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Orientational Anisotropy in the Polydomain Lamellar Phase of a Lyotropic Liquid Crystal Penny L. Hubbard, Kathryn M. McGrath, and Paul T. Callaghan* MacDiarmid Institute for AdVanced Materials and Nanotechnology, School of Chemical and Physical Sciences, Victoria UniVersity of Wellington, Wellington 6001, New Zealand ReceiVed NoVember 8, 2005. In Final Form: January 10, 2006 Diffusion-diffusion correlation measurements by NMR are used to investigate the degree of orientational order in the lamellar phase of Aerosol OT (bis(2-ethylhexyl) sodium sulfosuccinate) and water at a range of surfactant concentrations (25, 33, and 50 wt %). We show that true isotropy of the domains is found at the lowest concentration but that at higher concentrations deviations from isotropy can be found, as evidenced by asymmetry on the 2D correlation distributions. We further discuss the signficance of asymmetry in diffusion-diffusion exchange experiments, 2D distributions that should always be symmetric in steady state.
Introduction This paper presents a further investigation of the ostensibly lyotropic liquid crystal system Aerosol OT (bis(2-ethylhexyl) sodium sulfosuccinate) and water. Although the lamellar phase of this binary amphiphillic system is believed to exist over a wide concentration range,1-4 we have previously shown that, at the lower end of the concentration range, significant L3 character is evident.5 Previous 2D PGSE NMR diffusion-diffusion correlation and exchange studies have provided information about the global defect structure and the macroscopic sample alignment of lamellar phase lyotropics.6-8 DEXSY studies reveal information regarding both domain sizes in unaligned samples6 and the defect spacing in aligned samples,7 whereas DDCOSY reveals the orientation distribution of lamellar directors.9 In this paper, these twodimensional pulsed gradient spin-echo (PGSE) NMR methods are used to study AOT/water lamellae at three concentrations, 25, 33, and 50 wt %. In these measurements, the self-diffusion coefficients along each of the Cartesian axes are correlated, these correlations being visualized by a density plot obtained by performing a 2D Laplace inversion on the exponentially decaying 2D data sets. This present paper follows a study in which equilibrating AOT/ water samples at 25 and 50 wt % were compared with the results of an electron microscopy study.5 Here we restrict ourselves to samples of ∼3 months equilibration, presenting the diffusiondiffusion correlation maps obtained from the DDCOSY NMR experiments and showing how these can reveal orientational behavior. The paper will start with the use of 2H NMR spectroscopy, a first-order means of investigating orientational order, and address, in passing, some issues concerning deuteration or nondeuteration of the water solvent. Our principal finding in * To whom correspondence should be addressed. E-mail: paul.callaghan@ vuw.ac.nz. (1) Rogers, J.; Winsor, P. A. Nature 1967, 216, 477. (2) Winsor, P. A. Mol. Cryst. Liq. Cryst. 1971, 12, 141. (3) Faiman, R.; Lundstrom, I.; Fontell, K. Chem. Phys. Lipids 1977, 18, 73. (4) Winsor, P. A. Chem. ReV. 1980, 68, 1. (5) Hubbard, P. L.; McGrath, K. M.; Callaghan, P. T. J. Phys. Chem. (submitted). (6) Callaghan, P. T.; Godefrey, S.; Ryland, B. N. Magn. Reson. Imaging 2003, 21, 243-248. (7) Hubbard, P. L.; McGrath, K. M.; Callaghan, P. T. Langmuir 2005, 21, 4340-4346. (8) Furo´, I.; Dvinskikh, S. V. Magn. Reson. Chem. 2002, 40, S3-S14. (9) Callaghan, P. T.; Furo´, I. J. Chem. Phys. 2004, 120, 4032-4038.
