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Highly Ordered Parabolic Focal Conics in Lyotropic Systems G. Platz* and C. Thunig Universita¨ t Bayreuth, Universita¨ tsstrasse 30, 95440 Bayreuth, Germany Received September 5, 1995. In Final Form: November 30, 1995X Parabolic focal conics develop at 10-20 wt % surfactant in the two-phase lamellar-isotropic regions of various systems (SDS-hexanol-decane-water, alkylpolyglucoside APG600-fatty alcohols pentanol, hexanol, decanol, dodecanol, tetradecanol, oleyl alcohol). Extended regular quadratic two-dimensional lattices are formed in microslides (0.05-0.4 mm thickness) when only a small amount (10-15 wt %) of the isotropic phase is present. Five different focal planes can be visualized with the polarization microscope. The midplane focus gives pictures which look like primitive two-dimensional lattices of equally sized vesicle droplets. The 1:1 mixtures give irregular pattern formation. Removal of the isotropic phase by a 20 min centrifugation at 3000g leads to ordinary focal conics. Parabolic focal conics seem to be formed when the isotropic phase and the coexisting lamellar phase have comparable compositions, and this leads to the assumption that both phases should be in a near-critical state. The formation of parabolic focal conics looks more like a spinodal demixing than a crystallization process with nucleation. The very regular parabolic focal conics are transient states which change to mosaic textures, which look very similar to hexagonal fan textures, whereas polycrystalline parabolic focal conics transform to ordinary focal conics after several days or weeks.
1. Introduction The different microstructures of liquid crystalline phases result in characteristic polarization microscopic textures. Smectic A phases frequently give pseudoisotropic orientation between two glass surfaces so that no birefringence can be recognized by perpendicular observation.1-3 The smectic sheets are ordered by steric forces in these cases. Oily streaks, focal conics, and polygonal textures are found in the other thermotropic smectic phases. Lyotropic lamellar phases give a similar variety of smectic textures. Dilute lamellar lyotropic phases are frequently found in surfactant solutions containing fatty alcohols. It is of interest that there are almost three different lamellar phases in these systems, namely LRl, LRl-h, and LRh.4 The different phases appear one after the other on increasing fatty alcohol concentrations at the same surfactant concentration. The only phase which makes pseudoisotropic orientation is the Lah phase which appears at the highest fatty alcohol concentration. LRl phases which appear at the lowest fatty alcohol concentrations show the texture of thermotropic smectic C phases, LRl-h of smectic E.5 The molecules in the sheets of thermotropic smectic phases, except smectic A, are in somewhat tilted states. It can be assumed that this is also the case for lamellar-lyotropic phases different from LRh. Focal conics are typical for smectic phases with highly constant interlamellar distances. Very detailed information about this texture is given in various papers, e.g. refs 6-9. The structure has two characteristic line defects which form a pair on an ellipse and a hyperbola in a plain X
Abstract published in Advance ACS Abstracts, March 1, 1996.
(1) Lehmann, O. Flu¨ssige Kristalle; Verl. W. Engelmann: Leipzig, 1904. (2) Friedel, G. Ann. Phys. 1922, 18 (9), 273. (3) Demus, D.; Richter, L. Textures of Liquid Crystals; Verlag Chemie: Weinheim, 1978; Chapter 4.4. (4) Platz, G.; Thunig, C.; Hoffmann, H. Ber. Bunsenges. Phys. Chem. 1992, 96 (5), 667-677. (5) Platz, G.; Po¨like, J.; Thunig, C.; Hofmann, R.; Nickel, D.; von Rybinski, W. Langmuir 1995, 11, 4250-4255. (6) Bouligand, Y. J. Phys. 1972, 33, 525-547. (7) Bouligand, Y. J. Phys. 1972, 33, 715-736. (8) de Gennes, P. G. The Physics of Liquid Crystals; Clarendon Press: 1974. Bidaux, R.; Boccara, N.; Sarma, N.; de Seze, L.; de Gennes, P. G.; Parodi, O. J. Phys. 1973, 34, 661-671.
