Structure of Mesh Phases in Cationic Surfactant Systems with Strongly

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Langmuir 2009, 25, 2622-2628

Structure of Mesh Phases in Cationic Surfactant Systems with Strongly Bound Counterions: Influence of the Surfactant Headgroup and the Counterion Sajal Kumar Ghosh and V. A. Raghunathan* Raman Research Institute, Bangalore 560 080, India ReceiVed August 20, 2008. ReVised Manuscript ReceiVed December 10, 2008 We have studied the phase behavior of concentrated aqueous solutions of cetylpyridinium bromide (CPB) and sodium 3-hydroxy-2-naphthoate (SHN) using X-ray diffraction and polarizing optical microscopy. The phase behavior of this system is found to be very similar to that of the cetyltrimethylammonium bromide (CTAB)-SHN-water system, reported by us recently (Ghosh, S. K., et al. Langmuir, 2007, 23, 3606), but with the important difference that the mesh-like aggregates in the present system have square symmetry, instead of the hexagonal symmetry seen in the earlier case. A random mesh phase without long-range correlations of the in-plane structure, as well as an ordered mesh phase, where the mesh-like aggregates lock into a three-dimensional lattice, are observed, as in the CTAB-SHN-water system. The mesh-like aggregates do not form when the hydroxynaphthoate counterion is replaced by either salicylate or tosylate, which are also known to bind strongly to the surfactant micelle. Instead, the phase behavior of these ternary mixtures is akin to that of the CPB-water binary system; the only liquid crystalline phase observed being the hexagonal phase made up of cylindrical micelles. These results show the extreme sensitivity of the structure and stability of mesh phases to subtle changes in the interheadgroup interactions.

Introduction Intermediate phases provide a topological link between hexagonal and lamellar lyotropic liquid crystalline phases. They are of three types: bicontinuous phases made up of a threedimensional (3-D) network of cylindrical micelles, twodimensional (2-D) ribbon phases consisting of long ribbon-like aggregates, and mesh phases consisting of 2-D mesh-like aggregates, which can also be described as bilayers with a regular array of monodisperse pores.1,2 Mesh phases themselves are of two kinds: ordered mesh phases, where the mesh-like aggregates lock into a 3-D lattice, and random mesh phases consisting of a periodic stacking of these aggregates with no long-range positional correlations of the in-plane structure. The random mesh phase can be distinguished from a lamellar phase consisting of regular bilayers by the presence of an additional diffuse peak in the small angle region of the X-ray diffraction pattern.3 Diffraction patterns of oriented samples show that the diffuse peak occurs in a direction normal to that along which the set of peaks corresponding to the lamellar periodicity appears, indicating that the former indeed arises from in-plane inhomogeneities with short-range positional correlations.4 The micellar morphology is determined by the effective shape of the surfactant molecule, which can be described in terms of the shape parameter p ) V/al, where V is the volume of the chain, a is the interfacial area per molecule, and l is the extension of the chain normal to the interface.5 Simple morphologies with * Corresponding author. (1) Holmes, M. C.; Leaver, M. S. In Bicontinuous Liquid Crystals; Lynch, M. L., Spicer, P. T., Eds.; Surfactant Science Series; CRC Press: Boca Raton, FL, 2005; Vol. 127, pp 15-39. (2) Many authors do not classify bicontinuous cubic phases as intermediate phases, although they are usually found between hexagonal and lamellar phases. As discussed in ref 1, bicontinuous noncubic intermediate phases have been proposed in the literature, but their existence has not yet been unambiguously confirmed. (3) Ke´kicheff, P.; Tiddy, G. J. T. J. Phys. Chem. 1989, 93, 2520. (4) Leaver, M. S.; Holmes, M. C. J. Phys. II (France) 1993, 3, 105. (5) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. J. Chem. Soc., Faraday Trans. 2 1976, 72, 1525.

