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Langmuir 1996, 12, 6336-6340
Shear Alignment of a Rhombohedral Mesh Phase in Aqueous Mixtures of a Long Chain Nonionic Surfactant Claire E. Fairhurst, Michael C. Holmes,* and Marc S. Leaver Department of Physics and Astronomy, University of Central Lancashire, Preston PR1 2HE, U.K. Received July 16, 1996. In Final Form: September 30, 1996X In a recent paper (Burgoyne, J.; Holmes, M. C.; Tiddy, G. J. T. J. Phys. Chem. 1995, 99, 6054) we showed that binary mixtures of the poly(oxyethylene) surfactant, nonaethylene glycol mono(11-oxa-14,18,22,26tetramethylheptacosyl) ether (C30EO9), in 2H2O exhibited an extensive intermediate mesh phase between a higher temperature lamellar phase and a lower temperature hexagonal phase. Here, we present small angle neutron scattering results obtained from a sample of the hexagonal phase shear aligned in a couette type flow cell and then gently heated into the intermediate mesh phase. The scattering pattern shows a 6-fold symmetry of the (110) reflection and indicates that the structure of the phase is a six connected rhombohedral mesh with space group R3h m. The unusual structure is explained by the competition between the need to reduce surface curvature on raising temperature because of decreasing head group hydration and the repulsive interaggregate head group overlap (HGO) interaction.
Introduction Bicontinuous cubic phases are often found at compositions between hexagonal and lamellar phases1-3 of concentrated surfactant water systems. They have received considerable attention in the literature because of their complexity and also because of their relationship to structures seen in biological membrane systems. However, cubic phases are not the only possible type of phase that can occur in this region of the phase diagram. A number of so-called “intermediate” phases have been identified which are anisotropic in structure and consequently birefringent.4-32 There is still discussion in the * Author to whom correspondence should be addressed. X Abstract published in Advance ACS Abstracts, December 1, 1996. (1) Lindblom, G.; Rilfors, L. Biochim. Biophys. Acta 1989, 988, 221. (2) Seddon, J. M. Biochim. Biophys. Acta. 1990, 1031, 1. (3) Fontell, K. Adv. Colloid Interface Sci. 1992, 41, 127. (4) Spegt, P. A.; Skoulios, A. Acta Crystallogr. 1966, 21, 892. (5) Skoulios, A. Ann. Phys. 1978, 3, 421. (6) Hendrikx, Y.; Charvolin, J. J. Phys. (Paris) 1981, 42, 1427. (7) Leigh, I. D.; Mcdonald, M. P.; Wood, R. M.; Tiddy, G. J. T.; Trevethan, M. A. J. Chem. Soc., Faraday Trans. 1 1981, 77, 2867. (8) Chidichimo, G.; Vaz, N. A. P.; Yaniv, Z.; Doane, J. W. Phys. Rev. Lett. 1982, 49, 1950. (9) Rendall, K.; Tiddy, G. J. T.; Trevethan, M. A. J. Chem. Soc., Faraday Trans. 1 1983, 79, 637. (10) Alpe´rine, S.; Hendrikx, Y.; Charvolin, J. J. Phys. Lett. 1985, 46, L27. (11) Chidichimo, G.; De Fazio, D.; Ranieri, G. A.; Terenzi, M. Mol. Cryst. Liq. Cryst. 1986, 135, 223. (12) Ke´kicheff, P.; Cabane, B. J. Phys. (Paris) 1987, 48, 1571. (13) Hyde, S. T. J. Phys. Chem. 1989, 93, 1458. (14) Ke´kicheff, P.; Tiddy, G. J. T. J. Phys. Chem. 1989, 93, 2520. (15) Ke´kicheff, P. J. Colloid Interface Sci. 1989, 131, 133. (16) Anderson, D. M. Colloq. Phys. 1990, 51, C7-1. (17) Anderson, D. M.; Davis, H. T.; Scriven, L. E.; Nitsche, J. C. C. Advances in Chemical Physics, Vol. LXXVII; Prigogine, I., Rice, S. A., Eds.; John Wiley: New York, 1990; p 337. (18) Gutman, H.; Luz, Z.; Wachtel, E. J.; Poupko, R.; Charvolin, J. Liq. Cryst. 