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Conformal Roughness in the Adsorbed Lamellar Phase of Aerosol-OT at the Air-Water and Liquid-Solid Interfaces Z. X. Li, J. R. Lu, R. K. Thomas, and A. Weller Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road, Oxford OX1 3QZ, U.K.
J. Penfold,* J. R. P. Webster, and D. S. Sivia ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, U.K.
A. R. Rennie Department of Chemistry, King’s College London, Strand, London WC2R 2LS, U.K. Received February 8, 2001. In Final Form: May 10, 2001 At concentrations greater than the critical micellar concentration, cmc, Aerosol-OT, AOT, adsorbs at the air-water and liquid-solid interfaces as a lamellar phase, with long-range lamellar ordering normal to the surface or interfaces. Coincident with the specular Bragg scattering from the ordered structure is pronounced off-specular scattering, characteristic of conformal roughness in the multilayer structure. A detailed analysis of the off-specular scattering, interpreted in terms of a correlation length of the conformity and an amplitude of the fluctuations, is presented. Additional off-specular scattering is observed, and its origin, arising from an effect analagous to that responsible for Newton’s interference fringes in optics, is discussed. Analysis of both the specular reflectivity and off-specular scattering is consistent with increasing structural order with increasing temperature.
Introduction Surface or interfacially induced ordering, or the adsorption of an ordered phase, has been described in a variety of lyotropic surfactant systems. We have previously reported the adsorption of the lamellar phase of AerosolOT at the solid-liquid and air-water interfaces,1,2 where a highly ordered multilayer structure adjacent to the interface was observed. Lee et al.3,4 reported micellar ordering on a shorter length scale for the cationic surfactant, tetradecyl trimethylammonium bromide, at the air-water interface. Smit et al.5 subsequently predicted surface micellar ordering from their computer simulations in model surfactant solution surfaces and interfaces. Surface-induced ordering of triblock copolymer micelles at the solid-liquid interface has been observed by Gerstenberg et al.6 Hamilton et al.7,8 reported highly ordered shear-induced structures at the liquid-solid interface for the viscoelastic surfactant mixture of cetyltrimethylammonium 3,5-dichlorobenzoate and bromide, where a near surface hexagonal structure of aligned rods was observed. Cevc et al.9 reported the observation of (1) Li, Z. X.; Lu, J. R.; Thomas, R. K.; Penfold, J. Faraday Discuss. 1996, 104, 127. (2) Li, Z. X.; Weller, A.; Thomas, R. K.; Rennie, A. R.; Webster, J. R. P.; Penfold, J.; Heenan, R. K.; Cubitt, R. J. Phys. Chem. B 1999, 103, 10800. (3) Lee, E. M.; Thomas, R. K.; Penfold, J.; Ward, R. C. J. Phys. Chem. 1989, 93, 381. (4) Lu, J. R.; Simister, E. A.; Thomas, R. K.; Penfold, J. J. Phys. Chem. 1993, 97, 13907. (5) Smit, B.; Hilbers, P. A. J.; Essellink, K.; Rupert, L. A. M.; Van Os, N. M.; Schlijper, A. G. Nature 1990, 348, 624; J. Phys. Chem. 1991, 95, 6361. (6) Gerstenberg, M. C.; Pedersen, J. S.; Smith, G. S. Phys. Rev. E 1998, 58 (6), 8028. (7) Hamilton, W. A.; Butler, P. D.; Baker, S. M.; Smith, G. S.; Hayter, J. B.; Magid, L. J.; Pynn, R. Phys. Rev. Lett. 1994, 72, 2219. (8) Butler, P. D.; Hamilton, W. A.; Magid, L. J.; Hayter, J. B.; Slawecki, T. M.; Hammouda, B. Faraday Discuss. 1996, 104.