homogeneous curvature, such as spheres, cylinders and planar bilayers, correspond to p ) 1/3, 1/2, and 1, respectively. If direct mesh-like aggregates enclosing the chains are approximated as homogeneous surfaces, then they can be shown to correspond to values of p lying between 1/2 and 2/3;6,7 inverted mesh surfaces enclosing polar regions correspond to higher values of p. The occurrence of mesh-like aggregates between cylindrical micelles and planar bilayers can thus be rationalized. Although detailed experiments on surfactants such as sodium dodecyl sulfate (SDS) suggest that mesh phases are likely to occur in many surfactant systems between the hexagonal and lamellar phases, they are expected to occur at high surfactant concentrations and over very narrow composition ranges.8 Therefore, experiments on mesh phases in these systems are very difficult. Until recently, only two classes of surfactants were known to form mesh phases over wide enough composition ranges to facilitate detailed investigations, namely, nonionic poly(oxyethylene glycol) alkyl ethers of the type CnEOm9-17 and anionic perfluoroalkanoates.3,4,18 Most of the studies on mesh phases in poly(oxyethylene glycol) alkyl ethers have been carried out on C16EO6.10,12-17 Here, a metastable ordered mesh phase is observed upon cooling from (6) Hyde, S. T. J. Phys. (Paris) 1990, C7, 209. (7) Hyde, S. T. Pure Appl. Chem. 1992, 64, 1617. (8) Ke´kicheff, P.; Cabane, B. J. Phys. (Paris) 1987, 48, 1571. (9) Funari, S. S.; Holmes, M. C.; Tiddy, G. J. T. J. Phys. Chem. 1992, 96, 11029. (10) Funari, S. S.; Holmes, M. C.; Tiddy, G. J. T. J. Phys. Chem. 1994, 98, 3015. (11) Burgoyne, J.; Holmes, M. C.; Tiddy, G. J. T. J. Phys. Chem. 1995, 99, 6054. (12) Fairhurst, C. E.; Holmes, M. C.; Leaver, M. S. Langmuir 1997, 13, 4964. (13) Funari, S. S.; Rapp, G. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 7756. (14) Leaver, M.; Fogden, A.; Holmes, M.; Fairhurst, C. Langmuir 2001, 17, 35. (15) Imai, M.; Nakaya, K.; Kawakatsu, T.; Seto, H. J. Chem. Phys. 2003, 119, 8103. (16) Imai, M.; Sakai, K.; Kikuchi, M.; Nakaya, K.; Saeki, A.; Teramoto, T. J. Chem. Phys. 2005, 122, 214906. (17) Baciu, M.; Olsson, U.; Leaver, M. S.; Holmes, M. C. J. Phys. Chem. B 2006, 110, 8184. (18) Puntambekar, S.; Holmes, M. C.; Lever, M. S. Liq. Cryst. 2000, 27, 743.

10.1021/la803605t CCC: $40.75  2009 American Chemical Society Published on Web 01/29/2009

