Observation of Two Biaxial Nematic Mesophases in the

Universidade Federal de Roraima, 69310-270 Boa Vista, RR, Brazil. Received September 27, 2002. In Final Form: November 20, 2002. The phase diagram of ...
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Langmuir 2003, 19, 1127-1132

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Observation of Two Biaxial Nematic Mesophases in the Tetradecyltrimethylammonium Bromide/Decanol/Water System Antonio A. de Melo Filho,† Antonio Laverde, Jr.,‡ and Fred Y. Fujiwara*,‡ Instituto de Quı´mica, Universidade Estadual de Campinas, Caixa Postal 6154, 13083-970 Campinas, SP, Brazil, and Departamento de Quı´mica, Universidade Federal de Roraima, 69310-270 Boa Vista, RR, Brazil Received September 27, 2002. In Final Form: November 20, 2002 The phase diagram of the nematic mesophases present in the tetradecyltrimethylammonuim bromide/ n-decanol/water system was determined. Two distinct biaxial nematic mesophases with opposite diamagnetic and optical anisotropies were identified using 2H NMR spectroscopy and optical microscopy with polarized light. Two nematic biaxial phases were observed in a very narrow region between the two uniaxial nematic mesophases. The sequence of phase changes, hexagonal-calamitic NC-biaxial NBX+-biaxial NBX--discotic ND-lamellar mesophases, was observed with increasing decanol content. The phase transition between the two biaxial mesophases is first order, while the phase transitions between the NC and NBX+ and the NBX--ND mesophases are second order. The order parameters of the ionic headgroup of the surfactant, determined from the 2H quadrupolar splittings, indicate that the average micelle size decreases with the decanol content in the NC and NBX+ mesophases and increases with the decanol content in the NBX- and ND mesophases.

Introduction Since the first discovery of a nematic lyotropic mesophase in the sodium decyl sulfate/decanol/water system by Lawson and Flautt,1 nematic mesophases have been observed in several other surfactant systems.2 These uniaxial nematic liquid crystals are composed of discrete micelles with orientational order but without positional order, and the distinguishing characteristic of these nematic phases in comparison with the widely encountered hexagonal and lamellar lyotropic mesophases is their relatively low viscosity, which results in a homogeneous alignment of these uniaxial phases in magnetic fields used in NMR spectroscopy. Two classes of uniaxial nematic mesophases were identified with positive and negative diamagnetic anisotropies (∆χ ) χ| - χ⊥). Those with a negative diamagnetic anisotropy, denoted ND, were characterized by X-ray diffraction studies to be composed of disklike micelles,3,4 and those with a positive diamagnetic anisotropy, denoted NC, were composed of cylindrical micelles.5 Yu and Saupe first observed the existence of a biaxial nematic mesophase, NBX, in the system potassium laurate/ n-decanol/D2O in the region of the phase diagram between the uniaxial NC and ND mesophases.6 A biaxial phase was observed in the same region in the sodium decyl sulfate/ decanol/water system.7 Studies of the temperature dependence of the birefringence of the nematic mesophases * Corresponding author. E-mail: [email protected]. † Universidade Federal de Roraima. ‡ Universidade Estadual de Campinas. (1) Lawson, K. D.; Flautt, T. J. J. Am. Chem. Soc. 1967, 89, 5489. (2) Forrest, B. J.; Reeves, L. W. Chem. Rev. 1981, 81, 1. (3) Amaral, L. Q.; Pimentel, C. A.; Tavares, M. R.; Vanin, J. A. J. Chem. Phys. 1979, 45, 2940. (4) Charvolin, J.; Levelut, A. M.; Samulski, E. T. J. Phys. Lett. 1979, 40, 1587. (5) Figueiredo Neto, A. M.; Amaral, L. Q. Mol. Cryst. Liq. Cryst. 1981, 74, 109. (6) Yu, L. J.; Saupe, A. Phys. Rev. Lett. 1980, 45, 1000. (7) Bartolino, R.; Chiaranza, T.; Meuti, M.; Compagnoni, R. Phys. Rev. A 1982, 26, 26.

