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J . Phys. Chem. 1988, 92, 2646-2651
Epitaxial Relatlonships during Phase Transformations in a Lyotropic Liquid Crystal Y. Ranson and J. Charvolin* Laboratoire de Physique des solides, associt? au CNRS (LA 2), bdtiment 510, and LURE, bdtiment 209, UniversitP Paris-Sud, 91405 Orsay, France (Received: July 28, 1987; In Final Form: November 17, 1987)
We have studied structural transformationsof liquid crystalline phases in the lyotropic system hexaethylene glycol mono-n-dodecyl ether (CI2EO6)/H20.The growth of monocrystals of lamellar and hexagonal phases in a monocrystal of cubic phase has been followed by optical microscopy and small-angle X-ray and neutron scatterings. We demonstrate the existence of epitaxial relationships between particular reticular planes of these three phases: the (2111 planes of the cubic phase are in relation with the (001) planes of the lamellar phase and with the (lo)planes of the hexagonal phase. These are the planes of highest density of matter in the three phases. In the case of the transformation of the cubic phase into the hexagonal phase, we demonstrate also that the cylinders of amphiphilic molecules of the hexagonal phase grow parallel to the ( 111 ) directions of the cubic phase.
Introduction The essential features of the structures of lyotropic liquid crystals formed by amphiphilic molecules in the presence of water are now well established and acknowledged. Their most frequent organizations with translational order are the so-called ”lamellar” phases with 1D periodicity, “cubic” phases with 3D periodicity (most often with space group Ia3d), and ”cylindrical” phases with 2D periodicity (most often hexagonal with space group p 6 m ) . They are classically represented as in Figure 1. Details about phase diagrams, structural characterizations, and less frequent modes of organization can be found in basic review This state of description introduces a new question concerning the nature of the processes taking place as one structure transforms into another when the variables of the phase diagrams are changed. The problem appears much more complex here than in the classical case of atomic or molecular crystals, as the structural transformations in lyotropic liquid crystals imply dramatic topological changes. For instance, in Figure 1, the lamellar phases can‘be topologically described as assemblies of an infinite number of infinite cells of water and amphiphiles, the cubic phases as assemblies of two infinite cells of one medium separated by a film of the other, and the cylindrical ones as assemblies of an infinite number of infinite cells of one medium separated by a film of the other! Therefore, the transformation of one structure into another requires changes in the connectivity of the cells and films, Le., in physical terms, ruptures and fusions. These phenomena might either take place randomly, through the destruction of the first phase and the building of the second one, or occur in an organized way, if the structural elements of the second structure grow from structural elements of the first one. The question of the phase transformation can therefore be addressed in two steps. The first step must be the search for epitaxial relations between reticular planes of the two phases during the transformation. If this is so, the second step will be to determine what happens in these planes and between them during the transformation. For reasons given below, we have chosen to study the transformations of the lyotropic liquid crystalline phases of the mixture hexaethylene glycol mono-n-dodecyl ether (C,2E06)/H20,whose phase diagram is presented in Figure 2, from ref 5. At concentrations of C12E06,greaterthan 35 wt %, the system presents the three phases described above: a cubic phase (Q,) with space group f a 3 8 lies at intermediate temperatures and concentrations between a lamellar structure (L,) and a hexagonal structure (H,) of type I (oil in water).’ (1) Ekwall, P. Ado. Liq. Cryst. 1975, I, 1. (2) Luzzati, V. In Biological Membranes; Chapman, D., Ed.: Academic:
New York. 1968. (3) Cha’rvolin, J. J . Chim. Phys. Phys.-Chim. Eiol. 1983, 80, 15. (4) Sadoc, J. F.; Charvolin, J. J . Phys. (Les Ulis, Fr.) 1986, 47, 683. (5) Mitchell, D. J.; Tiddy, G.; Waring, L.; Bostock, T.; McDonald, M. P J. Chem. Soc., Faraday Trans. 1 1983, 79, 915. (6) Ranpn, Y.; Charvolin, J. J . Phys. (Les Ulis, Fr.) 1987, 48, 1067. (7) The notation L,, Q,, Hawas proposed by Luzzsti,* and we shall adopt it in the rest of the text.
