorhombic n-paraffins, it is possible to calculate thermodynamic quantities directly as a function of chain length (Dollhopf et al., 1981). The summed enthalpy of all thermotropic transitions to produce the melt is given by:

冢

3 Htot  H  1  m and

冢

冣

for even-chain paraffins

4.4 Htot  H 1  m

冣

for odd-chains.

58

THERMOTROPIC DISORDER IN n -PARAFFIN CRYSTALS

Exo

Endo

30

40

50

60 T (°C)

70

80

90

Fig. 4.1. Sequential DSC scan for n-hexatriacontane. The first small endotherm corresponds to the monoclinic to orthorhombic transition. The second endotherm is the orthorhombic to hexagonal (rotator) transition followed by the melting endotherm.

Here H (984 cal mol1CH2) is the melting enthalpy of polyethylene. The melting point of a chain with m carbons is given by:

冢

1  1 1 6.86 m Tmelt Tmelt

冣

 where Tmelt  414.6K. Recently, Smolenskii et al. (2002) formulated another expression to predict paraffin chain melting without distinguishing between odd- and even-chains. A formula in the form:

Tm 

a

d (N b)c

was proposed where, for example, a  25.755; b  9.73, c  1.85, d  117.73 predicts melting temperatures in C. Previously, Broadhurst (1966) had proposed a relationship in the form: n a Tm  T0 n b later modified to Tm  To

n a n ln n b

where a  1.5, b  5.0, To  144.7C to predict the melting of orthorhombic n-paraffins. Other relationships are discussed by Dirand et al. (2002). Crystallization of paraffins from the melt has been studied by Weidinger et al. (2003) with suspended droplets. Nucleation rates correlate with the formation of initial solid monolayers on the droplet surface. Such solid monolayers, which form 3 above the melting point, have been characterized via surface tension measurements and X-ray scattering (Wu et al., 1993a,b; Ocko et al., 1997). They exist as a rectangular rotator phase for chain lengths 16  m  30, a tilted rotator phase for

HIGH TEMPERATURE CHAIN PACKING

59

the interval 30m44 and a tilted crystalline layer for m 44. Extensive studies, in suspended droplets, of paraffin nucleation by a transient rotator phase have been published by Kraack et al. (2000a,b). Perdeuterated n-alkanes are often employed as relatively non-perturbative probes of crystalline structure and transitions. A systematic study of the melting point difference between the isotopically subsituted n-paraffins (Dorset et al., 1991a) reveals that the melting point of the deuterated species is always lower than that of the allhydrogenated species. The larger zero-point vibrational energy of the lower mass perhydrogenated chains would lead to stronger van der Waals intermolecular interH D H actions (Lacks, 1995). The relation between Tmelt  Tmelt and Tmelt is linear,  Tmelt moreover, suggesting a law of corresponding states for the two isotopic species. That is to say, given the difference in the internal energy minima, Dand H for the corresponding crystal structures (with identical layer packing and unit cell symmetry), the * D,H D,H reduced melting temperatures, calculated from Tmelt  kBTmelt  , should be identical. Using a derived energetic difference from the implied linear relationship above, a value ␦  (H  D)/D can be found experimentally that agrees well with the experimental values for CH4 versus CD4 (Grigor and Steele, 1968).

4.2

Diffraction and microscopical studies of high temperature chain packing

From the previous chapter, it is clear that the change in layer packing must be accompanied by a characteristic change in diffraction patterns. For example, in the single crystal X-ray study of n-C33H68 (Piesczek et al., 1973), the transition of one polymorphic form to another was discerned by changes in unit cell symmetry (systematic absences, distribution of diffracted intensity) as well as certain changes in unit cell axial lengths and angles. In powder diffraction measurements, this would be followed by changes in the intense “subcell” intensities at wide angle in addition to the spacing of low-angle lamellar reflections. Recently, the sequence of transitions for n-C23H48 has been given (Rajabalee et al., 1999a): Oi → Odci → Rv → RI → RII → liquid, where Odci is an orthorhombic structure in space group Pnam. The next higher oddchain homolog has the transition sequence: Oi → Odci → Mdci → Rv → RI → RII → liquid. Equivalent crystal structures have been given in Chapter 3. The rotator phase forms Rn are discussed below. In electron diffraction studies, single microcrystals of the polymorphs will give distinctive single crystal patterns. A hexagonally disordered form of n-paraffins, in the so-called “rotator” phase, was originally recognized by Müller (1932) to occur before the melting point. This phase can be suppressed for pure n-alkanes at high pressures (Würflinger and Schneider, 1973). As this transition is approached, gradual changes in the diffraction

60

THERMOTROPIC DISORDER IN n -PARAFFIN CRYSTALS (a) 1.80

Hexagonal chain packing

1.70 a/b

o - C32 D66 - C32 H66

1.60

1.50 20

30

40

50

60

70

T (°C) (b) 1.75

True rotator n-C36 D74

1.65 a /b

n -C32 D66

1.55

n-C32 H66 1.45 20

30

40 50 60 No. of carbons

70

80

90

Fig. 4.2. (a) Plot of a/b ratios for a n-paraffin and its perdeuterated analog heated to the rotator phase; (b) expressed a/b ratios for a homologous series of n-paraffins heated near their melting points. (Dorset, D. L. (1991) Structural interactions between n-paraffins and their perdeuterated analogs; binary compositions with identical chain lengths. Macromolecules 24, 6521–6526.)

pattern with increasing temperature will be observed. For example, in electron diffraction studies of heated single orthorhombic paraffin layers (Dorset, 1991a), the change in the a/b ratio of the lateral chain unit cell edges increases gradually from about 1.49 to 1.55 (Fig. 2.7(a)), upon which there is a discontinuous jump to 1.73  √3, the value expected for the true hexagonal unit cell (Fig. 4.2). For the even-chain paraffins, this behavior persists to n-C38H78, after which the rotator phase is not formed. Perdeuteration can also affect this behavior, first, by lowering the transition temperature (again by decreasing the intermolecular van der Waals attraction).

HIGH TEMPERATURE CHAIN PACKING

61

Although the rotator phase is observed on heating n-C32D66, it is not seen for n-C36D74 until the melt is cooled (Stehling et al., 1971). For the latter perdeuterated n-paraffin analog, the a/b ratio approaches 1.68, just before the melt but the √3 limit is never reached (Dorset, 1991a). Although the disordered chain packing in the rotator phase is similar for single layers of many n-alkanes, there are also distinctions that can be made in the three-dimensional layer stacking. Larsson (1967) realized that the true symmetry of some n-paraffins in this phase was orthorhombic, not hexagonal, for example, for n-nonadecane, although individual lamellae had hexagonal symmetry. The space group of the next higher odd-chain homolog, n-C21H44, in its rotator phase was identified to be Fmmm by Ungar (1983). For longer odd-chain paraffins a further trigonal modification in space group R 3m was observed at higher temperatures and a C-centered form was recognized for n-C23H48 in a limited temperature range on heating and in n-C25H52 on cooling the melt. Using X-ray diffraction, a sequence of rotator phases is found for a number of n-alkanes as temperature is increased toward the melting point. Five separate rotator phase crystal structures (Fig. 4.3) have been listed (Denicolo et al., 1983; Doucet et al., 1984; Sirota et al., 1993, 1995; Sirota and Singer, 1994), some of which have tilted chain layers. Specifically, the RII phase is an untilted hexagonal lattice with 5 Phases identified

• Order parameters –Distortion (D) –Tilt magnitude (
) –Tilt direction ()

RII

RIV

RI

RIII

Define distortion D = 0 in hexagonal RII phase:

A B

D ≡ 1–

A B

RV

Fig. 4.3. Schematic representation of five identified rotator phases. Unfilled circles represent the chain-end positions in the second layer of a bilayer structure. Gray circles for the RII phase represent the third layer of a trilayer structure. Arrows represent the tilt direction in the tilted layers. The schematic drawing illustrates the distortion of the hexagonal packing when D is non-unitary. (Figure kindly provided by Dr E. B. Sirota and used by permission.)

62

THERMOTROPIC DISORDER IN n -PARAFFIN CRYSTALS

a trilayer sequence. The RI, also untilted, contains a rectangularly distorted layer packing with a bilayer stacking sequence. The RIV has tilted chain layers in an overall monoclinic structure while the tilted layer RIII form is a triclinic structure. The RV phase is similar to RI except that the chains are slightly tilted. A plot of unit cell constants with increasing temperature was made by Vand (1953) as n-hexatriacontane was heated toward the melt. A change in the smoothly decreasing slope of unit cell density was noted near the rotator transition of 73.5C. However, the lamellar spacing was found to be virtually independent of temperature so that the density change was strongly anisotropic, corresponding to the observed lateral expansion of the lattice to the orthohexagonal layer constants a  8.40, b  4.85 Å, nearly the experimental values reported by Larsson (1967). Although, for a time, an actual chain rotor was imagined (Andrew, 1950; Kobayashi, 1978) for this phase, it is clear that it really cannot occur, since the phase is also found in many lipids where alkyl chains are covalently tethered to an immobilized part of the molecule (e.g. a polar head group). Ungar and Masic (1985) proposed that the actual structure should be an average over variously oriented orthorhombic subcells in a single layer. Scaringe (1992), on the other hand, discovered a trigonal layer packing for the n-paraffins (plane group p3) that would give a composite symmetry of P62m for odd-paraffins and P31m for the even-chains (Fig. 4.4). The cross-section per molecule is 19.9 Å2. Construction of this symmetry required that the symmetry of the coordination shell should be adjusted first before generation of a packing motif by a particular space group. The proposed packing accounts reasonably for the observed energy difference between the orthorhombic and hexagonal layers and predicts the actual lateral unit cell constant a  4.80 Å. An advantage of this model is that it overcomes the need for actual chain rotors (e.g. Yamamoto et al., 1994) which would encounter considerable energetic barriers.

Fig. 4.4. Ordered domain of an n-paraffin layer rotator phase structure. (Used by permission of Dr R. P. Scaringe from Scaringe, R. P. (1992) Crystallography in two dimensions: comparison of theory and experiment for molecular layers. Trans. Am. Crystall. Assoc. 28, 11–23.)

HIGH TEMPERATURE CHAIN PACKING

63

Crystals of n-alkanes grown in the rotator phase have a circular habit (Toda et al., 1991) with no faceting, consistent with Scaringe’s model but not with those incorporating multiply twinned layers. As epitaxially oriented n-paraffins are heated near the rotator phase transitions, 00l lamellar reflections in 0kl single crystal electron diffraction patterns are restricted in resolution (Fig. 4.5) while the strong reflections from the polymethylene chain packing are virtually unchanged (Dorset et al., 1984). Attenuation of the number of orders of the lamellar reflections had also been noted in powder diffraction experiments (Craievich et al., 1984a). The data were interpreted as a disordering of the lamellar interface. That is to say, the ideal lamellar interface can be imagined to be convoluted with a Gaussian term, expressing the disorder. The Fourier transform of this disorder term, also Gaussian, screens the diffraction information expressing the lamellar repeat by suppressing its resolution (Dorset, 2000a). When the chain length is too large to permit formation of a stable rotator phase, another disorder mechanism occurs. However, there is ample evidence for metastable and transient rotator phases below and above the chain length limits for the stable rotator phases (Sirota, 1998; Sirota and Herhold, 1999, 2000). These may (a)

(b)

Fig. 4.5. Changes in 0kl pattern from n-hexatriacontane (a) as it is heated near its rotator phase (b).

64

THERMOTROPIC DISORDER IN n -PARAFFIN CRYSTALS

nucleate the solid on cooling the melt and may explain the absence of odd–even chain effects for n-paraffin freezing points. Transient rotator phases may also play a role for the nucleation of paraffin crystals from solution (Sirota, 2000). At very long chain lengths, just before the melting point, the orthorhombic lattice begins to expand laterally, just as before, reaching an a/b  1.55 limit (Dorset, 1991a) (Fig. 4.6). Crystals grown in this phase have a lenticular habit (Toda et al., 1991). If the layer is then cooled to restore the orthorhombic electron diffraction pattern and then reheated, a somewhat larger initial a/b ratio is observed. Morphologically, striations begin to appear parallel to the crystal [010] axis and just before the melting point, the electron diffraction pattern (Fig. 4.7) strongly resembles those observed from the C-form of fatty acids (Dorset, 1983), corresponding to the Kitaigorodskii (1961) O[0, 2] layer (Dorset et al., 1992). The axis of the striations is the bs ⬇ 5.00 Å length. Heating epitaxially crystallized samples near the melting point again attenuates the 00l lamellar reflections, indicating a disordered lamellar interface before melting. Interpreting low angle diffraction data from n-C94H190 just below the melting point, Fischer (1971) had previously stated that there was evidence for premelting of the chains at the crystal lamellar surface. Such striations along the bs  5.0 Å axis were also observed optically, for example, on single crystals of n-C33H68 with a rotator phase (Piesczek et al., 1973), as well as other chain lengths (Takamizawa et al., 1982). Very pure n-C36H74 shows a complicated series of striations in the light microscope on heating, first along the long lozenge axis (parallel to as) followed by striations along the shorter one (parallel to bs), in accord with the electron microscopic results of Keller (1961). These striations correspond to the growth of so-called “roof structures,” that is, local formations of crystalline pleats in either the the O[1, 0] or O[0, 2] layers predicted by Kitaigorodskii (1961), as shown in various X-ray (Sullivan and Weeks, 1970; Kawaguchi, 1978; Mandelkern et al., 1994; Reynhardt et al., 1994) electron diffraction (Khoury, 1963; Dorset et al., 1992) or Raman (Royaud et al., 1990) studies. Appearance of interfacial disorder was also anticipated from early small angle X-ray studies on n-C84H170 (Rånby et al., 1960). Thermotropically induced disorder in paraffin layer packing also produces a continuous diffuse scattering signal in single crystal electron diffraction patterns (Dorset et al., 1991b), as illustrated by Fig. 4.5. Such continuous diffuse scattering can be difficult to interpret, since it is related inevitably to the Fourier transform of a single unit cell (Amorós and Amorós, 1968). However, some distinctions can be made if physical measurements are carried out on a cryo-electron microscope at very low temperatures (e.g. 4K). In a view down the chains the best model for the observed diffuse scattering is a thermal one since the signal can be extinguished at very low temperature. This model is not valid for the projection onto the chains (Fig. 4.8(a)), however, since the continuous scattering remains strong at 4K. While a thermal diffuse scattering calculation correctly accounts for the positions of the observed signal, the intensity distribution is opposite from the predicted values. A disorder model invoking slight longitudinal chain translations (Fig. 4.8(b)) accounts for the

(a)

(b)

a/b

1.61

1.61

n-C50H102

1.59

1.59

1.57

1.57

1.55

1.55

1.53

1.53

1.51

1.51

1.49

1.49 10

20

30

40

50

60

70

80

Previously heated samples

Crystallized samples (from toluene) 10 20 30 40 50 60 70 80 90 100

90

(c)

n-C60H122

(d) 1.61

n-C94H190

n-C82H166 1.60

1.59

a /b

1.57 1.55

1.55

1.53 1.51 1.50

1.49 10

20

30

40

50

60 70 T (°C)

80

90 100 110

10

20

30

40

50

60 70 T (°C)

80

90 100 110

Fig. 4.6. Changes in a/b ratios for longer paraffins that do not exhibit rotator transitions. (Dorset, D. L., Alamo, R. G., and Mandelkern, L. (1992) Premelting of long n-paraffins in chain-extended lamellae. An electron diffraction study. Macromolecules 25, 6284–6288.)

66

THERMOTROPIC DISORDER IN n -PARAFFIN CRYSTALS b*

(a)

(b)

a a*

b

>T

(c)

Fig. 4.7. Changes in electron diffraction and bright field images from n-C94H190 as these monolayer crystals are heated toward the melting point. In the sequence of electron diffraction patterns (a) the average rectangular layer O(0, 0) packing transforms to the Kitaigorodskii O(0, 2) layer. The sectorized motif in (b) transforms to unidirectional bend contours (c). (Dorset, D. L., Alamo, R. G., and Mandelkern, L. (1992) Premelting of long n-paraffins in chain-extended lamellae. An electron diffraction study. Macromolecules 25, 6284–6288.)

observed diffraction intensity. Hence, diffuse scattering demonstrates an early stage of longitudinal chain disorder. To summarize, diffraction studies on heated crystals, indicate that two disordering mechanisms can take place. One involves a concerted longitudinal motion along the

HIGH TEMPERATURE CHAIN PACKING

(a) (1)

67

(2)

b*

b* c*

c*

(4)

(3)

b* c*

b*

c* a

(b) (5) c

b* c*

Fig. 4.8. (a) Various models have been proposed for 0kl diffuse scattering in epitaxially oriented polyethylene chains including (1) TDS, (2) chain kinks, (3) torsional rotation. Only longitudinal shifts as in (b) account for the strong streaks observed either without (4) or with (5) some thermal component. (Dorset, D. L., Hu, H., and Jäger, J. (1991) Continuous diffuse scattering from polymethylene chains—an electron diffraction study of crystalline disorder. Acta Crystall A47, 543–549.)

chain axes to form oblique layers in pleats. The other is the gradual lateral expansion of the unit cell, including disorder of the lamellar interface, which can jump discontinuously into the rotator phase when the chain length permits it to occur. Molecular dynamics simulations of the rotator phase (Ryckaert et al., 1987) also indicate that longitudinal chain motion and accumulation of conformational defects can participate in the disordering process.

68

4.3

THERMOTROPIC DISORDER IN n -PARAFFIN CRYSTALS

Vibrational spectroscopic measurements of n-paraffins at high temperature

While diffraction techniques are useful for description of overall packing arrangements as temperature is increased, there are many important details of the emergent crystal disorder that remain undetected. As stated above, when single microcrystals of an epitaxially oriented paraffin are heated toward the rotator phase, the disorder at the lamellar interface, accounting for the resolution attenuation of 00l lamellar reflections (Dorset et al., 1984) can only be modeled approximately as a falloff of occupancy factors for the methylene positions. The induction of nonplanar conformational disorder in heated n-paraffin chains was inferred by the study of dielectric relaxation of ketonated chain models (Müller, 1937, 1938). Incorporation of a single ketone group as a probe, which is freely soluble in the chain lattice (Oldham and Ubbelohde, 1940), indicated that chain flexibility occurs at higher temperature. Torsional freedom of the chains was implied when symmetric and asymmetric diketonated probes were compared (Müller, 1940). Much more information is available from vibrational spectroscopic measurements. The vibrational modes of an ordered chain molecule (see Snyder, 1980), end group vibrations excluded, are nearly totally delocalized; that is to say, the normal coordinates extend over the entire chain, involving all groups equally. The vibrational frequencies of an ordered chain are consequently dependent on the chain length in a systematic way. This is manifested in “band progressions,” a series of bands whose spacing varies in a continuous manner, normally tending to be smallest at the beginning and at the end of a progression. The number of such progressions is equal to the number of different types of internal displacement coordinates and the number of modes in a given progression equals the number of internal coordinates of the identified type. Band progressions for the polymethylene chain were worked out by Snyder and Schachtschneider (1963), Schachtschneider and Snyder (1963), and Snyder (1960). For the ordered polymethylene chain, the assignment of progression bands is facilitated by the relative simplicity of the derived compounds, especially the n-paraffins. Predictions for the polymethylene chains (Snyder and Schachtschneider, 1963; Snyder, 1980) are probably more accurate than those for any other chain molecule type. An important part of this calculation involves evaluation of a transferable set of force constants. The polymethylene chain force constants have been essential in the spectral analysis for the conformationally disordered chain, therefore involving relationships between observed spectra and molecular disorder. Because vibrational frequencies depend on molecular structure and because molecular vibrations occur at frequencies much higher than conformer lifetimes, it is possible to distinguish between conformers. The difficulty in determining conformational disorder increases exponentially with increasing disorder, for example, the concentration of gauche bonds. For systems that tend to remain highly ordered, the methods described below can provide relatively detailed information about the

VIBRATIONAL SPECTROSCOPIC MEASUREMENTS

69

molecular disorder. For highly disordered systems, a detailed analysis is impractical. The complexity of the problem is underscored when a liquid alkane is considered since ca. one-third of the C–C bonds are gauche at room temperature. These are distributed randomly among and along the chains. The observed spectrum of a liquid, therefore, consists of a superposition of spectra from an enormous number of different conformers—each with its unique spectrum. The problem is not totally intractable, however. Disorder promotes the spatial location of vibrational modes within the chains, so that there are bands and spectral features in the infrared or Raman spectra that represent sequences of C–C bonds with specific conformations, and there are also less well-defined spectral features that indicate certain types of average conformational structure (Snyder, 1967, 1992; Cates et al., 1994). Among the sequences that have been identified are: gg, gtg
, and gtg, which are represented by bands at 1353, 1306, and 1366 cm1, respectively (Fig. 4.9). These bands are known to belong to spatially localized methylene wagging modes. The concentrations of these sequences can be determined using the corresponding bands in the spectra of liquid n-alkanes as the intensity reference, since the concentrations of the sequences are known for the liquids. This set of bands has been used, for example, to measure the conformational disorder in crystalline n-paraffins (Maroncelli et al., 1982) and their mixtures (Clavell-Grunbaum et al., 1997). By infrared, bands similar to those just described are available for the estimation of chain-end disorder. For example, the fraction of penultimate C–C bonds that is gauche can be estimated from the band at 1341 cm1 (Snyder, 1967). Other bands in A B C D E

gtg

gg eg

F

gtg


G H

A B

I

C E D F G H I 1360

1340 1320 Frequency (cm–1)

1300

Fig. 4.9. Infrared spectra from various waxes illustrating bands due to various types of conformational defects. (Figure provided and used by permission of Dr R. G. Snyder.)

70

THERMOTROPIC DISORDER IN n -PARAFFIN CRYSTALS

the infrared (Maroncelli et al., 1982) and Raman (Kim et al., 1989a) can measure other kinds of chain-end conformation. Such bands and spectral features have been used in the analysis of chain-end disorder for the binary n-alkane mixture C46/C50 (Kim et al., 1989b) or for orthorhombic n-paraffins in various crystalline phases (Kim et al., 1989a). Special features due to CD2 inclusions also facilitate determination of gauche bond concentrations at specific positions near the chain ends (see below). The Raman LAM-3 band to determine chain-end disorder is especially informative for mixtures because relative concentrations of chain-end disorder can be evaluated for the separate components. The method employs the k  3 band of the LAM-k (longitudinal acoustic mode, mode k) that appears prominently in the lowfrequency Raman spectra of crystalline n-alkanes (Mizushima and Simanouti, 1949). These modes are designated “longitudinal acoustic” because the atoms move in the direction of the chain to form an acoustic-like standing wave. Since the introduction of gauche bonds near the chain ends has the effect of decreasing the length of an all-trans chain, there is a characteristic upward shift in frequency. Chain-end order also involves a variety of conformations to effectively broaden the LAM bands, the broadening therefore a measure of disorder. Normalization of the broadening to chain length can be important for characterization of temperature dependence of chain-end disordering for chain mixtures (Snyder et al., 1993; Clavell-Grunbaum et al., 1997). The ratio of the number of gt to tt conformation for a pair of adjoining C–C bonds can be conveniently determined in the infrared if the linkage methylene is deuterated and all others are hydrogenated (Snyder et al., 1993; Maroncelli et al., 1985c). Two well-separated CD2 rocking bands appear. One of these, near 652 cm1, is associated with the gt pair and the one near 620 cm1 with the tt pair, so that the ratio of intensities gives the gg/tt concentration ratio. This method has been used to measure the distribution of gauche bonds in the orthorhombic and hexagonal phases of C21H44 (Maroncelli et al., 1985a) and in the binary C19/C21 mixtures (Maroncelli et al., 1985b). The shape of the infrared methylene scissors band near 1465 cm1 provides information about the methylene subcell. Normally the scissors band consists of either one or two components. If there is one component, the subcell is “parallel” (i.e. with polymethylene chain planes parallel to one another), as in M or T. If there are two components, the subcell is most likely O⊥. In that case, if the room-temperature separation between component bands is 10–11 cm1, and if the band widths are nearly equal, the subcell is the type found for the odd-numbered n-paraffins (Snyder et al., 1996). The relation between the methylene subcell and the shape of the 720 cm1 rocking band is qualitatively the same as that for the scissors band. Again the lower frequency limit of the methylene rocking vibration near 720 cm1 is well-defined and changes according to the methylene subcell type. If the chains are perpendicular to one another, the band is split; if they are parallel, it is a singlet. This information can be used to follow chain polymorphism, or be combined with powder X-ray data to identify polymorphs (Larsson, 1966). Certain C–H stretching modes

VIBRATIONAL SPECTROSCOPIC MEASUREMENTS

71

are also sensitive to the crystal structure as well as the presence of nonplanar chain conformers (Snyder et al., 1982; MacPhail et al., 1984). In certain situations, infrared spectroscopy determines whether the chains in a crystal are “in register,” that is, longitudinally ordered to form lamellar arrays. Outof-register (nematic-like) structures have been reported for pure n-C21H44 (Hagemann et al., 1987) or for a 1 : 1 C50/C60 solid solution (Zhang and Dorset, 1990a). Both were nucleated by vapor deposition onto a substrate. The transformation to an in-register, lamellar form was induced by annealing. For the former sample that transformation could be monitored by infrared spectroscopy, that is, by reaching a spectrum where all methylene rocking bands (1050–720 cm1 progression) appear as doublets (Snyder, 1961, 1979; Hagemann et al., 1987). The infrared or Raman spectra of different polymorphic crystalline phases of a sample differ in many ways. Hence a temperature plot of almost any spectral feature that can be expressed quantitatively will show an inflection when going through each phase transition. Detection of phase transitions has a sensitivity similar to that of DSC, as demonstrated for the crystalline n-alkanes (Maroncelli et al., 1982). Identification of infrared bands sensitive to the incorporation of nonplanar conformational defects in the chains (Snyder et al., 1981) revealed a number of intermediate phases that occur as the crystal is heated toward the rotator phase. Discontinuous changes in the infrared spectrum are observed. If certain sites along the n-alkane chain are labeled by deuterium, then the conformation around the adjacent ethylene bond can be identified by a characteristic absorption frequency (near 650 cm1). The relative intensity of the relevant gauche band is also directly related to the concentration of defects at a given chain site. The defect concentration for n-paraffins heated near the rotator phase is therefore highest at the chain ends, decreasing in concentration along methylene group positions moving toward the chain center (Snyder et al., 1983; Maroncelli et al., 1985a). Since the static defect energy for a kink is in the range 6.7–7.9 kcal mol1 (Boyd, 1975), there is a disadvantage to placing them in the center of the orthorhombic crystal structure. By contrast, interpretation of attenuated 00l diffraction intensities from heated n-paraffins (e.g. Fig. 4.5) can just as easily accept a uniform distribution of conformational defects along the chain as well as one where these defects are concentrated at the chain ends (Fig. 4.10). Due to the retraction of effective chain length by the inclusion of such defects, there will be partial vacancies created at the lamellar surface in either 3b

O

c

Fig. 4.10. An incorrect model for n-paraffin chains heated near the rotator transition illustrating, however, the geometry of included conformational defects. (Dorset, D. L., Moss, B., Wittmann, J. C., and Lotz, B. (1984) The premelt phase of n-alkanes: crystallographic evidence for a kinked chain structure. Proc Natl Acad. Sci. USA 81, 1913–1917.)

72

THERMOTROPIC DISORDER IN n -PARAFFIN CRYSTALS

case, and this alone accounts for the attenuation of the diffraction intensities. Initially, at lowest temperature, end-gauche defects are the most commonly observed deviation from an all-trans planar chain, an observation also confirmed by solid state nuclear magnetic resonance (NMR) measurements (Basson and Reynhardt, 1990, 1991). However, infrared and Raman measurements indicate that many chains retain an all-trans conformation in the rotator phase (Zerbi et al., 1981). The ratio of absorption intensity near 1300 cm1, compared to the peak at 890 cm1 can also measure the concentration of nonplanar chain defects. Observations on n-C50H102 and n-C60H122, which have no rotator phases, indicate the incorporation of nonplanar defects just below the melting point in a true pre-melting process (Kim et al., 1989a). These observations directly refute the so-called “kink-block” model for chain conformational defects, that would place these defects uniformly along the chain length (Blasenbrey and Pechhold, 1967)—for example, Fig. 4.10.

4.4 1.

2.

Summary The thermotropically disordered packing of polymethylene chains, or “rotator” phase, can be accommodated in a number of different layer packing types. Such disorder is encountered only within limited chain length regions and can also be influenced by isotopic substitution of D for H. While diffraction measurements have characterized the order of rotator phases, they have not been able to characterize fully their disorder. Vibrational spectroscopy has been much more successful for accurately describing the increased concentration of nonplanar chain defects near the chain ends as the n-paraffin crystal is heated toward its melting point.

5 Binary and multicomponent solids of n-paraffins

5.1

Introduction

Quantitative crystal structures of n-paraffin binary solids are of paramount importance for understanding chain packing in waxes. However, the early interpretation of binary phase diagrams (Piper et al., 1933; Mazee, 1957, 1958; Nechitailo et al., 1957, 1960; Topchiev et al., 1957; Turner, 1971) with powder X-ray diffraction measurements overlooked at least one important factor that contributes to the stability of solid solutions. Examination of a randomly oriented bulk powder sample did not permit mutual orientations of individual crystallites in a fractionated solid to be visualized. On the other hand, such information is accessible to transmission electron diffraction. Also, spectroscopic data have improved the structural model for such multicomponent solids by including the important contribution of conformational defects. In the following, rules for the stabilization of solid solution formulated by Kitaigorodskii (1961) (see Chapter 1) will be evaluated with newly available single crystal data from microareas. While the earlier-formulated volumetric rules are generally correct, the symmetry restrictions must be reconsidered.

5.2 5.2.1

Solid solutions Binary combinations

In an early powder X-ray diffraction study of n-paraffin binary solid solutions (Piper et al., 1931), only a single lamellar spacing was observed for each intermediate composition, its value dependent on the molar concentration. This was generally true unless the chain length difference were greater than four carbon atoms. Moreover, for intermediate concentrations, the resolution of the lamellar spacings was shown to be attenuated to just a small number of diffraction orders. When the difference in chain length was small, for example, two carbons, the lamellar spacings for the intermediate compositions could be plotted on a straight line (Vegard’s law). In other early work (Kitaigorodskii et al., 1958; Mnyukh, 1960), a near plateau in observed lamellar spacings was found for higher concentrations of a longer chain component, indicating, perhaps, that this longer chain length, by itself, was determining the average lamellar thickness.

74

BINARY AND MULTICOMPONENT SOLIDS

Various attempts were made to explain the disorder at the lamellar interface, implied by the attenuated resolution of 00ᐉ reflections in the powder X-ray patterns. Asbach et al. (1979) constructed models for calculating structure factors incorporating various longitudinally displaced chain lengths, with and without terminal conformational disorder. The former model, without defects, gave the best match to the observed intensity data. The n-C23H48/n-C24H50 binaries, investigated by Denicolo et al. (1984), revealed that the triclinic form of the pure even-chain paraffin exists only for solids with high concentration of either component; otherwise the binary structure was that of an orthorhombic layer. Binary combinations in two rotator phases, on the other hand, are continuous over all concentrations. A Gaussiantype function was used to model the disorder with fractional atomic occupancies at the lamellar interface (Craievich et al., 1984b). Very little change was observed in the lateral unit cell spacings with increasing composition, an observation confirmed by independent investigators for the n-C23H48/n-C25H52 binaries (Retief et al., 1985). It was originally thought that the previous odd-even chain combination should completely fractionate (Kitaigorodskii, 1961), whereas the odd-odd combination should be continuous. However, Mazee (1958b) also noted the continuous solubility of the odd-even combination: n-C35H72/n-C36H74, a claim disputed by Kitaigorodskii (1961). It is clear that, without single crystal diffraction measurements, the interpretation of powder diffraction data from n-paraffin binary solid will always be ambiguous. The first attempt to carry out a single crystal structure analysis of n-paraffin solid solution was made by Lüth et al. (1974) by X-ray diffraction for approximately 3 : 1 n-C20H42/n-C22H46. Although both pure paraffins pack in a triclinic unit cell (also the triclinic methylene subcell), the single crystal precession patterns clearly showed the unit cell geometry for the solid solution to be orthorhombic, space group Bb21m (equivalent to A21am when redefined so that a ⬇ 7.5 Å, and b ⬇ 5.0 Å). It was again clear that a statistical occupancy of the outer carbon positions was needed to explain the attenuation of 00ᐉ reflections. Claims of continuous co-solubility are in clear violation of Kitaigorodskii’s (1961) symmetry rules for the formation of stable solid solutions, since both the solid solution unit cell—and methylene subcell—symmetry are each higher than that of the pure components. However, a detailed phase diagram reveals that the triclinic structure is stable for binary solids only when the minor component is present at less than about 10 mol%. However, Kitaigorodskii et al. (1958) also recognized that the co-packing of dissimilar chain lengths in a triclinic polymorph could not maintain the efficient methyl packing of the layer interfaces, because of resultant vacancies at the chain ends. Only an orthorhombic layer structure could accommodate the molecular volume differences with least effect on internal energy. The first quantitative single crystal structure analysis of a solid solution structure was made from electron diffraction intensity data collected from a nearly 1 : 1 combination of n-C32H66/n-C36H74 (Dorset, 1990c). For the 0kᐉ electron diffraction pattern from epitaxially oriented material (Fig. 5.1), the sampled crystal structure resembled that of n-C34H66, in accord with Kitaigorodskii’s symmetry rules, that is, the space group symmetry Pca21 of the pure components was retained on average.

SOLID SOLUTIONS

(a)

Theoretical melting line

80

75

(b) 80

Melt

70

Solid solution, H subcell

70

60

Solid solution, H subcell Solid solution, O⊥ subcell

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 XC36

T (°C)

T (°C)

Melt

60

Solid solution, O⊥ subcell

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 XC36

Fig. 5.1. Electron diffraction (0kᐉ) of 1 : 1 n-C32H66/n-C36H74 solid solution (above). Binary phase diagrams (below): (a) n-C32H66/n-C36H74, with predicted melting line; (b) n-C33H68/ n-C36H74, with predicted melting line.

Unit cell constants for pure n-tetratriacontane (Nyburg and Potworowski, 1973) are: a  7.42, b  4.96, c  90.05 Å. The average value for c/2  45.77 0.67 Å is very close to the predicted value. Again using a chain occupancy model to account for the distribution of shorter chains within a lamella (Fig. 5.2), a reasonable match could be found to the observed intensities. The observed consistency of unit cell symmetry of this 1 : 1 solid solution with that of the pure components is deceptive, however. For n-C32H66/n-C36H74 and n-C33H68/n-C36H74 binaries (Dorset, 1985a), both combinations apparently form stable solid solutions over all concentrations (Fig. 5.1), the latter disagreeing with Kitaigorodskii’s (1961) continuous symmetry requirements, but substantiating Mazee’s (1958b) observation. Averages of lamellar spacings (c/2) for representative electron diffraction patterns (Fig. 5.3) duplicated the result shown by Mnyukh (1960), indicating that the longer chain component seemed to dominate the lamellar spacing when it was most abundant. However, attempts to explain the indices of the most intense 01ᐉ reflections did not support a single symmetry for all intermediate concentrations. When individual electron diffraction patterns were evaluated separately (Dorset, 1987a), the crystal structures for a single nominal concentration could be shown to vary greatly (Fig. 5.4) from microarea to microarea, sometimes

76

BINARY AND MULTICOMPONENT SOLIDS

1.0

p 0.5

17

15

13

11 9 7 5 Carbon number

3

1

(a) 50

(b) 50

1/2C (Å)

1/2C (Å)

Fig. 5.2. Carbon atom occupancy values 1-p indicated from a potential map (x). These values are somewhat overstated and should be multiplied, for example, by 1/4 (o) to give a better fit of the structural model to the observed intensity data. (Dorset, D. L. (1990) Direct structure analysis of an n-paraffin solid solution. Proc. Nat. Acad. Sci. USA 87, 8541–8544.)

45

42

45

0.5 XC36

1.0

42

0

0.5

1.0

XC36

Fig. 5.3. Experimentally measured average of electron diffraction lamellar spacings. (a) n-C32H66/n-C36H74; (b) n-C33H68/n-C36H74. (Dorset, D. L. (1985) Crystal structure of n-paraffin solid solutions:an electron diffraction study. Macromolecules 18, 2158–2163.)

resembling, on average, an even-chain paraffin structure, sometimes an odd-chain paraffin structure, that is, shifting locally from space group Pca21 to A21am. It can be shown that both layer packings contain the same monolayer. The only difference is the subtle relationship between the methyl end groups in successive monolayers in the bilayer unit cells. For any average layer packing mimicking paraffin n-CmH2m 2, the measured lamellar spacing is also very close to that of the pure n-paraffin, verifying the result of the indexing rule, ᐉ  m, 2m 2, for the two most

n-C32H66 /n-C36H74

(a) C36 0.2

C35 C34

0.1

C33

0.9 1.0

1.0

0.8

0.5 0.3 1.0 0.8

0.8

0.5 0.6

0.2

0.2

n-C32H66/n-C36H74

(b) 1.0

1.0 1.0

C36 1.0 0.5

C35

0.1

1.0 1.0

C34

1.0

0.6 1.0 0.4

1.0 1.0

C33

C321.0

0.5

1.0

C321.0

0

01

0.2

0.3 0.4

0.5

0.6 0.7

0.8 0.9

10

0

01

0.2

0.3 0.4

XC36

n-C33H68/n-C36H74

(c) 1.0

C35 0.3 1.0

C34 0.5

C33

0.5

0.6 0.7

0.8 0.9

10

XC36

0.5 0.6

1.0

1.0

n-C33H68/n-C36H74

(d) 1.0

0.5 0.4 1.0

1.01.0 0.7

C321.0–0.5

0.1

C35 C34

0.1

C33

1.0 1.0 0.9 1.0

1.0

0.9

0.4

0.8 1.0

1.0

0.6 1.0 1.0 0.2

C321.0

0

01

0.2

0.3 0.4

0.5 XC36

0.6 0.7

0.8 0.9

10

0

01

0.2

0.3 0.4

0.5

0.6 0.7

0.8 0.9

10

XC36

Fig. 5.4. Local microarea structures of solid solutions as indicated by indices of 0kᐉ electron diffraction patterns (see Fig. 3.11(c)). The samples in (b) and (d) correspond to (a) and (c), respectively, the difference being an aging of the sample for two years. (Dorset, D. L. (1987) Role of symmetry in the formation of n-paraffin solid solutions. Macromolecules 20, 2782–2788.)

78

BINARY AND MULTICOMPONENT SOLIDS n-C32H66/n-C36H74

n-C33H68/n-C36H74

48

49

47

48

46

47

ls(Å)

ls(Å)

(a)

45

46

44

45

43

44

42

43

0

0

0.2 0.4 0.6 0.8 1.0

0.2 0.4 0.6 0.8 1.0

XC36

XC36

(b) 48 C36 C34

46

C35

45

Measurement (Å)

Measurement (Å)

47

44 C33

43 42 42

43

44

45 46 Theor

47

48 (Å)

C30 40 C29

39 38

C28

37 37

38 39 40 (Å) Theor

Fig. 5.5. (a) Plots of lamellar spacing versus concentration for the individual structures identified in Fig. 5.4(b),(d); (b) correlation of the average lamellar spacings for index-identified structures to the spacing of the corresponding pure n-paraffin. On the right are the similar correlations of local structures found for a refined paraffin wax. (Dorset, D. L. (1987) Role of symmetry in the formation of n-paraffin solid solutions. Macromolecules 20, 2782–2788.)

intense 01ᐉ reflections (see Fig. 3.11(c)). Plots of lamellar spacings corresponding to local crystal structures indicate a step-like increase of these spacings (Fig. 5.5). The reason for local concentrations of average structures corresponding to either odd- or even-orthorhombic paraffin chain packings has been explained (Fig. 5.6) by the ease of transforming from one to the other by just a shift of some chains by one methylene group (Dorset, 1987a). Discontinuities in crystal structures for n-paraffin binary solid solutions have been investigated further. In fact, it is not possible to claim a continuous crystal structure for even–even, odd–even, or odd–odd combinations

SOLID SOLUTIONS (a)

79

n-C33H68 c

b (b)

c

n-C34H70

b (c)

n-C32H66 c

b

Fig. 5.6. Reason for the ease of transforming from one local crystal structure to another, including symmetry change. In (c) the initial even-chain structure packing can shift some chains by one methylene unit to give an average odd-chain like structure. (Dorset, D. L. (1987) Role of symmetry in the formation of n-paraffin solid solutions. Macromolecules 20, 2782–2788.)

