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Langmuir 1997, 13, 3706-3714
Micellar Cubic Phases and Their Structural Relationships: The Nonionic Surfactant System C12EO12/Water P. Sakya,† J. M. Seddon,*,† R. H. Templer,† R. J. Mirkin,‡ and G. J. T. Tiddy§ Department of Chemistry, Imperial College, London SW7 2AY, U.K., Department of Chemistry, Southampton University, Southampton SO17 1BJ, U.K., and Unilever Research, Port Sunlight Laboratory, Quarry Road East, Bebington, Wirral, Merseyside L63 3JW, U.K. Received February 20, 1997. In Final Form: April 28, 1997X We present the binary phase diagram of the system dodecaoxyethylene mono-n-dodecyl ether (C12EO12)/water, which is the first pure surfactant system found to exhibit three different type I (oil-in-water) micellar cubic phases. As hydration increases the hexagonal, HI, phase transforms into a cubic, I1, phase of space group Pm3n, which, on further hydration, forms a second micellar cubic phase of space group Im3m (phase designated as Im3m). In addition, a third micellar cubic phase, of space group Fm3m, forms at low temperature and high hydration, adjacent to the L1 micellar solution. We have succeeded in growing monodomains of the hexagonal, and some of these cubic phases and have thereby investigated the epitaxial relationships between the phases. The results suggest an “undulating cylinder” mechanism for the Im3mHI transition.
Introduction Although lyotropic cubic phases have been the subject of considerable study over recent years, it is still unclear how many different structures there are and where they occur in the phase diagrams. There are two classes of cubic phase: the bicontinuous cubics (denoted by the symbol “V”) are so called because (for oil-continuous, type II systems) they consist of a single, continuous bilayer of amphiphilic molecules which divides space into two interwoven, continuous networks of water; i.e. the phase is continuous in water and in amphiphile. For watercontinuous type I systems the positions of the water and amphiphile are simply reversed (note that the subscripts 1 and 2 are also used to refer to type I and type II systems, respectively). The basic structures of the bicontinuous cubic phases are now well established, at least for the genus 3 structures of space groups Pn3m and Ia3d, although direct evidence for the commonly accepted structure of the bicontinuous Im3m phase (cubic phase of space group Im3m) is still quite scant. However, less attention has so far been paid to the second type of cubic mesophase: the micellar cubics (indicated by the symbol “I”). These consist of discrete micellar aggregates arranged on cubic lattices (see below). Until recently, the structures of only two micellar cubic structures had been confirmed. The Fd3m cubic phase (cubic phase of space group Fd3m) has only so far been observed in type II systems (although one example of a type I Fd3m phase, with a very large lattice parameter of a ) 386 Å, has been reported in a sodium dodecyl sulfate/butanol/toluene/brine system1 ) whereas, conversely, the Pm3n cubic phase (cubic phase of space group Pm3n) appears to occur only in type I systems. However, a recent paper by Gulik et al.2 provides substantial evidence for the existence of two previously unknown micellar cubic phases, along with the Pm3n cubic * Author to whom correspondence should be addressed. E-mail:
[email protected]. † Imperial College. ‡ Southampton University. § Unilever Research. X Abstract published in Advance ACS Abstracts, June 15, 1997. (1) De Geyer, A. Prog. Colloid Polym. Sci. 1993, 93, 76. (2) Gulik, A.; Delacroix, H.; Kirschner, G.; Luzzati, V. J. Phys. II 1995, 5, 445.
S0743-7463(97)00184-4 CCC: $14.00
phase. These I1 structures were identified with two gangliosides (natural membrane lipids containing charged, bulky oligosaccharide polar head groups), denoted GM1 and GM1(acetyl). In GM1, Pm3n and Fm3m phases were found adjacent to the lamellar LR and normal hexagonal HI phases, whereas in GM1(acetyl), Im3m and Fm3m phases were found adjacent to the L1 micellar solution phase. The reproducibility of the phase behavior was poor, and it was consequently impossible to determine a precise phase diagram. It should be noted that the Im3m micellar cubic phase has the same space group as, but an entirely different structure from, one of the bicontinuous cubic phases. In addition, a recent paper3 shows that another micellar phase, in this case of 3-D hexagonal symmetry (spacegroup P63/mmc), exists in the C12EO8/water binary phase diagram. The n-alkyl polyethylene glycol ethers, more commonly known as poly(oxyethylene) surfactants, are widely used as emulsifying agents and detergents. They have the general chemical formula CH3(CH2)n-1(OCH2CH2)mOH, shortened to CnEOm. They are an ideal system for studying the factors which control lyotropic liquid crystalline phase behavior, as one can synthesize a range of poly(oxyethylene) surfactants with different head group lengths (m) and chain group lengths (n). In this paper we show that the system dodecaoxyethylene mono-n-dodecyl ether (C12EO12)/water forms all three type I micellar cubic phases (Pm3n, Im3m, and Fm3m) adjacent to each other in the same phase diagram. The chemical structure of C12EO12 is
In determining the phase diagram, we have found that merely by changing temperature, we can pass from the hexagonal HI phase to the Im3m and Pm3n phases and from the Im3m phase to the Pm3n phase. We have attempted to grow monodomains of these phases and hence obtain the epitaxial relationships between them, allowing us to gain an insight into the underlying mechanism of the transitions between the phases. (3) Clerc, M. J. Phys. II 1996, 6, 961.