the results reported here is that there is a tendency for the lamellae to align over time, a phenomenon reported in recent work on a polyoxyethylene (C12E5/SDS/decane/water) lamellar phase system.7 However, although this nonionic surfactant system exhibited preferential alignment of the lamellae normal to the vertical (i.e., z axis or magnetic field axis) direction, we will show here that preferential alignment of AOT/water is orthogonal, i.e., with the vertical axis lying in the planes of the lamellae. Further, we will demonstrate the seemingly paradoxical result that the higher the surfactant concentration (i.e., greater viscosity) the greater the tendency to align. Indeed, at the lowest surfactant concentration of 25 wt %, there is no evident alignment and a perfectly isotropic distribution of directors persists. Note that we choose to denote the orientation in which the bilayers contain the z axis as |z, although in such an orientation the bilayer director is perpendicular to the z axis, so that an alternative notation might equally be ⊥z for this case. However, we reserve the notation ⊥z for the situation where the bilayer normal is parallel to z. Experimental Section NMR Sample Preparation. Aerosol OT or bis(2-ethylhexyl) sodium sulfosuccinate (Sigma, purity 99%) and distilled water were mixed at weight ratios of 25:75, 33:67, and 50:50. Samples were also prepared with 90% H2O/10% D2O and with pure D2O for the purpose of carrrying out 2H NMR spectroscopy. Samples were sealed in 10 mm NMR tubes and agitated on a vortex mixer for several minutes. Each sample was then left to equilibrate at 298 K for ∼3 months. Some experiments were repeated after 1 year. NMR Experiments. The experiments were performed using an AVANCE 300 MHz Bruker spectrometer. The double pulsed gradient spin-echo (PGSE) pulse sequences are shown in Figures 1 and 2. Three-dimensional data sets were acquired using 1024 data points in the spectral dimension and 32 data points in both diffusion dimensions. Four scans were co-added for each 3D data set to increase the signal-to-noise ratio. The maximum gradient was 8.5 G/mm, with a pulse duration (δ) of 6 ms (6.5 ms including the gradient ramp time) and diffusion encoding time (∆) of 30 ms. Gradients may be applied along any of the laboratory x, y, or z directions. Note that the z axis is vertical in the laboratory frame, being both the gravitation field and magnetic field direction. The temperature was stabilized at 298 ( 0.5 K using a heating element and air cooling system, monitored by a thermocouple and regulated by a PID algorithm. The 3D data file containing the FID signals was Fourier transformed in the spectral dimension. The peak of interest (water,
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Figure 1. DDCOSY PGSE NMR pulse sequence in which gradient pulse pairs are applied orthogonally; in this case x followed by y. All possible combinations of the gradient pairs were applied both orthogonally and collinearly.
Figure 2. DEXSY PGSE NMR pulse sequence in which gradient pulse pairs are applied collinearly, along all possible axes. The encoding pairs are separated by a mixing time, τm′ ) τm + ∆. 4.7 ppm) was then integrated to produce a two-dimensional matrix, whose rows and columns are labeled by the diffusion parameters, (γδg)2(∆-δ/3). This matrix was then subjected to a two-dimensional Laplace inversion to produce a correlation map of 25 × 25 logarithmically spaced diffusion intensities. In the DDCOSY experiment, the two diffusion coefficients are obtained over contiguous time intervals, as shown in Figure 1. In the DEXSY experiment (see Figure 2), the gradients are applied colinearly, with a variable mixing time (τm′ ) τm + ∆). The transverse component of magnetization was stored along the longitudinal axis during this time to reduce T2 relaxation effects. A homogeneity-spoiling magnetic field gradient was applied between the 90° storage pulses to destroy any unwanted magnetization that remains in the NMR transverseplane, as shown in Figure 2. The effects of eddy currents were reduced by the addition of a 10 ms delay before data acquisition. The ideal DDCOSY distribution for an isotropic polydomain lamellar phase is shown in Figure 3. This distribution was calculated using the theory given in ref 5, assuming that the diffusion rate normal to the lamellae (Dpar) is 0.1 Dperp, the diffusion rate in the s-dimensional plane transverse to the lamellar director. Note that when the successive gradient pairs are applied orthogonally, a distinctive off-diagonal pattern is apparent. That pattern results from water molecules experiencing restricted diffusion within the duration of one gradient pulse pair (∆1) and unrestricted diffusion within the other (∆2).
Figure 3. Ideal polydomain lamellar distribution obtained from a DDCOSY NMR pulse sequence in which contiguous gradient pulse pairs are applied (a) collinearly, and (b) orthogonally. In this case Dpar ) 0.1Dperp.