Mesh Phase BehaVior in Cationic Surfactant Systems

the lamellar phase, which slowly transforms into a bicontinuous cubic phase.10,13 The role of the chain length in stabilizing different intermediate phases has been well documented in this class of surfactants. Shorter hydrocarbon chains are found to favor bicontinuous cubic phases, whereas longer ones induce mesh phases.16 Interestingly, all ordered mesh phases seen in these systems belong to the space group R3jm, corresponding to a threelayer stacking of three-coordinated hexagonal mesh.13,14,16 Mesh phases have also been seen in some anionic surfactants.3,4,8,18 A variety of intermediate phases, such as ribbon, ordered mesh, and bicontinuous cubic, have been seen in the SDS-water system, albeit over very narrow ranges of composition.8 The ordered mesh phase seen in this system has tetragonal symmetry (space group I4mm), corresponding to a two-layer stacking of four-coordinated square mesh. On the other hand, mesh phases have been observed over wide composition ranges in aqueous solutions of some surfactants with stiffer fluorocarbon chains.3,4,18 In these systems, the structure of the mesh phase is found to depend critically on the type of the counterion. For example, only a random mesh phase (LRD) is seen in cesium perfluorooctanoate (CsPFO),4 whereas its lithium counterpart shows an ordered tetragonal I4mm phase in addition to the LDR phase.3 Further, the ordered mesh phase seen in tetramethylammonium perfluorodecanoate (TMAPFD) has a rhombohedral R3jm structure.18 The above observations suggest that a balance between the aggregate flexibility, determined by the chain length or degree of fluorination, and the interfacial curvature, determined by the headgroup size or the nature of the counterion, decides whether a bicontinuous cubic phase or a mesh phase is formed in a particular system.1 We have recently introduced another type of surfactant system exhibiting mesh phases. It consists of the cationic surfactant cetyltrimethylammonium bromide (CTAB) and the organic salt sodium 3-hydroxy-2-naphthoate (SHN).19,20 The hydroxy naphthoate counterion binds strongly to CTAB micelles21 and changes the aggregate morphology from cylindrical to mesh-like. These mesh-like aggregates form a random mesh phase in dilute solutions and an ordered mesh phase at lower water content. The ordered mesh phase has a rhombohedral structure belonging to the space group R3jm, consisting of a three-layer stacking of three-coordinated hexagonal mesh. The ordered mesh phase disappears on replacing CTAB by its shorter chain analogue dodecyltrimethylammonium bromide (DTAB), and only a random mesh phase was observed in these mixtures.20 In the case of poly(oxyethylene glycol) alkyl ethers, decreasing the chain length is known to result in bicontinuous cubic phases. This difference in the behavior suggests that conditions for the stability of mesh phases in the present system are different from those in systems studied earlier. Therefore, we have undertaken a systematic study of the influence of different structural parameters of this surfactant system on the structure and stability of mesh phases. In the present study we investigate the influence of the cationic surfactant headgroup on the structure and stability of mesh phases, keeping the chain length and counterion the same as those of CTAB. The surfactant used is cetylpyridinium bromide (CPB). Similar to CTAB, aqueous solutions of CPB show the 2-D hexagonal phase over a wide concentration range. For low amounts of added SHN, the phase diagram is akin to that of the CPB-water binary system. At higher SHN content, a random (19) Krishnaswamy, R.; Ghosh, S. K.; Lakshmanan, S.; Raghunathan, V. A.; Sood, A. K. Langmuir 2005, 21, 10439. (20) Ghosh, S. K.; Ganapathy, R.; Krishnaswamy, R.; Bellare, J.; Raghunathan, V. A.; Sood, A. K. Langmuir 2007, 23, 3606. (21) Mishra, B. K.; Samant, S. D.; Pradhan, P.; Mishra, S. B.; Manohar, C. Langmuir 1993, 9, 894.

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mesh phase is found. Interestingly, this system forms a fourcoordinated square mesh, instead of the three-coordinated hexagonal mesh seen in the CTAB-SHN system.20 In dilute solutions, these form a random mesh phase, but upon decreasing the water content, they lock into an ordered tetragonal mesh phase. The observation that small changes in the surfactant structure can result in mesh phases of different symmetries is important in motivating a detailed study of the energetics of these systems, which are presently very poorly understood. If the addition of a strongly bound counterion to an ionic surfactant is a general recipe for forming mesh phases, then it would be possible to observe and study these phases in a wide variety of systems. To check this possibility, the role of the strongly bound counterion on the phase behavior of the CPB-water system was probed by replacing SHN by sodium salicylate (SS) and sodium tosylate (ST). The influence of these salts on the phase behavior is found to be very different from that of SHN; they do not alter the cylindrical morphology of the surfactant aggregates found in the CPB-water binary system, and the hexagonal phase is the only ordered phase seen in these systems over the range of surfactant concentrations studied (10-80 wt %).

Materials and Methods Cetylpyridinium bromide (CPB), 3-hydroxy-2-naphthoic acid (HNA), sodium tosylate (ST) and sodium salicylate (SS) were purchased from Aldrich. Sodium 3-hydroxy-2-naphthoate (SHN) was prepared by adding an equivalent amount of sodium hydroxide to an ethanol solution of HNA. Ternary solutions of the surfactant and organic salt were prepared in deionized water at different values of the salt to surfactant molar ratio R, and over a wide range of water content. The samples were kept for 2 weeks in an oven at 40 °C for equilibration. Samples were taken between a glass slide and a coverslip for microscopy observations. For X-ray diffraction studies they were taken in glass capillaries (Hampton Research). Well-aligned samples of many of the more concentrated solutions were obtained by sucking them into 0.5 mm diameter capillaries. The capillaries were flame sealed, and the sealed ends were dipped in glue as an additional precaution against loss of water. Diffraction patterns were obtained using Cu KR (0.154 nm) radiation from a rotating anode X-ray generator (Rigaku, UltraX 18) operating at 50 kV and 80 mA. Data were collected on an image plate detector (Marresearch). Exposure times were typically about an hour. Observations were made upon heating the samples from ambient temperature up to 80 °C and upon subsequent cooling. No indication of any metastable structures or chemical degradation was found in any of the samples.