0022-3654/88/2092-2646$01.50/0
Our experimental methods are X-ray and neutron scatterings, which do not affect by any artifact the delicate processes of crystal growth. We demonstrate in this article the existence of epitaxial relations between reticular planes of the three phases of Cl2EO6/H20and describe them. In a future article we shall describe the processes taking place in these planes and discuss the possible mechanisms of the phase transformations.
Experimental Section Two factors favor the choice of the system C12E06/H20.One is the ability of its cubic phase to grow the large monocrystals needed to study epitaxial relatiom6 The second is the nonverticality of the boundaries of the cubic phase in the phase diagram, which permits the growth of lamellar or hexagonal crystals in a cubic monocrystal to be followed by varying the temperature.8 The phase diagram was controlled by optical observations with a polarizing microscope. The phases were characterized by their classical textures: oily streaks and clover leaves for the lamellar phase, complete optical isotropy for the cubic phase, and cloudy texture and striations for the hexagonal phase.9 It is easy to detect the growth of textures of anisotropic lamellar or hexagonal phases in the isotropic cubic phase with this method. However, it is very difficult to develop it to the point of determining precise epitaxial relations, particularly when an isotropic phase is involved. We therefore developed methods for performing X-ray scattering studies on monocrystals of Q,, La, and H,, as their diffraction patterns give direct access to the relative spacings and relative orientations of the reticular planes. Neutron scattering was also used when X-ray scattering investigations failed because of the configuration of the sample, as explained below. Sample Preparation. The nonionic surfactant hexaethylene glycol mono-n-dodecyl ether, CH~(CH2)11(0CH,CH2)60H or CI2EO6,was obtained from NIKKO Chemicals Co., Ltd. A sample, exhibiting the hexagonal/cubic/lamellar sequence of phases with increasing temperature, was prepared at 62 wt % of C,2E06in water. Another sample of C12E06with a composition of 50 wt %, presenting the simpler hexagonal/fluid isotropic sequence, was also prepared in order to confirm the role of the cubic phase in some phenomena observed with the first sample. The samples were prepared by weighing the appropriate amounts of surfactant and water in glass vials, which after sealing were incubated in an oven at 40 OC for several weeks to ensure complete homogenization. We controlled this procedure by optical microscopy so that it did not affect the sequences of phases. Optical Microscopy. The samples were drawn into flat-sided capillaries with wall separations of 0.4 mm (microslides, Vitro (8) In most monoalkyl lyotropic systems the limits of the phase domains are nearly vertical, and the only available parameter for driving the transformations is the concentration, which does not allow for an easy continuous study. See, for instance, the concentration gradient experiment given in the following: Ktkicheff, P.; Cabane, B. J . Phys. (Les Ulis, Fr.) 1987, 48, 1571. (9) Rosevear, F. B. J . A m . Oil Chem. SOC.1954, 31, 628.
0 1988 American Chemical Society
Lyotropic Liquid Crystal Phase Transformations
The Journal of Physical Chemistry, Vol. 92, No. 9, 1988 2647
I (C)
( b) Figure 1. Schematic representations of the most frequent structures: (a) “lamellar’’phase with 1D periodicity; (b) Iu3d “cubic” phase with 3D Periodicity; (c) “hexagonal” phase with 2D periodicity.
I
X-ray
beam
la)
X-ray
beam
(b)
Figure 3. X-ray scattering geometries: top views of inserted capillaries. The long axis of the capillaries is normal to the figure, and the incident beam is normal to the long axis. n is the director of the lamellar phase, with a radial distribution. Sections of the lamellae are represented by concentric thin circles whose spacing is not to scale. (a) face configuration, the beam parallel to the direction n of the part of the sample illuminated by the beam; (b) side configuration,the beam perpendicular to the director n of the part of the sample illuminated by the beam.