Results Sample Characterization. Figure 4 shows the 2H NMR spectra for AOT/D2O at a range of concentrations. The higher concentration samples show very similar powder patterns with D2O and 90:H2O 10:D2O, but the 25 wt % 90:H2O 10:D2O sample has a spectrum exhibiting greater isotropy, an effect that we ascribe to a greater defect structure in the latter solvent. Note that for the D2O spectra the dependence of the quadrupolar splitting on the surfactant-to-solvent ratio is linearly dependent on AOT wt %, suggesting that all of the samples are in the swelling regime (see inset, Figure 3), whereby the surfactant is fully hydrated and the excess water resides in layers between the AOT bilayers. The 33 and 50 AOT wt % D2O spectra both appear to exhibit a classic powder pattern, commonly observed in isotropic systems.8 The 25 wt % sample has an extra peak in the center of the outer D2O spectrum doublet, indicative either of the presence of excess water within the system10 or the existence of superposed L3 character.11 Alternatively, it could arise from the presence of
Figure 4. 2H NMR spectra of AOT/D2O at 298 K at a range of concentrations - 25, 33, and 50 wt %. Inset: Dependence of quadrupolar splitting on AOT wt %.
multilayer vesicles for which diffusion around the vesicle induces sufficiently rapid reorientation of the director for isotropic averaging of the quadrupole interaction. However, such a picture would require the onset of highly restricted water diffusion, something that we do not observe in our measurements. (10) Klose, G.; Eisenbla¨tter, S.; Ko¨nig, B. J. Colloid Interface Sci. 1995, 172, 38-446. (11) Gotter, M.; Strey, R.; Olsson, U.; Wennerstrom, H. Faraday Discuss. 2005, 129, 327-338.
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Figure 5. 1H DDCOSY spectra with gradients applied along g1x,g2y in the subsequent PGSE encoding for the AOT wt % of (a) 25%, (b) 33%, and (c) 50%.
Figure 6. 1H DDCOSY spectra with gradients applied along g1x,g2z in the subsequent PGSE encoding for the AOT wt % of (a) 25%, (b) 33%, and (c) 50%.
Figure 7. 1H DDCOSY spectra with gradients applied along g1z,g2y in the subsequent PGSE encoding for the AOT wt % of (a) 25%, (b) 33%, and (c) 50%.
Diffusion-Diffusion Correlation Experiments: Orthogonal Encoding. The quadrupolar splitting of the deuterium spectra informs us about the local anisotropy of these liquid crystalline systems and can be sensitive to the orientation of the lamellae. The results presented here allow a ready comparison of the three lamellar phase systems to be made and as such, allow the individual characteristics of these comparative systems to be probed via the changes in the correlation plots, as the surfactantto-solvent ratio is varied. All data reported here were obtained after >2 months equilibration; however, a number of experiments were repeated after 1 year, and the results were reproduced. Figure 5 shows the results of the orthogonal DDCOSY experiment, performed with g1x,g2y encoding. These data, which resemble the model isotropic distribution shown in Figure 3b, clearly show by their symmetry the isotropic distribution of lamellar directors in the xy plane. Note that although the pattern for 50 wt % appears ideal, at 25 wt %, there exists an additional
diagonal feature at slow diffusion rates. Although this additional feature is also seen in the 33 wt % sample, it is very weak. However, when taking the remaining combinations of gradient orientation, that is, g1x,g2z and g1z,g2y, the symmetry of these offdiagonal features is not maintained through the entire concentration range. Although the low concentration sample remains symmetric for all possible gradient-encoding combinations, suggesting global isotropy of domain orientation, by contrast, the 33 and 50 wt % samples show a tendency for lamellae to preferentially align so that the z axis lies in the plane of the bilayer i.e., |z. This alignment is revealed by an apparent asymmetry in the off-diagonal intensity, as shown in Figures 6 and 7. The most prominent effect is observed in the midrange concentration sample (33 wt %), where there is negligible intensity for restricted diffusion along the z axis. Remarkably, this deviation from isotropy is not observed in the 2H NMR spectra, where we would expect to see a sharper doublet instead of a powder pattern for a fully aligned lamellar
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Figure 8. 1H DDCOSY spectra with gradients applied along g1z,g2z in the subsequent PGSE encoding for the AOT wt % of (a) 25%, (b) 33%, and (c) 50%, and g1x,g2x.