perpendicular to the ellipse. Both focal conics are confocal. This means that one focal conic passes a focal point of the other one. For example, if the ellipse is a circle the confocal line is a straight line which passes the center of the circle. The lamellae form a torus in this case. The optical axis of any focal conic region and therefore the polarization microscopic texture can be easily constructed for each point in the focal conic region. The axis is clearly defined by three points on it. These are the point of observation and a location on each of both focal conics (ellipse and hyperbola). There is a special form of focal conics which gives highly symmetric textures. The focal lines form two confocal parabolae. Different parabolic regions are connected, thus forming a quadratic texture pattern.9 It is known that such textures grow from lamellar phases which are in a pseudoisotropic orientation if this orientation is a stress situation for the phase. The theoretical and experimental background of parabolic focal conics have been treated in detail.10-20 It is the purpose of this paper to outline the experimental conditions for parabolic focal conic textures with nearly perfect lateral order. The parabolic focal conics presented in this paper only appear in two-phase lamellar-isotropic regions of various lyotropic systems. The (9) Rosenblatt, Ch. S.; Pindak, R.; Clark, N. A.; Heyer, R. B. J. Phys. 1977, 38, 1105-1185. (10) Asher, S. A.; Pershan, P. S. J. Phys. 1979, 40, 161-173. (11) Ouchi, Y.; Takanishi, Y.; Takezoe, H.; Fukuda, A. Jpn. J. Appl. Phys. 1989, Part 1, 28 (12), 2547-51. (12) Hudson, S. D.; Lovinger, A. J.; Larson, R. G.; Davis, D. D.; Garay, R. O., Fujishiro, K. Macromolecules 1993, 26 (21), 5643-50. (13) Nicholson, L. K.; Teng, Q.; Cross, T. A. J. Mol. Biol. 1991, 218 (3), 621-37. (14) Rout, D. K.; Choudhary, R. N. P. Mol. Cryst. Liq. Cryst. 1989, 166, 75-90. (15) Meeten, G. H.; Navard, P. J. Polym. Sci. Part B: Polym. Phys. 1988, 26 (2), 413-19. (16) Donald, A. M.; Viney, C.; Ritter, A. P. Liq. Cryst. 1986, 1 (3), 287-300. (17) Benton, W. J.; Miller, C. A. Prog. Colloid Polym. Sci. 1983, 68 (Front. Colloid Sci.), 71-81. (18) Benton, W. J.; Toor, E. W.; Miller, C. A.; Fort, T., Jr. J. Phys. 1979, 40, 107-110. (19) Hirsch, E.; Wittmann, J. C.; Candau, F. J. Dispersion Sci. Technol. 1982, 3 (4), 351-372. (20) Candau, F.; Ballet, F.; Debeauvais, F.; Wittmann, J. C. J. Colloid Interface Sci. 1982, 87 (2), 356-374.
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Figure 1. Phase diagram intersection from 15% SDS in water to 15% SDS in 1:1 hexanol-decane mixtures at 25 °C. I represents the isotropic phase, La represents the lamellar phase, and Cr is a dispersion of solid SDS.
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patterns are transient figures which change with time to polygonal or ordinary focal conic textures. 2. Experimental Section Sodium dodecyl sulfate (SDS) from Serva in quality p.A., hexanol p.A., and decane fraction were used without further purification. Water was bidistilled. For the SDS-hexanol-decane-water phase diagram intersection, proper amounts of an isotropic solution of 15 wt % SDS in water and a dispersion of 15 wt % SDS in 1:1 hexanol-decane were mixed together at 25 °C and magnetically stirred for 10 min. Ten milliliters of the solutions were held in 25 mL test tubes for 2 weeks. The phase volumes were determined after this time by visual observation. The milky slightly viscous dispersion of SDS in hexanol-decane which is stable for several minutes is obtained when SDS is stirred into a solution of hexanol-decane. After partial sedimentation, the dispersion can be homogenized again by shaking. The temperature dependence was estimated in the same test tubes in steps of 5 K. The phase volumes were measured after 24 h. Microcuvettes (50 × 5 mm, microslides from Camlab England) with a capillary thickness of 0.05 mm, 0.1 mm, 0.2 mm, and 0.4 mm were used for observations with a Zeiss-Standard polarization microscope. The differential interference contrast picture was obtained from a Zeiss Axiophot microscope. The probe solutions were homogenized by shaking, soaked into microslides by capillarity forces, and sealed with polymer wax (from Camlab). A table centrifuge (3000g) was used for phase separation of lamellar-isotropic emulsion-like systems.