indicated that the nematic-biaxial phase transitions are second order.7-10 Quist11 identified two biaxial phases in the region between the NC and ND mesophases in the sodium dodecyl sulfate/decanol/water system. The author concluded that the phase transitions between the biaxial phase and the NC and ND phases in the sodium dodecyl sulfate/decanol/ water system are first order and not second order as observed for the potassium laurate/decanol water system. The author identified biaxial phases in two small islands in the region between the NC and ND regions using the deuterium quadrupolar splitting in the NMR spectra. Two different biaxial nematic phases were observed that align with the largest component of the diamagnetic susceptibility tensor, either parallel or perpendicular to the magnetic field, and were denoted NBX+ and NBX-, respectively. The transition between the biaxial phases was not studied, and the phase boundary between the two biaxial phases was not determined. The first-order NC-NBX and ND-NBX phase transitions were attributed to a variation in the aggregate shape. A biaxial nematic phase is also formed by the addition of small amounts of decylammonium chloride instead of decanol to the potassium laurate/water system.12,13 A biaxial nematic phase was also observed in the quaternary system sodium decyl sulfate/decanol/sodium sulfate/ water.14,15 The ND-NBX-NC phase transitions were characterized as second-order based on the temperature dependence of the birefringence.14 (8) Galerne, Y.; Marcerou, J. P. Phys. Rev. Lett. 1983, 51, 2109. (9) Boonbrahm, P.; Saupe, A. J. Chem. Phys. 1984, 81, 2076. (10) Melnik, G.; Photinos, P.; Saupe, A. J. Chem. Phys. 1988, 88, 4046. (11) Quist, P. Liq. Cryst. 1995, 18, 623. (12) Oliveira, E. A.; Liebert, L.; Figureido Neto, A. M. Liq. Cryst. 1989, 5, 1669. (13) Nicoletta, F. P.; Chidichimo, G.; Golemme, A.; Picci, N. Liq. Cryst. 1991, 10, 665. (14) Vasilevskaya, A. S.; Kitaeva, E. L.; Sonin, A. S. Russ. J. Phys. Chem. 1990, 64, 599. (15) Pinto, A. V. A.; Barbosa, A. A. Mol. Cryst. Liq. Cryst. 1998, 309, 29.

10.1021/la026618z CCC: $25.00 © 2003 American Chemical Society Published on Web 01/17/2003

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In this study, we report a detailed phase diagram of the nematic mesophases in the tetradecyltrimethylammonium bromide (TTAB), n-decanol, and water system. This system has been studied previously,16,17 but a biaxial phase was not observed. Two distinct nematic biaxial phases were identified in this study in addition to the NC and ND uniaxial nematic phases, and the phase transitions between these nematic mesophases were characterized. Experimental Section Tetradecyltrimethylammonium bromide (TTAB) was obtained from Aldrich and was recrystallized twice from a mixture of ethanol and ethyl acetate and dried under vacuum. A critical micelle concentration (cmc) of 3.8 × 10-3 mol L-1, determined by conductivity measurements, agrees with the values in the literature.18 The same value of the cmc determined was observed before and after recrystallization. n-Decanol was distilled using a Vigreux column, and the middle fraction was collected. All samples were prepared using distilled deionized water containing 10 wt % D2O. TTAB-d3 was prepared by the reaction of equimolar quantities of tetradecylamine and deuterated methyl iodide in the presence of potassium bicarbonate in methanol at 5 °C. After the initial addition of CD3I, excess CH3I was added to achieve exhaustive methylation. The tetradecyltrimethylammonium iodide obtained was reacted with silver oxide in methanol and filtered, and the hydroxide was neutralized with hydrobromic acid. After drying, TTAB-d3 was recrystallized from ethyl acetate. 2H NMR measurements were performed with a Varian Gemini 2000 spectrometer at 46 MHz in 5 mm sample tubes. The texture of the nematic phases under polarized light was observed and photographed using an Olympus Model CBA-K microscope between lamellar plates with a sample thickness of 0.2 mm or using sample holders with circular concave cavities with 16 mm diameters and a maximum depth of 0.5 mm. Samples were oriented in a 1.4 T magnet in order to achieve a homotropic texture for conoscopic observations, which were performed with a Zeiss Model Axiophot microscope.