© 1997 American Chemical Society
Micellar Cubic Phases
Epitaxial relationships are the relationships of orientation and geometry between adjacent phases. From these orientational relationships one can glean a large amount of information about how the geometries, symmetries, and hence structures of the two phases are related. To do this, we first need to prepare an aligned sample, which is placed in the path of a point X-ray source. An aligned sample, also known as a monodomain, or “single crystal”, will produce a diffraction pattern of discrete spots (as opposed to a powder sample, which produces smooth “rings” of diffraction). These patterns can be considered as “slices” taken through the reciprocal lattice. By seeing how the monodomain diffraction pattern changes on transition from one of the phases to the other, we can find the epitaxial relationship between the two phases. From this a mechanism for the transition can be deduced. The first step is to grow monodomains of the phases of interest. We have experience in growing and indexing monodomain diffraction patterns of the type I systems n-octyl-1-O-β-D-glucopyranoside/water and n-octyl-1-S-βD-glucopyranoside/water.4 Epitaxial relationships have been determined for the similar type I system C12EO6/ water,5-8 where epitaxies were found for the HI-LR, LRIa3d, and HI-Ia3d transitions. A recent study of this system using time-resolved X-ray diffraction has also been carried out.9 This involved the use of laser-induced temperature jumps to change from one phase to another. Through study of the kinetics of the phase transition, a nucleation and growth mechanism was suggested. This study can be seen as complementary to studies of epitaxial relationships, which is not itself a “real time” technique, in the sense that it is unlikely that we will obtain a diffraction pattern for an actual transition state between two liquid crystalline phases. However, as the timeresolved work was based only on powder diffraction, no extra information was produced on the epitaxy of the transitions. So far there have been no such direct studies of the epitaxial relationships of phase transitions involving micellar cubic phases, although indirect results for the HI-Pm3n transition have been inferred from powder diffraction data on DTAC (dodecyltrimethylammonium choride)/water.10 This study was based on the projection of the electron density distribution of the Pm3n phase in the direction of growth of the hexagonal cylinders. The basic aim was to compare electron density maps of the HI and Pm3n phases, in order to find an epitaxy which conserved the densest planes. However, this study was not based on actual epitaxial relationships determined experimentally. Materials and Methods Sample Preparation. C12EO12 was synthesized at the Unilever Research Port Sunlight Laboratory. The sample purity was determined by liquid chromatography to be 98.8%. Apart from drying over P2O5, all samples were used without further purification. The material was that employed previously,11 which had been stored in a sealed container at low temperature. To determine the phase (4) Sakya, P.; Seddon, J. M.; Templer, R. H. J. Phys. II 1994, 4, 1311. (5) Ranc¸ on, Y.; Charvolin, J. J. Phys. (Paris) 1987, 48, 1067. (6) Ranc¸ on, Y.; Charvolin, J. J. Phys. Chem. 1988, 92, 2646. (7) Clerc, M.; Levelut, A. M.; Sadoc, J. F. Colloid Phys. 1990, 51, C7-97. (8) Clerc, M.; Levelut, A. M.; Sadoc, J. F. J. Phys. II 1991, 1, 1263. (9) Clerc, M.; Laggner, P.; Levelut, A. M.; Rapp, G. J. Phys. II 1995, 5, 901. (10) Mariani, P.; Amaral, L. Q.; Saturni, L.; Delacroix, H. J. Phys. II 1994, 4, 1393. (11) Mitchell, D. J.; Tiddy, G. J. T.; Waring, L.; Bostock, T.; McDonald, M. P. J. Chem. Soc., Faraday Trans. 1 1983, 79, 975.