1990, 7, 335. (19) Auvray, X.; Perche, T.; Anthore, R.; Petipas, C.; Rico, I.; Lattes, A. Langmuir 1991, 7, 2385. (20) Ke´kicheff, P. Mol. Cryst. Liq. Cryst. 1991, 198, 131. (21) Funari, S. S.; Holmes, M. C.; Tiddy, G. J. T. J. Phys. Chem. 1992, 96, 11029. (22) Hagsla¨tt, H.; So¨derman, O.; Jo¨nsson, B. Liq. Cryst. 1992, 12, 667. (23) Henriksson, U.; Blackmore, E. S.; Tiddy, G. J. T.; So¨derman, O. J. Phys. Chem. 1992, 96, 3894. (24) Kilpatrick, P. K.; Blackburn, J. C.; Walter, T. A. Langmuir 1992, 8, 2192. (25) Blackburn, J. C.; Kilpatrick, P. K. J. Colloid Interface Sci. 1993, 157, 88.
S0743-7463(96)00697-X CCC: $12.00
literature as to which structures are possible and which structures have been identified experimentally. The observed or proposed structures divide topologically into three broad types according to symmetry: rectangular ribbon structures,5,6,8,10,19,22,33 layered mesh structures,5,12,14,15,19,20,32 and bicontinuous structures16,17,19 which do not have cubic symmetry. Ribbon structures are relatively easy to identify from X-ray scattering and from the asymmetry parameter seen in their 2H NMR spectra.5,6,8,10,19,22,33 Mesh structures are much less easy to identify and there are several possible structures based on tetragonal and rhombohedral symmetries. If there are connections between the mesh layers, they can become bicontinuous. In many papers, the identification of tetragonal or rhombohedral phases, mesh or bicontinuous, is left ambiguous usually because there is insufficient information to make a definitive identification. There are only a few examples where authors have identified bicontinuous phases. For example, the rhombohedral, RR, phase in the SDS/water system was suggested to be bicontinuous34 because it was adjacent to a bicontinuous cubic phase, QR, and probably separated from it by a second-order transition. Hyde has cast doubt on this conclusion because periodic minimal surfaces with tetragonal or rhombohedral symmetries are expected to have a higher associated bending energy cost than their cubic phase counterparts.35 Clearly there is still some doubt about the precise structures that these systems form and also about the interactions that are responsible for favoring one structure over another. The poly(oxyethylene) surfactant, nonaethylene glycol mono(11-oxa-14,18,22,26-tetramethylheptacosyl) ether (C30EO9), in 2H2O32 has been shown to exhibit an extensive (26) Schnepp, W.; Disch, S.; Schmidt, C. Liq. Cryst. 1993, 14, 843. (27) Auvray, X.; Petipas, C.; Rico, I.; Lattes, A. Liq. Cryst. 1994, 17, 109. (28) Funari, S. S.; Holmes, M. C.; Tiddy, G. J. T. J. Phys. Chem. 1994, 98, 3015. (29) Hagsla¨tt, H.; Fontell, K. J. Colloid Interface Sci. 1994, 165, 431. (30) Svitova, T. F.; Smirnova, Y. P.; Pisarev, S. A. Colloid J. (Transl. Kolloidn. Zh.) 1994, 56, 370. (31) Zheliaskova, A.; Derzhanski, A.; Degovicx, G.; Laggner, P. J. Dispersion Sci. Technol. 1994, 15, 575. (32) Burgoyne, J.; Holmes, M. C.; Tiddy, G. J. T. J. Phys. Chem. 1995, 99, 6054. (33) Hagsla¨tt, H.; So¨derman, O.; Jonsson, B. Langmuir 1994, 10, 2177. (34) Ke´kicheff, P.; Cabane, B. Acta Crystallogr. 1988, B44, 395. (35) Hyde, S. T. Pure Appl. Chem. 1992, 64, 1617.