Results and Discussion Figure 1 presents a partial phase diagram of the tetradecyltrimethylammonium bromide/n-decanol/water system at 22 °C. The solid points in Figure 1 represent the nematic mesophases studied in the single-phase regions. All samples were characterized by 2H NMR spectroscopy, and the variation of the deuterium quadrupolar splitting of the partially deuterated water was used to establish the phase boundaries. Representative mesophases in each region were characterized by their texture using polarizing microscopy, and the presence of the biaxial phases was confirmed by conoscopic observations. Figure 2 presents an expanded region of a traditional ternary phase diagram of this system. Two distinct biaxial nematic mesophases were found in addition to the nematic NC and ND mesophases in a very narrow region of the phase diagram between the uniaxial nematic phases. A first-order phase transition was observed between the two biaxial phases. Figure 3 presents a 2H NMR spectrum of one of the samples observed in the two-phase region between the biaxial phases. First-order phase transitions were observed between the NC and hexagonal phases, and between the nematic phases and the isotropic phase. The boundaries of these two-phase (16) Saupe, A.; Xu, S. Y.; Plumley, S.; Zhu, Y. K.; Photinos, P. Physica A 1991, 174, 195. (17) Arabia, G.; Chidichimo, G.; Golemme, A.; Ukleja, P. Liq. Cryst. 1991, 10, 311. (18) (a) Lianos, P.; Zana, R. Chem. Phys. Lett. 1980, 76, 62. (b) Selpu´lveda, L.; Corte´s, J. J. Phys. Chem. 1985, 85, 5322. (c) Domı´ngues, A.; Fernades, A.; Gonza´les, N.; Inglesias, E.; Monternegro, L. J. Chem. Educ. 1997, 74, 122.

Figure 1. Phase diagram of the tetradecyltrimethylammonium/n-decanol/water system at 22 °C. The water used contained 10% D2O. The data points in the figure represent the samples studied in the single-phase regions. Symbols: H, hexagonal mesophase; NC, nematic calamitic mesophase; NBX+ and NBX-, nematic biaxial mesophases; ND, nematic discotic mesophase; L, lamellar mesophase; I, isotropic phase.

regions are not indicated in Figures 1 and 2 since they were not well-defined in this study. The calamitic nematic phase, NC, has a positive diamagnetic anisotropy and aligns with the director parallel to the magnetic field. The optical anisotropy of this phase is negative. The binary TTAB/water system forms a nematic phase in a very narrow range of concentrations between the hexagonal and isotropic phases, which was observed in previous studies.19,20 Nematic mesophases are normally not observed in binary surfactant/water mixtures. Decanol stabilizes the nematic NC phase, which is stable over a wider range of water concentrations. At higher decanol concentration, the discotic ND phase is formed, which has a negative diamagnetic anisotropy and aligns with the director perpendicular to the magnetic field. The optical anisotropy of this phase is positive. The ND nematic phase is formed only in a narrow range of decanol concentrations but over a wide range of water concentrations. The two biaxial phases aligned differently in magnetic fields. The biaxial phase designated NBX+ aligns with the principal axis with the largest diamagnetic susceptibility (in the algebraic sense) parallel to the magnetic field. The diamagnetic anisotropy, ∆χ ) χ33 - (χ11 + χ22)/2, of a biaxial mesophase can be defined as positive when the largest component of the diamagnetic susceptibility is larger than the average value of the diamagnetic susceptibilities of the other two principal axes. Hence, when ∆χ > 0, a biaxial phase will align with the axis with the largest diamagnetic susceptibility parallel to the magnetic field as would an uniaxial phase with a positive diamagnetic anisotropy. ∆χ can be defined as negative when the smallest diamagnetic susceptibility is less than the average value of the susceptibilities of the other two principal axes. In this case, a biaxial mesophase will align with the axis with the smallest diamagnetic susceptibility perpendicular to the magnetic field as would a uniaxial phase with a negative diamagnetic anisotropy. The orientation of a biaxial nematic mesophase in magnetic fields has been described previously.13 Normally, the alignment of the nematic phases in the magnetic field can be determined by comparing the initial (19) Boden, N.; Radley, K.; Holmes, M. C. Mol. Phys. 1981, 42, 493. (20) Photinos, P.; Xu, S. Y.; Saupe, A. Phys. Rev. A 1990, 42, 865.

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Figure 2. Expanded region of the ternary phase diagram of the tetradecyltrimethylammonium bromide/n-decanol/water system at 22 °C. The concentrations are in weight fractions, and the water used contains 10% D2O.

