Langmuir 2001, 17, 7245-7250
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Studies of Domain Size of Hexagonal Liquid Crystals in C12EO8/Water/Alcohol Systems Anil Kumar,† Hironobu Kunieda,*,† Carlos Va´zquez,‡ and M. Arturo Lo´pez-Quintela*,†,§ Graduate School of Engineering, Yokohama National University, Tokiwadai 79-5, Hodogaya-ku, Yokohama 240-8501, Japan, and Departamento de Quı´mica Fı´sica, Facultad de Quı´mica, Universidad de Santiago E-15782, Santiago de Compostela, Spain Received April 26, 2001. In Final Form: August 21, 2001 The broadening of the most intense lines observed in the X-ray diffraction patterns has been used to determine the domain sizes of hexagonal liquid crystals in C12EO8/water/alcohol systems. A linear “master” relationship between the sizes and the distance to the isotropic phase-transition boundary line (H1 f Wm) was observed as the temperature, surfactant, and glycerol volume fractions were varied. This linear relationship is interpreted as the feature of a “glassy” state formed by the crystallites, which grow until their glass-transition temperature is attained. The master relationship indicates that both temperature and volume fraction induce the glass transition, hindering a further growth of the crystal domains. A fractal dimension close to one for these cylindrical domains is obtained, and an estimation of the number of bounded cylinders inside a domain has been made. For systems containing propylene glycol and propanol, the observed increase in domain size on approaching the phase boundary is much larger than for glycerol systems, which seems to be related to the different influence of the alcohols on the surfactant aggregation and its structure, as it was previously reported for these alcohols. A large increase of the domain sizes by aging the samples, as it is usually observed for common glassy systems, is also reported.
Introduction In past years, a great interest has been devoted to elucidating the self- organization of structures formed in concentrated surfactant systems1,2 which exhibit a rich behavior, ranging from very fluid “hard-sphere” microemulsions to very viscous “gel-like” liquid crystals.3,4 Although many of the possible envisaged applications for such systems remain to be explored, one of the most interesting applications is related to the use of such systems as templates for producing nanomaterials or nanocomposites.5,6 However, one of the main limitations is the small size of the “nanocrystals” present in these surfactant systems. The sizes are, of course, in the range of other ordinary organic/inorganic crystals, but taking into account the large size of the unit cells involved here, in comparison with the ordinary crystals, the number of unit cells per crystal domain is very low. The large size of the unit cells is due to the fact that the crystal positions are occupied by micelles (spherical, cylindrical, etc.) instead of simple atoms or molecules. Therefore, the ordered space in these “micelle crystals” is usually very * To whom correspondence should be addressed. Phone and fax: +81-45-339-4190. E-mail:
[email protected]. † Yokohama National University. ‡ Universidad de Santiago. § On sabbatical leave from the University of Santiago de Compostela. (1) Jo¨nsson, B.; Lindman, B.; Holmberg, K.; Kronberg, B. L. Surfactants and Polymers in Aqueous Solution; John Wiley & Sons: Chichester, England, 1998; Chapter 3. (2) Laughlin, R. G. The Aqueous Phase Behaviour of Surfactants; Academic Press: London, 1994; Chapter 5. (3) Hyde, S.; Andersson, S.; Larsson, K.; Blum, Z.; Landh, T.; Lidin, S.; Ninham, B. W. The Language of Shape. The Role of Curvature in Condensed Matter: Physics, Chemistry, and Biology; Elsevier: Amsterdam, 1997; Chapter 4. (4) Evans, D. F.; Wennerstro¨m, H. The Colloidal Domain. Where Physics, Chemistry, Biology, and Technology Meet.; Wiley-VCH: New York, 1999; Chapter 10. (5) Antonietti, M.; Hentze, H.-P. Adv. Mater. 1996, 8, 840. (6) Go¨ltner, C. G.; Antonietti, M. Adv. Mater. 1997, 9, 431.