M dhlt
Hexagonal
0
25
50
1 75
C,,EO,(%W/WI
Figure 2. Phase diagram of CI2EO6/H20,from ref 5 . The full lines separating the phases represent biphasic regions. The arrow locates the sample at 62 wt % CIZE06,which is predominantly studied here. Dynamic Inc.) and observed with a polarizing microscopy (Leitz) equipped with a camera and a heating stage. X-ray Scattering, the X-ray scattering investigations were carried out with the sample of C I 2 E o 6at a composition of 62 wt % (see the arrow in Figure 2 ) in thin-walled Lindemann glass capillaries. The incident beam was normal to the long axis of the capillary. Monocrystals of cubic phase were grown in capillaries of 1.5mm diameter.6 The sample could be oriented in the beam by rotation of the capillary around its long axis, at defined angles read on a goniometer. We also made observations with monocrystals of lamellar phase. They could not be obtained in capillaries of 1.5-mm diameter. However, it is known that oriented samples of L, can be obtained by squeezing the lamellar phase between closely spaced parallel plates.Io In the absence of flat Lindemann capillaries, we adapted this method by drawing the sample between two circular Lindemann capillaries of different diameters (1.3 and 1.5 mm), one inserted into the other, so that the sample remains confined between two circular walls with 0.1-mm spacing. The lamellar monocrystals are obtained by heating the sample into the fluid isotropic phase and cooling it down through the fluid isotropic/lamellar phase transition. The lamellae grow parallel to the walls of the capillaries, i.e., along concentric cylinders of diameter 1.3-1.5 mm. Such inserted capillaries allow us to experience different scattering geometries, simply by moving them in the incident beam. When the incident beam intercepts the middle of the capillary (face configuration), the scattering vectors are in a plane locally parallel to the lamellae (see Figure 3a). When the incident beam intercepts the edge of the capillary (side configuration), the scattering vectors are in a plane locally normal to the lamellae (see Figure 3b). The X-ray diagrams were obtained on the high flux source of synchrotron radiation at LURE with the small-angle scattering spectrometer DI6. The equipment is that of a classical monochromatic Laue camera,” with point beam collimation (0.5” diameter). A helium-filled chamber is placed between the sample and the detector to eliminate parasitic scattering from air. Photographic film is used as the detector to record bidimensional sections of reciprocal space. The parameters of the experiments (10) Vries, J. J.; Berendsen, M. J. C. Nature (London) 1969, 221. 1139. (11) Comb, R.; Lambert, M.; Launois, H.; Zeller, H. R. Phys. Reu. B: Condens. Matter 1913, 8, 511.
Figure 4. Neutron scattering geometry from ref 12. The incident beam is perpendicular to the director n of the lamellar phase. The angle between the scattered and incident beams is 28. The 2D detector is normal to the incident beam. are X = 1.304 A, AX/X = 2 X sample to film distance D = 250 mm, and the range of scattering vectors (s = 2 (sin @/X) explored 7 X ,&-I < s < 80 X ,&-I with As = 3 X ,&-I. The temperature of the sample was regulated by water circulation in the sample holder and measured with a thermocouple close to the capillary. Neutron Scattering. The neutron scattering investigations were also carried out with the sample at 62 wt 7%of C&06 (see the arrow in Figure 2 ) . In this case, we could directly apply the multisandwich methodlo with quartz plates, which are transparent to neutrons (such an experiment is impossible with X-rays because the plates used, either of quartz or glass, are too absorbant). For this experiment, the sample was drawn into a set of quartz plates spaced 50 gm apart, and the whole set was contained in a sealed quartz cell whose section was 10 mm X 5 “.I2 The experiments were performed at the reactor ORPHEE of L.L.B in C.E.N Saclay, on spectrometer Paxy with an x-y multidetector. The sample-detector distance was D = 1954 mm, the wavelength X = 3.5 A, and the wavelength spread AX/X = 5%. We worked with protonated C12E06in D 2 0 so that the scattered intensity depends essentially on the contrast of the amphiphilic molecules with respect to D 2 0 and therefore on the relative distribution of the amphiphiles and the water. The scattering geometry is shown in Figure 4: the incident beam is perpendicular to the normal n of the quartz plates. Such a geometry is equivalent to the side configuration described in the case of the X-ray scattering experiments. The temperature of the sample was regulated by water circulation in the sample holder and measured with a thermocouple close to the sample.
LameUar/Cubic Transformation Optical Observation of the Growth of L, in Q,. A sample at 6 2 wt % of C12E06was introduced into a 0.4-mm flat-sided capillary and observed with the polarizing microscope. It was slowly cooled from the lamellar phase into the cubic phase to allow the growth of a cubic monocrystal! The sample was then warmed into the biphasic region separating the two phases. A photograph of this biphasic region is presented in Figure 5. We see illuminated areas, corresponding to monocrystals of L,, growing in the black area, corresponding to the large monocrystal of Q,. The (12) KEkicheff, P.; Cabane, B.; Rawiso, M. J . Phys. Lett. 1984, 45, 813.