© 1996 American Chemical Society
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Figure 2. Geometry of the couette flow cell. The two concentric cylinders represent two concentric quartz glass cylinders with a 1 mm gap between the two which contains the sample. The outer cylinder rotates with respect to the inner cylinder. The sample shear direction is along the x-axis and the incident neutron beam is along the z-axis.
Figure 1. Structure of the tetragonal and two rhombohedral mesh phases. All structures are viewed along the c direction and the successive layers labeled A, B, and C. (a) A centered tetragonal mesh with layer C underlying layer A and no connections between the layers. (b) The rhombohedral mesh phase with an ABC type packing. (c) An alternative mesh structure of hexagonally packed holes. Note that some nodes overlie each other. Table 1. Summary of the Line Positions and Tetragonal and Rhombohedral Indexations for the 55% Sample at 25 °C tetragonal
rhombohedral
line no.
dobs
intensity
plane
dcal
plane
dcal
1 2 3 4 5 6 7 error a/nm c/nm
8.85 7.48 5.72 4.85 4.52 4.21 3.86
S VVS W W VW W M
101 002 200 211 202 220 004
9.09 7.48 5.72 4.84 4.54 4.05 3.74 (0.11 11.4 15.0
110 003a 113 301 213 303 006a
8.85 7.48 5.71 4.98 4.58 4.22 3.74 (0.33 17.7 22.5a
a Note that the (003) and (006) indexations where incorrectly stated as (002) and (004) in ref 32, this also affects the indexation of reflections 3, 4, and 5 but makes no difference to the other parameters calculated in the paper except that c ) 22.5 nm.
mesh intermediate region in its phase diagram extending from ca. 32% to ca. 60% by weight and from 33 °C downward. There were three possible indexations of the seven line X-ray scattering pattern, two being centered tetragonal and one rhombohedral. The three possible indexations, the known volume fraction of alkyl chains, and the fact that the surface area per molecule Sa is constant in hexagonal and lamellar phases, and therefore by implication in the intermediate phase, allow the model structures to be tested. No bicontinuous structure of any symmetry fitted the experimental results. Only two structures were found to be consistent: a centered tetragonal mesh, Figure 1a, and a rhombohedral mesh, Figure 1b. Their indexations are summarized in Table 1. Reference 32 showed that it was possible to distinguish
between the tetragonal and rhombohedral models. Four of the seven X-ray reflections fade on increasing the water content. These reflections, 3, 4, 5, and 6,32 corresponded to reflections of the type (hkl) for the rhombohedral mesh structure while reflections of the type (hk0) or (00l) remained, which was consistent with a loss of correlation between the mesh structures in adjacent layers. The centered tetragonal structure provided a less satisfactory explanation for the concentration dependence since reflections from planes (101), (002), and (004) remained while (200), (211), (202), and (220) faded. The conclusion of this paper was that the structure of this intermediate phase was the rhombohedral mesh structure of Figure 1b. However, at first sight this structure appears to be counterintuitive, since it has a genus of 3.35 Why does the system not adopt a lower genus structure such as a tetragonal mesh or adopt the simpler three connected rhombohedral mesh structure shown in Figure 1c? It was to confirm the structural identification and to address these questions that we embarked on the current study. Hamley et al.36,37 have used shear alignment to study intermediate phases in diblock copolymer melts. We used the same technique to obtain aligned samples of the intermediate phase in the C30EO9/2H2O system. This has enabled the mesh structure to be better delineated and the epitaxial relationship with the lower temperature hexagonal H1 phase to be studied. Experimental Section The materials and samples preparation are given in ref 32. A 42% by weight surfactant sample was prepared and showed the following sequence of phase transitions by optical microscopy:
H1 r 27 °C f Η1 + Int. r 28 °C f Int. r 32 °C f Int. + LR r 35 °C f W + LR where H1 is the hexagonal phase, Int. is the intermediate phase, LR is the lamellar phase, and W is very dilute aqueous solution. The sample was introduced into the couette type shear cell38 on LOQ, the small angle neutron scattering facility at ISIS, CLRC, Didcot, Oxon, U.K. The geometry of the cell is such that the incident neutrons are along the z axis and the scattering vector lies in the xy plane. The shearing direction is along the x axis, Figure 2. At 23 °C in the hexagonal phase it was sheared at the minimum shear rate. The shearing was then stopped and the (36) Hamley, I. W.; Koppi, K. A.; Rosedale, J. H.; Bates, F. S.; Almdal, K.; Mortensen, K. Macromolecules 1993, 26, 5959. (37) Hamley, I. W.; Gehlsen, M. D.; Khandpur, A. K.; Koppi, K. A.; Rosedale, J. H.; Schulz, M. F.; Bates, F. S.; Almdal, K.; Mortensen, K. J. Phys. II 1994, 4, 2161. (38) Cummins, P. G.; Hayter, J. B.; Penfold, J.; Staples, E. Chem. Phys. Lett. 1987, 138, 436.
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Figure 3. Scattering from a shear aligned 42% by weight surfactant sample of C30EO9/2H2O at 23 °C and in the hexagonal phase. The direction of shear is parallel to the x axis. The two arcs are the scattering from the (10) planes of the hexagonal rods. sample rested at constant temperature for 10 min before the first scattering pattern was recorded. This showed the phase to be aligned with the hexagonal phase rods parallel to the shear direction, Figure 3. Temperature was controlled using recirculating water from a Haake bath and was stable to 0.1 °C. The experimental arrangement was such that accurate, absolute temperature measurement of the sample in situ was difficult, so the known phase transitions of this sample were used to calibrate the temperature of the system. The temperature was increased in successive steps of 1 °C with a wait of at least 15 min before recording each neutron scattering pattern.
Fairhurst et al.
Figure 4. Sample as in Figure 3 but at a temperature of 27 °C where both hexagonal and intermediate phases are present. The two arcs are the scattering from the (10) planes of the hexagonal rods and the (003) planes of the intermediate phase. The developing inner ring corresponds to the (110) reflection of the intermediate phase.
Results Only one reflection was observed at 23 °C in the Q range (0.002-0.20 Å-1), Figure 3, but its position agreed well with previous small angle X-ray scattering (SAXS) results32 on this sample in which three diffraction orders indexed to a hexagonal, H1 structure. The two arcs situated on the y axis are the reflections from the (10) planes of the hexagonal lattice and indicate that the phase was aligned with the hexagonal rods lying parallel to the x-axis. Its position corresponds to a d-spacing of 8.43 ( 0.05 nm, which remains constant up to the H1 to H1 + Int. phase transition at 27 °C. At this point a second ring at smaller Q appears and the original arcs fade but do not disappear, Figure 4. By 30 °C in the intermediate single phase, the inner ring has strengthened and shows some internal structure, Figure 5. Traces of the original arcs remain. Again comparison with SAXS results32 shows the smaller Q ring to correspond to line d1 in the original indexation of the powder and the residual arc to line d2. The former corresponds to d1 ) 10.6 ( 0.1 nm and the latter to d2 ) 8.6 ( 0.1 nm (note: the corresponding values for a 55% by weight sample in Table 1 are 8.85 and 7.48 nm). Again both reflections change little with temperature in the intermediate phase. It is apparent from ring d1 that it has a 6-fold rotation symmetry, Figure 5. Plotting the intensity around the ring as a function of angle, Figure 6 clearly shows that there are maxima at 0° and 60° measured to the y-axis, which indicates a hexagonal symmetry for this reflection. Comparison with the two models for the mesh shows that d1 comes from the (101) planes of the tetragonal mesh or from the (110) planes of the rhombohedral mesh. A 6-fold symmetry associated with the latter set of planes is natural
Figure 5. Sample as above but at a temperature of 30 °C in the intermediate phase. The two arcs are the scattering from the (003) planes of the intermediate phase. The inner ring corresponds to the (110) reflection of the intermediate phase. Note the 6-fold rotation symmetry of the latter reflection.
