摘要:

DISCUSSIONS OF THE FARADAY SOCIETY No. 25, 1958 CONFIGURATIONS AND INTERACTIONS OF MACROMOLECULES AND LIQUID CRYSTALS THE FARADAY SOCIETY Agents f o r the Society’s Publications : The Aberdeen University Press Ltd. 6 Upper Kirkgate AberdeenThe Faraday Society reserves the copyright of all Communications published in the " Discussions" PUBLISHED . . . 1958 PRINTED IN GREAT BRITAIN AT THE UNIVERSITY PRESS ABERDEENA GENERAL DISCUSSION ON CONFIGURATIONS AND INTERACTIONS OF MACROMOLECULES AND LIQUID CRYSTALS A GENERAL DISCUSSION on Configurations and Interactions of Macromolecules and Liquid Crystals was held in the Department of Chemistry, University of Leeds (by kind permission of the Vice-Chancellor) on the 15th, 16th and 17th April, 1958. The President, Sir Harry Melville, K.C.B., F.R.S., was in the Chair and over 260 members and visitors were present.Among the distinguished overseas members and guests welcomed by the President were the following: Dr. Acloque (France), Dr. K. Altenburg (Germany), Dr. H. Benninga (Netherlands), Prof. Dr. S. E. Bresler (Leningrad, U.S.S.R.), iMr. J. Bussink (Netherlands), Prof. D. G. Dervichian (France), Dr. E. W. Fischer (Germany), Mr. M. G. Gotz (Germany), Mr. Y. M. de Haan (Netherlands), Dr. F. Halverson (Stamford, U.S. A.), Dr. B. Hargitay (Belgium), Dr. K. Heckmann (Gottingen), Dr. J. Hijmans (Netherlands), Dr. M. Joly (France), Mr. R. Koningsveid (Netherlands), Kr. V. A. Kropatshev (Leningrad, U.S.S.R.), Dr. M. Kryszewski (Poland), Dr. H. Lippmann (Germany), Prof. V. Luzzati (France), Prof.Dr. W. Maier (Germany), Dr. M. B. Matthews (Chicago, U.S.A.), Dr. H. Morawetz (New York, U.S.A.), Mr. H. Mustacchi (France), Dr. F. Patat (Germany), Prof. S. A. ]Rice (Chicago, U.S.A.) Mr. C. Ruscher (Germany), Dr. H. Schuller (Germany), Mr. A. Skoulios (France), Dr.H. Tompa (Belgium), Dr. J. Trommel (Netherlands), Mr. G. A. Voetelink (Oklahoma, U.S.A.), Dr. de Vries (France), Mr. R. A. Vroom (Netherlands), Prof. D. F. Waugh (Cambridge, U.S.A.), Dr. Karl-Heinz Weber (Germany), Dr. K. Westrik (Netherlands), Dr. J. Willems (Germany), Dr. Wippler (France).A GENERAL DISCUSSION ON CONFIGURATIONS AND INTERACTIONS OF MACROMOLECULES AND LIQUID CRYSTALS A GENERAL DISCUSSION on Configurations and Interactions of Macromolecules and Liquid Crystals was held in the Department of Chemistry, University of Leeds (by kind permission of the Vice-Chancellor) on the 15th, 16th and 17th April, 1958.The President, Sir Harry Melville, K.C.B., F.R.S., was in the Chair and over 260 members and visitors were present. Among the distinguished overseas members and guests welcomed by the President were the following: Dr. Acloque (France), Dr. K. Altenburg (Germany), Dr. H. Benninga (Netherlands), Prof. Dr. S. E. Bresler (Leningrad, U.S.S.R.), iMr. J. Bussink (Netherlands), Prof. D. G. Dervichian (France), Dr. E. W. Fischer (Germany), Mr. M. G. Gotz (Germany), Mr. Y. M. de Haan (Netherlands), Dr. F. Halverson (Stamford, U.S. A.), Dr. B. Hargitay (Belgium), Dr. K. Heckmann (Gottingen), Dr. J. Hijmans (Netherlands), Dr. M. Joly (France), Mr.R. Koningsveid (Netherlands), Kr. V. A. Kropatshev (Leningrad, U.S.S.R.), Dr. M. Kryszewski (Poland), Dr. H. Lippmann (Germany), Prof. V. Luzzati (France), Prof. Dr. W. Maier (Germany), Dr. M. B. Matthews (Chicago, U.S.A.), Dr. H. Morawetz (New York, U.S.A.), Mr. H. Mustacchi (France), Dr. F. Patat (Germany), Prof. S. A. ]Rice (Chicago, U.S.A.) Mr. C. Ruscher (Germany), Dr. H. Schuller (Germany), Mr. A. Skoulios (France), Dr.H. Tompa (Belgium), Dr. J. Trommel (Netherlands), Mr. G. A. Voetelink (Oklahoma, U.S.A.), Dr. de Vries (France), Mr. R. A. Vroom (Netherlands), Prof. D. F. Waugh (Cambridge, U.S.A.), Dr. Karl-Heinz Weber (Germany), Dr. K. Westrik (Netherlands), Dr. J. Willems (Germany), Dr. Wippler (France).CONTENTS PAGE GENERAL INTRODUCTIOW- Structure Arrangements of Macromolecules. By J.D. Bernal . . 7 I. LIQUD CRYSTALS- On the Theory of Liquid Crystals. By F. C. Frank. . . 19 Liquid Crystalline Structure in Polypeptide Solutions. Part 2. By The Structure of the Liquid-Crystal Phases of Some Soap + Water Solubility in Soap Solutions. Part 10. Phase Equilibrium, Structural and Diffusion Phenomena involving the Ternary Liquid Crystalline Phase. By A. S. C. Lawrence . . 51 GENERAL ~IscussIoN.-Mr. C. G. Cannon, Prof. F. C. Frank, Prof. W. Maier, Dr. G. W. Gray, Dr. A. S. C. Lawrence, Dr. A. J. Hyde, Dr. G. Dervichian, Dr. K. Heckmann, Mr. K. G. Gotz, Dr. K. H. Weber . . 59 Conmar Robinson, J. C. Ward and R. B. Beevers . . 29 Systems. By V. Luzzati, H. Mustacchi and A. Skoulios . . 43 11. MACROMOLECULES- Introduction, By W.T. Astbury . . 80 The Entropy of a Flexible Macromolecule. By H. C. Longuet-Higgins 86 Available Methods of Estimating the Most Probable Configurations of Simple Models of a Macromolecule. By H. N. V. Temperley . 92 Chain Configurations in Crystals of Simple Linear Polymers. By C. W. Bunn and D. R. Holmes . . 95 Order-Disorder Transitions in Structure Containing Kelical Molecules. By A. Klug and (the late) Rosalind E. Franklin . . 104 Oriented Growth in the Field of Organic High Polymers. By J. Willems . . 111 Study of Single Crystals and their Associations in Polynws. By A. Keller and A. O’Connor . . 114 Molecular and Group Association Equilibria in Polymers Containing Some Comments on the Theory of Denaturation. By Stuart A. Rice, The Stability of the Helica DNA Molecule in Solution. By Julian M.Molecular Association Induced by Flow in Solutions of some Macro- 5 Widely Spaced Interacting Groups. S y H. Morawetz. . . 122 Akiyoshi Wada and E. Peter Geiduschek . . 130 Sturtevant, Stuart A. Rice and E. Peter Geiduschek . . 138 molecular Polyelectrolytes. By M. Jcly . . 1506 CONTENTS PAGE Structure Molecular Forces and Aggregation Reactions of Macro- molecules of Complex Polymers. By S . E. Bresler . . 158 Optical Rotation and Infra-Red Spectra of Some Polypeptide and Protein Films. By A. Elliott, W. E. Hanby and B. R. Malcolm . 167 The Polypeptide Chain Configurations of Native and Denatured Collagen Fibres. By E. M. Bradbury, R. E. Burge, J. T. Randall and G. R. Wilkinson . . 173 The Interactions of ms- 6- and K- Caseins in Micelle Formation. By David F. Waugh . . 186 Polynucleotide Conformations. By Richard S. Morgan . . 193 On the Structure of some Ribonucleoprotein Particles. By (the late) Rosalind E. Franklin, A. Klug, J. T. Finch and K. C. Holmes . . 197 GENERAL DrscussroN.-Prof. M. Dole, Prof. S. E. BresIer, Dr. A. Sack, Dr. M. E. Fisher, Mr. H. N. V. Temperley, Prof. H. Morawetz, Dr. D. A. Marvin, Dr. E. W. Fischer, Mr. A. Kel!er and Mr. A. O’Connor, Dr. R. Westrik and Dr. C. V. Monk, Prof. F. C. Frank, Dr. C . W. Bunn, Dr. D. J. R. Laurence, Dr. K. V. Shooter, Dr. R. A. Cox, Dr. A. R. Peacocke, Prof. Stuart A. Rice and Dr. E. P. Geiduschek, Mr. K. G. Gotz, Dr. G. A. Gilbert, Dr. M. Kryszewski, Dr. G. B. B. M. Sutherland, Prof. D. D. Eley, Dr. A. Elliott, Dr. G. R. Wilkinson and Dr. E. M. Bradbury, Dr. R. E. Burge, Dr. P. M. Cowan, Mr. D. M. G. Armnstrog . 199 Author Index . . 235

ISSN:0366-9033    

DOI:10.1039/DF9582500001

出版商:RSC    

年代:1958

数据来源: RSC

摘要:

GENERAL INTRODUCTION STRUCTURE ARRANGEMENTS OF MACROMOLECULES BY J. D. BERNAL Dept. of Physics, Birkbeck College, Malet St., London, W.C. 1 Received 1 1 th February, 1958 The printed title of this discussion is necessarily an abbreviated one and does not give a sharp enough idea of the range and limitations of the subject to be covered. A more correct title would be The Configurations and Close Znteractions of Macromolecules and their Expressions : in solutions, in liquid crystals and in the solid state. The papers will deal with one or the other aspects of this field and will, for the most part, not go beyond it. In this introductory contribution I have chosen what is the easiest part of the subject namely the discussion of the actual spatial arrangement of atoms inside macromolecules under the various conditions in which we study them.First, I try to define what is meant by macromolecules for the purposes of this discussion. The simplest definition is included in the word itself-a macro- molecule is simply a big molecule-but the question is how big, and here we have to draw what appears at first to be a somewhat arbitrary line, let us say a molec- ular weight of not less than 5000. An upper limit however will be much more difficult to formulate. If we take this as the size of a medium virus particle at 4 x 107, this gives a range of 8000 between them or a 20-fold difference in linear scale corresponding to the range between a cube of side 20A to one of 400A. But though this definition may not be precise, for we can probably go beyond it on both sides for special macromolecules, it corresponds to more than an arbitrary blocking-out of a certain size of particle.It really represents a range of structures which have something in common. In the old days they would have been called colloidal particles and they would have been defined by their external properties, that is, their possibilities of remaining in the state of a sol or of being coagulated in different ways. Here, with our greater knowledge, we are more concerned with their internal structure. This is a deliberate restriction for the purpose of this discussion. A general discussion on the configurations and interactions of macromolecules should go beyond the close interactions which we will discuss here to consider those between these colloidal particles in solution and in a more condensed gel state-the discussion of the long-range forces.But this it was thought would take us too far afield and necessitate a conference of at least twice the length so we had to confine ourselves to a discussion of the conditions which fix the internal structure of the larger types of macromolecules and the relations of macromolecules of all sizes to each other when they are in close contact, that is, when they are in the form of dense solids or fibres. This reduces the physical part of the discussion to that of interactions at normal chemical interatomic distances-those dealt with in the decreasing hierarchy of interaction energies from homopolar through ionic and hydrogen bonds to van der Waals’ bonds.We will not, in general, be considering macro- molecules as a whole but only in part-where they touch each other-and deter- mining what fixes their internal configurations. Now the peculiar complexity of macromolecules as well as their main interest -both in themselves and on account of their biological and industrial importance 78 STRUCTURE ARRANGEMENTS OF MACROMOLECULES -depends fundamentally on the fact that they are composed of atoms held together by forces of very different strengths. I speak here of forces although it is a very old-fashioned analogy because a force is the shortest word to refer to the shapes of mutual potential energy curves containing minima of different depths. When I say a strong force I usually mean one with a very deep trough and a very narrow one at the same time, as shown in fig.1. This is the characteristic of macro- molecules and their association, and what I have called a long time ago-a word which has not really stuck in chemistry-their heterodesmisity. But unlike most heterodesmic compounds, such for instance as inorganic oxy-salts and simple molecular crystals where there are two different kinds of bonds in the structure, in most macromolecules and their associations there are three, four, or even five different grades of forces building them up. The first grade is essential for the very existence of a macromolecule, these are the homopolar forces which link up, so to speak, the skeleton or more often merely (0) FIG. 1 .-Shape of energy curves for different types of interatomic forces (diagrammatic only) : (a) homopolar bond, (b) hydrogen bond, (c) van der Waals’ bond.the backbone of the whole structure. Until recently the chemist was satisfied both in analysis and synthesis if he had established this skeleton or found the structural formula. Many of these macromolecules, indeed nearly all of them, are polymers. Most are linear polymers. The chemist’s task used to be deemed to be complete when he had established for any polymer the nature of the monomers of which it consisted and their mode of attachment, their order in a chain or their mode of branching and cross-linking in more complicated cases. However, as long as our interests were largely physical more than chemical, or let us say, biochemical rather than simple chemical, the knowledge of the actual skeleton of the macromolecules was not enough to determine the most interesting properties-the chemical or the colloidal properties of the macromolecule.This is because, as we all now recognize, a linear polymer can, while retaining all its covalent forces, be found in a large number of different conformations or con- figurations-as I think we should call them in this discussion-and so avoid the more special meaning of the word conformation in chemistry. The freedom of rotation around single bonds and other variations in the skeleton leads to a very large number of these possible configurations. The actual determination of these configurations will not be the main object of our discussions here. For apart from the interesting contribution of Morgan, Deer and Beers on the structureJ .D. BERNAL 9 of adenine polynucleotide and of Franklin and Klug on ribonucleoprotein par- ticles, this is more a discussion on physico-chemical properties than on X-ray structure determination. Here for the most part we will take the configurations, as far as they have been determined for granted, and see how they relate on the one hand to intermolecular forces and on the other to the physical chemical properties of the resulting structures. What 1 want to do in this introductory lecture is merely to set out what might be called the grammar of the subject, to try and arrange the possible configurations in some kind of logical spatial order so that we can see the relations that exist between the subjects treated in the various detailed scientific papers that will come later.I will take the knowledge of the physical forces for granted and discuss mainly the geometrical limiting factors that determine how these physical forces lead to the different patterns-not only those that have already been observed, but those that are geometrically possible and may yet be made. It is hardly worth recalling here the kind of forces we shall have to deal with. They are set out for comparative purposes in table 1 at end. Main chain homopolar forces I have already spoken of but here I must add a group of homopolar forces which are particularly important in configuration, namely those of the relatively weak homopolar cross-links that can exist both in natural and artificial polymers chiefly the S-S link so important on the one hand in proteins and on the other in vulcanized rubbers, and also ester links between carboxy side-groups and hydroxyls.The phenomena of denaturation and of vulcanization depend on the breaking or making of such cross links. The breaking of the main links, however, falls rather outside our field into that of the decomposition or hydrolysis of the polymers essential for analysis or digestion. The next strongest force, that of the ionic or salt bond, has played a relatively small part in polymer systems which have been carefully studied though we get hints of it for instance in the paper by Waugh on the role of calcium in casein formation and by Bresler on the stabilizing function of doubly charged ions. While energetically such links may be as strong as some of the homopolar links, they cannot be so permanent a feature in that they can be readily affected by the ionic environment particularly in water solution.Overwhelmingly the most im- portant force determining configuration is the hydrogen bond whether that between oxygen and oxygen in carboxy links discussed by Dr. Morawetz or the common CO . . . NH hydrogen bond of the proteins which appears in a large number of the papers presented. Finally, we come to the London-van der Waals’ forces predominant in the hydrocarbon-covered polymers and playing a considerable role elsewhere. For all the kinds of macromolecules heretofore studied-which do not contain extended electron orbits of a metallic character-these van der Waals’ forces may be treated as acting only between immediately contiguous atoms in different molecules or in different parts of the same molecule.With them are usually taken the omnipresent repulsive forces, ill understood theoretically but relatively easy to deal with practi- cally on the old conception of the billiard ball, or as we would now rather say, the rubber-ball-type of atom limiting the closest approach of atoms in different molecules or in different parts of the same molecule. These steric considerations may be the determining factor in configuration, the simplest case being the spiral nature af polytetrafluoroethylene (PTF) which was shown by Bunn to be due to the impossibility of a simple straight paraffinoid arrangement of CF:! groups. At least a qualitative account of most of the structures actually determined for polymer or polymer associations can be explained in terms of these forces and a quantitative explanation is clearly possible although the amount of com- puting required for it would stid be rather forbidding.As already indicated the kind of macromolecules that we will be dealing with here are nearly all of them polymers but they include certain molecules that, because they are found in Nature and are not very large, we are not accustomed to10 STRUCTURE ARRANGEMENTS OF MACROMOLECULES call polymers, namely the long-chain hydrocarbons. Even if they do not come strictly into the definition given above for macromolecules with respect to molec- ular weight, their peculiar properties of aggregation which are discussed here in the section on liquid crystals may point the way to an understanding of the behaviour of far longer chained polymers.Most of the polymers we will be dealing with here are linear. Later no doubt the colloid chemist will have to deal with arrangements of small molecules linked not only by a pair of bonds into chains but also by three bonds into sheets or by four bonds or more into three-dimensional aggregates, the familiar ino, phyllo and tecto series of mineralogy. However, not only the synthetic chemist but the organic cell seems to find it easier to start by a linear polymerization process and to make the more complicated structures they need by methods of coiling or folding the original polymer into fibres, sheets or massive structures. We will find that there is enough complexity in the various configurations of linear polymers without introducing at this stage those due to branching or looping or higher degrees of complexity in the arrangement of the covalent forces.In order to approach the problem in some kind of order we will consider first of all the intrinsic limitations on the configurations of isolated linear polymer molecules, then the associations formed by small numbers of such molecules, double and treble coiling, and finally the far more complex structures formed from aggregations of similar or dissimilar polymer molecules either in the extended or in the folded form. Isolated linear polymer molecules have been known now for some 30 years in a great variety of possible configurations. Despite the knowledge gained in the intervening period there is still much that can be usefully said about the pure thermodynamics of these configurations and contributions to this theme will be found in the papers of Longuet-Higgins, Temperley, Bunn and Rice who have all worked with the essential assumption that the intrinsic determination of con- figuration-that is its determination apart from interaction between non-neigh- bouring monomers-is very weak.For on account of the relative freedom of rotation and the small amount of steric hindrance-except in such extremely simple polymers as the polymethylenes-the energies of the different configurations will not differ much among themselves. In my opinion, however, it would be a pity to neglect, except possibly because of its mathematical complexity, the relatively small restoring forces which tend to keep small portions of a linear polymer in some regular relationship to each other ; either straight, or in the more general case curved and at the same time twisted.Neglecting heat motion every linear polymer should, therefore, have in general the form of a helix taking as extreme cases those of a straight line and a circle. In the latter case, steric limitations will ensure either that the circle is completed producing a ring molecule or that the circle is slightly twisted into a close sprung helix (see fig. 2). Even without heat motion, however, such in- trinsically determined configurations are likely to be unstable in the sense as having higher potential energies than closely coiled or folded forms, for whatever the nature of the polymer there will be at least van der Waals’ forces which can be exerted between its covering atoms and those of another part of the same chain.In other words, quite apart from entropy considerations, the two configurations which are known as F (fibrous) or G (globular) would be likely to be found and in the absence of strong interactions with either neighbouring fibres or a medium favouring a large surface the globular will have the lower internal energy. Looked at mechanically the essential feature of a linear polymer is its lack of lateral rigidity even if it is not-as some rubber models would make it--com- pletely flexible at every point and therefore more like a chain than a string, it still can hardly be expected to stand up all by itself and therefore it requires some lateral support.The same considerations apply even to such polymers which are only weak in one direction, those of the lath-shaped variety such for instance asJ . D . BERNAL 11 the paraffins. Here we have a very powerful analogy, as Astbury was the first to point out, between the behaviour of the monomolecular chains of linear polymers and the gross physical fibres which are used in industry. All the processes in the classical textile industry, those of drawing out, spinning, coiling, crimping and folding, all indeed except weaving itself for which we have not yet found a molecular analogue, have their parallel in the molecular field. Spirally coiled wool fibre contains in itself many more grades of molecular spirals.Several examples of these phenomena are brought out in the subsequent dis- cussions. The essential static argument is that configuration is determined by the balance between the energy of deformation of the flexible chain and that gained by folding back on itself. Perhaps the clearest case is shown by the work FIG. 2.-Arrangements of simple polymer chain : (a) straight polymer-successive links collinear ; (b) high pitched spiral polymer-successive links nearly collinear but twisted ; (c) ring polymer-successive links nearly collinear but untwisted ; (d) low pitched spiral polymer-successive links as in (c) but twisted to allow coiling. of Keller, whose beautiful studies of regular folding of polymethylene molecules show that the favoured fold is l20A or some 100 methylene residues.In this way overall packing is almost as close as in a long-chain hydrocarbon except for the few residues taken up in the actual turnover of the folds. We badly need a quanti- tative theory of this static instability to balance that of the statistical arguments used for rubber. The fact that such arguments for configurations have served so well in the past is that they have mainly dealt with molecules which for steric reasons could not pack very conveniently, at least in the unstretched state. This irregularity would seem to have a decisive role to play in the appearance of rubber- like-that is entropy-elasticity in polymers. Where, however, hydrogen bonds exist the tendency to the coiled or folded forms is very much increased.Here the requirement is that all hydrogen containing OH or NH2 groups should be bonded to a corresponding receptor 0 or OH and the type of structure will depend on whether this bonding is predominantly inside the same polymer chain or between one polymer chain and the next, giving the classical Astbury ct and /3 configurations later so beautifully explained in the Pauling cc-helix and pleated sheet structures. Even without a complete analysis of the geometrical configuration of any protein, we have plenty of physico-chemical12 STRUCTURE ARRANGEMENTS OF MACROMOLECULES evidence, the presence of more or less protected hydrogen bonds of this sort particularly the work of Linderstrram-Lang and Bresler on the exchangeability of the hydrogens thus protected or left unprotected by denaturation.Even without a quantitative theory we are beginning to see, partly as a result of papers presented here, something of the factors that determine under what conditions a regular linear polymer will coil or alternatively will fold. CuiZing will be favoured by the presence of large inflexible monomers which ensure that any abrupt turn will lead to considerable energy increase through lack of effective packing. Folding will be favoured by the presence of small flexibly joined monomers in conditions where parallel packing of straight runs of polymer give low energy arrangements. Freedom of the molecule favours coiling, that is the dissolved or swollen state. Lateral compression or solvent-free conditions favour folding. Drawing or stretching favours both uncoiling and unfolding for here the lateral bonding between straight chains comes most into play.Irregular polymers such 2s proteins should favour a mixture of coiling and folding. Special flexible links which fit badly into a coil such as proline will favour a bend. Here, however, as Kendrew has shown in the myoglobin structure, the folding is not of a simple back and forth parallel character, but three-dimensional and very com- plicated. The mEjor geometrical feature which applies to the inner linking of polymers, when van der Waals’ hydrogen bonds or other stronger forces such as S-S groups are present, is that there are no such limitations of symmetry such as holds for the more extended regular three-dimensional piling of ordinary crystals.Pauline, in effect, liberated us from the restrictions of two-, three- and four-fold rotation and screw axes into the much wider world of irrational spiral symmetry. The corresponding X-ray patterns can now be analyzed by Bessel functions, in the use of which Cochran, Watson and Crick have made such rapid and significant advances in the field of protein and DNA structures. By moving out of the crystallographic limitations and entering a new geometrical world we have to consider the possible configurations of single spirals, their mutual relations and their further complication by folding. From what has already been said it is evident that it is very academic to treat a linear polymer in isolation. It cannot avoid having internal relations and if in bulk, apart from very dilute solutions, also having external relations with other polymer molecules of the same or different kind.The protean nature of macro- molecules arises from these interactions which are to be the main subject of our discussion. It is indeed, through their relations with their neighbours, that other physical factors such as solvents and temperature affect the arrangement of macromolecules. Temperature, for instance, affects the linkages between neigh- bouring lengthy macromolecules and permits them greater freedom which may itself be a co-operative phenomenon leading to a kind of two-dimensional melting such as discussed in Klug’s paper for polytetrafluoroethylene. Of particular interest here is Luzzati’s communication which shows the variety of structures in what used to be called micelles in soap melts and solutions.Here he has demonstrated the existence of a new kind of liquid crystal in which the carboxy groups form a solid array while the hydrocarbon chains attached to them are in other respects free and liquid. The complex possibilities of structures which are partly melted and partly solid is also brought out in the paper of Lawrence, and the mixtures of soap and sterol molecules with the production of myelinic figures whose complex he has simply explained. Conditions favouring the existence of straight forms of polymers or at most of simple coiled forms may be various. Two striking new methods of achieving this are being reported here by Willems who has succeeded in orienting polymers on crystals such as sodium chloride and by Joly who has done the same by dynamical methods of rapid shearing tending to form not only parallel chains but associatioiis based on them.J. D .BERNAL 13 The extremely beautiful cholesteric phenomena studied by Conmar Robinson, in the case of some synthetic polypeptides show the extent of coiling and folding even in a non-ionic solvent which he has analyzed by an elegant balancing of birefringence and optical rotating studies. Besides conditions leading to the loosening of the molecules such as occur in all the liquid crystalline stages of polyiners there are also those that are deter- mined by their greater attachments to each other. These attachments can be in the form of hydrogen bonding or they may be strengthened by secondary linking.This formation of cross linking by homopolar bonds or vulcanization is a very general phenomenon. It is related to the inner and outer cross-linking characteristic of the deizatirration not only of proteins but of other polymers as discussed by Rice. These latter phenomena? depending as they do on high degree of irregularity can still be treated best thermodynamically but we are beginning to knGw enough about the actual ordering of polymeric molecules to be much more detailed in our treatment of the variety of regular arrangements. The most radical change which can occur in polymers in all states, solid, liquid or gaseous, is that of depolymerization and repolymerizaticn. This is, in general, outside our field but one aspect still lies within its confines, that is the simultaneous depolymerization and repolymerization that occurs in the classical ring-chain transformation, first carefully studied in polyoxymethylene-a universal phenom- enon among the simpler polymers and occurring in the crystalline state. When found in the more complicated polymers it is the probable explanation of the G-F transformation, globular-fibrous transformation? studied in such detail in insulin by Waugh.The logical ordering of macromolecular structures is best done to bring out the hierarchical nature of the larger and more complicated forms (see table 2, fig. 3 at end). The primary structure is that of the chain itself as determined, for instance, by chemical analysis even in the most complicated cases of proteins and nucleic acids.Next follows secondary structure already referred to as that determined by links, van der Waals’ or hydrogen bonds or other between relatively close members of the chain. This is the feature that gives rise to the various spiral forms. Next and necessarily less regular is the tertiary structure characterized by coiled coiling or by folding. Folding is not necessarily tertiary in itself as Keller has shown for the polymethylenes that folding may supervene without preliminary coiling in which case it is strictly secondary. Where, however, folding is imposed on previous coiling there is necessarily a degree of uncoiling at the places where the folding occurs and it is this comparative rigidity of the coiled structure that un- doubtedly gives rise to the extreme complexities-until recently defying analysis -of the globular proteins.We now, however, know, thanks to the beautiful work of Kendrew that the typical a-helix protein of haemoglobins does consist of relatively short stretches of some 20A of helices joined together by uncoiled sectors. The relative amount of coiled and uncoiled chain in globular proieins was first determined by Doty using optical rotation methods and a further ayplica- tion of this method to both artificial and natural polypeptides is being given here by Elliott and Hanby. There is intrinsically no reason why the complexity of a macromolecule should be limited to the tertiary stage. Indeed the larger natural macromolecules must be constituted in just the same way. There could be further foldings on the already folded chains but no such example has yet been studied in sufficient detail to bring out its precise geometry. The further complexity that does occur is due to combinations between different chains in the uncoiled, coiled or folded states.The simplest of such arrangements is the parallel packing of polymer chains in straight or spiral con- figurations. This is usually of the two-dimensional hexagonal close-packed type (see fig. 4). Only where different chains are the same length such as occurs for instance in elongated virus crystals is it possible to get end-on coherence and hence three-dimensional crystals. More usually the result is a fibre regular in14 STRUCTURE ARRANGEMENTS OF MACROMOLECULES only two dimensions. Such regular fibres held together laterally by long-range forces besides occurring in viruses have been demonstrated by Huxley and others in muscle and is here discussed by Luzzati as occurring in one of the phases of soap melts. FIG.3.-Hierarchy of polymer complexes : (a) primary structure-no intrachain links, polypeptide in j? links (after Pauling) ; (6) secondary structure--coiling with intrachain hydrogen bonds, polypeptide in a helix (c) tertiary structure-folded coils, melhaemoglobin molecule (after Kendrew) ; (d) quaternary structure (homogeneous type), linked groups of tertiary molecules, (e) quaternary structure (heterogeneous typeblinking of different types of ternary form (after Pauling) ; haemoglobin structure (hypothetical structure) ; protein and primary ribonuclease, tobacco mosaic virus (after Franklin).In the close packing of spiral molecules, however, difficulties of accommodation must occur if all the spirals are of the same kind-right- or left-handed. They can engage effectively with each other only when the pitch is low (see fig. 5), and this spiral close packing has been shown by Franklin to occur in dry tobacco mosaic virus. For high-pitched spirals, as Klug and Fr a n k h show in their paper, accommodation is more difficult. This may be a reason why such spirals tend to be multiple, for multiple spirals can pack much more economically than single onesJ . D. BERNAL 15 To understand the mechanism of multiple coiling with cross-links between the elements, it is easiest to begin with a topological consideration of cross-linking between straight polymer chains.The simplest possible way of combining two polymer chains is by adhering side by side. Such a compound is formally ana- logous to a diatomic molecule, but because it extends in three dimensions it is essentially more complicated. In a diatomic molecule each component is effec- tively monovalent, that is without regarding double bonds as essentially different from single ones. But when one such bond between two spherical atoms is re- placed by a whole series of bonds between two parallel chains forming a kind of ladder (see fig. 5 ) monovalent linking is not necessarily limited to two chains. ... . . . . . . . . . . . . . . . . .......... ........... . . . . . . . . . . . . . . . . . . . .... .... . .. . . . . ...... . . . . . . . (4 (4 (b) FIG. 4.-Types of packing of long chain molecules : (a) molecules of equal lengths forming sheets, (b) molecules of unequal lengths forming fibrous aggregates (tactoids) ; (c) cross section of both types showing simple hexagonal packing. The same arrangement could give rise to three chains if the bonds at diEerent parts of the chains point in different directions, to a flat network of chains such as are produced in the /I form of the protein fibres such as silk, or finally to a com- pletely cross-linked fibrous block. In general, however, the chains will not be straight and parallel but will have their own tendency to spiral form and therefore the simplest combination is not a parallel-sided ladder but a double spiral. Now the most famous of these double spirals is that of the DNA structures and corresponding polynucleotides of the RNA type discussed by Morgan and his associates in their paper. When three chains are involved there is a treble spiral now typified by the collagen structure which will be discussed by Bradbury and his associates.Double and multiple spirals will be formed most easily from the same types of molecules that necessarily have a concordance in the period of their twist. Of greater biological interest, however, are those where two different kinds of polymer molecules are twisted together. This requires a very considerable con- cordance and so far it is only known in what appears to be the all-important case of the nucleoproteins particularly the DNA-protamine complexes found by Wilkins to be already crystalline in live sperm cells.Even more complex structures can be formed by associations together of already coiled and folded molecules, This seems to be the case for a very large number of proteins in which the globular molecule itself may be considered as an association of smaller globular molecules sufficiently stable to withstand the disruptive forces of the solution. These associations may be in different orders. For instance in insulin the normal form in solution has a molecular weight of some 44,000 but this is not found in most of the crystal forms which show a molecular weight of16 STRUCTURE (a’) - ARRANGEMENTS OF MACROMOLECULES a pair of chains forming limited ladder ; a‘ plan :J ::ition} sets of chains forming unlimited sheet ; c‘ plan triplet of chains forming spiral ladder ; d’ section simple spiral ; ‘, e section ;, ;yon} triplet of linked spirals.pair of linked spirals ; FIG. 5.-Types of bonding of crosslinked polymers each forming one link per monomer.J . D. BERNAL 17 33,000 indicating the presence in the former of four and of the latter of three sub- molecules of 11,080 closely held together. In turn these units of 11,000 seem to be composed of two identical units of 5,500 each of which consists of two unequal protein chains. The haemoglobin series shows a number of different degrees of multiplicity from the simple kind found in the myoglobin of molecular weight of about 17,000 to those of the foetal haemoglobins of 34,000 and the normal 4 haematin haemoglobin of 56,000.The components of these may not be of the same kind though it is too early now to tell what the difference is. A case where they are definitely different is being discussed at this conference by Waugh in the case of the cc, and K caseins which can be separated and can also be made to combine to form a variety of complexes either soluble or insoluble as in the coagulation of curds, the latter involving the presence of calcium. Discussions of other types of association will also be presented in Bresler’s paper. The greatest complexity so far met is, however, found in the structures of viruses which will be reported on by Franklin and Klug. Here, unlike the sperm nucleoprotein we have an association between what appears to be a single or few stranded nucleic acid polymer and a number of relatively small protein molecules arranged in what is effectively a regular quasi-crystalline pattern either in the form of an indefinite spiral as in tobacco mosaic virus or in that of a closed sphere-turnip yellow, tobacco bushy stunt, and other spherical viruses.This discussion by no means exhausts the complexities that can exist in macro- molecules even without recourse to the long-range forces which give rise to the larger scale structures such as micelles, tactoids, coacervates, and gels. However, the field covered by the present discussion should be full enough to point the way to the analysis of further complexities. We may hope that in the present dis- cussion the experiences of workers using very different methods, X-ray, physical- chemical, spectroscopic and optical rotation, will open further perspectives.I hope I may consider my task fulfilled if I have indicated the frame in which his picture can be set. TABLE 1 .-TYPES OF lNTERPARTICULATJ2 FORCES order of magnitude of interac- range of kinds of unit between mechanism tion energy action A which such forces act name kcaI/mg mole homo- electron sharing 60 polar hydrogen action of incom- 6 bond pletely screened hydrogen atom attached to one atom or other polarizable atoms ionic coulomb attrac- 10-20 tion between ions or charged atoms of different sign van der mutual induction 1-2 Waals of moments from electrically apolar molecules 1-2 electron deficient in organic atoms com- pounds 2.4-3.2 OH- and NH- usually groups in re- 2.7 lation to OH and CO 2-3 basic NHz or NH3 groups and acid coo groups, halogens, etc. ‘CHz+-CH3 / 3-5 groups and halogens examples all organic com- pounds long chain polymers water, acids, sugars, urea, purines (nucleic acids) proteins soaps basic hydrochlor- ides, zwitterions, glycine paraffins and hydrophobic molec- ules or parts of molecules18 STRUCTURE ARRANGEMENTS OF MACROMOLECULES TABLE 2.-oRDERS OF MACROMOLECULAR STRUCTURES order of order of nature of last magnitude of magnitude of stage binding molecular particle name of particle weight dimensions simple molecule homopolar 50-200 10 A3 (monomer) bonds chain polymer the same 1000- 5 X 1 0 X homo or hetero 100,Ooo 1 m A coiled polymers hydrogen bonds the same 10 x 10 x or S - S link 500 A folded or coiled coil the same 10,OOO- 50A3 polymer 100,000 globular particle homogeneous agglom- ionic or cryo- 50,000- 100 A3 ated particle hydric forces l,OOO,O00 20 x 20 x twined fibres 1000A3 heterogeneous agglom- the same 10,000,OOO 200 A3 erated particles, or loox 100 examples amino acids, purines, porphyrins, sugars, lipids silk fibroin ,%type denatured proteins cellulose, rubber coiled fibrous protein a-type desoxyri bose nucleic acid smaller globular pro- teins, ribonuclea5e larger globular proteins, haemoglobin, seed globulins haemocyanin, fibrous insulin, collagen nucleoproteins, lipo- nroteins, mucoproteins, fibre aggregates x 5000 8, etc., smaller viruses