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The Journal ofPhysica1 Chemistry. Vol. 92. No. 9, 1988
100 Hm L
I
Figure 5. Photograph (29 "C) of lamellar monocrystals (illuminated
area) growing in one monocrystal of cubic phase (block area). The common orientation of all the edges of these monocrystals suggests the existence of an epitaxial relation between the two phases. common orientation of all the edges of these lamellar monocrystals suggests the existence of an epitaxial relation between the lamellar phase and the cubic phase. X-ray Scattering. We performed X-ray scattering experiments with monocrystals of L, in inserted capillaries. A side configuration pattern of La is shown in Figure 6a. W e see very sharp Bragg reflections, corresponding to a very well oriented lamellar phase ( d = 48 A). The director n of the phase (axis [OOl])is in the plane of the figure. A face configuration pattern of L, is shown in Figure 6b. No Bragg reflections should be observed because this section ofthe reciprocal space is parallel to the (001)
side configuration
Rancon and Charvolin layers of the lamellar phase, and the director n (axis [ O O l ] ) is normal to the figure. A single rather weak Bragg ring can still be seen however due to some disoriented lamellae between the two capillaries. The diffuse scatterings in these figures will be discussed in a forthcoming article. Figure 6b' shows the pattern corresponding to that of Figure 6b after cooling the lamellar sample in the face configuration into the cubic phase. The indexing ofthe spots observed in this pattern shows that this section of the reciprocal cubic space is one of the (21 I1reciprocal planes with the [ 1121 axis normal to the figure. This transformation shows that the [Ool] axis of the lamellar phase in Figure 6b is parallel to a (21 I ) axis ofthe cubic phase in Figure 6b'; in other words, the (001) planes of L,. Le.. its lamellae, are parallel to the (21 I)planes of Q,. This is indicative of an epitaxial relation between L, and Q,. Figure 6a', which is the pattern corresponding to that of Figure 6a after the sample in the side configuration was cooled into the cubic phase, should provide a test for our interpretation. Indeed. such a section of the reciprocal cubic space should show Bragg spots of the (2111 reticular planes, appearing on the same horizontal line as the (001) spots of L, in Figure 6a. In fact nothing is observed, most likely because of the dispersion of the intensity among the many spots of the cubic phase. This unfavorable situation is emphasized here with the side configuration, because of the smallness of the scattering volume intercepted by the incident beam on the edge of the capillary. This is why we tried to work on a side configuration with a sample of larger volume, using neutron scattering with the multisandwich method described in the Experimental Section. Nrutron Scattering. Figure 7a represents the diffraction pattern of the oriented lamellar phase. The director n ([OOI]axis) of the lamellae is in the plane of the figure. The circular ring at .sWl = 2 X IO-' .k1 is due to an imperfect alignment of the sample. When the oriented lamellar phase is cooled down into the cubic phase, the pattern of Figure l a transforms into that of Figure 7b where (21 I1 spots are visible on a circle at s2,, = 2 X IO A-'.
'
face configuration
t
Fiyre 6. X-ray scattering patterns of the sample at 62 wt % CllEOdbetween inserted capillaries: (a and b) lamellar phase (35 "C): (a'and b') cubic phase (27 "C); (a and a') ride configuration: (band b') face configuration. The scattering around the beam stop is due to imperfect collimation. The horizontal streak at the ccntcr of thc side configuration patterns is due to specular reflection on the glass walls of thc capillaries.
Lyotropic Liquid Crystal Phase Transformations
( b)
The Journal ofPhysica1 Chemistry, Val. 92. No. 9, 1988 1649
(a)
Figure 7. Neutron scattering patterns of (a) the lamellar phase (35 'C) and (b) the cubic phase (25 "C). The squares represent the bcam stop. The two series of intensity levels in the two figurs arc independent. The bottoms of the patterns were outside the window of the 2D detector.