(Dirand et al., 1996; Jouti et al., 1995a, b) and discontinuities may occur also for the lowest temperature rotator phase (Dirand and Achour-Boudjema, 1996). However, Mondieig et al. (2004) postulate continuity for n-C25H52/n-C27H56 binary solid solutions. A full three-dimensional X-ray structure of a binary paraffin solid solution was reported by Gerson and Nyburg (1994) using crystals grown by slow evaporation of solutions in n-dodecane. Least equivocal results were obtained from a sample of n-C24H50/n-C26H54. Although the initial concentration of the ingredients had been equimolar, gas chromatography indicated that the mole fraction of the shorter chain component in the crystal was 0.77. Cell constants were: a  4.992, b  7.503, c  67.448 Å, ␣  90.02, ␤  90.00, ␥  89.95. The space group was assumed to be orthorhombic, Bb21m (again, equivalent to A21am when cell axes are redefined), so that the solid solution symmetry was again larger than that of the pure components. The average crystal structure was claimed to mimic n-C27H56, that is, the average lamellar thickness was greater than that of the longest pure component. This implies that the longer chains retain an all-trans conformation and that methyl groups protrude into the interlamellar space. Similarly, a limiting chain length of n-C23H48 had been claimed for the n-C20H42/n-C22H46 binaries (Lüth et al., 1974). From the indexing rules given above for the most intense 01ᐉ reflections, the anticipated model for the n-C20H42/n-C22H46 binary should be n-C21H44; the n-C24H50/n-C26H54 binary should resemble n-C25H52. Also the observed lamellar spacings conform to the values for the respective pure n-alkanes (Nyburg and Potworowski, 1973). Another analysis of X-ray intensity set (Dorset, 1999c) from the latter binary (Gerson and Nyburg, 1994) reveals (Fig. 5.7) that the last carbon position in the model, accounting for the predicted average C27 chain length in space group A21am, cannot be justified in preference to the layer packing with a flat average lamellar surface. This implies that nonplanar chain conformers must exist near the chain ends

80

BINARY AND MULTICOMPONENT SOLIDS (a)

(b)

+O

+B

B/2

+O

+B

B/2

Fig. 5.7. Electron density maps, [1 0 0] projection for 3 : 1 n-C24H50/n-C26H54. (a) Using phases of Gerson and Nyburg (1994); (b) using new crystal structure (Dorset, 1999c). (Dorset, D. L. (1999) Electron crystallography of the polymethylene chain. 2. The lamellar interface of n-paraffin solid solutions. Zeitschrift f. Kristallograph. 214, 229–236.)

of the longer component, in accord with vibrational spectroscopic measurements of similar binary solids in this concentration range (Maroncelli et al., 1985b). Hence, the actual layer models must conform to the electron diffraction results. The crystal structure of a 3 : 1 n-C24H50/n-C26H54 solid solution was determined in three-dimensions from electron diffraction data (Dorset, 1999c) and correspond to the n-C25H52 orthorhombic structure in space group A21am, where c/2  33.26 Å. Fractional occupancies of atomic coordinates for the chain-end carbon atoms in a chain monolayer are displayed graphically in Fig. 5.8. Recently, an extensive effort has been made to give a more systematic view of binary n-paraffin packing by a combination of differential scaning calorimeter (DSC) measurements and powder X-ray diffraction. Since thermal measurements themselves are often insufficient for construction of phase diagrams, powder diffraction lines in the 2␪ range 34–60 (Cu K␣ radiation assumed) have been indexed to identify the average crystal structure of the material at mole fraction xB and temperature T (Rajabalee et al., 1999b). Examples include the study of odd-even and even-odd combinations of near chain length, for example, n-C18H38/n-C19H40 (Metivaud et al., 1998), n-C22H46/n-C23H48 (Nouar et al., 1997b, 1998a), n-C23H48/ n-C24H50 (Sabour et al., 1995; Nouar et al., 1997a), n-C25H52/n-C28H60 (Hammami and Mehrota, 1995), in addition to earlier studies by Mazee (1958a,b). Their phase diagrams have similar characteristics (Achour et al., 1998). Similarly, even–even combinations have been studied, for example, n-C20H42/n-C22H46 (Achour-Boudjema et al., 1996), n-C22H46/n-C24H50 (Achour et al., 1998), n-C24H50/n-C26H54 (Gerson and Nyburg, 1994; Achour-Boudjema et al., 1996), n-C26H56/n-C28H60 (Provost et al., 1998), and n-C44H90/n-C50H102 (Hammami and Mehrota, 1995). Also the odd–odd combinations have been characterized, for example, n-C21H44/n-C23H56 (Jouti et al., 1995b), n-C23H56/n-C25H52 (Jouti et al., 1995a; Rajabalee et al., 1999a,b),

SOLID SOLUTIONS

81



C /2 0

5

10

15

20

25

30

35

Measurement (Å)

Fig. 5.8. Fractional occupancies of solid solution in Fig. 5.7, indicating an average n-C25H52like structure. (Dorset, D. L. (1999) Electron crystallography of the polymethylene chain. 2. The lamellar interface of n-paraffin solid solutions. Zeitschrift f. Kristallograph. 214, 229–236.)

and n-C21H44/n-C23H48 (Jouti et al., 1995b). Again, the phase diagrams with a given chain parity paring are found to be very similar (Achour et al., 1998). An overview of binary phase diagrams with new examples has been published by Mondieig et al. (2004). The occurrence of small, but significant lateral unit cell expansions (e.g. n-C23H58/n-C25H52) has been described by Retief et al. (1985). Further studies of this lateral expansion have been discussed for other binaries by Chazengina et al. (1996). The attempt was made, therefore, to characterize these binary relationships in absolute terms, viz. a typical sequence of crystal structures for single phases. As an example, for n-C18H40/n-C19H40, the sequence of homogeneous and binary phase structures at low temperature with increasing xC19 might be (Metivaud et al., 1998): Tp → Tp Op → Op Mdci → Mdci → Mdci Oi → Oi The intermediate crystal form of n-C24H50/n-C26H54, studied by Gerson and Nyburg (1994) in space group Bb21m (equivalent to A21am with axial shifts) has been criticized by Rajabalee et al. (1999b) since it could not be justified from their indexed powder patterns. Electron crystallographic determinations, on the other hand, justify this unit cell assignment (Dorset, 1999c). This leads to a fundamental question. Can discontinuous low temperature binary phase diagrams of n-paraffins be drawn accurately from powder diffraction data? Powder X-ray measurements, sampling the crystalline bulk, imply that there is an average structure for any solid solution, and hence the domain boundaries, can be drawn (Rajabalee et al., 1999a,b). Electron diffraction measurements sample and reveal local microdomains. While a single crystal structure might dominate a given molar combination of n-paraffins, there are often two or more coexistent crystal forms (Dorset, 1987a) so that the lines between putative domains are blurred. Chevallier et al. (1999) have criticized electron diffraction studies of polydisperse n-paraffin samples deposited on a grid from evaporated dilute solutions to be somehow “non-representative” of the true material. Yet the same laboratory (Provost et al., 1998) has confirmed that binaries crystallized from dilute solution retain the

82

BINARY AND MULTICOMPONENT SOLIDS

same structures as those crystallized from the co-melt. There are also disagreements among X-ray diffractionists about the interpretation (indexing) of powder patterns (Mondieig et al., 2004). In our work, we have constantly maintained that the average structure measured by powder diffraction, despite the great care taken to index these patterns, may not reveal the complete picture about the binary (or multicomponent) crystalline mass. On the other hand, since electron diffraction does not easily obtain a complete overview of any solid mass, sufficient measurements must be made to build-up the most completely representative statistical distribution of structures in the material. At any rate, we do not draw phase diagrams in this book with the confidence exhibited by other laboratories (e.g. Mondieig et al., 2004) because we feel that this task is not possible. Indeed, even for pure n-paraffins, it has been shown (Chapter 3) that the energetic contribution to layer stacking is very small compared to that of the monolayer packing. With conformational defects at the lamellar interface in solid solutions, this component will be even smaller. This suggests that it may be more appropriate to consider just the layer packing when interpreting phase diagrams rather than space group symmetry. Does the distribution of local structures (in terms of space group) suggest the occurrence of “coring” in these solids so that cores of one average crystal structure would be surrounded by another packing resulting, for example, from the depletion of one component? Efforts to detect such a structural variation with adjacent 10 m diameter samples revealed that the local crystal structure in a region is reasonably uniform. On the other hand, alloy grains can have a continuously uniform structure for diameters up to 200 m (Gordon, 1968), so this question of coring may not yet be answered. For orthorhombic paraffins, the average lamellar spacing for a stable binary solid solution lies somewhat above the line connecting the lamellar spacings of the two pure components (as predicted by Vegard’s law). However, it is also clear that the longer chain component must be retracted somewhat in its total length to account for the average lamellar spacing. In the two concentration series mentioned above (n-C32H66/n-C36H74 and n-C33H68/n-C36H74), only about 2% kink concentration per average C–C single bond in the layer can be tolerated for the longer component before it jumps to the next longest average lamellar length (Fig. 5.9). Most of the conformational defects are again contained at the lamellar interface, as found also from vibrational spectroscopic measurements (Maroncelli et al., 1985b; Kim et al., 1989b) for thermotropically disordered lamellae in the previous chapter. For binary solid solutions, most of the conformational disorder is located in the longer chain component (Clavell-Grunbaum et al., 1997). Relative freedom of chain segment motion in the solid solution was also probed by solid state nuclear magnetic resonance (NMR) (Fenrych et al., 1997). Despite this disorder, surface decoration experiments and atomic force microscopy demonstrate that the paraffin solid solution surfaces are still, on average, atomically flat with enough of a crystalline order to nucleate the next chain monolayer (Dorset and Annis, 1996).

(b)

n-C32H66/n-C36H74

(1)

(a)

# Orders

20

n-C32H66/n-C36H74 C32 2

C33

C34

C35

C36

10

% Kinks/single bond

1 0

0.1

0.2

0.3

0.4

0

0.5 0.6 XC36

0.7

0.8

0.9

1.0

n-C33H68/n-C36H74 C33

C34

C35

n-C33H68 /n-C36H74

C36 (2)

2

20

0 0

0.1

0.2

0.3

0.4

0.5 0.6 XC36

0.7

0.8

0.9

1.0

# Orders

1 10

0

0.1

0.2

0.3

0.4

0.5 0.6 XC36

0.7

0.8

0.9

1.0

Fig. 5.9. (a) Maximal kink populations for structures suggested in Fig. 5.4(b),(d). In the calculation, enough kinks q were included in the longest chain to make it conform in length to the lamellar thickness or the largest average paraffin length that dominates the concentration domain. The number of kinks was divided by 33 to provide the average concentration over all internal bonds of n-C36H74 and is multiplied by the mole fraction of the longer chain component to give kink concentration per bond in the crystal structure. A limit of 2% is approached before transition to the next longest lamellar structure. (Note that the kink distribution really should be concentrated at chain ends.) (b) The resultant number of 00ᐉ diffraction orders for various binary concentrations of the respective solid solutions. (Dorset, D. L. (1987) Role of symmetry in the formation of n-paraffin solid solutions. Macromolecules 20, 2782–2788.)

84

BINARY AND MULTICOMPONENT SOLIDS

(a) (b)

60 55

Cnmax

50 45 40 35 30

25

30

35

40

45 Cnmin

50

55

Fig. 5.10. Two linear relationships describing the boundary between stable solid solutions and fractionated solids. (o) Earlier study of Mathiesen and Smith (1985); (x) study of Dorset (1990). (Dorset, D. L. (1990) Chain length and the co-solubility of n-paraffins in the solid state. Macromolecules 23, 623–633.)

The volumetric rule for a stable solid solution formulated by Kitaigorodskii (1961) seems to be useful for predicting the stability of n-paraffin binaries, at least up to chain lengths encompassing n-C37H76 (Dorset 1993). The limiting value for e  1 /r often seems to be near 0.84, although the stability of an n-C44H90/n-C50H102 series of solid solutions (e  0.86) depends on its thermal history (Hammami and Mehrota, 1995). Using available published data for paraffin solid solutions, Mathiesen and Smith max min (1985) had suggested a boundary line for stability: C m  1.224C m  0.411. With data available from solutions composed of longer n-paraffins (Dorset, 1990b), this min boundary line was shifted somewhat (Fig. 5.10) to C max m  1.33C m  7.22. It was once claimed that two greatly dissimilar length n-paraffins could form a solid solution by virtue of one length being half the longer one (Bonsor and Bloor, 1977). While this is not true for extended chain paraffin lamellae, there is a case to be made for when chains in one of the components can fold. For example, quickly quenched co-melts of polyethylenes of molecular weight 1000 and 2000, the latter folding in the lamellae, will form solid solutions (Smith and Manley, 1979). This observation has been verified recently for very long pure n-paraffins that can undergo chainfolding, for example, 1 : 1 (w : w) combinations of n-C162H326 with: n-C194H390, n-C210H422, n-C246H494, or n-C258H518 (Ungar and Zeng, 2001). Above a phase transition, binary phases exist with fully crystalline lamellae where ciliae from longer molecules protrude into an interfacial layer.

SOLID SOLUTIONS

85

The chain length difference between components also dictates how closely solid solutions mimic ideal behavior, for example, already implied by the observation of Piper et al. (1931) cited above. For example, this can be verified using the BraggWilliams theory (Lee, 1977) to interpret the experimental melting points of intermediate compositions of a solid solution. Combinations of all-hydrogenated n-paraffins with their equal chain length perdeuterated analogs follow ideal solution behavior upon melting (Dorset, 1991a). When it exists, the lower temperature orthorhombic to hexagonal (rotator) phase transition is also quite linear with composition, connecting the transition temperatures for the pure components. There is very little difference in molecular volume for the two analogs, approximately 0.5% per methyl group, with CD2 being smallest (Lacks, 1995). In a number of other stable binary solid solutions of all-hydrogenated paraffins (Dorset, 1990b), the melting line is nearly ideal, with nonlinearity seen for the rotator transition, when it exists. Nonideality of this latter pre-melt transition can occur if the chain length difference is as small as two carbons. For binary combinations, a variety of rotator phases exist as found for the pure n-paraffins (Sirota et al., 1992, 1995) although the RV phase is somewhat suppressed. Evidence has been found also for a re-stacking of RII from a trilayer to a bilayer structure (Sirota et al., 1992). Hengstenberg (1928) found that samples of n-paraffins of length n-C60H122 and higher did not diffract to include well-defined lamellar reflections and a “nematic” ordering of the chain packing was proposed, as discussed by Mnyukh (1960). Zhang and Dorset (1990a) found that binaries of n-C50H102/n-C60H122, epitaxially crystallized from the vapor phase, exhibited similar behavior, as did the pure ingredients (see Chapter 3). It was only after the samples were annealed in the presence of the nucleating substrate that stable lamellar structures be grown, leading to the expected spacings near the line defined by Vegard’s law. The significance of this finding will be apparent below when multicomponent paraffin waxes are described. 5.2.2

Multicomponent solutions

Multicomponent n-paraffin solid solutions are also found in certain refined paraffin waxes. Phase diagrams of ternary assemblies indicate regions where the composite crystal structure resembles pure components (e.g. near vertices) or where they adapt mixed phase structures similar to the binaries (Nouar et al., 1998b). One important source is crude petroleum with a high-molecular weight n-paraffin content, where a skewed Gaussian or normal logarithmic distribution of chain lengths in the wax can in respective distillate fraction (Edwards, 1957; Tegelaar et al., 1989). The other major source is synthetic, including routes for producing polyethylene catalytically from ethylene (Billmeyer, 1972), or the Fischer-Tropsch synthesis, where the combination of carbon monoxide with hydrogen forms an array of n-paraffins in the presence of a metal catalyst (Schulz, 1999). If the chain distribution is normal logarithmic, then the X-ray lamellar spacing will correspond to a pure paraffin somewhat larger (about one carbon atom) than the mean chain length value (Dirand et al., 2002).

86

BINARY AND MULTICOMPONENT SOLIDS

Refined petroleum waxes, in particular, have been extensively studied by physical probes. A number of highly refined products, as well as a hard microcrystalline wax from the asphaltene fraction, were examined by powder X-ray diffraction (Chichakli and Jessen, 1967) to reveal the orthorhombic subcell packing of the chain combinations. Transmission and reflection electron diffraction studies have revealed the orthorhombic layer packing (Nelson, 1933; Trillat and Hirsch, 1933; Rigamonti, 1936; Tanaka, 1938, 1940; Vainshtein et al., 1958). Electron microscopic observations revealed the screw dislocation growth of lozenges, found also in crystals grown from the pure ingredients. Crystallization of a diesel wax in a sectorized habit, very similar to that of chain-folded polyethylene, was shown by scanning electron microscopy (Bennema et al., 1992), even though the chain lengths of this wax are much too short to induce their folding. This habit can be grossly modified in the presence of certain additives, for example, pour point depressants such as stearyl methacrylate. Lamellar reflections were also observed in powder patterns from middle distillate waxes (Srivastava et al., 1992). In some cases, malcrystalline forms can be observed (Rhodes et al., 1927; Edwards, 1957; Zocher and Machado, 1959) in the form of needles that are actually rolled-up lamellae. These seem to be induced by the presence of iso-alkanes or aromatic alkane derivatives from the naphthene fraction. Fischer–Tropsch products have also been characterized in their lamellar forms. A fractional cut with a mean chain length near n-C28H58 has been extensively studied by NMR and powder X-ray diffraction (Lourens and Reynhardt, 1979; Basson and Reynhardt, 1992a,b). From this work, a four-domain model, as shown in Chapter 1, was proposed. In addition the behavior of various Gaussian distributions of n-paraffins centering at the same mean chain length but with different half-widths were compared to the measurements of the synthetic product. Several orders of lamellar reflections were observed when the distribution of chain lengths was very narrow but only one or two reflections were observed when it was wider (Basson and Reynhardt, 1992b). Crystal structure analyses on simulated and actual medium distillate cuts were based on electron diffraction data (Dorset and Basson, 2000). In all cases, an average lamellar structure was found with no indication of where a light oil fraction might be included into the lamellar interface. That single crystals of a petroleum wax could be epitaxially oriented to study their structures was first demonstrated (Dorset, 1987a) for Gulfwax®, one of the refined products originally investigated by Chichakli and Jessen (1967). Consistent with observations of the binary solid solutions, a number of local orthorhombic crystal structures were detected on the micron scale, each agreeing in lamellar thickness with the identified average (odd- or even-chain) n-alkane length (Fig. 5.5). Similar distributions were observed for other paraffin waxes examined subsequently. Powder X-ray analyses of multicomponent n-paraffin assemblies have indicated a sequential crystallization of solids as the material is cooled (Dirand et al., 2002) from the liquid state and held at successively lower temperatures. For example, a normal logarithmic distribution of C18-C36 with an average chain length of 23, initially crystallizes with an average carbon number of 32.5 0.5 when just crossing

SOLID SOLUTIONS

(a)

87

(b)

Fig. 5.11. Electron diffraction patterns from refined paraffin waxes. (a) From a birthday candle; (b) from a flat distribution of even-chain n-paraffins from C26 to C36.

the crystallization onset temperature. This converts to an average chain length of 31.6 at room temperature. A second crystallization gives an average chain length value of 27.4 0.4, transforming to a value of 26.8 at room temperature. A final crystallization gives an average length of 30.0 0.5, converting to 27.7 at room temperature. On the other hand, electron diffraction (Dorset, 1987) indicates that a commercial paraffin wax (“Gulfwax”) crystallized from the melt contains individual microdomains with structures similar to orthorhombic n-C28H58, n-C29H60, and n-C30H62, that is, analogous to findings for binary solid solutions. The lamellar spacings of the wax solid solutions correspond closely to those of the pure n-alkanes and the index rule for the 0kᐉ patterns correspond closely to those expected for the orthorhombic structures. In other words there are no crystal structures indicative of fractional carbon numbers. The first single crystal structure of a refined paraffin wax was determined (Dorset, 1995b) for microcrystals grown by epitaxially orienting a sample obtained from a candle (Fig. 5.11), presumably with a Gaussian distribution of chain length concentrations. The lamellar thicknesses were sharply distributed around n-C29H60 so that their diffraction patterns gave orthorhombic cell parameters: a  7.42, b  4.96, c  76.58 Å in space group A21am. The chain packing model (Fig. 5.12(b)), incorporating-chain end fractional occupancies, were in agreement with observed intensity data. This determination was compared to one made for an artificial wax comprising all the even-chain paraffins from n-C26H54 to n-C36H74 in a “flat,” or equimolar distribution of components. The average crystal structure, evaluated from electron diffraction patterns of epitaxially oriented samples (Fig. 5.11(b)), was n-C33H68, with cell constants: a  7.42, b  4.96, c  87.94 Å, retaining the same space group as before. Improved crystallization of the Gulfwax® permitted the structure determination to be carried out in projection from electron diffraction

88

BINARY AND MULTICOMPONENT SOLIDS c

b (a)

(b)

Fig. 5.12. Crystal structures of waxes in Fig. 5.11. (a) Flat wax; (b) birthday candle wax. (Dorset, D. L. (1995) The crystal structure of waxes. Acta Crystall. B51, 1021–1028.) (a)

XCn

0.2

0.1

31

32

33

34

35 36 Cn

(b)

37

38

39

Lamellar termination

Occupancy

0.2

0.1

31

32

33

34

35 36 Chain position

37

38

Fig. 5.13. (a) Simulation of chain length distribution of a wax with Mw/Mn  1.003; (b) the chain-end occupancy model used corresponds to a combination of all-trans chains, given the fractional chain distribution in (a). (Dorset, D. L. (2000) Chain length distribution and the lamellar crystal structure of a paraffin wax. J. Phys. Chem. B104, 8346–8350.)

SOLID SOLUTIONS

89

intensities (Dorset, 1997b). Although the average lamellar length was nearly equally distributed around n-C29H60 or n-C30H62, a pattern from the latter type was chosen in space group Pca21. The cell constants were: a  7.42, b  4.96, c  79.29 Å. The crystal structure again matched the observed intensity data reasonably well. Recently, a three-dimensional crystal structure based on electron diffraction intensities was completed for another commercial refined petroleum wax (Dorset, 1999d ). A three-dimensional structure was determined for another refined paraffin wax marketed by Fluka (Dorset, 1999d ). DSC measurement indicates this material to melt at 328K. The average lamellar structure resembles n-C31H64 packing in space group A21am, where a  7.46, b  4.97, c/2  41.2 Å. The non-unitary occupancies of the terminal carbon positions are revealed in the one-dimensional Fourier transform of the 00ᐉ structure factors. Vibrational spectroscopic measurements on multiple component paraffin solid solutions (Clavell-Grunbaum et al., 1997) indicate that the amount of conformational disorder, for example, for three-alkane solids, will occur for the middle chain length component. Upon heating the longer component will disorder most with increasing temperature. For a quarternary combination, the next-to-shortest chain length component was most disordered at room temperature. There are features of lamellar disorder expressed in the spectroscopic study of waxes that cannot be captured by crystallographic analyses. For example, Stokhuyzen and Pistorius (1970) described the chain length distribution of a wax that was later compositionally simulated (Fig. 5.13) for a three-dimensional electron diffraction determination (Dorset, 2000b). This analysis, furthermore, hoped to model the attenuation of low-resolution lamellar reflections by the known chemical composition of the chain assembly, assuming all-trans components. For such a narrow distribution (polydispersity Mw/Mn  1.003), this model was, in fact, successful. The model wax packed in space group A21am, where a  7.42, b  4.96, c  92.86 Å, similar to the n-C35H72 crystal structure in polymorph B (Fig. 5.14(a)). On the other hand, at a slightly higher polydispersity (1.009), a model wax in the n-C32H66 orthorhombic structure, packing in space group Pca21 (a  7.42, b  4.91, c  85.0 Å) (Fig. 5.14(b)), the all-trans compositional model was not successful (Rademeyer and Dorset, 2001). In this case the best fractional occupancy model was one that placed lower values at terminal carbon positions than predicted by the chemical composition (Fig. 5.15). Thus, all conformationally disordered carbon chain sites detected by vibrational spectroscopy need not lie on crystallographically repeated positions that would contribute to the Bragg reflections. (Other types of crystallographic disorder in these solid solutions have been detected by high resolution electron microscopy and include edge dislocations and growth boundaries, Fryer et al., 1997.) Following earlier models (Fisher, 1971; Strobl, 1972; Strobl et al., 1974), the relative interlamellar disorder for stable paraffin solid solutions can be assessed by an occupancy model for chain-end positions (Dorset, 2000a), corresponding to an effective interlamellar distance that would account for partial voids. From these phenomenological models, distinctions can be made between various classes of stable solid solutions. For example, binary solid solutions are less ordered than pure paraffins but ternary

90

BINARY AND MULTICOMPONENT SOLIDS c

(a)

+ +

b

c

(b)

+

+ O +

b

+

Fig. 5.14. (a) Crystal structure of the wax in Fig. 5.13. (Dorset, D. L. (2000) Chain length distribution and the lamellar crystal structure of a paraffin wax. J. Phys. Chem. B104, 8346-8350.) (b) Crystal structure of the wax in Fig. 5.15. (a) 14 12

Content (%)

10 6 6 4 2 0 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Carbon number (b) 1.0

Lamellar termination

Occupancy

0.8

0.6

0.4

0.2

0.0 22

23

24

25

26

27

28

29

30

31

32

33

34

35

Chain position

Fig. 5.15. (a) Chain length distribution of a wax where Mw/Mn  1.009; (b) chain occupancies used in the crystal structure. The statistical occupancy of all-trans chains (䉱 ) did not match the observed diffraction data whereas a random occupancy model (䊉) was more successful. (Rademeyer, M. and Dorset, D. L. (2001) J. Phys. Chem. B105, 5139–5143.)

MISCIBILITY GAP

91

solid solutions need not be less ordered than the refined multicomponent paraffin waxes (Dorset, 2000a). Although lamellar solid solutions exhibit most chain disorder near the lamellar interfaces, this, in itself, does not provide a complete picture of wax structure. Again, it also obscures the fact that the average lamellar surface of paraffin solid solutions is flat, as revealed, for example, by atomic force microscopy and surface decoration experiments (Dorset and Annis, 1996). Indeed the simple lamellar solid solution structure described here is not the only packing option open to the waxes, as will be discussed in the final chapter. 5.3 5.3.1

Miscibility gap Binary combinations

When the volume parameter e is somewhat less than 0.84, materials can be crystallized from the melt that initially resembles a solid solution Kitaigorodskii (1961). An example is the binary combination of n-C30H62 with n-C36H74 (Dorset, 1986b, 1990b). The electron diffraction pattern from freshly crystallized material (Fig. 5.16(a)), with a lamellar row attenuated in resolution, denotes the usual disorder at the lamellar interface described above. After the solid equilibrates at room temperature for a time, the resolution of the lamellar row increases with superlatticelike reflections appearing within the lamellar row (Fig. 5.16(b), (c)). Low-dose electron microscopy reveals the growth of another lamellar array in the initial solid (Fig. 5.16(d)). The positions of the superlattice reflections change with the composition of the solid although they are nearly constant for a given composition and can be predicted by a weighted random average of lamellar sequences for pure components. For freshly crystallized materials, the lamellar spacings lie very close to the line defined by Vegard’s Law (Fig. 5.17) and there appears to be two or more local crystal structures for any nominal concentration. Growth of a superlattice had originally been observed by Mazee (1958b) for binary combinations of n-C30H62 with n-C35H72 that had been equilibrated for a year. The C30/C36 binary combination, on the other hand, only requires two days to separate so that marked changes in the diffraction pattern are noted and combinations: n-C28H58/n-C34H70 or n-C32H66/n-C37H76 separate on a similar timescale (Dorset, 1990b). The line separating stable solid solutions from this slowly fractionating solid (Fig. 5. 18) is therefore rather sharp. A comparative study of the 1 : 1 n-C30H62/n-C36D74 binary by small angle neutron scattering (SANS) and small angle X-ray scattering (SAXS) (Annis et al., 1996) supports these observations. An initial intimate co-mixing of the protonated and deuterated chains evolves into a fractionated solid with separated n-C36D74, evidenced by the growth of a SANS Bragg peak with an 84 Å d-spacing. The short chain-length domain for the appearance of the superlattice in the presence of n-C36H74 as longest component was reported to include n-C28H58 to n-C31H64 (Gilbert et al., 1996a, 1999; Gilbert, 1999a,b). When nC 31, solid solutions are stable and when nC  28, eutectics were reported. However, as will be shown, there is a very sharp line

92 (a)

BINARY AND MULTICOMPONENT SOLIDS (b)

(c)

(d)

Fig. 5.16. Sequence of electron diffraction patterns from 1 : 3 n-C32H66/n-C37H76. (a) Initial solid solution; (b) increase in resolution as mixing endotherm appears; (c) appearance of superlattice; (d) domains of superlattice (IS) in a n-C30H62/n-C36H74 metastable solid solution (SS) undergoing fractionation. (Dorset, D. L. (1990) Chain length and the co-solubility of n-paraffins in the solid state. Macromolecules 23, 623–633.)

defining the chain length differences separating binaries that will actually crystallize within a miscibility gap from those crystallizing as eutectics of solid solutions. The boundary exists at n-C30X62/n-C36X74, for example, where X  D, H, and depends on the isotopic identity of the shorter chain (Fig. 5.18). Calorimetrically, the fractionation is characterized by a small endotherm (Fig. 5.19(a)). The magnitude of its transition enthalpy depends on composition, much like the Tammann (1925) rule for eutectics. However, this phase separation is not a eutectic process. Calculation of a theoretical eutectic temperature by the Schroeder-Van Laar equation (Fig. 5.19(b),(c)) does not predict the position of the characteristic endotherm (while the prediction is quite accurate for eutectoid or true

MISCIBILITY GAP (a)

93

(b)

C30 /C36

50

l s (Å)

l s (Å)

50 40

40 30

(c)

C36 C35 C34 C33 C32 C31 C30

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 XC36

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 XC36 (d)

c30 / c36 3 22 11 88 7

93 4

3

7 5 13

2 10

14

5 1 3

3 8 5

4

1

5

8 10

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 XC36 (e)

(f)

l s (Å)

15

10 0.5 XC

1.0

Fig. 5.17. Metastable C32/C37 system. (a) X-ray lamellar spacings of modulated superlattice (strongest lamellar reflections); (b) average electron diffraction lamellar spacings; (c) apparent crystal structure when the most intense lamellar spacing is compared to 01ᐉ reflections (see Fig. 3.11(c)); (d) simulated superlattice model; (e) Fourier transform of (d); (f) sequence of model lamellar spacings (from Fourier transforms similar to (e)) versus concentration—compare to (a) and (b)) versus. concentration. (Dorset, D. L. (1990) Chain length and the co-solubility of n-paraffins in the solid state. Macromolecules 23, 623–633.)

eutectic combinations, as will be shown below). An interesting case for incompletely mixed n-C44H90/n-C50H102 chains has been discussed (Hammami and Mehrota, 1995) where the eutectic temperature is predicted by the Schroeder-Van Laar equation but the eutectic composition is not. The partially determined phase diagram actually corresponds to a miscibility gap. The observations are all consistent with the occurrence of a miscibility gap, since the transitions are rather sluggish and superlattice type solids are produced (see Amelinckx and Van Dyck, 1993).

94

BINARY AND MULTICOMPONENT SOLIDS

C37 Fractionated solid C30 H62 / C36 H74 C36

C30 D62 / C36 H74

1 C30 H62 / C36 D74 C30 D62 / C36 D74

C35 Cn
= 1.20 Cn–1.60 C30 D62 / C35 H72 Cn


C34

Metastable solid solution

C30 H62 / C34 H70 Stable solid solution

C30 D62 / C34 H70 C33

C30 D62 / C33 H68

C32

C30 D62 / C32 H66

C31 C28

C29

C30

C31

C32

Cn

Fig. 5.18. Plot of Cn versus Cn
indicating binary phase behavior and defining three domains. These are the boundaries between stable solid solutions and metastable solid solutions and between metastable solid solutions and eutectics. (Dorset, D. L. and Snyder, R. G. (1995) H-D isotope and chain length dependence of phase separation in quenched n-alkane binary combinations in the crystalline state. Macromolecules 28, 8412–8418).

Vibrational spectroscopy has also been a successful tool for studying phase separation of n-alkanes. An infrared method for determining and monitoring lateral compositional heterogeneity in crystalline mixtures of polymethylene chains has been described by Snyder et al. (1992). The heterogeneity may involve microdomains, such as that occur in the early stages of microphase separation in metastable solid solutions or may involve a number of essentially homogeneous phase coexisting near to, or at, equilibrium. This method has characterized component separation in n-alkanes (Snyder et al., 1992, 1994), and alkyl methyl esters (Snyder et al., 1995).

MISCIBILITY GAP

95

(a) T
on

T
max

T

H CH 30/C36

X36 = 0.46

30

40

50 60 70 Temperature (°C)

Melt n: H lutio bcell o s su id Sol ylene h t me Solid solution O⊥ methylene subcell

70

T (°C)

90

Theoretical melting line

(b)

Theoretical eutectic point

60

50

Fractionated solid, O⊥ methylene subcell 0

(c)

80

0.1

0.2

0.3

0.4

0.5 0.6 XC36

0.7

0.8

0.9

1.0

80 Melt 70

T (°C)

Solid so H methylution subcellel ne

Solid solution O⊥ methylene subcell

60

Fractionated solid, O⊥ methylene subcell

50 0

0.1

0.2

0.3

0.4

0.5 X

0.6

0.7

0.8

0.9

1.0

Fig. 5.19. Appearance of mixing endotherms for (a) two combinations of C30/C36. An apparent isotherm due to this small endotherm is not predicted by the Schroeder-Van Laar equation for eutectics as in typical metastable solid solutions; (b) C30/C36; or (c) C32/C37. (Dorset, D. L. (1990) Chain length and the co-solubility of n-paraffins in the solid state. Macromolecules 23, 623–633.)

96

BINARY AND MULTICOMPONENT SOLIDS

CH 30 domain

D CH 30 isolated in C36 domains

Absorbance

L

∆

CH 30 bands

1485

1475

1465 1455 Frequency (cm–1)

1445

Fig. 5.20. Use of CH2 scissors band information for definition of isolated chains or growth of domains. (Snyder, R. G., Goh, M. C., Srivatsavoy, V. J. P., Strauss, H. L., and Dorset, D. L. (1992) Measurement of the growth kinetics of microdomains in binary n-alkane solid solutions by infrared spectroscopy. J. Phys. Chem. 96, 10008–10019.)

The method requires that the methylene subcell should be orthorhombic perpendicular, which is usually the case for n-paraffin mixtures. In addition, one of the components should be perdeuterated. Normally this isotope substitution is made for the component for which aggregation is to be measured. The degree to which this component is aggregated can be derived from the shape of the CD2 scissors band near 1085 cm1. (Alternatively if CH2 is isolated within CD2, the scissors band is detected near 1470 cm1.) In addition, some information about the average state of aggregation of the hydrogenated component(s) can be obtained from the shape of the CH2 band. The shape of the scissors band is sensitive to chain aggregation because the lateral interchain vibrational coupling of a given isotope is disrupted by the presence of chains of the other isotope, this because hydrogenated and deuterated chains do not interact through vibrational coupling. One can therefore estimate the average domain size from the magnitude of splitting of the CD2 and CH2 bands (Fig. 5.20). In a mixture that contains mainly hydrogenated chains, each deuterated chain in the minor component is surrounded by hydrogenated chains. An isotopically isolated, co-solubilized, deuterated chain therefore represents the smallest possible domain. In that case the CD2 scissors band consists of a single component—because there is no possibility of interchain coupling. At the other extreme, the mixture of two components has undergone complete phase separation. It now consists of effectively infinite domains of hydrogenated and

MISCIBILITY GAP

97

deuterated chains, respectively. The splitting observed will be the same as that for isotopically pure components, for example, about 10.6 cm1 for CH2 and about 5.7 cm1 for CD2 at room temperature. Any mixture that displays this amount of splitting can be assumed to be completely phase-separated. Intermediate states of chain aggregation yield intermediate degrees of splitting. A quantitative relationship between splitting and aggregate size has been worked out, so that the measured value of the splitting can be used the average size of the aggregates (Snyder et al., 1992). More complete information about the state of aggregation is available from the shape of the scissors band. This can be evaluated by comparing the shape of the scissors band for a given mixture to the shapes observed for reference materials, that is, randomly mixed hydrogenated and deuterated chains at various H/D concentration ratios. If the shape of the scissors band can be simulated by the corresponding band of one of the pure reference materials, then the component can be assumed to be “dissolved” in the mixture, that is, randomly distributed. If a combination of scissors bands from more than one of the reference materials is needed to match the observed band, then it can be concluded that the particular component is found in more than one phase. The compositions of the various phases can be estimated by extending this approach. Raman spectroscopy via perdeuterated probes was used to follow the phase separation (Snyder et al., 1992, 1994) and remixing (Snyder et al., 1993). At first, comparison with electron diffraction results, as well as neutron and low-angle X-ray measurements (Annis et al., 1996), was confusing. Vibrational spectroscopic data were interpreted in terms of lateral domains growing in the solid, while the change detected by diffraction measurements was a longitudinal separation. Recently this confusion was resolved after the crystal structures of two such solids were determined (Dorset and Snyder, 1996) from electron diffraction intensities. After crystallographic phases were assigned to the lamellar reflections from the equilibrated solid, it was clear, from the relative depths of density wells between average lamellar densities, that not all lamellae could be infinitely wide but that some also had to be restricted laterally (Fig. 5.21). For 3 : 2 and 2 : 3 combinations of n-C30H62 with n-C36H74, therefore, models (Fig. 5.21) were derived that explained the total diffraction patterns very well, again reconciling earlier diffraction and spectroscopic data. The crystal structure no doubt approximates an incommensurately modulated solid. It was also noted that there was an isotopic sensitivity to the observation of this sluggish phase separation (Snyder et al., 1994; Dorset and Snyder, 1995). Phase diagrams and electron diffraction patterns from n-C30H62/n-C36H74, n-C30H62/n-C36D74, and n-C30D62/n-C36D74 are all similar (Figs 5.22 and 5.23) but the phase diagram of n-C30D62/n-C36H74 is that of a eutectic solid (discussed in the following section). Since the volume difference between (CH2) and (CD2) is only 0.5%, the total molecular volume reduction of the smallest chain length component, if perdeuterated, is just enough to induce a more rapid fractionation of the components (Snyder, et al., 1992, 1994). The phase separation of n-C30H62/n-C36D74 also can be enhanced, however, when this solid is adsorbed to graphite (Gilbert et al., 1996b). In the absence of this influence, the boundary between metastable solid solutions and the eutectic solids is

98

BINARY AND MULTICOMPONENT SOLIDS (a)

b

(b) C36

c C36

C36

C30

C30

C36

C36

C30

0 C36

C30

0

100

50

150

200

250

d (Å) (c)

A

B

C30

C36

C30

C30 /C36 0.41/0.59

C30 /C30 0.61/0.39

Fig. 5.21. (a) Longitudinal sequence of chain layers in fractionated modulated C30/C36 structures; (b) crystal structure of C30/C36 fractionated solids; (c) block arrays of chains suggested for two concentrations of C30/C36. (Dorset, D. L. and Snyder, R. G. (1996) Crystal structure of modulated n-paraffin binary solids. J. Phys Chem. 100, 9848–9853.)

again rather sharp (Fig. 5.18). It is also interesting to note that dramatic isotope effects can occur at mean molecular weights well below the values (e.g. chain-folded polymer range) where isotopic segregation was originally predicted (Buckingham and Hentschel, 1980). The isotope effect appears to be more of a function of decreased molecular volume due to reduced zero-point vibrational energy for the deuterated species, than to the effect of decreased C-H(D) bond lengths (Lacks, 1995).

MISCIBILITY GAP (a)

(b) Melt

70

T (°C)

70

T (°C)

99

60

Hexagonal

60

Orthorhombic 50

50

Mixing endotherm 0

0.5 XC36H74

1.0

0

60

70

T (°C)

(d) 80

T (°C)

(c) 70

50

0

0.5 XC36D74

1.0

1.0

60 50

40

0.5 XC36D74

0

Mixing endotherm 0.5 XC36H74

1.0

Fig. 5.22. Phase diagrams for C30/C36 combinations illustrating isotope effects. (a) C30H62/ C36H74; (b) C30H62/C36D74; (c) C30D62/C36D74; (d) C30D62/C36H74. (Dorset, D. L. and Snyder, R. G. (1995) H-D isotope and chain length dependence of phase separation in quenched n-alkane binary combinations in the crystalline state. Macromolecules 28, 8412–8418).

It is obvious that the phase separation for a solid held in a miscibility gap requires chain diffusion. The prospects for transverse and longitudinal diffusion modes were investigated theoretically by Farmer and Eby (1987), who stated that lattice vacancies must migrate. Lateral diffusion could accommodate paraffin chains as rigid rods whereas the longitudinal diffusion would involve a more complicated conformational jog of the chain across a lamellar interface. Using radioactive tracers, Narang and Sherwood (1980) measured the self-diffusion in crystals of n-C20H42. Although quite different diffusion constants were found for the two modes, it was not certain what influence crystal defects would have on these measured quantities. Nevertheless, optical studies (Yamamoto and Nozaki, 1995; Yamamoto et al., 1997) have established that molecular diffusion in perfect crystalline areas is quite possible, especially when the chains are in the rotator phase. A classic study of interlayer diffusion in co-sediments of pure n-paraffins was made by Ungar and Keller (1979), who monitored the changes via powder X-ray diffraction and DSC. Interlayer mixing was observed at temperatures well below that of the rotator phase transition and were enhanced by elevated pressure. The co-mixing, moreover, could not be correlated to any known transition temperature. Although the longitudinal diffusion mechanism was not specified, it was postulated that chain

100

BINARY AND MULTICOMPONENT SOLIDS (b) 50

(a)

ls (Å)

ls (Å)

50

40

45

41 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

XC36H74

XC36D74

(c)

(d) 50 ls (Å)

ls (Å)

50

40

40 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

XC36D74

XC36H74

Fig. 5.23. Plots of average lamellar spacing with increasing concentration of C36 in C30/C36 binaries: (a) C30H62/C36H74; (b) C30H62/C36D74; (c) C30D62/C36D74; (d) C30D62/C36H74. (Dorset D. L. and Snyder, R. G. (1995) H-D isotope and chain length dependence of phase separation in quenched n-alkane binary combinations in the crystalline state. Macromolecules 28, 8412–8418).

protrusions from one layer to the next would be facilitated by vacancies on apposing layers, citing earlier work by Strobl et al. (1974). Longitudinal interlamellar chain diffusion is also proposed to explain the structure of certain diesel waxes (Craig et al., 1998, 1999). A sequence for fractionation has been proposed by Gilbert (1999). First it is clear from diffraction evidenced that quenching from the melt produces uniform lamellae in the initial solid. Voids within the solid solution would then promote migration of longer, and conformationally more disordered chains. Since the activities for longitudinal diffusion is four times less than for lateral diffusion (Dorset and Snyder, 1996), the former mode is preferred so that a system of alternating chain sequences is formed. As the longitudinal diffusion progresses so does the aggregation of similar length chains into lateral domains. Finally, further ordering (e.g. transition from gauche to trans at chain ends) will complete the ordering process. This involved scheme is very interesting but does not explain how the average solid solution can be reformed very quickly by annealing the fractionated solid at the small peak of the so-called “mixing” endotherm, for example, near 45C, while an orthorhombic layer packing is still maintained (Snyder et al., 1993). In their determination of the

EUTECTIC SOLIDS—PARTIAL CO-SOLUBILITY

101

kinetics of phase separation for these metastable solid solutions, Snyder et al. (1992) followed the lateral growth of segregated components by vibrational spectroscopy while the longitudinal separation has been detected primarily by diffraction techniques. It is difficult to compare these observations. Remixing of the separated solid initially involves an increase of conformational disorder at the small mixing endotherm is approached and complete co-solubilization occurs as the peak temperature is reached (Snyder et al., 1993). Again, how do these observations account for the creation of an average lamellar solid solution from a rather complicated superlattice structure? Recently, Sirota (2001) has interpreted low-angle X-ray data from such systems, invoking a longitudinal diffusion model to explain the entropic microphase separation. 5.3.2

Multicomponent combinations

A miscibility gap can also be found for a three-component solid, where the combination of two ingredients behaves initially as if it is a “pseudo-component.” For example, the flat (i.e. 1 : 1 : 1) distribution of n-C28H58, n-C32H66, and n-C36H74 initially behaves like a solid solution when it is recrystallized from the melt (Dorset and Snyder, 1999a). The small de-mixing endotherm appears when the solid equilibrates, coincident with the appearance of superlattice reflections in the electron diffraction pattern. However, the resolution increase of low-angle lamellar reflections in this pattern is not as extensive as was observed for the n-C30H62/n-C36H74 binaries. Determination of its crystal structure, reveals that the initial phase separation crystallizes out lamellae of solid solutions, rather than pure ingredients. However, after equilibrating the solid for over a year, there are further changes in the pattern, including a resolution increase of the 00ᐉ row. Solution of the crystal structure from this new dataset (Dorset and Snyder, 1999a) now indicates that nearly pure lamellar segments have separated. In this phase separation, the equimolar combination of n-C28H58 and n-C32H66 behaves as if it were a pseudo- n-C30H62 ingredient in the presence of n-C36H74 (Fig. 5.24).

5.4

Eutectic solids—partial co-solubility

The next step encountered, as the volume difference between chains increases, is the eutectic separation of two paraffins that are still partially co-soluble. The phase diagram is characteristic and the liquidus curve can be predicted reliably with the Schroeder–Van Laar equation (Fig. 5.25), given the heats of fusion for the two components. Electron diffraction patterns (Fig. 5.26) again indicate a superlattice component is present with spacings that are relatively invariant with concentration (Dorset, 1985a). Plots of lamellar distances, therefore, reveal constant spacings over large concentration ranges (Fig. 5.27). Superlattice domains, therefore, can coexist with domains that are nearly pure shorter or longer chain components. This was initially

(a)

C33

(c)


2 mW

C /2 0

10

20

30

40

50

60

70

80

90

T (°C) (b) C34

(d)

C31

C34

C33




C /2

(1) (e)


C36

C28

C36

C28 c36 c32

C36

C36

C28

C36

c32 c28

C /2

(2)

Fig. 5.24. Three-component arrangement of 1 : 1 : 1 C28/C32/C36. (a) Growth of mixing endotherm; (b) sequence of diffraction patterns after initial solid solution begins to fractionate; (c) initial solid solution structure; (d) structure of first fractionated solid; (e) final fractionated solid. (Dorset, D. L. and Snyder, R. G. (1999) Phase separation of a metastable three-component n-paraffin solid solution. J. Phys. Chem. B103, 3282–3286.)

EUTECTIC SOLIDS—PARTIAL CO-SOLUBILITY (a)

(b)

T (°C)

80

Melt

70

Pure C40H82 +Liquid

60

Theoretical eutectic C40H82 + Eutectic, mixed O⊥ and H methylene subcell

T (°C)

80

60

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 XC44 (d) 100

Pure n-C60H122 + Liquid

80 70

n-C60H122 + Eutectic O⊥ methylene subcell

60

Pure n -C50H102 + Liquid

80 70

n-C50H102 + Eutectic O⊥ methylene subcell

60

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 XC60

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 XC50 (f) 100

(e)

Melt

90

T (°C)

Melt

90

Theoretical eutectic

50

C40H82 + eutectic, O⊥ methylene subcells

(c) 100

Melt

70

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 XC40

T (°C)

103

Melt

90 90 80 70

Melt Pure n-C60H122 + Liquid n -C60H122 + Eutectic O⊥ methylene subcell

T (°C)

T (°C)

100

80

Pure n-C60H122 + Liquid

70 60

H methylene subcell

50 n-C60H122 + Eutectic, O⊥ methylene subcell

60 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 XC60

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 XC60

Fig. 5.25. Binary phase diagrams of eutectics: (a) C30/C40; (b) C28/C44; (c) C38/C60; (d) C40/C50; (e) C28/C60. All liquidus curves are predicted by the Schröder-Van Laar equation. (Dorset, D. L. (1990) Chain length and the co-solubility of n-paraffins in the solid state. Macromolecules 23, 623–633.)

verified by image analysis of low dose electron micrographs, using reflections characteristic of the superlattice component or the single ingredient. More recently a high-resolution lattice image (Fig. 5.28) was obtained (Zhang and Dorset, 1989b) that revealed clearly the need for a tight epitaxial boundary between the two domains, that is, the meeting at methyl end planes. The crystal structure of a 1 : 1 n-C30H62/n-C40H82 solid has been determined recently (Dorset, 1997c). The lamellar repeat of the (nearly) pure n-C40H82 component can be separated from the intensity data from the superlattice and can be used to verify the structure of this domain. The layer packing in the superlattice is very similar to the one found for n-C30H62/n-C36H74 (Fig. 5.29), containing both a lateral and longitudinal separation of pure ingredients.