ISSN:0366-9033    

DOI:10.1039/DF9582500007

出版商:RSC    

年代:1958

数据来源: RSC

摘要:

I. LIQUID CRYSTALS ON THE THEORY OF LIQUID CRYSTALS BY F. C. FRANK H. H. Wills Physics Laboratory, University of Bristol Received 19th February, 1958 A general theory of curvature-elasticity in the molecularly uniaxial liquid crystals, similar to that of Oseen, is established on a revised basis. The= are certain significant differences : in particular one of his coefficients is shown to be zero in the classical liquid crystals. Another, which he did not recognize, does not interfere with the determination of the three principal coefficients. The way is therefore open for exact experimental determination of these coefficients, giving unusually direct information regarding the mutual orienting effect of molecules. 1 . INTRODUCTION One of the principal purposes of this paper is to urge the revival of experi- mental interest in its subject.After the Society’s successful Discussion on liquid crystals in 1933, too many people, perhaps, drew the conclusion that the major puzzles were eliminated, and too few the equally valid conclusion that quanti- tative experimental work on liquid crystals offers powerfully direct information about molecular interactions in condensed phases. The first paper in the 1933 Discussion was one by Oseen,l offering a general structural theory of the classical liquid crystals, i.e. the three types, smectic, nematic and cholesteric, recognized by Friedel2 (1922). In the present paper Oseen’s theory (with slight modification) is refounded on a securer basis. As with Oseen, this is a theory of the molecularly uniaxial liquid crystals, that is to say, those in which the long-range order governs the orientation of only one molecular axis.This certainly embraces the classical types, though in the smectic class one trans- lational degree of freedom is also crystalline. Other types of liquid crystal may exist, but are at least relatively rare : presumably because ordering of one kind promotes ordering of another-it is already exceptional for one orientational degree of freedom to crystallize without simultaneous crystallization of the translational degrees of freedom. Fluidity (in the sense that no shear stress can persist in the absence of flow) is in principle compatible with biaxial orientational order, with or without translational order in one dimension. It is very unlikely that trans- lational order in two dimensions, and not in the third, can occur as an equilibrium situation.The existence of a three-dimensional lattice is not compatible with true fluidity. A dilute solution with lattice order, which appeared to be fluid, would not be considered a liquid crystal from the present viewpoint, but rather a solid with a very low plastic yield stress. The Oseen theory embraces smectic mesophases, but is not really required for this case. The interpretation of the equilibrium structures assumed by smectic substances under a particular system of external influences may be carried out by essentially geometric arguments alone. The structures are conditioned by the existence of layers of uniform thickness, which may be freely curved, but in ways which do not require a breach of the layering in regions of greater extension than lines. These conditions automatically require the layers to be Dupin cyclides and the singular lines to be focal conics.Nothing, essentially, has been added 1920 LlQUlU CRYSTALS to the account of these given by Friedel, and not much appears to be needed, though a few minor features (the scalloped edges of Grandjean terraces, and scalloped frills of battonets) have not been fully interpreted. The case is quite different for the nematic and cholesteric liquid crystals. This is particularly clear for the former. In a thin film, say, of a nematic substance, particular orientations are imposed at the surfaces, depending on the nature or prior treatment of the materials at these surfaces ; if the imposed orientations are not parallel some curved transition from one orientation to the other is required.Curvature may also be introduced when, say, the orienting effect of a magnetic field conflicts with orientations imposed by surface contacts. Something analogous to elasticity theory is required to define the equilibrium form of such curvatures. It is, however, essentially different from the elasticity theory of a solid. In the latter theory, when we calculate equilibrium curvatures in bending, we treat the material as having undergone homogeneous strains in small elements : restoring forces are considered to oppose the change of distance between neighbouring points in the material. In a liquid, there are no permanent forces opposing the change of distance between points : in a bent liquid crystal, we must look for restoring torques which directly oppose the curvature.We may refer to these as torque- stresses, and assume an equivalent of Hooke’s law, making them proportional to the curvature-strains, appropriately defined, when these are sufficiently small. It is an equivalent procedure to assume that the free-energy density is a quadratic function of the curvature-strains, in which the analogues of elastic moduli appear as coefficients : this is the procedure we shall actually adopt. Oseen likewise proceeded by setting up an expression for energy density, in terms of chosen measures of curvature. However, he based his argument on the postulate that the energy is expressible as a sum of energies between molecules taken in pairs. This is analogous to the way in which Cauchy set up the theory of elasticity for solids, and in that case it is known that the theory predicted fewer independent elastic constznts than actually exist, and we may anticipate a similar consequence with Oseen’s theory.It is worth remarking that the controversial conflict between the “swarm theory ” and the ‘‘ continuum theory ” of liquid crystals is illusory. The swarm theory was a particular hypothetical and approximative approach to the statistical mechanical problem of interpreting properties which can be well defined in terms of a continuum theory. This point is seen less clearly from Oseen’s point of departure than from that of the present paper. 2. BASIC THEORY We first require to define the components of curvature. Let L be a unit vector representing the direction of the preferred orientation in the neighbourhood of any point.The sign of this vector is without physical significance, at least in most cases. If so, it must be chosen arbitrarily at some point and defined by continuity from that point throughout the region in which L varies slowly with position. In multiply-connected regions it may be necessary to introduce arbitrary surfaces of mathematical discontinuity, where this sign changes without any physical discontinuity. At any point we introduce a local system of Cartesian co-ordinates, x, y , z, with z parallel to L at the origin, x chosen arbitrarily perpen- dicular to z, and y perpendicular to x so that x, y, z form a right-handed system.Referred to these axes, the six components of curvature at this point are (see fig. 1) :F . C. FRANK 21 # X Splays. t l = a4, s2 = n5, b2 = ag. - + bLY : bx Y X Twists. X Bends. FIG. 1. We postulate that the free energy G of a liquid crystal specimen in a particular configuration, relative to its energy in the state of uniform orientation, is expressible as the volume integral of a free-energy density g which is a quadratic function of the six differential coefficients which measure the curvature : G = gdr, (4) (5) J U g = kini + +kdaiaj, (i, j = 1 . . . 6, kc = kji), where summation over repeated suffixes is implied. In so far as there was arbitrariness in our choice of the local co-ordinate system (x, y, z), we require that when we replace this by another equally permissible one (x’, y’, 2’) in which we have new curvature components n’i, g shall be the same function as before of these curvature components : g = kia’i + +kQdia).(6) This requirement will impose restrictions on the moduli, ki, kg. The choice of the x-direction was arbitrary, apart from the requirement that it should be normal to z, which is parallel to the physically significant direction L :22 LIQUID CRYSTALS hence any rotation of the co-ordinate system around z is a permissible one. Putting z' = y , y' = - x , z' = z, gives us the equations : kl = k5, k2 =- k4, k3 = k6 = 0, 1 (7) kll = k55, k22 = k441 k33 = k66, k12 = -kk45, k14 = -k25, k13 = k16 == k23 = k26 = k34 = k35 = k36 = kqg = k56 = 0 J The working is omitted here : the simpler examples of eqn.(13-17) below exhibit the principle. A rotation of 45" gives a further equation kll - k15 - k22 - k24 = 0, and rotation by another arbitrary angle just one more (8) k12 + k14 0, (9) k12 =- k14 = k25 =- k45. (10) Thus, of the six hypothetical moduli ki two are zero and only two are independent : ki = (kl k2 0 - kz kl 0), (1 1) which with those obtained previously gives while of the thirty-six kij eighteen are zero and only five are independent : k12 k22 0 k24 k12 0 0 k33 0 0 - k12 k24 0 k22 - k12 (kl1 - k22 - k24) k12 0 -kl2 kl1 0 0 0 0 0 kl1 k12 0 -kl2 (kll - k22 - k24) 0 (12) 0 0 ! k33 -y, z' = -2. This gives us If the molecules are non-polar with respect to the preferentially oriented axis, or, if polar, are distributed with equal likelihood in both directions, the choice of sign of L is arbitrary. It is a significant convention in our definition of curvature components that z is positive in the positive direction of L : and if z changes sign, one of x and y should change sign also to retain right-handed co-ordinates.Hence a permissible transformation in the absence of physira2 poIarity is L' =- L, I kij = x' = x, y' = Since, compared with (2), the coefficients with indices 1, 5 and 6 have changed sign, the required invariance of (6) gives us the equations kl = 0, kS = 0, k6 = 0, kl2 = k13 = k14 = k25 = k26 = k35 = k36 = k45 = k46 = 0. (14) (1 5 ) and (from the second order terms in which only one factor has changed sign) : Some of this information is already contained in eqn.(7-10). The effect upon (1 1) and (12) is that kl and k12 vanish. There is a further element of arbitrariness in our insistence on right-handed co-ordinates, unless the molecules are enantiomorphic, or enantiomorphicallyF. C. FRANK 23 arranged. Empirically, it appears that enantiomorphy does not occur in liquid crystals unless the rno!ecules are themselves distinguishable from their mirror images, and that it also vanishes in racemic mixtures. In the absence of enantio- rnorphy, a permissible transformation is x’ = x, y’ = --y, z’ = z, giving whence, by the same argument as before (omitting the redundant information), k2 = 0 and k12 = 0. (17) Hence, while (15) with (11) and (12) expresses the most general dependence of free energy density on curvature in molecularly uniaxial liquid crystals, kl vanishes in the absence of polarity, k2 vanishes in the absence of enantiomorphy, and k12 vanishes unless both polarity and enantiomorphy occur together.The general expression for energy density in terms of the notation of eqn. (1) is g = ki(si + ~ 2 ) + k2(t1 + t2) + hkii(si + ~ 2 ) ~ + -&k22(ti + f212 + *k33(bi2 + b22) By introducing + k12(S1 + S2)(tl f t2) - (k22 k24)(SlS2 f tlt2)- (18) so = --kl/kll, t o = -k2/k22, (19) and g’ = g + +kllS02 4- !&22to2, (20) i.e. by adopting a new and (in the general case) lower zero for the free-energy density, corresponding not to the state of uniform orientation but to that with the optimum degree of splay and twist, we obtain the more compact expression g’ == +kli(sl + s2 - SOY + +k22(ti + t2 - toI2 + +k33(bi2 + b22) (21) An alternative form of this expression is given as eqn.(25) below. + k12(~1 + ~2)(t1 + t2) - (k22 + k 2 4 k S 2 + tlt2). 2.2 COMPARISON WITH OSEEN’S THEORY According to Oseen, the energy is expressed by + K33W * WL)2 + 2K12(c7 ’ L)(L V x L)ldT. (22) We are not concerned with the first integral, which is not related to the de- pendence of energy on curvature (and which plays only a minor role in Oseen’s theory). It is the integrand of the second integral which should be compared with our free-energy density g. Noting that L . v x L = 3Ly/3x - 3Lx/3y = -(tl + t2), v . L = 3Lx/3x + 3L& = (q + SZ), ((L . V)L)2 = (3Lx/3z)2 + (3L,132)2 = (b12 + b29, (23) we see that with (24) Oseen’s expression is equivalent to (18), except that the latter contains the additional terms, - @2/2nz2)K1 = k2, (p2/in2)K11 = k22, (p2/m2)K22 = kll, - (p2/m%12 = k12, (p2imW33 = k33, k i h + ~ 2 ) - (k22 + k24)(~1~2 + tit2).24 LIQUID CRYSTALS This accords with the anticipation that Oseen was in danger of missing terms by adopting a Cauchy-like approach to the problem. The first omission is not very important, since it is virtually certain that there is no physical polarity along the direction L in any of the normal liquid crystal substances which were discussed by Oseen; and kl is then zero.The second omission is of more general significance : but (s1s2 + tlt2) relates to an essentially three-dimensional kind of curvature. It occurs in pure form (with (s1 + s2) and (?I + t 2 ) equal to zcro) in what we may call " saddle-splay ", when the preferred directions L are normal to a saddle-surface; and then contributes a positive term to the energy if (k22 + k24) is positive.It is zero if L is either constant in a plane or parallel to a plane. It may be disregarded in all the simpler configurations which would be employed for the determination of moduli other than k24, provided only that (k22 + k24) is non-negative. The most gratifying result of the comparison is to notice that there is one term in Oseen's expression which can be omitted, namely the last, since K12 is always zero under the conditions which justify omitting the term kl(s1 + s2). For many purposes we actually have a simpler result than Oseen's. In detailed application, he in fact assumed K12 = 0, supposing this to be an approximation. We may conveniently use relations (23) to cast eqn.(21) into co-ordinate-free notation : g' Skll(V . L - SOY + 3k220.. V x L + to)2 + .Izk33((L. V)L)2 -. k12(V * L)(L V x L) - %k22 + k24)((V L)2 where 3L 2 3L 2 3L 2 + (G) +($) -+-($), or (V . L)2 + (V x L)2 - (VL: AL) in a fully arbitrary system of co-ordinates. 3. PARTICULAR CASES 3.1. THE SMECTIC STATE According to Oseen, the smectic state corresponds to the vanishing of all the moduli except k22 and k33 (our notation). The (free) energy is then minimized when L . V x L = O , ( L . V ) L = O . (26) The second of these equations states that a line following the preferred direc- tion of molecular axes is straight : the first, that the family of such straight lines is normal to a family of parallel surfaces (defining the surface parallel to a given curved surface as the envelope of spheres of uniform radius centred at all points on the given surface).Hence he formally predicts the geometry explicable by molecular layering without apparently appealing to the existence of layers : their real existence he explains separately by use of his Q integral. The present writer considers this a perverse approach. We need to explain why k22 and k33 are so large that the other moduli are negligible, and can do so from the existence of the Iayering. There is no real need to employ the theory of curvature strainsF. C. FRANK 25 to interpret smectic structures, until one requires to deal with small departures from the geometrically interpretable structures, which will be permitted if the other moduli are merely small, instead of vanishing, compared with k22 and k33. Before leaving the subject of the smectic state, we may remark that to explain deformations in which the area of individual molecular layers does not remain constant, it is necessary to invoke dislocations of these layers.It is likely that these dislocations are usually combined with the focal conic singularity lines, being then essentially screw dislocations. 3.2. THE NEMATIC STATE The nematic state is characterized by so = 0, to = 0, k12 = 0, corresponding to the absence both of polarity and enantiomorphy. There are four non-vanishing moduli, kll, k22, k33 and k24. The last has no effect in “planar” structures. Hence Zocher’s 3 three-constant theory is justified (his kl, k2, kt are the same as k l l , k33, k22).Formerly, this appeared to be only an approximate theory, negiect- ing k12 which appeared in the theory of Oseen. The simplest way to measure the moduli is to impose body torques by imposing magnetic fields. k22 can be determined straightforwardly; kll and k33 are more difficult to separate from each other. There is evidence that they are about equal. Using the experimental data of Frkederickz and of Foex and Royer, Zocher shows that if they are equal the value for p-azoxyanisole is 1.0 x 10-6 dynes. Information about the rdative magnitude of these moduli is obtainable from the detailed geometry of the “ dis- inclination ” structures described in $ 4 . The fact that there is not another unknown in k12 ought to encourage a complete experimental determination of the moduli for some nematic substances.3.3. THE CHOLESTERIC STATE Enantiomorphy, either in the molecules of the liquid-crystal-forming substance, or in added solutes, converts the nematic into the cholesteric state. kz + 0, and the state of lowest free energy has a finite twist, 10 = k2/k22. In the absence of othcr curvature components, there is only one structure of uniform twist, in which L is uniform in each of a family of parallel planes, and twists uniformly about the normal to these planes. The torsion has a full pitch of 2 r / t o : but since L and - E are physically indistinguishable, the physical period of repetition is “/to. When, as is usually the case, this is of the order of magnitude of a wave- length of light or greater, it can be measured with precision by optical methods.Some additional information should be obtainable by perturbing this structure with a magnetic field. Uniform twist can also exist throughout a volume when the repetition surfaces are not planes, but curved surfaces : for example, spheres, though in this case there has to be at least one singular radius on which the uni- formity breaks down. Since the cholesteric substances, like the smectic substances (though for entirely different reasons) give rise to structures containing families of equidistant curved surfaces, their structures show considerable geometric similar- ity to those of the smectic substances. This was appreciated by Friedel, who also realized that it was misleading, and that the cholesteric phases are in reality thermo- dynamically equivalent to nematic phases.3.4. THE CASE kl 0 If Icl + 0, the state of lowest free-energy density has a finite splay, SO = kl/kll. This can only exist when the molecules are distinguishable end from end, and there is polarity along L in their preferred orientation. Then, almost inevitably, the molecules have an electric dipole moment, and therefore, unless the material is an elcctric conductor, the condition v . L + 0 implies v . P + 0 (where P is the electric polarization), so that finite splay produces a space-charge. As a second consideration, it is not geometrically possible to have uniform splay in a three- dimensionally extended region. The simple cases of uniform splay are those in26 LIQUID CRYSTALS which L is radial in a thin spherical shell of radius 2/so, or a thin cylindrical shell of radius l/so.These considerations relate this hypothetical polar class of liquid crystals to the substances which produce " myelin figures " : but since the only allowed structures for this class have a high surface-to-volume ratio, a theory of their Configurations which does not pay explicit attention to interfacial tensions will be seriously incomplete. 4. " DISINCLINATIONS " The nematic state is named for the apparent threads seen within the fluid under the microscope. Their nature was appreciated by Lehmann and by Friedel. In thin films they may be seen end on, crossing the specimen from slide to cover- slip, and their nature deduced from observation in polarized light.In this position they were named Kerne and Komergenzpunkte by Lehmann, positive and negative nuclei (noyaux) by Friedel. They are line singularities such that the cardinal direction of the preferred axis changes by a multiple of n on a circuit taken round one of the lines. They thus provide examples of the configurations excluded (under the name of " Moebius crystals ") from consideration in the establishment of a general definition of crystal dislocations.4 In analogy with dislocations, they might be named " disinclinations ". It is the motion of these disinclination lines which provides one of the mechanisms for change of configuration of a nematic specimen under an orienting influence, in the same way as motion of a domain boundary performs this function for a ferromagnetic substance.It is the lack of a crystal lattice which allows the discontinuities of orientation to have a line topology, instead of a topology of surfaces dividing the material into domains, in the present case. Disinclination lines occur in cholesteric as well as in nematic liquid crystals. The actual configuration around disinclination lines was calculated by Oseen for the case kll = k33, k12 = 0, the latter assumption actually being exact. Then if L is parallel to a plane and $ is the azimuth of L in this plane, in which XI, x2 are Cartesian co-ordinates, the free energy is minimized in the absence of body torques when (27) The solutions of this equation representing disinclinations are (28) n being an integer.These configurations are sketched in fig. 2. Changing $0, merely rotates the figure in all cases except n = +2, for which three examples are shown. Of these, the first or the third will be stable, for a nematic substance according as k33 or kll is the larger, In the other cases, non-equality of kll and k33 should not make drastic changes, but only changes of curvature in patterns of the same topology. Thus, for n = -2 or - 1, if k33 is larger than kll the bends will be sharpened, and conversely. This would be observed as a non-uniform rotation of the extinction arms with uniform rotation of polarizer and analyzer. The ratio of kll and k33 can thus be determined from a simple optical experiment. In cholesteric substances 40 is not constant, but a linear function of the co- ordinate x3, normal to the x ~ , x2 plane : except for the case n = 2, with kll =I= k33, which should show a periodic departure from linearity near the core, from which the relative magnitudes of k22 and (kll - k33) could be deduced, though the observations would not be simple.Oseen was puzzled at the non-occurrence of configurations corresponding to a q p X 2 + a2+/3p = 0. 4 = 3n$ + $0, tan $ = XZ/Xl, + = c In r + const., r = (x12 + x&. (29) The reason is obvious : unlike n in (28), c is not restricted to integral values, and can relax continuously to zero. Alternatively stated, this configuration requires an impressed torque at the core for its maintenance.F. C. FRANK 27 At the time Friedel and Oseen wrote their papers, the values of the disinclina- tion strength n which had been observed were - 2, - 1, 1, 2.Since then the case n = 4 has been observed by Robinson 5 in the radial singularity of a choles- teric " spherulite". The non-occurrence of high values of I n I is explained by the fact that the energy is proportional to n2. The fact that higher values than one occur indicates a relatively high energy in the disorderly core of the disinclin- ation line, which must be as large as its field energy so that it becomes profitable for a pair of disinclinations to share the same core. n = - 2 4- -1, n- - I Q- -'iY n- I 9- t v FIG. 2. 5. k24 Let us leave aside the question of how to determine k24, necessarily involving the observation of three-dimensional curvatures, until we have better information about the moduli of plane curvature, kll, k22 and k33. 6. RELATIONSHIP TO THE ORDINARY ELASTIC CONSTANTS Let us take note that the molecular interactions giving rise to liquid crystal properties must also be present in solids. This indicates that conventional elastic theory is incomplete : the direct curvature-strain moduli should also be included. This is true, but does not seriously invalidate the accepted theory of elasticity. Consider the bending of a beam, of thickness 2a, to a radius R. Then the stored free energy according to ordinary elasticity theory is gE = Eu2/24R2, where E28 LIQUID CRYSTALS is Young’s modulus. The stored free energy arising from a curvature modulus k (correspmding to kll or k33 according to the molecular orientation in the beam) would be gk = k/2R2. gk/gE = 12k/Ea2. Taking k as 10-6 dyne, and E as 1010 dyne/cm2, this ratio is unity when a is about 3.5 x 10-8 em, and negligible for beams of thickness as large as a micron. Thus, on the visible scale, the curvature-elastic constants are always negligible compared with the ordinary elastic constants, unless the latter are zero. Their ratio is 1 Oseen, Trans, Faraday SOC., 1933, 29, 883. 2 Friedel, Anales Physique, 1922, 18, 273. 3 Zocher, Trans. Faraday SOC., 1933,29,945. 4 Frank, Phil. Mag., 1951, 42, 809. 5 Robinson, this Discussion.