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diagram, samples of varying weight percent compositions ((1 wt %) were prepared by weighing dried surfactant (ca. 0.5 g) into small vials and adding dropwise the required amount of distilled water. After being reweighed and sealed, the samples were left to hydrate for several days after which they were mixed with a spatula, reweighed, and sealed again before use. Samples were prepared for powder diffraction in 1.5 mm glass Lindemann capillaries or by being sealed between thin mica sheets in custom-built metal holders (for sample rotationssee below). The aligned samples used to determine epitaxial relationships were prepared in 0.2 mm flat capillaries. To prepare these flat capillaries, 1 mm round Lindemann capillaries were sandwiched between two copper blocks containing rectangular 0.2 mm deep notches, and heated in an oven set at 740 °C for 40 min until the glass had softened sufficiently to permit them to flatten to a thickness of 0.2 mm under the weight of the upper block. After the capillaries were cooled back to room temperature and removed from the block, the C12EO12 was added to the top of these capillaries, melted, and shaken down to the bottom of the tube and the correct mass of water was then added onto this. The capillary was then repeatedly heated and cooled until the sample became homogeneous. However, because of the thinness of the samples it often took several weeks before the samples were homogenized. Sometimes a concentration gradient remained which had to be scanned across until the desired composition was found. Optical Microscopy and X-ray Diffraction. Optical observations were made using a Nikon Labophot polarizing microscope fitted with a Linkam heating stage (sample temperature accuracy (0.3 °C). The powder X-ray diffraction patterns were obtained using a Guinier line diffraction camera fitted with a bent quartz crystal monochromator adjusted to isolate the CuKR1 radiation with a wavelength of 1.5405 Å. The X-rays for this camera were produced by a Philips PW 2213/20 generator operating at 40 kV and 30 mA. The images were detected using photographic film. Exposure times varied according to the phase under study but were typically between 6 and 48 h. Even in round 1.5 mm capillaries there was a tendency for alignment, giving rise to “spotty” diffraction patterns. To overcome this a specially designed sample rotation device was used.12 The accuracy of the sample temperature for this camera was approximately (1 °C. Subsequently, a more sophisticated X-ray diffraction system was used to obtain the monodomain diffraction patterns. The X-rays for this apparatus were produced by a GX20 rotating anode X-ray generator (Enraf-Nonius, Netherlands) operating at 30 kV and 25 mA, with a 100 µm focus cup, and were focused by Franks optics to a point of dimensions 160 × 110 µm. This was used in conjunction with a custom-built CCD two-dimensional detector.13 X-ray diffraction images, even with narrow flattened capillaries, were produced in 60 s or less. The image was then processed and indexed from the same computer terminal. This short exposure time allowed us to scan through a given sample, searching for large monodomains. The presence of Peltier temperature control (range, -30 to +100 °C; precision, (0.03 °C; estimated accuracy of sample temperature, (0.3 °C) also allowed us to run temperature scans where the sample was very slowly heated or cooled (average rate of 0.1 °C/min), and diffraction images were taken every degree, or fraction of a degree. The estimated accuracy of the measured X-ray spacings was (0.5 Å. (12) Mirkin, R. J. Ph.D. Thesis, University of Southampton, 1992. (13) Templer, R. H.; Gruner, S. M.; Eikenberry, E. F. Adv. Electron Phys. 1988, 74, 275.
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Calculations. From the measured lattice parameters of the micellar cubic phases, the space group symmetry, and the volume fraction of the surfactant, we can calculate the radius rsurf of the micelle, the radius rpar of the paraffinic core, and the area per molecule Ah at the polar-nonpolar interface, assuming the micelles to be spherical. Similarly, we can also calculate these quantities for the hexagonal HI phase. The symbols used in the calculations are as follows: Msurf/Mpar/Mpol, molar mass of surfactant molecule/ paraffinic moiety/polar moiety; vsurf/vpar/vpol, volume of surfactant molecule/paraffinic moiety/polar moiety; Vuc, unit cell volume; Vsurf/Vpar/Vpol, volume per unit cell of surfactant/paraffinic moiety/polar moiety; Fsurf/Fpar/Fpol, density of surfactant/paraffinic moiety/polar moiety; Fw, density of water (0.99987 g cm-3 at 0 °C; 0.99999 at 5 °C; 0.99224 at 40 °C; 0.98807 at 50 °C; 0.98324 at 60 °C); φsurf/φpar/φpol, volume fraction of surfactant/paraffinic moiety/polar moiety; a, lattice parameter; c, weight fraction of surfactant; ν, number of micelles per unit cell; rsurf/rpar, radius of micelle/paraffinic core; Ah, area per molecule at the polarnonpolar interface. The volume fraction of surfactant is given by
(
φsurf ) 1 +
)
Fsurf(1 - c) Fwc
-1
(1)
Similarly, the volume fraction of paraffin chains is
(
φpar ) 1 +
)
MpolFpar MsurfFpar (1 - c) + MparFpol MparFw c
-1
(2)
The molar mass of the surfactant molecule Msurf is simply the sum of the masses of the paraffinic and polar parts, Mpar + Mpol. For C12EO12 the molar masses Msurf, Mpar, and Mpol are 714.95, 169.32, and 545.63 g mol-1, respectively. Taking the volumes of the CH2, CH3, CH2CH2O, and OH groups to be 27, 54, 60.9, and 17 Å3, respectively14 (minor adjustments to the values quoted in this reference were made for consistency), the corresponding volumes vsurf, vpar, and vpol are calculated to be 1,099, 351, and 748 Å3. Hence the densities Fsurf, Fpar, and Fpol are calculated to be 1.080, 0.801, and 1.211 g cm-3, respectively. Substituting the masses and calculated densities into eq 1 and 2 allows us to calculate φsurf and φpar, and hence the radius of either the paraffinic core, rpar, or the micelle, rsurf, given by the generalized equation
rx )
( ) 3a3φx 4νπ
1/3
(spheres); rx )
(
)
x3a2φx 2π
1/2
(cylinders) (3)
The area per molecule at the polar-nonpolar interface is
Ah )
3νpar 2νpar (spheres); Ah ) (cylinders) (4) rpar rpar Results and Discussion
Phase Behavior. From the previous study11 it was clear that C12EO12 forms cubic (I1) and hexagonal (HI) phases over a wide composition and temperature range, and there were indications of several different cubic phases existing in this system. Penetration scans showed that two cubic phases were present at room temperature. The presence of more than one cubic phase was deduced by (14) Herrington, T. M.; Sahi, S. S.; Leng, C. A. J. Chem. Soc., Faraday Trans. 1 1985, 81, 2693.