Figure 3. 2H NMR spectrum of a system with two biaxial nematic mesophases. The sample composition is 38.88% TTAB, 5.28% decanol, and 55.84% water containing 10% D2O. The molar ratio of decanol:TTAB was 0.2884. 2 H NMR powder pattern of the nonoriented mesophase with the spectrum of the homogeneously oriented mesophase. The residual quadrupolar splitting of a spin I ) 1 nucleus with an axially symmetric electric field gradient can be expressed as

1 3 ∆ν ) (e2qQ/h)Szz (3 cos2 Ω - 1) 2 2

(1)

where e2qQ/h is the quadrupole coupling constant and Ω is the angle between the mesophase director and the direction of the magnetic field. Szz ) 〈3 cos2 θ - 1〉/2 is the order parameter21 of the principal axis of the electric field gradient at the deuterium nucleus, θ is the angle between that axis and the director, and the angular brackets represent an average over the distribution of angles due to rapid molecular motion. The powder pattern of a nonoriented mesophase which presents all possible values of Ω will evolve into a doublet when the mesophase is homogeneously aligned with a separation ∆ν equal to or one-half the maximum width of the powder pattern when Ω equals 0 or 90°, respectively.2 The alignment of the mesophase director can be easily determined by rotating the sample tube of the oriented sample around an axis perpendicular to the magnetic field. However, this procedure is not possible with cryogenic magnets where the magnetic field is parallel to the sample tube axis. In many of the samples studied, the initial powder pattern of the nonoriented mesophases was difficult to observe since the deuterium quadrupolar splittings of (21) Saupe, A. Naturforsch. A 1965, 20, 571.

HOD in some phases are small and the mesophases orient rather quickly in the magnetic field used. To determine the sign of the diamagnetic anisotropy, the biaxial phases were first oriented in a conventional iron-core magnet where the magnetic field direction is perpendicular to the axis of the sample tube. The NC and NBX+ mesophases will align with the director parallel to the magnetic field and perpendicular to the axis of the sample tube. In the case of the ND and NBX- phases, the samples were oriented while spinning the sample tube in order to force the director to orient parallel to the axis of the NMR sample tube as well as perpendicular to the field. Hence, the mesophases were homogeneously aligned with an orientation that differs by 90° from their equilibrium orientation in a cryogenic magnet where the magnetic field is applied parallel to the axis of the sample tube. In this manner, it was possible to observe the initial and equilibrium separation of the quadrupolar splitting of the nematic mesophases when placed in the cryogenic magnet of the NMR spectrometer and to determine the sign of the diamagnetic anisotropy. For mesophases with a positive ∆χ, the initial spectrum that corresponds to a perpendicular alignment of the director will result in a doublet with twice that of the original value when the mesophase aligns parallel to the magnetic field. Mesophases with a negative ∆χ will present a quadrupolar spitting which will be half the initial value. The two biaxial phases presented different textures under a polarizing microscope. The NBX+ biaxial phase presents a texture similar to that of the NC uniaxial mesophase, while the NBX- biaxial phase has a texture similar to that of the ND mesophase. Conoscopic observations of the NC mesophase oriented by magnetic fields with the director perpendicular to glass interface indicated a negative optical anisotropy. When the biaxial NBX+ mesophase was oriented in a similar manner, the samples showed the same optical anisotropy as the NC phase. The ND phase has a positive optical anisotropy, and the NBXbiaxial phase presented the same behavior when oriented in the same manner. The variation in the quadrupolar splittings of HOD with the decanol or with the water content indicated a secondorder phase transition between the NC and NBX+ phases, and between the NBX- and ND mesophases. A series of samples were prepared containing TTAB substituted with a N-CD3 group in order to confirm the second-order phase transitions between the uniaxial and biaxial phases and to observe the variation of the order parameter of the surfactant headgroup. These samples, whose compositions are shown in Table 1, were carefully prepared with a constant TTAB:water ratio. Figure 4 presents the variation

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Table 1. Compositions, in Weight Percent, of the Samples Used To Obtain the Data Shown in Figure 4a sample