ISSN:0366-9033    

DOI:10.1039/DF9582500019

出版商:RSC    

年代:1958

数据来源: RSC

摘要:

LIQUID CRYSTALLINE STRUCTURE IN POLYPEPTIDE SOLUTIONS. PART 2. BY CONMAROBINSON, J. C. WARD AND R. B. BEEVERS Courtaulds Ltd., Research Laboratory, Lower Cookham Rd., Maidenhead, Berks Received 1 1 th February, 1957 The model previously published describing the arrangement of the molecular orientation in the cholesteric-like twisted structures found in solutions of poly-y-benzyl-L-glutamate and poly-y-methyl-L-glutamate has been confirmed. The relationship of this structure to that found in a racemic solution of the L and D enantiomorphs of poly-y-benzyl- glutamate is explained. A tentative model of the arrangement of the rnolecirles in the twisted structure is discussed in the light of X-ray and other evidence. In part 1 1 of this series a liquid crystalline structure which was found in bire- fringent solutions of poly-y-benzyl-L-glutamate (PBLG) and of poly-y-methyl-L- glutamate (PMLG) was described, This structure in a number of ways resembles that formed by various esters and ethers of cholesterol 2 and is characterized by a helical twist of very large and uniform pitch. A model describing the three- dimensional distribution of the molecular orientations in space was proposed as being consistent with the polarization-microscopic observations.This model, which has since received considerable confirmation, is shown in fig. 1. FIG. 1.-Model of the twisted structure. A', Y and 2 are Cartesian co-ordinates. 5 and r) are given by the equations : 2 n z 2 n z 8 = XCOS-+ P Ysin- P ' 2.572 2nZ P P y = Yccs--Xsin--, so that 5, r ) and 2 form a twisted co-ordinate system.The rod-like inolecules all lie at right-angles, or nearly at right-angles, to Z, the axis of torsion and parallel to 6. (The planes drawn in fig. 1 are not intended to indicate that the molecules are segregated into planes, the polarization microscope having provided no evidence on this point.) Since the highest refractive index is for light vibrating parallel to the long axes of the molecules, if the structure is observed in a direction parallel to Y, both the refractive index and the retardation will show a maximum value for every 2930 LIQUID CRYSTALLINE STRUCTURE IN POLYPEPTIDE SOLUTIONS path for which 8 is at right-angles to Y and a minimum value where it is parallel to Y. This gives rise to periodic lines a distance S apart (where 2s = P, the pitch of the torsion) which are visible even in natural light, and similarly spaced bands of retardation colours when observed between crossed nicols.If the observation is made in a direction parallel to 2 no periodicities are seen but only the uniform areas described in part 1. For light travelling in this direction, however, the structure has a very high form optical rotatory power which can be shown to be a function of the torsional pitch. (This form optical rotatory power of the multi- molecular structure is distinct from, and greater by several powers of ten than, the form optical rotatory power arising from the a-helical configuration which the individual molecules of these polypeptides are known to assume.3s4) The value of S is dependent on solvent, concentration and temperature, but in any solution in which these are uniform, the structzrre will be the same and as shown in fig.1. On the other hand the orientation of the Cartesian frame of reference X, Y, 2 may change continuously from one part of the solution to another, and produce a particular macroscopic pattern of orientation which ex- tends throughout the birefringent phase. The texture * of a specimen of the material is the three-dimensional pattern thus produced, but the structzrre of any smallt cube of material will be the same throughout every texture though its orientation will be different. Fig. 10 and 11 of part 1 show two different textures which formed in glass capillaries. In the first the visible lines are everywhere parallel to the axis of the capillary; in the other they show a more complicated arrangement, but in each the structure is as in fig.1. When the concentration of the polypeptide does not exceed a concentration A (dependent on temperature and molecular weight) the solution is isotropic, while above a concentration B only the birefringent phase exists. Between A and B both the isotropic and the birefringent phase exist in different proportions, though the concentration of each phase remains constant in accordance with the phase rule. In this two-phase system the birefringent phase may be found dis- persed in the isotropic phase in the form of spherical droplets which show charac- teristic spiral patterns (fig. 5 and 6, part 1) when the microscope is focused on a plane through their centre) and which show the same periodicities as the texture of the undispersed phase of equal concentration.Each of these spherulites shows a single radial line of dislocation, so that the sphere has polarity. A complete description of the molecular orientation in the spherulitic texture which would give rise to these patterns has been put forward by Prof. M. H. L. Pryce and Prof. F. C. Frank, as we shall explain in the appendix. It will be seen that their very elegant treatment is consistent with the supposition that every very small volume of the spherulite has the structure shown in fig. 1. This considerably strengthens our confidence in the correctness of our model. Further confirmation has been obtained from quantitative measurements of the optical rotatory power.Several attempts have been made to explain the optical rotatory power of cholesteric liquid crystals.5~ 6.7 De Vries7 has deduced a theoretical expression for this, a simplified form of which, in terms of observable quantities is 0 =- 4.5 x 104n2PfX2 where 8 is the optical rotation observed parallel to the axis of the twisted structure in deg. fmm, n is the birefringence of what we may refer to as the untwisted medium, h is the vacuum wavelength of light in microns and P is the pitch of the helix in microns. The negative sign indicates the optical rotation is in the opposite sense to the twist of the helix. No data were available to de Vries which would have allowed him to verify his relationship but the polypeptide solutions with their * This word has been used by Friedel in his description of liquid crystals.ti.e. small compared with the dimensions invoived in describing the pattern, but containing a large number of molecules.C. ROBINSON, J . C. WARD AND R . B . BEEVERS 31 large spacings which can conveniently be varied by altering the concentration or the solvent are suitable for providing such data. As has already been briefly reported by Robinson and Wards it has been possible to confirm this equation by measurements on 14 different solutions, covering a range of both concentra- tion and solvents. It was not possible to obtain a dependable value for n from the twisted structure in the optically active polypeptide solution, but it was found that a racemic mixture of the D and L enantiomorphs formed a birefringent solu- tion which, when introduced into a glass capillary, became highly oriented, and exhibited a constant birefringence throughout the solution (except near the menisci).The value of this birefringence was reproducible, the material in fact having formed a single uniaxial liquid crystal. This nematic structure which is obtained in the racemic mixture corresponds, we believe, to the untwisted form of the structure in the L enantiomorph solution. The value of the birefringence so obtained agrees with that calculated (using the above formula) from the optical rotatory power of the several solutions of PBLG. The results, therefore, not only show that de Vries's equation holds for the PBLG structures but demonstrates quantitatively that the " cholesteric " structure obtained with either enantiomorph may be looked upon as a twisted form derived from the nematic structure, the former arising as a result of the left- or right-handedness of the L or D enantio- morph.This work will be reported in more detail in a later paper. We may therefore have some confidence that our model correctly represents the distribution of molecular orientation within the structure. This in itself tells us little concerning the molecular distribution and how it varies with the concentration, but some insight into this has been obtained by other means as we shall explain later. Nine preparations of PBLG were used covering the range of molecular weight shown in table 1. The preparations were purified by dissolving in chloroform and precipitated by poured into a large excess of methanol. The specific preparation R 3 R 10 R 4 R 2 R S R 8 R 9 R 6 R 11 TABLE 1 'ISPJC 0-106 0.188 0.190 0.269 0.500 0.68 1.1 1 1 *22 1 -92 residues per molecule 60 90 102 135 274 385 673 728 1255 viscosities of their 0.5 % solutions were determined, and their molecular weights estimated by using Doty, Bradbury and Holtzer's 3 relationship connecting the molecular weight of this polypeptide with the limiting viscosity.The preparation of poly-y-benzyl-D-glutamate (PBDG), was of fairly low molecular weight as were the two samples of poly-y-methyl-L-glutamate (PMLG). All observations were made in a room thermostatted at 22" C. While not under observation solutions were kept in a water thermostat at this temperature.EXPERIMENTAL Solutions were made up by weighing the polymer and solvents into 2 ml stoppered bottles. After prolonged shaking on a slow stirrer and then standing until the regular structure appeared, the visible periodicity was measured with a low-power microscope while the bottle was immersed in a liquid of suitable refractive index. The time required for the regular structure to appear varied from hours to a few weeks according to the32 LIQUID CRYSTALLINE STRUCTURE IN POLYPEPTIDE SOLUTIONS 5 0 - 4 0 c - E 8 30- --? - c 0 .- L E! 2 0 - QI c 0 10- system being observed. The volume of the solution was calculated from the density of the solvent and the density of the polymer (taken as 1.3), any contraction on dissolving being neglected. Some of the smallest values of S were measured by filling a glass capillary with the solution and observing the sealed capillary in an immersion liqJid under higher magnification. The optical rotation was measured in fused glass cells fitted with ground glass stoppers ar,d having parallel sides 1 mm apart.A polarization micro- scope was used for this purpose. - DEPENDENCE OF A AND B POINTS ON MOLECULAR WEIGHT Fig. 2 and 3 show how the A point (the concentration above which the isotropic phase cannot exist) and the B point (the lowest concentration at which the birefringent phase can exist) depend on the molecular weight. A and B are in m1/100ml. The A points S I I * I C * ~ * ~ ~ ~ 0 - Apoints 8- Bpoints FIG. 2.-Molecular weight dependence of the A and B points. PBLG in dioxan.1 I . a . . . . . . . 0 2 200 4 0 0 bOO 8 0 0 1000 1 2 0 0 residues per molecule FIG. 3.-Mo~ecdar weight dependence of the A and B points. PBLG in methylene chloride.C . ROBINSON, J . C . WARD A N D R . B . BEEVERS 33 could be determined with little difficulty within rather wide limits, but the B points could only be determined approximately owing to the difficulty of detecting small amounts of the isotropic phase when dispersed in the birefringent phase, and because of the long period required to bring about separation. It will be seen that A and B have much the same values for either dioxan or methylene chloride as the solvent. A similar impression was obtained with the other solvents less systematically studied : chloroform, rn-cresol, dichloracetic acid.The results show how increasing the molecular length extends the concentration range over which the birefringent phase is stable. Bernal and Fankuchen 9 suggested that for aqueous birefringent solutions of tobacco mosaic virus which will be discussed in a later section, the A point might be inversely proportional to I and the B point to I*, where I is the length of the molecule. It is clear that these relationships do not hold for the polypeptide solutions. DEPENDENCE OF s ON CONCENTRATION Fig. 4 and 5 show the dependence of S, the visible periodic spacing, on concentration, sol- vent and molecular weight. The B point determined the lower concentration limit of obser- vation (the spacing as stated remaining constant between A and B) while the upper limit O \ , , , , , , 2:o 2 0 4 0 b 0 8 0 100 concentra tion(m>lOOml) FIG.4.-Double logarithmic plot of S against concentration. PBLG in dioxan. was determined by the viscosity preventing observations being made within a reasonable time. The results for dioxan (fig. 4) show that S is proportional to l/C2 and independent of molecular weight. Similar results obtained for PBLG (R5) and for the two samples of PMLG in rn-cresol are shown in fig. 5. The value of S obtained at a given concentration depends to a marked extent on the solvent used. Thus, for a concentration of 20 m1/100 ml the values of S for PBLG were (approximately) : CHC13 0.10, CHC12 0.04, dichloracetic acid 0.03 and rn-cresol0-007 mm. The results obtained in chloroform and methylene chloride between 20 and 30 m1/100 m! were, however, too erratic to allow the slope of the curve to be determined, sometimes a comparatively large spacing being obtained which after a few days changed to a lower B34 LIQUID CRYSTALLINE STRUCTURE I N POLYPEPTIDE SOLUTIONS value.It is not yet clear whether this was due to impurities or to the structure being less stable in these solvents. Yang and Doty 10 have shown from the dispersion of the optical rotation that the molecules of PBLG are in the randomly coiled configuration in isotropic solutions in dichloracetic acid. It was therefore interesting to find the regular periodicities and optical rotation associated with the twisted structure in the more concentrated solutions (see plate la). However, Downie, Elliott, Hanby and Malcolm 11 have shown that if such a 8 - R 5 0 - PMLC,I 0 - PMLC,2 I I -I * r'o 2 0 4 0 concentration (m1;/10ornl.) FIG. 5.-Double logarithmic plot of S against concentration.PBLG and PMLG in m-cresol. birefringent solution is heated until it becomes isotropic, the solution shows positive optical rotation ; while the more dilute solutions which Yang and Doty studied showed negative optical rotation. Downie, Elliott, Hanby and Malcolm interpreted this as indicating that the more concentrated solutions were in the a-helical configuration. It would seem, then, that here as in the other polypeptide solutions showing the twisted structure, the molecules are in the a-helix co&uration. X-RAY INVESTIGATIONS One preparation, R 5, of PBLG was used throughout. Dioxan was used as a solvent on account of its relatively high transparency to X-rays.The solutions were introduced into 1-0 mm or 0.5 mm diameter Pantak capillaries having a wall thickness of 0.01 mm. Two distinct methods of filling the capillaries were used. In the fmt the solution was sucked into the capillary with the aid of a micro-syringe and the capillary then sealed ; in the second the desired amount of solid PBLG and solvent were introduced into the capillary, which was sealed, and only used for X-ray irradiation when the uniformity of the microscopic spacings showed that equilibrium had been reached. In either case some solvent was liable to be lost during the manipulation, so S was measured microscopically and C determined from the S against C relationship of fig.4. In the racemic solution of PBLG and PBDG which showed no visible periodicity, the original concentration of the solution was used.PLATE la.-?BLG (R 5 ) in dichloracetic acid ; natural light ; concn. 33-3 rn1/100 ml ; s = 18.4 >: 10-4 crn. [To face page 34PLATE 1 (b), (c), (d). PLATE 1b.-X-ray diffraction pattern ; PBLG in dioxan ; capillary vertical ; concn. PLATE ]lc.-X-ray diffraction pattern ; PBLG in dioxan ; capillary vertical ; concn. 46 m1/100 ml. PLATE Id.-X-ray diffraction pattern ; racemic solution of PBLG and PBDG ; capillary 38.0 ml/l00 ml. (The outermost ring is due to the solvent.) vertical ; total concn. 20.8 m1/100 ml.C. ROBINSONy J . C. WARD AND R . B . BEEVERS 35 The first method of filling generally gave some limited area of the capillary where the visible lines were parallel to the capillary axis (cf, part 1, fig.10). With the second method there was no shearing to produce orientation, and the appearance more resembled fig. 11 of part 1. We shall refer to the first of these arrangements as the oriented texture and the second as the unoriented texture. The photographs were taken in Z I ~ C U O on flat film, the capillaries being vertical. Nickel-filtered copper Ka radiation was used in conjunction with a collimator and a 0.5 mm pinhole. The X-ray photographs of the isotropic solutions of PBLG showed no reflections in- dicating spacings of less than 508, that were not given by the solvent. The birefringent solutions all showed a ring, the diameter of which depended on the concentration, indicating a spacing d which changed continuously with concentration from 18 to 29A (see plates l b and lc).As the concentration increased, this ring became less diffuse. The prepara- tions with oriented texture showed in addition two more or less pronounced equatorial FIG. 6.-Double logarithmic plot d against concentration. R5 in dioxan. spots or arcs on this ring. In no case was a photograph obtained showing only equatorial spots, and in no case were reflections indicating any other spacing which varied with the concentration observed. Although efforts were made to focus the beam on the best oriented portion of the structure, this, especially in the more fluid preparations, often deteriorated or changed its position before the experiment was complete, and it is therefore doubtful if any of the pictures corresponded to a completely oriented texture.The experimental data showing how this X-ray spacing, dy depended on the concentration are given in fig. 6 as a double logarithmic plot. A racemic solution containing equal proportions of PBLG and PBDG (total poly- peptide concentration = 21 m1/100 ml), showing very regular orientation in the polar- ization microscope,8 gave a ring with more pronounced equatorial spots (plate Id), in- dicating a value 23 8, for d. This does not quite fall on the curve for PBLG (fig. 6), but the discrepancy may be due to accepting too low a figure for the concentration which may have increased by evaporation while filling the capillary. There was some reason to suspect that the orientation when actually irradiated was not as perfect as that shown in the microphotograph previously published.* Unfortunately owing to the very small quantity of PBDG available only one concentration of the racemic solution was investigated. The value for 100 % PBLG included in fig.6 was taken from the data of Bamford, Hanby and Happey.12 The full line is the best straight line drawn through this and the other experimental points. The data, though insufficient to allow us to determine the structure, may be discussed in relation to models which are suggested by the other properties of PBLG solutions and our general knowledge of liquid crystalline solutions. The molecules of PBLG and PBDG being in the a-helical configuration may be looked upon as rigid rods from which the side chains, when fully extended,36 LIQUID CRYSTALLINE STRUCTURE IN POLYPEPTIDE SOLUTIONS project radially.The length of each molecule (in A) is equal to the number of residues it contains multiplied by 1-5,13 while the diameter 2r of the cylinder described by the side chains when the molecule rotates about its axis is 28.2A, a value obtained from atomic models and the known dimensions of the cc-helix. It seemed a reasonable possibility that the uniaxial liquid crystalline structure of uniform birefringence given by the racemic solutions might have the molecules arranged parallel and in a two-dimensional hexagonal array, as was found by Bernal and Fankuchen19 to be the case in solutions of tobacco mosaic virus (T.M.V.). Sufficiently concentrated oriented solutions of T.M.V.give four re- flections on the equator corresponding to the first four reflections of planes parallel to the axis of orientation having the spacings d, d / d 3 , d / 4 4 , d/2/7. On dilution this relationship is maintained as long as the diminished intensity of the higher order reflections allows them to be observed, and d remains proportional to C-4. These relationships would be expected from the arrangement shown in fig. 8 or 9 (when there is no twist about the Z-axis) if no measurable dilution takes place parallel to the length of the molecules, the molecules moving apart in direc- tions at right-angles to their axes so as to fill the available space uniformly. It should be remembered, however, that the birefringent polypeptide solution is neither simply a liquid nor a crystal, but may be looked upon as either a some- what disordered crystal, or as a liquid arranged in a partially ordered way, so that even if dilution parallel to the length of the molecules was negligible, the arrange- ment in the plane at right-angles to their length (the 7, Z plane) might have any degree of order between hexagonal and the completely random.It follows that the twisted structure of the PBLG solutions might similarly be found to be a structure in which the torsion is superimposed on a hexagonal array of parallel molecules, 2, the axis of torsion lying, for instance, either as in fig. 8 or 9. The amount of torsion per molecule required to produce the observed values of S, and of the optical rotation is very small and its effect on the structure of a small region which is nevertheless sufficiently large to give sharp X-ray re- flections may be neglected.Thus only the orientation of the hexagonally packed rods, and not the distance between the planes, is affected by the structural twist. The broken line in fig. 6 is calculated on the assumption of a two-dimensional hexagonal array with no dilution parallel to the long axes of the molecules. Its equation is w1/3 x 1024 - 1-61 x 104 - 2Nd2qP d2 C = where C is the concentration in m1/100; W = 219, the residue weight; N = Avogadro’s number ; d is the distance between the (1010) planes in A ; q = 1.5 A, the length of the projection of one residue on the axis of the a-helix 13 and p = 1-3, the assumed density of the polymer.The full straight line through the experi- mental values has a slope of approximately - 2.3 instead of - 2.0, but is nowhere far removed from the calculated curve. If this difference in the slope is considered to be significant, in spite of the considerable size of the experimental errors, it may indicate that there is some dilution along the 6 axis. It is of interest to examine theoretically the X-ray diagrams which would be expected from some more fully defined twisted and untwisted structures and to compare these with the observed patterns. We shall assume that the spacings of between 18 A and 29 A which are indicated by the strong X-ray reflection arise from planes or approximations to planes which lie parallel to the direction ( of preferred orientation.We shall further assume (throughout this discussion) that the molecular axes lie exactly parallel to the 6 axis, Fig. 7 summarizes the expected patterns. An oriented texture of the twisted structure is defined to be an arrangement of the structure in which the Z-axis (fig. 1) lies radially in the capillary, the X-axis longitudinally, and the Y-axis tangentially. A disoriented texture is one in whichC. ROBINSON, J. C. WARD AND R . B. BEEVERS 37 these axes, although still rectangular at any point, are oriented in a random way in different parts of the capillary. A hexagonal arrangement is defined to be a hexagonal arrangement of parallel rods as shown in fig. 8 or 9. A random P B LC (twisted structures) o r ie n ted tex r u re arranqement -, hexaqonal random case ,@ -@ (d 1 f fuse) (ii) @ case 2 PBLC+PBDC (untwisted structure’) oriented texture hexaqonal a rra nqe men t random arranqement (d i f f u J e) (iii) disorien red texture hexaqonal random disoriented texture (diffuse) (4 FIG.7a and b.-Expected X-ray diffraction patterns from some arrangements of parallel rod-like molecules.38 LIQUID CRYSTALLINE STRUCTURE IN POLYPEPTIDE SOLUTIONS arrangement is defined to be an arrangement of parallel rods in which the nearest neighbour distance in the 7 2 plane varies in a random manner. An oriented texture of the untwisted structure is one in which the [ (or X ) axis is parallel to the axis of the capillary. Since only one spacing has been observed, only the first hexagonal spacing d has been considered, and only the corresponding principal maximum for random arrangements. The special simple case of the untwisted mixture of D and L FIG.8.-Hexagonal arrangement Case 1. The axis of torsion, Z, to the (1010) plane. of rods. is normal 3 FIG. 9.-Hexagonal arrangement of rods. Case 2. The axis of torsion, 2, lies along the crystallographic axis u. polypeptides is first assumed to exist as a perfectly hexagonal arrangement of rods, and secondly as a random arrangement. There are two likely twisted hexagonal arrangements (case I and case 11) which will be considered. CASE THE AXIS OF TWIST (2) BISECTS THE ANGLE BETWEEN THE CRYSTALLO- GRAPHIC AXES (x AND - u, SAY) (fig. 8). The (1010) planes give equatorial spots. The (1100) and (0110) planes give equatorial arcs extending 60" on either side of the equator (fig.7a (i)). CASE 2 . T H E AXIS OF TWIST (2) LIES ALONG ONE CRYSTALLOGRAPHIC AXIS (SAY U) (fig. 9). The (1100) planes give rise to a continuous ring. The (1010) and (Olio) planes give equatorial arcs which extend only to 30" on either side of the equator (fig. 7a (v)). (The Z-axis mentioned above is as defined earlier in the paper and not the conventional z crystallographic axis.) The experimental patterns obtained with the more oriented textures of the twisted structure (given by the first method of filling the capillary) are composed of a continuous circle showing greater density over two equatorial arcs (plate lb and c). This is in good qualitative agreement with that predicted by the hexagonal structure, case 2 (fig. 7a(v)). The diffuseness of the patterns decreased within, creasing concentration. The disoriented textures (second method of filling)C .ROBINSON, J . C . WARD AND R. B . BEEVERS 39 only gave a diffuse ring as predicted. The untwisted structure in the racemic solution showed diffuse equatorial spots on a fainter continuous ring which would be predicted from a somewhat disoriented texture of an imperfect hexagonal arrangement. We may conclude that all the X-ray pictures we have are consistent with the models we have put forward. The absence of the higher-order reflections in the photographs is not evidence against the possibility of a hexagonal arrangement. In T.M.V., Bernal and Fankuchen found only one, and at most two, reflections in comparable concentra- tions, four reflections only being obtained in the dried gel.It is understandable that the reflections from the higher order planes would be less intense the more fluid the system. On the other hand the absence of any other reflection of com- parable intensity which would have indicated a primary spacing which differed from that expected from hexagonal spacing accords with the models we have put forward while the presence of the equatorial spots in the photographs of the more oriented textures shows that the arrangement in the 72 plane is far from completely random. In the analysis presented, it has been assumed that the molecules are parallel to the &axis. The fact that the birefringence of the untwisted structure as cal- culated from the optical rotatory power of the twisted structure is (at least ap- proximately) independent of the concentration supports this assumption, as do the considerations in the next section which show how closely packed the molecules lie in the oriented birefringent solutions. Further observations under more precisely defined conditions are clearly re- quired but on the present evidence an arrangement of molecules in the 7 2 plane, not completely hexagonal and not completely random seems most probable for PBLG solutions, the whole structure being twisted about the Z-axis so as to give the observed microscopic periodicity.Some comparatively small dilution may take place along the &axis but no regular spacings in this direction are observed. FREEDOM OF MOVEMENT OF THE MOLECULES Although this picture must remain tentative it may be fruitful to consider certain consequences which follow if the spacing given by a hexagonal arrange- ment is assumed as a first approximation. The distance in the 7 2 plane between the molecular centres is (see fig. 8) 2 , 4 4 3 ~ 4 .. The diameter 2r of the cylinder described by the PBLG molecule with side chains fully extended by rotating about its axis is 28.2A. (This was obtained by adding the known distance of the /3 carbon atom from the axis of a-helix, 9.50& to the length of the remainder of the side chain obtained from measurements with Courtauld atomic models.) Hence D = (2d/1/3) - 28*2A, where D is the nearest approach of two side chains in neighbouring parallel molecules at a given concentration. Table 2 shows how the value of D at the B point depends on the molecular weight of PBLG.The molecular axes can approach still nearer, since as can be shown with models the side-chains are just far enough apart to allow interleafing. There is also the possibility of the side chains becoming folded. In column 5, 4 = tan-1 (DIZ), where I is the length of the molecule, is given. This is the angle which a molecule must rotate through at the concentration of the B point in order to come in contact with the extended side chains of a neigh- bouring molecule. These values show that even at the lowest concentration at which the birefringent phase exists for each molecular weight, very little dis- placement, from the parallel position could bring two neighbouring molecules into contact. It is easy to see how the parallel array once formed will not readily be destroyed.In the last column is given 8 (= mils) which is the angle of twist40 LIQUID CRYSTALLINE STRUCTURE I N POLYPEPTIDE SOLUTIONS per molecule in the 2 direction. Since, for the concentrations of dioxan solutions which have been investigated, S = kl/C2 and d = k2/C3, where kl and k2 are constants, we see that 8 = k3CQ. So we find that the angle of deviation from the parallel position is not only very small even in the higher concentrations, but decreases on dilution. preparation TABLE 2 . 4 AND 0 AT B POINT FOR PBLG IN DIOXAN I = mean length of molecules A B point (ml/ 100 ml) D at B point A d = tan-l(D/Z) e = g x 180" R 4 156 32.6 - 3.8 - 5.4' R 5 311 13.9 + 7.0 1" 36' 1.5' R 9 1010 10.1 + 12.2 0" 42' 0.9' R 11 1883 9.1 + 14-4 0" 26' 0.7' If we consider a polypeptide molecule in the a-helix configuration as presenting a helical arrangement of dipoles, then in the PBLG solutions where all the spirals are of one sense (right-handed) we can expect that the forces of attraction between molecules arising from these dipoles would tend to impose a unidirectional twist on the array of parallel molecules. The smallness of the angle and the fact that it decreases continuously on dilution suggests that it arises from a dynamic equilibrium.No accurate figures for the temperature coefficient of S have been obtained owing to the marked hysteresis, but it would seem that the value of S is approx- imately doubled on heating a dioxan solution from 20 to 40°C.The twisted structures which we have described as forming spontaneously in certain polypeptide solutions seem to be very similar to those formed by choles- terol derivatives. The much longer rigid molecules of the polypeptides, however, allow the structure to exist even at considerable dilution, while the larger periodicity which is then observed lends itself more readily to quantitative observation. Although more work is needed before the structure is fully understood, its general nature and its relationship to the nematic or untwisted structure now seems to be clear. The twisted structure is more highly organized than other liquid crystalline systems which have been described. It combines a high degree of organization with a left- or right-handed twist which is characteristic of its composition and environment. The solutions may nevertheless be surprisingly fluid 1 and may dissolve other components without the qualitative nature of the structure being changed. It is conceivable that such highly organized, yet reproducible, liquids may play a role in chemical reactions involving some of the highly specific, optically active molecules present in biological systems.However, a periodicity of the same order as that found in PBLG solutions would easily be overlooked in biological units having a diameter not much greater than S, the repeat distance, while the form optical rotation would also be overlooked in a thin specimen. It might therefore be rewarding to re-examine some biological systems with these points in mind. All the polypeptides used in this research were synthesized by Mr.W. E. Hanby of this laboratory. The X-ray photographs were taken by and discussed with Mr. L. Brown of Courtaulds' Acetate and Synthetic Fibres Laboratory, Coventry. We are grateful to Prof. M. H. L. Pryce and Prof. F. C. Frank for discussions which led to the interpretation of the spherulite structure given in the appendix, and to Prof. J. D. Bernal for further discussions. Our thanks are due to Dr. C. H. Bamford for valuable criticism. We are much indebted to Mr. J. P. Hetherington for much painstaking assistance throughout this research.C . ROBINSON, J . C . W A R D AND R . B . BEEVERS 41 APPENDIX THE SPHERULITIC TEXTURE A model of the way in which the molecules are arranged to form the special “ texture ” of the twisted structure which arises in the spherulite has been put forward in a private communication from Prof.M. H. L. Pryce and Prof. F. C. Frank. This was described by them in the following words. “ Consider a spherical surface, and the family of small circles and one great circle on this sphere which are all tangent to a line PQ itself tangent to the sphere at P. This family of circles corresponds to the intersections of the sphere and all planes passing through PQ. It also corresponds to a stereographic projection on to the sphere, for the pro- jection point P, of a family of parallel straight lines ruled on a plane normal to the diameter through P, all these straight lines being parallel to PQ. Now repeat the construction using a second line PQ’, likewise tangent to the sphere at P, but making an angle a with FIG.10. FIG. 11. PQ. Now, by the conformal property of the stereographic projection, at every inter- section of a circle of the first family with a circle of the second, the angle at the intersection is ci. We may make a sequence of such families numbered n = 1, 2, 3, . . . making angles nr with the first. If now, instead of doing this on one sphere, we do it on a suc- cession of concentric spheres of radius YO + nc, with the singular point P moving out along a radius, then in each spherical shell we may arrange the molecules with their long axes parallel to the directions of its appropriate family of circles. Then every molecule will be nearly parallel to its neighbours in the same shell (the error being small everywhere except near to the singular radius) and will be inclined at an angle a to neighbours on the same radius in neighbouring shells.On any cross-section of this model, except cross- sections through the singular radius OP, the locus on which molecules make any given constant angle to the plane of section is a spiral. If the angles 8 and 180” f B are equivalent, as they are for this case, it is a double spiral.” Fig. 10 and 11 are tracings obtained by photographing a ball on which a family of circles had been constructed in accordance with this scheme. All the microscopically observed properties of the spherulites are accounted for by the Frank-Pryce model if linear propagation of light through the spherulite is assumed, and if we merely need to42 LIQUID CRYSTALLINE STRUCTURE IN POLYPEPTIDE SOLUTIONS consider a thin slab of material coincident with the plane of sharp focus of the microscope objective. Such an assumption is not quite as drastic as it might seem, since we are here only concerned with tracing the path of the visible spacings, and not with their origin. If we consider a median section of the spheres shown in fig. 10 cut parallel to the plane of the paper and consider light propagated in a direction perpendicular to this plane, then at points A and B the birefringence of the section will vanish. The locus of A and B on successive concentric spheres will appear between crossed plane-polarizers as a dark double spiral, as was observed. When the plane-polarizers were replaced by crossed circular-polarizers, the spiral remained dark, showing that the lack of birefringence on the spiral is not due to a coincidence between the principal directions of the structure and the planes of polarization of the polarizers, but to the fact that the light was pro- pagated parallel to the optic axis of the structure. The above agrument predicts a black double spiral. The observed one was not per- fectly black, presumably because of departure from linear propagation, or to effects arising from material outside the plane of sharp focus of the objective. 1 Robinson, Trans. Faraday Sac., 1956, 52, 571. 2 Friedel, Ann. Physique, 1922, 18, 273. 3 Doty, Bradbury and Holtzer, J. Amer. Chem. SOC., 1956,78,947. 4 Moffitt and Yang, Proc. Nat. Acad. Sci., 1956, 42, 596. 5 Oseen, Trans. Faraday SOC., 1933, 29, 883. 6 Maugin, Bull. SOC. Franc. Min., 191 1, 34, 6, 71. 7 de Vries, Acta Cryst., 1951, 4, 219. 8 Robinson and Ward, Nature, 1957, 180, 1183. 9 Bernal and Fankuchen, J. Gen. Physiul., 1941, 25, 11 1, 120, 147. 10 Yang and Doty, J. Amer. Chem. SOC., 1957, 79, 761. 11 Downie, Elliott, Hanby and Malcolm, Proc. Roy. SOC. A , 1957, 242, 325. 12 Bamford, Hanby and Happey, Pruc. Roy. SOC. A, 1951,205,30. 13 Pauling, Corey and Branson, Proc. Nat. Acad. Sci., 1951, 37,205.