low, with the amount of disordered interfaces being an important part of the global system. However, to our knowledge, there are not any studies that take into account the presence of this very important interfacial space. The existence of this “disordered” space in the “micelle crystals” can be easily seen in the poor resolution usually observed in the X-ray diffraction patterns obtained from these systems. For many applications, it is very important to know the amount of “disorganized space” and how it can be reduced. The aim of this work is focused precisely in this direction. As a first step, we have studied how the domain crystal size in surfactant systems is affected by different parameters like concentration, temperature, aging, etc. For the study, we have chosen a well-known system extensively studied before in our laboratory, namely, the water/C12EO8 inside the hexagonal liquid crystalline, H1, phase.7 In this paper, we report the influence of temperature and concentration of surfactant on the domain size and the influence of the presence of different alcohols (glycerol, 1-propanol, and propylene glycol). It has been shown that7 a hexagonal liquid crystal (H1) changes to an isotropic solution (Wm) with increasing glycerol content due to the dehydration of the ethylene oxide chain, whereas propylene glycol or 1-propanol molecules tend to penetrate into the palisade layer of the aggregates, and the micelles are downsized with an increase in the alcohol content. As we will show here, both types of alcohols also have a different influence on the domain size, which seems to be related to the different behaviors discussed above. Experimental Section Materials. Homogeneous octaethylene glycol dodecyl ether (C12EO8) was procured from Nikko Chemicals Co. For constructing phase diagrams and SAXS measurements, glycerol (Wako (7) Aramaki, K.; Olsson, U.; Yamaguchi, Y.; Kunieda, H. Langmuir 1999, 15, 6226.
10.1021/la010615p CCC: $20.00 © 2001 American Chemical Society Published on Web 10/13/2001
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Kumar et al. were obtained from the mean values of the Gaussian and Lorentzian fittings and showed good reproducibility.
Results
Figure 1. Typical Gaussian and Lorentzian fits of the most intense diffraction peaks in the hexagonal liquid crystalline phase region, H1, of C12EO8/water/alcohol systems. Pure Chemicals, Tokyo, 99%), propylene glycol (1,2-propanediol, Wako Pure Chemicals, Tokyo, 99%), and 1-propanol (Tokyo Kasei Kogyo, Tokyo, 99.5%) were used. All reagents were used without further purification. Samples were prepared with Milliporefiltered water. Phase Diagrams. All chemicals were weighed and sealed in ampules having a narrow constriction. All samples were mixed thoroughly by using a vortex mixer accompanied by heating and by using repeated centrifugation of the samples containing liquid crystals. The samples were kept in a water bath controlled at constant temperature ((0.05 °C) for several hours. A hexagonal liquid crystal was distinguished by the observation of optical birefringence under crossed polarizers and the relative peak positions in a SAXS spectrum. SAXS Measurements. SAXS measurements were performed on a small-angle goniometer with 15 kW of Cu KR radiation (Rikagu, Rint 2500) at 20 °C. For the measurements, samples of liquid crystal were sandwiched between two layers of polyethylene terephthalate film (Mylar seal method). Crystallite Size Determination: Data Fitting. Small-angle X-ray diffraction patterns were fit to Gaussian and Lorentzian profiles in the angular range of the mean peak position. From this fitting procedure, the following parameters were extracted: peak position, peak area, height, and width. A baseline subtraction was done previously to fit the SAXS pattern. When overlapping is present, two Gaussian and Lorentzian profiles were used to consider the contribution of the closest reflections to the main peak. In Figure 1, typical Gaussian and Lorentzian fits are shown. The average crystallite size, Dhkl, was determined by applying the Debye-Scherrer formula to the main peak:
Dhkl (Å) )
kλ β cos(θ)
(1)
where k is a nondimensional shape factor which normally ranges between 0.9 and 1.0 (in our case k ) 0.9), λ is the X-ray wavelength (in angstroms), β is the integral breadth (in radians), and θ is the Bragg angle (in radians).8 The integral breadth is calculated by dividing the integrated peak area over the peak intensity. The values for domain sizes (standard error ) 5%) reported here (8) International Union of Crystallography. International Tables for X-ray Crystallography; Dordrecht: Holland, 1985; Part III, pp 318323.