104

BINARY AND MULTICOMPONENT SOLIDS

(a)

(c) 0.5 Å–1

0 b*

c*

(b)

0.3 Å–1

0

Fig. 5.26. Electron diffraction of C30/C40 eutectic. (a) Nearly pure C40 domain; (b) superlattice of C30/C40; (c) schematic representation of 0kᐉ superlattice pattern showing strong “solid solution” reflections and weaker superlattice reflections. (Dorset, D. L. Crystal structure of an n-paraffin binary eutectic solid. An electron diffraction determination. J. Phys. Chem. B101, 4870–4874.)

C30 / C40

C28/ C36

(b) 50

50

l s (Å)

l s (Å)

(a) 60

40

30

45

40

35 0

0.5 XC40

1.0

(c)

0 (d)

C28/ C36

0

0.5 XC36

1.0

90 80

7

7

l s (Å)

1 4 3 5 5 7 9 6 6 C36 C34 C32 1 2 1 1 1 1 C30 1 3 4 1 2 2 4 1 13 1 2 C28 35 3 8 1 2

0.5 XC30

70 60 50 40

1.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 XC60

Fig. 5.27. Lamellar spacings observed in X-ray diffraction patterns from eutectics in Fig. 5.25. (Dorset, D. L. (1990) Chain length and the co-solubility of n-paraffins in the solid state. Macromolecules 23, 623–633.)

EUTECTIC SOLIDS—PARTIAL CO-SOLUBILITY

105

Fig. 5.28. High-resolution lattice image of C30/C40 eutectic showing boundary between superlattice and nearly pure C40 phase. (Dorset, D. L. (1997) Crystal structure of an n-paraffin binary eutectic solid. An electron diffraction determination. J. Phys. Chem. B101, 4870–4874.)

(a)

C40

C30

 (z)

C30

0

10

20

30

40

50

60

70

80

90

Z (Å) (b) C30 \ C40 1 : 1

Fig. 5.29. Crystal structure of the superlattice solid in C30/C40. (a) Analysis of lamellar sequence; (b) model block structure for chain domains. (Dorset, D. L. (1997) Crystal structure of an n-paraffin binary eutectic solid. An electron diffraction determination. J. Phys. Chem. B101, 4870–4874.)

106

5.5

BINARY AND MULTICOMPONENT SOLIDS

Eutectic solids—no co-solubility

Eventually, as the volume difference becomes very large, the two n-paraffins are no longer co-soluble. A characteristic phase diagram for n-C28H58/n-C44H90 is represented in Fig. 5.25 and the liquidus curve is again predicted acurately by the Schroeder-Van Laar equation (Dorset, 1990b). The primary and secondary crystallization of pure components can be observed directly by light microscopy, indicating oriented overgrowth of one component on the other. Plots of lamellar spacings from X-ray powder diffraction data, for example, for the n-C28H58/n-C60H122 binary (Fig. 5.27) reveal the presence of only two pure components over the whole concentration range. The proposed co-solubility of chains, where one component is nearly half the chain length of the other (Bonsor and Bloor, 1977) has also been shown by other authors (Petitjean et al., 2002) to be in error. Although detailed electron diffraction determinations of such totally separated binary solids have not been undertaken, the structure of the solid can be inferred easily from the above study of eutectics formed from solid solutions. That is, there will be two domains of pure material with an exact epitaxial interaction across boundary methyl end planes. The nature of this interaction is also clear from the study of n-paraffin/diluent eutectics for which an epitaxial relationship exists between the two components (Dorset et al., 1989).

5.6

Effect of chain folding on phase separation

As mentioned above, there are fewer constraints on relative chain lengths for the stabilization of solid solutions when chain folding is permitted (Ungar and Zeng, 2001). However, for some combinations, for example, C162 with C210, a metastable “semicrystalline” solid will fractionate into a more ordered triple layer phase. It is possible that the chain packing then forces the projecting cilia of the interlayer between crystalline layers to crystallize, so that the sandwiched interlayer is also strictly crystalline (Zeng and Ungar, 2002). The thicker lamellae contain both short and long chain components. This new crystallization phenomenon occurs for a binary combination with a chain length ratio between 1.3 and 1.7 and a component molar ratio near 1.1. In this case, the triple layer superlattice will be the stable low temperature form. When, however, the chain length ratio is lower, the triple layer superlattice is not observed, for example, in C162 and C194 alkanes. The structure of the low temperature solid has not been determined, however. Chain folding has also been incorporated into the model for fractionated diesel waxes (Craig et al., 1998). This model, however, is inconsistent with the extended chain packing anticipated for the typical paraffin molecular weights involved in such assemblies.

SUMMARY

5.7

107

Conclusions

From the above considerations, it is clear that a sequence of crystal structures characterizes the transition from stable solid solutions to fully phase-separated eutectics, when the volume difference between the chains is the continuous variable. In all cases, the primary concern is to minimize non-overlap volume in order to achieve a stable solid state structure. For stable solid solutions, this is possible through a combination of translational disorder of nearly cylindrically symmetrical molecules and the accumulation of nonplanar conformational disorder at the chain ends. This situation is initially true for metastable solid solutions, grown from the melt, but unraveling of the conformational defects makes the volumetric differences between components more apparent so that they must separate by some, as yet undefined, diffusion process to a more efficient packing of laterally and longitudinally separated lamellae. A similar superlattice also exists for the eutectic solids formed from solid solutions but is epitaxially matched to another domain of a nearly pure component. Finally the pure components themselves will be tightly associated across this methyl end-plane interface. In none of these structures is the concept of a “mechanical mixture” appropriate.

5.8 1.

2.

3. 4.

Summary The volumetric constraint for stabilization of n-paraffin solid solutions is in accord with Kitaigorodskii’s observations, so long as the chains remain extended (unfolded). The crystal structure of binary and multicomponent solid solutions (including refined paraffin waxes) is lamellar, wherein a stable average chain stem structure is maintained. However, there is no continuity in space group symmetry for a concentration series of solid solutions. In fact, crystal structure analyses reveal that adjacent microareas can crystallize in different space groups. Vibrational spectroscopic measurements reveal that the chain-end regions of solid solution lamellae are stablilized by conformational disorder in order to form a strictly flat boundary lamellar surface. Otherwise extended chains are assumed. Chain-folding greatly extends the chain length difference stabilized in a solid solution. In terms of volumetric difference between chains, a sharp boundary exists between stable solid solutions and fractionated mixtures within a miscibility gap. Crystal structures reveal that the phase separation within the miscibility gap involves both lateral and longitudinal chain segregation. These structures appear to be incommensurately modulated.

108

5.

BINARY AND MULTICOMPONENT SOLIDS

Across another sharp volumetric boundary line from the binaries exhibiting miscibility gaps, eutectic structures occur. These incorporate a block of a nearly pure phase with a superlattice similar to the one described for miscibility gaps. The border between these domains is epitaxial so that “mechanical mixtures” do not exist for n-paraffin eutectics.

6 Some functional substitutions in n-paraffins

6.1

Introduction

It is useful to consider a polymethylene chain where one or more atoms in the chain are substituted by a heteroatomic species, in order to determine the resultant volumetric effects on molecular conformation and layer packing. The replacement of hydrogen by deuterium has already been discussed in previous chapters. Total replacement of hydrogen by fluorine produces the perfluoroalkanes, chains that are neither hydrophilic nor oleophilic. In other instances, an individual methylene unit can be replaced by an oxygen or a sulfur to form, respectively, a dialkyl ether or sulfide. As mentioned earlier, replacement of a terminal methyl group by a bromine or iodine can often generate nearly isomorphous crystalline analogs. For lamellar packing, chain substitutions simply require the lateral surface area used to pack the substituent group should be matched by the methylene chain packing, that is, the subcell type and chain tilt are varied to achieve this balance. In some cases, such a match of cross-sectional areas might demand an interdigitation of chain ends to compensate for a particularly bulky substituent—a concept, introduced in Chapter 3 with the crystal structure of 1-phenyl decane, that will be addressed anew in a later chapter on the cholesteryl esters.

6.2

Perfluoroalkanes—crystal structure

Neglecting any other chemical consideration, because of the difference in van der Waals radii (r) (Zefirov, 1997), it is not expected that total replacement of hydrogen (r  1.16 Å) by fluorine (r  1.40 Å) would permit the all-trans zigzag conformation of the n-alkane chain to be preserved at atmospheric pressure. As the polyethylene unit cell can be regarded as a paradigm for n-paraffin chain packing, that of poly (tetrafluoroethylene) can similarly be treated as a model for the chain conformation and packing of the shorter n-perfluoroalkanes. Using the difference in van der Waals radii between fluorine and hydrogen, Bunn and Howells (1954) explained the helicity of the poly (tetrafluoroethylene) chain, finding that the chain should complete a 180 twist after a repeat of 13-CF2 units. They also noted the similarity of an oligomer chain packing (n-C16F34) to that of the infinite polymer at temperatures above 30C. More recently (Jang et al., 2003), the importance of electrostatic

110

SOME FUNCTIONAL SUBSTITUTIONS IN n -PARAFFINS

interactions, specifically a Coulombic repulsion term, has been proposed to explain the chain helical conformation. This viewpoint is not generally accepted, however (Dunitz et al., 2003). Using the Fourier–Bessel transform of a helix, Clark and Muus (1962a,b) presented a more detailed analysis of the polymer chain packing above and below the two major transitions at 19 and 30C, previously observed by Bunn and Howells (1954). At low temperature (e.g. 0C), the polymer structure was found to be triclinic with a  b  5.59 Å, c  16.88 Å, ␤  119.3. At 25C, the structure became hexagonal where a  5.66 Å, c  19.50 Å. The lower temperature form was described as a 136 helix packing with no unusual disorder. At higher temperature, there are small angular displacements of the helices around their long axes, as well as a slight untwisting of the molecule to form a 157 helix. Above 30C, the molecules untwist further and the conformation becomes irregular. At very high pressures, planar conformations of the molecules are reported to exist in subcells similar in form to the O⬜and M found for polymethylene chains (Eby et al., 1990). Starkweather (1986) discussed the crystalline polymorphism of the perfluoroalkanes, including transition temperatures and enthalpies for the various members of a homologous series. From hexagonal crystallographic parameters, a  5.705 0.022 Å, c  1.33m 1.907 Å, for n-CmF2m 2. It is clear, therefore, that the chains pack in untilted, rectangular layers, since the perfluoromethylene increment corresponds to that of the chain repeat itself. In an attempt to solve the crystal structure from Weissenberg oscillation data on perfluoroeicosane, n-C20F42, Schwickert et al. (1991) proposed structural models for the crystalline forms existing below 143C and above 73.2C, but did not analyze data for the intermediate structure. The highest temperature form was found to be rhombohedral, a three-layer structure in space group R3 m, with cell constants: a  b  5.70 Å, c  85.00 Å. In terms of cylindrical molecular packing, this chain assembly would be quite analogous to one of the polymethylene rotator phases (Ungar, 1983). The lowest temperature form was found to be a highly twinned monoclinic cell with a  9.65, b  5.70, c  28.3 Å, ␤ ⬇ 97, with a proposed space group Pa. The helix conformation was found to be 157 for both polymorphs. Electron diffraction studies of a longer homolog, polytetraflurotetracosane, n-C24F50, yield somewhat different results. It was already known from previous transmission diffraction studies of n-C16F34 hexagonal plates or of homologs (Fig. 6.1), that the hexagonal diffraction pattern could be well explained by a cylindrically disordered rotor (Dorset, 1977). In this study, the diffraction patterns from the perfluoroalkane and from perfluoro-fatty acids were found to be identical. (Earlier reflection high-energy electron diffraction (RHEED) measurements on the perfluoridated fatty acids (Chapman and Tabor, 1957) had established that the chains were untilted in the lamellar layers.) At room temperature, electron diffraction patterns from n-C24F50, epitaxially oriented on KCl or NaCl substrates, were used to obtain h0l and hhl patterns (Fig. 6.2). From systematic absences, the space group was determined to be orthorhombic Fmmm, again resembling a bilayer rotator phase of n-alkanes (Ungar, 1983). Unit cell constants were measured: a  5.68, b  9.84, c  67.4 Å (Zhang and Dorset, 1990b). A chain rotor model gave a good fit to the observed hhl intensities.

PERFLUOROALKANES—CRYSTAL STRUCTURE

111

Fig. 6.1. Electron diffraction pattern (hk0) from solution-crystallized n-C24F50.

(a)

(b)

Fig. 6.2. Electron diffraction from n-C24F50 epitaxially crystallized on KCl: (a) h0l; (b) hhl. (Zhang, W. P. and Dorset, D. L. (1990) Epitaxial growth and crystal structure analysis of perfluorotetracosane. Macromolecules 23, 4322–4326.)

A subambient phase transition was observed by differential scanning calorimeter (DSC) for n-C24F50 (Dorset, 1995a) near 50C (Fig. 6.3). (Starkweather (1986) observed a transition at 70.5C.) Diffraction indicates a more highly ordered orthorhombic layer packing. Systematic absences in h0l; and hhl patterns indicate the space group is either Pca21 or Pcab, and there is no sign of twinning. With axial transposition the cell constants are very similar to the higher temperature form: a  9.84, b  5.68, c  67.4 Å. There is very good agreement of lamellar intensities between the two polymorphs. Attempts have been made to solve the crystal structure by direct methods (C. J. Gilmore and D. L. Dorset, unpublished results). While a bilayer packing motif can be described, it is difficult to fit a specific chain

112

SOME FUNCTIONAL SUBSTITUTIONS IN n -PARAFFINS (a) Exo

(c)

Endo

(b)

–100

0

100

200

T (°C)

Fig. 6.3. Subambient phase transitions of n-C24F50 and their effects on the hhl electron diffraction pattern.

model to it. From the potential maps, it is apparent that there must be maximal ordering of the chains near their centers with some increasing disorder toward the ends. A crystal structure of perfluro-n-hexane has been determined by R. Boese at low temperature (private communication transmitted by Dunitz et al., 2003), revealing the chain conformational twist. A fascinating series of hybrid molecules, where one part of the chain is fluorocarbon and the other part is paraffinic, that is, F(CF2)n(CH2)mH, abbreviated FnHm, were synthesized and characterized by a group at the IBM Research Laboratory in San Jose, CA (Rabolt et al., 1984; Russell et al., 1986). Later, liquid crystalline modifications of these materials were observed (Viney et al., 1989a,b, 1990). The X-ray diffraction data are not very informative. However, as will be discussed below, packing models that include the interpacking of fluorocarbon (cross-section 28.3 Å2) and hydrocarbon (cross-section 18.5 Å2) segments totally ignore the fact that these separate moieties are immiscible with one another (see below). In fact the molecules are, in a way, a form of detergent, so that any logical packing scheme should sequester the two chain segments. Reasonable chain packing schemes have been suggested by Höpken (1991). The layer packing has been finally visualized in the crystal structure of 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 17-tridecafluoroheptadecan-1-ol, an analog of F6H11 (Lapasset et al., 1996), shown in Fig. 6.4. The ca. 4 Å contact between hydrocarbon segments compensate for the ca. 5 Å fluorocarbon segment contacts by a greatest tilt of the former chain moiety (although the latter segments are also slightly tilted). The two molecular moieties remain separated in layers in the bilayer packing motif. One thing not anticipated before the crystal structure determination is that the alkyl chain segments do not pack with a methylene subcell but rather one of the cross-chain packings predicted by Segermann (1965).

PERFLUOROALKANES—BINARY PHASES

(a)

113

(b)

Fig. 6.4. Crystal structure of 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 17-tridecafluoroheptadecan-1-ol in two views. One view (b) clearly reveals the cross-chain packing of the n-alkyl segments.

6.3

Perfluoroalkanes—binary phases

Binary combinations of perfluoroalkanes follow rules for the formation of stable solid solutions similar to those found for the n-paraffins (Dorset, 1990d). For example, the value of the Kitaigorodskii (1961) volume parameter e, indicating co-solubility of components, is similar to the condition for stable n-alkane solid solutions. For example, chain length differences of two perfluoromethylene units are stabilized in solid solutions (Fig. 6.5(a)) while those of four units are not (Fig. 6.5(b)). In the former case, the least stable combination of n-C12F26/n-C14F30, where e  0.83, shows a dramatic divergence from the ideal melting point line, even though the intermediate lamellar X-ray spacings are near the line defined by Vegard’s law. When e  0.67 (e.g. n-C12F26/n-C16F34), a eutectic solid is formed and the liquidus curve is well predicted by the Schroeder–Van Laar equation (Dorset, 1990d). By e  0.57 the components are totally fractionated. At low temperature, there is absolutely no co-solubility of the perfluoroalkanes with n-alkanes of comparable chain length (Fig. 6.6). The liquidus curve cannot be explained by the melting temperatures and heats of fusion of the pure ingredients, since the melting temperature of intermediate compositions is nearly flat over the whole compositional range. Observations in a polarizing microscope explain this seemingly unusual behavior. The binary liquids are only co-miscible at high temperature. For example, 500 ml of perfluorohexane added to 500 ml of hexane will give a 1030 ml solution at 25C and the two components fractionate at 22.5C (Höpken, 1991). Co-mixing of these chemically dissimilar chains is an endothermic process. Calculations (Dunitz et al., 2003) reveal that, for example, a hexane— perfluorohexane heterodimer interaction has a higher binding energy than do the homodimers. On the other hand, such behavior is not observed for aromatic mixtures comprising hydrocarbon and fluorocarbon components, for reasons discussed by Dunitz et al. (2003).

(a)

100

Ideal solid solution melting

90 80

0

(c) 130

0.5 XC14F30

20 19 18

Ideal eutectic liquidus

70

n-C12F26 /n-C14F30 21

l s (Å)

T (°C)

(b)

n-C12F26 /n-C14F30

110

0

1.0

0.5 XC14F30

1.0

n-C14F30 /n-C16F34

120 T (°C)

Ideal solid solution melting

n-C14F30 /n-C16F34

(d) 24 23 l s (Å)

110 Expt melting curve

22 21 20

100

0

0.5 XC16F34

1.0

0

0.5 XC16F34

1.0

Fig. 6.5. Binary phase diagrams of perfluorocarbon solid solutions. (a) n-C12F26/n-C14F30; (b) X-ray diffraction lamellar spacings for (a); (c) n-C14F30/n-C16F34; (d) X-ray lamellar spacings for (c). (Dorset, D. L. (1990) Binary phase behavior of perfluoroalkanes. Macromolecules 23, 894–901.)

(a)

180

Exp liquidus

n-C19H40 /n-C20F42

160

120

30 Ideal liquidus

100 80

ls (Å)

T (°C)

n-C19H40 /n-C20F42

(b)

140

60

25

40 20

20 0

Exp liquidus

170

n-C20H42 /n-C20F42

30

130

29

110

0.5 XC20F42

1.0

n-C20H42 /n-C20F42

(d)

150

28

Ideal liquidus

ls (Å)

T (°C)

(c)

0

1.0

0.5 XC20F42

90

27

70

26

50

25

30 0

0.5 XC20F42

1.0

0

0.5 XC20F42

1.0

Fig. 6.6. Eutectic relationships between n-paraffins and similar chain length perfluoroalkanes. (a) n-C19H40/n-C20F42 phase diagram; (b) X-ray lamellar spacings of (a); (c) n-C20H42/n-C20F42 phase diagram; (d) X-ray lamellar spacings of (c). (Dorset, D. L. (1990) Binary phase behavior of perfluoroalkanes. Macromolecules 23, 894–901.)

116

SOME FUNCTIONAL SUBSTITUTIONS IN n -PARAFFINS

(a)

(b) 90

n-F12H6 /n-F12H8

n-F12H6 /n-F12H8

80

Low temperature polymorph 40 Ideal solid solution melting

60

l s (Å)

T (°C)

70

50

High temperature polymorph

30

40 20

30 0 (c)

0.5 XF12H8

0

1.0 (d)

n-F12H8 /n-F12H12

1.0

n-F12H8 /n-F12H12 50

90 80

Ideal solid solution melting

70

40 l s (Å)

T (°C)

0.5 XF12H8

60

30

50 40

20 0

0.5

1.0

0

XF12H8 (e)

(f)

n-F10H12 /n-F12H10 90

1.0

n-F10H12 /n-F12H10 50 Low temperature polymorph

80 70

40 ls (Å)

T (°C)

0.5 XF12H12

60

High temperature polymorph 30

50 40

20

30 0

0.5

1.0

XF12H10

(g) 90

Low temperature polymorph 0

(h)

n-F8H12 /n-F12H8

0.5 XF12H10

1.0

n-F8H12 /n-F12H8

80 40

60

Incommensurate solid?

50

l s (Å)

T (°C)

70

40

30

30 20

20 0

0.5 XF12H8

1.0

0

0.5 XF12H8

1.0

Fig. 6.7. Phase diagrams of diblock FmHn materials and their powder X-ray lamellar spacings. (Dorset, D. L. (1990) Binary phase behavior of perfluoroalkanes. Macromolecules 23, 894 –901.)

PERFLUOROALKANES—BINARY PHASES (b) 170 160 150 140 130 120 110 100 90 80

n-F12H8 /n-C20F42

n-F12H8 /n-C20F42

° = 598.50 cal mol–1 40 Ideal liquidus

l s (Å)

T (°C)

(a)

30

20 0

(c) 100 90 80 70 60 50 40 30 20

0.5 XC20 F42

0

1.0

0.5 XC20 F42

1.0

(d) n-C20H42 /n-F12H8

n-C20H42 /n-F12H8

l s (Å)

T (°C)

40

30

20 0

0.5 XF12H8

1.0

(e)

0

0.5 XF12H8

1.0

(f) n-C20H42 /n-F8H12 Observed liquidus

35

Theoretical liquidus

30

Theoretical liquidus

Theoretical liquidus 0

0.5 XF8 H12

n-C20H42 /n-F8H12

40 l s (Å)

40

T (°C)

117

1.0

30

20 0

0.5 XF8 H12

1.0

Fig. 6.8. Binary phase diagrams of diblock FmHn materials with n-paraffins or perfluoroalkanes with corresponding X-ray lamellar spacings. (Dorset, D. L. (1990) Binary phase behavior of perfluoroalkanes. Macromolecules 23, 894 –901.)

Binary phase relationships between the hybrid fluorocarbon–hydrocarbon chain molecules discussed above, that is, FnHm, have also been studied (Dorset, 1990d). Near homologs, for example, F12H6/F12H8 are continuously co-soluble for both crystalline forms (Fig. 6.7). When the fluorocarbon chain length is constant, there can be a difference in paraffinic moiety of four methylene groups for co-solubility, for example, F12H8/F12H12. However, if the chain lengths are approximately the same but the molecular identity of the moieties is interchanged, that is, FnHm/FmHn, the lower temperature polymorph may fractionate. Association of a constant chain length, for example, F12H8 with either a pure perfluoroalkane or alkane (Fig. 6.8), shows that

118

SOME FUNCTIONAL SUBSTITUTIONS IN n -PARAFFINS

the diblock material with a dominant fluorocarbon moiety is co-soluble with the perfluoroalkane in the liquid phase but not with the alkane itself. Also F8H12 is cosoluble with n-C20H42 in the liquid phase, where now the paraffinic moiety of the diblock dominates. This again underscores the amphiphilic nature of these molecules. Eutectics have been described for F12H10/n-C8H18 and F12H10/n-C12H26 (Höpken, 1991).

6.4

Heteroatoms in chains—crystal structures

Substitutions of a central methylene unit in a chain by an oxygen atom have been studied. Kohlhaas (1940) described the crystal layer packing of dicetyl ether, CH3(CH2)15–O–(CH2)15CH3. The unit cell dimensions are: a  5.571, b  7.452, c  87.70 Å, ␤  116.9, so that the chain packing is obviously the O[1, 0] type predicted by Kitaigorodskii (1961). This packing was also verified by RHEED and transmission electron diffraction measurements (Schoon, 1938). Thioether analogs apparently have a similar structure. If, on the other hand, the interposed group is –NH2–, the chain packing is rectangular in the O⊥ methylene subcell. There appear to be no good model crystal structures for any of these internally substituted n-alkane derivatives. The van der Waals radius of oxygen (1.29 Å) and of sulfur (1.84 Å) (Zefirov, 1997) are both smaller than the maximum radius of a methylene group (2.24 Å) (Zefirov, 1994). It is, therefore, not the bulk of this inclusion, itself, that forces the chain packing to be oblique instead of rectangular. The reason for a preferred oblique chain packing may be indicated by representative polyether and polysulfide crystal structures. For example, a number of polyether structures have been determined quantitatively from fiber X-ray data (Tadokoro, 1979) in which non-trans conformations can be found near the ether linkage, although stable all-trans forms also exist for those with a larger number of interposed chain methylene groups. Nonplanar conformations can also be found in the crystal structure of poly (ethylene sulfide) (Dorset and McCourt, 1997) even though the longer polythioethers can retain planar zigzag conformations (Tadokoro, 1979). (Nonplanar conformations are also encountered in the crystal structures of thioether analogs of fatty acids, see Chapter 8.) Thus, an effective thickening of the chain cross-section near the heteroatom due to localized nonplanar conformations would necessitate some compensation by the polymethylene chain packing—the typical mechanism being chain tilt. The eutectic relationship of the major monoclinic polymorph with the like chain length odd-paraffin indicates this (see below) (Fig. 6.9). Recently, the solid state structure of dicetyl ether was determined by electron crystallography (Dorset et al., 2000). Two polymorphs were observed. The major, monoclinic form observed by Kohlhaas (1940) crystallizes in space group Aa, where a  5.59, b  7.40, c  88.86 Å, ␤  116.2. The projected chain packing (Fig. 6.10(b)) reveals a conformational twist imposed on the polymethylene chain due to the heteroatom insertion. The second, minor form

HETEROATOMS IN CHAINS—CRYSTAL STRUCTURES (a)

80

Liquid solution (melt)

T (° C)

Rotator phase 70

Undefined solid solution

60

50

(Fractionated solid?)

0

(b)

T (° C)

Paraffin rotator and liquid

119

0.5 XdiC18NH Liquid solution (melt)

70

1.0

Possible melting line for co-soluble orthorhombic polymorphs?

60

Paraffin orthorhombic crystal and liquid 50 Eutectic solid (orthorhombic paraffin and monoclinic ether) 40 0

0.5 XdiC16O

1.0

Fig. 6.9. Binary phase diagrams of heteroatom chain structures with like-chain length n-paraffins. (a) n-Heptatriacontane with dioctadecyl amine; (b) n-tritriacontane with dicetyl ether. (Dorset, D. L., Clavell-Grunbaum, D., and Snyder, R. G. (2000) Internal heteroatom substitution and the layer packing of polymethylene chains. J. Phys. Chem. B104, 532–537.)

c b (a)

(b)

a/2+ O+

+

c/2+

Fig. 6.10. Crystal structures of (a) dioctadecyl amine; (b) dicetyl ether, monoclinic form. (Dorset, D. L., Clavell-Grunbaum, D., and Snyder, R. G. (2000) Internal heteroatom substitution and the layer packing of polymethylene chains. J. Phys. Chem. B104, 532–537.)

120

SOME FUNCTIONAL SUBSTITUTIONS IN n -PARAFFINS

Fig. 6.11. Crystal structure of 1,12-dibromododecane.

is orthorhombic (space group A21am: a  7.42, b  4.96, c  90.2 Å) strongly resembling the crystal structure of n-tritriacontane in its B-polymorph. It is seemingly the conformation around the ether linkage, and hence the cross-sectional chain area near the heteroatom, that leads to the type of layer packing. The phase diagram also indicates co-solubility of the orthorhombic polymorph with the paraffin. Nonplanar conformational disorder does not seem to be a consideration for N, Ndioctadecylamine. Its crystal structure (Dorset et al., 2000) was also determined from electron diffraction data and shown to strongly resemble the B-polymorph of n-C37H76 (Fig. 6.10(a)). The space group is A21am, where a  7.52, b  5.04, c  100.0 Å. The structural similarity to the odd-chain alkane is not difficult to understand since the van der Waals envelopes of a secondary amine and a methylene are not greatly different. (Only one hydrogen is missing.) van der Waals radii of C and N are similar (Bondi, 1964). Moreover, nitrogen bond distances to the neighboring carbons and the angle: C–N–C are not greatly different from those of a homogeneous polymethylene sequence. Addition of terminal halogens (Br, I) to approximate the van der Waals radius of a terminal methyl group (Pauling, 1960), sometimes leads to isomorphous structures. There is some distortion of the crystal structure of even-chain paraffins when both termini are halogenated. For example, the structure of 1,12-dibromododecane was determined by Kulpe et al. (1981) to crystallize in space group P21/c with cell constants: a  5.50, b  5.40, c  24.8 Å, Z  2. Unlike the parent paraffin where all chain layers have the same tilt direction, this structure (Fig. 6.11), packs with alternating tilts of successive layers. Nevertheless, the methylene subcell packing is still T, where as  4.27, bs  4.97, cs  2.53, ␣  86.4, ␤  106.7, ␥  112.9. The longer 1,18-dibromooctadecane homolog has a similar crystal structure (Nakamura et al., 1993), as does the 1,14-dibromotetradecane homolog (Uno and Nakamura, 2003). The ␣, ␻-dichloro-substituted alkanes, for example, 1,16dichlorohexadecane, have similar crystal structures (Nakamura and Shimizu, 2004). Halogen substitutions at the chain ends can form either tilted or nontilted layers. For example, the Kitaigorodskii O[0, 0] layer is formed from 1,10-dibromodecane and 1-bromooctadecane while the O[1, 0] layer crystallizes for 1-iodooctadecane

UNSATURATION

121

(Dorset, 1983). 1-Bromooctadecane was also found to crystallize in a O[1, 0] layer (Nakamura, 1981). 6.5

Heteroatom substitutions—binary phases

Dihexadecyl ether forms continuous solid solutions with dihexadecyl sulfide (Dorset, unpublished data). However, this ether in the monoclinic polymorph forms a eutectic with the n-C33H68 alkane but the orthorhombic polymorph may be continuously co-soluble with the alkane (Fig. 6.9(b)). Di- (n-octadecyl) amine also forms a continuous solid solution with n-C37H76 (Fig. 6.9(a)), revealing that interposition of the amine group does not totally disrupt the lateral rectangular layer packing of chains. However, the characteristic lozenge crystal habit is greatly distorted by this inclusion, indicating the formation of local defects. For the halogen-substituted n-paraffins, 1,10-dibromodecane forms continuous solid solutions with 1,10-diiododecane. The paraffin n-C19H40 forms a eutectic with either 1-iodo- or 1-bromooctadecane in the lowest temperature form but there is a higher temperature form (rotator phase?) that is co-soluble. The same observation has been made for the paraffin n-C21H44 with 1-bromoeicosane. Near homologs of 1-iodo n-paraffins (eg. n-C18H35I and n-C16H33I) fractionate in the solid state (Smith, 1932). 6.6

Unsaturation

The effect of removing two hydrogens from adjacent methylene groups in a chain on chain packing can be significant. Almost all information on polymethylene chains with double bond inclusions has been obtained from the fatty acids (Chapter 8); such chains commonly incorporate cis-double bonds.

c b (a)

c a (b)

Fig. 6.12. Crystal structure of 15-trans-triacontene. (Dorset, D. L. and Snyder, R. G. (1999) Effect of chain unsaturation on polymethylene lamellar packing:solid state structure of a symmetric trans-alkene. Macromolecules 32, 8139–8144.)

122

SOME FUNCTIONAL SUBSTITUTIONS IN n -PARAFFINS 70

T (°C)

65

60

55

50 0.0

0.5 XC30

1.0

Fig. 6.13. Binary phase diagram of 15-trans-triacontene with n-triacontane. (Dorset, D. L. and Snyder, R. G. Effect of chain unsaturation on polymethylene lamellar packing: solid state structure of a symmetric trans-alkene. Macromolecules 32, 8139–8144.)

An electron crystallographic determination has been reported recently (Dorset and Snyder, 1999b) for 15-trans-triacontene, which is observed to pack in rectangular layers with the O⬜ methylene subcell (Fig. 6.12). The pseudo-orthorhombic unit cell is space group Aa, where a  7.48, b  4.99, c  79.6 Å. In this three-dimensional determination, the chains are found to be twisted in skew and anti-skew conformations at the single bonds adjacent to the unsaturation. This conformation is similar to the one found for a polyalkenamer that also packs with this methylene subcell (Natta et al., 1969). While it is easy to understand that a cis-olefin will fractionate in binary solids with the alkanes with like carbon number (Small, 1986), this is also true of nalkane interactions with the trans-alkenes (Fig. 6.13).

6.7 1.

Summary

Heteroatom substitutions can have a profound influence on the layer packing of polymethylene chains. 2. As seen in previous chapters, least disruptive is the substitution of H by D, even though thermal properties of the chain are affected. 3. Linkage substitution of NH for CH2 has little effect on the chain layer packing. Substitution of an ether linkage, on the other hand, will affect the layer packing because a gauche conformation is preferred near the linkage, hence expanding the local chain cross-sectional area. Thioether substitutions are obviously more disruptive.

SUMMARY

4.

5.

123

Halogens, such as Br and I, can successfully mimic the van der Waals radius of the terminal methyl group. Crystal structures can be similar to the n-alkanes but thermal properties are affected by the substitution. Insertion of a trans- double bond will disrupt the layer packing because the chain adapts a nonplanar conformation near this linkage.

7 Lipid alcohols

7.1

Introduction

Natural waxes contain free polar components, among these being the alcohols and the fatty acids that are esterified to form the major fraction of the solid (Warth, 1947). The lipid alcohols are the less polar of the two. In most waxes, the linear saturated monofunctional fatty alcohols, are the major components; sometimes also secondary alcohols and/or ␣,␻-difunctional alcohols are present as minor components. In animal waxes, sterols can also be present, most commonly cholesterol. Plant cuticles can contain long-chain alcohols as a major wax component (Mark et al., 1998).

7.2

Crystal structure of primary fatty alcohols

Primary fatty alcohols crystallize in three polymorphs, as demonstrated by extensive powder X-ray studies (Watanabe, 1961, 1963). The form preferentially expressed depends on chain length, where the hydrogen bonding network is compared energetically to the packing of the polymethylene portion. 7.2.1

Tilted layer polymorphs

The monoclinic or ␥-forms of the fatty alcohols are energetically favored for many even-chain alcohols while a rectangular layer structure is observed for the odd-chains in the series. However, as with n-paraffins, there is also an even/odd effect on the favored layer packing, that is, due to the number of methylene groups in the chain (Watanabe, 1963). For example, the tilted chain ␥-polymorphs are preferred for all even fatty alcohols beyond n-dodecanol, but, beyond a chain length of 29 carbons, the tilted chain packing is also observed for the odd-chain alcohols. The crystal structure of n-hexadecanol was determined in its monoclinic form, crystallizing in space group A2/a (Abrahamsson et al., 1960) and is illustrated in Fig. 7.1. The unit cell constants are: a  8.95, b  4.95, c  88.1 Å, ␤  122.38, Z  8. Chains in the O⬜ subcell are tilted with an axis approximately parallel to the crystal (202) plane. This corresponds to the O[0, 2] layer packing of Kitaigorodskii (1961), observable also in the characteristic hk0 electron diffraction pattern from thin crystals (Precht, 1976a). The crystal structure of the near homolog, n-octadecanol, has

CRYSTAL STRUCTURE OF PRIMARY FATTY ALCOHOLS

125

Fig. 7.1. Crystal structure of n-hexadecanol.

also been determined (Seto, 1962), with cell constants: a  8.96, b  4.93, c  99.7 Å, ␤  123.05, in the same space group. The crystal structure of n-eicosanol has also been reported (Watanabe, 1963). A more accurate analysis of this polymorph was reported recently by Michaud et al. (2000). In this polymorph, there is an infinite hydrogen bonding network with these linkages directed perpendicular to the shortest unit cell axis. Unit cell constants have been given for a homologous series (Precht, 1976a) in the monoclinic form. Other possible monoclinic structures have been proposed as well (Precht, 1974, 1976b), corresponding to Kitaigorodskii’s oblique layers. Crystals in this form have a characteristic lozenge habit with the acute angle between boundary {110} faces being near 59 (Amelinckx, 1954, 1955). Substitution of the terminal methyl group with a bromine can lead to an isomorphous structure for many polymethylene compounds. A striking exception to this is demonstrated by the crystal structure of 11-bromoundecanol (Rosen and Hybl, 1972), which differs from that of n-dodecanol. The disorder induced by the heavy atom substitution is expressed in a number of ways. First, there is a superlattice expressed by the unit cell constants: a  47.10, b  5.26, c  31.14 Å, ␤  132.9 in space group P21. The chains pack in tilted layers in a herringbone type arrangement, shown by the packing of the average chain subcell in Fig. 7.2. The methylene chain packing itself is a different subcell (T ) than found for n-dodecanol. Rosen and Hybl (1972) described a periodic sequence of kinks in the methylene chain that propagates through the superlattice. In addition, there is a wave-like deviation of the terminal bromines from a perfect plane. 7.2.2

Rectangular layer polymorph

A rectangular layer ␤-polymorph is preferred by the odd-chain n-alkanols up to n-nonacosanol, beyond which the tilted layer structure predominates (Watanabe, 1963). The untilted structure exists as a metastable form for the lower even-chain alcohols (Precht, 1974, 1976b), and is permitted when the hydrogen bonding network plays a decisive role in the molecular packing (Watanabe, 1963). Electron diffraction measurements on the untilted layer packing of n-octadecanol (Dorset, 1979), combined with observation of preferred sublimation patterns of thin crystals, indicated that the hydrogen bonding chain direction must be oriented perpendicular

126

LIPID ALCOHOLS

Fig. 7.2. Average crystal packing of 11-bromoundecanol.

to the shortest unit cell axis (near 5.0 Å). It is clear from the characteristic electron diffraction patterns that the methylene subcell is the untilted O⬜ packing of n-paraffins (Precht, 1976b; Dorset, 1979). The electron diffraction intensities have been used quantitatively to determine the layer packing in projection (Li, 1963; Precht, 1976b; Dorset, 1979). From low-angle X-ray diffraction measurements, the lamellar spacings were shown (Precht, 1976b) to increase according to the relationship: d001  2(2.595)n 3.817 Å for a chain with n carbon atoms. The structure is not really orthorhombic, however, although the monoclinic angle is rather small, between 91 and 92. Lozenge crystals of the rectangular layers resemble those from n-paraffins, since they grow by screw dislocations (Amelinckx, 1956a,b; Dawson and Watson, 1957) and have an angle near 67 between the {110} faces. An X-ray crystal structure has been reported (Seto, 1962) for the ␤-form of n-heptadecanol. Unit cell constants are a  5.03, b  7.40, c  94.6 Å, ␤  91.30. The space group is P21/c, Z  8. The reported chain packing model is rather unusual (Fig. 7.3), proposing a half occupancy of methyl groups on the outermost lamellar layer, caused by the gauche conformation of one of the chain ethylene groups next to the hydroxyl function to arrive at a favorable hydrogen bonding network in the bilayer. Precht (1976b) has proposed a similar structure for the even-chain alcohols in this polymorph. Although the rectangular layer packing is not favored for longer even-chain alcohols (Watanabe, 1963), it can be grown, as shown in the crystallization studies of Amelinckx (1956a,b). Electron diffraction patterns from this polymorph of n-triacontanol have been observed for material epitaxially nucleated on benzoic acid. 7.2.3

Rotator phases

Similar to the n-paraffins, long-chain alcohols form rotator phases before transforming to the melt. According to Watanabe (1961, 1963), the rotator ␣-phases exist in

CRYSTAL STRUCTURES OF OTHER FATTY ALCOHOLS AND THIOLS

127

(a)

(b)

Fig. 7.3. Crystal structure of n-heptadecanol.

chains longer than 12 but shorter than 34 carbons. For even-chains shorter than or equal to 16 carbons, the rotator phase is formed from the ␤-crystal polymorph, whereas for longer chains, the ␥-form transforms to this disordered structure. In the chain length range from 14 to 26 carbons, the crystal to ␣-phase transition is reversible. For longer even-chain alcohols the rotator is observed only when the solid is crystallized from the cooled melt. As evidenced by electron diffraction patterns (Frede and Precht, 1974), the usual ␣-form structure involves tilted chains, although occasional patterns of an untilted form have been observed. This observation is supported by X-ray measurements. Seto (1962) gives unit cell constants: a  8.44, b  4.87, c  49.1 Å, ␤  93 from a single crystal in this form. Frede and Precht (1974) observed up to seven lamellar orders in low-angle powder X-ray measurements to derive a relationship for the lamellar spacing: d  2.536(n  1) 6.69 Å, for chains with n atoms. Seto (1962) also observed a metastable form for n-heptadecanol that was truly a trigonal structure with cell constants: a  4.86, c  139 Å, in space group R3 m. The rotator phases of primary fatty alcohols have been related to those for the n-paraffins after an extensive examination of chain length series from C12 to C26 (Sirota and Wu, 1996). For the shorter alcohols, the RII phase is the normal one and for binary solid solutions, the second metastable form is RI. For longer alcohols (e.g. 1-heptadecanol and 1-octadecanol), the stable rotator form is RIV while a R
V packing can exist at lower temperatures. Hydrated alcohols pack in the RII form most commonly but can have RV and RIV variants.

7.3

Crystal structures of other fatty alcohols and thiols

Bifunctional ␣,␻-diols have been characterized in the solid state. The crystal structure of 1,16-hexadecanediol was reported by Nakamura and Yamamoto (1994) and

128

LIPID ALCOHOLS

(a)

(b)

Fig. 7.4. Crystal structure of ␣,␻-polymethylene diols. (a) 1,16-hexadecanediol; (b) 1,13-tridecanediol.

is shown in Fig. 7.4(a). The unit cell constants in space group P21/n are: a  31.396, b  5.207, c  4.98 Å, ␤  91.71. The packing of alternate tilted chain layers is very similar to the chain packing of the ␣,␻-dibromoalkanes. Crystal structures of homologous members have been determined, in order to evaluate the consistency of the chain packing. These structures include: 1,10-decane diol (Nakamura and Sato, 1999a), 1,12-dodecane diol (Nakamura and Setodoi, 1997), 1,14-tetradecane diol (Nakamura and Sato, 1999b), and 1,18-octadecane diol (Nakamura and Watanabe, 2001). The methylene subcell in individual tilted chain layers is T. A more systematic view of odd–even effects on chain packing density and melting point, derived from crystal structures, has been provided by Thalladi et al. (2000a). They reported the crystal structures of ␣,␻-alkane diols from C2 to C10. Above n  4, chain layers in even-members crystallize in space group P21/n or P21/c. The carbon backbone is all-trans and the overall packing is very efficient so that the ␤-methylene group fits in the hollow provided by the hydrogen bonded chain network at the layer surface. For the odd-chain members, the space group is P212121 in a three-dimensional array. The energetic disadvantage, that is, decrease in packing density, arises from the need to form a gauche twist near one of the hydroxyl groups in order to allow the formation of a hydrogen bonded network. These pack (Fig. 7.4(b)) in untilted chain layers with the O⊥ methylene subcell. Representative structures of homologs include: 1,11-undecane diol (Nakamura et al., 1999), 1,13-tridecane diol (Nakamura et al., 1997) (Fig. 7.4(b)), 1,15-pentadecane diol (Nakamura et al., 2000), 1,19-nonadecane diol (Nakamura et al., 2001c), and 1,23-tricosane diol (Nakamura et al., 2001d). The dithiols, for example, 1,12-dodecane dithiol (Nakamura et al., 2001a) and 1,20-eicosane dithiol (Nakamura et al., 2001a) also pack with tilted chain layers

BINARY PHASE BEHAVIOR OF FATTY ALCOHOLS

129

but the chain tilt is the same direction for each layer, rather than alternating directions. The odd-membered dithiol series has also been investigated. Again, a comprehensive overview of odd–even effects has been provided by Thalladi et al. (2000b). They determined the crystal structures of the homologous series from C2 to C10. When n 4, the even-chain dithiols pack in space group P1. In projection onto the axes, a hexagonal molecular boundary simply indicates how the molecules can pack efficiently. On the other hand, the polyhedral outline of odd-membered dithiols in space group P2/c leads to a less efficient packing. In no case are actual S–H . . . . S hydrogen bonds found to be important. Rather the terminal thiol groups seek an efficient packing in a way similar to terminal methyl groups in n-alkanes. A secondary alcohol crystal structure has also been determined in projection (Welsh, 1956). The crystal structure of 14-heptacosanol in the most stable of two observed polymorphs crystallizes with cell constants: a  8.14, b  4.95, c  73.2 Å, ␤  104 in space group P21/c. The methylene subcell packing is O⬜, so that the layer packing is again Kitaigorodskii’s O[0, 2]. While the bulk of the secondary alcohol function is partially compensated by the chain tilt in a layer, there is also an expansion of the longer methylene subcell distance to 7.8 Å. Lamellar spacings of other secondary alcohols have been listed by Piper et al. (1931).