ordered membrane structures of the phospholipid dimyristoyl phosphatidylcholine (DMPC) at the air-water interface. Gompper and Zschecke10 have used a simple Ginzburg-Landau model to predict the wetting of lamellar phases at the oil-water interface, and the origin of repulsive and attractive forces between membranes has been discussed in the context of “unbinding transitions”.11 In this paper we describe an extension of our earlier reported observation on the surface-induced ordering of the lamellar phase of Aerosol-OT at the air-water and liquid-solid interfaces,1,2 and present a detailed analysis of the specular reflectivity and off-specular scattering that arises. The specular reflectivity is analyzed as a periodic function of decreasing order, extending from the interface, using a maximum entropy reconstruction. In addition to the appearance of pronounced “Bragg” peaks due to the multilayer structure, coincident with those peaks in the specular reflectometry are strong ridges of intensity in the off-specular direction. These occur at values of constant qz (component of wave vector transfer perpendicular to the surface). It is well established12-14 that such offspecular features are characteristic of conformal roughness in multilayer assemblies, and we present here a quantitative analysis, from which the correlation length of the in-plane roughness is obtained. (9) Cevc, G.; Fenzl, W.; Sigl, L. Science 1990, 249, 1161. (10) Gompper, G.; Zschecke, S. Springer Proc in Phys, vol. 66; Lipowsky, R., Richter, D., Kremer, K., Eds.; Springer-Verlag: Berlin, Heidelberg, 1992. (11) Lipowsky, R. Nature (London) 1991, 349, 475. (12) Zabel, H. Appl. Phys. 1994, A58, 159. (13) Press, W.; Tolan, M.; Stettner, J.; Seeck, O. H.; Schlomka, J. P.; Nitz, V.; Schwalowsky, L.; Mu¨ller-Buschbaum, P.; Bahr, D. Physica B 1996, 221. (14) Sinha, S. K.; Sanyal, M. K.; Satija, S. K.; Majkrzak, C. F.; Neumann, D. A.; Homma, H.; Szpala, S.; Gibaud, A.; Morkoc, H. Physica B 1994, 198, 27.
10.1021/la010211x CCC: $20.00 © 2001 American Chemical Society Published on Web 08/10/2001
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Langmuir, Vol. 17, No. 19, 2001 5859 width); and the typical measurement time was ∼1 h per sample. The use of the multidetector allowed a range of off-specular or background scattering to be determined on either side of the specularly reflected peak. The latter could be used for the subtraction of a nonlinear background along the specular reflection direction. This is important for the concentrated surfactant solutions, as the background is not usually flat when there is strong small angle scattering from the bulk solution. The geometry for the off-specular measurements is shown in Figure 1a. The linear multidetector on CRISP (oriented vertically) and the area detector on SURF were mounted in the vertical plane (z-direction), and the surface of the sample is horizontal in the x-y plane. Figure 1b shows the range of qz - qx covered in a single measurement (at 0.8°): in the angular range 0.35 to 1.8° the qx range covered is approximately 10-5 to 10-3 Å-1, where qx is defined as
qx )
Figure 1. (a) Neutron scattering geometry for the specular and off-specular measurements at grazing incidence. (b) qx qz region accessible with an area detector on the SURF reflectometer, for an angle of incidence, θ, of 0.8°.
Experimental Details The neutron reflection measurements were made on the reflectometers CRISP15 and SURF16 at the ISIS pulsed neutron facility at the Rutherford Appleton Laboratory, as previously described for the air-liquid17 and liquid-solid18 interfaces. The two reflectometers view a liquid hydrogen moderator (producing a Maxwellian distribution of thermal neutrons with a peak in the distribution at a wavelength ∼ 2.5 Å) and collect data using the “white beam” time-of-flight method in a 20 ms time frame (at the source frequency 50 Hz). Measurements were made with the sample in the horizontal plane, using fixed angles of incidence and neutron wavelengths, λ, in the range 0.5-6.5 Å, to provide a broad range of scattering vectors qz (where qz ) 4π sin θ/λ and θ is the glancing angle of incidence). At the air-liquid interface, measurements were made at the angles 0.8 and 1.5° to cover the qz range 0.027-0.5 Å-1. At the liquid-solid interface, measurements were made at the angles 0.35, 0.8, and 1.8° to cover the qz range 0.012-0.5 Å-1 (note that data are only plotted out to a qz,max of 0.15 Å-1, at which point the sample dependent background becomes significant). The measurements were made using a linear multidetector aligned in the vertical plane on CRISP, and using a two-dimensional multidetector on SURF (the data from the horizontal cells of the detector were summed over the beam (15) Penfold, J.; Ward, R. C.; Williams, W. G. J. Phys. E 1987, 20, 1411. (16) Penfold, J.; Richardson, R. M.; Zarbakhsh, A.; Webster, J. R. P.; Bucknall, D. G.; Rennie, A. R.; Jones, R. A. L.; Cosgrove, T.; Thomas, R. K.; Higgins, J. S.; Fletcher, P. D. I.; Dickinson, E.; Roser, S. J.; McClure, I. A.; Hillman, A. R.; Richards, R. W.; Staples, E. J.; Burgess, A. N.; Simister, E. A.; White, J. W. J. Chem. Soc., Faraday Trans. 1997, 93, 3899. (17) Lee, E. M.; Thomas, R. K.; Penfold, J.; Ward, R. C. J. Phys. Chem. 1989, 93, 381. (18) Fragneto, G.; Thomas, R. K.; Rennie, A. R.; Penfold, J. Science 1995, 267, 657.