Figure 9. 1H DDCOSY spectra with gradients applied along g1x,g2x in the subsequent PGSE encoding for the AOT wt % of (a) 25%, (b) 33%, and (c) 50%.
phase. This suggests that the deviation from isotropy is not great and that the DDCOSY technique has much greater sensitivity to partial alignment of the lamellae. Of course, the time scale for each technique is somewhat different, around 30 ms for the DDCOSY and ∼1 ms (inverse of the spectral width) for the 2H spectroscopy. Note that the axial geometry of our superconducting magnet system does not permit polar reorientation of the z axis but only azimuthal rotations (in the x-y plane) around the z axis. This prevents our determining whether magnetic field or wall alignment effects dominate in any alignment phenomena. However, the very weak nature of the observed alignment and the time taken (>1 month) for the samples to exhibit alignment5 suggests the role of wall effects. In earlier DDCOSY experiments7 on the nonionic surfactant, C12E5/H2O, preferential alignment was also found. However this alignment favored ⊥z domains (bilayer normals along z) rather than |z (bilayer normals perpendicular to z) as in the case of AOT/water. We note that this tendency for AOT/water bilayers to orient in the |z mode may well be consistent with alignment driven by a tendency of the bilayers to lie parallel to the sample tube glass surface. What is particularly intriguing is the greater tendency for bulk alignment in the case of 50 wt % and the absence of any significant bulk alignment at 25 wt %. We suggest that the smaller interlamellar repeat distance and the stronger interbilayer forces at higher concentrations, may assist the propagation of wall-induced orientation well into the bulk. By contrast, in the more fluid 25 wt % sample, these propagation forces may be much weaker. Further, the inherent L3 character of the 25 wt % sample may drive it toward greater intrinsic isotropy. It is worth noting that the |z alignment is consistent with homeotropic wall behavior. In the earlier study on C12E5/H2O, it was postulated that, despite a tendency of the bulk to align ⊥z
over time, a persistent |z fraction remained, presumably at the walls. Such behavior has been referred to12 as “escaped-radial” (ER), and is characteristic of mesophases with a large ratio, K24/K and small ratio Wθ/K where K24 is the saddle-splay elastic constant, Wθ is the wall anchoring strength, and K is the sum of the conventional splay, twist, and bend constants. In this parlance, the present AOT/water system might be described as planepolar (PP), the case where, K24/K is small and Wθ/K is large. Diffusion-Diffusion Correlation Experiments: Collinear Encoding. With the contiguous gradient pulse pairs applied collinearly, a diagonal pattern is expected, as shown in Figure 3a. Figure 8a-c shows the results for zz encoding and Figure 9a-c for xx encoding, for all three samples. Note that these collinear DDCOSY experiments are essentially equivalent to DEXSY with minimum mixing time. As explained elsewhere,5 off-diagonal features in the lower concentration samples suggests the presence of a defect structure at length scales smaller than the domain sizes, which are on the order of 10-100 microns. For collinear xx encoding, the DDCOSY behavior is distinctly different from that for zz encoding, in the case of the lowest concentration sample. Although the 50 wt % data reveals again a typical diagonal distribution, most intense at fast correlations where the diffusion is unrestricted (Figure 9c), the 2D xx correlation maps for 25 and 33 wt % (Figure 9, panels a and b) have off-diagonal features, characteristic of exchange between domains over the 30 ms duration between the pulse pairs. Figure 9a shows a stronger off-diagonal character for xx encoding for 25 wt % than in the case of zz encoding (Figure 8a). It would appear that defects in the 25 wt % sample reduce the apparent domain size more effectively for diffusion along the z axis than along the x axis. This suggests that domain defects provide more (12) Crawford, G. P.; Doane, J. W. Mod. Phys. Lett. 1993, 7, 1785-1808.