Figure 1. Binary phase diagram for the system C12EO12/water. Dashed lines indicate phase boundaries whose positions are not precisely known. Narrow two-phase coexistence regions are not indicated. Table 1. X-ray Diffraction Data for a 50.2 wt % C12EO12 Sample at 40 °C Indexed to the Space Group Im3m with a Lattice Parameter a ) 73.8 Åa hkl
h 2 + k2 + l2
dobs/Å
dcal/Å
Iobs
110 200 211 220
2 4 6 8
52.2 37.1 30.0 25.8
52.2 36.9 30.1 26.1
vvs s s m
a I obs denotes the observed intensities, which were visually estimated and, in the tables which follow, range from vvs (extremely strong), through m (medium), to vw (very weak).
Table 2. X-ray Diffraction Data for a 50.2 wt % C12EO12 Sample at 11 °C Indexed to the Space Group Pm3n with a Lattice Parameter a ) 119.0 Å hkl
h2 + k2 + l2
110 200 210 211 220 310 222 320 321 400 410 330/411 420 421 432/520
2 4 5 6 8 10 12 13 14 16 17 18 20 21 29
dobs/Å 59.4 53.2 48.4 42.5 37.4 34.6 33.0 31.8 29.7 28.8 28.0 26.7 25.8 22.0
dcal/Å
Iobs
59.5 53.2 48.6 42.1 37.6 34.4 33.0 31.8 29.8 28.9 28.0 26.6 26.0 22.1
not obs s s m vvs s s m m vvs s s m s m
the observation of refractive index discontinuities in the viscous isotropic region of the sample when viewed between crossed polarizers. On cooling, another cubic phase was also found. By examining a range of samples of fixed compositions on the heating stage of a polarizing microscope, we were able to obtain accurate transition temperatures. Small angle X-ray diffraction was used to identify the space group of each of the cubic phases. The resultant phase diagram is given in Figure 1. Indexing of the Im3m, Pm3n and Fm3m phases is presented in Tables 1, 2, and 3, respectively. Though indexing of powder diffraction patterns has enabled us to identify the space groups of the cubic phases, there is no direct evidence to tell us whether these phases are bicontinuous or micellar. However, their positions in the phase diagram, at higher hydrations than the HI phase, strongly suggest that all three are I1 phases. In addition, the variation in intensity of the diffraction peaks for the
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Langmuir, Vol. 13, No. 14, 1997 3709
Table 3. X-ray Diffraction Data for a 32.0 wt % C12EO12 Sample at 5 °C Indexed to the Space Group Fm3m with a Lattice Parameter a ) 104.0 Å hkl
h 2 + k2 + l2
dobs/Å
dcal/Å
Iobs
111 200 220 311 222 400
3 4 8 11 12 16
59.6 52.9 36.9 31.2 30.0 25.8
60.0 52.0 36.8 31.4 30.0 26.0
s s m m w vw
three phases is similar to the variation in intensity exhibited by the micellar cubic phases identified in the systems GM1/water and GM1(acetyl)/water.2 Whereas the bicontinuous cubics possess negative Gaussian interfacial curvature, the micellar cubics have positive Gaussian interfacial curvature and are “discontinuous”, consisting of discrete micellar aggregates. The structure of the Pm3n micellar cubic phase, in particular, has been the subject of some debate. Tardieu and Luzzati15 correctly deduced that the phase contains more than one kind of structure element but incorrectly suggested a combined rod/micelle model. This has now been discarded in favor of a packing of two types of discrete micellar aggregates, two of one type and six of the other per unit cell. Two alternative models have been proposed to take this into account. Fontell et al.16 suggested a rodlike model, whereas Charvolin and Sadoc17 described the structure as being analogous to the packing of polyhedra in cubic clathrate hydrates (Figure 2). In Fontell and co-workers’ model it is suggested that the structure consists of short rods, with an axial ratio close to 1.3:1; at one type of site these rods tumble isotropically to form a locus of a sphere, whereas in the other type of site they rotate about one axis to form the locus of a disk. All the micelles have the same shape, but the micelles at the different sites are differentiated by differing degrees of rotational freedom. In Charvolin and Sadoc’s model the structure consists of two spherical and six disk-shaped (oblate) micelles per unit cell. This model eliminates the need for dynamic disorder but does not appear fully consistent with the NMR lineshape from the Pm3n phase observed in lyso phosphatidylcholine.18 However, detailed X-ray scattering19 and freeze-fracture electron microscopy20 studies of the Pm3n phase suggest that this latter model is correct. We will use it as the basis for our theoretical discussions. We will also use similar models to describe the structure of the Im3m and Fm3m cubic phases. For all three micellar cubic phases the structure consists of discrete micelles of amphiphile arranged on a cubic lattice and separated by a continuous film of water. For an extensive discussion of the radii, geometry, and packing of lipid aggregates in micellar cubic phases, the analogy with foams, and the relationship to noncongruent infinite periodic minimal surfaces, see the recent paper by Luzzati and co-workers.21 For the Pm3n cubic phase, the positions of the micelles in the unit cell are given in Figure 2a. Black circles represent the spherical micelles, and pale gray circles represent the disk-shaped micelles. Thick lines outline the unit cell cube, while fine black and gray (15) Tardieu, A.; Luzzati, V. Biochim. Biophys. Acta 1970, 219, 11. (16) Fontell, K.; Fox, K. K.; Hansson, E. Mol. Cryst. Liq. Cryst. Lett. 1985, 1, 9. (17) Charvolin, J.; Sadoc, J. F. J. Phys. (Paris) 1988, 49, 521. (18) Eriksson, P.