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.