We note that two of them are on the same horizontal line as the (001) spots of La in Figure 7a: here we obtain the result expected above for the side configuration test. The other 121 I)spots on the circle at 2 X k'correspond to contributions of cubic monocrystals with different orientations around their common (21 I ) axis between the different quartz plates. Finally, we deduce from the equality ofsmland szII that the spacing dmlof the (001) planes in L, is equal to the spacing dZt1 of the (21I)planes in Q.. The epitaxial relation between L. and Q. is confirmed and clarified more precisely since the (001) planes of L, not only are parallel to the (21 I)planes of Q. but also have the same spacing. Epitaxial Relation between Le and Q .. X-ray and neutron scattering investigations show that the lamellae of L, transform into the (211) reticular planes of Q, when the temperature is lowered. The optical observations show also the existence of such an epitaxial relation when the sample is heated from Q. into L.. This latter situation is difficult to analyze with X-ray or neutron scattering because 1 monocrystal of Q. could yield up to 12 monocrystals of L, (there are 12 possible (21 I ) planes among the 121 I ) family of reticular planes).
Cubic/Hexagonal Transformation Optical Obseruafion ofthe Growth oJH, in Q .. A sample a t 62 wt %of C,,E06 was introduced in a 0 . 4 " flat-sided capillary and observed with the polarizing microscope. It was slowly cooled from the lamellar phase into the cubic phase to allow the growth of a cubic monocrystal? This monocrystalline cubic sample was then cooled into the biphasic domain separating the cubic and hexagonal phases. A photograph of the biphasic region separating Q, and Ha is presented in Figure 8a. The texture observed is quite unusual: the hexagonal phase appears as an assembly of thin illuminated needles parallel to some specific directions in the black background of the cubic phase. These needles appear parallel to four directions. which can be coarsely analyzed as the projection of the heights of a regular tetrahedron on the plane of the photograph. This suggests that H, is growing from the unique monocrystal of Q. with some precise angular relations." Indeed the role of the cubic phase in this growth phenomenon is confirmed by the fact that no needles are observed when the hexagonal phase grows directly from the fluid isotropic phase as is the case with the sample at 50 wt %of C,,E06 (see Figure 8b). ( 1 3 ) A similar growth of the hexagonal phase in the cubic phase of C,,EO,/H,O WBP observed in an N M R experiment: Henrikson, U.:Klawn. T. J. P h w . Chem. 1983.87.3802. The authors deduce from their data that crystalliics of hexagonal phase grow along a tetrahedral orientation pattern. They therefore propose B tetrahedral Structure with space group Pn3 for the cubic phase. They also mention that the magnetic field has an effect on the orientation of the tetrahedron. We showed in a previous paper that the space group of the cubic structure is indeed Ia3d.6 We could not observe any influence of the magnetic field on the growth when repeating the NMR
experiment.
(b)
0.5mm
T Y
0.5m m
Figure 8. (a) Sample at 62 w t % Cu,EO,. Photograph (22 "C) of the hexagonal phase (illuminatedarea) growing in one monocrystal of cubic phase (black area) under slow cwling. The four directions of growth of the needles are indicated by the arrows. (b) Sample at 50 wt R CnEOc. Photograph (29 "C) of the hexagonal phase (illuminated area) growing in the fluid isotropic phase (black arca) under slow cooling.
It is important to notice here that when we turn the sample between the polarizen, the needles become black when their long axis is parallel or perpendicular to one of the polarizers. This indicates that one of their optical axes is parallel or perpendicular to their long axis. Since in a hexagonal phase the optical axes are parallel and perpendicular to the cylinders, we deduce that the cylinders can grow parallel or perpendicular to the long axis of the needles. Moreover the needles have macroscopic sizes, particularly along their length, which implies a propagation of the angular relations over fairly large distances. X-ray Dffraction. We performed experiments with the C,zE06 sample a t 62 wt % in a simple capillary of 1.5-mm diameter. 1. Results. Figure 9 shows two patterns: The one on the left refers to one large monocrystal of cubic phase. The one on the right is obtained with the same capillary cooled slowly from the cubic monocrystal into the hexagonal phase. This second pattern exhibits a limited number of Bragg spots that are on circles whose radii fit thespacing ratios 47, d?, 4 z . 47. ...,which is specific of a hexagonal phase, with sIo= (48 .&-I. The Bragg spots are organized in a very symmetric manner, which however corresponds neither to the classical hexagonal pattern of a monocrystal of hexagonal phase nor to the classical pattern of a polycrystalline powder of hexagonal phase. One monocrystal of Q. therefore leads to several monocrystals of H a with discrete orientations. The symmetry of the pattern suggests that these monocrystals of hexagonal phase are not randomly oriented with respect to the cubic phase and with respect to each other. If we compare the two pattems in Figure 9 and, more generally, whatever the section of the reciprocal space considered, each spot at 4 7 from the hexagonal phase lies exactly at the same place
2650 The Journal of Physicor Chemisfry. Vol. 92, No. 9. 1988
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R a n p n and Charvolin
20 LO 60 80
io3 s (2)
b
b'. '23
6
C'/
-651
d
Figure 9. On the left, scattering pattern of a monocrystal of cubic phase (28 "C)and its indexation. On the right. pattern of the hexagonal phase (14 "C) obtained from the cubic monacrystal. Spots a belong to the 2D lattice normal to the [TI I ] axis of Q,: spots b belong to the one normal to [ l i l ] : spots c. c', and d belong to the one normal to [Ili]: spots d also belong to the 2D lattice normal to [ I I l l . The scattering around the beam stop. at the centers of the photographs, is duc to imperfect collimation.