ISSN:0366-9033    

DOI:10.1039/DF9582500029

出版商:RSC    

年代:1958

数据来源: RSC

摘要:

THE STRUCTURE OF THE LIQUID-CRYSTAL PHASES OF SOME SOAP + WATER SYSTEMS BY V. LUZZATI, H. MUSTACCHI AND A. SKOULIOS Centre de Recherches sur les Macromol&xles, 6 rue Boussingault, Strasbourg, France Received in French, 6th January, 1958 ; trarislated by A. KLUG X-ray diffraction studies have been made of the mesomorphic phases of some soap + water systp,ms. The soaps used were the laurate, myristate, palmitate and stearate of sodium and of potassium. The phase diagram has been investigated over the whole range of concentration and for temperatures up to 110°C. The structures of the neat soap and middle soap phases have been determined and are found to be common to all the soaps. In addition, several new phases have been discovered in the intermediate zone between the neat soap and middle soap regions of the phase diagram, and the structures of some of these have been determined.It has been shown that in all the phases the hydrocarbon chains and the water are " liquid " in structure. The dimensions of the structural elements have been compared for different soaps. In a recent note 1 we have described the structures of two liquid-crystal phases of the system potassium palmitate + water, namely the neat soap and middle soap phases. In the present work we wish to extend these results to some other soap + water systems and to describe some new phases that we have discovered in the region of the phase diagram between middle soap and neat soap. Since all the soap + water systems have similar phase diagrams, we reproduce here, by way of example, only that for potassium palmitate 2 (fig.1). Below the curve T,, in fig. 1, is found the region of gel and coagel in which the system is not always in equilibrium. Above the curve there is isotropic solution. In the region between these two curves the system shows properties characteristic of liquid crystalline structures (high viscosity, optical anisotropy, etc.). It is in this region that the phases whose structures we shall describe here are to be found. Our investigations have been carried out on the sodium and potassium salts of lauric acid (Clz), myristic acid (CI~), palmitic acid (C16) and stearic acid (CIS). EXPERIMENTAL The fatty acids were supplied by the Eastman Kodak Company. The soaps were prepared by neutralizing alcoholic solutions of the fatty acids with alcoholic solutions of the base.The salts obtained were dried by evaporating at 105°C in vacuum. X-ray diagrams were obtained by means of a Guinier-type focusing camera of diameter 12.5 cm used with a bent-quartz monochromator. We have also used a Philips diffracto- meter with Geiger counter recording: the diffractometer was set up for the transmission technique, with the addition of a bent quartz monochromator placed between the X-ray tube and the specimen, and an electric furnace. The specimens were enclosed in a cell consisting of two thin mica windows clamped tightly in metal holders. Since all the diffraction lines observed lie in the central region of the X-ray diagram (1/120 < l / d < 1/15 A-l), it was necessary to have good focusing and collimation conditions.The diagrams were obtained using only CuKq radiation isolated by adjustment of the monochromator, and the angular region obscured by para- sitic scattering was cut down by a system of slits. This arrangement ensures that broaden- ing of the diffraction lines through inadequate collimation is negligible. We have in- vestigated the variation in the X-ray diagrams as a function of soap concentration and of temperature (up to 1 10°C) systematically over the phase diagram. 4344 STRUCTURE OF LIQUID-CRYSTAL PHASES In our previous 1 calculations of the sizes of the structural elements formed by the soap molecules we used, as a first approximation, a value for the density of soap very little different from that of the surrounding water.The accuracy of the experimental data, however, justifies the use of more precise values of the density. We assume that in all the structures two different regions of density can be distinguished : (i) the region occupied by the hydrocarbon chains of the soap molecules, and (ii) that occupied by the water and the polar ends of the soap molecules. We consider the surface of separation between the two regions to lie half-way between the carbon atom and the “c 4660 -7 I I I 0 %weight of 3oop FIG. 1.-Phase diagram of the potassium palmitate + water system. oxygen atoms of each carboxyl group. All the dimensions given below are to be under- stood as referring to the hydrocarbon region so defined. We showed previously that, in middle soap and neat soap, the hydrocarbon chains were “ liquid ”, and we now assume that they have a density equal to that of the corresponding paraffin at the same tempera- ture.The density of the water is modified by a correction factor to take account of the inclusion of the oxygen atoms of the carboxyl group and of the presence of the cations. If the concentration by weight of the hydrocarbon chains is cp, the density of the paraffin 6, and that of water 6,, then the ratio of the volume occupied by the hydrocarbon chains, vp, to that occupied by the water, el,, is In the following table we have given the values of the ratio 6,/8, for the different soaps These values were obtained by extrapolating the published data 3 for 6, to the temperature of the observations (lOO°C), and allowing for the presence of the cations in the water (but neglecting the variation of 6, with the soap concentration).soap KC12 KC14 KC16 KC18 NaC12 NaC14 NaC16 N a c ~ s 6,/& 0.60 0.61 0-63 0.65 0.67 0.69 0.71 0.73 PHASE M : MIDDLE SOAP In our earlier work 1 we showed that the middle soap phase is formed by a set of in- definitely long cylinders, arranged in a regular two-dimensional hexagonal array, and45 separated from one another by water. The polar groups of the soap molecules lie at the surface of these cylinders and the hydrocarbon chains are in a liquid state filling the interior V . LUZZATI, H . MUSTACCHI AND A . SKOULIOS 60 50 - 1 5r 50 40 30 X soap FIG. 2.-The distance d between the axes of the cylinders (full line) and the diameter ds of the cylinders (broken line) plotted as functions of the soap concentration for three different soaps : 4- KClz at 80°C ; h KC16 at 100°C ; 0 NaCls at 100°C.a b FIG. 3.-(u) Schematic structure of middle soap; (6) cross-section of a cylinder. of the cylinders (fig. 3). From the dimensions of the unit cell of the hexagonal array and the volume ratio vP/vw, it is possible to calculate the diameter of the cylinders, the thickness of the layer of water between them, and the surface area available on the average to each polar group. Fig. 2 shows sets of experimental results for the middle soap phase of three46 STRUCTURE OF LIQUID-CRYSTAL PHASES of the different soaps. It is clear that, within the limits of experimental error, the diameter of the cylinders is independent of the concentration at any one temperature.The measurements carried out on the other soaps confirm this result and enable some generalizations to be made. In the following table we have plotted the values of the cylinder diameter ds and the specific surface area S per polar end-group for the different soaps at 100°C. soap KC12 NaC12 KC14 NaC14 KC16 NaC16 KCl8 NaCls d, (in A) 29-1 29.0 32.3 32.4 37.4 37.3 41.8 41.9 S (in A2) 545 54-0 54.5 55.0 53.5 53.0 53.0 53.5 It is clear that : (i) the diameter of the cylinders does not depend on the cation but only on the length (ii) the diameter of the cylinder varies regularly with the length of the hydrocarbon (iii) the specific surface area per polar end-group is the same for all the soaps. We have shown previously 1 that neat soap consists of a set of plane parallel equi- distant sheets, each formed of a double layer of soap molecules, and separated from each other by a layer of water.The hydrocarbon chains are in the " liquid " state and the polar groups lie at the surface of the sheets (fig. 5). Just as with middle soap, one can calculate the thickness of the sheets and of the layers of water between them, and also the specific surface area per polar group. The results for three different soaps are plotted in fig. 4. It is found that as the soap concentration increases, the thickness of the sheets of soap molecules increases, that of the water layers decreases, and the available surface area per polar group decreases. of the hydrocarbon chain ; chain ; PHASE L: NEAT SOAP INTERMEDIATE PHASES The intermediate zone of the phase diagram between the middle soap and neat soap regions (fig.1) has been considered by some authors 4 as a zone in which the system is in the form of a mixture of these two phases. This idea is not in agreement with our experi- mental results except with sodium laurate. The X-ray diagrams we have obtained in this region are not simply a superposition of the middle soap and neat soap diagrams, but show several new lines that cannot be identified except on the assumption that inter- mediate phases exist. In some respects, however, the X-ray diagrams of the middle soap, neat soap and intermediate phases all resemble one another, notably in the fact they all show a series of sharp lines in the central region, and a diffuse band at a spacing of about 4.5 A.The presence of this band and the displacement of the lines as a function of temperature1 indicate that, in the intermediate phases too, the hydrocarbon chains are in a " liquid " state. Experimental investigations in this region are fairly difficult because the range of existence (in terms of concentration) of each phase is very limited. It has proved very difficult to prepare specimens containing only one phase ; more often than not two co-existing phases are obtained. Nor has it been rare to find at times three phases in one specimen, a phenomenon which is apparently in contradiction with the phase rule. This anomaly can be explained by the lack of homogeneity, something which is difficult to avoid in such viscous systems. It is only by examining a large number of specimens of slightly varying composition and comparing the intensities of the diffraction lines, that we have been able to distinguish the diffraction pattern corresponding to each phase.For the soaps studied by us, and under the conditions of our observations, we have been able to identify three phases in the intermediate zone. (a) Phase H : Complex Hexagoiiul We have recorded up to six lines characteristic of this phase giving spacings in the ratio 1 : d3: d8: 47: 16 : dE. There is thus present a two-dimensional hexagonal lattice like that of middle soap. The values of the lattice distance d (see fig. 6 ) for the various soaps are given in the following table : soap NaC14 NaC16 NaCl8 KC16 KC18 d (in A) 93 108 1 24 105 114V . LUZZATI, H .MUSTACCHI AND A . SKOULIOS 47 The length of side of the unit cell of this phase is thus very nearly twice that of the middle soap phase. We have tried to deduce a structure for this phase by taking into account the unit cell dimensions, the ratio of the volumes occupied by the hydrocarbon 20 90 80 70 60 I % soap FIG. 4.-(a) The inter-sheet spacing d (full line) and the thickness ds of the sheets of soap molecules (broken line) plotted as functions of the concentration, for three different soaps. (6) The specific surface area per polar end-group as a function of the concentration. -I- KC12 at 80°C; a KC16 at 100°C; 0 Nac18 at 100°C. a b FIG. 5.-(a) Schematic structure of neat soap; (6) section of a soap double layer. chains and by the water, and the relative intensities of the diffraction lines.model we have found satisfying these conditions is shown in fig. 6. The best (6) Phase C: Cubic phase, and their Bragg spacings are in the ratio : We have only been able to record the first four lines of the X-ray diagram of this48 STRUCTURE OF LIQUID-CRYSTAL PHASES These ratios are characteristic of a face-centred cubic lattice. We have confirmed that the symmetry is cubic by observations with a polarizing microscope, for, of all the phases described in this paper, only the phase C is optically isotropic. The length of side of the face-centred cubic unit cell for the various soaps is given in the following table : soap KC12 KC14 KC16 a (in A) 55.6 64.1 70.4 Since the face-centred cubic lattice corresponds to one of the ways of close-packing identical spheres, it seems reasonable to conclude that in this phase the hydrocarbon chains are arranged in the form of spheres surrounded by water.The radius of the spheres calculated from the dimensions of the unit cell and the composition of the system is, how- ever, too great ; for it is about 10 % greater than the length of a fully extended hydrocarbon b 1 I- --- - - U FIG. 6.-Schematic structure of the complex hexagonal phase ; (b) section of one of the structural elements. chain. Furthermore, the distance between the surfaces of two neighbouring spheres is too small (2.4A with potassium laurate). These difficulties can be avoided by assuming that the spheres tend to flatten somewhat in the region of closest contact and become polyhedra, dodecahedra in this case.(c) Phase 0: Deformed Middle Soap This phase is intermediate between middle soap and the complex hexagonal phase. It is characterized by the presence in the X-ray diagram of two lines, one on each side of the first line of the middle phase, when the latter line is present. This phase is probably derived from the middle soap phase by a deformation of the lattice of the latter, the hexago nal lattice becoming orthorhombic. This lattice change would very likely be accompanied by a deformation of the cylinders, the circular section becoming elliptical. However, the experimental data are not adequate to establish this structure unambiguously. The three phases just described are the only ones we have been able to find in the intermediate zone of the phase diagram at temperatures less than 100°C.The possi- bility that other phases exist at higher temperatures is not excluded. In fig. 7 we have represented schematically the range in soap concentration over which the various phases occur. For the reasons given earlier, we have not been able to deter- mine the positions of the boundaries between these ranges with any high precision. It is clear from fig. 7 that the same phases are not found in all soaps. Phase C occurs only in the potassium soaps with a short hydrocarbon chain, and phases H and 0 are found in sodium soaps and in potassium soaps having a long chain. MICROTEXTURE The specimens of middle soap are usually quite homogeneous in texture, as shown by the fact that the diffraction lines are continuous and show no spottiness or other irregular- ities.However, in the neighbourhood of the intermediate zone of the phase diagram,V . LUZZATI, H . MUSTACCHI AND A . SKOULIOS 49 the lines are often broken up into a mass of fine spots, each spot corresponding to one " microcrystal " in the specimen. Specimens containing the phases Hand 0 are generally rather homogeneous, although in many cases a large number of small crystallites oriented at random are observed to be present. The phase C, on the other hand, has a coarse " microcrystalline " texture with no preferred orientation present. In neat soap it most often happens that a number of fairly large domains all having the same orientation are formed ; the orientation is such that the sheets of soap molecules tend to set them- selves parallel to the mica windows of the specimen holder.This orientation effect becomes very pronounced in specimens of high soap concentration. We have observed that the spottiness in the X-ray diagrams of all the intermediate phases is the more marked the shorter is the hydrocarbon chain length. I I I I I I 1 . . . ' . . - ' 1 45 50 55 60 65 70 45 50 55 60 65 70%- FIG. 7.-Range of existence of the different phases as a function of concentration for the various soaps studied at 100°C. DISCUSSION THE STRUCTURAL ARRANGEMENT OF THE HYDROCARBON CHAINS AND OF THE WATER We have emphasized above that the hydrocarbon chains are " liquid " in struc- ture. By this we mean that the arrangement of chains in the hydrocarbon regions resembles the disordered configuration of a paraffin liquid more than it does the regular arrangement of chains in a crystal.It is worth noting that the long-range order in the system is as perfect as that of a crystal and that this is nevertheless compatible with the occurrence of such marked short-range disorder. It is this existence of a structure, which is composed of liquid domains capable of being organized in a crystalline (or semi-crystalline) lattice and which seems to be characteristic of " amphipathic " substances, that gives to these substances some of their special properties. The structure of the water on the atomic level plays a part only in layers of water of thickness less than that found in middle soap. In thicker layers the water behaves as a continuous medium. In fact, we have shown that the diameter of the cylinders of middle soap depends only on the length of the hydrocarbon chain and on the temperature, over a range where the distance between cylinders can take on very different values. In neat soap, on the other hand, every change in the thickness of the water layers is accompanied by a change in the structure of the soap layers.50 STRUCTURE OF LIQUID-CRYSTAL PHASES MESOMORPHIC " STASES " All the structures that we have described above are types of liquid crystals according to the definition of Friede1,s with the exception of phase C which is crystalline. The neap soap structure is of the smectic type. The structures of the middle soap phase and of phases H and 0 resemble the Friedel nematic " stase ", but possess an additional degree of order, the structural elements being not only parallel-the only condition for the nematic " stase "-but also equi- distant. This may be compared with one of the phases of tobacco mosaic virus in water, described by Bernal and Fankuchen.6 1 Luzzati, Mustacchi and Skoulios, Nature, 1957, 180, 600. 2 McBain and Lee, Oil and Soap, 1943,20, 17. 3 Timmermans, Plzysico-chemical constants of pure organic compounds (Elsevier Publishing Company Inc., New York, Amsterdam, London, Brussels, 1950). McBain, Vold, R. D. and Vold, M. J., J. Amer. Chem. Soc., 1938, 60, 1866. 5 Friedel, 2. Krist., 1931, 79. 6Bernal and Fankuchen, J. Gerz. Physiol., 1941, 25, 111.