Phase Behavior of C12EO8 in Aqueous Polyol Solutions. The phase diagrams of water/C12EO8 were constructed as a function of alcohol content at a constant volume fraction of surfactant (φs ) 0.52), and the results are shown in Figure 2. Glycerol, propylene glycol, and 1-propanol were used as alcohols. The phase diagrams of water/C12EO8/polyols systems at constant temperature (T ) 25 °C) have been reported in our previous studies7 and are shown in Figure 3a-c as a reference. It is evident from Figure 2 that C12EO8 forms the H1 phase over a wide composition and temperature range, and there is a shrinking in the H1 region when polyol (glycerol or propylene glycol) is replaced by 1-propanol (Figure 2c). The liquid crystal region disappears at the higher polyol content in all of the systems. It can be observed that the melting temperature of the H1 phase decreases as the alcohol content increases, and the H1 phase changes to an isotropic micellar solution when the temperature is raised above certain values. It is known that a short-chain alcohol such as ethanol raises the cmc (critical micelle concentration) of a surfactant and breaks the micelle structure.9,10 Therefore, for propanol and propylene glycol, the hexagonal liquid crystal phase (H1) would turn into an isotropic micellar phase with increasing volume fraction of alcohol (φ) by the same mechanism. For glycerol, however, the change to the isotropic phase takes place via the dehydration of the ethylene oxide chains. It can be observed that when temperature is increased further, a liquid crystal turns into an isotropic solution.11 It is considered that this “melting” is induced by the increase in thermal motion of surfactant in the liquid crystal.12 Domain Size Investigation. From Figures 2a-c and 3a-c, it has been observed that the hexagonal liquid crystal (H1) region extends over a wide range in all of the phase diagrams, and, hence, we have chosen different compositions at various temperatures to investigate the growth of domains of the H1 phase. These points are marked by (g) in the phase diagrams. In the C12EO8/water/glycerol system at 25 °C (Figure 3a), we first concentrate our experiments on the domain size of the H1 phase at constant temperature (T ) 20 °C) by varying either alcohol content or surfactant content in the systems. Initially, we measured the domain size of hexagonal liquid crystal at different volume fractions of surfactant (φs ) 0.45, 0.52, and 0.65), keeping the volume fraction of alcohol constant (φ ) 0.2). The results are shown in Table 1. It is evident that when we proceed from the left boundary of the H1 phase to the mid region of the H1 phase (Figure 3a), the domain size decreases from 112 to around 80 nm. Furthermore, when we move from the mid region to the right-hand boundary of the H1 phase, domain size increases. These results clearly indicate that the growth of the domain of the H1 phase is highly related to the location of the points under investigation. If they are close to the boundary of the H1 phase, the growth of the domain size is higher than that of the H1 phase lying in the mid region. (9) Ude, M.; Urabata, T.; Katamaya, A.; Kuraki, N. Colloid Polym. Sci. 1980, 258, 1202. (10) Meguro, K.; Uneo, M.; Esumi, K. In Nonionic Surfactant Physical Chemistry; Schick, M. J., Ed.; Marcel Dekker: New York, 1987; p 153. (11) Laughlin, R. G. The Aqueous Phase Behaviour of Surfactants; Academic Press: London, 1994; p 121. (12) McMillan, W. L. In Liquid Crystals and Ordered Fluids; Johnson, J. F., Porter, R. S., Eds.; Plenum Press: New York, 1994; pp 141-146.
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Figure 2. Influence of the temperature on the stability of the hexagonal, H1, liquid crystalline phase in the presence of different alcohols: (a) glycerol, (b) propylene glycol, (c) n-propanol. I corresponds to the isotropic phase region.