3. Results 3.1. Formation of Parabolic Focal Conics. The phase diagram of 15% SDS in water and 15% SDS in 1:1 mixtures decane/hexanol at 25 °C is given in Figure 1. Figure 2a,b shows that the lamellar region propagates to higher decane content when the temperature is raised. The isotropic phases which are located at both sides of the lamellar phase do not show the typical flow birefringence of dilute sponge phases. Polarization microscopic pictures of the lyotropic single phase region at 25 °C result in focal conic textures of a lamellar phase. There are not any pseudoisotropic orientations. The texture is formed immediately after preparation in microslides. The LRl-h phase of systems containing fatty alcohols give such a texture.21 Figure 1 shows that there are two different compositions with nearly equal volumes of an isotropic and a lamellar phase. The lamellar phase at the water-rich position is the upper phase whereas the lamellar phase at the decane(21) Platz, G.; Thunig, C.; Po¨like, J.; Kirchhoff, W.; Nickel, D. Colloids Surf. A 1994, 88, 113-122.
Figure 2. Volume fractions of the lamellar and the isotropic phases as a function of the temperature: (a) 15% SDS in 40% hexanol-decane, 1:1, and 60% water (the lower phase is lamellar); (b) 15% SDS in 20% hexanol-decane, 1:1, and 80% water (the upper phase is lamellar).
rich position is the lower one. Turbid emulsions are obtained when both mixtures are homogenized by shaking strongly. The emulsions are stable for several hours and can easily be soaked into microslides by capillary forces. The microscopic pictures of these emulsions show quite different behavior. The water-rich emulsion seems to be optically isotropic. However there is a strong flow birefringence. Differential interference contrast (DIC) pictures prove that the emulsion contains large vesicular aggregates (Figure 3). These multilamellar vesicles do not change within several days. The microscopic pictures show that the vesicle dispersion contains little lamellar phase. Therefore it is obvious that without shear there is a 1:1 mixture of lower isotropic phase and upper vesicular dispersion of a condensed lamellar phase in the isotropic phase. The decane-rich emulsion is only weakly turbid. The microscopic pictures show that considerable amounts of birefringent droplets are dispersed in an isotropic phase (Figure 4). This lamellar phase which appears at the bottom of the reagent glass is therefore not in a condensed state. Some of the droplets contain pseudoisotropic regions which appear dark in perpendicular observation under the polarization microscope. These regions become bright when the microslide is tilted whereas true isotropic regions remain dark. Pseudoisotropy occurs in lamellar phases which are oriented perfectly parallel to the glass walls. The optical axis is perpendicular to the surface of the microslide in these cases. Some of the pseudoisotropicisotropic borders are fenced in by strongly birefringent oily streaks. It must be noted also that the liquid crystalline droplets found in Figure 4 look like those of nematic or biaxial lamellar phases. They contain strongly distorted dark crosses. Maltese crosses with undistorted dark crosses which are typical for dispersions of smectic A or LRh phases are hardly found.
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Figure 3. Differential interference contrast picture of the emulsion which is obtained after shaking an 1:1 mixture of the upper lamellar phase and the lower isotropic phase (water rich side of the phase diagram intersection) at 25 °C 1 h after preparation between microscope slide and cover glass (15% SDS, 68% water, 17% hexanol-decane, 1:1). The bar represents 100 µm.
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Figure 5. After 24 h an irregular pattern of parabolic focal cones has developed from the sample shown in Figure 4. See Figure 4 for details.
Figure 6. Regular pattern of a weak centrifugalized lamellar phase 24 h after soaking into a 0.1 mm microslide: 3000g for 2 min, midplane focus. See Figure 4 for details.
Figure 4. A 1:1 mixture of lamellar and isotropic phase homogenized by shaking for 1 h after soaking into a 0.1 mm microslide. Birefringent droplets which contain pseudoisotropic regions are dispersed in the isotropic phase. A λ-plate was used in order to obtain a good color contrast. Details: All polarization microscopic pictures were taken from 15% SDS, 51% water and 34% 1:1 decane-hexanol at 25 °C which separates into an lower lamellar and an upper isotropic phase in 1:1 volume fraction (decane-rich side of the phase diagram intersection, Figure 1). The bars represent 100 µm.