2π (cos θs - cos θ1) λ
(1)
The AOT was obtained from Sigma and purified by liquid/liquid extraction as previously described,2 and its purity was assessed by surface tension. High-purity water was used throughout (Elga Ultrapure), and the methods of cleaning the glassware and Teflon troughs used in the neutron experiments have been described elsewhere.17 The D2O was obtained from Fluorochem. The sample temperatures were maintained at (1 °C using a thermostated bath (Haake). For the liquid-solid interface measurements a block of crystalline silicon was polished in the 〈111〉 direction and cleaned to provide an hydrophilic surface using standard procedures.19 Measurements were made for 2% and 5% h-AOT in D2O at the air-water and liquid-solid interfaces. For the liquid-solid interface measurements the temperature was varied from 5 to 45 °C, and for the air-water interface the measurements were made at 25 °C.
Results Specular Reflectivity. The specular reflectivity for 2% and 5% h-AOT/D2O at the air-water and liquid-solid interfaces has a series of well-defined Bragg peaks, characteristic of an ordered lamellar structure extending from the surface into the bulk fluid (see Figure 2). The concentration and temperature dependence of this structure and its relationship to the bulk structure have been discussed in detail elsewhere.1,2 The qz values of the Bragg peaks correspond to a lamellar d spacing in the range 150-280 Å (dependent upon temperature and concentration). The data shown in Figure 2a and b are for two different temperatures, 10 and 35 °C. The reflectivity data are consistent with increased surface ordering with increasing temperature. The volume fraction distribution of solvent obtained from a maximum entropy reconstruction20 of the specular reflectivity for 2% h-AOT/D2O at the liquid-solid interface at both 10 and 35 °C is also shown in Figure 2 (Figure 2c and d). In the maximum entropy analysis, the solvent volume fraction is constrained to be within the limits 0.0-1.0. The volume fraction distributions obtained from the maximum entropy reconstruction are broadly consistent with a damped oscillatory function. The amplitude of the periodic function is smaller at the lower temperatures, and the damping is more pronounced (that is, the structure decays more rapidly with distance): consistent with increased interlayer roughness at lower temperatures. The periodic structure extends ∼0.5 µm from the interface into the bulk solution. Where a detailed comparison has been made, the surface d spacings for 2 (19) Fragneto, G.; Thomas, R. K.; Rennie, A.; Penfold, J. Langmuir 1996, 12, 6036. (20) Geoghegan, M.; Jones, R. A. L.; Sivia, D. S.; Penfold, J.; Clough, A. S. Phys. Rev. E 1996, 63, 825.