Figure 3. Phase diagrams of water/alcohol/C12EO8 systems at 25 °C as a function of the volume fraction of surfactant, φS, and the volume fraction of alcohol, φ, in the systems: (a) glycerol, (b) propylene glycol, and (c) n-propanol (taken from ref 7). Wm, H1, V1, II, and Wm + H1 indicate a micellar phase, a hexagonal liquid crystalline phase, a bicontinuous cubic phase, a two-phase equilibrium solvent-rich/surfactant-rich solution, and a two-phase equilibrium of Wm and H1, respectively. Table 1. Domain Size of H1 Phase in C12EO8/Water/ Alcohol Systemsa composition (φ/φS)
aging time (h)
0.2 Gly/0.45 0.2 Gly/0.52 0.2 Gly/0.65 0.1 Gly/0.52 0.35 Gly/0.52 0.4 Gly/0.52 0.4 Gly/0.52 0.2 Gly/0.52 0.2 Gly/0.52 0.2 Gly/0.52 0.2 Gly/0.52
instant instant instant instant instant instant 16 3 16 18 4
temp (°C) 20 20 20 20 20 20 28 20 20 30
0.2 PG/0.52 0.2 PG/0.52 0.2 PG/0.52 0.4 PG/0.52 0.4 PG/0.52 0.1 PrOH/0.52 0.2 PrOH/0.52 0.2 PrOH/0.52 0.2 PrOH/0.52
instant 16 5 instant 10 instant instant 18 4
17 17 30 20 20 20 20 30
size (nm)
cool
112 90 107 90 100 105 128 100 140 161 77
cool
65 164 142 162 230 85 150 170 150
309820
309820
a Gly, glycerol; PG, propylene glycol; PrOH, n-propanol; instant, instantaneous.
A similar trend is observed when the domain size is measured at different volume fractions of glycerol (φ ) 0.1, 0.2, 0.35, and 0.4) at constant φs (0.52). We observed that the liquid crystals at φ ) 0.4, which is near to the one-phase micellar region, have higher domain size than the liquid crystals lying in the mid region (φ ) 0.1 and 0.2). The results shown above correspond to instantaneous SAXS measurements. In other words, liquid crystals (H1) were sandwiched between two layers of polyethylene
terephthale film, and SAXS measurements were done very quickly without delay. In the next step of our investigations, we prepared the samples as mentioned above and left them at constant temperature for a few hours (viz. 3-20 h) to see the influence of aging. It has been observed from Table 1 that there is a big growth of domain size with aging. For example, at φ ) 0.2, domain size is usually observed around 90 nm (instantaneous), 100 nm for a 3 h aging, and 140 nm for a 16 h aging at the same temperature. When we increase the temperature of the same sample from 20 to 30 °C, the domain size increases to around 161 nm, which is almost twice the value measured instantaneously. We replaced glycerol by propylene glycol and 1-propanol and investigated the growth of the domain size of the H1 phase by varying the volume fraction of alcohol (φ) at different temperatures with and without aging, and the results are shown in Table 1. In the presence of propylene glycol, there is a tremendous growth in domain (from 65 to 162 nm) when the volume fraction of alcohol (φ) is increased from 0.2 to 0.4. The domain size increases up to around 230 nm for a 10 h aging. In the presence of 1-propanol, domain size increases from 85 to 150 nm when φ is just increased from 0.1 to 0.2. Furthermore, when we increased the temperature of the same sample from 20 to 30 °C, the domain size increases from 150 to 170 nm. When we cool again the sample to 20 °C, the domain size approaches its original value (150 nm). Discussion The domain sizes obtained in this study are in the range 65-230 nm and were derived, as it was explained above, from the broadening of the diffraction peaks. The broad-
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ening of the diffraction peaks can be due to three different factors:13 (1) instrumental effects; (2) effects due to the finite size of the crystals; and (3) effects due to imperfections of the lattice. Because we are only interested in the relative values of the crystal sizes, and due to the fact that in surfactant systems (and polymer systems, in general), the instrumental broadening is much smaller than the other factors considered above, we have neglected this contribution in our calculations. The separation of the broadening effects corresponding to (2) and (3) is much more difficult. Let us first consider the lattice imperfections. There are two types of imperfections, but only the so-called second-kind imperfections contribute to the line broadening. These imperfections are due to a correlated displacement of the positions of the micelles in the unit cells, that is, the unit distances grow larger as the micelles are located far away from each other. We think that this second kind of imperfection does not contribute much to the broadening in our samples due to the following reasons: (1) because of the correlation, this kind of imperfection is important only in large crystals, which is not the case considered here because the crystals contain only