while it is difficult to explain for the former set of planes from the tetragonal mesh. This, together with the loss of reflections on dilution,32 see Introduction, identifies the intermediate phase unequivocally as a rhombohedral mesh. Discussion Although the intermediate phase is clearly identified as rhombohedral with a space group R3h m, the scattering does not distinguish between the six-connected structure (Figure 1b) and the three-connected structure (Figure 1c). Neither does it distinguish between mesh and bicontinuous structures. Bicontinuous structures may be dismissed from evidence presented in ref 32; the parabolic focal conic optical texture associated with the intermediate phase is
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Figure 6. Variation in scattering intensity taken around the (110) reflection (Figure 5) and plotted as a function of the angle made with the y-axis. Only one quadrant is shown, this being the average of the results from all four quadrants. Two maxima clearly occur at 0° and 60° indicating the 6-fold symmetry. Table 2. Comparison of Structural Parameters for Lamellar, Hexagonal, and the Two Possible Intermediate Mesh Phase Structuresa phase
temp, °C
structure
lamellar, LR intermediate
50 25
intermediate
25
hexagonal, H1
13
sheets rhombohedral mesh 3 connected rhombohedral mesh 6 connected cylinders
rhc/nm Sa/nm2 1.35 3.23
0.64 0.52
2.21
0.69
2.60
0.67
a
The fits are made to experimental results for the 55.04% sample at the temperatures shown.
strong evidence of a layered structure as is the loss of certain reflections with increasing water content, indicating loss of correlation between layers. Distinguishing between the six-connected and three-connected structures is more difficult because they are related through Babinet’s principle to the same scattering pattern. The sixconnected structure may be regarded as a hexagonal arrangement of surfactant nodes while the three-connected structure is a hexagonal arrangement of holes in a surfactant matrix. In many experimental studies it has been shown that at the transition from the H1 to the LR phase the surface area per head group at the water/alkyl chain interface, Sa, is constant within experimental error. In ref 32 we simplified the two proposed rhombohedral structures by simulating the surfactant aggregates with rods and boxes for the connections and nodes, respectively. By then using the unit cell dimensions obtained from the SAXS measurements together with the volume fraction of alkyl chain, it was possible to estimate Sa and mean thickness of the mesh layers, rhc. The six-connected structure gives the best agreement; see Table 2. The six-connected structure is also more likely when the interactions driving the formation of the phase are considered. In ref 32 we showed that two interactions account for the changes in phase structure. Firstly, there is the progressive decrease in the hydration of the poly(oxyethylene) head groups with increasing temperature leading to a decrease in surface curvature and, secondly, the repulsive head-group overlap interaction (HGO)32,39,40 between surfactant aggregates. Raising the temperature from the hexagonal phase causes the surfactant molecules (39) de Gennes, P. G. Adv. Colloid Interface Sci. 1987, 27, 189. (40) Israelachvili, J.; Wennerstro¨m, H. J. Phys. Chem. 1992, 96, 520.