-O.; Lindblom, G.; Arvidson, G. J. Phys. Chem. 1985, 89, 1050. (19) Vargas, R.; Mariani, P.; Gulik, A; Luzzati, V. J. Mol. Biol. 1992, 225, 137. (20) Delacroix, H.; Gulik-Krzywicki, T.; Mariani, P.; Luzzati, V. J. Mol. Biol. 1993, 229, 526. (21) Luzzati, V.; Delacroix, H.; Gulik, A. J. Phys. II 1996, 6, 405.
Figure 2. (a) Positions of micelles in the Pm3n unit cell. (b) Polyhedral representation of the structure of the Pm3n micellar cubic phase.17 Each polyhedron represents a micelle of amphiphile plus its associated water.
lines mark out the positions of the micelles. They show that the spherical micelles pack on a body-centred cubic lattice, while the oblate micelles are arranged in parallel rows on opposite faces of the unit cell cube. In order to pack space completely each disk-shaped micelle, plus its encasing cage of water, takes up the shape of a tetrakaidecahedron, and each spherical micelle, plus the water that surrounds it, takes up the shape of a dodecahedron. These fit together in space to produce the structure shown in Figure 2b. It must be emphasized that because we are looking at type I systems, each polyhedron represents the shape of an amphiphilic micelle together with the film of water which surrounds it. The Fm3m and Im3m micellar cubic phases consist of the same basic structure of discrete micellar aggregates embedded in a continuous water matrix. But, unlike the Pm3n phase, the structures of the Im3m and Fm3m phases consist of only one type of micellar aggregate, rather than two, and the packing of these micelles onto a cubic lattice is rather simpler than is the case with Pm3n. The phase Im3m appears to consist of a packing of quasispherical micelles on a body-centred cubic lattice (Figure 3a). In order for these micelles, plus their encasing cages of water, to pack space completely, each will on average have the shape of a tetrakaidecahedron. These fit together to form the complete structure shown in Figure 3b. Similarly, the phase of space group Fm3m appears to consist of a packing of quasi-spherical micelles on a facecentred cubic lattice (Figure 4a). To pack space completely each micelle, plus the water that surrounds it, will on average have the shape of a dodecahedron. These dodecahedra then pack together to form the complete structure shown in Figure 4b.
3710 Langmuir, Vol. 13, No. 14, 1997
Figure 3. (a) Positions of micelles on a body-centred cubic lattice. (b) Polyhedral representation of the structure of the Im3m micellar cubic phase.
Using the Surface Evolver software package, Phelan, Weaire, and Brakke22 have computed three different structures which they claim are the three most stable structures of monodisperse foam. It is interesting to note that these arrangements of macroscopic foam bubbles have polyhedral structures which closely match the nanoscopic polyhedra which pack to form the three type I micellar cubic phases. A Monte Carlo simulation study of an model surfactant/ water system has been carried out, where the surfactant consisted of 4 or 6 identical nonpolar “tail” segments and 4, 6, 8, or 12 identical polar “head” segments,23 thus having some similarity in structure to the poly(oxyethylene) surfactants. Various types of simple micellar cubic phases (sc, fcc, bcc) were observed to form, as well as a structure with eight micelles per unit cell, which was denoted “quasiHCP”, but which actually appears to correspond to the cubic phase Pm3n (R. G. Larson, personal communication; see also Figure 5 in ref 23). The stability of these phases appeared to increase in the following order: sc, fcc, bcc, and “quasi-HCP” (i.e., space groups Pm3m, Fm3m, Im3m, and Pm3n). It is interesting to compare this with the order we have found experimentally for the C12EO12 cubic phases with increasing water content (Figure 1), which is Fm3m, Im3m, and Pm3n. The calculated dimensions of the micelles in the Fm3m and Im3m cubic phases are listed in Table 4, along with (22) Phelan, R.; Weaire, D.; Brakke, K. J. Phys. II 1995, 5, 1649. (23) Larson, R. G. Chem. Eng. Sci. 1994, 49, 2833.
Sakya et al.