7.4

Binary phase behavior of fatty alcohols

Data on binary phases of the primary fatty alcohols are somewhat sparse. Yamamoto et al. (1990) have determined phase diagrams for binary combinations of n-heptadecanol and n-octadecanol. Continuous solubility of the two alcohols in the ␤-polymorph exists up to a mole fraction of 0.80 for the longer alcohol, upon which a ␥-type structure is found. (This behavior is analogous to binaries of shorter n-paraffins.) On heating the crystalline phase, the normal rotator phase of the alcohol is found, and is compared to the RII structure of the n-paraffins where the a/b ratio of the chain subcell is less than 兹3. However, on cooling from the melt, another rotator is found before nucleation of the normal ␣-phase. This ␣
-phase resembles the paraffin RI rotator phase structure, which is face-centered orthorhombic. A similar characterization was made for the binary combinations of 1-eicosanol with 1-docosanol (Sirota and Wu, 1996). Amelinckx (1958) studied the binary phase behavior of longer fatty alcohols. Both the combinations n-tetracosanol/n-hexacosanol and n-docosanol/n-hexacosanol were found to form solid solutions in the rectangular layer structure, even though the monoclinic tilted layers are preferred for the pure alcohols. It was shown that only 10% of the n-C24H49OH was needed to form the rectangular layer packing. A step-wise increase of constant lamellar spacing was observed with increasing concentration of the longer component that was not understood. For the n-C24H49OH/n-C26H53OH binaries, there are a number of steps whereas for n-C22H45OH/n-C26H53OH pairs, a

130

LIPID ALCOHOLS

single lamellar thickness persists above 50 mol% of the longer chain. The step-wise increase of lamellar spacings has been encountered more recently in the electron diffraction studies of n-paraffin binaries, as discussed in Chapter 5. Control of the binary lamellar spacing by the longer ingredient was also observed on average in X-ray studies of n-paraffin binaries (Mnyukh, 1960). The importance of such interactions to actual plant waxes has been established by Mark et al. (1998), who have carried out Fourier transform infrared (FTIR) studies on two plant cuticles for which the wax component was largely a long chain alcohol. The doublet at approximately 720–730 cm1 was very prominent, indicating that the component wax had high crystallinity in the common orthorhombic perpendicular methylene subcell packing. In general, multicomponent primary alcohol assemblies in waxes pack with untilted chains (Kreger and Schamhart, 1956). In binary assemblies, 5% addition of longer chains to shorter ones is sufficient to abolish the tilted chain packing. Addition of 5–10% of shorter chains to longer ones leads to the same result (Piper et al., 1934).

7.5

Crystal structure of cholesterol

Cholesterol is the major sterol moiety of mammalian lipids and a component of wool wax. It can be found in either hydrated or anhydrous crystal forms, respectively, with plate or needle habits (Small, 1986). The hydrated form packs as a bilayer structure, shown in Fig. 7.5. Its crystal structure was solved by Craven (1976, 1979) who found it to pack in space group P1 with cell constants: a  12.39, b  12.41, c  34.36 Å, ␣  91.9, ␤  98.1, ␥  100.8. The bilayer thickness is 33.9 Å. Molecular planes are nearly parallel to one another and the molecular axes lie approximately parallel to the [1, 2, 4] direction in the crystal making an angle of 17.4 to c*. Although there are eight molecules in the asymmetric unit, the diffraction symmetry is almost 2/m. For the bilayer packing, each layer contains a subcell with two cholesterols that are similar to one another. All of the isoprenoid side chains have a bent conformation. +

++ + +

+ +

Fig. 7.5. Crystal structure of cholesterol hydrate.

THERMOTROPIC BEHAVIOR OF CHOLESTEROL

131

Fig. 7.6. Crystal structure of anhydrous cholesterol.

Although the hydrogen bonding of hydrated cholesterol is weak (Craven, 1976), allowing tunnels to be formed theoretically in the structure after water removal, the reported structure of the anhydrous form is quite different (Shieh et al., 1977, 1981) although the space group is again P1 with eight molecules in the unit cell. The cell constants are: a  14.172, b  34.029, c  10.481 Å, ␣  94.64, ␤  90.67, ␥  96.32. There is no well-defined bilayer structure (Fig. 7.6). Molecular planes and axes are not aligned to one another. Although there is still a pseudosymmetry within the group of eight molecules, it comprises a cluster of four with no hydrogen bonding pattern among them. Also, the conformations of the isoprenoid side-chains are both bent and fully extended.

7.6

Thermotropic behavior of cholesterol

The discrepancy between postulated (Craven, 1976) and observed (Shieh et al., 1977) anhydrous crystal structures is explained by a characterization of the molecular thermotropic behavior (Small, 1986). Within a sealed environment, cholesterol monohydrate is dehydrated to an anhydrous form at 86.4C. This transforms to a smectic liquid crystal at 123.2, and then to a melt at 156.8. The anhydrous form converts to a second polymorph at 39, probably identical to the one formed from the monohydrate. With no water present, however, no mesophase occurs, so that the second polymorph melts at 157.0. Interestingly enough, hydration is most easily achieved with the lower temperature anhydrous structure.

132

LIPID ALCOHOLS

7.7 Examples of binary phase behavior of cholesterol with simple derivatives Rancid cholesterol contains simple oxidized by-products, some of which are cytotoxic. Dorset (1992) determined the binary phase diagrams of cholesterol with 7-ketocholesterol, and 25-hydroxycholesterol, two common oxidized derivatives, and showed that these are partially co-soluble with the sterol (Fig. 7.7). The low angle X-ray spacings of cholesterol with these derivatives also show that there is a continuity with changing mole fraction. The crystal structures of the oxidized forms, however, are quite different from those of the two forms of cholesterol cited above (McCourt et al., 1997). One oxygenated derivative, 7-ketocholesterol, packs in space group P21 with cell constants: a  11.405, b  6.288, c  35.393 Å, ␤  92.75. There are two molecules in the asymmetric unit. Molecules, originally in a bilayer for the non-oxidized parent (i.e. cholesterol), are shifted along the long molecular axes to accommodate one of the carbonyl oxygens in the hydrogen bonding scheme (Fig. 7.8). Also, a water molecule is incorporated into the packing scheme. The 25-hydroxycholesterol also packs in P21 with cell constants: a  10.840, b  14.533, c  16.093 Å, ␤  95.91. Again, there are two molecules in the asymmetric unit, but the molecules do not pack in well-formed layers; nor are the molecular

T (°C)

(b)

Ideal solid solution melting line

200

40

150 Theoretical liquidus

100

l s (Å)

(a)

35 30

0

200

0.5 X7keto

1.0

0

0.5 X7keto

1.0

0

0.5 X25-OH

1.0

Ideal melting curve

Theoretical liquidus for hypothetical eutectic

100

l s (Å)

T (°C)

40 150

35 30

0

0.5 X25-OH

1.0

Fig. 7.7. Phase diagrams and lamellar X-ray spacings of cholesterol with oxidized by-products. (a) 7-ketocholesterol; (b) 25-hydroxycholesterol. (Dorset, D. L. (1992) Binary phase behavior of angiotoxic oxidized cholesterols with cholesterol. Biochim. Biophysi. Acta 1127, 293–297.)

SUMMARY

(a)

133

(b) O3 O3 2.65

2.66

C27 C21

2.77

4.05

5.58

O7

O7

(a)

(b)

c a

Fig. 7.8. Crystal structure of 7-ketocholesterol. (McCourt, M. P., Ashraf, K., Miller, R., Weeks, C. M., Li, N., Pangborn, W., and Dorset, D. L. (1997) X-ray crystal structure of cytotoxic oxidized cholesterols: 7-ketocholesterol and 25-hydroxycholesterol. J. Lipid Res. 38, 1014–1021.)

axes parallel to one another. Rather, they are organized with opposing polarities in a monolayer, suggestive of one of the crystal forms found for cholesteryl esters (Fig. 7.9). This allows the hydroxyl groups from either end of the molecule to be involved in the hydrogen bonding scheme. Removal of all polar moieties on the cholesterol molecule, for example, in cholesteryl iodide (Carlisle and Crowfoot, 1945) also causes the molecules to pack in an antiparallel fashion, reminiscent of the packing in one of the monolayer forms of cholesteryl esters (see Chapter 10). The wide variety of steroid crystal packing motifs has been reviewed (Duax and Norton, 1975; Griffin et al., 1984).

7.8 1.

Summary Polymorphism of ␣-monoalcohols and ␣,␻-dialcohols is similar to that of the n-paraffins in that there is an even/odd effect of chain carbon number on preferred layer packing. Again simple methylene subcells are expressed by these structures.

134

LIPID ALCOHOLS

b c

Fig. 7.9. Crystal structure of 25-hydroxycholesterol. (McCourt, M. P., Ashraf, K., Miller, R., Weeks, C. M., Li, N., Pangborn, W., and Dorset, D. L., (1997) X-ray crystal structure of cytotoxic oxidized cholesterols: 7-ketocholesterol and 25-hydroxycholesterol. J. Lipid Res. 38, 1014 –1021.)

2.

3.

4.

Binary combinations of monoalcohols can be stabilized in solid solutions. Additions of 10% of a second component to a long-chain alcohol packing in an oblique layer will produce a rectangular layer lamellar packing motif, again similar to the case of n-paraffin binary solid solutions. Step-like increments of lamellar spacings for solid solutions are observed when the concentration of a longer component is increased. This behavior is also found for n-paraffin solid solutions. Cholesterol exemplifies a substance where more than one molecule is included in the asymmetric unit of the crystal structure. Oxidized by-products can be partially co-soluble in solid cholesterol.

8 The fatty acids

8.1

Introduction

There is much that can be learned about the packing of perturbed polymethylene chains from the crystallographic literature on fatty acids. For no other class of polymethylene compounds has there been such a wealth of quantitative information about the effect of unsaturation, heteroatom substitution, and chain branching on layer packings. There are also numerous polymorphic forms for many of the acids. The nomenclature of the various fatty acid polymorphs can be rather confusing. New conventions emerge and overlap with older ones, sometimes using an older designation for a completely different structural type. In this chapter the naming system used in the original Swedish structural characterizations of these compounds will be retained. The chapter could be much longer than it is. In this discussion, only the free fatty acids are considered, without the influence of counterions or solvent. Although important, very little attention is paid to amphipathic properties of these molecules in deference to the basic understanding of close packing motifs, given a certain covalent perturbation to the chemical structure. This is because many of the characteristic deviations from linear polymethylene chain geometry encountered in waxes and polymers have been investigated quantitatively in the various fatty acids.

8.2

Crystal structures of normal chain fatty acids

In the solid state, normal chain fatty acids exist in a variety of polymorphs. This nomenclature assigns a sequential letter symbol in order of decreasing lamellar spacing (Francis et al., 1930; Stenhagen and Sydow, 1953). Polymorphs of the even-chain acids receive simple capital letters whereas the odd-chain acids receive primed capital letters. Certain polymorphs are produced by rapid cooling of the melt whereas others are crystallized from solvents, also depending in part on the chain length of the acid (Stenhagen and Sydow, 1953; Sydow, 1956a). The type of solvent used (polar, nonpolar) also influences the polymorphs expressed (Stenhangen and Sydow, 1953). Furthermore, the distribution of polymorphs and polytypes has been described for various crystallization temperatures (Sato et al., 1988). As originally predicted by Kohlhaas and Stüber (1939), hydrogen bonded dimers involving the carboxyl groups

136

THE FATTY ACIDS

are the rule rather than the exception. Numerous studies of the growth of fatty acids in their various polymorphs (Amelinckx, 1953, 1954, 1956a,b; Anderson and Dawson, 1953; Sato and Okada, 1977a,b) have been made. The spiral growth mechanism involving screw dislocations was found to include diffusion across a formed lamellar surface as well as attachment to growth steps at the dislocations (Beckmann and Boistelle, 1985). In addition to various twins, polytypes have also been observed (Verma, 1955; Verma and Reynolds, 1953). 8.2.1

Even-chain acids

There are three common polymorphs of the even-chain normal fatty acids, as reviewed by Sydow (1956b). These saturated fatty acids are physiologically significant, so are often given nonsystematic names related to their natural origin. Early electron diffraction characterizations also identified three polymorphs (Trillat and Hirsch, 1933). Reflection electron diffraction measurements on single crystals (Thiessen and Schoon, 1937; Schoon, 1938) accurately determined the amount of chain tilt to the layer surface in projections along the lozenge crystal diagonals. Two polymorphs of stearic acid (n-octadecanoic acid) and one polymorph of palmitic acid (n-hexadecanoic acid) were examined. The two polymorphs, B and C, correspond, respectively, to the Kitaigorodskii (1961) O[1, 0] and O[0, 2] layers. Crystals of both are lozenge-shaped with an acute angle of 74 for the former and 56 for the later between the boundary {110} faces (Verma, 1955). It was also shown that the latter polymorph, favored also from the melt, would appear in multilamellar films made from dipping a surface through a Langmuir–Blodgett monolayer (Germer and Storks, 1937, 1938). Quantitative transmission electron diffraction on oriented microcrystals (Dorset, 1976d) showed how the characteristic O⬜ hk0 diffraction pattern could be observed from B-form crystals of behenic acid (n-docosanoic acid) when they were tilted around the shorter unit cell axes corresponding to the chain inclination. The A-form of lauric acid (n-dodecanoic acid) is grown by slow growth from solvent and has a remarkable structure (Sydow, 1956c; Goto and Asada, 1978a). The unit cell is centrosymmetric triclinic but because of an obvious centering operation, it is most convenient to describe the space group as A1 , rather than P1 . Cell constants are a  5.415, b  25.964, c  35.183 Å, ␣  69.82, ␤  113.14, ␥  121.15. As shown in Fig. 8.1, carboxyl groups in clusters of three molecules of a layer share the end plane with methyl groups in clusters of three antiparallel molecules, in a head-to-tail packing arrangement, thus forming a superlattice structure. The methylene chain subcell is T and the chains are tilted with respect to the lamellar interface plane by 64. The superlattice is caused by constraints to the carboxyl group packing in the crystal, each of the three unique polar groups having a different conformation with respect to the polymethylene chain. The second crystal polymorph, which can be grown rapidly from solvent, is form B. After the description of the chain layer packing by Müller (1927), the X-ray structure was determined for stearic acid (n-octadecanoic acid) in two projections

CRYSTAL STRUCTURES OF NORMAL CHAIN FATTY ACIDS

137

Fig. 8.1. Crystal structure of lauric acid, A-form.

(Sydow, 1955a, Larsson and Sydow, 1966) to show that the molecules pack in a monoclinic unit cell P21/a, with a  5.591, b  7.404, c  43.99 Å, ␤  94.6. The structure derived from the reported coordinates has an all-trans chain inclined 66 to the methyl end planes in the O⬜ subcell. The layer packing is therefore the Kitagorodskii O[1, 0] type. However, diffuse scattering was noted in the X-ray patterns (Larsson and Sydow, 1966) and thought to express some disorder in the carboxyl group packing. More recently, a full three-dimensional crystal structure analysis of stearic acid in this B polymorph has been carried out (Goto and Asada, 1978b). Although the measured unit cell constants are only slightly different after a conversion of the one ␤-angle to another (a  5.587, b  7.386, c  49.33 Å, ␤  117.24), there is a major change in the conformation around the C(2)–C(3) single bond from trans to gauche (Fig. 8.2). The polymethylene layer packing is otherwise unchanged. The description is complicated by the report (Kaneko et al., 1990) of a so-called “E-form” of the acid, also with the same layer packing (orthorhombic subcell and a 64 chain tilt) and space group with cell constants: a  5.603, b  7.360, c  50.789 Å, ␤  119.40. This structure has the all-trans conformation originally attributed to the B-form (Fig. 8.3). Given the previous convention for naming polymorphs, this “E-form” should be designated as a variant of the B (perhaps B1)-structure, since an earlier use of this polymorph symbol was made (see below). As will be

138

THE FATTY ACIDS

Fig. 8.2. Crystal structure of stearic acid, B-form.

shown below, there was also evidence for B and B1 forms for the ␻-brominated acid that was a strict isomorphous analog to lauric acid in this polymorph—and again disorder in the carboxyl group packing was suspected (Larsson, 1963a). As found for the similar monoclinic packing of even-chain n-paraffins, there are also polytypic structures for the two B-forms, so that there are two bilayers in one unit cell. The one with the gauche-conformation next to the carboxyl group was reported by Kaneko et al. (1994a) and is shown in Fig. 8.4(a). The cell constants in space group Pbca are: a  7.404, b  5.591, c  87.662 Å. The all-trans layers have a similar polytype (Kaneko et al., 1994b), shown in Fig. 8.4(b), also packing in space group Pbca, where a  7.359, b  5.609, c  88.41 Å. As with the parent crystal structures the all-trans chains give a slightly longer unit cell c-axis length. Both structures again retain the Kitaigorodskii O[1, 0] layer packing. The C-polymorph, often crystallized from the melt (Stenhagen and Sydow, 1953) packs in a Kitaigorodskii O[0, 2] layer, that is, with chains inclined 56 to the end plane and in the O⬜ methylene subcell (Sydow, 1956b). The first crystal structure in this polymorph was determined for lauric acid in projection (Vand et al., 1951). The first three-dimensional determination (Fig 8.5), of stearic acid, was actually based on powder X-ray data (Malta et al., 1975), since it is difficult to grow this acid as a

CRYSTAL STRUCTURES OF NORMAL CHAIN FATTY ACIDS

139

Fig. 8.3. Crystal structure of stearic acid, B1-form.

single crystal. The space group is again P21/a with cell constants: a  9.36, b  4.95, c  50.7 Å, ␤  128.4. Thus, the C-form layer packing involves a tilt of chains around the second-largest (ca. 5.0 Å) methylene subcell axis (expanding a 7.40 Å edge to 9.36 Å), whereas the B-form packing tilts the chains around the largest subcell axis (ca. 7.5 Å), expanding a 4.95 Å edge to 5.59 Å. Homologous behavior is mostly, but not entirely, subject to chain length. As shown for the C-polymorph of different fatty acids (Abrahamsson and Sydow, 1954), the values of the a- and b- unit cell edges actually decrease asymptotically to respective values 9.21 Å and 4.95 Å while the ␤-angle decreases to an asymptotic value of 127.28. On the other hand, the c-axis distance (and hence d001) obeys a linear relationship with chain length. Similar behavior can be shown for different chain length series in other polymorphs. Single crystal structures of fatty acids in the C-form have been reported recently for the homologous series from C6 to C14 chains by Bond (2004). 8.2.2

Odd-chain acids

An analogous sequence of polymorphs exist for the odd-chain normal fatty acids. The A
form of pentadecanoic acid was determined in projection by Sydow (1954a).

140

THE FATTY ACIDS

(a)

(b)

Fig. 8.4. Polytypes of stearic acid: (a) B-form; (b) B1-form.

It crystallizes in space group P1 with cell constants: a  4.25, b  5.01, c  42.76 Å, ␣  89.83, ␤  111.08, ␥  112.17. Hydrogen-bonded dimers are packed with chains tilted 66 to the end planes in the T methylene subcell. This is the form grown by slow growth from solution. The B
-structure of this acid, grown from the melt, was also determined in projection by Sydow (1954b). This also packs in a triclinic unit cell, space group P1 with cell constants: a  5.543, b  8.061, c  42.58 Å, ␣  114.30, ␤  114.22, ␥  80.62, but the methylene subcell packing is O⬜. The chains are tilted to the methyl end plane by 61. More recently, the three-dimensional structure of heptadecanoic acid was reported by Goto and Asada (1984), as depicted in Fig. 8.6. Cell constants in the same space group are: a  5.561, b  8.018, c  47.90 Å, ␣  114.18, ␤  114.96, ␥  80.22 from which the analogy to the lower homolog structure is clear. The C
-polymorph structure is represented by n-hendecanoic acid (Sydow, 1955a) and very much resembles the C-polymorph of the even-chain acids by retaining the Kitaigorodskii O[0, 2] layer packing. Cell constants in space group P21/a are: a  9.622, b  4.915, c  34.18 Å, ␤  131.28. Chains are tilted to the methyl end

CRYSTAL STRUCTURES OF NORMAL CHAIN FATTY ACIDS

141

Fig. 8.5. Crystal structure of stearic acid, C-form.

Fig. 8.6. Crystal structure of n-heptadecanoic acid, B
-form.

planes by 59 and pack in the O⬜ subcell. As mentioned above, the single crystal structures of a complete homologous series from hexanoic to pentadecanoic acid in C or C
forms have been reported by Bond (2004). The C
form has been characterized for C7, C9, and C11 chain lengths and a new C-centered C-form for C13 and C15 chain lengths. Following the approach of Boese and co-workers (see Chapter 3), the melting point alternation of the saturated fatty acids has been explained by a

142

THE FATTY ACIDS

consistently lower crystal packing density for the odd-chain compounds in their high temperature polymorphs, when compared to the even-chain acids. 8.2.3

Very short fatty acids

Since systematic layer packing characteristics in fatty acids depend on the existence of suitably long polymethylene chains, the shorter acids have different crystal structures. However, the hydrogen-bonded dimers are maintained in all structures, as is the parallel packing of chains. For propionic (n-propanoic) (Strieter et al., 1962) and valeric (n-pentanoic) (Scheuerman and Sass, 1962) acids the layer packing is antiparallel, somewhat suggestive of the A-form but is not a superlattice. Their structures are depicted in Fig. 8.7. Butyric (n-butanoic) acid (Strieter and Templeton, 1962) packs with parallel chain layers (Fig. 8.7(c)). The odd-acids crystallize in space group P21/c whereas the even-acid crystallizes in C2/m. 8.2.4

Heteroatom substitution

In early crystallographic studies, many polymethylene chain structures were determined from an identified characteristic methylene subcell scattering in combination (a)

(b) (c)

Fig. 8.7. Crystal structures of short-chain fatty acids: (a) proprionic acid; (b) valeric acid; (c) butyric acid.

CRYSTAL STRUCTURES OF NORMAL CHAIN FATTY ACIDS

143

with Patterson maps. However, the possibility for an isomorphous heavy atom replacement was beneficial for the analysis of more complicated molecular packings. An isomorphic derivative can be obtained when the terminal methyl group is replaced by bromine or iodine, since the van der Waals radii are nearly the same (Pauling, 1960). Such isomorphism was demonstrated when crystallographic unit cell parameters for stearic acid were compared to those from ␻-bromo- and iododerivatives of n-heptadecanoic acid (Larsson, 1964). All three acids were found to crystallize in both B- and C-polymorphs. For the B-polymorph, the sequence of measured unit cell parameters for CH3-, Br-, I- derivatives of the heptadecanoic acid are, respectively, a  5.591, 5.67, 5.68 Å; b  7.404, 7.44, 7.38 Å; c  49.38, 49.2, 50.4 Å; d001  43.85, 44.0, 44.1 Å; ␤  117.37, 116.6, 119.0. The ␻-halogenated analog of lauric acid, 11-bromoundecanoic acid, was studied most extensively. It has an A-form which has not been characterized. However, the B-form crystallizes from solvent (Larsson, 1963a) with cell constants: a  5.73, b 7.54, c  34.8 Å, ␤  118.8, in space group P21/a. The difference between these parameters and those from the B-form of stearic acid are similar to the asymptotic convergence with chain length mentioned above for the C-polymorph. Associated with an ordered carboxyl group packing (see above), there is also a B1 form of the acid (Larsson, 1963a). The crystal structure of the C-form has been solved in projection (Larsson, 1962). It crystallizes in space group P21/a with cell constants a  9.66 (9.52), b  4.96 (4.96), c  28.07 Å (27.62 Å), ␤  99.90 (96.92), where the parenthetic values are for the strictly isomorphous lauric acid in the C-polymorph. Again the chains are tilted by 54.3 to the methyl end planes and the subcell packing is O⬜. Two additional polymorphs are found for 11-bromoundecanoic acid that do not appear in the native fatty acids. As with the even- and odd-acids in conventional polymorphs, these also pack as hydrogen-bonded dimers. The D-form (Larsson, 1963b) crystallizes in space group P21/c with cell constants: a  5.63, b  5.33, c  44.05 Å, ␤  92.17. The methylene subcell is T for chains tilted 41, representing an ideal accommodation of the carboxyl group cross-section with that of the chain packing in layers stacked with opposing tilt values (Fig. 8.8). The E-form (not to be confused with the designation given more recently for the B1 polymorph) crystallizes (Larsson, 1963c) in P1 with cell constants: a  4.80, b  11.72, c  12.41 Å, ␣  107.18, ␤  92.57, ␥  81.43. The methylene subcell is T and the chains are tilted by 40. Another type of heavy atom substitution had been investigated in the thioether analog of lauric acid, 3-thiadodecanoic acid (Abrahamsson and Westerdahl, 1963). Its crystal structure is shown in Fig. 8.9. The compound packs in space group P1 with cell constants: a  4.69, b  5.10, c  29.30 Å, ␣  95.13, ␤  92.60, ␥  114.80. Chains are tilted 57 to the end planes and in this structure the M methylene subcell was encountered for the first time. It is obvious that this sulfur-containing analog is much less successful as a structural isomorph than are the terminal halogen derivatives because the chain bends near this linkage. The layer packing is similar to those found for some branched chain fatty acids, as will be shown below.

144

THE FATTY ACIDS

Fig. 8.8. Crystal structure of 11-bromoundecanoic acid, D-form.

Fig. 8.9. Crystal structure of 3-thiadodecanoic acid.

Synthetic lipid structures based on heavy atom substituted fatty acids can deviate somewhat from the native structures. This might be expected for analogs based on 3-thiadodecanoic acid. For example, a 1,3-diglyceride of the acid packs with chains bent at the carbon connecting the sulfur atom to the carboxyl group (Larsson, 1963d). Although the molecule has a herringbone arrangement with oppositely tilted chains linked to glycerol, the methylene subcell is O⬜. The 1,3-diglyceride of 11-bromoundecanoic acid (Hybl and Dorset, 1971), on the other hand, also packs with the correct molecular conformation, with all-trans chains, and with the correct T subcell. However, as indicated by quantitative electron diffraction studies of the acyl shift of the 1,2-diglyceride, the natural 1,3-diacyl product packs with chains tilted 76 to the methyl end plane (Dorset and Pangborn, 1979), rather than the 45 tilt angle observed for the ␻-brominated analog.

8.3

Crystal structure of unsaturated fatty acids

Unsaturated fatty acids are a common ingredient of biological lipids and are thought to control the fluidity of membrane bilayers when bound to phospholipids. The designation for polymorphic forms is somewhat unfortunate, because it can be confused

CRYSTAL STRUCTURE OF UNSATURATED FATTY ACIDS

145

easily with designations given to other lipids although they refer to quite different chain layer packings. For example, the low-melting crystal form is named ␥, whereas the high-melting form is named ␤, not to be confused with a well-known polymorph of glycerides. There is also an ␣-polymorph, not to be confused with the rotator phase of lipids. The first structure determination of an unsaturated fatty acid was carried out for the low melting ␥-form of oleic acid (13-cis-octadecenoic acid) by Abrahamsson and Ryderstedt-Nahringbauer (1962). It crystallizes in space group P21/a as a pseudoorthorhombic structure with cell constants: a  9.51, b  4.74, c  40.6 Å. In the crystal, it packs as a boomerang-like structure (Fig. 8.10) with pseudomerohedry through the double bond. Structurally, the ␥-form of erucic acid is quite similar (Kaneko et al., 1993). Although the cell constants and chain tilt (56.5) suggest a Kitaigorodskii O[0, 2] layer packing, the methylene subcell is the rarely observed O
. Again the carboxyl groups are associated as hydrogen-bonded dimers. If the double bond is moved to form petroselinic acid (6-cis-octadecenoic acid), the molecules pack in a polytypic type double layer in space group Pbca, with cell constants: a  7.311, b  5.565, c  88.01 Å (Kaneko et al., 1992a), as shown in Fig. 8.11. Chains on the carboxyl side (tilted 68) are too distorted to have a welldefined methylene subcell packing but those on the methyl side pack in O⬜ (64) in the Kitaigorodskii [1, 0] layer. The crystal structure of the longer erucic acid (13-cisdocosenoic acid) was also determined in a low melting ␥1-form, distinct from the ␥-polymorph (Kaneko et al., 1992b). This variant ␥1-structure (Fig. 8.12) is triclinic, P1 , with cell constants: a  5.642, b  5.197, c  44.16 Å, ␣  91.20, ␤  90.85, ␥  117.32. Chain tilts are 58 on the methyl side and 57 on the carboxyl side. Unlike the true ␥-form, the methylene subcell packing is T . The higher melting ␤-form has also been investigated for the unsaturated acids. For example, the higher melting polymorph of oleic acid was determined by Kaneko et al. (1997) and is shown in Fig. 8.13. The layer packing is unusual in that carboxyl and methyl groups share the layers alternately, somewhat like the situation with A-polymorphs of even-chain normal saturated acids. The triclinic space group is P1

Fig. 8.10. Crystal structure of oleic acid, ␥-form.

146

THE FATTY ACIDS

Fig. 8.11. Crystal structure of petroselenic acid, ␥-form.

Fig. 8.12. Crystal structure of erucic acid, ␥1-form.

Fig. 8.13. Crystal structure of oleic acid, ␤-form.

with cell constants: a  9.317, b  5.543, c  35.284 Å, ␣  87.90, ␤  82.82, ␥  86.18. Chains pack in the T subcell and are inclined by 45. The high-melting polymorph of petroselenic acid has a somewhat different crystal structure (Kaneko et al., 1992c), as shown in Fig. 8.14, even though the space group is again P1 , however, with cell constants: a  5.359, b  8.874, c  41.391 Å, ␣  90.49,

CRYSTAL STRUCTURE OF UNSATURATED FATTY ACIDS

147

Fig. 8.14. Crystal structure of petroselenic acid, ␤-form.

Fig. 8.15. Crystal structure of linoleic acid.

␤  89.12, ␥  113.81. There are two unique carboxyl group conformations arising from steric hindrance at the polar interface. One side of the molecule (methyl end) is packed in the M subcell, wheras the other utilizes the O⬜ subcell. When two cis-double bonds are found in the fatty acid, for example, linoleic acid, the molecule will pack with an “S” shape (Ernst et al., 1979). The crystal structure is monoclinic (Fig. 8.15), space group P21/c, where: a  42.98, b  4.632, c  9.377, ␤  109.38. Chains are inclined by 57 and, like the low-melting form of oleic acid, pack in the O
 subcell. The crystal structure of the honeybee pherome, 9-keto-trans-2-decenoic acid was determined by Cromer and Larson (1972). It crystallizes in space group P21/c, where a  9.584, b  8.642, c  13.371 Å, ␤  96.97. As shown in Fig. 8.16(a), there is a conformational twist in the chain near the double bond, reminiscent of the nonplanar conformation found for 15-trans-triacontene (Chapter 6). Finally, the structure of an acetylenic fatty acid, 4-octadecynoic acid, was determined by Mo (1979). This crystallizes in space group P1 , with cell constants: a  8.71, b  5.475, c  45.13 Å, ␣  92.55, ␤  95.13, ␥  123.95. Chains packing in the T subcell are inclined by 70 to the methyl end plane. As shown in Fig. 8.16(b), there is a conformational bend in the chain. Also, there are two different carboxyl group conformations with disordering of positions (not shown in the

148

THE FATTY ACIDS

(a)

(b)

Fig. 8.16. Crystal structures of interesting unsaturated acids: (a) 9-keto-trans-2-decenoic acid; (b) 4-octadecynoic acid.

packing diagram). Two other acetylenic analogs of stearic and behenic acids were investigated by Müller (1927). These packed in monoclinic cells in the Kitaigorodskii O[0, 2] layer, similar to the C-form of the saturated parents.

8.4

Crystal structure of cyclopropane-containing fatty acids

Bridging a carbon–carbon single bond with a methylene group to form a cyclopropyl inclusion creates a class of fatty acids found in some bacteria. There are features of their crystal structures that are shared by the unsaturated acids. When the inclusion is trans, the polymethylene chain packing is virtually undisturbed. The crystal structure of trans-D, L-9,10-methylene octadecanoic acid was solved in projection by Brotherton et al. (1958). Cell constants are: a  9.75, b  4.98, c  41.1 Å, ␤  89.47 in space group P21/a, suggestive of the Kitaigorodskii O[0, 2] layer. The only effect of the methylene substitution is a small bend in the acyl chain. The cis-isomers of such chains pack with a more distorted layer structure. For example, the crystal structure of lactobacillic acid (cis-D or L-11,12-methylene octadecanoic acid), was solved in projection by Craven and Jeffrey (1960). The unit cell is P1 with constants: a  5.64, b  5.19, c  41.1 Å, ␣  88.2, ␤  89.0, ␥  56.6. There is a bend at the chain center and, unlike all of the fatty acids considered so far, the carboxyl groups do not form dimers but pack in infinite hydrogenbonded chains. On the other hand, hydrogen-bonded dimers are found in the crystal

CRYSTAL STRUCTURES OF BRANCHED-CHAIN FATTY ACIDS

149

Fig. 8.17. Crystal structure of DL-11,12-methylene octadecanoic acid.

structure of its racemate (Craven and Jeffrey, 1959), depicted in Fig. 8.17. The unit cell is monoclinic, space group A2/a, where: a  8.93, b  5.10, c  88.6 Å, ␤  98.

8.5 8.5.1

Crystal structures of branched-chain fatty acids Oxygen-substituted fatty acid chains

In previous chapters on n-alkane and alcohol structures, it was shown that a keto function can be substituted on a polymethylene chain without appreciably affecting the methylene chain packing. Secondary alcohol derivatives, on the other hand, enlarge the O⬜ subcell somewhat along its longest axis. Similar behavior can be demonstrated for fatty acid derivatives. Incorporation of a keto function will be shown below for a methyl-branched fatty acid. Recently, the crystal structure of DL (i.e., rac)-12-hydroxystearic acid was reported by Kuwahara et al. (1996). The racemate forms plate crystals whereas the chiral form crystallizes in helically twisted fibers. The chain packing is similar to one of the B-form variants discussed above. That is to say: the space group is P21/a, where a  5.488, b  7.831, c  44.24 Å, ␤  93.64. All-trans chains are tilted by 64.3 to the methyl end plane and the carboxyl groups form hydrogen-bonded dimers. As betrayed by the somewhat large unit cell b-value the O⬜ subcell is elongated in one direction to accommodate the side group which is also hydrogenbonded in an infinite chain. When the hydroxyl branch is moved closer to the carboxyl group, as in DL-2hydroxytetradecanoic acid (Dahlén et al., 1976), a centrosymmetric triclinic structure is formed: a  5.170, b  5.385, c  32.307 Å, ␣  79.97, ␤  101.14, ␥  121.92 The carboxyl groups retain the hydrogen-bonded dimerization but there is also an internal hydrogen bond from the hydroxyl group to this head group (Fig. 8.18). Chains tilted 53 pack in subcell M .

150

THE FATTY ACIDS

Fig. 8.18. Crystal structure of DL-2-hydroxytetradecanoic acid.

8.5.2

Methyl-branched chains

Methyl groups cannot be accommodated into the polymethylene chain packing as easily as can alcohol or keto oxygen functions. In an overview of these structures (Abrahamsson, 1959a; Abrahamsson and Fischmeister, 1959), there are two polymorphic forms: ␶ and . The lamellar spacing of the ␶-form depends on the position of the methyl group in the chain. That is to say, the methyl group must be fit somehow into the gap between chain layers. In the -polymorph, the lamellar spacing is independent of methyl position. As will be shown below, the methyl group forms the end of a crystallographic alkane chain, from which a carboxyl-containing branch occurs. Some branched acids, for example, those with methyls on the 6, 10, 11, and 12 positions of the chain, can crystallize in either polymorph. A table of lamellar spacings and subcells has been given by Abrahamsson (1959a). The simplest ␶-structure is that of isostearic acid (Abrahamsson and Lundén, 1972), depicted in Fig. 8.19(a) to show how the branch is accommodated into the interlamellar gap. The unit cell is triclinic, space group P1 , where, a  4.935, b  5.652, c  34.41 Å, ␣  95.22, ␤  95.21, ␥  103.62 Chains, tilted by 44, pack in the T subcell. The 13-keto derivative has a very similar structure (Fig. 8.19(b)) with very similar unit cell parameters, chain tilt, and the same subcell (Dahlén, 1972). There is no marked perturbation of the triclinic subcell by the keto branch, as there is also none for the common orthorhombic subcell. Other structures in this class, determined in projection, include that of 16-DLmethyl octadecanoic acid (Abrahamsson, 1958), which is triclinic, a  5.40, b  7.54, c  51.8 Å, ␣  145.63, ␤  105.70, ␥  60.30, where chains tilted by 57 pack in the T subcell. The 17-methyl derivative of octadecanoic acid (Abrahamsson, 1959b) is also triclinic: a  5.63, b  9.66, c  53.3 Å, ␣  93.50, ␤  134.0, ␥  101.20, retaining the previous subcell for chains tilted by 46. Here there is some distortion to the carboxyl group packing although dimers are maintained. The 9-DL-derivative of octadecanoic acid in this polymorph retains space group and subcell (Abrahamsson, 1956), where, a  4.97, b  14.77, c  51.91 Å, ␣  165.1, ␤  90.0, ␥  90.0. The chain sequence from the branch position to the methyl end is strongly bent whereas the portion nearer the polar groups has a more regular packing. The crystal structure of 14-DL-methyl octadecanoic acid (Abrahamsson, 1959c) packs in space group P1 , where, a  5.06,

CRYSTAL STRUCTURES OF BRANCHED-CHAIN FATTY ACIDS (a)

151

(b)

Fig. 8.19. Crystal structures of methyl-branched fatty acids in ␶-polymorphic form. (a) isostearic acid; (b) 13-keto-isostearic acid.

b  6.01, c  54.5 Å, ␣  135.1, ␤  91.7, ␥  107.3. Main chains in the T subcell are tilted by 49. Crystallographically, this structure is that of a butyl branched pentadecanoic acid and the branches are accommodated in the lamellar interface. Finally, Sydow (1958) described a remarkable (-) 2-methyl, 2-ethyl eicosanoic acid. Interdigitated chain layers were required to pack the two branches for this orthorhombic structure. However, due to the staggered arrangement of the interface, hydrogen-bonded carboxyl group dimers were not possible, only a continuous hydrogen-bonded chain. Several crystal structures have also been solved for the -polymorph. All of these have the methyl branch near the carboxyl group and the hydrogen-bonded dimer is maintained commonly even though this polar group is in a branch. For example, the packing of 2-DL-methyl octadecanoic acid is an octadecane chain with a carboxylcontaining side chain. The space group is P1 , where, a  5.07, b  5.76, c  52.5 Å, ␣  133.75, ␤  87.43, ␥  109.68 (Abrahamsson, 1959d) also with the T subcell. Its chiral form, on the other hand, packs in a monoclinic structure, space group P21, a  9.08, b  5.01, c  24.0 Å, ␤  116.62 (Abrahamsson, 1959e). Here the chains, sharing general conformational features of the racemic form, are

152

THE FATTY ACIDS

Fig. 8.20. Crystal structure of methyl-branched fatty acid in ␯-polymorph: keto-dodecanoic acid.

DL-2-methyl-7-

Fig. 8.21. Crystal structure of DL-3-bromostearic acid.

packed antiparallel and the carboxyl groups in this case only form continuous chains, not dimers. The subcell is O
⬜. Certain derivatives of the branched-chain acids have been determined in projection. When a 7-keto function is added to a racemic 2-methyl branched dodecanoic acid (O’Connell, 1968), a monoclinic structure, preserving a O
⬜ subcell, is also found (Fig. 8.20) in space group P21/c, where, a  9.122, b  5.061, c  30.784 Å, ␤  100.7. The chain tilt is 67.5 compared to 59 for the previous acid, and the

BINARY PHASE BEHAVIOR OF FATTY ACIDS

153

carboxyl groups are in hydrogen bonded dimers. The keto group causes a 7 twist of the chain. A DL-3-bromo octadecanoic acid is probably not isostructural with its methyl analog (Abrahamsson and Harding, 1966). The DL-2-bromo-stearic acid also is not isostructural (Müller, 1927). A triclinic structure was found for the former with the triclinic subcell is found (Fig. 8.21) where, a  5.68, b  5.63, c  32.8 Å, ␣  101.8, ␤  93.1, ␥  97.9. Here the functional alkane chain has an ␻-bromo termination. The chains are tilted 36 compared to a 46 tilt for the 2-DL-methyl octadecanoic acid. The 2-DL-bromo derivative crystallizes in a monoclinic cell, perhaps in a O[0, 2] chain packing.

8.6

Thermotropic behavior of fatty acids

Thermal transitions between various polymorphs are observed in normal chain fatty acids. There are no rotator phases for multilayer crystals. For the even-chain acids, the most stable A and B polymorphs transform to the higher-energy C-form irreversibly (Stenhagen and Sydow, 1953). These transitions are also monotropic for the ␻-halogenated analogs of the even-chain acids (Larsson, 1963a, 1964). However, 11-bromoundecanoic acid has the property of all polymorphs transforming to the E-form before melting, even though just the C-form is recrystallized from the melt, just as in the unhalogenated acids. The longer ␻-halogenated derivatives of heptadecanoic acids, on the other hand, more closely resemble the unsubstituted fatty acids in their thermal transitions. For the odd-chain acids, the transition of A
to C
is monotropic whereas the B
to C
transition is enantiotropic (Stenhagen and Sydow, 1953). The reversibility of the latter polymorphic stuctures compared to the irreversibility of structurally similar even-chain acid forms, has been attributed to the difference in chain conformation near the methyl group (Goto and Asada, 1978b). Given the three major polymorphs for cis-unsaturated fatty acids, the ␥-and ␣-forms transform reversibly with one another, with the ␥-polymorph being the lowest temperature form (Kim et al., 1988). Both of these transform slowly to the highestmelting ␤-polymorph upon standing. The ␥-polymorph is disordered at room temperature and the chain ends become more disordered as the crystals are heated toward the melting point (Kim et al., 1988). The other two polymorphs are highly ordered at low temperature.

8.7

Binary phase behavior of fatty acids

A classical study of fatty acid co-solubility in the solid state (Francis et al., 1930) indicated that equimolar combinations would form solid solutions when the chains differed by one, two, or three methylene units. Beyond this chain increment, fractionation should occur. For equimolar combinations of n with n 1 carbon acids, the lamellar spacing was found to be halfway between those of the two pure

154

THE FATTY ACIDS

components, according to Vegard’s law. If grown from the melt, the crystal habit would resemble that of the shorter acid whereas if grown from solution, it would resemble that of the longer acid. Tri-component solids, for example, n, n 1, n 2 carbons, would form solid solutions resembling the middle length acid. Later work seemed to indicate that larger chain-length differences could be stabilized as solid solutions (Slagle and Ott, 1933) but this view was obscured by the occurrence of various polymorphs in the crystalline solid. Francis et al. (1930) claimed that the continuous concentration series of palmitic and stearic acids would produce a series of lamellar spacings adhering closely to Vegard’s law. A later study (Frede and Precht, 1976) demonstrated that the increment with increasing stearic acid concentration was actually step-like, much as was found for the fatty alcohol binaries by Amelinckx (1958). The B- and C-polymorphs occur simultaneously between 2.5% and 10% concentration of shorter chains added to longer and at 10% addition of longer chains to shorter ones (Piper et al., 1934). Otherwise the B-polymorph is observed. Some work on binary combinations of branched chain and normal fatty acids has been reported (Abrahamsson, 1959a). If the normal acid chain length is smaller than the number of carbon atom chain containing the methyl branch (e.g. 14-DL-methyl stearic acid with n-tridecanoic acid), the two form a 1 : 1 molecular compound. The methylene subcell packing is O⬜ with the chain tilt close to that of the normal acid. If the unbranched acid length is longer (e.g. 14-DL-methyl stearic acid with stearic acid), a 1 : 3 molecular compound is formed, with the chain packing resembling the C-form of the normal-chain fatty acid.

8.8 1.

2.

3.

4.

Summary Saturated normal fatty acids crystallize in various polymorphic and polytypic forms, all involving simple methylene subcells. Again, there is an odd/even discrimination of preferred layer packing. ␻-Halogenated (Br, I) derivatives of saturated acids can crystallize as true structural isomorphs of the normal fatty acids but also new polymorphic forms can be introduced. Functionalization such as unsaturation and methyl-branching may lead to unusual methylene subcells to compensate for local perturbations to the chain cross-section. An extensive study of methyl-branched fatty acids reveals that the methyl group is never included within the layer polymethylene subcell packing. Instead it is forced into a lamellar interfacial domain. Keto-branches, on the other hand can be incorporated into the polymethylene lattice, as also found for substituted n-paraffins.