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Figure 10. 1H DEXSY spectra with gradients applied along g1x,g2x in the subsequent PGSE encoding, with a mixing time of 830 ms, for the AOT wt % of (a) 25%, (b) 33%, and (c) 50%.
effective pathways for interdomain diffusion, when diffusive displacements are vertical. The off-diagonal features in the collinear DDCOSY experiment for the 33 wt % sample are a little harder to interpret but may be due to the partial L3 character noted in the previous paper. At this concentration, and as apparent from Figures 6 and 7, there is preferential alignment of the lamellae with bilayer planes containing the z axis (|z). This means that solvent diffusion must be largely restricted by the lamellae, locally along x or y. Exchange between fast and slow is more rapid when motion is observed along x, probably consistent with the abundance of |z lamellae, and the consequent larger pool of spins for which motion is restricted when measured along x. Asymmetry in Long Mixing Time DEXSY Experiments. If one increases the effective mixing time from (τm′)min in a DEXSY experiment then off-diagonal features are expected to emerge as exchange between domains takes place. However, we would always expect such features to be symmetric, since in steady state exchange molecules migrating from a domain which is oriented for fast diffusion to one which is oriented for slow diffusion will be exactly balanced by molecules moving in the opposite direction. Figure 10 shows the results of the xx-encoded DEXSY experiment with a mixing time of 830 ms for each sample concentration (results for a range of different mixing times is shown in ref 5). In the globally isotropic 25 wt % sample, there are once more strong off-diagonal features in the distribution, features which are present from even the shortest τm′ times of 20 ms. The 33 wt % sample also shows off-diagonal intensity from 20 ms in the x-encoded experiment (data not shown), thus showing similarities to the low concentration sample. However, the zz-encoded DEXSY results are purely diagonal (data not shown), reflecting the asymmetry apparent in the preferential |z alignment of domains. The xx-encoded data for the 50 wt % sample is intriguing in that it appears to exhibit off-diagonal intensity with significant asymmetry. The only viable explanation is a difference in relaxation rates for slowly and rapidly diffusing spins. The origin of enhanced spin relaxation is the temporary immobilization of the water molecule on collision with the bilayer surface and the consequent lengthening of the dipolar interaction correlation time. In particular, it is possible that a spin on a water molecule in a domain whose structure leads to a fast relaxation rate may relax between gradient pulse pairs and be less visible when it subsequently enters a domain with a slow relaxation rate. In support of this contention, we note that for samples in which the H2O is diluted with D2O and for which spin relaxation is slower overall such asymmetry diminishes.
Finally, we note that the inverse Laplace method involves a mathematically ill-defined procedure in the sense that a number of different mathematical solutions may satisfy the constraints of the data.14 Furthermore, the process requires some regularization process, in which signal-to-noise is adjusted by means of a smoothing of the fit. We have followed a standard procedure in selecting the regularization parameter that just minimized chisquared.15 Despite these concerns we see no possibility that the algorithms used here can induce artifactual asymmetry, and indeed, we have shown that they do not do so when tested with simulated input data.6
Conclusions DDCOSY NMR has revealed that for NMR tubes oriented with their cylindrical axes parallel to the magnetic field (z direction) 33 and 50 wt %, AOT/water lamellar phases preferentially align with bilayer planes containing the vertical direction (|z). This is in stark contrast to the nonionic system, C12E5/water, where normal alignment (⊥z) is favored. These alignment effects are subtle and not at all apparent when using conventional powder pattern analysis via 2H NMR spectroscopy. The correlation maps found depend distinctly on concentration, demonstrating the inherent sensitivity of the double-PGSE correlation methods in the study of the mesophase structure. The 25 wt % sample proves to be globally isotropic while the 33 and 50 wt % samples tend to align. Our study suggests that barriers to diffusion may be more closely spaced for molecules diffusing in the xy plane, perhaps consistent with the mid-bilayer disks proposed by Callaghan et al.13 DDCOSY, utilizing variable gradient direction, and DEXSY NMR, using variable mixing time, can each provide useful probes of defect structure and domain sizes in bulk anisotropic media. However, their efficacy is improved when used with other techniques as a complementary method. For lyotropic liquid crystal phases, where complexity of morphology is so common, the additional insights provided by these new tools can only be useful. Acknowledgment. The authors thank the New Zealand Foundation for Research, Science and Technology, the Royal Society of New Zealand Marsden Fund, and the Centres of Research Excellence Fund for financial support. LA052998N (13) Callaghan, P. T.; So¨derman, O. J. Chem. Phys. 1983, 87, 1737-1744. (14) Venkataramanan, L.; Song, Y.-Q.-.; Hu¨rlimann, M. D.; Flaum, M. IEEE Trans. Signal Process 2002, 50, 1017-1026. (15) Provencher, S. W. Comput. Phys. Commun. 1982, 27, 229.