The pseudoisotropic regions begin to change after several hours. A rectangular pattern of parabolic focal conics occurs which seems to develop inside the pseudoisotropic region. There seem to be no starting positions and no nucleation points. The birefringence of the pattern appears very weak at the beginning of the pattern formation but becomes brighter when the pattern smoothly starts to grow out into the isotropic region. The propagation of the pattern boundary seems to proceed strictly parallel to the sides of the squares. The strongly birefringent droplets and the oily streaks are impediments for this process. A polycrystalline pattern is obtained in these cases, as shown in Figure 5. In order to remove the impediments for regular pattern formation, we separated most of the isotropic phase from the lamellar phase by 1 min centrifugation at 3000g. Now the lamellar phase filled the microslide, and a pseudo-
isotropic orientation of nearly the entire probe was observed. There were almost no lamellar droplets which could act as locations for distortions. However it is important to note that very small amounts of isotropic phase were present after centrifugation. These droplets were located at both sides of the microslide but never in the middle region. After some time a very regular pattern was obtained (Figure 6). It is very important to note that the removal of the entire isotropic phase by longer centrifugation prevents the formation of parabolic focal conics. When the separated lamellar phase which produces very regular patterns is centrifuged at 3000-4000g for 20 min, 5-10% of isotropic phase separate again. Now the lamellar phase gives ordinary focal conic textures but no parabolic focal conics. The developing of the very regular pattern may start from any border of the microslide. A very weak pattern moves into the pseudoisotropic region. The squares become brighter with time. This increasing brightness seems to develop from inside the pattern. The process looks like a spinodal decomposition. Very regular squares are obtained only when no concurring pattern formation process starts from another position at the sides of the microslide (Figure 6). 3.2. The Five Microscopic Focal Planes. The geometrical relations can be visualized by orienting the squares sides parallel to the polarizer-analyzer pair and focusing different planes. The upper and the lower focuses give squares (Figure 7a). The position of the centers
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Figure 8. The picture of the middle focus from Figure 7a shows yellow and blue squares when a λ-plate is inserted. See figure 4 for details.
Figure 7. (a, Top) The upper focus shows squares. The lower focus gives the same picture; however the edges of the lower squares are shifted to the center of the upper squares. (b, Bottom) The picture made in middle focus looks like a pattern of regularly ordered mutual penetrating spheres. Parameters given in Figure 6, 0.2 mm microslide. See Figure 4 for details.
change between upper and lower focuses. The centers of the upper squares are the etches of the lower squares. The midplane focus (Figure 7b) gives the picture which looks like rectangularly packed birefringent droplets or like a two-dimensional primitive lattice of vesicles. No more focal planes can be found in the early stages of the parabolic focal conics. A λ-plate in the 45° position between polarizer and analyzer is useful for recognizing the sign of birefringence.22 The blue color appears for positive birefringence; yellow, for negative birefringence. The λ-plate gives a checkered pattern of yellow and blue fields (Figure 8). These pictures are quite typical for parabolic focal conic textures and can be explained as follows (Figure 9): There are two confocal parabolae. The direction of the optical axis of the lamellar phase at any point of the phase is exactly determined by the line which passes the point of observation and touches both parabolae. This means that all lamellae which cut this line are oriented perpendicular to this local optical axis at the intersection point. In this way the focal conic texture can be constructed from point to point or from line to line without calculating very complicated mathematical expressions for the form of the lamellar sheets. The parabolate cut the surface of the microslide. The four intersection points form an elongated tetrahydron. (22) Beyer, H. Handbuch der Mikroskopie; VEB-Verlag Technik: Berlin, 1977; p 2.
Figure 9. Schematical explanation of the quadratic yellowblue λ-plate pattern. Microslide, polarizer, and analyzer are oriented parallel and perpendicular to the figure. Optical axis of λ-plate in a 45° direction to polarizer and analyzer. Solid lines: Parabolae with upper intersection points. Dotted lines: Parabolae with lower intersection points at microslide surface. The upper intersection points give the big square pattern (Figure 7a) of the upper focus with side length a0. The “spheres” of the middle focus (Figure 7b) are centered at the vertices of the parabolae. These points are the intersections of any solid line with any dotted line of this figure. The lines drawn in a (45° direction from the upper to the lower parabola of a single parabolic focal conic represent the mean direction of the optical axis projection into the microslide plane. See Figure 4 for details.