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and 5% AOT are similar, and the solid-liquid and air-liquid spacings are comparable. Both the surface and bulk spacings increase with decreasing temperature, and the surface spacings are systematically shorter than the bulk values.2 The structural analysis described above is consistent with increased surface order with increasing temperature. Analyses of the data, at different temperatures and concentrations, at the liquidsolid and air-liquid interfaces (not reported here), are all consistent with this trend. Salamat et al.21 have analyzed data for lamellar ordering at the liquid-solid interface in a different system (pentaethylene glycol n-dodecyl ether-sodium decylsufate) with an analytic expression for a damped undulating bilayer. The data shown in Figure 2, for AOT, cannot be described by such a well-defined functional form. It has, in detail, a more complex pattern, and this has implications for and limits any subsequent quantitative analysis of the off-specular data. Off-Specular Scattering. The off-specular data, plotted in the qz - qx plane, for 2% h-AOT-D2O at 25 °C at the air-water and liquid-solid interfaces are shown in Figure 3. At both the air-water and liquid-solid interfaces there is pronounced off-specular scattering, which coincides predominantly with the “Bragg” peaks in the specular intensity and is always a maximum at qx ) 0. The most significant feature is the intense off-specular scattering coincident with each Bragg peak and at a constant qz. This has been observed in many multilayer structures, and is attributed to conformal roughness.12-14 The curvature associated with these constant qz streaks at low values of qz (see particularly the 0.8° data in Figure 3a and b) is due to refraction effects (see for example ref 22) and is accommodated within the distorted wave Born approximation.22 The additional off-specular scattering, seen emanating from the first-order Bragg peak in the 0.35 and 0.8° data in Figure 3b and in the 0.8° data in Figure 3a, is due to an effect analagous to the formation of what Pynn23 referred to as Newton’s interference fringes in optics. Newton’s interference fringes occur at constant wavelength (qz1) and constant qz2 (where qzi ) 2π/λ sin θi, qz ) qz1 + qz2, and sin θ1,2 are the incident and scattered angles), and are coincident at qx ) 0. The scattering seen at higher values of qx, qz, for the 1.8° data in Figure 3b, is associated with small angle scattering from the bulk solution. The bulk small angle scattering is distinquished from the surface off-specular scattering because it is centered on the transmitted beam, whereas the latter is centered on the reflected beam. There is evidence (not shown in Figure 2) that the amount of small angle scattering decreases with increasing temperature. Figure 4 shows a qx cut through the off-specular qx qz map for 2% h-AOT-D2O at the liquid-solid interface for the second-order Bragg peak, at a constant value of qz of order of 0.07 Å (actual value depends on temperature2), in the temperature range 5-40 °C (the vertical axes are shifted for clarity). In the Born approximation, Sinha et al.14 have written an expression for the cross section of the diffuse scatter-
Figure 2. (a) Specular reflectivity for 2% h-AOT-D2O at the hydrophilic silica-solution interface at 10 °C. (b) As in part a, except for T ) 35 °C. (c and d) Volume fraction profiles associated with the solid lines in parts a and b.
(21) Salamat, E.; de Vries, R: Kaler, E. W.; Satija, S.; Sung, L. Langmuir 2000, 16, 102. (22) Holy, V.; Kubena, J.; Van den Hoogenhof, W. W.; Va´vra, I. Appl. Phys. A 1995, 60, 93. (23) Pynn, R. SPIE vol. 1738, Neutron Optical Devices and Applications; Society of Photographic Instrumentation Engineers: Redondo Beach, CA, 1992; p 270.
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Figure 3. (a) Off-specular scattering (qx - qz map) for 2% h-AOT in D2O at the air-solution interface at 25 °C for (i) θ ) 0.8° and (ii) 1.5°. (b) As in part a, except for 2% h-AOT in D2O at the liquid-solid interface at 25 °C for (i) 0.35°, (ii) 0.8°, and (iii) 1.8°.
ing for a periodic multilayer,
2π Sdiff(q) ) A q2z
N
∑ij exp(-1/2q2z (σ21 + σ2j + δ2|i j|))∆Fi∆Fj exp(iqz(z1 - zf))ij(q) (2)
where
ij(q) )
∫∫dxdy[exp(q2z Cij(x,y)) - 1] exp(i(qxx + qyy))
(3)
A is the illuminated area, N is the number of layers, σ21 is the value of 〈δz2i 〉, ∆Fi is the scattering length density difference across the interface i, and δ is the error in layer spacing. Unless Cij(F) ) 0 for i * j (completely uncorrelated roughness), the structure in Sdiff(qz) will mimic the structure in the specular reflectivity. For Gaussian roughness fluctuations of the self-
Figure 4. Scattered intensity versus qx for 2% h-AOT in D2O at the liquid-solid interface in the temperature range 10-35 °C, at qz ∼ 0.07 Å-1.