as one (211)spot from the cubic phase. This is proof of the existence of an epitaxial relation between Q. and H. since the (21I ) reticular planes in Q,, become the (IO)reticular planes of
H . . From these observations, we can try to mnstruct the reciprocal lattice of the whole hexagonal phase as built by a superposition of 2D reciprocal lattices of hexagonal monocrystals. If we mnsider the 24 121 I \ spots in Q. associated with the 47 spots in H,, the only way to obtain 2D hexagons is to partition the 24 spots into four subsets of 6 spots, each subset building a 2D hexagon normal to a ( I 1 1 ) direction of the reciprocal cubic cell. Such a construction is shown in Figure IO, illustrating the fact that all the v'i spots of the hexagonal phase can be placed on four hexagons normal to the ( I 1 I ) directions of cubic cell. This organization is indeed apparent in the right pattern of Figure 9, where spots a belong to one hexagon, spots b belong to another one, while spots c and c' belong to a third one. This is also true for the higher orders at v'?,v'z, 47, _..,whatever the section of the reciprocal space considered. Therefore one monocrystal of Q. gives exactly four monocrystals of H .. This leads to a view of the reciprocal space of the whole hexagonal phase as being a superposition of four classical 2D hexagonal reciprocal lattices (sIo= (48 .&)-I), each of them being normal to one of the ( I I I ) directions that were present in the monocrystal of Q,. 2. Inferprefafion.W e have seen that the reciprocal space of the hexagonal phase, grown from a cubic monocrystal, consists of four reciprocal 2D hexagonal lattices normal to the ( 1 1I )
Figure 10. Partition of the 24 (21 I ) spots of Q. in four hexagons normal to the ( I I I ) directions of the cubic cell. One of these four hexagoniis $@ned, for instance, by considering the following spots: 112, 271, 12,! 112,2li,i21. Theplanecontainingthis hexagonisnarmaltothe[III]
direction. directions of the reciprocal cubic lattice. Each reciprocal 2D lattice is representative, in the real space, of cylinders of amphiphiles parallel to a director n that is one of the ( I 1 1 ) directions of the cubic monocrystal. The cylinders build a 2D hexagonal lattice (parameter d = Z/(s,,v'/J) = 5 5 A) in the plane normal to the director n.
The Journal of Physical Chemistry, Vol. 92, No. 9, 1988 2651
Lyotropic Liquid Crystal Phase Transformations
‘
/
Figure 11. Scheme of the growth of H, in Q,. The cubes represent some cells of a unique monocrystal of cubic phase. When the sample is being cooled, hexagonal bundles of cylinders are growing along the four possible (1 1 1 ) directions existing in the cubic monocrystal.
La
Qa
Ha
Figure 12. Representation of the epitaxial relations between the lamellar phase (left), the cubic phase (middle), and the hexagonal phase (right). The Iu3d cubic phase is viewed along one (1 11) direction, from ref 14. The black and white rods are the axes of amphiphilic cylinders; the dotted lines are their projection onto the plane of the figure.