Each intersection point of both parabolae with the surface of the microslide is the location of four parabolae which are oriented in 90° positions to one another. The whole space is filled by a rectangular pattern of such parabolic focal conics. The right and left borders of the microslide are strong distortions for this geometrical figure. Therefore we observe another orientation and different textures near these boundaries. In most cases the focal conics become less and less bright near the left or right boundary of the microslide until pseudoisotropic orientation is reached. Very close to the boundary, birefringence occurs again because the lamellar planes are oriented in direction to the observer (Figure 6). However, it is also possible that the parabolic focal conics reach up to the focal conic texture near the boundary. The big squares of Figure 7 in the upper focus are the locations of four upper parabolae; the four lower parabolae are the location of the big square of the lower focus. The λ-plate pictures of the midplane focus are squares whose lengths are half the lengths of the big squares which are formed by the four upper or lower intersection points of
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neighboring parabolae (Figure 8). The optical axis within these squares changes from point to point. The observer recognizes only the projection of the optical axis into the plane of the microslide. Each of these projections is given by a line from the upper to the lower parabolae. The birefringence of the pseudoisotropic oriented lamellar phase is positive which can be shown with a λ-plate and tilting the microscope table for 10-20° in 45° position between polarizer and analyzer. Therefore we obtain blue color for all directions of the projection between zero and 90°. A 45° position results the strongest effect. A yellow color is obtained for all projection directions between 90° and 180° with a maximum effect of 135°. The optical axis at a single point of observation changes its direction at different altitudes within the microslide. However the maximum change goes from 0° to 90° for a blue square and from 90° to 180° for a yellow square. The microscopic picture results from the sum of all these optical axis. Therefore blue and yellow triangles are found for each pairs of parabolae. Each blue triangle is connected with the yellow triangle of the next pair of parabolae, and each yellow triangle is connected with the yellow triangle of the next pair of parabolae. Thus we obtain a square chequered pattern of yellow and blue fields. Blue and yellow fields are separated by narrow regions without visual birefringence. These regions which appear dark when the λ-plate is removed are the locations of the parabolae themselves. The dark crosses within the “spheres” of Figure 6 are the locations of two confocal parabolae of a single parabolic conic. The locations of the upper and lower points of intersection of four parabolae give no sharp figure in this primary state of the focal conics. The big square pattern which is obtained for the upper focus is the network of the upper parabolae themselves; the big square patterns of the lower focus are the lower parabolae. The equation of the parabolae is given by
z)
1 2 x 2r0
where z and x are axes perpendicular and parallel to the microslide walls, respectively. r0 is the focal length of the parabolae. The thickness of the microslide is h0. The distance of the section points of the parabolae of the surface is a0. Therefore we obtain h0 ) a02/r0 - r0. In Figure 9 a0 is the length of the squares formed by the four upper or lower intersection points of neighboring parabolae with the microslide surface (Figure 7a) and twice the length of the λ-plate squares from Figure 8. We have measured a0 values in microslides from 10 to 40 µm. In systems with irregular patterns, different a0 values are found within the same sample. Smaller squares are also found near the boundary of the microslide. In all cases the a0 values are much smaller than the thickness of the microslide. This means that the parabolae are strongly elongated. The parabolic focal conics are well developed after 2024 h. Five different optical focus regions can be recognized now (Figure 10a,b). The upper focus gives sharp pictures from the intersection points of the four parabolae which form the big square pattern. The next plane focuses into the top region of the parabolae whose intersection points are at the bottom of the microslide (upper middle focus). Dark regions appear within the square pattern which look like lenses. These lenses are formed by the vertices of the parabolae with lower intersection points. The next focus is exactly the middle of the parabolic focal conics. The lenses of the upper and lower parabolae form a cross with a dark center (Figure 10b). The center of the cross remains dark when the sample is rotated. This position is a
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Figure 10. Ten-day-old sample which developed bright fourleaf clovers in between dark lenses or dark crosses. Parameters given Figure 6, 0.2 mm microslide. (a, Top) The upper middle focus picture results in dark lenses which change to dark crosses in the midplane focus position. (b, Bottom) The dark lenses appear again at the lower middle focus however their direction has rotated by 90°. See Figure 4 for details.