a small amount of unit cells in these surfactant systems due to the fact that the unit cells are very large (see below); (2) for this kind of imperfection, an increase of the line broadening with the scattering angle has been predicted13 in contrast with the broadening due to the finite size of the crystals, which does not change with the scattering angle. Although we can only observe a small number of peaks in the studied systems, we did not observe much variation of the broadening with the scattering angle. Therefore, we think that the main changes in the line broadening are due to the changes in the finite size of the crystals. From the results we have obtained, it can be seen that the highest values of the crystal domains are obtained at the borderlines of the phase transition to the isotropic phase. As the samples were prepared by cooling from the isotropic to the ordered phase, we can consider that the formation of the hexagonal phase from the isotropic solution takes place according to a nucleation and growth mechanism. A possible explanation of the results comes as follows: Let us assume that the nuclei (crystal domains) which are formed from the new hexagonal phase grow until they reach a size for which the “glass temperature” corresponds to the temperature of the experiment. At this stage, they cannot grow any further and a “frozen glasslike structure” should be obtained. On approaching the phase boundaries, viscosity is largely reduced (as it can be visually observed). Therefore, the domains can grow to much larger sizes. This phenomenon then resembles what is commonly observed in polymerization reactions, where the reaction is stopped when the sizes are large enough to reach a glass temperature equal to the temperature of the reaction.14 Because, in our case, what is important for the domain growth is the distance to the phase-transition boundary line and not the temperature (or volume fraction) itself, we can define a parameter, ∆, for characterizing this distance, as follows:
Figure 4. Domain size (s) versus the relative temperature separation from the equilibrium phase boundary, ∆T (square symbols) (vertical points in Figure 1), and relative surfactant volume fraction separation from the phase boundary, ∆φS (triangles) (horizontal points in Figure 3), for nonaged glycerolcontaining samples.
Figure 4 shows the domain size versus the relative temperature separation from the equilibrium phase boundary, ∆T (square symbols), for nonaged glycerolcontaining samples (vertical lines in Figure 1). One can observe an approximate linear relationship. To explain this linear behavior, one can think of ∆T as a parameter which should be somehow inversely proportional to the glass temperature, Tg, of the system. For polymers, the glass temperature is related to the molecular weight, M, by the Fox-Flory equation15
∆Tg ) (Tg∞ - Tg) ) A/M
(3)
where Tg∞ represents the glass transition for an infinite mass (bulk) polymer, and A is a constant characteristic of the kind of polymer considered. Assuming the abovementioned inverse proportionality between ∆T and ∆Tg and that the domains can have a fractal structure, (M ∝ sD, where s and D are the size and the fractal dimension of the domains, respectively16), one can then write
∆T ) k sD
(4)
in which X represents either temperature (T) or volume fraction (φ), and the sub-index “eq” refers to the nearest (vertical or horizontal) point of the equilibrium phase boundary.
This equation predicts a relation between ∆T and the size of the domains considered as fractal units. The fact that we obtain linear relationships between ∆T and s gives an indication that D should be close to 1. In fact, this is in perfect agreement with the probable “picture” of the liquid crystals in this hexagonal region: clusters of fine cylinders which should resemble one-dimensional fractal objects. We are aware, however, that the domain length span covered in this study is too short to name the objects as fractals, but they behave, in the short length covered, as if they were fractals. Figure 4 also contains three points (triangles) corresponding to changes in the relative surfactant volume fraction separation of the phase boundary, ∆φs (horizontal lines in Figure 3). It can be seen that these points approximately follow the same linear relationship found for the temperature. Because a glassy state can be attained by freezing the system and also by increasing the volume fraction, a similar behavior should be expected for both
(13) Roe, R.-J. In Methods of X-ray and Neutron Scattering in Polymer Science; Oxford University Press: New York, 2000; Chapter 3. (14) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: New York, 1953.