ISSN:0366-9033    

DOI:10.1039/DF9582500043

出版商:RSC    

年代:1958

数据来源: RSC

摘要:

SOLUBILITY IN SOAP SOLUTIONS PART 10.PHASE EQUILIBRIUM, STRUCTURAL AND DIFmJSION PHENOMENA INVOLVING THE TERNARY LIQUID CRYSTALLINE PHASE BY A. S . C. LAWRENCE Dept. of Chemistry, Sheffield University Received 3 1 st January, 1958 The structural features described here are discussed in terms of interaction between the ionized group in a soap and the polar group of the organic compound in the presence of water ; as partial miscibility in a three-component system ; and as a balance between the resultant enhanced solubility and the opposing insolubility of the hydrocarbon chains. The regularity of the structures is due, in part at any rate, to the necessity for long-chain molecules to pack into layer lattices when in a condensed state. Charge effects are markedly absent. The upper and lower limits to the existence of the ternary liquid crystal- line phase are described.With aliphatic solutes, the lower limit is found to depend upon the polar groups in both soap and solute and upon the length and shape of their hydro- carbon chains ; correlation with melting temperature of the solute is shown. It is now well recognized that organic substances insoluble or sparingly soluble in water are much more soluble in an aqueous solution of any soap ; their solubility increases with increase of soap concentration. It was pointed out by the writer in 1937 1 that, when the organic third component, called additive for brevity, contains a polar group such as -OH, -COOH, -NH2 or, as shown later, C H group, the solubility of both soap and additive are enhanced as, indeed, might be expected from simple thermodynamic considerations. Later, McBain intro- duced the unfortunate name “ solubilization ” to include solubility of both polar and non-polar substances, ignoring the differences between the two systems.It has been shown in this laboratory that the system soap + water + polar sub- stance is the simple one of 3 partially miscible components and is peculiar only in that there exists an area of ternary liquid crystalline phase; this, although novel, is analogous to the well-known cases where the ternary phase is a liquid or solid solution.2 Complete triangular equilibrium diagrams have been worked out for the system sodium dodecylsulphate + water + caproic acid and for the same soap plus water and n-octylamine; 3 Dervician 4 has published the diagram for the system potassium caprate + n-octanol + water.It should also be noted that, for aliphatic additives containing more than 5 normal carbon atoms, the region of isotropic solution included in McBain’s solubilization is a small part of the whole system. It is often convenient to work with a chosen concentration of soap and observe the changes with progressive addition of additive; with larger amounts of the latter, the overall concentration of the soap is much reduced but the soap/water ratio, which is important, is unchanged. The general result for any soap, anionic or cationic, with aliphatic homologous alcohols, carboxylates, amines, etc., in which the number of normal C atoms is 5 or more and so long as they are above their melting points is shown in fig.1.1 The initial soap concentration must be at least about 10 %; below that concentration, only two liquid layers are formed with the soap plus some water mainly in the organic-rich layer.3~ 5 5152 SOLUBILITY IN SOAP SOLUTIONS In fig. 1,1 E is the point at which separation into two layers occurs at high concentration of additive. If the additive is solid at room temperature, then it crystallizes at its T f - aAT for the other components but, around E, this AT, is not more than 2 to 3°C. It was observed, however, that at lower con- centrations, ternary liquid crystalline systems persist where AT, is much larger. An extreme case is cholesterol, m.p. 148-5, which remains in the liquid crystalline state at room temperature with cholesterol to soap ratio of 1 mole : 1 mole.This is not a metastable condition since sufficient cholesterol can be dissolved in a soap solution at 100°C, so that, on cooling, some crystallizes out and remains in equilibrium with the saturated liquid crystalline phase. The reverse procedure was therefore tried : a single crystal of either cholesterol or cholesterol hydrate (the latter are more readily prepared) is placed on a microscope slide and flooded FIG. 1.-Sodium dodecyl sulphate + water + caproic acid system at 25°C. with soap solution. It is viewed by polarized light with the Nicols at 45". As soon as the soap solution touches the crystal, a gelatinous membrane is formed; this retards attack but it gradually becomes more fluid, the soap penetrates further and surface tension pulls the ternary liquid crystalline phase into more or less spherical anisotropic lumps.At the same time, the exteriors of the liquid crystals are dissolving away into the exterior soap solution but more slowly than the in- vasion of the crystal. Fig. 2 shows the sequence of the events but without the initial membrane formation ; the sequence shown took 40 min from start to com- plete solution. This experiment was then tried on dodecanol and similar results obtained but the higher homologues formed no liquid crystal phase, but only a very slow solu- tion direct to an isotropic state over 10 to 12 h. When, however, they were heated on a hot stage, the penetration process and liquid crystal formation set in suddenly at a temperature Tp characteristic of each substance and below its melting point.Fig. 3 shows this transition temperature for the homologous even-number fatty acids in a number of soap solutions. Tp was found not to change with concentra- tion of soap over wide limits : e.g. for myristic acid in Teepol, T, was 30°C for concentration of soap from 5 to 33 7;. It is seen that the penetration temperature lies below the m.p. of the solid ; that it is not merely a thermal opening- up of the solid is shown in that Tp is clearly also dependent upon the nature of the Fig. 4 shows T, for the even-number iz-alkanols.A. S. C . LAWRENCE 53 FIG. 3.-M.p. x and Tp, 0 for fatty acids in 15 % solution of various soaps. I6 I 18 20 , 10 I 2 14 Cn FIG. 4.-M.p. x and Tp. 0 for n-alkanols in 15 % solutions of various soaps.54 SOLUBILITY IN SOAP SOLUTIONS polar group of the soap.The chain length of the soap seems to affect the slope of the curves : e.g. the two c16 soaps as compared with the C12 ones. The Teepol curve lies surprisingly high compared with the n-C12 sulphate ; this may be due to the chain branching in the Teepol. It was also found that samples of fatty acids not quite pure and melting a few degrees below the true value also had their Tp lowered by an equivalent amount. Mixtures of stearic and palmitic acids were made up and their freezing points and Tp in 15 % Teepol observed ; fig. 5 shows the eutectic for f.p. in agreement 7c 6( 0; 5 ( 4c 3c I with the results of Francis, Collins and Piper 6 and a eutectoid graph for Tp with the minimum at the same composition as that for f.p.Since we have found in these ternary systems marked shape effects upon phase equilibria and solubility, we tried oleic and elaidic, erucic and brassidic, and stearolic and behenolic acids ; the results are shown graphically in fig. 5 ; ,Tp could not be measured for oleic acid as it was below 0" (in Teepol). A lower limit to the phenomenon is set by the Krafft point of the soap, i.e. the temperature at which its solubility in water drops to a very small value : for Teepol this is below 0" but is considerably higher for the straight-chain soaps. MYELINIC FIGURES When cholesterol is dissolved in soap solutions, many rings, usually short fat sausages, are seen ; the ring is sharply defined, strongly birefringent and con- 43 .b .4 I .2 tains isotropic solution. This form of the liquid crystalline phase is rarely seen Compori tion FIG. 5.-M.p. and rp in 15 % Teepol with aliphatic solutes where the penetra- ternary phase at T', first by formation of a membrane around the solid and then by bulging into hemispherical anisotropic forms and finally sometimes to spherul- ites. Ekwall et al.7 using carboxylate soaps, find various structures during the penetration into liquid alcohols, c6, C7 and Cg ; we also find similar features at temperatures above Tp, as was the case in Ekwall's studies. It seems doubtful whether the liquid crystalline sausages formed should be called " myelinic " ; the latter are tubes filled with liquid ; these " sausages " are birefringent across the lumen of the tube.They are, in fact, temporarily distorted liquid crystalline spherulites. In myeline formation, water is diffusing into a solute, forming the membrane of sufficient strength; further swelling must result in expansion and the tubular forms result from their smectic liquid crystalline nature ; i.e. they have one plane of easy fluid shear so that telescopic extension of the tubes results. The long axes of the molecules forming the membrane are, of course, normal to the length of the tube. In the penetration of soap solution into a homogeneous solid (or liquid) amphi- philic substance, the soap molecules, as well as water, must diffuse through the membrane first formed. From bulk diffusion experiments in which decanol was solution for mixtures of stearic and palmitic tion ofthe soap leads to liquid crystalline acids.A .S . C. LAWRENCE 55 placed on top of 15 % soap solution,8 a membrane of liquid crystalline material was formed through which soap passed readily into the decanol with a small amount of water. In two days, the decanol layer had become a paste of ternary liquid crystalline phase and it was only after 3 months that water had diffused in sufficiently to double approximately its volume. With these ternary systems, it would appear that the solid which forms myelines in water must contain two components-soap and a long-chain amphi- phile which, it will be noted, is the type of mixture which has an exceptionally large surface plasticity on aqueous solutions 9-and it usually appears to be hetero- geneous. Sodium laurate and lauric acid in equimolar proportions form myelines in water ; very slowly at room temperature but much more rapidly at 40°C (i.e.above the m.p. of lauric acid). Oleic and sodium laurate give them quickly at 80- 60 y 4 0 - a. ; - / / ?;I, , p , , , / / ( 0 C“ Y 8 10 12 14 16 18 2 0 2 2 FIG. 6.-M.p. x - x , and Tp 0- -0 for saturated, cis and trans ethylenic and - - - - acetylenic fatty acids ; in 15 % Teepol. room temperature. When, however, the K soap and oleic mixture was tried, no myelines were formed ; only liquid crystalline bulges which fioated free as liquid crystalline spherulites after the manner of the penetration solubility process. PHASE EQUILIBRIA IN SOAP $- WATER $- AMPHIPHILE SYSTEMS The general picture of the ternary phase diagram at room temperature is now well established but little work has been reported upon temperature changes and equilibrium at higher temperatures and nothing upon lower temperature limits of existence.In this laboratory we have accumulated data on parts of several systems over the temperature range from 210°C to below 0” and can now form a general picture. if we keep the soaplwater ratio constant and add various amounts of amphiphile, we can plot TIC diagrams as for binary systems by using the Krafft point as the “freezing point” for soap + water as one component and the orthodox melting point of the additive as the other. Fig. 7(a) shows the picture diagrammatically for systems in which the m.p. of the organic amphiphilic com- ponent is below the Krafit point ; 7(b) shows a reverse case in which it is above.Fig. 7(a) includes three classes in which the three broken lines represent room temperature : (i) is that in which no liquid crystalline ternary phase is formed ; EX is a saturation point at which the single liquid phase becomes saturated and forms two liquid phases. This is found with low molecular weight amphiphiles,56 SOLUBILITY I N SOAP SOLUTIONS usually with a small solubility in water; e.g. butanols, eresols, aniline, benzyl alcohol, etc. Case (ii) is that shown in fig. 1. It is found generally for all amphi- philes containing 5 or more n-C atoms; of the two isotropic solutions beyond E, one may be a gel which with some soaps, e.g. carboxylates, only becomes fluid at about 130°C. The point B has always been well above both m.p. of amphiphile and Krafft point of soap ; it is usually above 100°C.With cholesterol and sodium dodecyl sulphate in equimolar amount and the soap in 20 % of aqueous solution, B was 195°C. EX frequently slopes backwards as shown. For (iii) we have two possibilities. With normal soaps whose Krafft point is above 0", the first solid component to separate is pure soap. If the Krafft pt. is itself below zero (as with Teepol) and m.p.A still lower, then ice is the first solid to appear on cooling. All of these cases have been found. The separation of soap from solutions of X K .Pt I P'* 1.0 soap so1n I compoittion X \ I ~otroplc iolution \ 2 Irottoplc 1 Soap Sol" I.( composition FIG. 7.-Temp./comp. phase equilibrium. (a) m.p. of A below Krafft point.(b) m.p. of A above Krafft point. C120S03Na and C16Me3NBr in mixtures of water and lower amines has been observed : e.g. with NEt3, NPr3, N-isoPr3, N-BuzH, N-BuzMe, N-isoBu2, N- sec.Bu2, etc. Also from lauric acid in C120S03Na solutions at the water-rich corner of the triangular diagram. Fig. 7(b) in which m.p.A is above the Krafft pt. it is clear that the amphiphile freezes out first. Since, however, stable liquid crystalline systems persist at room temperature over part of the concentration range, there must be some sort of eutectoid graph. With C120S03Na + water + lauric acid, the freezing point drops rather slowly at first from pure lauric acid and dips more steeply later. The graph exaggerates the dip. This type of behaviour is that of all soaps and all fatty amphiphiles with m.p.above room temperature, i.e. roughly from Cl2 upwards. SOLID SOLUTION FORMATION During the examination of the dodecanol in sodium dodecyl sulphate system in this laboratory, Mr. K. Hume observed the existence of a large amount of solid persisting above the m.p. of the alcohol and the Krafft pt. of the soap, 23-8"C and 22-23' respectively. The material, with slow cooling, formed large crystals of a perfection never seen in soap crystals; in place of the usual mosaic of im- perfect flakes, uniform six-sided single plates existed: these appeared to be rhombic plates with two opposite corners truncated. On warming on a hot stage in the polarizing microscope, they were seen to melt uniformly and sharply, at(b) FIG. 9.-Crystals of solid solution of sodium dodecyl sulphate + water + dodecanol.Crossed Nicols. x 60 [To face page 57A . S. C . LAWRENCE 57 temperatures falling from 32" to 29°C with increasing additions of dodecanol. On further heating the isotropic solution becomes cloudy by formation of the liquid crystalline phase and clears at a higher temperature. Tetradecanol be- haves similarly but does not clear at 100". Analysis showed these crystals to contain water which was determined by distillation in xylene (Dean and Stark method). Another sample was dissolved in 50 % ethanol in water and the dodecanol extracted by petroleum ether ; the soap was determined by the methylene blue method. It was then realized that, after removal of all water, the soap should remain in the boiler insoluble in xylene while the dodecanol will be in solution in it; the soap filtered easily and was washed, dried and weighed and the xylene removed from the dodecanol which was also weighed.No similar solid phase was observed in the ternary system in which dodecoic acid replaced dodecanol as the third component. Crystals of the solid solution are shown in fig. 9. DISCUSSION In the absence of water, ionic soaps of all kinds are generally poorly soluble in organic liquids; with water present, high solubilities are found with lower molecular weight substances containing a polar group; e.g. ethanol, di- and tri-propylamines and butylamines, di-ethyl ketone, phenols, etc. With higher homologues (C5n and above) ternary liquid crystalline phase is formed; this is of the smectic type and is therefore a layer lattice.In the presence of caproic acid in excess, 7 molecules of water per molecule of sodium dodecyl sulphate is the minimum amount to convert all the soap to liquid crystalline phase at room temperature; i.e. to prevent any solid soap crystallizing out. The maximum which the smectic phase can hold is 110 molecules of water/molecule of soap- that is about 10 % soap in water; with more water the system breaks down to two liquid phases. Similar figures are obtained with the same soap in n-octylamine.3 The system is visualized as one in which the ionized head of the soap molecule and the polar group of the added amphiphilic substance are forming a local solu- tion while the attached hydrocarbon chains are insoluble. The closeness of the packing is attested by the Ay produced by the additives, by the very large surface plasticity of the binary layer adsorbed on the water, and by the - A V on mixing the components; Mr.B. Boffey has shown in this laboratory that the partial specific volume of soap and water decreases on addition of additive. The smectic layer arrangement is a sandwich of which the centre is a layer of water whose thickness is from 8 to 13Ow for 7 to 110 moles water/mole of soap. The water can be regarded as held together by its own high internal pressure and the liquid crystalline nature by the terminal polar groups being in local solution in the water. Crystallization in 3 dimensions require them to crystallize from the water. The high temperatures of the transition from smectic to isotropic solution do not require large specific forces in the planes-of the polar heads because increase of temperature does not increase the solubility of the hydrocarbon tails.Given that water separates, it cannot form a bulk phase because the soap and amphiphile polar heads are dissolved in it ; it must form either an emulsion or the smectic liquid crystals and we cannot preclude lateral attraction between polar groups. On the other hand, the water evaporates readily from the additive-rich liquid crystals and measurements of vapour pressures of ternary systems by Mr. Boffey show large positive deviations from Raoult's law. In the soaps and amphiphiles, we have the necessary condition for this abnormally low attachment of A to B since the shape and amphiphilic nature of the molecules reduce markedly the extent to which complete homogeneity on a molecular scale can be achieved.The aggregation of soaps in water is a similar case which, in the formation of micelles, is an incipient separation into two phases: i.e. the extreme case of positive deviation from Raoult's law. The structural properties all follow from the smectic layer lattice but it is clear that the plane of fluid flow is the water58 SOLUBILITY I N SOAP SOLUTIONS inside the sandwich whereas in classical smectic melts it is the plane of terminal methyl groups. Shearing is therefore a process which breaks up the unit of the sandwich structure; this may be the explanation of the silky thread texture in the very high viscosity region in which any reformation of larger units is extremely slow ; in the organic components-rich region, where viscosity is low, reformation to classical textures of focal conics and bgtonnets is rapid.In a myeline sheath we have the smectic layer lattice curved into a closed cylinder; there is therefore a longitudinal channel of water along which con- ductivity and diffusion can take place but not at right-angles to this direction (fig. 8). u 0 c z I i I I m y e I i n e I 1 sheath I I FIG. &-Soap + amphiphile + water myeline. It is sometimes suggested that addition of a wetting agent to water in contact with a lipid membrane initiates semipermeability by its wetting action but this is surely incorrect. The wetting agent can alter the permeability only by entering into the membrane and altering its nature; such action is particularly likely to occur when the membrane is composed of substances adsorbed from and in equilibrium with the solutions on either side of it. The diffusion results mentioned here are examples; they also illustrate the wide control, available by varying concentration or temperature, over the physical condition of such membranes. 1 Lawrence, Trans. Faraday SOC., 1937, 33, 325. 2 Faraday Soc. Discussions, 1954, 18, 239. 3 in course of publication. 4 Proc. 2nd Int. Congr. Surface Activity, 1957, 1, 327. 5 Lawrence and Stenson, 2nd Int. Congr. Surface Activity, 1957, 1, 388. 6Proc. Roy. Soc. A , 1937, 158,691. 7 Ekwall, Salonen, Krokfors and Danielsson, Acta Chem. Scand., 1956, 10, 1146. 8 Lawrence, 2nd Int. Congr. Surface Activity, 1957, 1, 475. 9 Blakey and Lawrence, Faraduy Soc. Discussions, 1954, 18, 268.

ISSN:0366-9033    

DOI:10.1039/DF9582500051

出版商:RSC    

年代:1958

数据来源: RSC

摘要:

GENERAL DISCUSSION Mr. C. G. Cannon (B.N.S. Ltd., Pontypool) (communicated): In his intro- ductory paper Prof. Bernal 1 discusses the important contribution that inter- molecular forces make to the configurations of molecules in close contact. He has focused attention on the range of action of hydrogen bonds, electrostatic interaction of atomic or molecular ions, and van der Waals’ forces. The last can be further subdivided into the non-polar and polar components, i.e. the dis- persion forces, and the interaction between permanent molecular dipoles. Since the interaction energies of these four mechanisms all lie roughly in the range 0-20 kcal/mole it is important to know their relative energies and whether or not one particular mechanism is dominant, when considering the configuration and packing of particular molecules.Dispersion forces are non-directional and lead to close-packed structures (e.g. crystalline CH4 and paraffin hydrocarbons). The interactions of molecular ions or dipoles develop maximum energy for a particular alignment and are thus directional forces. Hydrogen bonding is also a directional interaction. These directional forces lead, in general, to more open structures (e.g. ice crystal), in opposition to the dispersion forces. When two or more directional forces contribute to an intermolecular contact they may reinforce or may partly oppose. In this Discussion and elsewhere it is assumed that NH---O=C hydrogen bonding is responsible for the peptide -CONH- group interaction, but the -CONH- group is very polar, with a high polarizability, and the dipole-dipole interaction cannot be neglected.Recent applications of quantum theory to the study of the structure and pro- perties of molecules have shown, from the calculation of orbital moments, the contribution which the individual bonds and the non-bonding lone pairs of elec- trons make to the dipole moment of molecules or structural groups.2 Our under- standing of the mechanism of hydrogen bonding has also developed.3~ 4 We are therefore able to analyze more critically the interactions which have been rather loosely labelled “ hydrogen bonds ” whenever an X-H link is involved in a close contact. Let us first examine the conditions for the formation of an X-H---Y hydrogen bond. The proton acceptor atom Y must have lone pair electrons in an asymmetric orbit, e.g.sp, sp2, or sp3 hybrid. These lone pairs have a high- orbital moment which as Y approaches X-H will polarize the X-H bond. From our knowledge of the relative strengths of various hydrogen bonds another condition can be formulated. The X-H bond, as far as the distribution of its (J electrons is concerned, must be polarized in the -X-*-H+* sense, i.e. X more electronegative than H. This means that the hydrogen 1s atomic orbital is not fully utilized in the formation of the X-H bond and is available for overlap with the lone pair of Y to form a weak covalent H---Y bond. This covalency increases as the X - - - - Y distance shortens and at the same time the X-H bond lengthens until in the limiting case where the proton is symmetrical (e.g.(FHF)- ion) both bonds are equally partly covalent. Finally for maximum overlap between the X-H and lone pair orbitals they should be colinear, i.e. the proton should lie on the X---Y line (e.g. bonding in ice, or carboxylic acid dimers). Let us now examine the NH bond and its potential hydrogen bonding pro- perties. The orbital moment calculations of Burnelle and Coulson 5 show that in 1 Bernal, this Discussion. 2 Coulson, Vdence (Oxford, 1952), p. 207. 3 Coulson, Research, 1957, 10, 149. 4 Cannon, Spectrochimica Acta, 1958, 10, 341. 5 Burnelle and Coulson, Trans. Faraduy Soc., 1957,53,403. 5960 GENERAL DISCUSSION ammonia the bonds are NtS--H-*. The nitrogen bonding orbitals are approxim- ately sp3 hybrids so the lone pair must occupy an sp3 orbital.Since N H 3 is a gas we must conclude that the potential NH---N hydrogen bonding is so weak that the molecules do not associate. Since the asymmetric lone pair is present this must be due to the N-H bond polarity being in the opposite sense to that required for hydrogen bond formation. For an N-H group to form a hydrogen bond the electron density on the nitro- gen (apart from the oNH electrons) must be reduced by inductive or mesomeric effects in the molecule so that the a, electron distribution moves towards the N atom and reverses the bond polarity. The aromatic type conjugation (n-p) of the pyrrole molecule is an example. There is certainly n-p conjugation between the C-0 and the N lone pair in amides and peptides which stabilizes the planar CONH group.Detailed infra-red investigations show, however, that the amide NH is only a weak proton donor 1,2 and the change in NH frequency with polarizability of the solvent shows that it is relatively non-polar.7 We must conclude therefore that N-H- - -O=C The n-p conjugation, however, produces a polar OCN group with very polarizable molecular orbitals. With successive N alkyl substitution of the RCONH2 group this polarity is increased.7 From the published data on the dipole moment and refractive index of RCONHR’ model compounds we can calculate the approximate energy of dipole interaction of two -CON€€-- groups in the configuration of p proteins or polyamides, where the OCN directions are colinear. hydrogen bonding will be fairly weak. - 4 - - + Thus where p = dipole moment, a = polarizability, R = distance between dipoles.Taking p = 3.87 X 10-18 e.s.u., a = 20 cm3 (molar refractivity), and R = 5-2 A (computed from bond lengths and an N---0 contact of 2-88 A) the molar interaction energy = 3.1 + 0.17 = 3-3 kcal. The first term is the dipole-dipole energy and the second the dipole induction. Thus, energetically, dipole interaction of CONH groups will compete with hydrogen bonding. In the crystal structure of formamide 3 we have the crucial comparison between the relative strengths of the amide hydrogen bond and the amide dipole interactions. The most favourable configuration for amide hydrogen bonding occurs here when the formamide molecules form cyclic “ dimers ”, by hydrogen bonding of the NH bonds which are cis to the -0 (I) to the 0 of the adjacent molecule.H .. / // \ 0 :- - -H-N C-H H-C // N-H- - - :O \ .. / H 0 N---0 = 2,935A. The NH bonds and the 0 lone pairs are colinear with an N---0 distance of 1 Mizushima et al., Spectrochimica Acta, 1955, 7, 100. 2 Cannon, Mikrochimica Acta, 1955, 2-3, 555 ; J. Chem. Physics, 1956, 24, 491. 3 Ladell and Post, Acta Cryst., 1954, 7 , 559. 2-935 A.GENERAL DISCUSSION In the OCN direction the dipoles align (11) H H 1 .. I ..//c\N/H :O\(/”\H I H I :O H (11) N---0 = 2.888, 61 but the NH bond truns to the C=O is not colinear with the oxygen lone pair of the adjacent molecule. Thus in this direction the alignment of adjacent dipoles opposes the optimum configuration for hydrogen bond formation. In the direc- tion of dipole interaction the N---0 distance is 2-88 A, shorter than the hydrogen bond. We must conclude therefore that in the trans configuration of CONH groups in polyamides, polypeptides, and proteins it is the dipole-dipole interaction which controls the configuration and packing of the molecules.The weak hydrogen bond will only occur in favourable cases (e.g. cis-CONH in cyclic lactams, diketo- piperazine, etc.). The colinearity criterion of NH---0-C hydrogen bonding applied to test the validity of proposed a helical polypeptide structures is erroneous and the puzzling departures from NH- - -0 colinearity found in practice are now under- standable. The insensitivity of the NH stretching frequency to u -+p transforma- tions despite shifts in the amide I and amide I1 frequencies of up to 30 cm-1, are also explicable as due to changes in the alignment of OCN dipoles with little change in the N---0 distance.The dipole interaction will vary with the angle between adjacent dipoles and affect the OCN group frequencies, while the environment of the NH bond remains approximately unchanged. Prof. F. C. Frank (Bristul University) said: In reply to Prof. Bernal’s question regarding the Grandjean planes, I am sure that Oseen was right (and Friedel wrong to disagree with him) in interpreting the Grandjean planes as an optical illusion, explicable in terms of the optics of a twisted medium, without the existence of any real discontinuity planes at all. Prof. W. Maier (Freiburg i. Br.) said: In his paper Prof. Frank has given the theoretical terms which are needed in order to describe exactly the elastic properties of a liquid crystal and has discussed the characteristic phenomena on the “ grain boundaries ” of its homogenously oriented regions from a macroscopic point of view.Of course, there is yet another field of theoretical work which starts from the molecular point of view. There is, for example, the question why certain substances have nematic phases of the simple type and others do not, or-more quantitatively-the question of the connection between the thermal stability of the nematic order and the molecular properties of the substance. Dr. Gray has done a lot of wonderful chemical preparative work in this direction and has elucidated the above question very successfully. Now, I should like to mention that we have derived a theory of the nematic state which is based only on the existence of London’s dispersion forces between axial symmetric optically anisotropic molecules of the well-known type and which shows that a long-range order of the molecular axis of greatest optical polarizability will arise as soon as the anisotropy of the molecules is strong enough.In this theory the mean energy of a molecule in the field of the dispersion forces of all the other molecules is given by - + with C = characteristic function of the spatial arrangement of the molecules62 GENERAL DISCUSSION and their electronic transition moments; 8, = angle between the molecular axis of greatest polarizability and the optical axis of the liquid crystal ; S = degree of long range order of these molecular axes (S = 1 - 3 <sin28 averaged over all, molecules).The theory allows us to calculate the degree of order, the specific heat, the compressibility and the ultrasonic absorption in the whole region of the nematic phase of a substance as well as the energy of transition on the clearing point and the anomalous Cotton-Moutton effect in the isotropic liquid phase. As an example in the figure there is given the degree of long range order as it is calculated for p-azoxyanisole (dashed curve). The only experimental data which are needed for this calculation are the temperature of the transition nematic 3 isotropic, the jump in density at the transition and the density itself. These data are needed because neither the exact spatial arrangement nor the electronic transition moments are known and therefore the function C cannot be given without the use of experimental data.For comparison the figure shows the with <sin28 1 0.2.. 0.1 I 1 I I I 0 ' IGENERAL DISCUSSION 63 I considered a chain molecule depositing on a pre-existing bundle, and noted the way in which the average unattached length becomes finite at a critical tem- perature, and rapidly shortens as the temperature falls: on the other hand, one must lower the temperature a great deal before it is near to zero. If the chain is lo4 links long, there are still a hundred links of unattached chain when 99 % is attached, so that solubility is virtually suppressed. Thus, if we have a crystal- lization into a parallel bundle of chain molecules, we must expect it to be a hairy bundle, with loose ends sticking out of its surface.I suppose these loose ends to be trapped through the occupation of their proper crystalline places by other molecules. Now, the number of loose ends should be proportional to the number of molecules, and thus, per unit length, to the square of the fibril radius : but the surface area, per unit length, is proportional to the radius. Hence the number of loose ends per unit area increases with the radius 1 the crystal surface becomes more and more imperfect. This provides an effect, peculiar to very long molecules, which can oppose the Ostwald effect and stabilize a configuration with very many very thin fibrils. I think it likely that this conception has applications, if not to the nylon case which originally suggested it.Dr. G. W. Gray (Hull University) said: The coloured photomicrographs of the cholesteric-like twisted structures found in solutions of poly-y-benzyl-L- glutamate and poly-y-methyl-L-glutamate show homogeneous areas which are reminiscent of a texture of the cholesteric mesophase observed in a homologous series of fatty esters of cholesterol.1 These esters were first of interest to me be- cause plots of the cholesteric-isotropic transition temperatures recorded in the literature against the number of carbon atoms in the ester alkyl chain showed none of the regularities which have been found for a large number of homologous series of pure compounds exhibiting smectic or nematic meso- phases. The pure esters were therefore prepared and the cholesteric-isotropic and smectic-cholesteric transition temperatures measured.When the cholesteric- isotropic transition temperatures were plotted against the number of alkyl carbons, two smooth curves were' now obtained, showing the characteristic alternations between points for members with odd and even numbers of carbon atoms in the ester alkyl chain. The smectic-cholesteric transition temperatures, starting with cholesteryl octanoate, lay on a smooth curve which rose to a maximum at cholesteryl laurate and fell smoothly to cholesteryl stearate. Re- turning to the cholesteric-isotropic transitions, it was surprising to find that at first sight these were not reversible at the same temperature, within the limits of experimental error (& 0.25"C), the anisotropic cholesteric mesophase reappearing from 1-7°C below the cholesteric-isotropic transition temperature.It was eventu- ally found, however, that the mesophase is indeed reversible at the same tem- perature, but that it appears from the isotropic liquid in a homoetropic form which is not anisotropic, and therefore passes unobserved between crossed nicols. The transition may, however, be seen as a dark purple film with the naked eye. The transition observed between crossed nicols is the gradual development of focal- conic groups or other anisotropic textures in this homoetropic state. This homo- etropic condition is the texture which is so similar to the homogeneous areas in Dr. Robinson's slides. I t may be added that the cholesteric-isotropic transition point curve for these cholesteryl esters with an odd number of carbon atoms in the alkyl chain rises to a maximum and then falls, and is similar to the smectic- isotropic transition point curves for alkyl 4'-alkoxydiphenyl-4-carboxylates.At the time I suggested that this was a point of similarity between cholesteric and smectic mesophases. However, we have since found that nematic-isotropic transition point curves may rise to a maximum too, e.g., in compounds such as 4-p-n-alkoxybenzylidene-aminodiphenyls carrying a 2- or 2'-substituent of suf- ficient size to prevent coplanarity of the diphenyl ring system. The shape of the 1 Gray, J. Chem. SOC., 1956, 3733.64 GENERAL DISCUSSION cholesteric-isotropic transition point curve is therefore no more similar to that for smectic-isotropic transitions than it is for nematic-isotropic transitions, and offers no objection to the concept of the cholesteric mesophase as a modification of the nematic mesophase.Prof. Maier asked whether I had examined any homologous series of meso- morphic compounds in which the smectic-nematic transition point curve crossed the nematic-isotropic curve, so giving rise to a sequence from solid to nematic to smectic to isotropic liquid, with rising temperature. No such behaviour has been observed by me, nor do I consider it a likely eventuality, since it necessitates the postulation of a change from the less ordered nematic mesophase to the more ordered smectic mesophase with rising temperature. If any such series has been reported in the literature, it would be necessary to check the purity of the compounds very carefully.If the compounds were not pure, it would be easy to obtain a highly irregular disposition of the transition temperatures, and moreover the identification of the nature of the mesophases may be difficult. Both these difficulties could lead to a misinterpretation of the results and an apparent inversion of the normal sequence of solid to smectic to nematic to isotropic liquid, with rising temperature. Dr. A. S. C. Lawrence (Shefield University) said: Although soaps are not macromolecules, two papers have dealt with condensed phases showing liquid crystalline phenomena ; these together with Dr. Conmar Robinson’s interesting liquid crystalline polymer formed a group. The soaps form smectic-layer-type lattices compared with the essentially nematic type associated with fibrillar macro- molecules.However, the texture of the smectic mesoform is never a simple layer arrangement except where there is restraint from external forces as in Perrin’s stratified soap films or rarely as a result of shearing (Rinne). The usual texture is that of a micro-crystalline mass of focal conics; these also are subject to re- straint when viewed as a thin film between slide and coverglass. The ideal habit of the focal conics is, I think, a double cone in which the ellipse has become a circle with the long axis of the double cone normal to it ; with three quite different systems, I have seen these form on cooling an isotropic solution in a tube of 2 to 3 mm inside diameter: the cones form across the lumen of the tube.The first liquid crystals reorganized as such, Lehmann’s ammonium oleate, had this habit. When indefinitely elongated, we have the case of Luzzati’s “ sausages ” ; inter- mediate elongation gives, as pointed out by Friedel, the fan-like texture. With regard to the forces operating in these ternary liquid crystals, it is easy to say hydrogen bonding but that does not explain anything and we must first consider what needs to be attributed to specific binding forces. We know that, in the sodium dodecyl sulphate + water + caproic acid system, the minimum amount of water required to loosen-up the solid soap crystals to liquid crystals is 7 molecules of water per molecule of soap and that the maximum which can be held between the polar groups in the smectic sandwich structure is 110.Taking accepted values for the cross-sectional areas of soap and amphiphile molecules, we find that the maximum represents a layer of water 1lOA thick and we must explain why it does not run out. I suggest that as amphiphile is added, the solution becomes progressively more lipophilic until water segregates under the influence of its high internal pressure ; it cannot separate as a bulk phase because the polar groups of soap and amphiphile are still dissolved in it. These groups must lie in a planar arrangement because they cannot lie about among the hydrocarbon chains ; they could be on the surface of a spherical drop, i.e. as water in oil emulsion. However, they form the smectic layer lattices in preference probably because of the increasingly closer packing as amphiphile is added to soap.This is evidenced by Ay, the very large surface plasticity of binary adsorbed layers and by our measurements of the partial specific volumes of the components.1 1 unpublished work.GENERAL DISCUSSION 65 The only property which may require more specific forces in the plane of the " sandwiches " is their remarkable thermal stability ; the ternary smectic phase frequently persists to temperatures well above 100°C, and, in the extreme case of cholesterol + C120S03Na + H20, to 195°C. We may note again the absence of any effects due to the sign of the charge on the ionized soap group and on the amphiphile, if any. Dr. A. J. Hyde (Munchester) (partly communicated): In fig.7 of his paper, Dr. Lawrence shows a section through the 100 % amphiphile point of the tem- perature-phase composition diagram for a general soap + water amphiphile system. I should like to point out that, in the general diagram for any additive (which may or may not be amphiphilic), the two-phase area cannot extend all the way to the right-hand temperature axis. In all cases, the boundary EX, or some extension thereof, will bend over and meet the solid-liquid boundary between E and m.p.A, and there will be a one-phase system between the continuation of EX and the temperature axis. For an extremely hydrophobic additive, such as a paraffin, the continuation of EX will come down to a point very close to m.p.A and will probably be very steep but not infinitely so.Fig. 196 (from the work of McBain and Stewart) shows a system with an amphiphile sparingly soluble in water. A section through say 30 % soap solution and the oleic acid point would give a diagram rather like the upper part of fig. 76 of Lawrence's paper but reaching a single-phase system close to the oleic acid point. Fig. 19a shows part of a system worked on by myself and a section through say, 10 or 20 % soap solution and the benzyl alcohol point gives a diagram such as Lawrence's fig. 7a (line (iii) at room temperature), except that between 80 and 90 % additive, we reach the boundary of the two-phase system and go over to a single solution. It will be noticed that, if we work at about 50 % soap in the potassium-oleate system, or 30 % in the sodium-laurate system, and run in addi- tive, we go along a line rather like (iii) in Lawrence's fig.7a, except that we never have two coexistent solutions. I should like to ask Dr. Lawrence whether the boundaries at the additive corner have been studied extensively (especially at different temperatures), and whether they have been omitted from fig. 7? I should also like to defend the use of the term " solubilization "-at any rate when it is used in a well-defined sense. As Lawrence states on the first page of his paper, the system soap + water + additive, is the simple one of three partially miscible substances. The system has, however, a peculiarity which distinguishes it from those of the type acetic acid + water + chloroform. This is, that, whereas in the latter system the molecules of additive (chloroform), are uniformly distributed right down to the molecular level (except perhaps near the onset of turbidity, at the boundary of the single phase system), in the former system (at any rate near the water-rich corner), the additive molecules (in excess of their water solubility), whilst being uniformly distributed on a macroscopic scale, are concentrated in groups on a microscopic or micellar scale since they are located either in the surface or the interior of the soap micelle.The solutions are therefore not of the same kind on all different observational scales and 1 should like to suggest that the term " solubilization " be retained with reference to the formation of an isotropic solution at a soap concentration such that the micelles are discrete, independent entities.The term is probably most useful in referring to hydrocarbons whose solubility in water is approximately zero. It may even be quite useful in these systems up to relatively high concentra- tions of soap and additive in approaching the region of stable emulsions. Dr. A. S. C. Lawrence (Shefield University) said: Dr. Hyde suggests that the 2-liquid phase cannot extend all the way to the right-hand temperature axis in fig. 7 (my paper), i.e. to the 100 % amphiphile composition; and that the general Two widely differing cases are shown in a paper by ourselves.1 1 Faraday SOC. Discussions, 1954, 18, 256. C66 GENERAL DISCUSSION case requires EX to bend over and then fall so that all systems pass through a 1-phase liquid condition as 100 % amphiphile is approached.This is not correct as a statement of fact nor is the explanation acceptable. I am grateful to Dr. Hyde, however, for raising the point because the behaviour described by him as the general one does occur but only in what I regard as special cases. Consider the simplified phase diagram for sodium dodecyl sulphate + water 3- caproic acid shown in fig. 1.1 We consider adding the third component to a selected soap f water composition and therefore work along the line from Z to the additive apex, Z being the soap/water ratio. Here AZ is drawn from A as a tangent to the curve of the upper soap concentration limit below which the 2-liquid system exists; this value of Z , 43 % soap, is the minimum initial concentration which SOAP “0 FIG.1.-Sodium dodecyl sulphate 4- water -I- caproic acid system at 2 5 0 ~ . can show Hyde’s case for this system. It shows also that this case cannot be achieved if one accepts the limitation of starting with saturated soap solution + solid. Fig. 2 shows cases using the data obtained for the various phase transitions recorded in fig. 10 to 18 (in the paper cited by Hyde) in which 33 % Teepol was the initial material. The full curves are for n-octanol and represent, at the water- rich corner, experimental values whereas EA is sketched to follow fig. 1, A being known as zero solubility of water in octanol. The tangential AZ shows that the minimum concentration of Teepol for Hyde’s case is 56 %, where incidentally the soap “ solution ” is itself liquid crystalline.E, in fig. 1 of my paper, is the point at which AZ cuts the upper boundary of the 2-phase region and, for the 33 % solution of soap, we get my general case. The broken curve is for n-butanol using our value for E, the literature value for its solubility in water and a similar value for water in butanol. This is probably higher in all alcohols but values are not available. Here we get the triangle AMN (which is part of the 1-liquid phase area) and, consequently, Hyde’s case of 1-phase solution reaching to A. The value of E for normal pentanol is shown and this will also have a small I-phas area; M will be smaller as the corresponding solubility in water is only 2-2 %. For higher homologues M is SO small that M is at A and Hyde’s case can occur only above AZ.Benzyl alcohol has about the same solubility in water as n-pentanol. 1 not yet published.GENERAL DISCUSSION 67 Dervichian's potassium caproate + water + n-octanol is curious in that the E curve is a flat horizontal line at only 1 % soap. This is not general for these soaps since E is higher in the two cases cited by Hyde, potassium oleate + water + oleic acid and sodium laurate + water + benzyl alcohol. That these two systems satisfy Hyde's criterion is due to the lateral extension of the 1-phase system across the diagram and separating the liquid crystalline phase from the 2-phase region. It would be interesting to see the effect of raising the pH of a carboxylate system to suppress hydrolysis. soap M ti P FIG. 2.-Effect of solubility of water in amphiphile upon phase behaviour in the amphiphile-rich corner.0 n-pentanol, - octanol, - - - n-butanol. Hyde's general case applies to the carboxylates examined but not to the alkyl sulphate or trimethylammonium soaps which show his behaviour only at very large concentration. It will be a general case for the C4 and C5 homologous amphiphiles which have a finite triangle AMN of 1-phase system. For these cases, his suggestion of the boundary E bending over with increase of temperature and then falling (thus giving 1-phase system continuously to the 100 % amphiphile axis above some critical temperature) is, firstly, not needed; secondly, most un- likely because increase of temperature reduces the solubility of alkanols in water up to about 55°C after which it rises slowly so that solubility at 0" and 100" are about equal; carboxylic acids show no change with temperature.Hyde's suggestion requires the solubility of water in amphiphiles of c6 and above to move from A to some finite value M ; this is unlikely; heating a hydrocarbon chain does not make it a better solvent for water. Concerning Dr. Hyde's question about the boundaries at the additive corner, we have quite a lot of information. The common case is simple because amphi- philcs are poor solvents for soaps in the absence of water so that we have the case shown in fig. 3 ; that is, that neither 2- nor 1-liquid phase region reaches to the A axis as required for his general case but is separated from it by a narrow tongue of solid soap phase (+ solution) at low water concentrations.The f.p. of soap in amphiphile is not a Krafft point as it varies with concentration. Sodium alkyl sulphates are very poorly soluble in alkanols and carboxylic acids; ehe trimethylammonium soaps slightly more so and the alkylamine hydrochloride still more. I have not put m.p.A in this graph because the solid soap separation68 GENERAL DISCUSSION occurs with all lengths of carbon chain in A ; it happens even with ethanol and with the low di- and tri-alkylamines. Our graphs of the closure of the nicotine ring by soaps do not show the solid phase but the same behaviour was observed ; 1 at the higher soap and low water concentrations in the nicotine, solid soap crystal- lized out above room temperature. other phases solid soap composition s+w A or W (soap conct fired) A FIG. 3.-Freezing-point curve for cases where m.p.A is below the temperature of separationiof solid soap.I am grateful to Dr. Hyde for raising these points and giving me the opportunity to make the full position clearer. I have no comment to make upon “ solubiliza- tion ” but I would like to ask him what is solubilized by what in the amphiphile-rich 1-phase region which he is discussing. Dr. D. G. Dervicbian (Institut Pasteur, Paris) said: The ternary phase diagram for the system potassium caproate + octanol + water was presented at the 2nd In?. Congr. Surface Activity, 1957.1 Since then, 1 have examined the two ternary systems : (a) potassium caproate + methanol + water, (6) potassium caproate + butanol + water. Their preliminary diagrams are shown in fig.1 and 2. In these systems the alcohol has a much shorter hydrocarbon chain and its solubility in soap and water is not limited, so that one can pass from a point on the left-hand side (e.g. 20 % soap in water) to the opposite corner (pure alcohol) without the appearance of a new phase. This is in agreement with Dr. Lawrence’s observations that the solu bility of alcohols increases rapidly when the chain length diminishes, reaching the value of 17 molecules of amyl alcohol per molecule of sodium stearate. On the other hand, the system potassium laurate + octanol + water was also examined and evidence found again (as with caproate and octanol) for the existence of the 1 to 2 molecule proportion of long-chain alcohol to soap as upper limit 1 J. Colloid Sci., 1956, 11, 585.GENERAL DISCUSSION 69 of solubility.This indicates that association in a stoichiometric ratio Occurs only when the two chain lengths are sufficiently long. K caproate FIG. 1. Met han o! W e ter FIG. 2. Dr. A. S . C. Lawrence (Shefield University) said : Dr. Dervichian's two-phase diagrams for the lower alkanols are most valuable since they fill a gap in our know- ledge of these ternary systems. His three diagrams and our two * for water + * to be published shortly.70 GENERAL DISCUSSION caproic acid and the soaps, sodium dodecylsulphate and cetyl trimethylammonium bromide, show that the ternary liquid crystalline phase grows in from the liquid crystalline concentration range on the soap+water axis. For the “ synthetic ” soaps, this region has been ignored by all workers except for the study by Vold of dodecyl sulphonic acid and of its Na, K and Li soaps.1 It is clear from Dervichian’s diagrams that, if the added amphiphile reduces the soap concentra- tion range over which liquid crystal exists, as with MeOH, then addition of MeOH to any isotropic solution of soap can never produce the liquid crystalline phase.If, however, the Zc + I phase lower boundary dips towards the base, then we get my case of isotropic liquid --f 1s. -+ isotropic liquid, as occurs in his butanol and octanol diagrams. A most important difference seems to exist between carboxylate soaps, which form two liquid layers only up to a quite small concentration of soap, ca. 3 % or less, and our two soaps for which this phase boundary is 10 % for the C12 soap and 18.5 % for the c16.Here also is an important effect of chain length in the added alkanol (or fatty acid) ; up to c6, two liquids are formed ; with C7 and above a system results resembling only superficially an emulsion. These higher homologues when placed on top of a soap solution of sufficient concentration exhibit the phenomenon which has been mis-named “ spontaneous emulsification ”.2 The resultant colloidal system is seen, under a cover glass, by microscopic examination to have what we call the “string bag” structure. It is not a system of oil in water, or water in oil ; it is aqueous solution enclosed in a mass of membranes ; these are the “ string bag ” and the “ strings ” are strongly birefringent showing tiny-focal conic structure.Boiling does not destroy this cellular structure. I am not impressed by changes taking place at or near to stoichiometric ratios ; we have already reported some.3 The essential feature of the liquid crystalline phase is that it exists as a homogeneous phase over a wide range of concentrations of the three components. Its special interest is that it separates out as an ordered structure as a reult of what Professor Bernal referred to in his opening paper as “ cryoscopic ” forces. Without these, the soap would be solid in three dimen- sions ; the polar groups of soaps and amphiphile are in solution in the water ; the hydrocarbon chains are insoluble in it, hence, the liquid crystals. It is this picture that I had in mind many years ago when I first used the name lyotropic mesomorphism to distinguish partial loosening-up a solid lattice to the 1.c.one by a solvent as opposed to the classical thermotropic 1.c. melt where it is done by heat. Ternary 1.c. systems will be commoner than 2 component ones because it is more difficult to hold back the normal tendency to crystallize. In the three-component system, there must be some amphipathy and so the phe- nomena is particularly one shown by large molecules. It is the amphipathy which resolves the paradox of ordered structures being formed by solution forces. Dr. A. S. C. Lawrence (Shefield University) said: I would like to protest against the revival of the habit of speaking of soap micelles as if they were, when once formed, virtually indestructible and having rigid geometrical shapes.The micelle is a labile unit as is well demonstrated by a recent experiment. Waxoline Yellow IS (I.C.I.) recrystallized twice from ethyl acetate is dissolved in a soap solution whose concentration is about twice its c.m.c. ; after filtering and centrifuging, it is placed in a large beaker and illuminated by a convergent beam of light. No Tyndall cone is seen. Sufficient water is then added suddenly to dilute to one-half of the c.m.c. whereupon the Tyndall cone flashes up without observable time lag. In the very short time, the micelles have broken down to single molecules and 1 Vold, J . Amer. Chem. SOC., 1941, 63, 1427. 2 2nd Znf. Cungr. Surface Activity, 1957, 1, 475. 3 Hyde, Langbridge and Lawrence, Faraday SOC. Discussions, 1954, 18, 256.GENERAL DISCUSSION 71 thrown out the dye which then has to aggregate into clumps large enough to scatter light.After 1 to 2 days, the solution is colourless and the dye in large flocs on the bottom. Dr. K. Heckmann (Giittingen) (communicated) : Dr. Lawrence protests rightly against " the habit of speaking of soap micelles as if they were, when once formed, virtually indestructible and having rigid geometrical shapes ". To illustrate this point he describes an experiment where soap solution was diluted to a concentra- tion below the c.m.c., under which conditions the micelles decompose in a short time. Using a dilution apparatus according to Hartridge and Roughton, v. Biinau and Gotz in our Institute have found that the decomposition time of cetyltrimethyl- ammonium bromide micelles must be even shorter than 10-3 sec.These experi- ments underline the fact that shape and size of soap micelles correspond to a state of equilibrium and depend on temperature and concentration and, among other parameters, possibly on the state of orientation and rate of shear. When determining sizes and shapes of micelles, an alteration in these variable quantities is only admissible if it can be shown that such an alteration has no influence on the micelle structure. Thus, for instance, it is impossible to isolate micelles from their solutions by drying, centrifuging or filtering without altering them in the process, although this has repeatedly been attempted. The dependence of apparent size and shape of CTAB micelles on the state (c, T ) and the stability of these micelles under mechanical shear is reported else- where in this Discussion.Dr. K. Heckmann (Giittingen) said: Dr. Luzzati and his co-workers concluded from their X-ray measurements that certain middle-soap phases contain cylin- drical micclles. We are very glad to hear this result as we have been led to the same conclusion by an entirely different experimental approach. Mr. Gotz and I 1 have investigated the anisotropy of the electrical conductivity of polyeIectrolyte solutions under the influence of a shearing force. For soap micelles this anisotropy method supplements the X-ray investigations, especially in the region between the so-called middle-soap phase and the micellar solutions, as here the X-ray diagrams are diffuse and not easy to interpret. I therefore givc a brief report on the essential features of the conductivity anisotropy method.If a polyelectrolyte solution containing rod- or disc-shaped particles is exposed to a shearing force, for instance in the gap of a rotating Couette apparatus, the polyions become oriented in such a way that in the direction parallel to the axes of the Couette-cylinders the hydrodynamical resistance of rods is higher than for random distribution of particles, and that of discs is lower. So if the conductivity is measured parallel to the axes of the Couette cylinders, it is found that with in- creasing velocity gradient the electrical conductivity decreases for rods and in- creases for discs. The quantitative theory behind this method has been worked out by Schwarz 2 in our institute.It has been tested and confirmed using polyphosphate and graphitic acid solutions, which are known to contain rod-shaped and disc-shaped particles respectively. Of the several soap solutions we investigated, only those of CTAB and Na oleate showed anisotropy effects, both of these behaving in a manner character- istic for rods. From the behaviour of the saturation anisotropies, it is evident that the micelles are practically undamaged even at the highest velocity gradient we applied (3000sec-1). So far we have not been able to find any disc-shaped micelles. A quantitative analysis of the anisotropy velocity gradient curves gives the rotation diffusion constant from which an apparent characteristic length of the particles can be calculated.The relaxation of the anisotropy when the Couette 1 Gotz and Heckmann, J. Colloid Sci., 1958, 13, 266; 2. Elektrochem., 1958, 62, 281. 2 Schwarz, Z. Physik, 1956, 145, 563.72 GENERAL DISCUSSION apparatus is switched off may be used for the same calculations. The anisotropy technique, then, yields only apparent micelle lengths, which are larger than the real lengths due to strong micellar interaction. It would be interesting to combine the anisotropy method with X-ray investiga- tions, from which real lengths are obtained, and thus to determine the size of these interaction forces. Mr. K. G. Gotz (Guttingen) said): Dr. Luzzati and co-workers have shown that for " middle-soap phases " their X-ray diagrams can be interpreted by a hexa- gonal arrangement of indefinitely extended rod-shaped micelles.This agrees with 4c 35 30 "C 25 15 t ( - 5 10 I5 2 0 w t. % C TA 8 ) ( 7 ~ 1 6 ~ " ) FIG. 1.-Phase diagram CTAB 4 water. A, micelle-free solution ; B, isotropic micellar solution ; C , anisotropic solution ; D, crystalline phase ; C,, critical micelle concentration (diagrammatic) ; K.P. Krafft-point. results we have obtained by investigating the anisotropy of the electrical conductivity in more diluted flowing solutions. Fig. 1 shows a small section of the whole phase diagram of the system CTAB + water. Whereas the micellar phase is bounded at low concentrations by the critical concentration and at low temperatures by the crystalline phase, the boundary between the micellar and middle soap phases is characterized by a steady increase in the apparent length of the micelles.(The apparent lengths given in this diagram are greater than the real lengths due to micellar interaction.) Anisotropy measurements show that these CTAB-micelles are definitely rod- shaped. So we find that the transition from the micellar to the middle-soap phase is in good agreement with the description of the latter given by Luzzati and his co-workers. Dr. K. Heckmann (Guttingen) said; Dr. Luzzati mentioned his assumption that the middle-soap phases he investigated precede a region where the long cylindrical micelles decrease in length with decreasing concentration, and eventually becomes spheres. As Mr. Gotz has pointed out, this assumption is confirmed by the conductivity anisotropy method, at least for Na oleate and CTAB.GENERAL DISCUSSION 73 For this concentration range we developed a formula which, for a somewhat idealized model, combines the radii and lengths of the cylindrical micelles with the distances between their long axes and with the concentration of the solution.The equation is based on the following assumptions : (i) The cylindrical micelles are of uniform length and their ends are rounded (ii) The interior of the micelles is liquid and has the same density as the para& (iii) The micelles arrange themselves in hexagonal order. The equation is off into hemispheres. corresponding to the hydrocarbon chains of the soap ions. where D = r = I = V = c = distance between long axes of micelles in A, radius of liquid interior of micelles in A, length of cylindrical part of micelles in A, molar volume of paraffin in ml, concentration of soap in moles/l.10 20 wt.% FIG. l.-(a) Na oleate long spacings (D) as function of concentration; (b) length of cylindrical part of micelles, as calculated from eqn. (1) (substituting V = 300 ml and r = 21-1 A), plotted against concentration. The limiting case of I + 0 is practically identical with the formula for spherical micelles proposed by Hartley.1 Another limiting case (I --f a) is presumably the equation used by Luzzati and co-workers for their calculations of the micellar radii. In order to describe the real situation more accurately, eqn. (1) must be cor- rected primarily for thermal disturbances of the hexagonal array and for the distribution function of I, which for soaps, however, is relatively narrow.We were concerned with an estimation of the length of Na oleate (and CTAB) micelles as a function of concentration, and were especially interested to find the lower concentration limit at which electrical anisotropies can be obtained ( I = 0). 1 Hartley, Nature, 1949, 163, 767.74 GENERAL DISCUSSION We therefore had to define two of the four disposable parameters of eqn. (I), as follows. First, we assumed the radius r to be independent of concentration and equal to the length of a paraffin chain. Secondly, as values for D we used the so-called X-ray long-spacings which had been calculated for Na oleate by Kiessig 1 and by Harkins2 and co-workers. This is analogous to Hartley’s procedure. The derivation of these long spacings, however, is subject to theoretical reservations, and therefore the latter assumption must be made with due caution.The results of the calculation for Na oleate are seen in fig. 1. (For CTAB no X-ray data are available.) l(a) gives the Na oleate long spacings, (b) shows the lengths of the cylindrical parts of the micelles. It is seen that the cylindrical parts of the micelles start growing at a concentra- tion of about 6 % by weight (0-2 M). Below this point the micelles are spheres. It is interesting to note that this concentration of 0.2 M is known as the “ second critical concentration ”, since several workers have independently concluded that here Na oleate solutions undergo structural alterations (see, for instance, Ekwall.3) This fact, that the calculated concentration at which the micelles change their shape is identical with the second critical concentration, supports our view that the proposed equation and the additional hypotheses describe the structure of Na oleate solutions fairly well in the transition region between “ micellar solution ” and “ middle-soap phase ”.Dr. K. H. Weber (Leipzig) (conzmunicated): The line-shapes of the proton magnetic resonance absorption in the compounds of the homologous series of the 4 :4’-alkoxy-azoxy-benzenes H2n LlCn-O-C6H4-N=N--C6H4-O-C,H2n+l (n = 1 . . . 7 with the exception of n = 3) in the liquid crystal state were recorded as was the dependence on temperature, with the aid of a nuclear resonance spectro- meter.6 5 The second moments of the line shapes g(H) : .1 0 The strength H of the magnetic field was H = 7,750 gauss.were computed. The value of (AH2)exp decreases for each substance as the tem- perature increases, at first slightly and near the clearing point more strongly.4 The observed dependence of the second moments (AH2),,, on the temperature T can be explained quantitatively based upon the fact that the long axes of the molecules in consequence of the diamagnetic anisotropy of the investigated sub- stances are ordered in the direction of the magnetic field. The measurements of the anisotropy of the dielectric constant 6.7 demonstrate that the orientation caused by the magnetic field is perfect at a field strength H > 2,000 gauss. Be- cause of the thermal motion the molecules make hindered reorientations in a statistical manner about axes, which are perpendicular to the long axes of the molecules; therefore the long axes make angles 0, dependent on time, with the field H.Assuming rotations about the long axes of the molecules to be restricted only slightly and the frequencies v, of these reorientations to be greater 8 than lo5 c/sec, the relation for the second moment (AH2heor. = HPLS~ (2) 1 Kiessig, KolloidZ., 1941, 96, 252. 2 Harkins, Mattoon and Corrin, J. Amer. Chem. SOC., 1946, 68, 220. 3 Ekwall, J. Colloid Sci., suppl. 1 , 1954, 66. 4 Lippmann and Weber, Ann. Physik, 1957,20,265. 5 Liische, Kerninduktion (Berlin, 1957). 6 Maier, Barth and Wiehl, Z . Elektrochem., 1954, 58, 674. 7 Meier, Diplomarbeit (Freiburg i. Br., 1956). 8 Bloembergen, Purcell and Pound, Physic. Rev., 1948, 73, 679.GENERAL DISCUSSION 75 can be 1 dreived according to the theory presented by van Vleck 2 and by Gutowsky and Pake.3 p~ is a function of the intra-molecular nuclear magnetic interactions (dipole- and spin exchange-interactions) of the protons of one molecule; p~ can be theoretically calculated, if there are known the configuration of the protons of one molecule and the degree of freedom of motion of individual atomic groups.4 Supposing the molecular structure and the intra-molecular reorientations not to be changed in the temperature range of the liquid crystal state5 it must be AW(T) w S2(T) ; thereby the degree of order S is defined by (3) that is-according to (2)-the temperature dependence of the second moment must be caused by the temperature dependence of the orientation-due to inter- molecular interactions-of the long axes of the molecules.Applying the theory of co-operative phenomena 6 Zwetkoff 7 has derived the function S(T). We have tried to extend for any large angles 8 the theory of Zwetkoff, which is valid only for small fluctuations and which for this reason cannot give correct values of S especially near the clearing point. S = +(3 C O S ~ 0 - l)av., Defining as the energy of order (4) according to Zwetkoff, where a is a constant and (e2)max is the average of the square of the fluctuation angle 8 in the statistical distribution, then S can be easily calculated using the distribution function where #(8) = exp (K cos2 6), K = a/kT. (k is Boltzmann's constant, T is the absolute temperature.) We obtain J o For K < 1 we obtain and for K > 8 the semi-convergent series 3 3 15 111 1059 S = l - - - - - - - - - - for which S(0) = 0 and S(CO) = 1.The functions S(K) and - = 1 - are shown in fig. 1. Using the function (8) which Zwetkoff 7 has obtained with p-azoxy-anisole (n = 1) it follows from (4) and (6) that (9) 2K 4K2 8 K 3 1 6 ~ 4 32/65 ' 2 1: v = vo (exp CPS) - 11, TK(S) = exp (PS) - 1, 1 Weber, Diss. (Leipzig, 1957). 2 Van Vleck, Physic. Rev., 1948, 74, 1168. 3 Gutowsky and Pake, J . Cliem. Physics, 1950, 18, 162. 4 Weber, Ann. Physik, to be published. 5 Maier and Englert, Z. physik. Chem., 1957, 12, 123. 6 Bragg and Williams, Proc. Roy. SOC. A , 1934, 145, 699. 7 Zwetkoff, Acta physicochim., 1942, 16, 132.76 GENERAL DISCUSSION where = kT/vVo, (10) and v = 2/(02)max.(1 1) The function S = S(T, /3) which is contained in (9) is shown in fig. 2. In the temperature range of the liquid crystal state S 2 Smin and T 2 T,. There- 0.7 - 06. S ' 0 5- 0 4 - 0 . 3 - fore that temperature which according to (10) is given by Tmax = kTc11~ VO, 2 3 4 5 b 7 'cx 26 2 2 d k dS - 18 14 10 6 d- 0.7 S - 0.b 0 . 5 0 . 4 b } 0 . 8 3 0 .? 0.1 5 04 0.0 5 0 0.3 FIG. 2.-Degree of order S against T X = (T'1 - T)/Tcl. ( a) for V = VoS; (6) for V = Vo exp {(PS) - l}, P = 0.5 ; (c) for V = VO {exp (PS) - l}, can be identified with the temperature T',, of the clearing point. The functions Tmax(r6) and Smin(p) are shown in fig. 3. can be determined from the experimental temperature dependence of the second moment such that E{(AH2)exp - (AH2)theor.}2 becomes a minimum.j3 = 2.0 ; ((1) for V = VO exp {(PS) - I}, P = 2.0 (according to Zwetkoff). The constants p~ and77 GENERAL DISCUSSION The comparison between the value of pL determined in this manner and the calculated one for any structure of a molecule allows certain conclusions concerning the degree of freedom of intramolecular reorientations.1 For all the compounds 0.6 0.71 06 0 . 5 3 . 4 g x 0 3 0 2 01 d.5 ’ 2 . 0 2 5 FIG. 3.-rmax, , S ~ * and energy of order at the clearing point Vcl agahst p. I I I I I I 1 4 0 0 - 3 ‘ 9 0 I00 110 I20 1 3 0 T [“cl FIG. 4.-Experimental values of the degree of order S for p-azoxy-anisole ( I ? = 1). (optical) ; Zwetkoff (diamagn.) ; - Maier (infra-red). 0 from m; 0 Lippmann (magn.resonance) ; x Chatelain (optical) ; [7 Zwetkoff investigated by us ,8 = 0.5 f 0.3, with the exception of hexoxyazoxybenzene (n = 6) for which /3 is smaller. The S-values evaluated from S = ((AH2),,,/4~L]* are shown in fig. 4 for p-azoxy-anisole (n = 1). They are in a relatively good agreement with those values 1 Weber, Ann. Physik., to be published.78 GENERAL DISCUSSION which are obtained by other authors.1-3 Only the values obtained from infra-red investigations 4 are too small." The values determined for the other compounds are shown in fig. 5. S 0 0 0 0-6 0 . 4 TIOCI FIG. 5.-Experirnental values of the degree of order S for the homologous series of the alkoxy-azoxy benzenes. determined from the second moment data ; - determined from infra-red data (Maier 10).The applicability of the theory of co-operative phenomena to the molecular order in liquid crystal phases and the temperature dependence of the degree of order derived from this theory should be examined for the following. (i) If there are sufficiently exact measurements the dependence of S on tem- 1 Zwetkoff, Acta physicochim., 1942, 16, 132. 2 Lippmann, A m . Physik, in press. 3 Pellet and Chatelain, Bull. SOC. franc. Min., 1950, 73, 154. 4 We thank Prof. Maier, who has communicated to us his values. These are more * The S-values obtained from diamagnetic 12 and from optical data 12.14 are strongly dependent on the manner in which the internal field is computed. We have calculated ourselves the S-values marked with crosses ( x X ) in fig. 4 from the data of ne and no given by Pellet and Chatelain 14 for h = 0 .5 8 9 ~ considering the calculation of the internal field proposed by these authors. There can be obtained for each temperature three values of S differing about 5 %, i.e. from n,, no and from (n, - no). The values given in fig. 4 are average values. The agreement with the values obtained by magnetic resonance investigations becomes even better, if you consider that the clearing point of our substance is about 2°C higher than that given by Pellet and Chatelain. accurate than his published ones.5GENERAL DISCUSSION 79 perature can be examined, whether or not the experimental dependence is cor- rectly represented by the theore tically derived one. 0.32 for all the substances in the temperature range of the liquid crystal state (see fig. 3) appears to be met as seen in fig. 4 and 5. As far as there are differences they are inside the limits of errors. But it must be remarked that the molecular order in the immediate proximity of the clearing point can be strongly influenced by hectrophase fluctuations.1 (iii) We obtain for the energy of order Vcl at the clearing point from (8) and (12), (ii) The conclusion that S As can be seen from fig. 3, f@) is a straight line given in good approximation by f(p> = 2.2 4- 1*6,8, (14) x X . X x X n = I x n - 2 a * r x 1 0.05 0 01 ' ' ' ' ' ' ' " T X FIG. 6.-Degree of molecular order S against T X = (Tcl - T)/Tcl for methoxy- and ethoxy-azoxybenzene. for /3 < 2.5. In this way the heat of transition at the clearing point is Q =LV& where L is Loschmidt's constant. We obtain for the investigated compounds Q = 1000 i 200 cal/mole ; this value is comparable with the measured ones of Kreutzer and Kast.2 From the fact that the heat of transition at the transition point liquid crystal + isotropic liquid is normally greater for the smectic than for the nematic phases,3 it follows according to (13), (14) and fig. 2 that the dependence of the degree of order on the temperature should be less in the smectic phases than in the nematic ones. This conclusion is confirmed by the measurements of Maier 4 for the smectic phase of heptoxy-azoxybenzene (n = 7), as can be seen from fig. 5 (heptoxy-azoxybenzene is smectic for T < 92°C and nematic for T > 92°C). (iv) It follows from (10) and (12), T/Tmax = T/Tc~. Because T~~ iS a function only of p it follows according to (9), that with a given value of p, S is a function of T/Tcl. Therefore comparing various substances, whose values of @ do not differ from each other and defining T X = (T,1 - T)/Tcl as a reduced temperature, then at equal reduced temperatures T X equal values of S must result. That is, for the degree of order of such liquid crystals which agree in their values of B, the theorem of corresponding states is valid. This is verified as seen in fig. 6, where S against T~ is represented for methoxy- and for ethoxy-azoxybenzene (n = 1 and n = 2). 1 Hoyer and Nolle, J . Chem. Physics, 1956, 24, 803. 2 Kreutzer and Kast, Naturwiss., 1937,25,233. Kreutzer, Ann. Plzysik, 1938,33, 192. 3 Kast, 2. Elektrochem., 1939, 45, 184. Maier and Englert, Zphysik. Chem., 1957, 12, 123.