Results CPB-SHN-Water System. The molar ratio (R ) [SHN]/ [CPB]) was varied from 0.25 to 2.0, and for each value of R, Φs (wt % of CPB plus SHN) was varied from 10 to 80. Around 100 compositions were studied to obtain the ternary phase diagram. At R ) 0.25, the phase behavior is very similar to that of the binary CPB-water system (Figure 1 A). At low values of Φs a viscoelastic isotropic phase (I) is found, which shows weak flow birefringence. At higher Φs this isotropic phase transforms into an anisotropic liquid crystalline phase through a two phase region. The typical microscopy texture of this phase under crossed polarizers is shown in Figure 2. X-ray diffraction patterns of this phase shows two peaks with the magnitude of scattering vector q in the ratio 1:3. These reflections correspond to the (10) and (11) planes of a 2-D hexagonal lattice. At R ) 0.5 a lamellar phase coexists with an isotropic phase over a wide range of surfactant concentration (Φs e 35) (Figure 1 B). The extent of this two-phase region decreases progressively

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Figure 1. Phase diagram of the CPB-SHN-water system at R ) 0.25 (A), 0.5 (B), 1.0 (C), 1.35 (D) and 2.0 (E). I, H, LRD, and T denote the isotropic, hexagonal, random mesh, and tetragonal mesh phases, respectively. C denotes a multiphase region containing crystallites. The shaded areas in all the phase diagrams correspond to two-phase regions. (F) Phase diagram of the CPB-SS-water system at R ) 1.0.

as R is increased to 1 and 1.35 (Figure 1 C,D). The lamellar phase shows an oily streak texture characteristic of layered structures (Figure 3). X-ray diffraction patterns of unoriented samples of this phase show two peaks with their q values in the ratio 1:2. In addition, a diffuse peak is seen at smaller values of q, and hence this can be identified as a random mesh phase (LDR ) (Figure 4). In oriented samples, the diffuse peak appears in a direction normal to that along which the sharper peaks, arising from the lamellar periodicity, occur (Figure 5). Upon increasing the temperature at these concentrations, the LDR phase transforms into an isotropic phase. This transition temperature increases with increasing Φs. At higher values of Φs, a mosaic texture is observed under the microscope for R ) 0.5 and 1.0, which is very distinct from the textures of the hexagonal and lamellar phases (Figure 6). Upon heating, this texture transforms into the characteristic texture of the lamellar phase with a narrow temperature range over which both of them coexist. Homeotropically aligned regions in the lamellar texture (where the optic axis is normal to the substrate and hence appears dark under crossed polarizers) are found to remain dark upon cooling the sample into the phase with the mosaic texture. The transition temperature increases with

increasing Φs. X-ray diffraction patterns of this phase typically show six peaks, which cannot be indexed either on a onedimensional (1-D) lattice or a 2-D hexagonal lattice. Diffraction patterns of partially aligned samples reveal that the diffuse peak in the LDR phase becomes sharp and splits into two spots in the phase with the mosaic texture (Figure 7). The reflections from this phase can be indexed on a body-centered tetragonal lattice, corresponding to the space group I4mm (Table 1). This phase is found up to the highest composition investigated (Φs ∼ 80). The LDR -T phase boundary shifts toward higher values of Φs with increasing R. The T phase is not seen at R ) 1.35, and a multiphase region containing crystallites is found for Φs greater than about 75. The diffuse peak in the diffraction patterns of the LDR phase splits along qz at high values of Φs, indicating the development of out-of-plane correlations of the in-plane structure (Figure 8). Similar build up of out-of-plane correlations in the LDR phase is found at lower values of R as the T phase is approached from higher temperatures. The phase behavior at R ) 2.0 is very similar to that at R ) 0.25 (Figure 1 E). At low Φs, an isotropic viscoelastic gel is observed, which transforms to a 2-D hexagonal phase upon

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Figure 4. Diffraction pattern of the random mesh (LRD) phase of the CPB-SHN-water system at R ) 1.35, Φs ) 60, and T ) 30 °C.