9 Linear fatty acid esters

9.1

Introduction

Many animal or plant waxes contain a large amount of linear fatty acid esters, sometimes co-mixed with n-alkanes. It is important therefore to compare the crystallography of these wax esters, as pure materials and in blends, to multicomponent assemblies based on the alkanes, particularly since paraffin waxes are often used in blends with the more costly natural waxes in order to “extend” desired properties cheaply.

9.2

Pure esters—crystallography

In a previous chapter, the influence of an interposed heteroatom group on the chain cross-section was discussed for the dialkyl ethers and thioethers, demonstrating how deviations from chain planarity might lead to a preferential tilted chain layer packing. This is also a very important consideration for the linear chain esters. For example, in the crystal structure determination of the polyester, poly (-caprolactone) –[CH2–CO–O–(CH2)4]–, from fiber X-ray diffraction data, one group (Bittiger et al., 1970) claimed that the molecule should retain the strictly planar conformation of polyethylene while another group (Chatani et al., 1970) favored a twisted chain conformation near the ester linkage (Fig. 9.1). An independent single crystal electron diffraction analysis (Dorset, 1991c) supported the latter result (Fig. 9.2), as did a reanalysis of the published fiber X-ray data via direct phasing methods (Dorset, 1997a). These results agree with theoretical nonbonded energy analyses of typical polyesters (Liu and Boyd, 1990). For free molecules, there is only a slight energetic difference between trans and gauche conformation around the –O–C(sp3)- bond (Smith and Boyd, 1990). The presence of nonplanar conformers in the crystal structure depends on their ability to be accommodated into a dense layer packing. As found for dicetyl ether (Chapter 6), there appears to be an equilibrium between planar and nonplanar conformers resulting in two different chain layer packings. In a more recent analysis of the poly (␻-pentadecalactone) crystal structure (Gazzano et al., 2003), for example, the conformational twist near the ester linkage was not reported, perhaps due to insufficient data, but the avoidance of co-packed ester groups at the same level on neighboring chains is, again, a feature of this rectangular layer model.

156

LINEAR FATTY ACID ESTERS

(a)

(b)

Fig. 9.1. Proposed models for poly -caprolactone. (a) Bittiger et al. (1970); (b) Chatani et al. (1970).

Fig. 9.2. Crystal packing of poly -caprolactone.

PURE ESTERS—CRYSTALLOGRAPHY

157

(b) (a)

(1)

(2)

Fig. 9.3. (a) Crystal structure of ethylene di-11-bromoundecanoate; (b) crystal structure of 11-bromoundecanoic acid anhydride (figure provided by Dr W. A. Pangborn).

An extreme example of this internal chain twisting for a layer structure can be found in the crystal structure of an ethylene glycol diester (Fig. 9.3(a)) where two nonplanar conformations are found near the ester links. Ethylene di-(11-bromoundecanoate) was determined from single crystal data collected from three crystals (Dorset, 1970; Dorset and Hybl, 1972). The layer packing is Kitaigorodskii’s (1961) O[1, 0]; thus the monoclinic cell constants are: a  5.57, b  7.32, c  32.3 Å, ␤  94.1, space group P21/a. The orthorhombic perpendicular methylene subcell required for this layer packing has average dimensions: a  4.97, b  7.32, c  2.53 Å. The conformational deviations from planarity near the ethylene glycol moiety have a geometry very similar to the gtg1 “kink” in polymethylene chains. While there may not be a true gauche bond near the ester linkage in simple fatty acid esters, the deviation from planarity can be sufficient to cause crowding of linear chain packing when the ester linkages are near one another in a layer. This would be especially true for the symmetric fatty acid esters, that is, where the carbon lengths of the carboxylic acid and alcohol moieties in CH3(CH2)mCO–O(CH2)n)CH3 are equal. However, there are currently no complete X-ray crystal structures reported for symmetric wax esters. In 1938, Kohlhaas had shown that the unit cell dimensions for cetyl palmitate (hexadecyl hexadecanoate) were, a  5.49, b  7.45, c  88.78 Å, ␤  118.7, so that the chains would again pack in the Kitaigorodskii (1961)

158

LINEAR FATTY ACID ESTERS

O[1, 0] layer, but, unlike the case of dicetyl ether, the unit cell was proposed to contain a bilayer. Single lozenges grown from ether solution showed a 74.1 angle between boundary {110} faces, also a characteristic of the layer packing. From systematic absences in the Laue diffraction patterns, the space group was proposed to be P21/c. The lamellar spacing observed would therefore be: (c sin ␤)/2  38.94 Å. This observation was confirmed by quantitative electron diffraction studies on single microcrystals (Dorset, 1976c). Low-angle spacings from powder X-ray measurements indicate that symmetric esters always pack in a tilted chain layer (Lutz et al., 1967; Aleby et al., 1971). The least squares line through the homologous series indicates that the lamellar spacing can be predicted from d002  1.12 m 3.14 Å, where m is the number of carbons in the ester chain. Similar evidence for tilted chains in other esters is found from reflection electron diffraction (RHEED) data (Sutula and Bartell, 1962). Without success, Kohlhaas (1938) sought polymorphic forms in the symmetric fatty acid esters, given analogous observations made for fatty acids and also the similarity of their crystal habits. From transmission electron diffraction patterns alone, a rectangular layer packing was proposed for cetyl palmitate (Natta et al., 1935; Dorset, 1978) but, later (Dorset, 1989a), it was shown that the associated corrugated crystal grown from hot solvent was actually a random “ripple” structure of roof-like domains, however retaining the Kitaigorodskii O[1, 0] layer packing. Similar ripples had also been observed by Keller (1961) for heated orthorhombic paraffin crystals. For the esters, the chain axes are oriented, on average, perpendicular to the substrate surface, only because the ripples preserve a twinned oblique layer packing, orienting the twin plane in the desired direction. A fatty acid anhydride might be thought to be a possible model for a symmetric wax ester since the only functional difference is the incorporation of a second carbonyl group next to the bridging oxygen. The crystal structure of 11-bromoundecanoic acid anhydride was determined by Pangborn (1973). Similar to the oblique layer packing of symmetric esters, the space group is P21 with cell constants: a  23.72, b  5.32, c  9.68 Å, ␤  95.62. However, the molecular chain (Fig. 9.3(b)) is bowed with one end gauche conformational twist. Also, unlike the fatty acid esters, the methylene subcell packing is T . The angle between least squares lines though the fatty acid moieties is 150. The tilt angle of the chains to the approximate molecular two-fold axis is 64. There is no analogy to the fatty esters, therefore. Two crystalline forms are observed, however, for asymmetric esters, for example, by infrared measurements (Aleby and Fischmeister, 1969a,b; Aleby et al., 1971) and powder X-ray diffraction (Lutz et al., 1967; Aleby et al., 1971; Sullivan, 1974). It is interesting to note that, for the asymmetric esters, a rectangular layer packing (Kitaigorodskii O[0, 0]) is possible, possibly because the chains can pack so that the ester linkages will not lie next to one another—for example, as also found in the crystal structure of poly (-caprolactone) (Fig. 9.2). This untilted layer packing is observed often in electron diffraction experiments (Natta et al., 1935; Storks and Germer, 1937; Coumoulos and Rideal, 1941; Sanders and Tabor, 1951). Rectangular

PURE ESTERS—CRYSTALLOGRAPHY

159

layers are also found for asymmetric linear thioesters (Witnauer et al., 1957). An extensive study of chain packing for even-chain alcohol esters of fatty acids (Marosi and Schlenk, 1973) revealed that the rectangular layers are formed when the alkyl function contained one, two, or three methylene carbons more, or four or five methylene carbons fewer, than the acyl chain moiety. Diacid esters of long chain diols can also form rectangular layers when the diol moiety is of sufficient length. Although no complete single crystal structure exists for this rectangular crystalline polymorph, it will be found to be important for the stability of natural waxes containing mostly fatty acid esters of long chain alcohols. A preliminary analysis has been carried out for the orthorhombic form of myristyl stearate (Zhang et al., 1989; Dorset, 1995a), based on electron diffraction data. The space group is A21am with cell constants, a  7.63, b  4.98, c  87.8 Å. Obviously the chain packing is very similar to one of the odd-chain paraffin structures (B-polymorph). For crystals grown (epitaxially) from the melt, streaks always appear in the 0kl electron diffraction patterns, indicating a yet unidentified stacking disorder. The second crystal form of the asymmetric esters is very similar to that of the symmetric ones, and, in fact, the lamellar spacings for equivalent numbers of chain carbons are identical (Lutz et al., 1967). They proposed that the crystal structure of the ethyl esters should be equivalent to those of the symmetric esters, even though there is some discrepancy in space group assignment. In an initial analysis of the ethyl stearate crystal structure, Aleby (1962) had proposed the space group to be Aa with cell constants: a  5.59, b  7.40, c  57.1 Å, ␤  118. Based on a study of ethyl behenate, Mathiesen and Welsh (1965) found that, if the space group assignment were Ia instead, some distortions of the bonding parameters in the ethyl moiety became more regular. Although the earlier proposed bilayer packing was essentially correct, Aleby (1968a) corrected this determination in another new unit cell, where a  5.59, b  7.40, c  55.0 Å, ␤  113.5, to give the structure in Fig. 9.4. However, in the new cell, the space group is again Aa. The similarity of these grossly asymmetric esters to the more symmetric ones is indicated by a preliminary electron diffraction determination (Fig. 9.5) of stearyl myristate (octadecyl tetradecanoate) in the [0 1 0] projection, where a  5.60, b  7.40, c  86.20, ␤  115.0 (Dorset, 1995a). Although the structural model is not completely refined, it obviously exhibits the same bilayer packing as does the ethyl myristate. Methyl stearate packs in a similar layer structure (Fig. 9.6(a)) in space group A2/a (Aleby and Sydow, 1960), except that there are four molecular layers in the unit cell. The unit cell constants are: a  5.61, b  7.33, c  106.6 Å, ␤  116.78. There is also a polytypic form for this ester (Fig. 9.6(b)) similar to the one found for oblique layers of paraffins and fatty acids, again sharing the same layer packing (McGillavry and Wolthuis-Spuy, 1970), even though it is orthorhombic (space group Pnab). Cell constants are: a  5.61, b  7.35, c  95.15 Å. Hydroxyl group substitution within the polymethylene chain can drastically change the layer packing. The crystal structure of methyl 12-D-hydroxyoctadecanoate was determined by Lundén (1976). It packs in space group P21 with cell constants: a  8.380, b  4.861, c  25.59 Å, ␤  102.18. The chains therefore

160

LINEAR FATTY ACID ESTERS

Fig. 9.4. Crystal structure of ethyl stearate.

pack in a Kitaigorodskii O[0, 2] layer since the methylene subcell is O⊥. However (Fig. 9.7), the layer packing is head to tail with staggered molecules to accommodate the secondary alcohol functions in a continuous hydrogen bonded chain. This slightly decreases the shorter lateral subcell spacing to 4.86 Å but expands the longer one to 7.87 Å, exactly the behavior found in the crystal structure of a secondary alcohol (see Chapter 7). The expansion of the subcell to give a lateral area per chain of 19.1 Å2, is similar to the expansion observed when rotator phases are approached. Powder X-ray and infrared spectroscopic measurements (Lundén et al., 1997) indicate that the racemic structure packs in head to head bilayers. Finally, a monolayer structure was observed for n-propyl stearate, although the O[1, 0] layer packing is preserved (Aleby, 1968b), as indicated by the cell constants: a  5.59, b  7.39, c  30.0 Å, ␤  119.2. The packing diagram in Fig. 9.8 was generated, assuming the space group to be Pa. From the resultant bond distances and angles, however, there are some serious discrepancies from accepted values that may indicate an error in the assigned symmetry or in the data collection.

PURE ESTERS—CRYSTALLOGRAPHY

161

(a)

(b)

a c

Fig. 9.5. Electron diffraction study of stearyl myristate. (a) h0l pattern; (b) [0 1 0] potential map (half unit cell). (Dorset, D. L. (1995) Structural Electron Crystallography. NY: Plenum, p. 302. (a)

(b)

Fig. 9.6. Crystal structure of methyl stearate: (a) monoclinic form; (b) polytype.

162

LINEAR FATTY ACID ESTERS

Fig. 9.7. Crystal structure of methyl 12-D-hydroxystearate.

Fig. 9.8. Crystal structure of n-propyl stearate.

BINARY PHASE BEHAVIOR OF LINEAR FATTY ACID ESTERS

9.3

163

Thermotropic behavior of linear fatty acid esters

Strongly asymmetric fatty acid esters can be mesogenic, for example, n-butyl stearate. A carbonyl function shifted synthetically to different positions along a constant chain length has a strong influence on the thermal behavior, as shown by Baldvins and Weiss (1999). For example, in the series of positional isomer of n-butyl stearate, pentyl heptadecanoate, hexadecyl hexanoate, heptadecyl pentanoate, and octadecyl butanoate all form enantiotropic mesophases. Some of these are hexatic B or crystal B forms of rotors. Extremely asymmetric esters such as methyl and ethyl stearate, for example, have metastable ␣-phases with untilted chain packing and stable ␤-forms with tilted chain packing (see crystal structures above) (Lutton and Hugenberg, 1962). Hexyl hexadecanoate forms a monotropic mesophase. On the other hand, decyl dodecanoate is not mesomorphic, probably because of the crowding of ester linkages to a narrow region of the chain layer.

9.4

Binary phase behavior of linear fatty acid esters

Initial attempts to describe the binary phase behavior of long chain esters included studies of tetradecyl tetradecanoate with dodecyl octadecanoate, dodecyl hexadecanoate, and dodecyl tetradecanoate and of dodecyl tetradecanoate with hexadecyl decanoate and tetradecyl dodecanoate (Welsh, 1976). Unfortunately only the liquidus curves were observed on a microscope heating stage so it was difficult to discern the nature of the phase diagram. In unpublished studies (D. L. Dorset), it was found that when the chain lengths of the individual esters are kept constant, stable solid solutions can be stabilized. Examples include: hexadecyl hexadecanoate (cetyl palmitate)/tetradecyl octadecanoate (myristyl stearate), hexadecyl hexadecanoate (cetyl palmitate)/octadecyl tetradecanoate (stearyl myristate), tetradecyl octadecanoate (myristyl stearate)/octadecyl tetradecanoate (stearyl myristate). However, for the tilted chain polymorph in layer packing O[1, 0], near homologs do not form solid solutions, even though the Kitaigorodskii volumetric parameter, e  0.87 should accomodate them. The relevant example is hexadecyl hexadecanoate (cetyl palmitate)/octadecyl octadecanoate (stearyl stearate). Needless to say, the former ester also forms eutectic solids with eicosyl eicosanoate (arachidyl arachidate) and docosyl docosanoate (behenyl behenate). The extreme sensitivity of the inclined chain packing to slight differences in molecular volume has been observed in other work. For example, when it was thought that both octadecyl octadecanoate (stearyl stearate) and n-hexatriacontane shared two very similar polymorphic chain layer packings (Fig. 9.9), the possibility of a stable solid solution was explored (Dorset, 1989), also since the interaction of ketoalkanes with n-paraffins is favored. Although the effective chain length difference was only about one methylene group, only eutectic solids were observed because the ester only maintained the inclined chain packing while the paraffin

164

LINEAR FATTY ACID ESTERS b

(c) c (a)

(b) a c

Fig. 9.9. Interaction of chain species. (a) Hypothetical comparison of an oblique ester packing with that of an n-paraffin; (b) oblique layer packing for n-propyl stearate; (c) proposed orthorhombic structure for an asymmetric ester. (Dorset, D. L. (1986) Rectangular and oblique layer packings of alkane chains and the eutectic solid formed by their interaction. J. Polym. Sci. Part B. Polym. Phys. 27, 1161–1171.)

maintained the rectangular layers (Fig. 9.10). The situation did not change when the ester combined with n-hexatriacontane was slightly asymmetric, for example, tetradecyl octadecanoate (myristyl stearate). Hexadecyl hexadecanoate co-mixed with other heteroatom-substituted molecules of like chain length also may fractionate. For example, the ester is co-soluble with dihexadecyl sulfide but not with dihexadecyl ether, even though the thioether and ether form continuous solid solutions with one another (Dorset, unpublished data). The sensitivity to volume changes is less severe when the esters become more asymmetric. For example, docosyl tetradecanoate (behenyl myristate) forms continuous solid solutions with docosyl hexadecanoate (behenyl palmitate) (e  0.95) or with docosyl octadecanoate (behenyl stearate) (e  0.89). In this case, the rectangular packing is preferred, allowing molecules to shift translationally along their axes. The continuous co-solubility of n-butyl stearate and n-octadecyl butanoate has also been observed (Baldvins and Weiss, 1999). Francis, et al. (1930) noted that equimolar combinations of two homologous

BINARY PHASE BEHAVIOR OF LINEAR FATTY ACID ESTERS

165

(a) 80

70

T (°C)

(b) 60 80

70

60

0

0.1

0.2

0.3

0.4

0.5 Xss

0.6

0.7

0.8

0.9

1.0

Fig. 9.10. Eutectic phase relationship between n-hexatriacontane and octadecyl octadecanoate: (a) from heating experiments; (b) from cooled melts. (Dorset, D. L. (1989) Rectangular and oblique layer packings of alkane chains and the eutectic solid formed by their interaction. J. Polym. Sci. Part B. Polym. Phys. 27, 1161–1171.)

ethyl esters of normal fatty acids formed a solid solution with lamellar spacing resembling the pure ester with a chain two carbons longer than the largest component. The lamellar spacings given by them were also obviously those for rectangular layer forms and were acknowledged by these authors possibly to be a metastable form. For extremely asymmetric esters such as the methyl and ethyl derivatives of fatty acids (Lutton and Hugenberg, 1962), domains of stable solid solutions in the untilted chain ␣-form, can be found, for example, for palmitate and stearate, either for short alkyl lengths or combined methyl and ethyl esters. Increasing the chain length difference, for example, methyl stearate with either the lignoate or behenate can induce microaggregation phenomena similar to those seen with binary alkane combinations where the volumetric difference tolerated in a stable solid solution is just exceeded, that is, metastable solid solutions and/or eutectics of solid solutions (Snyder et al., 1995).

166

9.5

LINEAR FATTY ACID ESTERS

Multicomponent and other natural waxes

In an initial effort to mimic some of the natural waxes that are based on linear fatty acid esters, an equimolar distribution of docosyl esters of tetradecanoic, hexadecanoic, octadecanoic, and eicosanoic acids was combined and fused to make a waxy solid. Upon orientation on benzoic acid, the epitaxial crystals diffracted very much as if they were locally distributed in orthorhombic n-paraffin structures mimicking n-C40H82, n-C41H84, or n-C42H86 in space group A21am or Pca21 for odd- and eventypes, respectively (Dorset, 1995b) (Fig. 9.11). Similar behavior was observed when an artificial spermaceti wax was epitaxially oriented. This combination of waxes was composed of n-hexadecanol-based esters. When the untilted chain packing can MW2636

HW4050

30 32 34 m

44 46 m

BEHWX

40 42

CANWX

m

28 30 Yellow beeswax

50 52

m

m

Artificial beeswax

38 40 42

m

Fig. 9.11. Apparent local paraffinic crystal structures of waxes detected by electron diffraction measurements: MW2636, a flat wax constructed from even-chain n-paraffins from C26 to C36; HW4050, a flat wax constructed from even n-paraffins from C40 to C50; BEHWX, a synthetic wax from a flat distribution of behenyl alcohol esters of myristic through arachidic acids; CANWX, birthday candle wax; yellow beeswax from a natural source; “artificial beeswax” (1 : 2 MW2636/BEHWX).

MULTICOMPONENT AND OTHER NATURAL WAXES

167

occur, it is generated when pure longer tilted chain components are added to shorter chains at greater than 5% or if greater than 20% shorter components are added to longer ones (Piper et al., 1934). Preliminary studies of natural spermaceti, on the other hand, reveal an oblique layer packing similar to that of the cetyl palmitate component. (Despite previous analyses (Warth, 1947), it is not certain that this is the principle ester in spermaceti. Holloway (1968) stated that cetyl myristate should be the major component with significant amounts of cetyl laurate and palmitate.) Again, a tilted chain ester requires a strong contamination by vertical chain esters to obtain a mixture with vertical chains, and vice versa (Kreger and Schamhart, 1956). A mineral wax from lignite, also based on long chain fatty acid esters, was the subject of a quantitative crystal structure analysis (Dorset, 1997b). Montan wax has been described (Warth, 1947) as the combination: 58–59% wax esters (e.g. octacosyl esters of C20, C22, and C24 fatty acids and a number of higher esters) as well as 17–19% free fatty acids with lengths from C27 to C32. The orthorhombic methylene subcell had been characterized earlier (Basson and Reynhardt, 1988a). Electron diffraction patterns from montan wax, revealed this natural product to be nearly as crystalline as refined petroleum waxes and indexing patterns revealed that it behaved locally as if it were n-C29H60 or n-C30H62, that is, shorter than the average component claimed in the chemical analysis cited above. A pattern from the even-chain form was used for a crystal structure determination in space group Pca21 with a  7.42, b  4.96, c  39.68 Å. The agreement of the crystal structure (e.g. resembling, on average, an n-C30H62 layer) to the observed intensity data was reasonably good. However, only carbon atom positions were used for this determination. In principle, the inclusion of a carbonyl oxygen in the chain should have an effect on the intensities of the lamellar reflections (Lutz et al., 1967). However, these are attenuated in a solid solution, due to the disorder at the lamellar interface, and, for a variety of different molecular sites, their effect would be somewhat averaged out. It was also found that the melting point of the montan wax sample examined by electron diffraction was appreciably lower than the value given by Warth (1947). On the other hand, a more recent analysis of components (Presting and Kreuter, 1965), while confirming the presence of wax alcohols and fatty acids, reveals that n-paraffins in the carbon length range from C27 to C33, peaking at C29 and C31, are also important ingredients. The chain length found for all components agree with the mean chain lengths determined from electron diffraction patterns. Crystalline wax investigated by these authors also melted within the range measured by Dorset (1997b). Electron diffraction studies have also characterized a natural wax from peat, revealing the orthorhombic subcell packing (Parmon and Ivanova, 1986). Results from other multicomponent animal and plant waxes have been somewhat difficult to interpret. For example, after the methylene subcell packing was characterized for a South African bee honeycomb wax (Basson and Reynhardt, 1988b), electron diffraction studies were carried out on both North American (Dorset, 1995b) and South African (Dorset, 1997b) varieties. As found for a high-molecular weight Fischer–Tropsch wax, the lamellae are not fully separated when directly crystallized from the melt, although occasional observations of a single lamellar

168

LINEAR FATTY ACID ESTERS

spacing indicate the nascent layer thickness to be around 65.8 Å, corresponding to n-C51H104. The difficulty in crystallizing the lamellae may be due to the problem experienced anyway with n-paraffins of this length (Hengstenberg, 1928; Zhang and Dorset, 1990a). Carnauba wax, that had been studied previously by powder X-ray diffraction and nuclear magnetic resonance (NMR) (Basson and Reynhardt, 1988c) but again the electron diffraction patterns resemble those from polyethylene. Chemical analyses (a)

(b)

(c)

(d)

(e)

Fig. 9.12. Wooly alder aphid wax. (a) Wax streamers from insect; (b) electron diffraction from an individual streamer wax tubule; (c) electron diffraction from insect wax recrystallized from toluene; (d) electron diffraction (lamellar row) from epitaxially oriented insect wax; (e) RHEED of recrystallized insect wax layer. (Dorset, D. L. and Ghiradella, H. (1983) Insect wax secretion. The growth of tubular crystals. Biochim. Biophys. Acta 760, 136–142.)

MULTICOMPONENT AND OTHER NATURAL WAXES

169

(Warth, 1947) reveal it to contain 80–81% wax esters (mostly myricyl cerotate, a (fictitious) C30 chain alcohol esterified to a C26 chain acid) and 9–10% free fatty acids (lengths from 27 to 32 carbons). One observation of a lamellar spacing (Dorset, 1997b) indicated that the nascent lamellar thickness might be near 84.6 Å, corresponding to a 65-carbon paraffin. Annealing Fischer–Tropsch, bee honeycomb, and carnauba waxes in the presence of the nucleating substrate does much to improve the crystallinity (Dorset, 1999e). Lamellar spacings are consistently observed in single crystal diffraction patterns. For

[100] [110]

[110] [010]

Fig. 9.13. Schematic model of wax monolayer in tubule in relation to the orientation of the unit cell projection down the chain axes that are perpendicular to the tubular surface. (Dorset, D. L. and Ghiradella, H. (1983) Insect wax secretion. The growth of tubular crystals. Biochim. Biophys. Acta 760, 136–142.)

170

LINEAR FATTY ACID ESTERS

example the lamellar spacing is 66.5 1.4 Å or 66.4 1.2 Å, respectively, for North American and South African beeswaxes. The carnauba wax diffracts with a 42.2 1.9 Å lamellar spacing, similar to the low-angle X-ray value measured from a leaf wax from another Copernicia species (Kreger, 1951). A systematic characterization of powder patterns had been made by Kreger (1951) for numerous plant waxes and further data had been accumulated subsequently (Reynhardt and Riederer, 1991, 1994). Some insects synthesize nearly pure waxes that can be more easily characterized. For example, the cuticle wax from Prociphilus tesselatus, the wooly alder aphid (Meinwald et al., 1975), secretes nearly pure 15-oxotetratriacontyl 13-oxodotriacontanoate as wax streamers with 0.16–0.25 m diameter (Fig. 9.12(a)) as a defense mechanism against predators (Dorset, 1975; Dorset and Ghiradella, 1983). Electron micrographs (Fig. 9.12(b)) reveal the streamers to be hollow tubes and selected area patterns indicate the chains to be packed in a rectangular monolayer, produced also when lamellae are recrystallized from hot toluene (Fig. 9.12(c)). Epitaxial orientation reveals the lamellar spacing to be 88.1 Å (Fig. 9.12(d)) while (RHEED) measurements confirm the untilted chain packing (Fig. 9.12(e)). The orthorhombic unit cell for the recrystallized wax would therefore have dimensions, a  7.52, b  5.05, c  176.2 Å, resembling n-C67H136. Analysis of the existing data show the orientation of the methylene subcell to the streamer tube axis (Fig. 9.13), indicating that the fastest growth direction corresponds to the lowest energy attachment site for the growth of a paraffin lath (Boistelle and Aquilano, 1978). Less complete electron diffraction studies have been carried out on some insect larval waxes (Hurst, 1948, 1950).

9.6 1.

2.

Summary Long chain esters of linear alcohols and fatty acids pack in an oblique layer when the ester linkage is at the center of the molecule. This packing is also adopted by asymmetric esters although these can also form rectangular layers. Near homologs of symmetric esters do not form solid solutions, although the asymmetric esters are co-soluble in the solid state. The rectangular layer arrangement is the basis for fatty ester-containing waxes.

10 The cholesteryl esters

10.1

Introduction

Cholesteryl esters are major components of fatty deposits expressed by various mammalian lipid storage diseases, such as atherosclerosis (Small, 1970; Ginsburg, et al., 1984). In the context of waxes, wool greases are of major commercial importance (Hamilton, 1995), since they are the source of lanolin. Although long chain fatty acid esters are an important component of these greases and the derived wax sterols, presumably in the esterified form, also are a major ingredient. Comparison of cholesteryl esters to the n-paraffins or simple fatty acid esters provides an interesting, contrasting case where an approximate cylindrical symmetry of the molecules is lost. As is also found for a number of amphiphilic molecules (e.g. detergents), this introduces the possibility of mesomorphic behavior, including the cholesteric liquid crystal state named after these materials. In the crystalline state, there are opportunities for the co-packing of sterol nuclei with polymethylene chains, so that the methylene subcell packing, found for a wide variety of lipids, can be lost.

10.2

Crystal structures

Understanding multicomponent solids made up of cholesteryl esters is only possible when these are considered in context of the crystal structures of the pure components. Growth of suitable crystalline samples was possible when a good solvent with a very low vapor pressure (n-pentanol) was found, permitting the evaporation to progress very slowly. (The same idea was exploited when n-dodecane was used to crystallize n-paraffin solid solutions, see Chapter 5.) However, a listing of unit cell constants from this initial crystallization study (Barnard and Lydon, 1974) did not provide a systematic view of cholesteryl ester crystal packing. The detailed structures of materials at room temperature and lower temperature were necessary to present an accurate view of the densest as well as most disordered parts of the layer packing (Sawzik and Craven, 1980a; Craven, 1986). As shown in Chapter 7, different local packing densities are also found for cholesterol (Shieh et al., 1977, 1981; Craven, 1979; Hsu and Nordman, 1983), where there are again more than one molecule in the asymmetric unit.

172

THE CHOLESTERYL ESTERS

Starting with a homologous series of saturated fatty acid esters, it is clear that, beyond a chain length of six carbons, each crystal structure can be characterized as one of three basic layer packing motifs. Unsaturated acids also fall into one of two alternative monolayer structures also exhibited by the saturated series. 10.2.1

Bilayer packing

The easiest structures to understand, in context of “typical” lipid crystal packings, are the ones where the sterol nuclei layers are compensated by an interdigitated chain assembly with a well-defined methylene subcell. (This sort of layer packing arrangement was discussed earlier in Chapter 3 for 1-phenyl decane.) This packing form is found exclusively for fatty acid chain lengths of 14 carbons or more (Sawzik and Craven, 1980a) and the packing is possible, as an alternative polymorph, for esterified dodecanoic (lauric) and tridecanoic acids (Dorset, 1987b). There are no unsaturated esters that pack in this crystalline form. A representative crystal structure for this polymorph is that of cholesteryl myristate (Craven and DeTitta, 1976), shown in Fig. 10.1. The space group is A2 with a  10.260, b  7.596, c  101.43 Å, ␤  94.41. There are two molecules in the asymmetric unit, unrelated by the space group symmetry. Although packing in a different space group (P21), the analog of the stearate, cholesteryl 17-bromoheptadecanoate has a very similar layer structure (Abrahamsson and Dahlén, 1977). The layer packing in Fig. 10.1 can be subdivided into three parts. The acyl chains pack with a density of 1.02 g cm3 (Craven, 1986) with a very unusual methylene subcell. Abrahamsson and Dahlén (1976) originally identified it to be O⊥ in their original report but later realized it to be a hybrid HS1 subcell (Abrahamsson and Dahlén, 1977). For the myristate structure (Craven and DeTitta, 1976) this subcell packing is less well-defined. The tetracyclic sterol nuclei pack with a density of 1.18 g cm3 while the isoprenoid chains at the layer interfaces are almost liquid-like (evidenced also by highest thermal motion) with a density of only 0.75 g cm3 (Craven, 1986).

Fig. 10.1. Crystal structure of cholesteryl myristate (bilayer).

CRYSTAL STRUCTURES

10.2.2

173

Monolayer I packing

For acyl chains from 9 to 12 carbons in length, the stable crystalline form is termed monolayer type I. Crystal structures of the whole homologous saturated chain series have been determined (Dahlén, 1979; Guerina and Craven, 1979; Pattabhi and Craven, 1979; Sawzik and Craven, 1979a; Sawzik and Craven, 1980b). Again there are two molecules in the asymmetric unit and the space group is invariably P21. This layer packing will also include the structures of a number of unsaturated fatty acids including the nervonate (Sawzik and Craven, 1984a), one polymorph of palmitelaidate (Cho and Craven, 1989), and the palmitoleate (at two temperatures) (Sawzik and Craven, 1982, 1984b; Craven and Sawzik, 1984). It is interesting to note that cis- and trans-unsaturated fatty acid esters of the same chain length and location of double bonds are isostructural (Cho and Craven, 1987). Indeed, the extreme variations of chain direction in unsaturated fatty acids found in their own crystal structures (Abrahamsson and Ryderstedt-Nahringbauer, 1962; Ernst et al., 1979; Kaneko et al., 1992a–c, 1993, 1997) have no relevance to the cholesteryl esters when including them as a moiety for this or the other monolayer packing (see below). Instead, the double bond is incorporated within a kink in a chain that has an approximate cylindrical orientation. The same adjustment is found when the unsaturated acid is esterified to other bulky groups such as piperazinium (Luo et al., 1995). A representative crystal structure is that of cholesteryl dodecanoate (laurate), shown in Fig. 10.2 in its low temperature (Sawzik and Craven, 1980c) form. For this low temperature form, the unit cell constants are: a  12.983, b  8.838, c  31.803 Å, ␤  90.41. As seen in Fig. 10.2, the molecules are inclined with a tilt from 61 to 67 to the monolayer surface. Two B molecules pack with the sterol nuclei next and antiparallel to one another, whereas in the A molecules, there are acyl chains packing next to the tetracyclic moieties. The planes of the sterol nuclei

Fig. 10.2. Crystal structure of cholesteryl laurate (monolayer I).

174

THE CHOLESTERYL ESTERS

in the asymmetric unit are nearly perpendicular to one another. At room temperature (Sawzik and Craven, 1979a), the disordered lamellar interface contains both acyl and isoprenoid chains with high thermal motion (at room temperature) at this boundary. Lowering the temperature diminishes the amplitude of the oscillations and also the chain conformation. In general, while the increase in layer spacing is not directly related to the increment of chain length for the saturated series, there are changes in detail of the interfacial packing (Craven, 1986). This, in part, explains why a variety of unsaturated chain esters can be incorporated into this packing scheme. 10.2.3

Monolayer II packing

For the second type of monolayer, the molecular packing is dictated by an efficient antiparallel association of cholesteryl nuclei that are interlocked via the protruding methyl groups, an arrangement found previously for cholesteryl iodide (Carlisle and Crowfoot, 1945). The rings are highly tilted to the layer surface (Craven, 1986). Acyl chains are, therefore, thrust into a loosely associated interface, but again do not pack with a methylene subcell. A representative crystal structure is that of cholesteryl octanoate (Craven and Guerina, 1979a), shown in Fig. 10.3. The monoclinic space group is again P21 with cell constants: a  12.80, b  9.20, c  14.12 Å, ␤  93.81. For the saturated chain series, the same structure is found for fatty acids with 6–8 carbon atoms, the crystal structure of cholesteryl hexanoate also having been reported (Park and Craven, 1981). It is also found for a number of unsaturated chain esters including: the oleate (two temperatures) (Craven and Guerina, 1979b; Gao and Craven, 1986), the linolelaidate (Sawzik and Craven, 1983), and one form of the palmitelaidate (Srivastava and Craven, 1989). The ester with two trans double bonds

Fig. 10.3. Crystal structure of cholesteryl octanoate (monolayer II).

THERMOTROPIC BEHAVIOR

175

(linolelaidate) closely mimics the structure of one with one cis double bond (oleate). From cell constants, the packing is inferred for the cis-11-eicosenate, the erucate, and the elaidate (Sawzik and Craven, 1981). It is also interesting to note that the sterol packing is also shared by other shorter chain derivatives including the acetate (Sawzik and Craven, 1979b), the chloroformate (Chandross and Bordner, 1978) and the perfluoroproprionate (Tamura et al., 1987). For the long chain cholesteryl esters, there is only one molecule in the asymmetric unit, in contrast to the other packing types discussed above. 10.2.4

Other crystal forms

Unusual crystal forms can occur for small chain length esters. For example, cholesteryl pentanoate has an orthorhombic unit cell (Barnard and Lydon, 1974). The crystal structure of cholesteryl butanoate (butyrate) was solved recently by Han et al. (1994). The unit cell is monoclinic, space group P21 with cell constants: a  22.619, b  9.553, c  25.870 Å, ␤  94.73. The crystal structure has an almost nematic displacement of molecules within sheets. There are four molecules in the asymmetric unit. One of the polymorphs of cholesteryl palmitelaidate also represents a new packing form (Srivastava and Craven, 1989).

10.3

Thermotropic behavior

Thermotropic transitions for the cholesteryl esters can be complicated as outlined in Fig. 10.4 (taken from the summaries given by Ginsburg et al., 1984 and Small, 1986) and assembled from a number of sources (Barrall et al., 1967a,b; Davis et al., 1970a–c). As a general summary of this behavior for the saturated acid esters (Sawzik and Craven, 1980a), the monolayer II esters (carbon lengths 6–8) transform directly and monotropically to an isotropic melt. Cooling the melt produces the cholesteric liquid crystalline form and upon further cooling this slowly reforms the crystalline structure. Monolayer I esters, such as the undecanoate and laurate, also melt monotropically and transform through the cholesteric and smectic mesophases upon cooling. A second crystal form, originally misidentified as a monolayer II (Small, 1986) but actually identified by electron diffraction to be a bilayer polymorph (Dorset, 1987b), can crystallize from the cooled smectic state. Bilayer crystal forms with chain lengths from 13 to 15 carbons transform monotropically to the smectic and then reversibly to the cholesteric and then isotropic melt (Small, 1986). There has been much speculation about the local molecular packing in the two liquid crystalline forms. Dilatometry has been used to follow the gradual density changes for cholesteryl myristate as it was heated through the smectic and cholesteric mesophases to the true melt (Price and Wendorff, 1971). Discontinuities of the density were observed corresponding to the change in phase. It was also observed from X-ray measurements that the same ester abruptly changed its long spacing from about

176

THE CHOLESTERYL ESTERS 91.3

C1

I 87.2 Cholesteryl undecanoate

Ch 80.2

Sm C1

90.5

79

I 88 Ch

Cholesteryl laurate

81.5 Sm 79

C2 C1

72

Sm 80

85.5 I

Ch

C2

70.3

Cholesteryl myristate

Sm 77.1

81.8

Cholesteryl pentadecanoate

Ch

I

80.5 83.5 C2 Ch I 79.5 C
2

C1

75

Cholesteryl palmitate

Sm

83

I 79

Ch

Cholesteryl stearate

74.5 Sm

Fig. 10.4. Thermotropic behavior of saturated fatty acid esters of cholesterol. (Legends: C: crystalline; Sm: smectic; Ch: cholesteric; I: isotropic (melt).)

51 to 33 Å, an observation typical of those packing in the bilayer unit cell. Virtually no change was found for those esters packing in the monolayer I cell and the smectic phase spacing derived monolayer II crystal forms was nearly doubled (Sawzik, 1984). Electron diffraction measurements on the myristate epitaxially crystallized on benzoic acid (Dorset, 1985b) revealed that the lamellar reflections of the bilayer crystal actually sharpened as the material was heated to the smectic until an intermediate stage was reached where the 33 Å reflection was found in the same reciprocal lattice direction as the crystalline lamellar row (Fig. 10.5(b)). For solution-crystallized samples, the amorphous ring was noted at the phase transition by electron diffraction.

THERMOTROPIC BEHAVIOR

177

(a) (b)

(c) c*

c*

(d) c*

Fig. 10.5. Electron diffraction of epitaxially oriented cholesteryl myristate. (a) Room temperature; (b) pretransition to smectic (coexistence of crystal and liquid crystal); (c) smectic form; (d) solid cooled from melt. (Dorset, D. L. (1987) Thermotropic mesomorphism of cholesteryl myristate. An electron diffraction study. J. Lipid Res. 26, 1142–1150.)

For a chain length series for smectic lamellar spacings, the zero chain extrapolation is about the same length required for an untilted cholesteryl nucleus in the saturated chain series (Ginsburg et al., 1984), confirming an earlier analysis of Wendorff and Price (1973) that the molecular axes should be normal to the smectic layer. The extrapolated distance for the unsaturated chain smectics indicates that the tetracyclic nucleus should be tilted by about 54 (Ginsburg et al., 1984). Increments for the acyl chains, in both saturated and unsaturated examples, indicate that the chain axes, on average (since they are disordered) should be normal to the layer surface. When the lamellar spacings of crystals are compared to those of smectic mesophases (Sawzik, 1984) it is often concluded that the smectic packing should resemble that of the monolayer I structure, particularly the B pair of molecules. Nuclear magnetic resonance (NMR) spectroscopists, on the other hand, proposed a monolayer II type model (Ginsburg et al., 1984; Guo and Hamilton, 1993) but this is also similar to a molecular pair in monolayer I. These findings agree with the earlier prediction of Wendorff and Price (1973) that the molecules should be antiparallel with chains protruding into an interfacial region. There is less agreement about the nature of the cholesteric phase. It is often accepted that the molecular axes pack within sheets and that there is a helical twist of the sheets with respect to one another, that is, the cholesteric axis is perpendicular to the molecular axis (Ginsburg et al., 1984). Wendorff and Price (1973), on the other hand, interpreted their X-ray data to signify that the molecular axes in cholesteryl myristate were, on average, normal to a layer surface and that these layers were disordered with respect to one another. This would place the cholesteric helical axis parallel to the molecular axes. Electron diffraction observations on solution crystallized samples (Dorset, 1985b) indicate that the crystalline form is recrystallized from

178

THE CHOLESTERYL ESTERS

the smectic mesophase without any signs of disorder. On the other hand, when the material is recrystallized from the cholesteric phase there is a residual rotational disorder of the crystallites—in favor of the latter model.

10.4

Binary phase behavior

It is unfortunate that the initial interpretations of binary phase diagrams for the cholesteryl esters were made without knowledge of their crystal structures but in a more recent review (Small, 1986), even such knowledge did not seem to be very beneficial. A systematic understanding of these phase diagrams was possible when electron diffraction measurements were made for epitaxially oriented samples at various intermediate compositions, particularly when characteristic patterns from the monolayer I and bilayer polymorphs were identified (Dorset, 1987b, 1988). Within the monolayer I structure, saturated acid esters were found to form nearly ideal solutions when the chain difference was only one carbon atom, for example, cholesteryl decanoate/ cholesteryl undecanoate or cholesteryl undecanoate/cholesteryl dodecanoate (laurate) (Fig. 10.6(a)). This is noted by the step-like progression of lamellar spacings with (a) 100

(b) Liquid

(Cholesteric)

80 (Smectic)

(Cholesteric)

80 (Smectic)

70

Solid

60

70 65

Liquid

90

Solid

T (°C)

T (°C)

90

100

50

Solid monolayer I

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 XCHOL12

(c)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 XCHOL11 (d)

100

90 Liquid

(Cholesteric)

80 (Smectic)

70

80

(Cholesteric) (Smectic)

Theoretical solid solution

70

60 50

T (°C)

T (°C)

90

Liquid

Solid Solid (bilayer)

60 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 XCHOL11

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 XCHOL15

Fig. 10.6. Binary phase diagrams of cholesteryl ester solid solutions. (a) Cholesteryl undecanoate/cholesteryl laurate; (b) cholesteryl caprate/cholesteryl undecanoate; (c) cholesteryl nonanoate/cholesteryl undecanoate; (d) cholesteryl myristate/cholesteryl pentadecanoate. (Dorset, D. L. (1988) Co-solubility of saturated cholesteryl esters: a comparison of calculated and experimental binary phase diagrams. Biochim. Biophys. Acta 963, 88–97.)

BINARY PHASE BEHAVIOR

179

(a) 34 33

d001(Å)

32 31 30 29

0

0.1

0

0.1

0.2

0.3

0.4

0.5 XCL

0.6

0.7

0.8

0.9

1.0

(b) 55 54

d001(Å)

53 52 51 50 49 48 0.2

0.3

0.4

0.5 0.6 XCHOl15

0.7

0.8

0.9

1.0

Fig. 10.7. Lamellar spacings for cholesteryl ester solid solutions. (a) Cholesteryl undecanoate/cholesteryl laurate; (b) cholesteryl myristate/cholesteryl pentadecanoate. (Dorset, D. L. (1987) Cholesteryl esters of saturated fatty acids. Co-solubility and fractionation of binary mixtures. J. Lipid Res. 28, 993–1005.)

respect to Vegard’s law (Fig. 10.7(a)). Stable solid solutions exist when the chain length difference is two carbon atoms, for example, cholesteryl nonanoate/cholesteryl undecanoate, but the melting behavior becomes less ideal (Fig. 10.6(c)). Within the bilayer structure, the binary solids between cholesteryl tetradecanoate (myristate) and cholesteryl pentadecanoate show nonideal behavior for the crystal to smectic transition (Fig. 10.6(c)) and the sequence of lamellar spacings was originally interpreted to be continuous (Fig. 10.7(b)). However, after determination of a binary solid solution structure (see below) the relationship is now realized to be step-like, as

180

THE CHOLESTERYL ESTERS

discussed in Chapter 5 for the n-paraffins or in Chapter 7 for the fatty alcohols (Amelinckx, 1958) in their solid solutions. As the chain length difference increases, the fractionation becomes more and more pronounced, corresponding to the volumetric change. Galanti and Porter (1972), in their interpretation of the eutectic phase diagram between cholesteryl tetradecanoate (myristate) and cholesteryl octadecanoate (stearate) were able to demonstrate the utility of the Tammann (1925) plot of enthalpies for the eutectic solids to locate the position of the eutectic composition. If two different layer structures are preferred by the individual components, then there will be a eutectic interaction, just as found above for the interaction of n-paraffins with symmetric fatty acid esters of long chain alcohols. For example, in the most extreme case, cholesteryl dodecanoate (laurate) is polymorphic so the chain length difference between the two ingredients with different crystal forms is zero, that is, they fractionate. Interestingly, if cholesteryl dodecanoate is combined with cholesteryl tetradecanoate, the fraction of the former ingredient in the bilayer unit cell will form a solid solution with the myristate but the fraction in the monolayer I will not (Dorset, 1987b, 1988). Galanti and Porter (1972) had predicted a solid solution between cholesteryl undecanoate and cholesteryl myristate but later studies (Dorset 1987b, 1988) have proven that this is not possible, again because different crystal polymorphs are preferred by respective ingredients. Obviously different crystal forms will fractionate if the chain length difference is very large, for example, examples given by Griffen and Porter (1973), just as they will when the crystalline forms may be similar (Dorset, 1990a). Interactions between the monolayer I and monolayer II forms also lead to fractionation, for example, cholesteryl octanoate with cholesteryl nonanoate or cholesteryl octanoate with cholesteryl decanoate (Dorset, 1988). The fractionation of esters, each preferentially crystallizing in different layer forms is also exemplified by the interaction of saturated with unsaturated esters. For example, Krzewski and Porter (1973) correctly showed the eutectic interaction between cholesteryl stearate and cholesteryl oleate, a co-mixing of bilayer and monolayer II forms. A eutectic relationship was also shown for cholesteryl stearate and cholesteryl linoleate and these interactions were subsequently reconfirmed (Dorset, 1990e). Other saturated esters fractionate when co-mixed with these unsaturated esters (Small, 1986). Other speculations of some limited co-solubility in the crystalline state (Snow et al., 1988; Snow and Phillips, 1990) must, therefore, be rejected. The crystal structure of cholesteryl linoleate is currently unknown but was proposed to be similar to that of cholesteryl linolelaidate (Sawzik and Craven, 1983), containing two trans double bonds instead of two cis double bonds. If this were true then both would have a monolayer II structure and the esters should be co-soluble since the chain lengths are identical. Co-solubility with the linoleate was, in fact, claimed by Krzewski and Porter (1973). Initially, Small (1970) claimed a eutectic interaction between the two unsaturated esters but then changed his mind in favor of a solid solution (Small, 1986). A careful analysis of the binary combinations revealed that a peritectic relationship exists between them (Dorset, 1990a). The mesophases, on the other hand, are continuously co-soluble, as shown also by X-ray diffraction measurements.