to form aggregates with less surface curvature, driven by the decreasing hydration of the EO groups. This structure is a bilayer type structure consisting of surfactant nodes and water-filled holes. In addition, the repulsive HGO interaction between neighboring nodes in the same plane causes them to pack onto an hexagonal lattice within the bilayer plane. Between planes, the HGO interaction causes the nodes in adjacent planes to arrange themselves on a three-dimensional rhombohedral lattice, minimizing their repulsive interaction. In the three-connected structure, shown in Figure 1c, half the surfactant nodes in one plane would lie directly over nodes in the plane below. The six-connected structure therefore minimizes the HGO interaction between the surfactant nodes (see below). During the shearing of the H1 phase the surfactant rods become aligned by the shear field so that they lie along the shear direction (x-axis), the arcs in the scattering pattern indicating a reasonable degree of alignment, Figure 3. The geometry of this situation is shown in Figure 7a. At the transition into the rhombohedral mesh phase the (10) planes of the H1 phase become the (001) planes of the mesh phase. At the shear cell walls, the (001) planes of the mesh phase grow parallel to the xy plane. In the bulk, however, a significant proportion will not be parallel to the shear cell walls and this accounts for the fact that line d2 does not wholly disappear. In general, then, the 6-fold symmetrical reflections arise from the structure from within the mesh planes, i.e., the (110) reflections. Figure 7 shows that the relationship between the structures in the two phases is rather similar, a small expansion in the aggregate separation being all that is necessary in going from the (10) planes of the H1 phase to the (001) planes of the mesh phase. Figure 7b also shows the relationship between the mesh structure and the observed scattering pattern. It is now also possible to understand the epitaxial relationship between the hexagonal, H1, phase and the rhombohedral mesh phase. The mean node-node separation in the R3 h m phase is 36.7 nm in the direction parallel with the original hexagonal rod axis. Therefore, we propose that the R3 h m phase grows from the hexagonal phase by modulations developing along the hexagonal rods with a periodicity comparable to the final node separation of 36.7 nm. The developing surfactant nodes then connect to neighboring nodes establishing the mesh plane; see Figure 7a. Each node is six co-ordinated within the plane. The formation of the nodes is driven by the need of the system to reduce its mean surface curvature from that in the H1 phase. The positioning of the nodes is determined by the repulsive interaggregate HGO interaction, therefore within the (001) mesh planes the nodes will be arranged on a hexagonal lattice. The positioning of adjacent layers is also dictated by the repulsive HGO interactions so that the nodes in the layer below will be located under the holes in the layer above, Figure 1b. This results in the ABC packing shown in Figure 1b and a rhombohedral structure. It should be noted that this structure requires a shift in the relative positions of the nodes in one plane with respect to the plane above or below, Figure 7a as the rhombohedral structure is being formed. In Figure 7a the solid thin lines represent the rods forming a (10) plane in the hexagonal phase which become (001) plane in the rhombohedral phase (layer A). The rods in the next (10) plane are represented by the broken thin lines in Figure 7a. These do not exactly pass through the positions of the nodes in layer B of the (001) plane. Therefore there must be a small shift of circa 0.24 nm in each (001) layer with respect to its neighbors along a direction perpendicular to the original rod direction.
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Figure 7. (a, top) A schematic representation of the epitaxial relationship between the hexagonal (10) plane and the (001) planes in the rhombohedral mesh intermediate phase. The thin solid lines indicate the cylinder axes in the hexagonal phase and the (110) planes in the rhombohedral phase. The dashed lines indicate the position of the cylinders in the next plane above or below. (b, bottom) The scattering pattern arising from having the scattering vector in the (001) plane of the structure shown in part a.
Conclusions The neutron scattering from the shear-aligned sample of intermediate phase shows a distinct 6-fold symmetry and identifies the phase as a six-connected rhombohedral mesh phase, space group R3 h m, Figure 1b. Further the scattering shows the epitaxial relationship between the (10) planes of the hexagonal phase and the (001) planes of the intermediate phase. The system forms a rhombohedral mesh because the free energy is minimized by the formation of surfactant nodes with reduced surface curvature and by them avoiding each other in a rhombohedral arrangement despite the fact that the nodes must
form six links with neighbors rather than the four formed in the tetragonal phase. Acknowledgment. This work was supported by EPSRC Grant No. GR/K06754 and by CLRC neutron beam time at ISIS, Grant No. RB/5402. Claire Fairhurst thanks the University of Central Lancashire for a research studentship. We would like thank Andrew Fogden and John Diacic for useful discussions and Steve King for assistance with the neutron scattering experiments. LA960697V