Figure 2. Typical texture of the hexagonal phase of the CPB-SHN-water system under crossed polarizers at R ) 0.25, Φs ) 60, and T ) 45 °C.

Figure 3. Typical texture of the random mesh (LRD) phase of the CPB-SHN-water system under crossed polarizers at R ) 0.5, Φs ) 40, and T ) 45 °C.

increasing Φs. At much higher Φs, the added SHN does not dissolve fully and crystallizes out of the solution. The overall ternary phase diagram at 40 °C is shown in Figure 9. It is fairly symmetric about the line corresponding to equimolar compositions of CPB and SHN in the high and medium dilution regimes. CPB-SS/ST-Water Systems. The phase diagram of the CPB-SS system at R ) 1.0 is shown in Figure 1 F. At low Φs, an isotropic gel is observed. The phase diagram is dominated by the presence of the 2-D hexagonal phase. In this phase, X-ray diffraction patterns show three reflections with their q in the ratio 1:3:2 (Figure 10). No other liquid crystalline phases are observed in this system up to Φs ) 80. The phase diagram is quite similar to that of the CPB-water binary system. The phase diagram of the CPB-ST system is very similar to that of the CPB-SS system, and the lattice parameter a of the

Figure 5. Diffraction pattern of a partially aligned sample in the LRD phase of the CPB-SHN-water system at R ) 1.35, Φs ) 60, and T ) 30 °C. The bilayer normal is aligned along the z-axis.

hexagonal phase is also found to be comparable. a is 5.99 nm at Φs ) 50 and reduces to 4.95 nm at Φs ) 80.

Discussion Low amounts of SHN in CPB induce an isotropic viscoelastic gel. Observation of flow birefringence suggests the formation of worm-like micelles. Such behavior is quite common in ionic

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Figure 6. Typical texture of the tetragonal (T) phase of the CPB-SHN-water system under crossed polarizers at R ) 0.5, Φs ) 70, and T ) 50 °C.

surfactants upon adding simple inorganic as well as organic salts.22 Further increase in Φs brings the cylindrical micelles closer to arrange on a 2-D hexagonal lattice. The reappearance of the hexagonal phase at much higher R in the CPB-SHN system produces a symmetric ternary phase diagram. The analogous phase behavior at low and high R can be explained by the presence of highly charged aggregates at these compositions, although of opposite signs. The lattice parameters of these two hexagonal phases are comparable at similar water contents. Such phase behavior is quite common in mixtures of oppositely charged surfactants.23 Although SHN is not a surfactant, its effect on the phase behavior is very similar to that of an anionic surfactant. The diffraction pattern of the lamellar phase found at lower Φs contains a diffuse peak along q⊥, indicating that this is a random mesh phase. Upon decreasing the water content, diffraction patterns from aligned samples show the diffuse peak becoming sharper and gradually splitting into two (Figures 5 and 8). It indicates the development of positional correlations of the in-plane mesh structure across the bilayers. As the bilayers are brought still closer, by decreasing the water content further, the mesh-like aggregates get locked into a 3-D lattice, which is manifested by the appearance of a large number of reflections in the diffraction pattern. Microscopy observations show that the pseudo isotropic regions in the lamellar phase (where the optic axis is normal to the substrate) remain dark upon cooling down to the lower temperature ordered phase, indicating that the latter is also optically uniaxial. Similar observations have been reported in other mesh phase forming systems.3,20 X-ray data from the ordered mesh phase can be indexed on a 3-D tetragonal lattice with a body-centered unit cell, which is optically uniaxial (Table 1). The gradual development of out-of-plane correlations, and optical uniaxiality suggest a clear structural relationship between the random and tetragonal mesh phases. Further, the repeat period (d) of bilayers in the LDR phase closely matches the interlayer separation (c/2) of the tetragonal phase. As mentioned in the introduction, ordered mesh phases having tetragonal symmetry have been observed in other systems3,8 (Figure 11). The structure is made up a 2-D square mesh, with four cylindrical micelles meeting at each node. These are stacked (22) Cates, M. E.; Candau, S. J. J. Phys: Condens. Matter 1990, 2, 6869. (23) Kaler, E. W.; Herrington, K. L.; Murthy, A. K.; Zasadzinski, J. A. N. J. Phys. Chem. 1992, 96, 6698.