BINARY PHASE BEHAVIOR

181

(a)

(b)

Fig. 10.8. Imagined “cartoon” models for cholesteryl ester solid solutions. (a) Bilayer packing; (b) monolayer I packing. (Dorset, D. L. (1988) Co-solubility of saturated cholesteryl esters:a comparison of calculated and experimental binary phase diagrams. Biochim. Biophys. Acta 963, 88–97.)

Using the idea that similar crystal structures can support stable solid solutions if the chain length difference is not so great, a “cartoon” model was proposed (Dorset, 1988) for the solid solutions of monolayer I and bilayer type cholesteryl esters (Fig. 10.8). This model assumes that the only mechanism for co-solubilization is merely fractional occupancy at the end of the longest species. This idea seems to have merit for the nearly 1 : 1 solid solution of cholesteryl undecanoate with cholesteryl dodecanoate. Its X-ray crystal structure (Fig. 10.9) is again monoclinic, space group P21 with cell constants: a  13.005, b  9.005, c  31.421 Å, ␤  90.82 (Dorset and Pangborn, 1992). The Kitaigorodskii volume parameter e  0.97 also supports the fact that the measured spacings fall on the Vegard’s law line. The chain occupancy model is shown in Fig. 10.10. The notion of fractional occupancy must be abandoned, however, when the chain length difference becomes greater for this layer packing. For example, the crystal structure of nearly equimolar cholesteryl decanoate/cholesteryl dodecanoate is clearly that of a solid solution (McCourt et al., 1994). The space group is the same with cell constants: a  12.969, b  9.048, c  31.137 Å, ␤  91.12. In this structure (Fig. 10.11), there seem to be favored sites for packing the shorter and

182

THE CHOLESTERYL ESTERS

longer chains. This finding also holds for the crystal structure of a bilayer solid solution, even though the chain length difference is only one carbon atom. Nearly equimolar cholesteryl myristate/cholesteryl pentadecanoate (McCourt et al., 1996) packs in space group Cc with cell constants: a  102.6, b  7.59, c  10.20 Å, ␤  92.1. Again there is no fractional occupancy of outer chain atoms that can be

2C

B

A

O

a

Fig. 10.9. Crystal structure of nearly 1 : 1 cholesteryl undecanoate/cholesteryl laurate. (Dorset, D. L. and Pangborn, W. A. (1992) Molecular interactions in binary solids: crystal structure of a cholesteryl ester solid solution. Proc. Natl. Acad. Sci. USA 89, 1822–1826.)

BINARY PHASE BEHAVIOR

183

(a) 028 Occupancy 0.48 (b)

03 03 028

Fig. 10.10. Chain occupancy and thermal ellipsoids for 1 : 1 cholesteryl undecanoate/ cholesteryl laurate solid solution. (Dorset, D. L. and Pangborn, W. A. (1992) Molecular interactions in binary solids: crystal structure of a cholesteryl ester solid solution. Proc. Natl. Acad. Sci. USA 89, 1822–1826.)

C

O

a

Fig. 10.11. Crystal structure of a nearly 1 : 1 cholesteryl caprate/cholesteryl laurate solid solution. (McCourt, M. P., Strong, P., Pangborn, W., and Dorset, D. L. (1994) Structural determination and packing analysis of a cholesteryl caprate/cholesteryl laurate solid solution. J. Lipid Res. 35, 584 –591.)

184

THE CHOLESTERYL ESTERS

(a)

a c

(b)

Fig. 10.12. Crystal structure of a nearly 1 : 1 cholesteryl myristate/cholesteryl pentadecanoate solid solution. (a) Bilayer packing; (b) detail of interlayer packing. (McCourt, M. P., Li, N., Pangborn, W. A., Miller, R., Weeks, C. M., and Dorset, D. L. (1996) Crystallography of linear molecule binary solids. X-ray structure of a cholesteryl myristate/cholesteryl pentadecanoate solid solution. J. Phys. Chem. 100, 9842–9847.)

clearly identified (Fig. 10.12). There are some differences in the conformation of the ester linkages due to the chain mixing as well and the methylene subcell packing is decidedly O⊥, instead of the ambiguous subcell assignment given for the pure myristate and the HS1 cell found for the 17-bromoheptadecanoate. Preferred packing sites in a layer are also known for the solid solutions of other organic molecules (Myasnikova, 1993).

10.5 1.

2. 3.

Summary There are three major polymorphic packings for cholesteryl esters. Only one of these includes a sequestered chain packing with an actual methylene subcell. The preferred solid form depends on the nature of the esterified fatty acid chain (chain length, unsaturation). Solid solutions of two saturated chain cholesteryl esters are possible if the two homologs adopt the same polymorphic crystalline form. In solid solutions formed in the monolayer I polymorph, a chain length difference of one methylene group is randomly distributed in the average crystal structure. When the chain lengths differ by two methylenes, there are preferred packing sites for the longer and shorter chains. Preferred packing sites are also found for solid solutions in the bilayer polymorph, even when the fatty acid chains differ by only one methylene.

11 From waxes to polymers—the crystallography of polydisperse arrays

11.1

Introduction

Generally speaking, waxes often comprise multicomponent solid solutions of paraffins or paraffin-line (e.g. fatty acid ester) chains. Although diffraction has been long used to characterize these chain assemblies (Kreger, 1951), it is only recently that quantitative crystallographic techniques have uncovered the most important principles dictating chain assembly in the multiple component solid state. The wealth of single crystal information about wax components, reviewed in this book, also provides valuable insights into likely chain assemblies in other kinds of multicomponent arrays. Actual single crystal structure determinations of polydisperse wax chain assemblies have been made possible by electron diffraction studies of epitaxially oriented microcrystals, exploiting the most-informative view onto the chain axes (Dorset, 1995a). Electron crystallography has also determined how paraffinic solid solutions can become destabilized to induce phase separation, extending pioneering crystallographic work in the field by Kitaigorodskii (1961).

11.2 11.2.1

A review of chain packing arrangements for polydisperse assemblies n-Paraffin solid solutions

Based on available phase diagrams and powder X-ray diffraction data, n-paraffin crystal structures were used by Kitaigorodskii (1961) to predict the stability of binary solid solutions between two species. As discussed in Chapter 5, both volumetric and symmetric factors were seen by him to be important. First, the non-overlap volume between two molecules, , should not be too large so that the quantity e  1  /r (where r is the overlap volume) is not less than, say, 0.8. Second, if a molecule of crystal symmetry A were added to a molecule with crystal symmetry B, then the symmetry of the solid solution should either remain the same or be less than that of crystal B. This symmetry argument was based on the most thermodynamically stable polymorphs of any component substances. It will be recalled that Kitaigorodskii (1961) predicted that an even-chain n-paraffin would not form a stable solid solution with an odd-chain paraffin, since the former prefers a monoclinic

186

FROM WAXES TO POLYMERS

(a)

(b) 1 µm

Fig. 11.1. Low dose electron micrographs of epitaxially crystallized 1 : 1 n-C32H66/nC36H74 solid solution. (a) Lath crystals; (b) lamellar stacking observed at higher resolution. (Dorset, D. L. (2000) Electron crystallography of the polymethylene chain. 4. Defect distribution in lamellar interfaces of paraffin solid solutions. Zeitschrift f. Kristallographie 215, 190–198.)

chain packing whereas the latter prefers an orthorhombic structure. Experimental evidence, however, questioned this prediction (Mazee, 1958b). Further, it was wellknown that two even-chain paraffins, each crystallizing in a triclinic structure, would form orthorhombic, not triclinic, solid solutions beyond a certain concentration of the second component (Lüth et al., 1974), that is, a higher symmetry than the original guest lattice. It is apparent, therefore, that long-lived metastable crystal forms are very important for polydisperse linear chain substances. Practically speaking, these violate the reasonable thermodynamic rules for co-solubility established from principles of lowest-energy chain packing. Electron diffraction studies have facilitated the characterization of oriented paraffin solid solutions, based on samples epitaxially nucleated on substrates such as benzoic acid (Fig. 11.1). For example, odd-chain paraffins can freely co-mix with even-paraffins in their respective orthorhombic polymorphs (B-polymorph, space group A21am, for the former, and the Pca21 packing for the latter). There is no observed continuity of space group symmetry, however, only the rectangular layer packing is maintained. In addition, for any nominal concentration, there may be two or three local crystal structures (on a micrometer scale), each mimicking an archetypical pure odd- or even-chain n-paraffin crystal structure, where the lamellar spacing matches the theoretical value predicted for the average chain length (Nyburg and Potworowski, 1973). (These multiple solid solution crystal structures do not appear to result from “coring” during the solid solution growth. However, coring has been predicted for wax crystallization (Mazee, 1958b). Neighboring contiguous microareas appear to retain a single crystal structure. Thus, the local average chain packing is not immediately surrounded by another structure, caused by the depletion of one component.

A REVIEW OF CHAIN PACKING ARRANGEMENTS

187

However, on the grosser grain size of some metal alloys (see Gordon, 1968) coring might occur.) Extending the maximum chain length investigated to n-C60H122, the volumetric (e) conditions for co-solubility were found to be similar to those determined earlier by Mathiesen and Smith (1985). Multicomponent n-paraffin solid solutions were shown in Chapter 5 to resemble the binary combinations. The two-dimensional crystal structures of representative n-paraffin solid solutions (Dorset, 1990c) indicate a stable lamellar chain packing with concentration of defects at the crystal surface. Crystallography depicts the average structure as one with decreasing occupancy of methylene groups as one approaches the lamellar surface. Vibrational spectroscopy detects an increasing number of nonplanar chain defects as this surface is approached (Maroncelli et al., 1985b; Kim et al., 1989b). A subtle, but significant, variant of this packing scheme was proposed (Lüth et al., 1974; Gerson and Nyburg, 1994) from two single crystal X-ray structures of paraffin binary solids. Instead of the average flat lamellar surfaces, protruding chain ciliae were included in the structural model and even a mean lamellar thickness that was larger than the length of the largest paraffin component. Such a situation has never been observed by electron diffraction. Re-examination of the published X-ray results (Gerson and Nyburg, 1994) via electron diffraction (Dorset, 1999c) concluded that a flat lamellar surface, in agreement with the electron crystallographic model, would fit the diffraction intensities as well as the ciliated one and not involve as many variable parameters as used for the ciliated model. There are other indicators that lamellar solid solution surfaces are flat on average, for example, atomic force microscopy (AFM) measurements (Dorset and Annis, 1996). Also decoration experiments of the type introduced by Wittman and Lotz (1985), where polymethylene chain segments are deposited onto the (disordered) solid solution (001) face from the vapor phase, demonstrate that the solid solution surface can still nucleate epitaxial growth (Dorset and Annis, 1996), that is, this surface has, on average, crystallographic regularity. Finally, the crystal coherence for solid solution growth along [0 0 1] extends for several m, indicating that one lamellar surface serves as an effective nucleator for growth of the next monolayer, despite the accumulation of conformational disorder. Lateral expansions or contractions in the chain cross-sectional area can be accommodated in solid solutions as long as the change in area is not too large. For example, perdeuterated species are tolerated in hydrogenated paraffin assemblies with very similar chain lengths. On the other hand, dramatic isotope effects occur when the chain lengths are too dissimilar. Keto-substituted n-paraffins are solubilized in paraffin layers. Regions for solid state co-solubility of a symmetric ketone with an n-paraffin of the same length have been determined by Nakasone et al. (2000). It was shown in Chapter 7 that secondary alcohols will also not disrupt the rectangular chain packing in the O⊥ methylene subcell. Secondary amine linkages preserve the paraffin chain packing but an ether linkage may disrupt it if the gauche chain conformation near the heteroatom forces the chains to adopt an oblique layer packing. A certain fraction of the ether-linked material does retain the rectangular layer, however. Similarly, ester linkages can force a tilted layer packing, if they are crowded within the same layer of the neighboring

188

FROM WAXES TO POLYMERS

chains. This is particularly true for symmetric fatty alcohol esters of fatty acids where the conformational nonplanarity of the carbon backbone increases the chain cross-sectional area in the vicinity of this linkage. The layer, again, compensates for this area increase by chain tilt. Even for even-chain paraffins, where both oblique and rectangular layer polymorphs are permitted, there can be no solid solution formed with an ester of the same chain length because of the dissimilarity in chain cross-sections. On the other hand, asymmetric long chain esters pack in rectangular layers and are apparently co-soluble with n-paraffins of nearly the same chain length. From the extensive literature on branched chain fatty acids (Chapter 8) we see that methyl branches are not tolerated within polymethylene chain layers. No matter where the methyl branch occurs in non-folded chain layers, the protruding group will be forced into a layer interface. 11.2.2

Fractionation of n-paraffin solutions—the miscibility gap

As discussed in Chapter 5, the boundary line for solid solution stability, in terms of Cnmin versus Cnmax is very sharp. When it is traversed, a metastable solid solution is initially grown from the melt that dissociates, for example, over a year (Mazee, 1958b). When these solids are crystallized from the melt, initial differential scanning calorimeter (DSC) traces resemble those from a stable n-paraffin solid solution. After equilibration at room temperature, a small, low enthalpy “mixing” endotherm appears that is clearly associated with the dissolution. Vibrational spectroscopic measurements with perdeuterated probes indicate the growth of lateral islands (Snyder et al., 1992) from the original solid solution, whereas initial electron diffraction measurements detected a longitudinal change (Dorset, 1985a, 1986b), that is, the emergence of superlattice reflections. In addition, the chain-end disorder is less than found for stable solid solutions (Clavell-Grunbaum et al., 1997). High-resolution, low-dose electron micrographs depict the growth of the new solid within the original solid solution, related to electron diffraction measurements via their optical transforms (Dorset, 1990b). This phase separation behavior is characteristic of a miscibility gap. By analogy to metal alloys (Amelinckx and Van Dyck, 1993), the growth of fractionated solid within the miscibility gap is expected to be somewhat sluggish. The discrepancy between lateral or longitudinal changes in the solid was resolved by quantitative single crystal electron diffraction determinations (Dorset and Snyder, 1996). The block arrangements of nearly pure chain domains argue in favor of both lateral and longitudinal arrangements of nearly pure chain layers. When threecomponents are considered (Dorset and Snyder, 1999a), the behavior is even more complicated. The first paraffin pair can behave as a “pseudo-component” in the presence of the longest chain to bring about the initial, rapid phase separation, detected by superlattice reflections appearing along 00l. After a longer incubation period, layers of nearly pure components appear as the molecules rearrange into a very complicated sequence involving both longitudinal and lateral arrays of chain blocks. Although studies have not been carried out yet on multicomponent arrays, this pseudocomponent concept is likely to be relevant to the fractionation of wax assemblies.

THE CRYSTAL STRUCTURE OF WAXES

189

The boundary between the miscibility gap behavior and eutectic phase separation is also very sharp. This has been tested with perdeuterated n-paraffin probes (Snyder et al., 1994; Dorset and Snyder, 1995). For example, when either the longer chain component or both chains are perdeuterated in the n-C30/n-C36 binaries, the phase behavior and crystallographic changes are exactly those found for the all-hydrogenated n-C30H62/n-C36H72 series. However, for n-C30D62/n-C36H72, an eutectic solid forms directly from the melt. Perdeuterated chains have a slightly smaller volume than analogous hydrocarbons so the volumetric difference is greatest for this binary pair. The subtle difference in volume is enough that the stability boundary is traversed. The presence of multiple components (see Chapter 5) complicates the phase separation mechanism, that is, there is a sequence of structures that are formed as the components separate (Dorset and Snyder, 1999a). To date, only the crystal structures of ternary solids have been characterized in a systematic way. 11.2.3

Fractionation of n-paraffins—eutectic interactions

Electron diffraction patterns from eutectic solids include contributions from a nearly pure paraffin component (depending on the binary concentration) and a coexistent superlattice of the two chains (Dorset, 1986b). Unlike the solids grown within the miscibility gap, the positions of the 00l superlattice reflections do not depend very much on relative chain concentrations. The resultant superlattice was shown (Chapter 5) to contain regions of nearly pure chain lengths, arranged in both lateral and longitudinal blocks. The chain-end conformational disorder is less than found for solid solutions but greater than found when the components are totally immiscible (Clavell-Grunbaum et al., 1997). Eventually, with great enough volume differences, the component chains would be completely non-co-soluble for any concentration. It is expected that two pure n-paraffin blocks would be adjoined across (001) planes, with appropriate registry of the methyl end planes, where chain-end protrusions from one surface would project into hollows of the apposing surface, as explained by Kitaigorodskii (1961), and discussed in Chapter 2. 11.3 11.3.1

The crystal structure of waxes “Typical” lamellar wax structures

In an initial investigation of paraffinic wax crystallinity (see Chapter 5), a sample of a commercial petroleum distillate wax was epitaxially oriented on benzoic acid (Dorset, 1987a). The electron diffraction pattern revealed this material to be a stable solid solution. Again, there was an observed distribution of local crystal structures, as is the case for n-paraffin binaries. Later, the wax crystal structure was determined (Dorset, 1997b) from electron diffraction intensity data; again there was no structural difference from that of the stable binary paraffin solid solutions. A similar result was obtained (Dorset, 1995b) for a wax taken from a child’s birthday candle and also

190 (a)

FROM WAXES TO POLYMERS (b)

Fig. 11.2. Electron diffraction from petroleum wax: (a) diesel wax; (b) “Gulfwax.”

an artificial wax made up of a flat distribution of all even n-paraffins from n-C26H54 to n-C36H74. It is important to note here that the electron diffraction patterns from these waxes contain very sharp reflections and extend to very high resolution. Examples include a diesel wax (Fig. 11.2(a)) or a commercial refined wax (“Gulfwax”) (Fig. 11.2(b)). By contrast, earlier characterizations of petroleum waxes by light microscopy and X-ray diffraction (Chichakli and Jessen, 1967) had indicated the crystallinity to be very poor. In other words, although vibrational spectroscopy also reveals (Clavell-Grunbaum et al., 1997) a significant defect distribution at lamellar interfaces, wax microcrystals are very highly ordered in a crystallographic sense. Imposing a Gaussian model for chain-end occupancy, revising the previous analyses made by Strobl et al. (1974), the defect distribution can be shown (Dorset, 2000a) to penetrate further into the lamellar surface for complicated wax chain distributions than for simple paraffin binary solid solutions (Fig. 11.3). A Gaussian model for chain occupancy 1.0g(z), where g(z)  exp(a2z2), has been used conveniently (since the Fourier transform of g(z), G(u)  ␲1/2/ 2 exp (␲ 2u 2/a 2 ) will “sift” the lamellar reflections, determining what orders are retained in the wax diffraction pattern). At differing values for the Gaussian half-widths a (in Å) (Fig. 11.3), the correlation to the observed lamellar resolution is good. There is also agreement with the figure dav
calculated by Strobl (1972) and Strobl et al. (1974). Defining ds  L1.273m, where L is the lamellar thickness (c/2) and m the number of carbon atoms in the chain, one can then define ds
 ds/2, the distance from the lamellar gap center to the effective lamellar surface. A quadratic fit to Iobs(00l) (Fig. 11.3) allows estimation of I(000) by extrapolation. If ds  dav for an ordered crystal structure, the intensity distribution of a model without fractional occupancies can be used to find a scale factor for d2av  kI(000). Thus, in disordered structures, dav can be evaluated from I(000) estimates to give dav
 dav/2. This dav
, an estimate of disorder induced vacancies, was found to correlate well with the Gaussian occupancy model given above (Dorset, 2000a). Obviously this model assumes that all disorder sites can be simulated by crystallographic occupancies but models based only on known chain distributions (Rademeyer and Dorset, 2001) reveal this to be a

THE CRYSTAL STRUCTURE OF WAXES

191

a–1 = 5.0

I

a–1 = 4.0

a–1 = 3.0

a–1 = 2.0

a–1 = 1.0

Flat 2

4

6

8 10 12 14 16 18 20 22 24 26 28

Fig. 11.3. Effect of fractional atomic occupancies of chains in paraffin solid solutions on the low angle 00l “lamellar” electron diffraction intensities and their resolution. (Dorset, D. L. (2000) Electron crystallography of the polymethylene chain. 4. Defect distribution in lamellar interfaces of paraffin solid solutions. Zeitschrift f. Kristallographie 215, 190 –198.)

false assumption. Nevertheless, there also seems to be a correlation of this surface defect thickness with the breadth of the DSC melting endotherm. Although chain folding had been implicated at the lamellar surface of wax crystals by some authors (Chevallier et al., 1999) the work of Ungar and Zeng (2001) demonstrates that this cannot occur for lower molecular weight n-paraffins. There is no difference between the crystal structures of waxes taken from petroleum paraffin distillate cuts and the fractionated cuts made of waxes synthesized by the Fischer–Tropsch process. A somewhat complicated, four-domain, model had been originally proposed for Fisher–Tropsch waxes (Lourens and Reynhardt, 1979;

192

FROM WAXES TO POLYMERS

Le Roux and Loubser, 1980) based on solid state nuclear magnetic resonance (NMR) measurements made on rather narrow fractions of a synthetic product with a larger chain distribution. Electron crystallographic analyses (Dorset and Basson, 2000) of narrower Fischer–Tropsch wax distillate fractions again reveal the structures to be lamellar arrays, identical to the refined paraffinic petroleum waxes. As discussed in Chapter 9, multicomponent assemblies of fatty alcohol esters of fatty acids can also mimic the average structure found for lamellar paraffin waxes. This is true for artificial mixtures as well as for some natural waxes with a significant fatty ester component. Stable lamellar structures can also exist for some natural waxes with functionalized chains, for example, in montan wax from brown coal (Dorset, 1997b). Also, artificial assemblies of long chain esters of behenic acid can crystallize in rectangular lamellar layers (Dorset, 1995b), as can the chain assembly in a synthetic substitute for spermaceti. The position of the ester linkages on the component chains can, on the other hand, initiate fractionation, for example, the incompatibility of hexadecyl hexadeconate (cetyl palmitate) with n-hexatriacontane discussed in Chapter 9. For similar reasons, natural spermaceti may crystallize in oblique chain layers because cetyl palmitate is a major ingredient. If the actual chain length distribution was used to model the (phenomenological) site occupancy distribution at the lamellar surface, for example, a wax fraction characterized by Stokhuyzen and Pistorius (1970) with polydispersity index Mw/Mn  1.003, a very good fit was made to experimental electron diffraction intensity data, where the model-generated occupancy parameters accurately accounted for the chain packing scheme (Dorset, 2000a). This result, however, is fortuitous because a wax with a slightly broader distribution (Mw/Mn  1.009), mimicking a residual petroleum wax (Gupta and Severin, 1997), did not accurately model the fractional occupancies needed to fit experimental electron diffraction intensity data. Somewhat smaller occupancy parameters near the chain ends fit the data better (Rademeyer and Dorset, 2001). This observation is significant since it suggests that chain end defects need not lie on regular crystallographic sites. The fractional occupancies are, in themselves, meaningless if taken literally to indicate an actual distribution of “void” spaces. Nonplanar conformational defects, detected by vibrational spectroscopy (Clavell-Grunbaum et al., 1997), can also have a “noncrystallographic” distribution, detected only as a continuous diffuse signal in diffraction experiments. So far, the lamellar crystal structure of waxes appears to be self-consistent. This viewpoint changes quickly when branched-chain waxes, such as the “microcrystalline” wax from heavier petroleum distillates (Dorset, 2000c), or natural waxes (Dorset, 1999e), such as bee honeycomb or carnauba, or intact Fischer–Tropsch synthetic products (Dorset, 2000d ), are examined. After orientation of the wax on a substrate, there may be no initial evidence of a layered structure from electron diffraction patterns, which often strongly resemble the patterns from chain-folded polyethylene (Hu and Dorset, 1989). Only after the samples are annealed are characteristic low-angle reflections frequently observed by electron diffraction.

THE CRYSTAL STRUCTURE OF WAXES (a)

(b)

b*

(1)

∆z

193

l=m+2 l = 2m + 4 c*

l=m+2 l = 2m + 4

∆z (2)

(3) (1)

(2)

l = m, m + 2 l = 2m + 2, 2m + 4

(3)

Fig. 11.4. Various stages of chain longitudinal ordering and its effect on 0kl electron diffraction patterns. (1) Nematocrystalline packing with some average layer ordering; (2) more layer definition; (3) full lamellar ordering. In (2) and (3), respectively z changes from an integral multiple of cs/2 to a nonintegral multiple.

11.3.2

From wax to polymer crystal—interlayer bridges

A model for the structural change that occurs when broader chain distributions are crystallized from the melt was accidentally discovered when very long chain n-paraffins (e.g. n-C60H122) were deposited from the vapor phase onto an epitaxial substrate (Zhang and Dorset, 1989a). The sequence of structures is outlined by the cartoons in Fig. 11.4, associated with the corresponding 0kl electron diffraction patterns. Upon initial deposition, the chains retain only a common axial direction packing in the O⊥ polymethylene subcell with no longitudinal registry. The term “nematocrystalline” has been assigned to this packing scheme by analogy to nematic liquid crystalline phases. Upon annealing, the chains can reptate toward a lamellar end point, whereupon an irreversible change is made to the system, however, via intermediate stages. If there are enough long chains to bridge nascent layers, so that the interlamellar gap is still an integral multiple of the polymethylene repeat along the chain, then the strong (01l) “polyethylene” reflections remain as strong singlets, even though weak satellites can occur for more ordered systems. Only when true lamellae form, that is, when there are no bridging chain segments, can these intense singlet reflections split into strong doublets, because there is then a disparity between the interlayer gap spacing and the nearest integral multiple of the polymethylene repeat. For low molecular weight linear polyethylene that cannot undergo chain folding, for example, Mw  595, Mn  535 (polydispersity 1.11), the first solid crystallized from the melt onto benzoic acid will diffract very much like that of the infinite chain

194

FROM WAXES TO POLYMERS

(a)

Region of bridging chain segments –C/4

C /4

O

# Patterns

(b)

x

x

x x x x x

x x

x x x x x x

x x x x

x x x

x x x

37 38 39 40 41 42 43 44 Carbon number

Fig. 11.5. (a) Bridging atoms in the nematocrystalline structure of low molecular weight linear polyethylene; (b) apparent paraffin layer structures if the layers are considered to be true lamellae. (Dorset, D. L. (1999) Bridged lamellae:crystal structure(s) of low molecular weight linear polyethylene. Macromolecules 32, 162–166.)

polymer (Dorset, 1999b). In other words, this assembly is “nematocrystalline”. Upon annealing, some low-angle reflections appear but the intense (01l) reflections never split into doublets. A quantitative crystal structure analysis from threedimensional electron diffraction data reveals the presence of bridging segments across nascent layers (Fig. 11.5). Considering the reflection indices of the threedimensional patterns, however, it is clear that none of the orthorhombic space groups utilized by n-paraffins satisfies the observed extinction rules. The patterns (Fig. 11.6) represent a superlattice of the Pnam cell employed by the infinite chain polymer (Dorset, 2000e). If the nascent layered solid were considered to be a true lamellar array, the apparent local “paraffin-like” average structures detected by electron diffraction (see Fig. 11.5(b) ) would distribute over a broad range of even- or odd- chain layers (Dorset, 1999b). Why do lamellae never form at some end point? It is known (Prasad and Mandelkern, 1989) that, in this narrow polyethylene fraction, that a small, but significant, distribution of chains are included in a higher molecular weight tail of chain length distribution near MW800 (mean chain length of 57 methylene groups). These extended longer chains would never pack in lamellae with the observed layer spacing as small as 53.5 Å (mean chain length of ca. 41 methylenes) so they must bridge the layers to preserve the “nematocrystalline” order. In the projection down the chain axes then, the chain axial direction through the crystal is continuous. The narrowness

THE CRYSTAL STRUCTURE OF WAXES (a)

(b)

(c)

(d)

195

Fig. 11.6. Electron diffraction patterns from low molecular weight linear polyethylene. (a) hk0; (b) 0kl; (c) hhl; (d) h, 2h, l. (Dorset, D. L. (2000) Nematocrystalline chain packing: three-dimensional structure of low molecular weight linear polyethylene. J. Phys. Chem. B104, 10543–10548.)

of the chain distribution in terms of polydispersity (Mw/Mn) is of less importance than originally suspected. Several Fischer–Tropsch waxes, where Mw/Mn  1.03 were examined recently. When there is a fairly narrow distribution of chain lengths (Fig. 11.7(a) ), solid solutions crystallize as stable lamellae (Dorset and Basson, 2000, Dorset, 2000d ). However, if very small fractions of higher molecular weight components occur in a long tail that, nevertheless, do not greatly change the Mw/Mn value (Fig. 11.7(b) ), the nematocrystalline array will crystallize from the melt (Dorset, 2001). The crystal structures of the lamellar structures are shown in Fig. 11.8. The nematocrystalline chain packing, it turns out, is ubiquitous. The crystal structures of two intact Fischer–Tropsch waxes with this structure have also been determined, one at a relatively short (Dorset, 2001) mean chain length (C33) and the other (Dorset, 2000d ), a hard wax, with a longer mean chain length value (C63).

196

FROM WAXES TO POLYMERS SC120

Mol fract.

(a) 16 14 12 10 8 6 4 2 0 0

20

30 40 Carbon number

50

60

SC158

Mol fract.

(b)

10

8 7 6 5 4 3 2 1 0 17 21 25 29 33 37 41 45 49 53 57 61 65 69 Carbon number

(c)

SW300 12

Mol fract.

10 8 6 4 2 0 20 23 26 29 32 35 38 41 44 47 50 53 56 Carbon number

Fig. 11.7. Chain length distribution of three commercial Fischer–Tropsch waxes, where Mw/Mn  1.03. In the first two waxes the normal chain content is greater than 80%. For the latter it is only 50%.

Electron diffraction data resemble those from low molecular weight linear polyethylene (Fig. 11.9). Again the apparent unit cell symmetry does not fit any known orthorhombic paraffin cell. The bridging of nascent layers by chains (Fig. 11.10) creates a supercell of polyethylene. Looking end-on (Fig. 11.11), successive layers are not shifted to optimize an end plane packing but retain a continuous chain direction. The nematocrystalline packing can be found therefore for various mean molecular weight cuts of a Fischer–Tropsch wax. Comparing the structure of the wax in Fig. 11.7(b) with the chain length C33 to that of a hard Sasol “Paraflint®” (Fig. 11.12), where the mean carbon number is, for example, C63 (Dorset, 2000d), the bridging moieties are

THE CRYSTAL STRUCTURE OF WAXES

197

c (a) b

+ Ο +

+

+ Ο +

+

+ Ο +

+

(b)

(c)

–C/2

C /2

(d)

+ +

Ο

Fig. 11.8. Average layer packing of Fischer–Tropsch waxes with lamellar structures: (a) model MM3 wax; (b) model MM3C8 wax; (c) medium FT wax; (d) enlarged detail of (c) to emphasize lamellar interface. (Dorset, D. L. and Basson, I. (2000) Structural framework of a medium Fischer–Tropsch wax fraction determined by electron crystallography. J. Phys. D. Appl. Phys. 33, 2657–2663.)

clearly observed in the structure solution (Fig. 11.13). For example, it is also the chain packing adapted by some natural waxes (Dorset, 1999e), such as bee honeycomb wax and carnauba wax. Beeswax is known to contain fatty acid diesters of long chain diols, which could serve as the longer bridging entities in this case. Another deviation from true lamellar packing is found for methyl branched “microcrystalline” waxes. Electron diffraction patterns (Dorset, 2000c) resemble those from the polyethylene except that the intense (01l) singlet is also somewhat broadened. A chromatographic analysis of this wax reveals only 50% normal chain components. It is certain that methyl branched chains do not constitute the only deviation from linear chains. Naphthene components must also be present but probably

198

FROM WAXES TO POLYMERS

(a) (b)

C* C*

(c)

C*

Fig. 11.9. Electron diffraction from wax in Fig. 11.7(b).

(a)

(b)

Fig. 11.10. The bridged lamellar structure for a nematocrystalline Fischer–Tropsch wax.

THE CRYSTAL STRUCTURE OF WAXES

(a)

199

(b)

Fig. 11.11. View down chain axes for (a) lamellar wax; (b) nematocrystalline wax. (Dorset, D. L. (2001) Electron crystallography of the polymethylene chain. 5. Three-dimensional structure of a Fischer–Tropsch wax. Zeitschrift f. Kristallographie 216, 234–239.) (a)

(b)

Fig. 11.12. Electron diffraction from oriented, annealed synthetic waxes with nematocrystalline structure. (a) Paraflint®; (b) Shell Callista 158®. (Insets show lamellar reflections.) (Dorset, D. L. (2000) The bridged lamellar structure of synthetic waxes determined by electron crystallographic analysis. J. Phys. Chem. B104, 4613–4617.)

not in the most crystalline region (Altgelt and Boduszynski, 1994). Structure analysis reveals the presence of bridging chain segments. The same patterns can be obtained from pure 3-, 4-, or 5-methyl branched n-tetratriacontanes, for example, or from 3-methyl tritriacontane, when they are just crystallized from the melt. From the X-ray structures of branched chain fatty acids, it is well-known that methyl groups must always be sequestered into an interlamellar space. Fischer–Tropsch waxes with a significant branched chain component (e.g. Fig. 11.7(c) ) also produce this diffraction pattern. The packing model that would satisfy this requirement and lead to an

200

FROM WAXES TO POLYMERS

–c/3

c /3

(a) + +

(b)

–c /2

c /2 + +

+

(c)

Fig. 11.13. Potential maps for synthetic waxes after assignment of crystallographic phase model. (a) Sasol Paraflint®, enlarged detail of layer interface revealing methylene groups spanning layers; (b) Shell Callista 158®, overview of layer packing (c) enlarged detail of (b) revealing bridging chain segments. (Dorset, D. L. (2000) The bridged lamellar structure of synthetic waxes determined by electron crystallographic analysis. J. Phys. Chem. B104, 4613–4617.)

interdigitated chain layer is depicted in Fig. 11.14. This model, however, assumes that the chains are conformationally extended. An analogous crystal structure (Fig. 3.18) on the other hand indicates that this may not be true. The wax model also ignores the possible presence of naphthenic components within the layers.

11.4

What is wax and what is polyethylene?

From the above overview, it is clear that mere terminology for a polymethylene solid may be of little value for distinguishing actual crystal structures. Polymerization of

WHAT IS WAX AND WHAT IS POLYETHYLENE?

201

Lamellar interface

Fig. 11.14. Proposed chain packing for methyl branched waxes. (Dorset, D. L. (2000) Crystallography of real waxes. Branched chain packing in microcrystalline petroleum wax studied by electron diffraction. Energy Fuels 14, 685–691.)

methylene or ethylene groups to form respective linear chain distributions can end up with materials that cannot be otherwise distinguished. What is important is whether the chain distribution favors the formation of true lamellae or whether a significant fraction of bridging molecules is present to retain a nematocrystalline array. Obviously, any broad chain distribution can change its original physical properties if it is distilled or fractionated into a narrower distribution, as evidenced by Fischer–Tropsch products (Dorset, 2000d, 2001; Dorset and Basson, 2000). The distinct physical properties imparted by a preferred crystal structure can be striking. Lamellar systems concentrate defects at the chain ends. Since the van der Waals energy between layers is very small (Mnyukh, 1963), certainly minimized further by inclusion of non-crystallographic disorder in this region, the resulting material can be easily plastically deformed by mechanical forces. The presence of bridging molecules spanning nascent layers, on the other hand, insert covalent molecular “reinforcing rods” within an emergent interlayer gap so that the layers cannot be deformed easily by lateral forces. The resultant material, then, will tend to be hard and brittle, even though the chain polydispersity can be actually greater than that for a narrow “wax” distillate cut, or it may be similar. Extension of materials properties by blending inexpensive adducts (e.g. petroleum wax) into an expensive natural product (e.g. carnauba wax from Brazilian palm, an excellent hard polish) requires that the characteristic chain packing features are well-understood. In other words, the structural motif must be preserved to retain desired properties. Prediction of the crystallographic behavior for polydisperse linear chain arrays becomes even more complicated when chain folding is permitted in layers. Without discussing the controversial nature of random switchboard versus adjacent folds, it is clear that many of the volumetric strictures for stabilizing solid solutions are removed, at least kinetically, when admixtures are made of chains that can also fold. Progress has been made in understanding the underlying principles via the use of pure very long n-paraffins (Ungar, et al., 1985). Hopefully accurate crystal structure

202

FROM WAXES TO POLYMERS

analyses on well-characterized systems can be carried out in the future to complete the overview already obtained from the chain-extended arrays. To complicate the issue, it is also well-known that low-density chain-folded polyethylene will accommodate a small amount (e.g. 10 wt.%) of low molecular weight Fischer–Tropsch wax, thereby increasing the modulus of the polymer (Djokovic et al., 2003). Although chain-folded n-paraffins and chain-folded polyethylene structurally resemble one another, their thermal behaviors are quite different. For example, for the paraffin-chains, unfolding involves a series of discrete transformations. For the polydisperse polymer, on the other hand, the process of unfolding is continuous (Magonov et al., 2003).

11.5 11.5.1

Incentives for future characterization of waxes Critique of the Le Roux wax model

What have we learned from these studies? Resulting from an extensive physical chemical characterization, Le Roux proposed a four-domain model, shown in the introductory chapter of this book (Fig. 1.1), a model that has been copied by many investigators in their treatment of both natural and synthetic waxes. Twenty-five years later, with additional crystallographic information, some modifications might be suggested to this original model. For example, “rigid disordered” packing with methyl branches included within the polymethylene matrix must be kept to an absolute minimum, as found also for branched chain polyethylenes. Even for rapidly crystallized material, there is now evidence that methyl branches must be excluded from the lamellar layers and accommodated somehow within an interlamellar space. The somewhat loosely packed interlamellar region suggested in Le Roux’ model also is not supported by crystallographic studies. Since this is the region where molecular volumetric differences are accommodated in polydisperse arrays, inherent vacancies must be filled somehow by nonplanar conformational disorder, as demonstrated by spectroscopic data. There is little evidence to indicate that light “oil” components may be included in this interlamellar region. These certainly are not distilled away in vacuo, if indeed they are included in this region. Little needs to be said about the free, liquid oil fraction surrounding the crystalline portions of the wax. Slurries of Fischer–Tropsch product from a reactor are observed to be milky liquid with a solid precipitate in suspension. Again, the possible role of lower molecular weight oil fractions in the more solid wax regions, if any, is not determined. Again, if normal paraffins are the predominant component, solid waxes include surprisingly crystalline domains with a structure very similar to simple binary paraffin solid solutions. On the other hand, it must be recognized that crystallographic characterizations only take us so far in understanding the molecular packing in real waxes, since spectroscopy gives a much more realistic picture of the disorder needed to stabilize these solids. It is difficult to construct a quantitative model that includes

INCENTIVES FOR FUTURE CHARACTERIZATION OF WAXES

203

both spectroscopic and crystallographic results. On the other hand, it is clear that chain distribution alone will not account for the layer packing in a crystallographic model. 11.5.2

Directions for future work

A missing part of a general wax structural model is what happens when normal paraffins are no longer the major component. One such instance is if branched- or ring-containing components interact with the normal paraffins. For example, slack waxes have a high concentration of naphthenes and branched alkanes. The co-packing of methyl branched chains with normal paraffins has been discussed above. If, on the other hand, naphthenic components can also co-crystallize with normal chains, a suitable model has not been derived. There is only one crystal structure reported for the prototype of a simple naphthenic molecule (Merz, 2002). (However, alkane chains substituted on saturated rings may be more relevant (Ferris, 1955) but little is known about their crystal structures.) The presumed interdigitated bilayer structure of naphthenic components, also found for (polar) amphiphilic substances, will not be co-soluble with linear chain arrays, but there might be a stable epitaxial relationship between domains in a eutectic solid. In addition, the binary phase behavior of structural homologs has not been studied, not to mention the association of molecules with different ring moieties. As in the case of growth modifiers for diesel waxes (Kern and Dassonville, 1992) the “mal” crystalline forms of waxes, found in the “microcrystalline waxes” comprising extensive non-normal ingredients, may account for non-regular crystallization forms due to selective poisoning of certain crystal faces (Edwards, 1957). The origin of rolled lamellae, expressed morphologically as “needles” is less well-understood. The formation of such forms has been shown (Ferris, 1955) to depend on cooling rate for crystallization. It is interesting that rolling of lamellae into fibers is also noted for certain chiral detergents where alkyl chains are coupled to amino acids or carbohydrates. Plate crystals are formed only from racemic mixtures (Lehmann et al., 1990). Within the domain of natural waxes, it is astounding to note that no crystal structure currently exists for a symmetric wax ester. Although the tilted layer packing has been investigated for many years (Kohlhaas, 1938) and known to adopt one of the structures of polymethylene chains in the orthorhombic perpendicular subcell proposed by Kitaigorodskii (1961), the conformational geometry of the ester linkage has not been characterized in the solid state. While it may resemble the known linkage conformation of asymmetric esters in tilted layers, the reason for favoring tilted layers in these symmetric esters is not fully understood. It would also be important to determine the crystal structure of an asymmetric ester in the rectangular layer form. Perhaps the preparation of crystals by slow evaporation of a solvent with low vapor pressure will permit the crystallization of binary solids for their single crystal structure determination. In the realm of cholesteryl esters, an effort to characterize the binary solids in the bilayer and monolayer I polymorphs had been begun (see previous chapter). It was

204

FROM WAXES TO POLYMERS

soon found that a cartoon model, where molecules of different chain length are overlaid to build-up a statistical population, does not explain the solid state packing as well as it does for the n-paraffins. There are preferred packing sites for different chain lengths in the solid solutions. To better understand these relationships, a more complete sampling of binary compositions is required for crystal structure analysis. Moreover, there are no data on the monolayer II structure solid solutions. For the monolayer packings, it would be beneficial to collect diffraction data at low temperature to allow a more complete understanding of chain occupancies in the mixed solid. In the above discussion, the predominance of layered chain structures has been assumed. It was shown in Chapter 9 how tubular forms can also be significant structures for both insect and plant epicuticular waxes. In a recently published methodology for sequestering plant epicuticular waxes (Ensikat et al., 2000), it was stated that the tubular forms predominate when the major wax component is a secondary alcohol or a diketone, whereas lamellar forms are correlated with the dominance of primary alcohols. For the wax ester-based tubules of an insect wax (Dorset and Ghiradella, 1983), the tubular form could not be reformed when the material was recrystallized from solvent. How are these tubular forms produced, therefore? Given a mixture of different chemical species in such waxes that may be incompatible as solid solutions, what is the structural arrangement of the eutectic solid? For example, a eutectic arrangement is indicated for the co-mixture of fatty acids with fatty alcohols of the same chain length (Yoshida, 1942) but the solid state structure is not known. X-ray data indicate the existence of discrete blocks of pure components but can more intimately mixed structures also exist? Verily, there is much that remains to be done.

