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.