Figure 7. Diffraction pattern of a partially aligned sample in the T phase at R ) 0.5, Φs ) 80, and T ) 45 °C. Table 1. X-ray Diffraction Data from the Tetragonal Phase of the CPB-SHN-Water System at r ) 0.5 and Φs ) 80, Indexed on a 3-D Body-Centered Tetragonal Lattice Corresponding to the Space Group I4mma dexp (nm)

dcalc (nm)

plane

intensity

5.25 4.22 2.81 2.37 2.13 1.43

5.25 4.22 2.82 2.37 2.11 1.41

(101) (002) (211) (220) (004) (006)

s vs w w m w

a The calculated spacings (dcalc) are obtained from the relation (1/d)2 ) (h2 + k2)/a2 + l2/c2 with the condition h + k + l ) 2n, where n is an integer. The unit cell parameters are a ) 6.70 nm and c ) 8.43 nm. vs - very strong, s - strong, m - medium, w - weak.

with a two-layer repeat, with the centers of the squares in one layer placed on top of the nodes in the next. On dilution, the layers swell apart to form a lamellar structure where long-range positional correlations of the mesh structure are lost. Heating can also have a similar effect. Hence, the basic structural unit of the random mesh phase (LDR ) and the ordered mesh phase (T) can be expected to be the same.

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Figure 10. Typical diffraction pattern of the hexagonal phase of the CPB-SS-water system at R ) 1.0, Φs ) 60, and T ) 30 °C. Three peaks are seen at q ≈ 1.30, 2.25, and 2.60 nm-1.

Figure 8. Diffraction pattern of the LRD phase in CPB-SHN-water system at R ) 1.35, T ) 30 °C, and Φs ) 70. The contrast has been adjusted to show the splitting of the diffuse peaks along qz due to shortrange out-of-plane correlations. The bilayer normal is aligned along z.

Figure 11. Model for the ordered mesh phase indicating the tetragonal unit cell.

fraction. Assuming circular cylinders meeting four by four at each junction (Figure 11), the total volume of the rods in each unit cell can be equated to the surfactant volume fraction in the sample, resulting in the relation12

4πrm2(a - 2rm) + 16rm3 ) a2cφv ,

Figure 9. Partial ternary phase diagram of the CPB-SHN-water system at 40 °C. The concentrations are in wt %. I, H, LDR , and T are the isotropic, hexagonal, random mesh, and tetragonal mesh phases, respectively. C denotes a multiphase region containing crystallites. The dashed line indicates the line of equimolar composition of CPB and SHN.

To verify the above structure, the dimensions of the surfactant aggregates can be calculated from the known surfactant volume

(1)

where rm is the micellar radius, a and c are the lattice parameters of the ordered mesh structure, and φv is the volume fraction of the surfactant. φv was estimated from Φs and the densities of the constituent components. The above expression can also be used in the case of the LDR phase with a ) dd and c ) 2d. Values of rm calculated using this expression are given in Table 2. They (∼2.0 nm) are found to be comparable to the molecular length of the surfactant reported in the literature.24 γ is the ratio of the in-plane periodicity to the stacking periodicity and is equal to dd/d for the random mesh phase and to 2a/c for the T phase. γ increases with Φs in the random mesh phase, and the transition (24) Reiss-Husson, F.; Luzzati, V. J. Phys. Chem. 1964, 68, 3504.

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Table 2. Values of the Micellar Radius rm Obtained Using Eq 1 at Different Compositions and Temperatures in the CPB-SHN-Water Systema R

T (°C) Φs

0.5

45

1.0

30

1.35

30

40 60 70 80 60 70 80 50 60 70

φv 0.375 0.571 0.686 0.763 0.57 0.666 0.76 0.468 0.568 0.662

dd

d

7.17 6.62 6.52 4.95

a

c

rm

1.90 1.93 7.05 8.52 2.03 6.7 8.22 2.10 6.62 5.38 2.04 5.81 4.68 1.95 7.07 8.28 2.10 6.42 5.81 1.90 6.15 5.12 1.91 5.45 4.53 1.90