% TTAB

% decanol

% water

mesophase

1 2 3 4 5 6 7 8 9 10 11

40.03 39.99 39.94 39.89 39.85 39.82 39.79 39.77 39.73 39.66 39.53

4.89 5.00 5.10 5.22 5.32 5.40 5.46 5.51 5.61 5.78 5.98

55.08 55.02 54.96 54.89 54.83 54.78 54.75 54.72 54.66 54.56 54.49

NC NC NC NBX+ NBX+ NBX+ NBXNBXNBXND ND

a All samples were prepared using water containing 0.2% D O, 2 and 3% of the surfactant TTAB contained TTAB-d3 substituted with a NCD3 group.

of the deuterium quadrupolar splittings of the NCD3 group and of HOD with the decanol concentration. The data clearly show a first-order phase transition between the biaxial phases and indicate that the transitions between the biaxial phases and the adjacent uniaxial phases are second order. In this series of samples, the NC-NBX+-NBX--ND phase transitions are observed. The NC-NBX+ and the NBX--ND transitions are second order. This was confirmed by observation of the variation of the quadrupolar splittings of HOD with water content at a fixed [decanol]/[TTAB] ratio. The quadrupolar splittings of the NBX- and ND phases are very similar, and conoscopic observations were necessary to identify these mesophases. The hexagonalNC phase transition was clearly first order, but it was difficult to characterize the ND-lamellar phase transition since the 2H quadrupolar splittings of HOD in these phases are very small. However, the variation of the 2H quadrupolar splittings of the N-CD3 group of TTAB-d3 in a series of samples with increasing water concentration at a fixed [decanol]/[TTAB] ratio of 0.35 indicated a secondorder ND-lamellar phase transition in agreement with a previous study of this system.16 The observation of the H-NC-NBX+-NBX--ND-L phase transitions in this system with increasing decanol content contributes to the understanding of the changes in micellar shape and order in these mesophases. This system presents all the possible micellar shapes, which may be present in noncholesteric lyotropic nematic mesophases. On the basis of synchrotron X-ray diffraction experiments, it has been argued that the uniaxial NC and ND mesophases are not built up of cylindrical and disklike micelles, respectively, but of aggregates of statistically uniaxial shape, similar in the three nematic phases, and that the only change at the uniaxial-biaxial nematic transitions is the long-range-order.22,23 In a later study, these authors concluded that the shape anisotropy of the micelles is small and that there is an anisotropic distribution of alcohol in the micelles.23 The anisotropic distribution introduces an anisotropic distribution of the electric interactions between micelles and therefore allows for the existence of the biaxial and uniaxial nematic phases even though the micelles have a very small shape anisotropy. Other authors propose that the size and shape of the finite micelles present in these mesophases is responsible for the phase changes. The incorporation of neutral (22) Figueiredo Neto, A. M.; Galerne, Y.; Levelut, A. M.; Liebert, L. J. Phys. Lett. 1985, 46, L-499. (23) Galerne, Y.; Figueiredo Neto, A. M.; Liebert, L. J. Chem. Phys. 1987, 87, 1851.