ISSN:0366-9033    

DOI:10.1039/DF9582500059

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年代:1958

数据来源: RSC

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11. MACROMOLECULES INTRODUCTION BY W. T. ASTBURY Dept. of Biomolecular Structure, University of Leeds Received 15th May, 1958 It is not easy to follow after the comprehensive General Introduction with which Bernal has already set the scientific stage of this meeting, but I believe there still remain certain rather more specialized and personal considerations to which I can usefully draw your attention. As I see it, this Discussion is particularly opportune in the stimulating part it is bound to play in bringing together, and at last in intelligible focus, a number of experimental and theoretical approaches that have long been groping for such contacts. Of these “ co-ordinations ”, so to call them, I should like to say something first in relation to recent progress to- wards recognizing the configurations of polypeptide chains in proteins.To the well established, if still not yet completely elucidated, a- and ,%con- figurations there is to be added now, what was always there by implication, I suppose, especially in solution, the randomly-coiled state. While calculations, for example by Schellman,l have been carried out with varying promise on the probability of interchange between cc-helix and randomly-coiled, notable suc- cesses have been achieved on the experimental side by the application of light- scattering and optical-rotation tests and by deuteration studies. The results obtained along these lines by Doty and his collaborators at Harvard, by Elliott and his collaborators at the Courtaulds Laboratory, and by the Linderstrrm-lang school at the Carlsberg Laboratory are most impressive, and there will be plenty of references to them in the papers and discussions to follow.The exciting stage has now been reached of extrapolating from the synthetic polypeptides, where reversible transition from a-helices (right-handed if the residues are left-handed) to random coils has been demonstrated conclusively, to the globular proteins, and already with these too the strong indications are-as suggested also by X-ray diffraction studies-that they can be compounded at least in part of cr-helices; and, moreover, the proportions of the latter can again be reversibly modified to some extent. The rest of the globular protein molecule though-the bends where the helical runs join up and the so-called tertiary structure as a whole-is in general still pretty much as vague as ever, and in any event is presumably more or less peculiar to each species, being defined by further linkages as yet mostly only guessed at.Kendrew’s X-ray model of the myoglobin molecule offers a fascinating glimpse of the sort of thing to be expected. I want to recall old evidence and present some revitalizing new evidence for another polypeptide configuration in proteins that I have the feeling may eventually turn out to be scarcely less significant than the a- and P-configurations-meaning by the latter the more familiar “parallel p” as produced from the a-form by stretching; for this new-old configuration is also a @-form, what we call “ cross /3 ”, in which the 4.65 A reflection associated with interchain CO .. . HN linkages is not in its usual place on the equator of the fibre diagram but is on the meridian. It is the form we have come to connect specially with the phenomenon of “ super- contraction ”, that property of fibres of the k-m-e-f group of being able to contract under appropriate treatment to a length even shorter than the a-configuration. It was in the early thirties that Mrs. Dickinson and I first obtained a cross-/3 80W. T. ASTBURY 81 diagram, from a frog sartorius muscle that had been immersed in water at 60” or more. At that time we had little idea what it meant, but soon afterwards, while working with Bailey in the X-ray investigation2 which revealed how globular proteins unfold on denaturation and can then be drawn out into fibres giving a diagram of the type of &keratin and /3-myosin, we were surprised to find the same sort of thing again on stretching (by about 100 %) thin strips of “poached” egg-white ; surprised, because stretched denatured edestin, for example, had given a normal P-diagram, with the polypeptide chains running in the direction of stretching.We could only interpret the egg-albumin effect in terms of bundles of ,&chains which were actually thicker than the chains were long, and which were therefore oriented by stretching so as to leave the chains lying transversely. All through the thirties, too, we were developing the idea, never really abandoned, since, that muscular contraction, in the last resort, is a specialized manifestation in myosin, of the power of supercontraction common to the whole of the k-m-e-f group, while at the same time we were led to the view that the phenomenon was the result of the polypeptide chains being able to fall into transverse folds more pronounced even than those that defined the cc-form-this was in the bad old days before the %-helix, be it remembered, when the favoured scheme for the w o n - figuration was a square fold which was in effect the shortest possible lateral /?-fold, and which there was little difficulty therefore in imagining to be able to lengthen t ransversely.3 We owe to Rudall4 the first systematic X-ray examination of supercontraction, particularly in epidermin, the fibrous protein he had extracted from the epidermis, and it was he who pointed out in 1941 that the transverse folds that had been proposed for the supercontracted state would most likely lead to a cross-p pattern (see fig.1). He also showed how the cross-13 form may be reconverted to the cc-form by the action of saturated urea, for instance. Since then, a number of people-Woods, Whewell, Mercer, Sikorski and others-have continued the attack from a variety of angles, and it still goes on, indeed with the added impetus lately that “ natural ” cross-P structures have been discovered. These latter have made all the difference in the world to a problem that was never lacking in interest, to say the Ieast, and I should like to explain now how beautifully they have come to link up with the important discoveries by Keller also to be reported upon at this meeting.The two known “ natural ” examples of cross-/? structures are provided by bacterial flagella5 and the egg-stalk of the green lace-wing fly Chrysopa.6 The former, to judge by their X-ray diagrams and motility properties, are a kind of monomolecular muscles : the diffraction pattern comprises not only an a-diagram with a higher periodicity (about 410 A) like that of skeletal muscle, but a prominent 4-65A reflection on the meridian besides (fig. 3a). This, of course, represents the combination we had been postulating all along as the ultimate molecular basis of muscular activity, even though we had never actually observed it in whole muscle undcr conditions of physiological contraction. No wonder then that we suggested with increased confidence that the rhythmic localized shortening and lengthening implied by the bending movements of flagella rest too on an interchange between the 01- and supercontracted configurations.Thcre is still a considerable element of speculation, it must be confessed, in this interpretation of the structure and movements of bacterial flagella, but the case of Chrysopa is beyond doubt : the egg-stalk is a natural silk in which /3 poly- peptide chains lie transverse to the fibre axis ; in folds too, for stretching the stalks pulls them out into the parallel-/? form of the more familiar silks. And this is not all : the basal pedestal, which consists of a film of protein spread by the laying insect on the leaf surface before it proceeds to draw off the 15-20 ,u thread which constitutes the egg-stalk, shows the ,8 polypeptide chains standing perpendicular to the film, with the a and c axes in the plane of the film.It is as though the struc- tural components of the fibre are drawn off in the form of long “ jumping crackers ”.82 INTRODUCTION The co-ordination with the “ classical ” observations on the cross-fl state and above all with Keller’s discoveries is clear, and to my mind of a significance for protein studies that could be far-reaching. Keller has found that polyethylene (and other chain-polymers such as nylon) can build comparatively large orthodox crystals just as if they were short-chain hydrocarbons or fatty acids. They do this by the trick, somehow energetically more favourable in their case-and one can see in a general way why for more flexible chains it should provide a more probable path to good packing-of fording into shorter lengths; they take up what I have just called the “ jumping-cracker ” form, a chain of regular transverse folds that in polyethylene, for instance, are of the order of lOOA long.Chrysopa silk behaves similarly, and the analogue of the polyethylene crystal is the basal pedestal. How long the transverse folds are in the polypeptide is being investig- ated, but fig. 2a shows some promising high-spacing reflections on the equator that could very well turn out to be counterparts of those found by Keller with polyethylene. (It is the high-angle pattern in fig. 2a that is the transverse equiv- alent of that given by other wild-type fibroins in the parallel-p form. The cor- respondence becomes direct and obvious, of course, when the Chrysopa silk passes over into the parallel-IS form on stretching-a change, it should be emphasized, that is in no sense a mere rotation of micelles but a genuine intramolecular trans- formation; * see fig.2b.) Looking back over the years during which we at Leeds have many times been preoccupied with the often difficult business of orienting macromolecules for X-ray diffraction purposes, it is noteworthy how the technique we developed, of first making thin films in which the long molecules lay down flat and then trying to stretch narrow ribbons cut from such films and in any case photographing them with the X-ray beam parallel to the surface, may have owed much of its success to the comparative inflexibility of most of the structures with which we happen to have operated.I am thinking of cellulose and its derivatives and other polysaccharides, gelatin, a-proteins (including bacterial flagella), and nucleic acids; and of how, as is realized now, it was only with polypeptides set free from the stiffening effect of specific intramolecular linkages that we came across the “ anomaly ” of long transverse folds. The question of what decides whether or not a long chain-molecule shall take up a transversely folded configuration, and the magnitude of the “ driving force ”, is intriguing enough on any count, but is pre-eminently important, to my idea, in relation to muscular contraction and its proposed interpretation in terms of the supercontraction of myosin. It is hardly to be doubted now that the latter is the expression of a marked tendency of the a-configuration, in hot water or by other means, to uncoil and fall instead into transverse folds; but what is the likelihood of such a transformation taking place under physiological conditions, and could it exert a suffciently useful pull? The lot of the physicist is still not entirely a happy one when he tries to persuade the physiologist that his (the physicist’s) unnatural experiments do really have something to do with what happens in vivo, and this has been a trouble certainly with our studies of the elastic properties of myosin 8 (actually an actomyosin, as Szent-Gyorgyi and Straub discovered later) isolated from its physiological environment and “ d e natured,” too, from the orthodox biochemical standpoint ; but quite recently we have been able to shed the stigma to some small degree by obtaining a cross-/3 diagram (fig.36) also from actomyosin gel contracted by the agency of adenosine triphosphate (ATP). This has been accomplished by Pautard, and it is peculiarly timely and gratifying in the present context to have succeeded at last with such a near-physiological demonstration of transverse folding in actomyosin under the * Though it was apparently not appreciated at the time, Palmer and Galvin,’ to judge by their published X-ray diagrams of fibres made from denatured crystalline egg-albumin, seem to have brought about a similar intramolecular transformation from an imperfect cross-/l state to well oriented parallel+ by means of a second stretching in live steam.(4 (6) FIG.1 .-X-ray fibre diagrams and skeleton representations of (a) the " parallel-/3 " form and (b) the " cross+? " form of epidermin (Rudall). [To face page 82(a) (b) FIG. 2.-X-ray fibre diagrams of the egg-stalk of the lace-wing fly Clzrysopa : (a) in the natural cross-/3 form ; and (6) in the parallel-/3 form produced from (a) by stretching. (Fibre axis in both diagrams parallel to short edge of page) (Rudall).(a) (b) FIG. 3.-(a) X-ray diagram, taken with the beam parallel to the surface, of a thin film prepared from the flagella of B. subtilis (Beighton); (b) ditto of a thin film prepared from actomyosin gel contracted by the action of adenosine triphosphate (Pautard).FIG. 4.-Electron micrograph showing the eventual disintegration of Polytoma flagella into chains of uniform particles (Millard).W.T. ASTBURY 83 action of what muscle itself uses to cause contraction. The effect as disclosed by X-rays is so far only feeble, but even so, I believe that it already has to be reckoned with as a possible first intimation of the biological pointer we are looking for. My second ‘‘ co-ordination ” links up automatically with my first, because I should like to say something next about the phenomena of biological contractility in relation to what may be called the corpuscle-fibre paradox; by which I mean the curious situation that whereas man-made fibres, on the strength of lessons learned primarily from studies of natural fibres, are essentially ‘‘ molecular yarns ” spun from more or less &awn-out chain-molecules, it has come to pass that at least the initial stages in the construction of natural fibres are found now frequently to involve a stringing-together of unit “ beads ” of coiled-up and folded chains.A classical early, but still outstanding, indication along this line of inference was given by feather keratin,g whose magnificent X-ray photograph had every appear- ance of a corpuscular origin yet was also a fibre diagram based on strikingly stretchable chains in a kind of crumpled p-configuration, but since then there have been, to mention only a few other examples: Waugh’s fibrous insulin; Bailey’s tropomysin, a member of the k-m-e-f group that can also grow into large single crystals ; F-actin, formed by the reversible polymerization of G-actin, and the source of the higher axial periodicities in the diffraction diagram of skeletal muscle ; 10 and latest and most dramatic of all, Andrew Szent-Gyorgyi’s “ proto- myosins ”, small units weighing only about 5000 into which he has succeeded in splitting myosin simply by the action of urea, under certain specific conditions.11 Pcrhaps the most impressive illustration of the paradox that we have observed at Leeds is the rapid breakdown-merely in the process of preparing a specimen for the electron microscope-of flagella detached from the alga Polytomn.They disintegrate fist into the familiar eleven sub-fibrils, next into filaments, then finally into chains of particles of diameter about 175 A (fig. 4).5 Szent-Gyorgyi (Albert) supposes 12 that since even the myosin “ molecule ” turns out after all to be no other than strings of particles held together by secondary forces, contraction must mean the collapse, somehow, of such strings into shorter, fatter collections, We cannot forget, though, that myosin is also effectively an elastic molecular yarn constructed from polypeptide chains normally in the a- configuration but which can be stretched into the parallel-P configuration and supercontracted into the cross$ configuration ; and of course to harmonize these two descriptions dynamically-they remind one of the corpuscle-wave dilemma that used to divide the theory of light-is the problem. I believe the difficulty can be smoothed out now, not too speculatively, with the aid of the newer findings on the globular proteins that I mentioned at the beginning of this Introduction.The concept of regular linear sequences of packets of suitably coiled-up and folded polypeptides to explain in a more static sense both the apparent biogenesis and the X-ray diagrams of natural protein fibres is not new-various people have thought of that ; but the tendency has been at the same time to picture the globular proteins as mostly all-or-none structures, so to speak, ready to unfold irreversibly at the slightest provocation; and from such a combined viewpoint it was not so easy to go on to explain long-range biological contractility-at any rate, not so easy as in terms of the folding and unfolding of the chain-molecules of straight- forward molecular yarns which the X-ray diagrams originally suggested, perfectly correctly in the case of many fibre structures.Now, however, we know from, for instance, the optical studies of Doty and his collaborators that the presence of cx-configurational components can be demonstrated not only in the fibrous proteins where they were first discovered by X-rays, but in the make-up of orthodox globular proteins too; and, what is very much more, the proportions of these cr-components can be reversibly altered to some extent by suitably altering the environment. The co-ordinating, and crucial, step in the argument that I want to make here is that these intra-globular configurational changes must, in principle,84 INTRODUCTION be accompanied by shape changes, and changes in the direction and mode of contact with neighbouring corpuscles, so that, in a linear polymer, spiralization and overall length changes, which may be very considerable, can follow as a matter of course.To clinch this inference by direct experiment we have, most apt among the observations to be discussed presently, Bresler’s arresting findings with human serum albumin-how the axial ratio of the molecule, considered as an ellipsoid, increases progressively from 4 to 16 when the water + dioxane solvent at pH 10 is made more and more hydrophobic by increasing the dioxane concentration; and this takes place, indeed, without any change in the optical rotation, and therefore even without affecting the a-helical components ; that is, presumably, by modifying only the tertiary structure. Clearly, chains of serum albumin, if there were such things, would be susceptible of violent contortions.The mitotic cycle of chromosomes, as viewed under the ordinary optical microscope, provides the classical example of the spiralization of chains of FIG. 5.-Infra-red absorption spectra of films of untreated and heat-denatured egg-white protein (Parker). (Inset : X-ray diagram of the heat-denatured egg-white.) - untreated (thin film); - - - - after boiling (thin film); - * - - difference curve. biological particles at the visual level, but in a closely similar connection I should like to make special reference to a just recently published paper by Ambrose,lJ in which, with the help of the interference microscope, he reveals as never before how minute fibrils are built by the linear aggregation of intracellular particles, and how readily these fibrils fall then into helical forms.My third and last “co-ordination” is a pendant to the paper by Elliott, Hanby and Malcolm in which they once and for all abandon the exciting general- ization suggested by the Courtaulds Laboratory several years ago to the effect that the a-helical configuration could be diagnosed always by a carbonyl stretching frequency round about 1665-1 660 cm-1 as opposed to 25-30 wave-numbers fewer for the corresponding band given by the p-configuration. This criterion would have been invaluable, but from the beginning doubts arose till eventually, even before the coup de g r k to be administered at this meeting, came the unanswer- able exception of polyglycine 11, for which they found 1648 cm-1 while Crick and Rich 14 interpreted its X-ray diagram in terms of a helix with three residues per turn and residue-length about 3.1 A, stabilized by intermolecular hydrogen bonds, as compared with the x-helix, which has 3.6 residues per turn and a residue-length of 1.5A and is stabilized by intramolecular hydrogen bonds.Also Parker here at Leeds, working in the same field, made the observation, among others hard toW . T . ASTBURY 85 reconcile with the Courtaulds thesis, that boiled fish myosin, for instance, gave an excelient /I diffraction pattern with no detectable trace of a, yet still seemed mostly or from the proposed infra-red test ; and similarly with egg-white. It is the latter experiment that is illustrated in fig.5 ; albeit, for sentimental reasons dating back to the cross-,f3 story, again with a film of “poached” egg-white! Altogether, it must be accepted now that, whether or not the /3-configuration is recognizable by a characteristic frequency of the carbonyl absorption band, the or-coniiguration is not, other states of coiling-perhaps almost any substantial deviation from the /I-configuration-resulting in a frequency in the neighbourhood of that given by the genuine ol.-helix. On second thoughts, it looks as if this, my concluding “coordination”, might be described more appropriately as a “ de-coordination ”. 1 Schellman, Compt. rend. Lab. Carlsberg, Sku. chim., 1955, 29, no. 15. 2 Astbury, Dickinson and Bailey, Biochem. J., 1935, 29, 2351. 3 Astbury and Bell, Nature, 1941, 147, 696. Astbury, Proc. Roy. SOC. B, 1947, 134, 4 Rudall, Synip. on Fibrous Proteins, J. SOC. Dyers and Colourists, 1946, p. 15 ; Ad- 5 Astbury afid Weibull, NGtnre, 1949, 163, 280. Astbury, Beighton and Weibull, 6 Parker and Rudall, Nature, 1957, 179, 905. 7 Palmer and Galvin, J . Amer. Chem. Soc., 1943, 65, 2187. 8 Astbury and Dickinson, Proc. Roy. Soc. B, 1940, 129, 307. 9 Astbury and Lomax, Nature, 1934, 133, 794. ‘0 Asttury, Nature, 1947, 160, 388. 11 Szent-Gjzorgyi, A. G. and Borbiro, Arch. Biochem. Biopltys., 1956, 60, 180. 12 Szent-Gyorgyi, A., Science, 1956, 124, 873 ; J . Cell. Comp. Physiol., 1957, 49, ’ 3 Ambrose, Proc. Roy. SOC. B, 1957, 148, 57. 14 Crick and Rich, Nature, 1955, 176, 780. Schellman and Harrington, Compt. rerld. Lab. Carlsberg, Sir. chim., 1956, 30, no. 3. 303 (Croonian Lecture, 1945). vatices in Protein Clieniistry, 1952, 7, 255. Symp. SOC. Expt. Biol., 1955, 9, 282. Astbury and Marwick, Nature, 1932, 130, 309. Bear and Rugo, Ann. N. Y. Acad. Sci., 1951, 53, 627. suppl. 1, 311.