Figure 4. (a) Positions of micelles on a face-centred cubic lattice. (b) Polyhedral representation of the structure of the Fm3m micellar cubic phase. Table 4. Calculated Values of the Radius of the Micelle (or Rod) and That of the Paraffinic Core, the Volume Fractions of the Surfactant and of the Paraffin Chains, and the Interfacial Area per Molecule at the Polar/ Nonpolar Interface for the Fm3m and Im3m Phases, and, for comparison, the Hexagonal HI Phase phase
a/Å
Fm3m 104.7 Fm3m 101.1 Im3m 73.4 61.0 HI 59.8 HI
T/°C 5.0 0.0 40.0 60.0 50.0
csurf
ν
φsurf
0.300 4 0.284 0.320 4 0.304 0.502 2 0.481 0.502 0.479 0.540 0.518
rsurf/Å
φpar
26.9 26.6 28.3 22.2 22.6
0.091 0.097 0.145 0.153 0.165
rpar/Å Ah/Å2 18.4 18.2 19.4 12.5 12.8
57.3 58.0 54.3 56.1 55.0
the corresponding data for the hexagonal HI phase. In these calculations, we have taken the polar-nonpolar interface to lie between the hydrocarbon chain and the poly(oxyethylene) chain. However, according to Luzzati,21,24 who has introduced the concept of a variable polarapolar partition, this is not necessarily the case. In particular, he finds that, in the case of polyoxyethylene surfactants, the nonpolar region may actually contain some fraction of the polar groups, as well as the hydrocarbon chains. If this were the case φpar, and hence rpar, would be slightly larger than that calculated in Table 4. The differences between the values of rsurf and rpar for the hexagonal HI phase, and the Fm3m and Im3m micellar cubic phases, is surprisingly large. Whereas the thickness of the polar head group region (rsurf - rpar) is 8-10 Å for all three phases, the values for rpar increase from 12-13 (24) Luzzati, V. J. Phys. II 1995, 5, 1649.
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Figure 5. (a, top) Monodomain diffraction pattern of the HI phase of a 50 wt % C12EO12/water sample at 67 °C. (b, bottom) Indexing of the pattern.
Å in the hexagonal phase to 18-19 Å in the two micellar cubic phases. The latter value is longer than the length of a fully extended C12H25 chain, which is approximately 16.5 Å. This strongly suggests a deviation from perfectly spherical micelles, possibly to the slightly anisotropic rods of the proposed structure by Fontell et al.,16 or the disks of the Charvolin and Sadoc model.17 The aggregation numbers of the micelles in the Fm3m and Im3m cubic phases are 72-74 and 87 respectively, based on the data in Table 4. These values are very similar to the value of approximately 80 for the micellar cubic phases found in the Monte Carlo study23 discussed earlier. Furthermore, in this latter study the cubic phases were observed when the hydrophobic volume fraction was 0.18; this is not very different to the values of φpar reported in Table 4, at least for the Im3m cubic phase. The HI-Im3m Transition. By heating a flat capillary sample of composition 50 wt % C12EO12/water into the micellar phase, and then slowly cooling into the HI phase, we were able to grow monodomains of the HI phase. The wide face of the flat capillary was oriented perpendicular to the X-ray beam. Often the monodomains formed with the cylinders aligned parallel to the glass walls, but occasionally they grew perpendicular to the walls. In this latter case, the beam traveled along the direction of the cylinders (sometimes described as the n direction of the hexagonal phase), and hence diffraction patterns such as Figure 5a were obtained. The indexing of this pattern is given in Figure 5b. We sought out this latter alignment. The aligned sample was then further cooled into the Im3m cubic phase in 1 °C steps from 74 to 34 °C. A sequence of representative diffraction patterns taken during this process is given in Figure 6. What is noticeable is that there is very little change in the diffraction pattern throughout this sequence, even during the transition. The
Figure 6. Sequence of representative diffraction patterns taken during cooling of a 50 wt % C12EO12/water sample: (a, top) 45 °C, HI phase; (b, middle) 42 °C, HI/Im3m biphasic region; (c, bottom) 39 °C, Im3m phase.
transition was in fact impossible to spot from the diffraction patterns alone. To be sure that a transition did actually occur, the sample was observed through a microscope with crossed polarizers to verify that, on cooling, the birefringent hexagonal phase (when several domains are in view) did in fact turn into the optically isotropic cubic phase.
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Figure 7. Indexing of the monodomain diffraction pattern of the Im3m cubic phase shown in Figure 6c.
Sakya et al.
Figure 9. Temperature-dependence of the lowest order spacing d10 of the HI phase (open circles) and the lowest order spacing d110 of the Im3m cubic phase (filled triangles) for a 50 wt % C12EO12/water sample.
Figure 10. Suggested mechanism for the HI-Im3m transition. Undulations form in the hexagonal phase rods, with the rods being “pinched” at regular intervals, and this continues until the narrowest points along the rods are pinched off, and discrete micelles form.