γ

phase

1.08 1.31 1.65 1.60 1.23 1.24 1.70 1.10 1.20 1.20

LRD LRD T T LRD LRD T LRD LRD LRD

a dd is the spacing of the diffuse peak in the LRD phase, d is the lamellar periodicity, a and c are the lattice parameters of the T phase. All the lengths are in nm. γ ) dd/d for the LRD phase and 2a/c for the T phase.

to the ordered mesh phase occurs at γ ∼ 1.6. This observation is consistent with reports in the literature on some other systems exhibiting the random mesh f ordered mesh transition.18,20 In the CTAB-SHN system, a similar increase of γ with Φs is observed and the above transition occurs at γ ∼ 1.5. On the other hand, in the DTAB-SHN system, γ is found to decrease with Φs, and, interestingly, an ordered mesh phase is not found in this system.20 It seems very likely that γ has to increase with Φs and reach a critical value in order to induce an ordered mesh phase. This behavior can be understood in terms of the spatially modulated part of the interaction potential between the layers (due to the mesh-like structure), which can be expected to decay almost exponentially with a decay length of the order of the in-plane periodicity.25 Only when the separation between adjacent mesh-like layers is slightly lower than the mesh-size, the interaction potential will be strong enough to lock the layers into a 3-D ordered phase. The length of the alkyl chain of the surfactant, which determines the flexibility of the aggregates, is well-known to strongly influence its phase behavior. Both CTAB and CPB have cetyl chains, but their head groups differ. In place of the trimethylammonium headgroup in CTAB, CPB contains a pyridinium group. The observation of two different ordered mesh phases in these two systems suggests the critical role of interhead group interactions in determining the structure of the mesh phase. Since these interactions determine the curvature of the surfactant-water interface, it is possible that small changes in them can favor one of these structures over the other, which can be expected to differ in the amount of curvature because of the difference in the number of rod-like segments meeting at each node. This behavior is somewhat similar to that of perfluoroalkanoates, where Li+ counterions lead to the formation of a tetragonal mesh phase, whereas TMA+ counterions result in a rhombohedral mesh (25) Israelachvili, J. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1991.

phase.3,18 An analogous situation also exists in the case of inverted mesh phases of anhydrous soaps, where the tetragonal structure is found for calcium counterions and the rhombohedral structure for strontium counterions.26 In all these situations, small differences in the headgroup interactions, caused by changing the structure of the head groups in the present case and by varying the counterions in the other two, result in different structures of the ordered mesh phase. The addition of salt to a dilute ionic surfactant solution is well-known to induce the formation of long worm-like micelles, as found here for SS, ST, and low concentrations of SHN.21,22 Both SS and ST, which contain a benzene ring, do not change the cylindrical morphology of CPB micelles, other than making them longer. SHN containing a naphthalene group is found to transform the cylindrical micelles into mesh-like aggregates. It is not clear whether this difference in the phase behavior between SHN on the one hand, and SS and ST on the other, is just related to differences in their size, or whether other factors, such as their hydrophobicity, are also involved. Mesh-like aggregates have nonuniform curvature, unlike long cylindrical micelles and planar bilayers. Their cylindrical segments have positive mean curvature, whereas near the nodes they have negative Gaussian curvature. Therefore, the formation of such micelles can be understood if the strongly bound counterion has a preference for regions of negative Gaussian curvature. However, this cannot be the only reason for the formation of mesh phases in mixtures containing SHN, since rheological studies suggest that both SS and ST induce micellar branching, which also involves regions of negative Gaussian curvature, in some cationic surfactants.27

Conclusion The phase behavior of the CPB-SHN-water system has been determined using optical microscopy and X-ray diffraction. It is found to be very similar to that of the CTAB-SHN-water system, but with the difference that a tetragonal ordered mesh phase is observed in the present case, instead of the rhombohedral phase seen in the other. These results show that the structure of the ordered mesh phases is very sensitive to interheadgroup interactions, which determine the curvature of the micelle-water interface. It is also found that not all strongly bound counterions induce mesh phases in these cationic surfactants. Further experiments are necessary to understand the structural features of these ions that determine their ability to induce mesh phases in such mixed surfactant systems. LA803605T (26) Luzzati, V.; Tardieu, A.; Gulik-Krzwicki, T. Nature 1968, 217, 1028. (27) Raghavan, S. R.; Edlund, H.; Kaler, E. W. Langmuir 2002, 18, 1056.