References Abrahamsson, S. (1956) Acta Cryst. 9, 663–667 Abrahamsson, S. (1958) Acta Cryst. 11, 270–273. Abrahamsson, S. (1959a) Ark. Kemi 14, 65–83. Abrahamsson, S. (1959b) Ark. Kemi 14, 49–55. Abrahamsson, S. (1959c) Acta Cryst. 12, 206–209. Abrahamsson, S. (1959d) Acta Cryst. 12, 301–304. Abrahamsson, S. (1959e) Acta Cryst. 12, 304–309. Abrahamsson, S. and Dahlén, B. (1976) J. Chem. Soc. Chem. Commun., 117–118. Abrahamsson, S. and Dahlén, B. (1977) Chem. Phys. Lipids 20, 43–56. Abrahamsson, S. and Fischmeister, I. (1959) Ark. Kemi 14, 57–63. Abrahamsson, S. and Harding, M. M. (1966) Acta Cryst. 20, 377–383. Abrahamsson, S. and Lundén, B. M. (1972) Acta Cryst. B28, 2262–2567. Abrahamsson, S. and Ryderstedt-Nahringbauer, I. (1962) Acta Cryst. 15, 1261–1268. Abrahamsson, S. and von Sydow, E. (1954) Acta Cryst. 7, 591–592. Abrahamsson, S. and Westerdahl, A. (1963) Acta Cryst. 16, 404–409. Abrahamsson, S., Larsson, G., and von Sydow, E. (1960) Acta Cryst. 13, 770–774. Abrahamsson, S., Innes, M., and Nilsson, B. (1968) Ark. Kemi 30, 173–182. Abrahamsson, S., Dahlén, B., Löfgren, H., and Pascher, I. (1978) Progr. Chem. Fats Other Lipids 16, 125–143. Achour, Z., Sabour, A., Dirand, M., and Hoch, M. (1998) J. Therm. Anal. 51, 477–488. Achour-Boudjema, Z., Bouroukba, M., and Dirand, M. (1996) Thermochim. Acta 276, 243–256. Albon, N. (1976) J. Cryst. Growth 35, 105–109. Aleby, S. (1962) Acta Cryst. 15, 1248–1252. Aleby, S. (1968a) Acta Chem. Scand. 22, 811–818. Aleby, S. (1968b) Acta Chem. Scand. 22, 3146–3154. Aleby, S. and Fischmeister, I. (1969a) Ark. Kemi 31, 267–281. Aleby, S. and Fischmeister, I. (1969b) Ark. Kemi 31, 283–290. Aleby, S. and von Sydow, E. (1960) Acta Cryst. 13, 487–490. Aleby, S., Fischmeister, I., and Iyengar, B. T. K. (1971) Lipids 6, 421–425. Altgelt, K. H. and Boduszynski, M. H. (1994) Composition and Analysis of Heavy Petroleum Fractions. NY: Marcel Dekker. Amelinckx, S. (1953) Naturwissenschaften 40, 620–621. Amelinckx, S. (1954) Naturwissenschaften 41, 356–357.

206

REFERENCES

Amelinckx, S. (1955) Acta Cryst. 8, 530–577. Amelinckx, S. (1956a) Acta Cryst. 9, 16–23. Amelinckx, S. (1956b) Acta Cryst. 9, 217–224. Amelinckx, S. (1958) Crystallization of binary mixtures of long-chain alcohols In: Growth and Perfection of Crystals. R. H. Doremus, B. W. Roberts, and D. Turnbull, eds., NY: Wiley, pp. 586–591. Amelinckx, S. and Van Dyck, D. (1993) Electron Diffraction Techniques. Volume 2. J. M. Cowley, ed., Oxford: Oxford University Press, pp. 309–372. Amorós, J. L. and Amorós, M. (1968) Molecular Crystals. Their Transforms and Diffuse Scattering. NY: Wiley, p. 161. Anderson, N. G. and Dawson, I. M. (1953) Proc. Roy. Soc. (London) A218, 255–268. Andrew, E. R. (1950) J. Chem. Phys. 18, 607–618. Annis, B. K., Londono, J. D., Wignall, G. D., and Snyder, R. G. (1996) J. Phys. Chem. 100, 1725–1730. Asano, T. and Abe, H. (1984) J. Phys. Soc. Japan 53, 1071–1077. Asano, T., Mina, M. F., and Hatta, I. (1996) J. Phys. Soc. Japan 65, 1699–1704. Asbach, G. I. and Kilian, H. G. (1970) Ber. Bunsenges. Phys. Chem. 74, 814–823. Asbach, G. I., Geiger, K., and Wilke, W. (1979) Coll. Polym. Sci. 257, 1049–1059. Baldvins, J. E. and Weiss, R. G. (1999) Liq. Crys. 26, 897–912. Barnard, J. A. W. and Lydon, J. E. (1974) Mol. Cryst. Liq. Cryst. 26, 285–296. Barrall, E. M., Porter, R. S., and Johnson, J. F. (1967a) J. Phys. Chem. 71, 895–900. Barrall, E. M., Porter, R. S., and Johnson, J. F. (1967b) J. Phys. Chem. 71, 1224–1228. Bassett, D. C. and Keller, A. (1961) Phil Mag. 6, 345–358. Bassett, D. C. and Keller, A. (1962) Phil Mag. 7, 1553–1584. Bassett, D. C., Frank, F. C., and Keller, A. (1959) Nature 184, 810–811. Bassett, D. C., Frank, F. C., and Keller, A. (1963) Phil Mag. 8, 1753–1787. Basson, I. and Reynhardt, E. C. (1988a) J. Phys. D. Appl. Phys. 21, 1434–1437. Basson, I. and Reynhardt, E. C. (1988b) J. Phys. D. Appl. Phys. 21, 1421–1428. Basson, I. and Reynhardt, E. C. (1988c) J. Phys. D. Appl. Phys. 21, 1429–1433. Basson, I. and Reynhardt, E. C. (1990) J. Chem. Phys. 93, 3604–3609. Basson, I. and Reynhardt, E. C. (1991) J. Chem. Phys. 95, 1215–1222. Basson, I. and Reynhardt, E. C. (1992a) Chem. Phys. Lett. 198, 367–372. Basson, I. and Reynhardt, E. C. (1992b) J. Chem. Phys. 97, 1287–1295. Beckmann, W. and Boistelle, R. (1985) J. Cryst. Growth 72, 621–630. Bennema, P., Liu, X. Y., Lewtas, K., Tack, R. D., and Rijpkema, J. J. M. (1992) J. Cryst. Growth 121, 679–696. Bianchi, G. (1995) In: Waxes: Chemistry, Molecular Biology and Functions. R. J. Hamilton, ed., Dundee, Oily Press, pp. 175–222. Billmeyer, F. W. (1972) Textbook of Polymer Science. 2nd edn. NY: WileyInterscience. Bittiger, H., Marchessault, R. H., and Niegisch, W. D. (1970) Acta Cryst. B26, 1923–1927. Blasenbrey, S. and Pechhold, W. (1967) Rheol. Acta 6, 174–185.

REFERENCES

207

Blomquist, G. L. and Jackson, L. L. (1979) Progr. Chem. Fats Other Lipids 17, 319–345. Boese, R., Weiss, H. C., and Bläser, D. (1999) Angew. Chem. Int. Ed. 38, 988–992. Boistelle, R. and Aquilano, D. (1977) Acta Cryst. A33, 642–648. Boistelle, R. and Aquilano, D. (1978) Acta Cryst. A34, 406–413. Boistelle, R. and Lundager Madsen, H. E. (1978) J. Cryst. Growth 43, 141–147. Boistelle, R., Simon, B., and Pepe, G. (1976) Acta Cryst. B32, 1240–1243. Bond, A. D. (2004) New. J. Chem. 28, 104–115. Bond, A. D. and Davies, J. E. (2002) Acta Cryst. E58, o196–o197. Bondi, A. (1964) J. Phys. Chem. 68, 441–451. Bonsor, D. H. and Bloor, D. (1977) J. Mater. Sci. 12, 1559–1564. Boudet, A. (1984) J. Mater. Sci. 19, 2989–2996. Boyd, R. H. (1975) J. Polym. Sci. Polym. Phys. Ed. 13, 2345–2355. Braam, A. W. M. and Vos, A. (1980) Acta Cryst. B36, 2688–2692. Broadhurst, M. G. (1962) J. Res. Natl. Bur. Standards 66A, 241–249. Broadhurst, M. G. (1966) J. Res. Natl. Bur. Standards 70A, 481–486. Brotherton, T., Craven, B., and Jeffrey, G. A. (1958) Acta Cryst. 11, 546–551. Brummage, K. G. (1946) Proc. Roy. Soc. (London) A188, 414–426. Buckingham, A. D. and Hentschel, H. G. E. (1980) J. Polym. Sci. Polym. Phys. Ed. 18, 853–861. Bunn, C. W. (1939) Trans. Faraday Soc. 35, 482–491. Bunn, C. W. and Howells, E. R. (1954) Nature 174, 549–551. Carlisle, C. H. and Crowfoot, D. (1945) Proc. Roy. Soc. (London) A184, 64–83. Cates, D. A., Strauss, H. L., and Snyder, R. G. (1994) J. Phys. Chem. 98, 4482–4488. Chandross, R. J. and Bordner, J. (1978) Acta Cryst. B34, 2872–2875. Chapman, D. (1965) The Structure of Lipids. NY: Wiley. Chapman, J. A. and Tabor, D. (1957) Proc. Roy. Soc. (London) A242, 96–107. Chatani, Y., Okita, Y., Tadokoro, H., and Yamashita, H. (1970) Polym. J. 1, 555–562. Chazhengina, S. Yu, Kotel’ikova, E. H., and Filatov, S. K. (1996) Zh. Strukt. Khim. 37, 929–938. Chevallier, V., Provost, E., Bourdet, J. B., Bouroukba, M., Petitjean, D., and Dirand, M. (1999) Polymer 40, 2121–2128. Chibnall, A. C., Piper, S. H., Pollard, A., Smith, J. A. B., and Williams, E. F. (1931) Biochem. J. 25, 2095–2110. Chibnall, A. C., Piper, S. H., Pollard, A., Williams, E. F., and Sahai, P. N. (1934) Biochem. J. 28, 2189–2208. Chichakli, M. and Jessen, F. W. (1967) Ind. Eng. Chem. 59, 86–98. Cho, S. I. and Craven, B. M. (1987) J. Lipid Res. 28, 80–86. Clark, E. S. and Muus, L. T. (1962a) Z. Krist. 117, 108–118. Clark, E. S. and Muus, L. T. (1962b) Z. Krist. 117, 119–127. Clavell-Grunbaum, D., Strauss, H. L., and Snyder, R. G. (1997) J. Phys. Chem. B101, 335–343. Clydesdale, G. and Roberts, K. J. (1991) AIChE Symp. Ser. 87, 130–137.

208

REFERENCES

Coumoulos, G. D. and Rideal, E. K. (1941) Proc. Roy. Soc. (London) A178, 421–428. Courchinoux, R., Chanh, N., Haget, Y., Tauler, E., and Cuevas-Diarte, M. A. (1988) Thermochim. Acta 128, 45–53. Coutinho, J. A. P. and Ruffier-Méray, V. (1997) Ind. Eng. Chem. 36, 4977–4983. Coutinho, J. A. P., Dauphin, C., and Daridon, J. L. (2000) Fuel 79, 607–616. Cowley, J. M., Rees, A. L. G., and Spink, J. A. (1951) Proc. Phys. Soc. (London) A64, 609–619. Craievich, A. F., Denicolo, I., and Doucet, J. (1984a) Phys. Rev. B30, 4782–4787. Craievich, A. F., Doucet, J., and Denicolo, I. (1984b) J. Phys. (Paris) 45, 1473–1477. Craig, S. R., Hastie, G. P., Roberts, K. J., Gerson, A. R., Sherwood, J. N., and Tack, R. D. (1998) J. Mater. Chem. 8, 859–869. Craig, S. R., Hastie, G. P., Roberts, K. J., Sherwood, J. N., Tack, R. D., and Cernik, R. J. (1999) J. Mater. Chem. 9, 2381–2392. Craven, B. M. (1976) Nature 260, 727–729. Craven, B. M. (1979) Acta Cryst. B35, 1123–1128. Craven, B. M. (1986) In: Handbook of Lipid Research. Volume 4. The Physical Chemistry of Lipids from Alkanes to Phospholipids. D. M. Small, ed., NY: Plenum, pp. 149–182. Craven, B. M. and DeTitta, G. T. (1976) J. Chem. Soc. Perkin II, 814–822. Craven, B. M. and Guerina, N. G. (1979a) Chem. Phys. Lipids 24, 157–166. Craven, B. M. and Guerina, N. G. (1979b) Chem. Phys. Lipids 24, 91–98. Craven, B. and Jeffrey, G. A. (1959) Acta Cryst. 12, 754–761. Craven, B. and Jeffrey, G. A. (1960) J. Am. Chem. Soc. 82, 3858–3860. Craven, B. M. and Sawzik, P. (1983) J. Lipid Res. 24, 784–789. Craven, B. M. and Sawzik, P. (1984) J. Lipid Res. 25, 857–864. Cromer, D. T. and Larson, A. C. (1972) Acta Cryst. B28, 2128–2132. Dahlén, B. (1972) Acta Cryst. B28, 2555–2562. Dahlén, B. (1979) Chem. Phys. Lipids 23, 179–188. Dahlén, B., Lundén, B. M., and Pascher, I. (1976) Acta Cryst. B32, 2059–2063. Davis, G. J., Porter, R. S., and Barrall, E. M. (1970a) Mol. Cryst. Liq. Cryst. 10, 1–19. Davis, G. J., Porter, R. S., Steiner, J. W., and Small, D. M. (1970b) Mol. Cryst. Liq. Cryst. 10, 331–336. Davis, G. J., Porter, R. S., and Barrall, E. M. (1970c) Mol. Cryst. Liq. Cryst. 11, 319–330. Dawson, I. M. (1952) Proc. Roy. Soc. (London) A214, 72–79. Dawson, I. M. and Vand, V. (1951) Proc. Roy. Soc. (London) A206, 555–562. Dawson, I. M. and Watson, D. H. (1957) Proc. Roy. Soc. (London) A239, 349–364. Denicolo, I., Doucet, J., and Craievich, A. F. (1983) J. Chem. Phys. 78, 1465–1469. Denicolo, I., Craievich, A. F., and Doucet, J. (1984) J. Chem. Phys. 80, 6200–6203. Dirand, M. and Achour-Boudjema, Z. (1996) J. Mol. Struct. 375, 243–248. Dirand, M., Achour, Z., Jouti, B., Sabour, A., and Gachon, J. C. (1996) Mol. Cryst. Liq. Cryst. 275, 293–304.

REFERENCES

209

Dirand, M., Bouroukba, M., Chevallier, V., Petitjean, D., Behar, E., and Ruffier-Meray, V. (2002) J. Chem. Eng. Data 47, 115–143. Djokovic, V., Mtshali, T. N., and Luyt, A. S. (2003) Polym. Int. 52, 999–1004. Dollhopf, W., Grossmann, H. P., and Leute, U. (1981) Coll. Polym. Sci. 259, 267–278. Dorset, D. L. (1970) Crystal and molecular structures of the 1,3-diglyceride of 11-bromoundecanoic acid, ethylene di-11-bromoundecanoate and 2,4,7-trinitro9-fluorenone Ph.D. Thesis, University of Maryland. Dorset, D. L. (1975) Chem. Phys. Lipids 14, 291–296. Dorset, D. L. (1976a) Biochim. Biophys. Acta 424, 396–403. Dorset, D. L. (1976b) Acta Cryst. A32, 207–215. Dorset, D. L. (1976c) Bioorg. Khim. 2, 781–788. Dorset, D. L. (1976d ) J. Appl. Cryst. 9, 142–144. Dorset, D. L. (1977) Chem. Phys. Lipids 20, 13–19. Dorset, D. L. (1978) Z. Naturforsch. 33a, 964–982. Dorset, D. L. (1979) Chem. Phys. Lipids 23, 337–347. Dorset, D. L. (1980) Acta Cryst. A36, 592–600. Dorset, D. L. (1983) Ultramicroscopy 12, 19–28. Dorset, D. L. (1985a) Macromolecules 18, 2158–2163. Dorset, D. L. (1985b) J. Lipid Res. 26, 1142–1150. Dorset, D. L. (1986a) J. Macromol. Sci.—Phys. B25, 1–20. Dorset, D. L. (1986b) Macromolecules 19, 2965–2973. Dorset, D. L. (1987a) Macromolecules 20, 2782–2788. Dorset, D. L. (1987b) J. Lipid Res. 28, 993–1005. Dorset, D. L. (1988) Biochim. Biophys. Acta 963, 88–97. Dorset, D. L. (1989) J. Polym. Sci. B. Polym. Phys. 27, 1161–1171. Dorset, D. L. (1990a) Biochim. Biophys. Acta 1046, 57–63. Dorset, D. L. (1990b) Macromolecules 23, 623–633. Dorset, D. L. (1990c) Proc. Natl. Acad. Sci. USA 87, 8541–8544. Dorset, D. L. (1990d) Macromolecules 23, 894–901. Dorset, D. L. (1990e) Biochim. Biophys. Acta 1046, 195–201. Dorset, D. L. (1991a) Macromolecules 24, 6521–6526. Dorset, D. L. (1991b) Macromolecules 24, 1175–1178. Dorset, D. L. (1991c) Proc. Natl. Acad. Sci. USA 88, 5499–5502. Dorset, D. L. (1992) Biochim. Biophys. Acta 1127, 293–297. Dorset, D. L. (1993) Acta Chim. Hungar. (Models in Chemistry) 130, 389–404. Dorset, D. L. (1995a) Structural Electron Crystallography. NY: Plenum. Dorset, D. L. (1995b) Acta Cryst. B51, 1021–1027. Dorset, D. L. (1997a) Polymer 38, 247–253. Dorset, D. L. (1997b) J. Phys. D. Appl. Phys. 30, 451–457. Dorset, D. L. (1997c) J. Phys. Chem. B101, 4870–4874. Dorset, D. L. (1999a) Z. Krist. 214, 223–228. Dorset, D. L. (1999b) Macromolecules 32, 162–166. Dorset, D. L. (1999c) Z. Krist. 214, 229–236. Dorset, D. L. (1999d) Z. Krist. 214, 362–366.

210

REFERENCES

Dorset, D. L. (1999e) J. Phys. D. Appl. Phys. 32, 1276–1280. Dorset, D. L. (2000a) Z. Krist. 215, 190–198. Dorset, D. L. (2000b) J. Phys. Chem. B104, 8346–8350. Dorset, D. L. (2000c) Energy and Fuels 14, 685–691. Dorset, D. L. (2000d) J. Phys. Chem. B104, 4613–4617. Dorset, D. L. (2000e) J. Phys. Chem. B104, 10543–10548. Dorset, D. L. (2001) Z. Krist. 216, 234–239. Dorset, D. L. and Annis, B. K. (1996) Macromolecules 29, 2969–2973. Dorset, D. L. and Basson, I. (2000) J. Phys. D. Appl. Phys. 33, 2657–2663. Dorset, D. L. and Ghiradella, H. (1983) Biochim. Biophys. Acta 760, 136–142. Dorset, D. L. and Hsu, S. L. (1989) Polymer 30, 1596–1602. Dorset, D. L. and Hybl, A. (1972) Science 176, 806–808. Dorset, D. L. and McCourt, M. P. (1997) J. Macromol. Sci.—Phys. B36, 301–313. Dorset, D. L. and Moss, B. (1983) Polymer 24, 291–294. Dorset, D. L. and Pangborn, W. A. (1979) Chem. Phys. Lipids 25, 179–189. Dorset, D. L. and Pangborn, W. A. (1992) Proc. Natl. Acad. Sci. USA 89, 1822–1826. Dorset, D. L. and Snyder, R. G. (1995) Macromolecules 28, 8412–8418. Dorset, D. L. and Snyder, R. G. (1996) J. Phys. Chem. 100, 9848–9853. Dorset, D. L. and Snyder, R. G. (1999a) J. Phys. Chem. B103, 3282–3286. Dorset, D. L. and Snyder, R. G. (1999b) Macromolecules 32, 8139–8144. Dorset, D. L. and Zemlin, F. (1990) Ultramicroscopy 33, 227–236. Dorset, D. L. and Zhang, W. P. (1991) J. Electr. Microsc. Techn. 18, 142–147. Dorset, D. L, Moss, B., Wittmann, J. C., and Lotz, B. (1984) Proc. Natl. Acad. Sci. USA 81, 1913–1917. Dorset, D. L., Hanlon, J., and Karet, G. (1989) Macromolecules 22, 2169–2172. Dorset, D. L., Hanlon, J., McConnell, C. H., Fryer, J. R., Lotz, B., Wittmann, J. C., Beckmann, E., and Zemlin, F. (1990) Proc. Natl. Acad. Sci. USA 87, 1696–1700. Dorset, D. L., Strauss, H. L., and Snyder, R. G. (1991a) J. Phys. Chem. 95, 938–940. Dorset, D. L., Hu, H., and Jäger, J. (1991b) Acta Cryst. A47, 543–549. Dorset, D. L., Alamo, R. G., and Mandelkern, L. (1992) Macromolecules 25, 6284–6288. Dorset, D. L., Clavell-Grunbaum, D., and Snyder, R. G. (2000) J. Phys. Chem. B104, 532–537. Doucet, J., Denicolo, I., Craievich, A. F., and Germain, C. (1984) J. Chem. Phys. 80, 1647–1651. Downing, D. T., Kranz, Z. H., Lamberton, J. A., Murray, K. E., and Redcliffe, A. H. (1961) Austral. J. Chem. 14, 253–263. Duax, W. L. and Norton, D. A. (1975) Atlas of Steroid Structures. Volume 1. NY: Plenum. Dunitz, J. D., Gavezotti, A., and Schweizer, W. B. (2003) Helv. Chim. Acta 86, 4073–4092. Ebert, L. B., Scanlon, J. C., and Mills, D. R. (1983) Preprints ACS Div. Petrol. Chem. 28, 1353–1366.

REFERENCES

211

Eby, R. K., Clark, E. S., Farmer, B. L., Piermarini, G. J., and Block, S. (1990) Polymer 31, 2227–2237. Edwards, R. T. (1957) Ind. Eng. Chem. 49, 750–757. Ensikat, H. J., Neinhuis, C., and Barthlott, W. (2000) Int. J. Plant Sci. 161, 143–148. Ernst, J. and Fuhrhop, J. H. (1979) Liebigs Ann. Chem., 1635–1642. Ernst, J., Sheldrick, W. S., and Fuhrhop, J. H. (1979) Z. Naturforsch. 34b, 706–711. Ewen, B., Strobl, G. R., and Richter, D. (1980) Faraday Discuss. Chem. Soc. 69, 19–31. Farmer, B. L. and Eby, R. K. (1979) Polymer 20, 363–366. Farmer, B. L. and Eby, R. K. (1987) Polymer 28, 86–92. Fenrych, J., Reynhardt, E. C., and Basson, I. (1997) Chem. Phys. Lett. 275, 215–221. Ferris, S. W. (1955) In: The Science of Petroleum. Volume V. Part III (B. T. Brooks and A. E. Dunstan, eds.) Oxford, London, pp. 172–185. Fischer, E. W. (1971) Pure Appl. Chem. 26, 385–421. Flory, P. J. (1953) Principles of Polymer Chemistry. Ithaca, NY: Cornell University Press, pp. 507–511, 568–571. Francis, F., Piper, S. H., and Malkin, T. (1930) Proc. Roy. Soc. (London) A128, 214–252. Frede, E. and Precht, D. (1974) Kiel. Milchwirtsch. Forschungsber. 26, 325–332. Frede, E. and Precht, D. (1976) J. Am. Oil Chem. Soc. 53, 668–670. Fryer, J. R. (1989) J. Electr. Microsc. Techn. 11, 310–325. Fryer, J. R. (1993) Microsc. Soc. Amer. Bull. 23(1), 44–56. Fryer, J. R., McConnell, C. H., Dorset, D. L., Zemlin, F., and Zeitler, E. (1997) Proc. Roy. Soc. (London) A453, 1929–1946. Galanti, A. V. and Porter, R. S. (1972) J. Phys. Chem. 76, 3089–3093. Gao, Q. and Craven, B. M. (1986) J. Lipid Res. 27, 1214–1221. Garrido, J. and Hengstenberg, J. (1932) Z. Krist. 82, 477–480. Gazzano, M., Malta, V., Focarete, M. L., Scandola, M., and Gross, R. A. (2003) J. Polym. Sci. B. Polym. Phys. 41, 1009–1014. Germer, L. H. and Storks, K. H. (1937) Proc. Natl. Acad. Sci. USA 23, 390–392. Germer, L. H. and Storks, K. H. (1938) J. Chem. Phys. 6, 280–293. Gerson, A. R. and Nyburg, S. C. (1994) Acta Cryst. B50, 252–256. Gerson, A. R., Nyburg, S. C., and McAleer, A. (1999) J. Appl. Cryst. 32, 296–299. Ghogomu, P. M., Provost, E., Bouroukba, M., Dirand, M., and Hoch, M. (1998) J. Therm. Anal. 53, 49–56. Gilardi, R. D., Karle, I. L., and Karle, J. (1972) Acta Cryst. B28, 2605–2612. Gilbert, E. P. (1999a) Phys. Chem. Chem. Phys. 1, 5209–5204. Gilbert, E. P. (1999b) Phys. Chem. Chem. Phys. 1, 1517–1529. Gilbert, E. P., Reynolds, P. A., Brown, A. S., and White, J. W. (1996a) Chem. Phys. Lett. 255, 373–377. Gilbert, E. P., Reynolds, P. A., and White, J. W. (1996b) J. Phys. Chem. 100, 18201–18213. Gilbert, E. P., Reynolds, P. A., Thiyagarajan, P., Wozniak, D. G., and White, J. W. (1999) Phys. Chem. Chem. Phys. 1, 2715–2724.

212

REFERENCES

Gilby, G. W. (1983) Spec. Publ. Roy. Soc. Chem. 45 108–124. Ginsburg, G. S., Atkinson, D., and Small, D. M. (1984) Prog. Lipid Res. 23, 135–167. Gordon, P. (1968) Principles of Phase Diagrams in Materials Systems. NY: McGraw-Hill. Goto, M. and Asada, E. (1978a) Bull. Chem. Soc. Japan 51, 70–74. Goto, M. and Asada, E. (1978b) Bull. Chem. Soc. Japan 51, 2456–2459. Goto, M. and Asada, E. (1984) Bull. Chem. Soc. Japan 57, 1145–1146. Griffen, J. W. and Porter, R. S. (1973) Mol. Cryst. Liq. Cryst. 21, 77–98. Griffin, J. F., Duax, W. L., and Weeks, C. M. (1984) Atlas of Steroid Structures. Volume 2, NY: Plenum. Grigor, A. F. and Steele, W. A. (1968) J. Chem. Phys. 48, 1038–1046. Guenet, J. M. and McKenna, G. B. (1988) Macromolecules 21, 1752–1756. Guerina, N. G. and Craven, B. M. (1979) J. Chem. Soc. Perkin II, 1414–1419. Guo, W. and Hamilton, J. A. (1993) Biochemistry 32, 9038–9052. Gupta, A. K. and Severin, D. (1997) Petrol. Sci. Technol. 15, 943–957. Guy, A. G. and Hren, J. J. (1973) Elements of Physical Metallurgy, 3rd edn. Reading, MA: Addison-Wesley. Hagemann, H., Strauss, H. L., and Snyder, R. G. (1987) Macromolecules 20, 2810–2819. Hamilton, R. J. (1995) In: Waxes: Chemistry, Molecular Biology and Function. R. J. Hamilton, ed. Dundee, Scotland: The Oily Press, pp. 257–310. Hammami, A. and Mehrota, A. K. (1995) Fluid Phase Equil. 111, 253–272. Han, G. W., Craven, B. M., and Langs, D. A. (1994) J. Lipid Res. 35, 2069–2082. Hansen, J. H., Fredenslund, Aa., Pedersen, K. S., and Rønningen, H. P. (1988) AIChE. J. 34, 1937–1942. Hartman, P. (1963) Physics and Chemisty of the Organic Solid State, Volume 1. D. Fox, M. M. Labes, and A. Wesssburger, eds., NY: Wiley, pp. 369–409. Hatt, H. H. and Lamberton, J. A. (1956) Research (London) 9, 138–146. Hawk, P. B., Oser, B. L., and Summerson, W. H. (1954) Practical Physiological Chemistry, 13th edn. NY: McGraw-Hill, p. 97. Hayashida, T. (1962) J. Phys. Soc. Japan 17, 306–315. Hengstenberg, J. (1928) Z. Krist. 67, 583–594. Hepburn, H. R. (1986) Honeybees and Wax. An Experimental Natural History. Berlin: Springer Verlag. Holder, G. D., Enick, R. M., and Mohamed, R. S. (1996) Fluid Phase Equil. 117, 126–137. Holloway, P. J. (1968) J. Pharm. Pharmacol. 20, 775–779. Höpken, J. (1991) Fluorocarbon-hydrocarbon molecules. structural components for self-organizing materials Ph.D. Thesis, University of Twente. Hsu, E. C. H. and Johnson, J. F. (1974) Mol. Cryst. Liq. Cryst. 27, 95–104. Hsu, L. Y. and Nordman, C. E. (1983) Science 220, 604–606. Hu, H. and Dorset, D. L. (1989) Acta Cryst. B45, 283–290. Hu, H., Dorset, D. L., and Moss, B. (1989) Ultramicroscopy 27, 161–170. Hui, S. W. (1989) J. Electr. Microsc. Techn. 11, 286–297. Hurst, H. (1948) Discuss. Faraday Soc. 3, 193–210.

REFERENCES

213

Hurst, H. (1950) J. Exp. Biol. 27, 238–252. Hybl, A. and Dorset, D. L. (1971) Acta Cryst. B27, 977–986. Irani, C. A., Schuster, D. S., and Yin, R. T. (1985) Prepr. ACS Div. Fuel Chem. 30, 158–168. Jang, S. S., Blanco, M., Goddard, W. A., Caldwell, G., and Ross, R. B. (2003) Macromolecules 36, 5331–5341. Jayalakshmi, V., Selvavathi, V., Sekar, M. S., and Sairam, B. (1999) Petrol. Sci. Technol. 17, 843–856. Jetter, B., Schäffer, S., and Riederer, M. (2000) Plant Cell Environ. 23, 619–628. Jouti, B., Bourlet, J. B., Bouroukba, M., and Diraud, M. (1995a) Mol. Cryst. Liq. Cryst. 270, 159–173. Jouti, B., Petitjean, D., Provost, E., Bouroukba, M., and Diraud, M. (1995b) J. Mol. Struct. 356, 191–199. Kaneko, F., Kobayashi, M., Kitagawa, Y., and Matsuura, Y. (1990) Acta Cryst. C46, 1490–1492. Kaneko, F., Kobayashi, M., Kitagawa, Y., Matsuura, Y., Sato, K., and Suzuki, M. (1992a) Acta Cryst. C48, 1054–1057. Kaneko, F., Kobayashi, M., Kitagawa, Y., Matsuura, Y., Sato, K., and Suzuki, M. (1992b) Acta Cryst. C48, 1060–1063. Kaneko, F., Kobayashi, M., Kitagawa, Y., Matsuura, Y., Sato, K., and Suzuki, M. (1992c) Acta Cryst. C48, 1057–1060. Kaneko, F., Yamazaki, K., Kobayashi, M., Masamichi, K., Yasuyaki, M., Yoshiki, S., Sato, K., and Suzuki, M. (1993) Acta Cryst. C49, 1232–1234. Kaneko, F., Sakashita, H., Kobayashi, M., Kitagawa, Y., Matsuura, Y., and Suzuki, M. (1994a) Acta Cryst. C50, 245–247. Kaneko, F., Sakashita, H., Kobayashi, M., Kitagawa, Y., Matsuura, Y., and Suzuki, M. (1994b) Acta Cryst. C50, 247–250. Kaneko, F., Yamazaki, K., Kitagawa, K., Kikyo, T., Kobayashi, M., Kitagawa, Y., Matsuura, Y., Sato, K., and Suzuki, M. (1997) J. Phys. Chem. B101, 1803–1809. Karle, J. and Brockway, L. O. (1947) J. Chem. Phys. 19, 213–225. Karrer, P. (1954) Lehrbuch der Organischen Chemie (12–te Auflage). Stuttgart: Georg Thieme, pp. 32–43. Kawaguchi, A. (1978) Bull. Inst. Res. Kyoto Univ. 56, 68–79. Kawaguchi, A., Ohara, M., and Kobayashi, K. (1979) J. Macromol. Sci.—Phys. B16, 193–212. Kay, H. F. and Newman, R. A. (1968) Acta Cryst. B24, 615–624. Keller, A. (1961) Phil. Mag. 6, 329–343. Kern, R. and Dassonville, R. (1992) J. Cryst. Growth 116, 191–203. Kerr, H. W. and Lewis, M. H. (1971) Advances in Epitaxy and Endotaxy. H. G. Schneider and V. Ruth, eds. Leipzig: VEB Deutscher Verlag für Grundstoffindustrie, pp. 147–164. Khoury, F. (1963) J. Appl. Phys. 34, 73–79. Kim, Y., Strauss, H. L., and Snyder, R. G. (1988) J. Phys. Chem. 92, 5080–5082. Kim, Y., Strauss, H. L., and Snyder, R. G. (1989a) J. Phys. Chem. 93, 7520–7526.

214

REFERENCES

Kim, Y., Strauss, H. L., and Snyder, R. G. (1989b) J. Phys. Chem. 93, 485–490. Kinghorn, R. R. F. (1983) An Introduction to the Physics and Chemistry of Petroleum. Chichester: Wiley, p. 91. Kitaigorodskii, A. I. (1957a) Sov. Phys. Crystallogr. 2, 454–462. Kitaigorodskii, A. I. (1957b) Sov. Phys. Crystallogr. 2, 637–642. Kitaigorodskii, A. I. (1961) Organic Chemical Crystallography. NY: Consultants Bureau, pp. 177–215, 230–240. Kitaigorodskii, A. I., Mnyukh, Yu. V., and Nechitailo, N. A. (1958) Sov. Phys. Crystallogr. 3, 303–307. Kitaigorodsky, A. I. (1984) Mixed Crystals. Berlin: Springer-Verlag. Kobayashi, M. (1978) J. Chem. Phys. 68, 145–151. Kohlhaas, R. (1938) Z. Krist. 98, 418–438. Kohlhaas, R. (1940) Chem. Ber. 73B, 189–200. Kohlhaas, R. and Stüber, C. (1939) Chem. Ber. 72, 1962–1969. Kraack, H., Deutsch, M., and Sirota, E. B. (2000a) Macromolecules 33, 6174–6184. Kraack, H., Sirota, E. B., and Deutsch, M. (2000b) J. Chem. Phys. 112, 6873–6885. Kravchenko, V. (1946) Zh. Fiz. Khim. 21, 335–344. Kreger, D. (1951) Selected Topics in X-ray Crystallography from the Delft X-ray Institute. J. Bouman, ed. Amsterdam: North-Holland, pp. 303–324. Kreger, D. and Schamhart, C. (1956) Biochim. Biophys. Acta 19, 22–44. Krzewski, R. J. and Porter, R. S. (1973) Mol. Cryst. Liq. Cryst. 21, 99–124. Kubota, H., Kaneka, F., Kawaguchi, T., and Kawasaki, M. (2004) Cryst. Growth Des. 4, 369–375. Kulpe, S., Seidel, I., Szulzewsky, K., Steger, U., and Steger, E. (1981) Cryst. Res. Technol. 16, 349–356. Kuwahara, T., Nagase, H., Endo, T., Ueda, H., and Nakagaki, M. (1996) Chem. Lett., 435–436. Lacks, D. J. (1995) J. Chem. Phys. 103, 5085–5090. Lapasset, J., Moret, J., Melas, M., Collet, A., Viguier, M., and Blancou, H. (1996) Z. Krist. 211, 945–946. Larsson, K. (1962) Acta Chem. Scand. 16, 1751–1756. Larsson, K. (1963a) Acta Chem. Scand. 17, 221–226. Larsson, K. (1963b) Acta Chem. Scand. 17, 199–207. Larsson, K. (1963c) Acta Chem. Scand. 17, 215–220. Larsson, K. (1963d) Acta Cryst. 16, 741–748. Larsson, K. (1964) Acta Chem. Scand. 18, 272–273. Larsson, K. (1966) Acta Chem. Scand. 20, 2225–2260. Larsson, K. (1967) Nature 213, 383–384. Larsson, K. (1994) Lipids. Molecular Organization, Physical Function and Technical Applications. Dundee, Scotland: The Oily Press. Larsson, K. and von Sydow, E. (1966) Acta Chem. Scand. 20, 1203–1207. Lee, A. G. (1977) Biochim. Biophys. Acta 472, 285–344. Lehmann, C. W., Buschmann, J., Luger, P., Demoulin, C., and Fuhrhop, J. H. (1990) Acta Cryst. B46, 646–650.

REFERENCES

215

Le Roux, J. H. (1970) J. Appl. Chem. 20, 203–207. Le Roux, J. H. (1979) South African J. Sci. 75, 356–361. Le Roux, J. H. and Dry, L. J. (1972) J. Appl. Chem. Biotechnol. 22, 719–726. Le Roux, J. H. and Loubser, N. H. (1980) South African J. Sci. 76, 157–161. Levine, I. N. (1995) Physical Chemistry, 4th edn. NY: McGraw-Hill, pp. 332–342. Li, F. H. (1963) Acta Phys. Sinica 19, 735–740. Lieser, G., Lee, K. S., and Wegner, G. (1988) Coll. Polym. Sci. 266, 419–428. Liu, W. B. and Boyd, R. H. (1990) Macromolecules 1531–1539. Liu, X. Y. and Bennema, P. (1993) J. Appl. Cryst. 26, 229–242. Liu, X. Y. and Bennema, P. (1994) J. Cryst. Growth 135, 209–223. Lourens, J. A. J. and Reynhardt, E. C. (1979) J. Phys. D. Appl. Phys. 12, 1963–1972. Lundager Madsen, H. E. and Boistelle, R. (1976) Acta Cryst. A32, 828–831. Lundén, B. M. (1976) Acta Cryst. B32, 3149–3153. Lundén, B. M., Löfgren, H., and Pascher, I. (1977) Chem. Phys. Lipids 20, 263–271. Luo, J. Q., Ruble, J. R., and Craven, B. M. (1995) J. Lipid Res. 36, 332–342. Lüth, H., Nyburg, S. C., Robinson, P. M., and Scott, H. G. (1974) Mol. Cryst. Liq. Cryst. 27, 3337–3357. Lutton, E. S. and Hugenberg, F. R. (1962) J. Chem. Eng. Data 7, 208–209. Lutz, D. A., Eddy, C. P., and Hunter, J. J. (1967) Lipids 2, 204–207. MacPhail, R. A., Strauss, H. L., Snyder, R. G., and Elliger, C. A. (1984) J. Phys. Chem. 334–341. Magonov, S. N., Yerina, N. A., Ungar, G., Reneker, D., and Ivanov, D. A. (2003) Macromolecules 36, 5637–5649. Malta, V., Gojazzi, G., Zannetti, R., and Amati, L. (1974) Gazz. Chim. Ital. 104, 921–928. Malta, V., Celotti, G., Zannetti, R., and Martelli, A. F. (1975) J. Chem. Soc. B, 548–553. Mandelkern, L., Alamo, R. G., Sokolov, E. L., Li, Y., and Chu, B. (1994) Macromolecules 27, 2324–2326. Mark, S., Blume, A., and Riederer, M. (1998) Planta 204, 44–53. Maroncelli, M., Qi, S. P., Strauss, H. L., and Snyder, R. G. (1982) J. Am. Chem. Soc. 104, 6237–6247. Maroncelli, M., Strauss, H. L., and Snyder, R. G. (1985a) J. Chem. Phys. 82, 2811–2824. Maroncelli, M., Strauss, H. L., and Snyder, R. G. (1985b) J. Phys. Chem. 89, 5260–5267. Maroncelli, M., Strauss, H. L., and Snyder, R. G. (1985c) J. Phys. Chem. 89, 4390–4395. Marosi, L. and Schlenk, W. (1973) Liebigs Ann. Chem. 584–598. Marshall, A. T., Lewis, C. T., and Parry, G. (1974) J. Ultrastruct. Res. 47, 41–60. Mathiesen, A. McL. and Welsh, H. K. (1965) Acta Cryst. 18, 953–955. Mathiesen, R. R. and Smith, P. (1985) Polymer 26, 288–292. Matsui, N. (1988) In: Crystallization and Polymorphism of Fats and Fatty Acids. N. Garti and K. Sato, eds. NY: Marcel Dekker, pp. 395–422. Mazee, W. M. (1957) Anal. Chim. Acta 17, 97–106.

216

REFERENCES

Mazee, W. M. (1958a) J. Inst. Petrol. 44, 401–405. Mazee, W. M. (1958b) Am. Chem. Soc. Div. Petrol. Chem. Preprints 3(4), 35–47. McCourt, M. P., Strong. P., Pangborn, W. A., and Dorset, D. L. (1994) J. Lipid Res. 35, 584–591. McCourt, M. P., Li, N., Pangborn, W. A., Miller, R., Weeks, C. M., and Dorset, D. L. (1996) J. Phys. Chem. 100, 9842–9847. McCourt, M. P., Ashraf, K., Miller, R., Weeks, C. M., Li, N., Pangborn, W., and Dorset, D. L. (1997) J. Lipid Res. 58, 1014–1021. McGillavry, C. H. and Wolthuis-Spuy, M. (1970) Acta Cryst. B26, 645–649. Meinwald, J., Smolanoff, J., Chibnall, A. C., and Eisner, T. (1975) J. Chem. Ecol. 1, 269–274. Merk, S., Blume, A., and Riederer, M. (1998) Planta 204, 44–53. Merz, K. (2002) Acta Cryst. E58, o450–o451. Metivaud, V., Rajabalee, F., Cuevas-Diarte, M. A., Calvet, T., Mondieig, D., and Haget, Y. (1998) An. Quim. Int. Ed. 94, 396–400. Meusel, I., Barthlott, W., Kutzke, H., and Barbier, B. (2000) Powder Diffract. 15, 123–129. Michaud, F., Ventola, L., Calvet, M. T., Cuevas-Diarte, M. A., Solanus, X., Font-Bardia, M. (2000) Acta Cryst. C56, 219–221. Mizushima, S. and Simanouti, T. (1949) J. Am. Chem. Soc. 71, 1320–1324. Mnyukh, Yu. V. (1960) Zh. Strukt. Khim. 1, 370–388. Mnyukh, Yu. V. (1963) J. Phys. Chem. Solids 24, 631–640. Mo, F. (1979) Acta Cryst. B35, 2135–2140. Moelwyn-Hughes, E. A. (1965) Physical Chemistry. 2nd rev. edn. Oxford: Pergamon, pp. 297–342. Moews, P. C. and Knox, J. R. (1976) J. Am. Chem. Soc. 98, 6628–6633. Mondieig, D., Rajabalee, F., Metivaud, V., Oonk, H. A. J., and Cuevas-Diarte, M. A. (2004) Chem. Mater. 16, 786–798. Monger-McClure, T. G., Tackett, J. E., and Merrill, L. S. (1999) SPE Prod. Fac. 14, 4–15. Moss, B. and Dorset, D. L. (1983) Acta Cryst. A39, 609–615. Moss, B., Dorset, D. L., Wittmann, J. C., and Lotz, B. (1984) J. Polym. Sci. Polym. Phys. Ed. 22, 1919–1929. Müller, A. (1927) Proc. Roy. Soc. (London) A114, 542–561. Müller, A. (1932) Proc. Roy. Soc. (London) A138, 514–530. Müller, A. (1937) Proc. Roy. Soc. (London) A158, 403–414. Müller, A. (1938) Proc. Roy. Soc. (London) A166, 316–324. Müller, A. (1940) Proc. Roy. Soc. (London) A174, 137–144. Müller, A. and Lonsdale, K. (1948) Acta Cryst. 1, 129–131. Musser, B. J. and Kilpatrick, P. K. (1998) Energy and Fuels 12, 715–725. Myasnikova, R. M. (1993) Acta Chim. Hungar. (Models in Chemistry) 130, 363–375. Nakamura, N. (1981) Mol. Cryst. Liq. Cryst. 64, 313–318. Nakamura, N. and Sato, T. (1999a) Acta Cryst. C55, 1685–1687. Nakamura, N. and Sato, T. (1999b) Acta Cryst. C55, 1687–1689.