Figure 8. Representation of the epitaxial relationship between the hexagonal phase (top) and the Im3m micellar cubic phase (bottom). The direction of the HI phase cylinders (n or [001]) points in the same direction as the [111] direction of the Im3m phase.
The indexing of the monodomain Im3m diffraction pattern 6(c) is given in Figure 7. We have formed a single crystal of the Im3m phase, and we are clearly looking along the [111] direction of this phase. Hence there is a epitaxial relationship relating the direction of the cylinders of the HI phase to the [111] direction of the Im3m phase. This epitaxy is illustrated in Figure 8. The view along the [111] direction of Im3m is closely related to the cylinder direction of HI. For every cylinder of the hexagonal phase there is a column of spherical micelles in the Im3m phase. Figure 8 also shows the spacing between the (10) planes of the hexagonal phase, and the spacing between the (110) planes of the Im3m cubic phase. If the epitaxial relationship given in Figure 8 is correct, one would expect these spacings to be similar at the transition point. To verify our results we have, therefore, followed the temperature dependence of the (10) layer spacing of the hexagonal phase
and the (110) layer spacing of the Im3m phase (Figure 9). We do indeed find that the spacing between the (10) planes of the hexagonal phase is almost equal to the (110) layer spacing of the Im3m phase, giving further confirmation that the two phases are epitaxially related. This structural relationship gives us a very strong clue as to the mechanism of transition between the two phases. We know that each cylinder of the HI phase transforms into a column of quasi-spherical micelles in the Im3m phase. We suggest that this occurs via the mechanism shown in Figure 10. As temperature is reduced, the hydration of the hydrophilic head groups rises, increasing the desire for curvature. To accommodate this greater desire for curvature, the cylinders of the hexagonal phase start to undulate, as if the cylinders are being “pinched” at regular intervals. This “pinching” continues until the narrowest points along the rods are closed off and discrete micelles form. It must, however, be emphasized that although our experimental data tell us the start and end points of this mechanism, we have no experimental evidence which directly shows undulation of the cylinders of the hexagonal phase occurring. Hence we do not know the time scale for this mechanism, although it is likely to be fast. The mechanism for the HI-Im3m transition could also apply to the HI-L1 transition. In the latter case, one would again expect an increase in curvature to drive the regular pinching of the hexagonal phase and the formation of
Micellar Cubic Phases
micelles. But instead of arranging themselves in a stable body-centered cubic lattice, as is the case for the HIIm3m transition, these micelles would then would be randomly dispersed in solution. The Im3m-Pm3n and HI-Pm3n Transitions. Other transitions which are of interest are those between the Im3m and Pm3n phases and the HI and Pm3n phases. From the lattice parameters of the Im3m and Pm3n phases at their transition temperatures, we have calculated that the number of micelles per unit volume is the same for both. There are eight micelles in the Pm3n unit cell but only two in the Im3m unit cell. If the number of micelles per unit volume is the same, one would expect the volume of the Pm3n unit cell to be four times that of the Im3m unit cell, and the lattice parameter to be 41/3 times bigger. This is indeed found to be the case near the transition temperature, where a ) 74 Å for Im3m and a ) 119 Å for Pm3n. This suggests that the transition occurs by a rearrangement and deformation of the micelles, with no fusion events occurring, providing a low-energy transition pathway. We found that monodomains of the Pm3n phase could be grown, though not as easily as with the HI and Im3m phases. The preferred alignments of the Pm3n phase were with the [111] axis or the [100] axis perpendicular to the capillary walls (data not shown). To analyze the transition from the Im3m to the Pm3n phase, an aligned Im3m cubic phase was initially formed by cooling from an aligned hexagonal phase, as described in the previous section. The aligned Im3m phase was then further cooled into the Pm3n cubic phase. In the previous section we have already shown that the Im3m phase could be aligned with the [111] direction perpendicular to the capillary walls, producing a regular hexagonal pattern of spots (indexed in Figure 7). However our results for the Im3m-Pm3n transition were inconclusive. On cooling, the diffraction pattern of the aligned Im3m phase sample changed completely, but the alignment of the Pm3n phase which formed was not clear. It appears that either the monodomain of Im3m phase broke up during transition or a monodomain formed which we could not index. Thus we were unable to find a clear epitaxy between the two phases, suggesting that an epitaxial relationship may not exist here. For a narrow range of compositions at slightly lower hydrations, we can go directly from the HI phase to the Pm3n phase. However, the results for this transition were similar to those for the Im3m-Pm3n transition. On cooling from a HI phase, aligned with the cylinder direction n perpendicular to the walls of the capillary, to the Pm3n phase, the alignment was lost, and the new pattern which formed could not be indexed. This loss of alignment suggests that the cylinder direction of the hexagonal phase may not be epitaxially related to the [111] direction of the Pm3n phase. This latter result is at variance with the findings of a study of the HI-Pm3n transition in the type I system DTAC/water,10 which suggested that the n direction (the cylinder direction) of the hexagonal phase becomes the [111] direction of the micellar cubic phase and that the (10) planes of the hexagonal phase transform into the (211) planes of the Pm3n phase. However, it must be emphasized that these results were only theoretical predictions based on powder diffraction patterns and not actual epitaxial relationships determined experimentally. Phase Transition Mechanism. Whatever the details of the molecular mechanism involved in mesophase/ mesophase transitions, the sequence of cubic phases observed here has important implications for the underlying factors that determine surfactant mesophase forma-