Therefore from the whole reciprocal lattice of the hexagonal sample, we can build in real space a model in which hexagonal bundles of cylinders of amphiphiles grow along the ( 111 ) directions of the cubic cell. In other words, monocrystallites of hexagonal phase are oriented along the tetrahedral directions that are already present in the monocrystal of cubic phase. This is illustrated in Figure 11. This analysis is consistent with our previous observations under the polarizing microscope. Moreover, since the needles we saw by optical observation in Figure 8a are also tetrahedrally oriented, we can deduce that the directors of the cylinders are parallel to the long axes of the needles. Epitaxial Relation between Q, and H,. The (211) reticular planes of Q , transform into the (10)reticular planes of H,, and, moreover, the cylinders of amphiphilic molecules of the hexagonal phase grow parallel to the ( 11 1 ) directions of the cubic monocrystal.
Conclusion Our observations show the existence of epitaxial relations between lamellar, cubic, and hexagonal phases in the Cl2EO6/HZO system. The (211) planes of the cubic phase play a central role as they appear to be in a direct relationship with the (001) planes of the lamellar phase and with the (10) planes of the hexagonal phase. The particular importance of these (211) planes appears when considering the model proposed for the cubic structure with space group Ia3dI4 viewed along a ( 111) axis, as shown in Figure (14) Luzzati, V.;Spegt, P. A. Nature (London) 1967, 215, 701.
12, where we recognize the two interwoven labyrinths of amphiphilic rods connected 3 X 3. A ( 11 1) direction is the intersection of three (211) planes that are perpendicular to the plane of the figure. Figure 12 illustrates several features that help us to understand the observed epitaxial relations. The first point is that the (211) planes are the planes of highest density of matter in the cubic phase. Indeed, if we consider a slice of matter containing a crystallographic plane, we can see from Figure 12 that the volume of amphiphilic matter in such a slice is at a maximum when it is centered on a (2111 plane. (This result is consistent with some recent experiments of cryofract~re.’~)If, now, we turn to lamellar and hexagonal phases, their (001) planes and (10)planes are obviously those of highest density. Therefore, we deduce that the epitaxial relations discovered between the planes of the three phases are relations between planes of high density. The second point is that the spacing of these high-density planes is the same in the three phases ( d 2 , , ( Q , )= dool(L,)= dlo(H,) = 48 A). The third point concerns the relation between the crystallographic axes of Q , and H,. If we look at Figure 12, we distinguish two kinds of threefold axes perpendicular to the plane of the figure: the 3 axis (which are the rows of stacked knots6 and the 31 axis (which are screw axes made of amphiphilic rods). The spacing measured between these threefold axes (3 or 3,) is equal to 2 d 2 1 1 / d 3= 5 5 A. The same spacing is measured between the amphiphilic cylinders of the hexagonal phase which are aligned along the sixfold axes. Here again we find an agreement between the spacings of the axes in H, and Q , similar to that concerning the spacings of the high-density planes in L,, Q,, and H,. Moreover, the growth of the amphiphilic cylinders of H, (with sixfold symmetry) at the place of the threefold axes of Q , is crystallographically reasonable. Such a result shows the importance of the (1 11) axes of Q,, beside the (211) planes, in the cubic/hexagonal transformation. To summarize, we have established a first correspondence between the (001) planes of the lamellar phase and the (211) planes of the cubic phase and a second one between these (211) planes of the cubic phase and the (10) planes of the hexagonal phase, which can also be seen as a correspondence between the ( 11 1) axes of Q , and the axes of the amphiphilic cylinders in H,. These crystallographic correspondences create a framework for studying what happens within the planes and between them at the phase transitions. The characterization of these mechanisms, which will help in the approach to the topological problem of phase transformations, will be presented in a forthcoming article.
Acknowledgment. We thank S. Megtert for his experimental assistance on spectrometer Dl6 at LURE (Orsay). Thanks are also due to P. KEkicheff for his help during the neutron scattering experiments on spectrometer PAXY at L.L.B. (Saclay). The very careful reading of the manuscript by J. M. Seddon (University of Southampton) and his comments and discussions with V. Luzzati (CNRS Gif sur Yvette) were much appreciated. This work was partially supported by PIRSEM of CNRS, “GRECO microEmulsions”. Registry No. C12E06,3055-96-7. (15) Most frequently, in Iu3d cubic structures, the fracture propagates along (211) planes: Delacroix, H., et al., in preparation.