pseudoisotropic region because the optical axis which passes the maximum of the lower parabolae and the minimum of the upper parabolae is striktly perpendicular to the walls of the microslide. The next focus plane gives the lenses of the upper parabolae which are perpendicular to the lenses of the lower parabolae (lower middle focus). The last focus gives sharp pictures of the lower intersection points of the parabolae with the walls of the microslide. These locations are the centers of the squares formed by the upper intersection points. 3.3. Ageing Processes. The parabolic focal conics seem to remain unchanged in this state. However one can observe that the locations very close to the intersections become brighter although there is no change in the pattern itself. This strong birefringent region has the form of a small four-leaf clover which grows into the parabolic focal conics. The result is that the midplane focus pictures of the parabolic focal conics look more and more like squares (Figure 10b) and no longer like spheres (Figure 6). There are four-leaf clovers with a sharp center and with a diffuse center as for the upper as for the lower focal plane. The middle focus position results in a uniform pattern of diffuse four-leaf clovers. Therefore it is clear that the centers of the four-leaf clovers are the intersection points of the parabolae. After some time the regions in between the two leaves of two neighboring four-leaf clovers become also more birefringent. It looks like light beams coming out of the
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Figure 11. Distortion of regular parabolic focal conics in 0.4 mm microslide after 5 days. See Figure 4 for details.
Figure 12. Transition state after 5 days in 0.2 mm microslide. The texture changes with time to that of Figure 14. See figure 4 for details.
centers of the sharp four-leaf clovers, thus giving the picture of “crystallization”. In some cases, preferably in irregular patterns, some of these beam regions continue to grow and the parabolic focal conics near the growing beam regions are destroyed. An irregular focal conic texture is finally obtained. In regions with very regular patterns, the parabolic focal conics are changed also. However highly ordered stable states with high degrees of order are maintained. Figure 11 shows a transition state with a rhombic distorted parabolic focal conic structure. The squares of the original polycrystalline structure were oriented in 0° and in 45° positions to polarizer and analyzer. The extended dark crosses of the original structure which are formed by the lenses belonging to the parabolae have lost their rectangular angles. The structure can be obtained from the parabolic focal conics when the network of the lower intersection points remains unchanged and the network of the upper intersection points shifted from its original position. The original parabolic focal conic texture can be easily recognized in the region with squares in the 0° position. The 45° position shows a very strong birefringence in the 45° direction going from one four-leaf clover to the next one. The distortions of the parabolae may give different regular transient textures. Figure 12 shows continuous transitions from undistorted parabolic focal conics to such structures with lower symmetry. In some cases regular patterns of distorted parabolic focal conics are obtained which seem to be stable for longer times (Figure 13).
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Figure 13. Sample of Figure 12 photographed in another location. This texture is stable for very long time. See figure 4 for details.
Figure 14. Stable focal conics which developed from regular parabolic focal conics after 2 weeks. See Figure 4 for details.
However most transient states become more and more irregular. Mosaic textures (Figure 14) which look very similar to hexagonal fans are the final state. 3.4. Examples for Parabolic Focal Conics. It is of interest that parabolic focal cones were already described in the very similar system SDS-butanol-toluene-water in the same concentration region.19 Several examples of ternary surfactant, fatty alcohol, and water mixtures are given where parabolic focal conics can be found in the two-phase lamellar-isotropic region as well as in the SDS-hexanol-decane-water system: 22.5-39 wt % APG600, 2 wt % decanol; 10 wt % APG600, 2 wt % dodecanol; 10 wt % APG600, 0.2 wt % tetradecanol; 16 wt % APG600, 2.5 wt % oleyl alcohol; 20 wt % APG600, 8.6 wt % hexanol in 1 M NaCl solution; 10 wt % H91 (a phenol resin from Hoechst, Gendorf) in water. 4. Discussion Surfactant solutions and fatty alcohols are known to form three different types of lamellar phases (LRl, LRl-h, and LRh phase) which appear at the same surfactant concentration on increasing the fatty alcohol concentration. The LRh phase is the only phase with extended regions of equidistant lamellar planes. Only this phase prefers pseudoisotropic orientation. There are oily streaks at the beginning of the preparation. However these birefringent regions disappear with time, and the growing pseudoisotropic region remains in its stable state. Maltese crosses are formed when dilute LRh phases are in coexistence with the isotropic sponge phase (L3 phase).