Langmuir, Vol. 13, No. 14, 1997 3713
tion for water-continuous systems. Previously,11 it has been proposed that the major considerations are as follows: (i) the structure (size, shape) of micelles in dilute solution (spheres, rods, or disks) (when the interactions between the micelles become large enough, an ordered phase (mesophase) occurs); (ii) the maximum volume fraction that each different mesophase can tolerate, which increases in the sequence simple cubic f body-centered cubic (Im3m) f face-centered cubic (Fm3m) f Pm3n f hexagonal (HI) f lamellar (LR); (iii) the ordered phase formed is the one with the largest possible micellar curvature that can accommodate the volume of the aggregates. The sequence of cubic phases observed here clearly belies this simple picture, most obviously in the position of the Fm3m phase (for the Pm3n phase the presence of micelles of different sizes complicates the discussion, since polydisperse aggregates of the same shape can pack to higher volume fractions than monodisperse aggregates). It could be expected that the micelles of the Im3m phase are larger than those of the Fm3m phase. This is not immediately apparent from the data in Table 4; hence the simplistic approach of ref 11 needs to be considered with caution for different I1 cubic phases, although it has generally been found to be valid for the different classes of phase: I1, HI, L R. Epitaxial Relationships. In answer to the question of why epitaxial relationships may sometimes occur, Luzzati24 suggests that their existence lowers the kinetic barrier between phases and thus avoids the existence of metastable states. This idea can be illustrated if we compare the systems GM1/water and GM1(acetyl)/water2 with the system C12EO12/water. In the former two systems no clear phase diagrams could be mapped out because of the existence of metastable states, and no epitaxial relationships were found to exist between the phases. In the latter system there is much less metastability, and we have been able to determine a well-defined phase diagram, and, at least in the HI-Im3m transition, have shown that epitaxial relationships do exist. The study of epitaxial relationships has a number of associated problems. Luzzati24 points out the curious fact that all of the epitaxial relationships so far found seem to involve the [111] direction of cubic phases (or the cylinder direction of the hexagonal phase). This is because for most phases this is the “preferred alignment”. However, if on phase transition the alignment of the new phase is not a preferred alignment, then it seems likely that the monodomain will break up or that the phase will try to change to its most preferred alignment. For example, the epitaxy of the HI-Im3m transition was easily obtained, because the cylinder direction of the HI phase turns into the [111] direction of the Im3m phase, and both these orientations are preferred alignments of the two phases. The [111] axis is also a preferred direction for the Pm3n phase, and so if previous theoretical predictions10 were correct, one would expect a smooth change from [111] to [111] for the Im3m-Pm3n transition. The fact that no such smooth transition occurs rules out this epitaxial relationship. It seems that if there is a relationship, it does not give a preferred alignment of the Pm3n phase, and so on transition the monodomain of Im3m may try to reorient itself with respect to the capillary walls, and on doing so break up into many small domains of the Pm3n phase. Clearly we need to consider a number of factors before we decide whether what we are seeing is a true epitaxial relationship or just an alignment effect due to the walls. If the diffraction pattern breaks up during transition and a large number of spurious spots appear, before realigning, it is likely that the monodomain
3714 Langmuir, Vol. 13, No. 14, 1997
Sakya et al.
is breaking up and the phase is then realigning into its preferred alignment. Although the study of epitaxial relationships may be a useful approach to unraveling the mechanism of lyotropic phase transitions, there are several questions which our current method leaves unanswered. We suggest that a future enhancement of the technique would be to follow epitaxial relationships in real time, while a phase transition occurs. This might allow us to catch the real epitaxy of, for example, the HI-Pm3n transition before the monodomain breaks up. To do this we would need to study an aligned sample with the high intensity of synchrotron radiation.
simple arrangement of micelles on a body-centred cubic lattice (Im3m), the other a similar arrangement of micelles on a face-centred cubic lattice (Fm3m). These phases occur adjacent to the Pm3n micellar cubic phase. We have also succeeded in growing and analyzing monodomains of some of these phases, and the epitaxial relationship between HI and Im3m has been determined. This has allowed us to propose a likely transition mechanism between these two phases, involving the introduction of undulations in the cylinders of the hexagonal phase. However, the epitaxial relationships for the Im3m-Pm3n and HI-Pm3n phase transitions remain unresolved.
Conclusions
Acknowledgment. We thank Peter Duesing for providing Figures 3b and 4b. This work was supported by the EPSRC by Grants GR/C/95428, GR/F44052, and GR/H69229, a Quota studentship to P.S., and a CASE studentship to R.J.M.
We have determined the binary phase diagram of dodecaethylene mono-n-dodecyl ether in water. By indexing powder X-ray diffraction patterns, we have identified three type I micellar cubic phases (I1), two of which have only recently been discovered: one consists of a
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