REFERENCES

217

Nakamura, N. and Setodoi, S. (1997) Acta Cryst. C53, 1883–1885. Nakamura, N. and Shimizu, H. (2004) Acta Cryst. E60, o131–o133. Nakamura, N. and Watanabe, R. (2001) Acta Cryst. E57, o136–o138. Nakamura, N. and Yamamoto, T. (1994) Acta Cryst. C50, 946–948. Nakamura, N., Yamamoto, Y., Kobayashi, H., and Yoshimura, Y. (1993) Cryst. Res. Technol. 28, 953–957. Nakamura, N., Tanihara, Y., and Takayama, T. (1997) Acta Cryst. C53, 253–256. Nakamura, N., Setodoi, S., and Ikeya, T. (1999) Acta Cryst. C55, 789–791. Nakamura, N., Uno, K., Watanabe, K., Ikeya, T., and Ogawa, Y. (2000) Acta Cryst. C56, 903–904. Nakamura, N., Uno, K., and Ogawa, Y. (2001a) Acta Cryst. E57, o508–o510. Nakamura, N., Uno, K., and Ogawa, Y. (2001b) Acta Cryst. E57, o505–o507. Nakamura, N., Uno, K., and Ogawa, Y. (2001c) Acta Cryst. E57, o485–o487. Nakamura, N., Uno, K., and Ogawa, Y. (2001d) Acta Cryst. E57, o1091–o1093 Nakasone, K., Shirokawa, K., Urabe, Y., and Nemoto, N. (2000) J. Phys. Chem. B104, 7483–7489. Narang, R. S. and Sherwood, J. N. (1980) Mol. Cryst. Liq. Cryst. 59, 167–174. Natta, G., Baccaredda, M., and Rigamonti, R. (1935) Gazz. Chim. Ital. 65, 182–198. Natta, G., Bassi, I. W., and Fagherazzi, G. (1969) Eur. Polym. J. 5, 239–260. Nechitailo, N. A., Rozenberg, L. M., Terent’eva, E. M., and Topchiev, A. V. (1957) Dokl. Akad. Nauk SSSR 116, 613–616. Nechitailo, N. A., Topchiev, A. V., Rozenberg, L. M., and Terent’eva, E. M. (1960) Russ. J. Phys. Chem. 34, 1268–1272. Nelson, D. R. and Blomquíst, G. J. (1995) In: Waxes: Chemistry, Molecular Biology and Functions. R. J. Hamilton, ed. Dundee: Oily Press, pp. 1–90. Nelson, H. R. (1933) Phys. Rev. 44, 717–719. Niegisch, W. D. and Swan, P. R. (1960) J. Appl. Phys. 31, 1905–1910. Norman, N. and Mathiesen, H. (1961a) Acta Chem. Scand. 15, 1755–1760. Norman, N. and Mathiesen, H. (1961b) Acta Chem. Scand. 15, 1747–1754. Norman, N. and Mathiesen, H. (1964) Acta Chem. Scand. 18, 353–360. Norman, N. and Mathiesen, H. (1972) Acta Chem. Scand. 26, 3913–3916. Nouar, H., Petitjean, D., Bourdet, J. B., Bouroukba, M., and Dirand, M. (1997a) Thermochim. Acta 293, 87–92. Nouar, H., Petitjean, D., Bourdet, J. B., and Dirand, M. (1997b) J. Mol. Struct. 415, 277–284. Nouar, H., Petitjean, D., Bouroukba, M., and Dirand, M. (1998a) J. Mol. Struct. 443, 197–204. Nouar, H., Bouroukba, M., Petitjean, D., and Dirand, M. (1998b) Mol. Cryst. Liq. Cryst. 309, 273–282. Nyburg, S. C. and Gerson, A. R. (1992) Acta Cryst. B48, 103–106. Nyburg, S. C. and Lüth, H. (1972) Acta Cryst. B28, 2992–2995. Nyburg, S. C. and Potworowski, J. A. (1973) Acta Cryst. B29, 347–352. Nyburg, S. C., Pickard, F. M., and Norman, N. (1976) Acta Cryst. B32, 2289–2293.

218

REFERENCES

Ocko, B. M., Wu., X. Z., Sirota, E. B., Sinha, S. K., and Deutsch, M. (1997) Phys. Rev. E65, 3164–3182. O’Connell, A. M. (1968) Acta Cryst. B24, 1399–1405. Oldham, J. W. H. and Ubbelohde, A. R. (1940) Proc. Roy. Soc. (London) A176, 50–75. Organ, S. J. and Keller, A. (1987) J. Polym. Sci. B. Polym. Phys. 25, 2509–2430. Pangborn, W. A. (1973) Crystal and molecular structures of the anhydride of 11-bromoundecanoic acid and racemic glycerol 1,2 (di-11-bromo-undecanoate)3-(f-toluenesulfonate) Ph.D. Thesis, University of Maryland. Park, Y. J. and Craven, B. M. (1981) J. Korean Chem. Soc. 25, 131–139. Parman, V. S. and Ivanova, L. A. (1986) Khim. Tverd. Topl. 15–19. Pascher, I., Lundmark, M., Nyholm, P. G., and Sundell, S. (1992) Biochim. Biophys. Acta 1113, 339–373. Patel, S., Nelson, D. R., and Gibbs, A. G. (2001) J. Insect Sci. 1.4, 7pp (www.insectscience.org). Pattabhi, V. and Craven, B. M. (1979) J. Lipid Res. 20, 757–759. Pauling, L. (1960) The Nature of the Chemical Bond. 3rd edn. Ithaca, NY: Cornell University Press, pp. 257–264. Pedersen, K. S., Fredenslund, Aa., and Thomassen, P. (1989) Properties of Oils and Natural Gases. Houston: Gulf Publishing Company, p. 209. Pertsin, A. J. and Kitaigorodsky, A. I. (1987) The Atom–Atom Potential Method. Applications to Organic Molecular Solids. Berlin: Springer-Verlag. Petitjean, D., Pierre, M., Goghoumu, P., Bouroukba, M., and Dirand, M. (2002) Polymer 43, 345–349. Piesczek, W., Strobl, G. R., and Malzahn, K. (1974) Acta Cryst. B30, 1278–1288. Piper, S. H., Chibnall, A. C., Hopkins, S. J., Pollard, A., Smith, J. A. B., and Williams, E. F. (1931) Biochem. J. 25, 2072–2094. Piper, S. H., Chibnall, A. C., and Williams, E. F. (1934) Biochem. J. 28, 2175–2188. Pitzer, K. S. (1995) Thermodynamics, 3rd edn. NY: McGraw-Hill. Podolinskii, V. V. (1980) Dokl. Akad. Nauk SSSR 254, 1168–1172. Podolinskii, V. V., Taran, Yu. N., and Drykin, V. G. (1987) Sov. Phys. Crystallogr. 32, 588–592. Prasad, A. and Mandelkern, L. (1989) Macromolecules. 22, 914–920. Precht, D. (1974) Kiel. Milchwirtsch. Forschungsber. 26, 221–254. Precht, D. (1976a) Fette Seifen Anstrichm. 78, 189–192. Precht, D. (1976b) Fette Seifen Anstrichm. 78, 145–149. Presting, W. and Kreuter, Th. (1965) Fette Seifen Anstrichm. 67, 334–340. Price, F. P. and Wendorff, J. H. (1971) J. Phys. Chem. 75, 2839–2849. Provost, E., Chevallier, V., Bouroukba, M., Dirand, M., Ruffier-Meray, V., and Behar, E. (1998) Rev. Int. Fr. Petrol. 53, 27–33. Rabolt, J. F., Russell, T. P., and Twieg, R. J. (1984) Macromolecules 17, 2786–2794. Rademeyer, M. and Dorset, D. L. (2001) J. Phys. Chem. B105, 5139–5143. Rajabalee, F., Metivaud, V., Mondieig, D., Haget, Y., and Oonk, H. A. J. (1999a) Chem. Mater. 11, 2788–2795.

REFERENCES

219

Rajabalee, F., Metivaud, V., Mondieig, D., Haget, Y., and Cuevas-Diarte, M. A. (1999b) J. Mater. Res. 14, 2644–2654. Rajabalee, F., Negrier, P., Mondielig, D., and Cuevas-Diarte, M. A. (2002) Chem. Mater. 14, 4081–4087. Rånby, B. G., Morehead, F. F., and Walter, N. M. (1960) J. Polym. Sci. 44, 349–367. Rastogi, R. P. and Bassi, P. S. (1964) J. Phys. Chem. 68, 2398–2406. Rastogi, R. P. and Rastogi, V. K. (1969) J. Cryst. Growth 5, 345–353. Rawlings, A. V. (1995) In: Waxes: Chemistry, Molecular Biology and Functions. R. J. Hamilton, ed. Dundee: Oily Press, pp. 223–256. Refson, K. and Pawley, G. S. (1986) Acta Cryst. B42, 402–410. Reneker, D. and Geil, P. (1960) J. Appl. Phys. 31, 1916–1925. Retief, J. J. and Le Roux, J. H. (1983) S. African J. Sci. 79, 234–239. Retief, J. J., Engel, D. W., and Boonstra, E. G. (1985) J. Appl. Cryst. 18, 156–158. Revol, J. F. and Manley, R. St-John (1986) J. Mater. Sci. Lett. 5, 249–251. Reynhardt, E. C. (1986) J. Phys. D. Appl. Phys. 19, 1925–1938. Reynhardt, E. C. and Riederer, M. (1991) J. Phys. D. Appl. Phys. 24, 478–486. Reynhardt, E. C. and Riederer, M. (1994) Eur. Biophys. J. 23, 59–70. Reynhardt, E. C., Fenrych, J., and Basson, I. (1994) J. Phys. Cond. Matter. 6, 7605–7616. Rhodes, F. H., Mason, C. W., and Sutton, W. R. (1927) Ind. Eng. Chem. 19, 935–938. Riederer, M. and Schreiber, L. (1995) In: Waxes: Chemistry, Molecular Biology and Functions. R. A. Hamilton, ed. Dundee: Oily Press, pp. 131–156. Rigamonti, R. (1936) Gazz. Chim. Ital. 66, 174–182. Rosen, L. and Hybl, A. (1972) Acta Cryst. B28, 610–617. Royaud, J. A. M., Hendra, P. J., Maddams, W., Passingham, C., and Willis, N. A. (1990) J. Mol. Struct. 239, 83–102. Russell, T. P., Rabolt, J. F., Twieg, R. J., and Farmer, B. L. (1986) Macromolecules 19, 1135–1143. Ryckaert, J. P., Klein, M. L., and McDonald, I. R. (1987) Phys. Rev. Lett. 58, 698–701. Sabour, A., Bourdet, J. B., Bouroukba, M., and Dirand, M. (1995) Thermochim. Acta 249, 269–283. Sanders, J. V. and Tabor, D. (1951) Proc. Roy. Soc. (London) A204, 525–533. Sato, K. and Garti, N. (1988) Crystallization and Polymorphism of Fats and Fatty Acids. N. Garti and K. Sato, eds. NY: Marcel Dekker, pp. 3–7. Sato, K. and Okada, M. (1977a) J. Cryst. Growth 42, 259–263. Sato, K. and Okada, M. (1977b) J. Cryst. Growth 42, 264–271. Sato, K., Kobayashi, M., and Morishita, H. (1988) J. Cryst. Growth 87, 236–242. Sawzik, P. (1984) Crystal structures of cholesteryl esters Ph.D. Thesis, University of Pittsburgh. Sawzik, P. and Craven, B. M. (1979a) Acta Cryst. B35, 789–791. Sawzik, P. and Craven, B. M. (1979b) Acta Cryst. B35, 895–901. Sawzik, P. and Craven, B. M. (1980a) Proceedings of the International Conference on Liquid Crystals, Bangalore, India. S. Chandrasekhar, ed. Philadelphia: Heyden, pp. 171–178. Sawzik, P. and Craven, B. M. (1980b) Acta Cryst. B36, 215–218.

220

REFERENCES

Sawzik, P. and Craven, B. M. (1980c) Acta Cryst. B36, 3027–3033. Sawzik, P. and Craven, B. M. (1981) J. Appl. Cryst. 14, 351–352. Sawzik, P. and Craven, B. M. (1982) Acta Cryst. B38, 1777–1781. Sawzik, P. and Craven, B. M. (1983) J. Lipid Res. 24, 784–789. Sawzik, P. and Craven, B. M. (1984a) J. Lipid Res. 25, 851–856. Sawzik, P. and Craven, B. M. (1984b) J. Lipid Res. 25, 857–864. Schaerer, A. A., Bayle, G. G., and Mazee, W. M. (1956) Rec. Trav. Chim. 75, 513–528. Scaringe, R. (1991) In: Electron Crystallography of Organic Molecules. J. R. Fryer and D. L. Dorset, eds. Dordrecht: Kluwer, pp. 85–113. Scaringe, R. (1992) Trans. Am. Cryst. Assoc. 28, 11–23. Schachtschneider, J. H. and Snyder, R. G. (1963) Spectrochim. Acta 19, 117–168. Scheuerman, R. F. and Sass, R. L. (1962) Acta Cryst. 15, 1244–1247. Schoon, T. (1938) Z. Phys. Chem. B39, 385–410. Schoon, T. (1939) Chem. Ber. 72B, 1821–1827. Schriver, G. W., Lewtas, K., and Martella, D. J. (1996) In: Crystal Growth of Organic Materials. A. S. Myerson, D. A. Green, and P. Meenan, eds. DC: ACS, Washington, pp. 151–156. Schulz, H. (1999) Appl Catal. A186, 3–12. Schwickert, H., Strobl, G., and Kimmig, M. (1991) J. Chem. Phys. 95, 2800–2806. Segermann, E. (1965) Acta Cryst. 19, 789–796. Seto, T. (1962) Mem. Coll. Sci. Univ. Kyoto A30, 89–107. Severin, D. and Gupta, A. K. (1999) Petrol. Sci. Technol. 17, 967–980. Shearer, H. M. M. and Vand, V. (1956) Acta Cryst. 9, 379–384. Shieh, H. S., Hoard, L. G., and Nordman, C. E. (1977) Nature 267, 287–289. Shieh, H. S., Hoard, L. G., and Nordman, C. E. (1981) Acta Cryst. B37, 1538–1543. Simpson, T. D. and Miwa, T. K. (1977) J. Am. Oil Chem. Soc. 54, 54–88. Sirota, E. B. (1998) Langmuir 14, 3133–3136. Sirota, E. B. (2000) J. Chem. Phys. 112, 492–500. Sirota, E. B. (2001) Phys. Rev. E. 64, 050701: 1–4 Sirota, E. B. and Herhold, A. B. (1999) Science 283, 529–532. Sirota, E. B. and Herhold, A. B. (2001) Polymer 41, 8781–8789. Sirota, E. B. and Singer, D. M. (1994) J. Chem. Phys. 101, 10873–10882. Sirota, E. B. and Wu, X. Z. (1996) J. Chem. Phys. 105, 7763–7772. Sirota, E. B., King, H. E., Hughes, G. J., and Wan, W. K. (1992) Phys. Rev. Lett. 68, 492–495. Sirota, E. B., King, H. E., Singer, D. M., and Shao, H. H. (1993) J. Chem. Phys. 98, 5809–5824. Sirota, E. B., King, H. E., Shao, H. H., and Singer, D. M. (1995) J. Phys. Chem. 99, 798–804. Sirota, E. B., Herhold, A. B., and Varma-Nair, M. (2000) J. Chem. Phys. 113, 8225–8236. Slagle, F. B. and Ott, E. (1933) J. Am. Chem. Soc. 55, 4404–4415. Small, D. M. (1970) Adv. Exptl. Med. Biol. 7, 55–83.

REFERENCES

221

Small, D. M. (1986) The Physical Chemistry of Lipids. From Alkanes to Phospholipids. NY: Plenum. Smith, A. E. (1953) J. Chem. Phys. 21, 2229–2231. Smith, G. D. and Boyd, R. H. (1990) Macromolecules 23, 1527–1530. Smith, J. C. (1932) J. Chem. Soc. 737–741. Smith, P. and St. John Manley, R. (1979) Macromolecules 12, 483–491. Smith, P. and Pennings, A. J. (1974) Polymer 15, 413–419. Smolenskii, E. A., Ryzhov, A. N., Lapidev, A. L., and Zefirov, N. S. (2002) Dokl. Chem. 387, 297–301. Snow, J. and Phillips, M. C. (1990) Biochemistry 29, 2464–2471. Snow, J. W., McCloskey, H. H., Glick, J. M., Rothblatt, H., and Phillips, M. C. (1988) Biochemistry 27, 3640–3646. Snyder, R. G. (1960) J. Mol. Spectrosc. 4, 411–434. Snyder, R. G. (1961) J. Mol. Spectrosc. 7, 116–144. Snyder, R. G. (1967) J. Chem. Phys. 47, 1316–1360. Snyder, R. G. (1979) J. Chem. Phys. 71, 3229–3335. Snyder, R. G. (1980) In: Methods of Experimental Physics. Volume 16A (Polymers). R. A. Fava, ed. NY: Academic Press, Chapter 3. Snyder, R. G. (1992) J. Chem. Soc. Faraday Trans. 88, 1823–1833. Snyder, R. G. and Poore, M. W. (1973) Macromolecules 6, 708–715. Snyder, R. G. and Schachtschneider, J. H. (1963) Spectrochim. Acta 19, 85–116. Snyder, R. G., Maroncelli, M., Qi, S. P., and Strauss, H. L. (1981) Science 214, 188–190. Snyder, R. G., Strauss, H. L., and Elliger, C. A. (1982) J. Phys. Chem. 86, 5145–5150. Snyder, R. G., Maroncelli, M., Strauss, H. L., Elliger, C. A., Cameron, D. G., Casal, H. G., and Mantsch, H. H. (1983) J. Am. Chem. Soc. 105, 133–134. Snyder, R. G., Goh, M. C., Srivatsavoy, V. J. P., Strauss, H. L., and Dorset, D. L. (1992) J. Phys. Chem. 96, 10008–10019. Snyder, R. G., Conti, G., Strauss, H. L., and Dorset, D. L. (1993) J. Phys. Chem. 97, 7342–7350. Snyder, R. G., Srivatsavoy, V. J. P., Cates, D. A., Strauss, H. L., White, J. W., and Dorset, D. L. (1994) J. Phys. Chem. 98, 674–684. Snyder, R. G., Strauss, H. L., and Cates, D. A. (1995) J. Phys. Chem. 99, 8432–8439. Snyder, R. G., Liang, G. L., Strauss, H. L., and Mendelsohn, R. (1996) Biophys. J. 71, 3186–3198. Srivastava, R. C. and Craven, B. M. (1989) J. Lipid Res. 30, 893–898. Srivastava, S. P., Tandon, R. S., Verma, P. S., Saxema, A. K., Joshi, G. C., and Phatak, S. D. (1992) Fuel 71, 533–537. Srivastava, S. P., Verma, P. S., Tandon, R. S., Kumar, P., Chandola, H. C., and Joshi, G. C. (1992) Erdöl u. Kohle 45, 173–176. Ställberg, G., Ställberg-Stenhagen, S., and Stenhagen, E. (1952) Acta Chem. Scand. 6, 313–326. Starkweather, H. W. (1986) Macromolecules 19, 1131–1134.

222

REFERENCES

Stehling, F. C., Ergos, F., and Mandelkern, L. (1971) Macromolecules 4, 672–627. Stenger, H. G., Johnson, H. E., and Satterfield, C. N. (1984) J. Catal. 86, 427–480. Stenhagen, E. and von Sydow, E. (1953) Ark. Kemi 6, 309–316. Stokhuyzen, R. and Pistorius, C. W. F. T. (1970) J. Appl. Chem. 20, 1–6. Storks, K. A. and Germer, L. H. (1937) J. Chem. Phys. 5, 131–134. Stransky, K. and Streibl, M. (1971) Coll. Czech. Chem. Commun. 36, 2267–2280. Stransky, K., Streibl, M., and Kubelka, V. (1971) Coll. Czech. Chem. Commun. 36, 2281–2297. Stransky, K., Streibl, M., and Ubik, K. (1991) Coll. Czech. Chem. Commun. 56, 1123–1129. Strieter, F. J. and Templeton, D. H. (1962) Acta Cryst. 15, 1240–1244. Strieter, F. J., Templeton, D. H., Scheuerman, R. F., and Sass, R. L. (1962) Acta Cryst. 15, 1233–1239. Strobl, G. (1972) Koll. Z. Z. Polym. 250, 1039–1045. Strobl, G., Ewen, B., Fischer, E. W., and Piesczek, W. (1974) J. Chem. Phys. 61, 5257–5264. Strobl, G. R., Trzebiatowski, T., and Ewen, B. (1978) Progr. Coll. Polym. Sci. 64, 219–225. Sullivan, P. K. (1974) J. Res. Natl. Bur. Stand. 78A, 129–141. Sullivan, P. K. and Weeks, J. J. (1970) J. Res. Natl. Bur. Stand. 74A, 203–214. Sutula, C. L. and Bartell, L. S. (1962) J. Phys. Chem. 66, 1010–1014. Sydow, E. Von (1954a) Acta Cryst. 7, 529–532. Sydow, E. Von (1954b) Acta Cryst. 7, 823–825. Sydow, E. Von (1955a) Acta Cryst. 8, 557–560. Sydow, E. Von (1955b) Acta Cryst. 7, 810–812. Sydow, E. Von (1955c) Acta Chem. Scand. 9, 1119–1126. Sydow, E. Von (1956a) Acta Chem. Scand. 9, 1685–1688. Sydow, E. Von (1956b) Ark. Kemi 9, 231–253. Sydow, E. Von (1956c) Acta Chem. Scand. 10, 1–8. Sydow, E. Von (1958) Acta Chem. Scand. 12, 777–779. Tadokoro, H. (1979) Structure of Crystalline Polymers. NY: Wiley. Takamizawa, K., Ogawa, Y., and Ogama, T. (1982) Polym. J. 14, 441–456. Tammann, G. (1925) A Textbook of Metallography. NY: Chemical Catalog Co. Tamura, H., Sato, T., Ogawa, K., Yano, S., Sagaguchi, K., and Matsuura, Y. (1987) Chem. Lett., 503–506. Tanaka, K. (1938) Mem. Kyoto Univ. Ser. A. 21, 85–88. Tanaka, K. (1940) Mem. Kyoto Univ. Ser. A. 23, 195–205. Teare, P. W. (1959) Acta Cryst. 12, 294–300. Tegelaar, E. W., Matthezing, R. M., Jansen, J. B. H., Horsfield, B., and de Leeuw, J. W. (1989) Nature 342, 529–531. Tenchov, B. G. (1985) Progr. Surf. Sci. 20, 273–340. Thalladi, V. and Boese, R. (2000) New J. Chem. 24, 579–581. Thalladi, V. R., Boese, R., and Weiss, H.-C. (2000a) Angew. Chem. Int. Ed. 39, 918–922.

REFERENCES

223

Thalladi, V. R., Boese, R. and Weiss, H.-C. (2000b) J. Am. Chem. Soc. 122, 1186–1190. Thiessen, P. A. and Schoon, Th. (1937) Z. Phys. Chem. B36, 216–231. Toda, A., Miyaji, H., Ogawa, Y., and Takimaizawa, K. (1991) J. Mater. Sci. 26, 2793–2796. Topchiev, A. V., Nechitailo, N. A., Rozenberg, L. M., and Terent’eva, E. M. (1957) Dokl. Akad. Nauk SSSR 117, 1053–1055. Trillat, J. J. and von Hirsch, Th. (1933) J. Phys. (Paris) 7, 38–43. Trzbiatowski, T., Dräger, M., and Strobl, G. R. (1982) Makromol. Chem. 183, 731–744. Tsuji, M. (1989) Comprehensive Polymer Science. Volume 1. C. Booth and C. Price, eds. Oxford: Pergamon, pp. 785–840. Tsuji, M. and Ihn, K. J. (1995) Bull. Inst. Chem. Res. Kyoto Univ. 72, 429–442. Tulloch, A. P. (1969) Lipids 5, 247–258. Tulloch, A. P. (1972) J. Am. Oil Chem. Soc. 49, 609–610. Tulloch, A. P. and Hoffman, L. L. (1972) J. Am. Oil Chem. Soc. 49, 696–699. Turner, J. D. and Lingafelter, E. C. (1955) Acta Cryst. 8, 551–557. Turner, W. R. (1971) Ind. Eng. Chem. Prod. Res. Develop. 10, 238–260. Tuttle, J. B. (1960) Petroleum Products Handbook. V. B. Guthrie, ed. NY: McGrawHill, Chapter 10, pp. 1–17. Ubbelohde, A. R. (1978) The Molten State of Matter. Chichester: Wiley, pp. 154–160. Ueda, Y. (1986) Bull. Chem. Soc. Japan 59, 3771–3779. Ueda, Y. (1987) Bull. Chem. Soc. Japan 60, 2011–2017. Ungar, G. (1983) J. Phys. Chem. 87, 689–695. Ungar, G. and Keller, A. (1979) Coll. Polym. Sci. 257, 90–94. Ungar, G. and Keller, A. (1986) Polymer 27, 1835–1844. Ungar, G. and Masic, N. (1985) J. Phys. Chem. 89, 1036–1042. Ungar, G. and Organ, S. J. (1990) J. Polym. Sci. B. Polym. Phys. 28, 2353–2363. Ungar, G. and Zeng, X. B. (2001) Chem. Rev. 101, 4157–4188. Ungar, G., Organ. S. J., and Keller, A. (1988) J. Polym. Sci. C. Polym. Lett. 26, 259–262. Ungar, G., Stejny, J., Keller, A., Bidd, F., and Whiting, M. C. (1985) Science 229, 386–389. Uno, K. and Nakamura, N. (2003) Acta Cryst. E59, O708–O710. Uyeda, N., Kobayashi, T., Ishizuka, K., and Fujiyoshi, Y. (1978–1979) Chem. Scripta 14, 47–61. Vainshtein, B. K. and Pinsker, Z. G. (1950) Dokl. Akad. Nauk SSSR 72, 53–56. Vainshtein, B. K., Lobachev, A. N., and Stasova, M. M. (1958) Sov. Phys. Crystallogr. 3, 452–459. Vand, V. (1953) Acta Cryst. 6, 797–798. Vand, V. and Bell, I. P. (1951) Acta Cryst. 4, 465–470. Vand, V., Lomer, T. R., and Lang, A. (1949) Acta Cryst. 2, 214–220. Vand, V., Morley, W. M., and Lomer, T. R. (1951) Acta Cryst. 4, 324–327.

224

REFERENCES

Vandenburg, L. E. and Wilder, E. A. (1970) J. Amer. Oil Chem. Soc. 47, 514–518. Van de Streek, J., Verwer, P., Bennema, P., and Vlieg, E. (2002) Acta Cryst. B58, 677–683. Vegard, L. and Dale, H. (1926) Z. Krist. 67, 104–105. Verma, A. R. (1955) Proc. Roy. Soc. (London) A228, 34–49. Verma, A. R. and Reynolds, P. M. (1953) Proc. Phys. Soc. (London) 66b, 414–420. Viney, C., Russell, T. P., Dejero, L. E., and Twieg, R. J. (1989a) Mol. Cryst. Liq. Cryst. 168, 63–82. Viney, C., Twieg, R. J., Russell, T. P., and Dejero, L. E. (1989b) Liq. Cryst. 5, 1783–1788. Viney, C., Twieg, R. J., and Russell, T. P. (1990) Mol. Cryst. Liq. Cryst. 182B, 291–297. Warth, A. H. (1947) The Chemistry and Technology of Waxes. NY: Reinhold. Watanabe, A. (1961) Bull. Chem. Soc. Japan 34, 1728–1734. Watanabe, A. (1963) Bull. Chem. Soc. Japan 36, 336–340. Weidinger, I. M., Klein, J., Stöckel, P., Biller, E., Baumgärtel, H., and Leisner, T. (2003) Z. Phys. Chem. 217, 1597–1611. Welsh, H. K. (1956) Acta Cryst. 9, 89–90. Welsh, H. K. (1976) Mol. Cryst. Liq. Cryst. 33, 1–3. Wendorff, J. H. and Price, F. S. (1973) Mol. Cryst. Liq. Cryst. 24, 129–144. Westrum, E. F. and McCullough, J. P. (1963) Physics and Chemistry of the Organic Solid State. Volume 1. D. Fox, M. M. Labes, and A. Weissburger, eds. NY: Wiley, pp. 1–178. Williams, D. E. (1969) Acta Cryst. A25, 464–470. Witnauer, L. P., Lutz, D. A., Sasin, G. S., and Sasin, R. (1957) J. Am. Oil Chem. Soc. 34, 71–72. Wittmann, J. C. and Lotz, B. (1985) J. Polym. Sci. Polym. Phys. Ed. 23, 205–226. Wittmann, J. C. and Lotz, B. (1990) Progr. Polym. Sci. 909–948. Won, K. W. (1986) Fluid Phase Equil. 30, 265–279. Wu, X. Z., Sirota, E. B., Sinha, S. K., Ocko, B. M., and Deutsch, M. (1993a) Phys. Rev. Lett. 70, 958–961. Wu, X. Z., Ocko, B. M., Sirota, E. B., Sinha, S. K., Deutsch, M., Cao, B. H., and Kim, M. W. (1993b) Science 261, 1018–1021. Würflinger, A. and Schneider, G. M. (1973) Ber. Bunsenges. Phys. Chem. 77, 121–128. Yamamoto, T. and Nozaki, K. (1995) Polymer 36, 2505–2510. Yamamoto, T., Nozaki, K., and Hara, T. (1990) J. Chem. Phys. 92, 631–641. Yamamoto, T., Hikosaka, M., and Takahashi, N. (1994) Macromolecules 27, 1466–1472. Yamamoto, T., Aoki, H., Miyaji, S., and Nozaki, K. (1997) Polymer 38, 2645–2647. Yoshida, S. (1942) Proc. Imper. Acad. (Japan) 18, 377–381. Zefirov, Yu. V. (1994) Crystallogr. Rep. 39, 939–945. Zefirov, Yu. V. (1997) Crystallogr. Rep. 42, 111–116. Zemlin, F., Reuber, E., Beckmann, E., Zeitler, E., and Dorset, D. L. (1985) Science 229, 461–462. Zeng, X. B. and Ungar, G. (2002) Polymer 43, 1657–1666.

REFERENCES

225

Zerbi, G., Magni, R., Gussoni, M., Moritz, K. H., Bigotto, A., and Dirlikov, S. (1981) J. Chem. Phys. 75, 3175–3194. Zhang, W. P. and Dorset, D. L. (1989a) J. Polym. Sci. B. Polym. Phys. 27, 1433–1447. Zhang, W. P. and Dorset, D. L. (1989b) Proceedings of the Electron Microscopy Society of America at the 47th Annual Meeting, San Francisco, San Francisco Press, pp. 702–703. Zhang, W. P. and Dorset, D. L. (1990a) J. Polym. Sci. B. Polym. Phys. 28, 1223–1232. Zhang, W. P. and Dorset, D. L. (1990b) Macromolecules 23, 4322–4326. Zhang, W. P, Dorset, D. L., and Hanlon, J. (1989) Proceedings of the Electron Microscopy Society of America at the 47th Annual Meeting, San Francisco, San Francisco Press, pp. 662–663. Zocher, H. and Machado, R. D. (1959) Acta Cryst. 12, 122–125.

This page intentionally left blank

Subject index

activity coefficients 11 alcohol crystal structures diols and dithiols 127 halogenated 126 primary oblique 124 rectangular 125 secondary 129 trans-alkene crystal structure 121 binary phase diagrams 8 construction 9 Bragg–Williams equation 11 candle wax crystal structure 87 chain branching bromo 152 hydroxyl 129, 150 ketone 49, 151, 152 methyl 49, 150 chain decoration 45 chain disorder conformation 68 diffuse scattering 66 kink structure 71 retraction due to 83 chain folding 52 chain setting angle 53 chain tilt measurement from powder diffraction data 28 RHEED measurement 29 chain unsaturation fatty acid 144 paraffin 121 cholesterol binary phase diagrams with oxidized derivatives 132 crystal structure 130 phase transitions 131 cholesteryl esters binary phases eutectics 180 peritectic 180 solid solutions 78 crystal structures 171 bilayer 172

monolayer I 173 monolayer II 174 other crystal forms 175 solid solutions 181 crystallization 171 phase transitions 175 smectic structures 176 thermotropic behavior 175 coring 82, 186 crossed-chain packing 27 cross-sectional area balance of functional group with chain packing 32 crystal decoration 45 prediction 45 cycloalkane crystal structure 54 N,N-dialkyl amine crystal structure 120 phase diagram with n-alkane 119 dialkyl ether crystal structure 118 phase diagrams with n-alkanes 119 with dialkyl sulfides 121 dielectric relaxation description of chain flexibility 68 diesel wax 86 sectorization 86 differential scanning calorimetry construction of phase diagrams 8 polymorphic transitions 58 “shape factors” 9 diffusion between lamellae 99 1,3-diglycerides 144 electron diffraction 13 advantages 14 index rule for orthorhombic layers 43, 79 probe of local structure 82 enantiotropic phase transition 7 epitaxial orientation 42 eutectics 14 arrest period (Tammann) 11, 14, 180 cholesteryl esters 180 crystal structure 105

228 eutectics (Cont.) halogenated paraffins/paraffins 115 mechanical mixtures 15 ordered structures 15 paraffins/fatty esters 163 even–odd effect alcohols 124 fatty acids 142 paraffins 57 fatty acids anhydride 157 binary phase diagrams 153 melting point alternation 141 methyl branched ␶-form crystal structure 150 ␯-form crystal structure 151 normal chain 135 even-chain polymorphs, crystal structures 136 halogenated analogs 142 odd-chain polymorphs, crystal structures 139 short chains 142 thia-acid 143 phase transitions 153 polymorphs 136, 139, 142, 144, 149 polytypes 140 thermotropic phase behavior 153 unsaturated chain cis crystal structures 144 trans crystal structures 147 fatty esters asymmetric 158 binary phase diagrams 163 eutectic with paraffin 165 phase transitions 163 polymorphs 158 polytype 161 thermotropic transitions 163 thioester 159 symmetric 158 Fischer–Tropsch wax crystal structures 86, 191, 192, 196 narrow cut 86, 191 “flat” wax crystal structure 87 functional group accommodation by polymethylene chain packing 32 halogen substitution effect on chain packing fatty acids 82 paraffins 120 heteroatom substitution alcohols 125 fatty acids 142

SUBJECT INDEX paraffins 109 hydrogen bonding alcohols 125, 126 fatty acids 136, 139 index rule (electron diffraction) paraffin lamellae 43, 45 paraffin solid solutions 76 infrared spectroscopy identification of layer packing 70 methylene subcell 70 nonplanar conformations 70 lamellae growth from nematocrystalline packing 45 lamellar spacings alcohols 126 chain substitution sites 28 chain tilt identification 28 fatty esters 158 lower resolution due to chain disorder 63 due to mixed-chain lamellae 76 paraffins 38, 39, 41, 47 predictions 31 layer stacking, theoretical prediction 30 oblique 20 rectangular 20 Lennard–Jones potential 19 lipid alcohol binary phase behavior 129 crystal structure (primary alcohols) monoclinic 124 orthorhombic 125 diols 127 polymorphism 124 rotator phases 126 lamellar spacing 127 secondary alcohol 129 lipid thiols dithiols 128 longitudinal chain disorder 67 melting behavior 9 methyl branches fatty acids 150 paraffins 49 methylene-bridged chains 148 methylene subcell identification electron diffraction 29 infrared spectroscopy 70 powder X-ray lines 28 observed subcells hexagonal 26, 59 hybrid cells 27 monoclinic parallel 25

SUBJECT INDEX orthorhombic parallel 25, 26 orthorhombic perpendicular 23, 24 triclinic parallel 25 theoretical prediction monoclinic 23 orthorhombic 23 triclinic 22 miscibility gap 14 crystal structure 98, 102 detection by vibrational spectroscopy 96 effect of chain folding 98 isotope effect 94 mixing endotherm 95 multicomponent 102 observations in binary solids 17, 91 monodispersity 2 monotropic transition 8 naphthenes 51, 86 natural waxes 3 examples beeswax 167 carnauba 168 montan 167 spermaceti 167 wooly alder aphid 170 models 166 “nematocrystalline” packing 45, 197 oil, definition 4 packing energy 33, 44 n-paraffins chain diffusion 99 chain folding 54 crystal habit 38, 39, 40 crystal structures chain length dependence 33 long even-chain monoclinic structures 39 lamellar spacing 39 orthorhombic structures 40 crystal habit 40 lamellar spacing 41 lattice image 41 sectorization 44 triclinic structure 37 lamellar spacing 38 unit cell constants long odd-chain low-energy A-form 47 lamellar spacing 47 high-energy B-form 47 lamellar spacing 48 short even-chain 34, 35 short odd-chain 36 eutectics 101, 189

229

crystal structure 105 lattice image 105 paraffins 101 perfluoroalkanes 113 melting points, prediction 57 miscibility gap crystal structure 5, 98, 188 fractionation process, model 100 multicomponent assembly 101 origin 14 nucleation of crystals 58 perdeuterated melting 59 stability of binary phases with paraffins 85, 91 peritectics 14 phase transitions studied by diffraction and microscopy 59 studied by solid-state NMR 72 studied by vibrational spectroscopy 68 polymorphism 33 pre-melting when rotator phase disallowed 65 rotator phase 59 chain length limit 61 effect of perdeuteration 61 solid solution structure 79 crystal structures 79 effect of chain folding 106 effect of perdeuteration 85 ideality 84 incorporation of conformational defects 83 lamellar interface 82, 190 multicomponent 85 favored structures 85 sequential crystallization, favored structures 86 stability boundary 84 volumetric rule 84 perfluoroalkanes diblock with paraffin segment 112 binary phase diagrams 113 polymorphism 111 solid solutions 114 subambient phase transition 111 unit cell constants 110 petroleum waxes 4, 87 chain length distribution and structure 5, 88 conformational disorder 89 crystal forms 5 crystal structure 87, 189 lamellar surface 89 plasticity model for wax 6 polydispersity 2, 85 effect on wax structure 195 fatty esters 166

230 polyester crystal structure 155 polyethylene chain folding 53, 201 comparison to wax 200 crystal structure 52 low molecular weight linear 194 polymorphism 7, 31, 33 energetics 33 favored occurrence for paraffin chain lengths 33 paraffins 31, 33 solid solutions, concentration dependence 77 polytypism 31 potential function 19 powder X-ray diffraction 13 bulk measurement 17 deficiencies 17 identification of methylene subcells 27 lamellar spacings 12, 13, 28 pseudo-components 18 Raman spectroscopy detection of phase transitions LAM-3 band 70 Raoult’s law 9 rotator phase 59 alcohols 126 chain defects 63 effect of chain length 60 effect of perdeuteration 61 effect of pressure 59 fatty esters 163 forms 61 layer packing 61 packing forms 61 unit cell density 60 vibrational spectroscopy 69 Schroeder–Van Laar equation 10 paraffin eutectics 103 perfluoroalkane eutectics 115 sectorization paraffin crystals 44, 54 electron micrographs 44 polyethylene 3, 53 electron micrographs 53 solid solution 11 alcohols 129 chains containing heteroatoms 119

SUBJECT INDEX chain length difference for comiscibility of paraffins 15 cholesteryl esters 178 continuity 74, 80, 186 effect of chain substitution 187 fatty acids 153 fatty esters 163 Kitaigorodskii rules for stability 15 lamellar flatness 187 paraffin crystal structure 74 even–even 75, 80 even–odd 80 odd–even 75, 80 perfluoroalkanes 114 symmetry rules for co-solubility 15, 186 violation 16, 75 van der Waals radii, effect on chain packing carbon 19 halogen versus methyl 49, 120 hydrogen 19, 31 fluorine 109 methylene 118 oxygen 118 sulfur 118 Vegard’s law 12, 91 vibrational spectroscopy description of thermotropic disorder 68 volumetric boundary for co-solubility 15 wax beeswax 167 carnauba wax 168 definition 3 industrial problems 4 microcrystalline wax 192, 197 montan wax 167 peat wax 167 plasticity 4 spermaceti 167, 192 artificial 166 structural model (Le Roux) 5 critique 202 structures chain length distribution 4, 196 fractional occupancy model 192 lamellar 92 nematocrystalline 194 wooly alder aphid wax 170

Compound index

1-bromooctadecane 120 2-DL-bromooctadecanoic acid 153 3-DL-bromooctadecanoic acid 152 11-bromoundecanoic acid B-form 143 C-form 143 D-form 143 E-form 143 11-bromoundecanoic acid anhydride 157 11-bromoundecanol 126 n-butane 35 n-butanoic acid (butyric acid) 142 cholesterol anhydrous 131 hydrated 130 cholesteryl 17-bromoheptadecanoate 172 cholesteryl laurate 173 cholesteryl myristate 172 cholesteryl octanoate 174 cyclodoheptacontane 55 cyclohexatriacontane 55 cyclooctatetracontane 55 cyclotetratriacontane 55 n-decane 35 1,10-decane diol 128 1-decyl-␣-D-glucoside 151 1,10-dibromodecane 120 1,12-dibromododecane 120 1,14-dibromotetradecane 120 1,16-dichlorohexadecane 120 dihexadecyl ether (dicetyl ether) 118 dihexadecyl sulfide 121 1,10-diiododecane 120 N,N-dioctadecyl amine 120 13-cis-docosenoic acid (erucic acid) 146 1,12-dodecane diol 128 1,12-dodecane dithiol 128 dodecanoic acid (lauric acid) 136 n-dooctacontane 44 n-eicosane 37 1,20-eicosane dithiol 128 ethyl behenate 160 ethyl stearate 160 ethylene di-(11-bromoundecanoate) 157 n-hectane 53 hendecanoic acid, C
-form 140

n-hentriacontanone (palmitone) 49 n-heptacosane, B-form 48 14-heptacosanol 129 n-heptadecanol 127 n-heptadecanoic acid 141 n-heptane 37 n-hexacontane 65 n-hexane 35 1,16-hexadecane diol 128 n-hexadecanol 124 hexadecyl hexadecanoate (cetyl palmitate) 157 n-hexatriacontane monoclinic 39 orthorhombic 40 polytype 39 25-hydroxycholesterol 134 12-DL-hydroxyoctadecanoic acid 149 2-DL-hydroxytetradecanoic acid 150 1-iodo-3-methyltricosane 50 1-iodooctadecane 120 isostearic acid 151 7-ketocholesterol 133 9-keto-trans-2-decenoic acid 148 13-keto-isostearic acid 151 7-keto-2-methyl-dodecanoic acid 152 2-methyl-2-ethyl eicosanoic acid 151 methyl 12-D-hydroxyoctadecanoate 159 2-D(L)-methyl octadecanoic acid 151 2-DL-methyl octadecanoic acid 151 9-DL-methyl octadecanoic acid 150 14-DL-methyl octadecanoic acid 150 16-DL-methyl octadecanoic acid 150 17-DL-methyl octadecanoic acid 150 1-methyl pentacosane 50 methyl stearate 159 3-methyl tetratriacontane 50 4-methyl tetratriacontane 50 5-methyl tetratriacontane 50 3-methyl tritriacontane 50 cis-D(L)-11,12-methylene octadecanoic acid 149 trans-DL-9,10-methylene octadecanoic acid 148 1,19-nonadecane diol 128 1-nonadecyl cyclohexane 51

232

COMPOUND INDEX

n-nonane 37 9,12-cis-octadecadienoic acid (linoleic acid) 147 n-octadecane 38 1,18-octadecane diol 128 octadecanoic acid (stearic acid) B-form 138 B1-form 139 C-form 141 polytypes 140 6-cis-octadeceonic acid (petroselenic acid) 146, 147 13-cis-octadecenoic acid (oleic acid) 146 octadecyl tetradecanoate (stearyl myristate) 161 4-octadecynoic acid 142 n-octane 35 n-pentacontane 61 n-pentacosane 65 1,15-pentadecane diol 128 pentadecanoic acid A
-form 139 B
-form 140 n-pentane 36 n-pentanoic acid (valeric acid) 142 perfluoroeicosane 110 perfluorohexadecane 110

perfluorotetracosane 110 1-phenyl decane 51 poly (-caprolactone) 156 polyethylene 52 poly (ethylene sulfide) 118 polytetrafluoroethylene 109 propane 36 n-propanoic acid (proprionic acid) 142 n-propyl stearate 162 11-cis-retinal 51 squalene 51 n-tetracosane 37 1,14-tetradecane diol 128 tetradecyl octadecanoate (myristyl stearate) 164 3-thiadodecanoic acid 144 15-trans-triacontene 121 n-tricosane 47 1,23-tricosane diol 128 12-tricosanone 49 tridecafluoroheptadecan-1-ol 112 1,13-tridecane diol 128 n-tritriacontane A-form 48 B-form 48 1,11-undecane diol 128