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These maltese crosses are stable droplets with onion-like multilamellar sheets. We never found focal conics or parabolic focal conics in dilute LRh phases or in mixtures of coexisting LRh and L3 phases. The LRh phase is known to consist of uniaxial isotropic lamellae. Therefore the experimental results lead to the assumption that stable phases made of lamellar sheets which are isotropic within their lamellar plane are not able to form focal conics or parabolic focal conics. The LRl-h phase contains less fatty alcohol than the LRh phase. It is of interest that small regions with parabolic focal conics can frequently be found within the focal conic texture of this phase. However extended patterns are not formed. Focal conics and polygonal textures but no parabolic focal conics are the typical textures of this phase. Pseudoisotropic orientations are never achieved with LRl-h. A biaxial homogeneous (LRl) texture is always obtained when LRl-h is sheared. The LRl phase which is found at the lowest fatty alcohol concentrations has a biaxial texture like smectic C and not any pseudoisotropic regions. This comparison elucidates that none of the three lamellar phases which appear at lower surfactant concentrations has the properties which lead to extended parabolic focal conic regions. Indeed parabolic focal conics are only found in higher concentrated lamellar phases. Smooth transitions from LRh to LRl-h can be observed, and polygonal textures which look like distorted parabolic focal conics after a long period of ageing are found in the twophase LR-L3 region now. Parabolic focal conics develop from a pseudoisotropicoriented lamellar phase during stress relaxation. It is clear that the elastic forces which are necessary for this process are present in higher concentrations but are too weak in dilute and very dilute lamellar phases. However the question of how it is possible that very regular patterns develop from pseudoisotropic orientation nearly from inside the region but not from a crystallization like process remains unanswered. In a crystallization process the parabolic focal conics would be well developed one after the other during the spreading of the pattern. However the parabolic focal conics start to grow from a certain region, but the amplitudes increase slowly after the pattern has been completely formed. This type of formation looks like a spinodal decomposition of an unstable single phase to a two-phase system. There is another experimental fact which supports our assumption. When 1:1 mixtures of lamellar and isotropic phase are soaked into the microslide after homogenizing by shaking it is clearly observed that the isotropic regions disappear nearly completely during the formation of the parabolic focal conic pattern. Transport of material only by diffusion should be too slow for this process. It would also remain unclear why the amount of the lamellar phase should increase although the system was in equilibrium before. So we conclude that the isotropic and the lamellar phase should be in a nearly critical state together where the composition of both coexisting phases are not very different. In this case it is possible that the shear forces which act during the soaking into the microslide together with the wall interactions transform a nearly critical mixture of lamellar LRl-h and isotropic phase to a single phase of type LRh with pseudoisotropic orientation. How-
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ever the system is not stable after shear, and the LRl-h phase and the isotropic phase separate again in a spinodal decomposition. The spinodal phase separation may have a maximum rate at a distinct value and direction of the wavelength of the concentration fluctuations or undulations.10 The mechanism of such a process therefore shows schematically that regular but not irregular patterns are formed. In contrast to this assumption is the fact that we observed different square length values although we investigated the same mixtures. These different values may depend on different shear conditions during the preparation. It must be noticed that there seems to be no statistical distribution of quite different a0 values but a distribution with three different maxima around 12, 20, and 40 µm. In order to answer these questions we want to carry out experiments with well-defined shear conditions, and we will analyze the compositions of the coexisting phases. One must also take into account that the shear stress has a maximum value near the walls and is zero in the middle region. The phase will be ordered strongly near the walls, and no order is achieved in the middle region. Therefore concentration fluctuations should be located in the middle region but not near the walls. The formation of parabolic focal conics starts from these fluctuations, and one can understand why such highly elongated parabolae can be formed. Most of the isotropic phase must be removed in order to obtain highly regular parabolic focal conics because high amounts of isotropic phase which appear again after the formation will destabilize the pattern. Some isotropic phase must be present because the pattern formation leads to energetically unfavorable positions for a system with plain lamellae. The lamellae must be tilted there or some isotropic phase is present and fills these positions. The lamellar-isotropic phase boundary is a stable state, and therefore it is possible to lower the energy at the unstable locations. The parabolic focal texture is responsible for the fact that the lamellar sheets close to the glass surface have an orientation which is energetically unfavored. The maximum curvature of the lamellae is located near the midplane which is the intersection region of both confocal parabolae. The strongly elongated parabolae indicate that the lamellae close to the surface are close to a parallel orientation. However the most stable orientation parallel to the walls cannot be achieved. Therefore we assume that the isotropic phase must be located between the parabolic focal conics and the surface of the microslide in order to minimize wall effects which decrease the stability of the parabolic focal texture. Other positions with higher elastic energy are the parabolae themselves. However the most unstable locations should be the intersection points where parabolae of four different parabolic focal conics come together. Therefore one can understand that the destruction of the focal conics starts from these points. We assume that the parabolic focal conics are a kinetically stabilized transient metastable state during the process of forming focal conics. LA950736N