surfactants such as decanol in the micelles will reduce the intermicelle repulsion and favors a lower curvature or more planar micelle surface. There is experimental evidence for this anisotropic distribution of decanol in micelles.24 Amaral and co-workers26-30 have investigated the effect of decanol on the micellar shape and on the micellar bending energy in order to explain the NC-ND phase transition in the sodium dodecyl sulfate/decanol/ water system. These considerations can be extended to explain the formation of the intermediate biaxial mesophases. The hexagonal mesophase is composed of elongated micelles with hexagonal packing. The addition of decanol reduces the intermicellar repulsion, which results in a loss of the hexagonal order. Whether there is a significant change in micelle length at this transition is still unclear. Further addition of decanol results in the formation of biaxial shaped micelles, possibly elongated flattened (lathlike) micelles, which eventually form the NBX+ biaxial phase. A gradual change in the micellar shape would be responsible for the second-order NC-NBX+ transition. With further additional decanol, the micelles could assume a bilayer structure with shorter but broader dimensions that results in the formation of the nematic biaxial mesophase with opposite optical and diamagnetic anisotropies. This would result in a first-order phase transition between the two biaxial phases. With further addition of decanol, the shape anisotropy of these biaxial plates is gradually reduced to form bilayer micelles with an average cylindrical symmetry, which form the ND uniaxial mesophase. There is experimental evidence that the micelle shapes in the nematic phases are not very anisotropic.22-24,31,32 Therefore, small changes in the micellar shape and anisotropic distribution of the electric charge density of the micellar surface due to the segregation of decanol may be sufficient to modify the intermicelle interactions responsible for the micelle order in these mesophases. The quadrupolar splittings of TTAB-d3 can provide information regarding the size and degree of order of the micelles in these nematic mesophases. Order parameters of water determined from the deuterium quadrupolar splittings of deuterated water do not always reflect the degree of order of the micelles. The quadrupolar splitting of D2O in mesophases containing alkyltrimethylammonium salts is unusual. The quadrupolar splittings are unusually small and have been observed to decrease in magnitude, become zero, and change sign with increasing temperature.17,33 Consequently, the order parameter of the OD bond is not a reliable indicator of changes in the micellar shape and size. However, the order parameter Szz in eq 1 of the deuterated surfactant can be used to deduce changes in these proprieties. The principal axis of the electric field gradient can be assumed to lie along the C-D bond in aliphatic hydrocarbons. Due to the cylindrical symmetry of the -CD3 group, the order parameter of the N-CD3 bond can be calculated using the expression (24) Figueiredo Neto, A. M.; Galerne, Y.; Liebert, L. Liq. Cryst. 1991, 10, 751. (25) Hendrikx, Y.; Charvolan, J.; Rawiso, M. J. Colloid Interface Sci. 1984, 100, 597. (26) Amaral, L. Q. Liq. Cyrst. 1990, 7, 877. (27) Amaral, L. Q.; Santin, Filho, O.; Taddei, G.; Vila-Romeu, N. Langmuir 1997, 13, 5016. (28) Teixeira, C. V.; Itri, R.; Amaral, L. Q. Langmuir 1999, 15, 936. (29) Teixeira, C. V.; Itri, R.; Amaral, L. Q. Langmuir 2000, 16, 6102. (30) Amaral, L. Q. Braz. J. Phys. 2002, 32, 540. (31) Hendrikx, Y.; Charvolin, J.; Rawiso, M.; Leibert, L.; Holmes, M. C. J. Phys. Chem. 1983, 87, 3391. (32) Quist, P.-O.; Halle, B.; Furo´, I. J. Chem Phys. 1992, 96, 3875. (33) Quist, P. J. Phys. Chem. 1996, 100, 4976.

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Figure 4. Variation of the NMR deuterium quadrupolar splitting of (a) HOD and (b) NCD3 group of TTAB-d3 with decanol concentration in nematic mesophases of TTAB/decanol/water at 22 °C. The ratio of water/TTAB was maintained constant, and the water contained 0.2% D2O.

SN-CD3 ) (1/2)(3 cos2 θ - 1)Szz

(2)

where θ is the N-C-D bond angle. Since the C1-N(CD3)3 moiety also has a C3 symmetry, an equation analogous to eq 2 can be used to calculate the order parameter, SC-N, of the bond between the R-CH2 and the N atom. The magnitudes of these order parameters for the samples in Table 1 are presented in Figure 5 and were calculated assuming tetrahedral angles and a quadrupole coupling constant of 170 kHz.36 In addition, if one assumes that the axis of the extended hydrocarbon chain that passes through the rigid segment C2-C1-N has an average cylindrical symmetry, the order parameter of the chain axis, Sch ) 2SC-N, can be calculated using an equation analogous to eq 2 with θ ) 35.26°. These values of the headgroup order parameters can be compared with the order parameters of the headgroup of other surfactants determined from the quadrupolar splittings of the R-CD2 of the deuterated surfactants. The magnitudes of the order parameter Sch in the series of samples in Table 1 range from 0.18 to 0.22, which are typical values for the ionic headgroup in nematic mesophases.37,38 In biaxial mesophases, two independent order parameters are needed to describe the partial orientation of solutes with cylindrical symmetry13,39 since the relationship Sxx ) Syy ) (-1/2)Szz does not apply. Although it was not possible to determine (Sxx - Syy) in this study, the order parameter determined in the biaxial mesophases should reflect changes in the overall order of the supermolecular structure in these systems. The order parameter of the surfactant will be reduced by rapid molecular motion of the surfactant inside the micelle that changes its orientation with respect to the axis normal to the micellar interface. This motion should not be very dependent on the micellar shape or size and should be approximately the same in all mesophases. The order parameter will also be reduced by fluctuations of the angle between the principal axis of the micelle and the mesophase director and by lateral diffusion of the surfactant with the headgroup on the micellar interface that results in changes of the orientation of the surfactant (34) Holmes, C.; Leaver, M. S.; Smith, A. M. Langmuir 1995, 11, 356. (35) Guo, W.; Wong, T. C. Langmuir 1987, 3, 537. (36) Burnett, L. J.; Mu¨ller, B. H. J. Chem. Phys. 1972, 56, 3249. (37) Fujiwara, F. Y.; Reeves, L. W. J. Phys. Chem. 1980, 84, 653. (38) Fujiwara, F. Y.; Reeves, L. W. Can. J. Chem. 1980, 58, 1550. (39) Photinos, D. J.; Bos, P. J.; Doane, J. W.; Neubert, M. E. Phys. Rev. A 1997, 20, 2203.