(15) Fox, T. G.; Flory, P. J. J. Appl. Phys. 1950, 21, 581. (16) See, for example: Pfeiffer, P.; Obert, M. In The Fractal Approach to Heterogeneous Chemistry; Avnir, D., Ed.; Wiley: Chichester, England, 1989; pp 11-43.
∆X ) |Xeq - X|/Xeq
(2)
Liquid Crystals in C12EO8/Water/Alcohol Systems
Figure 5. Change of the domain size with the relative alcohol volume fraction distance from the phase boundary, ∆φ (vertical points in Figure 3). Propylene glycol- (circles) and propanol(triangles) containing systems show a much larger influence than glycerol (squares) systems.
Figure 6. Linear “master” relationship (lower line) between the crystalline domain sizes and the distance to the isotropic phase-transition boundary line (H1fWm) as the temperature (black circles) and surfactant (black squares) and glycerol (black triangles) volume fractions are varied. Propylene glycol ([) and propanol (0) deviate from the master curve mostly on approaching the phase boundary.
∆T and ∆φs as it is observed, and it is another support of our interpretation of the system as a “glassy state system”. Figure 5 shows the change of the domain size with the relative alcohol volume fraction distance from the phase boundary, ∆φ (vertical lines in Figure 3). The increase in domain size for propylene glycol- and propanol-containing systems is much larger than in the glycerol-containing ones. To interpret these differences, we have merged all of the previous data (Figures 4 and 5) in Figure 6. It can be seen that the influence of the glycerol content is the same as the temperature or surfactant concentration; however, for propanol- and propylene glycol-containing samples, the influence of the alcohol is much larger, indicating that in these cases, mostly near the phase boundaries (low values of ∆φ), other factors are involved. This may be related to the previously observed7 fact that these two alcohols tend to penetrate into the palisade layer of the aggregates, and the micelles are downsized, decreasing the viscosity at the phase boundary and, therefore, allowing a larger increase of the cylinder domains. On the other hand, the glycerol content can be assumed to have the same influence on the domain size as does the temperature or surfactant concentration,
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Figure 7. Influence of aging on the crystalline domain size for glycerol- (squares) and propylene glycol- (circles: φ ) 0.2; triangles: φ ) 0.4) containing samples.
bringing the system with the same “driving force” into the isotropic region. Finally, in Figure 7, one can observe the influence of aging on the domain size. A similar increase for all of the systems studied, independent of the composition of the system, is observed. However, for the same reasons given above, the increase in domain size for the propylene glycolcontaining samples is double the increase observed for the glycerol-containing samples. Assuming an exponential approach to the final equilibrium state and making a linear expansion near the equilibrium state, the observed approximate linear increase can be used to estimate the relaxation time of the samples to their final aged size. Values of 6.5 and 3.2 h-1 are obtained for the PG- and glycerol-containing samples, respectively. We can conclude that the systems we studied here are in a nonequilibrium state,17 which is frozen because the systems attain the “glass” transition temperature. There are only two samples which disagree with this picture, namely those corresponding to aging at a higher temperature and to posterior cooling. It can be seen that the final domain size (after increasing at high temperatures) decreases again and reaches approximately the same size as the samples which have not been heated. This is a typical reversible behavior, which seems to be superimposed to the irreversible glassy behavior discussed so far. However, a more systematic study should be carried out to completely clarify this “apparent reversibility” aspect of the systems. Taking into account that the fractal dimension obtained for these domains is close to 1, one can assume a cylindrical shape for these domains. From the data we have obtained, we can then make an estimation of the number of cylinders that are orderly packed inside a crystalline domain. The volume occupied by packing n successive shells of cylinders around one cylinder considered to be in the middle is given by
Vn+1 ) (2n + 1)2 V0
(n ) 0, 1, 2,...)