ISSN:0366-9033    

DOI:10.1039/DF9582500080

出版商:RSC    

年代:1958

数据来源: RSC

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THE ENTROPY OF A FLEXIBLE MACROMOLECULE BY H. C. LONGUET-HIGGINS Dept. of Theoretical Chemistry, Cambridge University Received 31st January, 1958 An approximate calculation is made of the configurational entropy of a flexible macromolecule. The value of the entropy per link is found to be of the same order of magnitude as the rotational entropy of a small rigid molecule. This result is used to investigate the association between a flexible molecule and a rigid lattice. It is found that dissociation occurs sharply at a certain critical temperature, and that the kinetics of this process yield an apparent activation energy proportional to the number of external bonds which are broken in detaching the molecule from the lattice. 1. INTRODUCTION In discussing the behaviour of macromolecules, either singly or in aggregation, it is necessary to make a clear distinction between two sorts of question.On the one hand one may wish to know how the potential energy of a macromolecule, or a pair of macromolecules, depends upon the precise configuration; on the other hand one may be interested, for example, in the thermodynamic force be- tween two segments of a large molecule whose configuration is not specified in detail, or between two macromolecules about which only statistical information is available. These two types of question fall respectively within the spheres of quantum mechanics and statistical mechanics, and are to a considerable extent logically independent, although the thermodynamic properties of an assembly depend in the last resort upon the detailed manner in which the quantum mechanical potential energy varies with configuration.Broadly speaking, the physical chemistry of macromolecules seems to be in- telligible on the basis of two main generalizations. First, the intran~olecular and intermolecular potential energies of macromolecules are almost certainly additive with respect to the structural units which they contain, the individual terms being of the same origin and having the same range as for small molecules. (Specific long-range interactions of a purely mechanical nature would be im- possible to reconcile with the present theory.) Secondly, the thermodynamic behaviour of macromolecules is dominated by the extremely large number of geometrical configurations which are consistent with a given value of the energy.This multiplicity of accessible configurations is particularly important in flexible polymers, and is reflected in the very large entropy difference between the crystal- line and fluid (or amorphous) phases. In brief, then, it is entropy rather than energy differences which distinguish the properties of flexible polymers from those of small or fully rigid molecules. The application of these basic ideas to physical systems has shed light on phenomena as diverse as the elasticity of rubber-like materials, the stability of colloids, the thermodynamical properties of polymer solutions, and the residual entropy of glasses. To take a single example : there are more ways of arranging the links in a chain if the ends are close together than if the ends are far apart ; hence, a decrease in entropy accompanies the extension of such a chain, and this is the essential explanation of rubber elasticity.In this particular theory, how- ever, it is not necessary to inquire about the absolute entropy of the randomly oriented chain ; it is enough to estimate entropy differences. Nevertheless, there are circumstances in which it is useful to have an estimate of the absolute entropy associated with the configurational disorder of a long chain moleculc. 86H. C. LONGUET-HIGGINS 87 In this paper I shall, therefore, attempt an absolute calculation of the configura- tional entropy in a simple special case. It will transpire that this entropy is pro- portional to the number of links in the chain, a result which is not intuitively self-evident, but has important physical consequences.Furthermore, the value of the entropy per link can be estimated to order of magnitude, and is shown to determine the conditions under which a flexible macromolecule will undergo a particular type of order-disorder transition. 2 - - , el.e2, 0, . . . el . e2, 2 - a, e2. e3, . . . 0, e2.e3, 2--cc , . . . . . . . . . . . . en,l. en, 2 - 01 2. A SIMPLE PROBLEM Consider a large molecule (see fig. la) consisting of n + 1 atoms of mass rn, joined by n bonds of equilibrium length 1 and force constant K. The two bonds at an atom are freely jointed, that is to say, there are no angular terms in the potential function. The interaction between non-bonded atoms is neglected. This model, though a drastically simplified representation of a real macromolecule, can be investigated with reasonable rigour and I shall use it to obtain an estimate of the configurational entropy, which is of particular interest in the present con- nection.Strictly speaking, in order to calculate the entropy it would be neces- sary to calculate the energies of the vibrational-rotational eigenstates, or to carry out an equivalent calculation. This would be a quite impossible task for a very large molecule, but may fortunately be circumvented by virtue of the fact that almost all the vibrational modes will be of such high frequency that each atom completes many vibrational cycles in the time taken for the molecule to bend appreciably. It therefore becomes possible to use the " adiabatic " approxima- tion in which the vibrational energy is regarded as an effective potential governing the motion in the other degrees of freedom.A further simplification arises from the fact that in an arbitrary angular configuration the vibration frequencies are high compared with kT/h ; hence if for a given set of valency angles the vibrational frequencies are v1, v2, . . . Vn, then the effective potential for the bending modes is the zero-point energy 3 On the basis of these approximations the partition function may be evaluated in a straight-forward manner.* The vibrational degrees of freedom are first separated from the " free " modes, and the partition function for the latter is evaluated semi-classically. If ei denotes the unit vector along the ith bond, the final expression for the partition function is n hi.i- 1 = 0, (2.4) where88 ENTROPY OF A FLEXIBLE MACROMOLECULE and (2.5) An immediate question is: how does the partition function, as defined by (2.1) to (2.5), depend upon n, the number of bonds in the molecule? In order to see this it is necessary to consider the frequency distribution in an arbitrary configuration. Now the off-diagonal elements in (2.4) are the direction cosines of the valency angles, of which in an arbitrary configuration a large number will be close to n/2. Therefore the determinant will roughly factorize into smaller determinants associated with sections of the molecule at the ends of which the valency angles are close to right-angles. Hence to a good approximation the integrand in (2.1) may be expressed in the form n ZtnY (41 n Cvr(4/vol = [Z’V, (4P, (2.6) where 2” depends on the distribution of the valency angles but is independent of the length of the chain.Consequently the free energy, given by the equation (2.7) i= I Fn(T, Y ) = - k T In Zn(T, V ) includes a term proportional to n, the number of bonds. Writing the partition function in the form we see that there is a tendency for the molecule to adopt configurations in which the distribution of valency angles is such as to maximize Z “ { , (e)). It may easily be shown, for example, that at very low temperatures the vibrational zero- point energy tends to straighten out the molecule since in the straight configuration the integrand in (2.1) is at a maximum. This effect is, however, small and is ignored in, for example, the statistical theory of rubber elasticity, which is a fully classical theory.The effect will, in any case, be of much less importance than the “ excluded volume effect ” in favouring one group of configurations as against another. I shall therefore replace every frequency v i in (2.1) by a mean frequency v, regarding V as independent of the valency angles. This leads at once to a greatly simplified expression for the partition function, namely (2.9) The free energy may thus be regarded as comprising three independent terms ; the first is associated with the free motion of one end of the molecule ; the second is asscciated with the 2n free motions in which the angular co-ordinates change; the third arises from the vibrational zero-point energy.The same statement may be made about the entropy. k[ln Y + 1 + 8 In (2.rrmkT/h2)] arises from the translational freedom of the first atom in the chain. Secondly, the entropy associated with the bending modes is proportional to the number of links and may be written as nAS1, where First, an amount of entropy (2.10) and thirdly, the vibrational entropy vanishes in the approximation made here. Particular interest attaches to the magnitude of A,!?,. Since v is of the same order of magnitude as VO, AS1 will be close to the rotational entropy of a diatomic molecule of reduced mass rn and bond length 1. An order of magnitude for AS1 may beH. C . LONGUET-HIGGINS 89 obtained from the rotational entropy of N2 at 25°C ; this is about 10 cal/mole deg.AS1 will of course be reduced if the potential function contains terms restricting the bending motions; on the other hand an increase in mass of the repeating units will lead to an increase in AS1 if these units are freely hinged together. 3. A CO-OPERATIVE PHENOMENON Rather than discussing the general implications of these results I shall now draw attention to a physical situation in which the configuration entropy gives rise to a somewhat startling effect. Let us imagine that our model polymer can conveniently be accommodated on a one-dimensional lattice of n + 1 sites, the distance between successive sites being I (see fig. lb). That is to say, each atom experiences a short-range attraction to one of these sites, the binding energy having FIG. 1. a fixed value - E .The rth atom can only be pulled away from the rth site if the (r + 1)th atom has already been disconnected from the (Y + 1)th site. (The nearest familiar analogy is the zip fastener.) In order to determine the thermo- dynamic behaviour of this system one must evaluate the change in free energy AF1 which accompanies the separation of the last bonded atom from the lattice. When the last bonded atom is pulled away, two vibrations are replaced by two bending motions, with each of which is associated an energy +kT. The change in encrgy is therefore (3.1) Assuming that the atom in the bound state has no vibrational entropy, the entropy change on separation is A E ~ = kT -I- E .90 ENTROPY OF A FLEXIBLE MACROMOLECULE this being a direct consequence of eqn.(2.10). The free energy change is therefore independent of the serial number of the atom being detached and is given by AF1= AE, - TA&= E - kTln (3.3) At sufficiently low temperatures it is clear that AF1 will be positive, so that each atom will tend to associate itself with the lattice as soon as the previous atom is in position. The thermodynamically stable situation will therefore be that in which most of the molecule is bound to the lattice. As the temperature rises, how- ever, there will come a point at which the second term in (3.3) outweighs the first. Above a certain critical temperature therefore, given by AF, will become negative and there will be a tendency for the rth atom to detach itself as soon as the (r + 1)th atom has come adrift. In mathematical terms, if the number of molecules in which r atoms are bound to the lattice is denoted by Nr then it is easily seen that (3.5) the sequence iV1, N2, .. ., forming a geometrical progression in which the common ratio is greater or less than 1 according as AF1 is positive or negative. Conse- quently as the temperature rises through T, all the chains tend suddenly to detach themselves from the lattice, this transition being more abrupt the larger the value of n. An obvious question is : for what value of E will AF1 become zero at 300"K? Assuming AS, = 10 cal/mole deg. we obtain (3.6) A larger value of AS1 would imply a larger value of E; hence for T' to be in the neighbourhood of room temperature the binding energy of each atom to the lattice should lie in the range 1 to 10 kcal/mole, a range in which the energies of hydrogen bonds are found to lie.Indeed, it seems more than likely that the co-operative phenomenon here described is responsible for the extreme sensitivity of certain macromolecular assemblies to temperature and other intensive variables. Nr+1 = NI ~ X P (rAFiIkT), E = AE, - kT = T(AS1 - k ) = 2.4 kcaljmole. 4. A KINETIC APPLICATION The co-operative system discussed in the foregoing section invites a cursory kinetic discussion. Let us set up the kinetic equations the last step, namely the removal of the last atom from its lattice site, being irreversible. We look for a solution of the form (4.2) Nr = A, exp (- P t ) ; Y = 1,2, . . ., n + 1, where /3 is independent of r. Defining a unimolecular rate constant ko by (4.3) we see that it is related to #I by the equation,H .C. LONGUET-HIGGINS 91 The application of straightforward algebra shows that /3 and the A, are related by the eigenvalue equation k2 - - k2, being the lowest eigenvalue. Investigation of eqn. (4.5) shows that if k2 > kl the rate constant ko is given approximately by this equation being more accurate the smaller the value of k3 and the larger the value of iz. The apparent activation energy for disengagement of the chains is t herefme d In k3 d In (1 - kl/k2) d kT2d In ko .=kT2[,+ dT + n -1n - , (4.7) dT (::)I dT in which, for large n, the most important term is the last and has the value The apparent activation energy is therefore n times the energy required to detach a single atom and can be very large indeed if the chain is long.(The case kl > k2 need scarcely be considered, since the problem then reduces to that of detaching a single atom.) The physical reason for this large activation energy is to be found in the equilibrium distribution of the chains according to the number of atoms which are bound to the lattice. Under the conditions just considered (k2 > kl) there will be a predominance of chains with most of their atoms attached to the lattice. Detachment of almost every chain therefore requires the successive removal of nearly all the atoms from their attractive sites, and this is the origin of the large apparent activation energy. The kinetic behaviour of this system is not, incidentally, consistent with the generalization that a very large activation energy implies the simultaneous breaking of a large number of bonds; it is enough that the bonds be broken in a definite succession. It is interesting to note that the rate of denaturation of some proteins shows just the sort of temperature dependence encountered here. I am indebted to Dr. R. A. Sack for stimulating criticism. Note added in proof (17th March, 1958): An excellent general discussion of the residual entropy of linear polymers has been given by Temperley.1 Temperley has used a classical model with discrete configurations, but has not considered the quantum mechanical partition function explicitly. 1 Temperley, J. Res. Nat. Bur. Stand., 1956, 56, 55.

ISSN:0366-9033    

DOI:10.1039/DF9582500086

出版商:RSC    

年代:1958

数据来源: RSC

摘要:

AVAILABLE METHODS OF ESTIMATING THE MOST PROBABLE CONFIGURATIONS OF SIMPLE MODELS OF A MACROMOLECULE BY H. N. V. TEMPERLEY Atomic Weapons Research Establishment, Aldermaston, Berkshire Received 23rd January, 1958 A summary is given of the present theoretical position for a linear polymer, and some new results for a branched polymer are published for the first time. The latter problem appears to be simpler in some respects. In a long hydrocarbon chain, the lengths of C-C links are distributed about a mean value, and successive links are inclined to one another at nearly the tetra- hedral angle, so that there are, effectively, up to three distinct ways of adding one more carbon atom to a given linear chain. The mathematical methods of dealing with such a molecule have to take account of several quite distinct facts.(a) There may be short-range correlations between the directions of successive links, e.g. it is known that the configuration of a hydrocarbon chain in which three successive links lie in a plane is energetically more favourable than any other. (b) Certain configurations are sterically impossible. (c) In many cases, the possibility of branching cannot be neglected. (d) There are interactions between the atoms in neighbouring molecules. For comparison with experiment we need various averages over a typical molecule, such as the number of configurations possible and the effective size of a molecule of given length. If we could neglect (b)-(d), the problem becomes one of “ random-walk ” type. It is fairly easy, in any given case, to take account of correlations between successive links, it being only necessary to replace the dgebraic variable occurring in the generating function for the random-walk problem by a matrix of fairly low order.lp2 Thus, restriction (a) does not materially complicate the problem.The effect of restriction (b) is dficult to calculate properly, but can be said to be essentially soluble if we merely want to investigate the number of configurations of the molecule. The result seems to be that the effect of (b) shows itself as a reduction of the “ entropy per link ”, in other words, the number of permissible ways of adding a new link to a long chain is significantly less than it is for a short one. (This fact vitiated many of the early treatments that attempted to apply perturbation methods to unrestricted random-walk theory.A reduction in the entropy per link means that “ almost all ” the configurations permitted by the unrestricted theory are ruled out.) Many workers have introduced the concept of an “effective length of segment” which implies that the actual chain, with effects (a) and (b) taken into account, should behave in a way very similar to a completely random chain with a smaller number of longer links. (For example, it is often useful to think of a long hydrocarbon molecule with only a small fraction of the linkages departing from the trans configuration. Thus, we have a number of “ plane-zig-zag ” segments connected by gauche linkages.) A recent analysis of a wide variety of experimental data 3 did seem to show that this concept was a physically valid one, the effective length being of the order of 10-30 C-C linkages for a hydrocarbon chain and 2-5 monomers for a rubber 92H .N. V. TEMPERLEY 93 chain. There was a little evidence that the effect of (d) could be more important in solids than in liquids or solutions. THE MONTROLL MODEL According to this model 4 the monomer is taken of invariable length, and suc- cessive links are constrained to lie along the nearest-neighbour bonds of some simple lattice, all configurations containing closed rings being deleted. The lattice corresponding most closely to the hydrocarbon chain is the diamond lattice, but the correspondence is by no means perfect. One is therefore led to ask whether results are sensitive to the lattice type, or to the number of dimensions (in view of the fact that the simple random walk is sensitive to the number of dimensions).Another question is whether the form of the results is sensitive to the “ excluded volume ”, e.g. what difference does it make if we delete configura- tions in which two non-neighbours in the chain approach within one lattice distance, instead of coinciding ? Montroll4 showed that the correct consequence of his model would be a progressive reduction in the entropy per link, as loops of larger and larger sizes were successively eliminated. This conclusion has been confirmed by Wall and others,s who build up non-crossing chains by means of a machine programme of “ random addition of links ”, the build-up of any chain being stopped, and a new chain started, as soon as the first loop occurs.It was found that the toraZ reduc- tion in “ entropy per link” quickly approached a limiting value. A similar conclusion was reached by Hammersley and Morton 6 for the diamond lattice, based on hand computation of a few very long chains. Temperley 1 has given reasons for thinking that “ the limiting entropy per link ” should be closely related to the Curie temperature for the corresponding Ising lattice, and the numerical agreement is indeed fairly good. Although no analytic solution is yet available for any of these models, even in two dimensions, it does now seem that we know enough about them to estimate the limiting “ entropy per link ” or “ effective number of choices ” in any reason- able case.The position about the other interesting properties, such as the effective size of a molecule of known total length, is much less satisfactory. We do not yet know, for example, in what circumstances the effective radius varies as N4 (as it would for a completely random walk), or as some different power of N, and the answer does not depend in any clear-cut way on the number of dimensions, but also seems to depend on the type of lattice, and to be a function of the excluded volume.5 Furthermore, there are indications that the limiting behaviour is ap- proached extremely slowly in three dimensions. (In number theory, one often meets situations in which the asymptotic behaviour is not realized until some slowly varying function like log (log N ) becomes large, but this type of thing does not seem to have been previously met in statistical mechanics.) One observation of Wall and others,s that the probability of formation of a ring is, for almost all lattices, inversely proportional to the square of the size of the ring, seems to indicate that the generating functions for the Ising lattice par- tition function and for the restricted random walk have similar analytic behaviour, which is reasonable (cp.Temperley 1 for a discussion of the analytic feature probably responsible for this behaviour). BRANCHED CONFIGURATIONS The Montroll model can also give a representation of a polymer in which unlimited branching is allowed, that is to say, we take our lattice, and select certain lines from it in such a way that they are all connected, but closed loops are absent; in other words, we form a Cayley tree, which is, according to the Montroll model, a possible configuration of a branched polymer, steric effects being allowed for.For simplicity, consider the plane square lattice (though some4 - 1 . . . . . . . . - 1 . . . . - I . . . . - 1 - 1 4 - 1 . . . . . . - 1 . . . . - 1 . . . . 0 , 0 - 1 4 - l . . . - 1 . . . . - 1 . . . . 0 A ( 3 ~ 2 0 ) ~ ~ ~ (1) where A is a constant of the order of unity. This result holds provided only that both M and N are large, independently of their ratio. Thus (2) gives us the number of ways in which a branched polymer containing MN points can be exactly “ folded up ” to form an M x N rectangle. Each choice of M and N corresponds to a diflerent set of possible configurations of the branched polymer, so that the total number of such configurations would be obtained by deriving an expression similar to (2) for all possible closed domains containing MN lattice points.The number of such domains can be estimated asymptotically by putting x = 1 in expression (1 1) of ref. (l), that is, we want the coefficient of zMN in z(l - 2 ) 3 1 - 5z + 722 - 423’ which is of the order of 3MN. Actually (3) enumerates precisely the closed domains of a particular type that can be formed on the square lattice, but it is possible to show that the total number of distinct domains is not greatly in excess of this. We can take a final step by saying that (2) does not depend very much on the shape of the domain, but mainly on the total number of lattice points, and it is known that the properties of the Ising model are not very sensitive to boundary con- ditions.7 Thus (2) is probably nearly right for any shape of domain, so that our estimate of the number of configurations of a branched-chain polymer is of the order of a factor of 9-10 per monomer (multiplying (2) by the result deduced from (3)). Thus, we have the strange situation that the polymer with branching is an analytically simpler problem than the linear polymer. The higher-order minors of (1) seem to be related to problems of solution and degradation of branched polymers, but we shall not pursue this matter further here. 1 Temperley, Physic. Rev., 1956, 103, 1. 2 Gillis, Proc. Cambr. Phil. SOC., 1955, 51, 639. 3 Temperley, J. Res. Nut. Bur. Stand., 1956, 56, 55. 4 Montroll, J. Chem. Physics, 1950, 18, 734. 5 Wall et al., J . Chem. Physics, 1954, 22, 1036; 1955, 23, 913 and 2314; 1957, 26, 6 Hammersley and Morton, J. Roy. Statist. SOC., 1954, 16, 23. 7 Temperley, Proc. Physic. SOC., 1957, 70, 192. 1742; 27, 186.

ISSN:0366-9033    

DOI:10.1039/DF9582500092

出版商:RSC    

年代:1958

数据来源: RSC