Figure 5. Magnitude of the order parameter of the C-N(CD3)3 bond for the samples shown in Table 1 at 22 °C determined from 2H quadrupolar spittings.

headgroup in relation to the principal axis of the micelle. These two latter effects will be very sensitive to changes in the shape and size of the micelles. The data in Figure 5 indicate a decrease in the order parameter of the surfactant headgroup with increasing decanol content in the NC and NBX+ mesophases. Therefore, in addition to the change from a uniaxial to a biaxial shape, the data indicate a decrease in the order parameter of the micelles, probably due to a reduction in the average size of the elongated micelles. The increase of the order parameter in the NBX- and ND phases with increasing decanol indicates an increase in the micellar size. This is consistent with a growth of the micelles with a biaxial shape and a gradual formation of larger bilayer micelles with an average cylindrical symmetry. On further increase in decanol, the system forms a lamellar system. The marked reduction of the quadrupolar splitting on formation of the NBX- mesophase is due to the change in the orientation of the director relative to the direction of the magnetic field due to the inversion of the sign of the diamagnetic anisotropy. After correcting for this effect, the order parameter in the NBX- mesophase is approximately 25% larger than that in the NBX+ biaxial phase near the phase transition. This increase in the order parameter on passing from the NBX+ to the NBX- phase after a very small increase in decanol content is probably due to the effect of the diffusion of the surfactant on the micellar surface rather than a marked increase in the size of the micelle. In planar disklike micelles, the director is perpendicular to the planar interface and the predominant orientation of the axis of the extended hydrocarbon

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chain will be parallel to the director. Diffusion the plane of the micelle will not reduce the order parameter. In the case of elongated micelles, the surfactant will spend a greater amount of time with the axis of the extended hydrocarbon chain perpendicular to the major axis of the micelle and consequently perpendicular to the director. This will reduce the order parameter of the surfactant headgroup. Preliminary studies of the temperature dependence of these nematic mesophases were carried out. In general, all nematic mesophases were stable between temperatures of approximately 5 and 0 °C to temperatures 25-40 °C higher. A very unusual behavior was observed for these mesophases at higher temperatures. On increasing the temperature, a more highly ordered hexagonal mesophase appears. This behavior was previously reported for this system by Saupe et al.16 in a limited range of decanol concentrations. Our results show that the formation of a smectic phase at higher temperatures occurs over a broad range of concentrations, and this aspect is under study. Conclusion The detailed study of the phase diagram of the TTAB/ decanol/water system identified the presence of two

de Melo Filho et al.

distinct biaxial nematic mesophases in the region of the phase diagram between the two uniaxial nematic mesophases. A first-order phase transition was observed between the two biaxial phases, and the phase changes between the biaxial phases and the adjacent uniaxial phases are second order. This is only the second lyotropic system where two different biaxial nematic mesophases have been identified. It is the first in which the phase boundaries of the biaxial phases have been defined and the phase transition between the mesophases has been fully characterized. Two biaxial mesophases were first observed in the sodium dodecyl sulfate/decanol/water system. Only one biaxial mesophase was identified in the potassium laurate/decanol/water6 and the potassium laurate/decylammonium chloride/water13 systems, and NMR studies showed that these biaxial phases have a positive diamagnetic anisotropy as defined here. A second biaxial phase with a negative diamagnetic anisotropy was not identified in these systems. Acknowledgment. The authors thank FAPESP for financial support. A.A.M.F. thanks CAPES for a fellowship and A.L.J. thanks FAPESP for a fellowship. LA026618Z