(5)
with V0 ) π(d + r)2 h, where d is the intercylinder space, r is the radius of the cylinder, and h is the height of the cylinder. The value of V1 (i.e., one shell of equal cylinders surrounding a central one) can be calculated from eq 5 by using previous values obtained18 for the intercylinder (17) It is clear that we are talking about a nonequilibrium state for the crystal domains and not for the crystal structure inside the domains which is, of course, in an equilibrium state.
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spacing (d ≈ 5 nm) and the radius of the cylinder (r ≈ 1.5 nm) and by taking a typical 100 nm domain size, which gives an “unrealistic” value of h ≈ 2 µm (for this approximate estimation, we approach the domain size as a sphere having a volume equal to the cylinders). If we take n ) 2 (i.e., four shells), then we obtain a more “realistic” value of h ≈ 200 nm. In this case, the ratio of h/rc (where rc represents the radius of the approximate cylinder formed by all of the cylinders fibered together) is about 10. A further increase in the number of shells (for n ) 3) gives again an “unrealistic” picture of cylinders with the ratio h/rc ≈ 1. For a 200 nm domain size, more “realistic” values are obtained for n ) 4 (seven shells) with rc ≈ 30 nm and h ) 800 nm (h/rc ≈ 30). As the number of cylinders which are orderly packed within a domain is of the order of 7n, the above calculations imply that only 50 cylinders (or less), for a 100 nm (or less) typical domain size, are packed together inside the crystal domain. We clearly see that the order is very small, and this, in turn, gives a poor resolution in the diffraction pattern. Although inside the domains there is an equilibrium-ordered structure, outside, that is, in the space among the domains, they are disorganized in a nonequilibrium (“glassy”) state. This indicates that an appreciable amount of the material remains disordered in these ordered phases. The ordering, however, increases very much on approaching the phase transition to the much less viscous isotropic micellar region. It is possible that the domains derived from X-ray diffraction “adjust” and “pack together” to give the much larger optical domains observed by polarization microscopy.19 Conclusions Although there were many studies in the past focused on the structural study of ordered phases in surfactant
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systems, almost all of these studies dealt with the formation of micellar units: their shape and how they gathered together to form the crystal cell units. There are almost no studies related to structures at a larger scale. From the present study of the dependence of the domain size with temperature, composition, and additives, for a typical hexagonal liquid crystalline phase, we have obtained a first “picture” of the system in a supra-unitcell scale. It comes out that the crystal domains consist of bounded cylinders (with an “effective” fractal dimension close to one) which grow in size by approaching the isotropic phase boundaries. Approaching the phase boundary by increasing the temperature has the same influence as approaching it by increasing/decreasing the phase volume fraction of surfactant, and also by increasing the glycerol content, so that a “master curve” can be drawn for these three parameters. A “glassy-like” behavior is claimed for the interpretation of this dependence of the domain size on the isotropic phase boundary. However, the influence of polypropylene glycol and propanol seems to be more complex. An increase larger than that predicted from the “master” linear relationship is observed on approaching the phase boundaries, which may be related to the penetration of these alcohols into the palisade layer and the corresponding decrease of the viscosity. Sample aging (from 2 to 30 h) also has a big influence on the domain size, as it is also observed in other common glassy systems.20 Acknowledgment. M.A.L.Q. wants to acknowledge a grant by the “Ministerio de Educacio´n, Cultura y Deporte”, Spain, to spend part of a sabbatical term at the Yokohama National University, Japan. LA010615P
(18) Kunieda, H.; Horii, M.; Koyama, M.; Sakamoto, K. J. Colloid Interface Sci. 2001, 236, 78. (19) De Vries, A. In Liquid Crystals; Saeva, F. D., Ed.; Marcel Dekker: New York, 1969; p 54.
(20) Larson, R. G. In The Structure and Rheology of Complex Fluids; Oxford University Press: New York, 1999; Chapter 4.