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Figure 5. Individual temperature plot from data in Figure 4 at 20 °C; the solid line is the calculated curve as described in the text.
affine form,23 then
Cij(F) ) C(F) ) σ2e-(F/ξ)2h
(4)
for all ij, where σ is the roughness amplitude, ξ is the cutoff length of the roughness (lateral coherence length), and h is the roughness exponent (h is related to the fractal dimensionality of self-affine surfaces, D ) 3 - h). F ) (x, y) and designates the position of a point on the surface with a height-height correlation of 〈ξ(F)ξ(0)〉. The measurements are made with a wide angular acceptance in the direction normal to the scattering plane, the y direction, resulting of an integration in eq 3 over qy, such that ij(q) reduces to
ij(qx,qz) )
∫dx [eq
2C(x)
z
- 1]e-iqxx
(5)
The integral in eq 5 can only be performed numerically, but Pynn23,25 has shown that, to a good approximation, it can be represented as a Voigt function.25 Using this approach, we have analyzed the off-specular data for the 2% h-AOT-D2O at the liquid-solid interface, in the region of the second-order Bragg peak (see Figure 4). The specular peak is modeled on a Gaussian and the off-specular intensity using the expression in eq 3, approximated by a Voigt function. A typical fit, for the data at 20 °C, is shown in Figure 5. The parameters obtained from the analysis are the relative intensities of the specular and off-specular contributions and the width of the specular Gaussian and of the Voigt function describing the off-specular scattering. As previously reported,1 there are in detail some variations in intensity from sample to sample and the origins of these variations are unknown. However, the observed temperature variations are qualitatively reproducible, and so we have restricted our detailed quantitative analysis to a temperature sequence on one sample and in terms of relative intensities. In principle, a complete analysis should provide a direct correlation between the interlayer roughness from the analysis of the specular reflectivity and in the description of the off-specular scattering (see eq 4). This has not proved possible for these data. The off-specular data at constant qz and as a function of qx are well described by the approach described above, except at the lower temperatures (5-15 °C), where some deviation in the shape of the intensity distribution from (24) Langridge, L.; Schmalian, J.; Marrows, C. H. J. Appl. Phys. 2000, 87, 5750. (25) Pynn, R. Phys. Rev. B 1992, 45, 603.
the Voigt function is observed. Similar deviations from the model for conformal roughness in a multilayer have been reported elsewhere for solid multilayers.13 There is evidence from the data in the temperature range 5-15 °C of a measurable contribution from small angle scattering, SANS, from the bulk solution to the scattering in the region of the off-specular intensity, and this is in part responsible for that deviation from the model line shape. However, it has not proved possible to obtain a reliable subtraction of the SANS contribution. The width of the Gaussian describing the specular peak (in the qx direction) is close to the instrumental resolution, implying long range order in the z direction, consistent with the observations from the analysis of the specular intensity as a function of qz. The relative intensities of the specular and off-specular scattering (in the region of the second-order Bragg peak) as a function of temperature are shown in Figure 6a, where each shows a maximum with temperature (∼20° for the off-specular and 25 °C for the specular intensity). Figure 6b shows the ratio of the specular to off-specular intensities (in the region of the second-order Bragg peak) as a function of temperature, and apart from the data for the lowest temperature, there is approximately a linear dependence. The in-plane correlation length, obtained from the width of the Voigt function, is plotted as a function of temperature in Figure 6c and increases from ∼1 to ∼6 µm in the temperature range ∼25-30 °C. A schematic representation of the main features of the structure is shown in Figure 4. Newton’s interference fringes23 occur when a film is illuminated, and irregularities at the upper surface scatter part of the incident radiation which is then reflected at a smooth film-substrate interface. The same surface irregularities further scatter the reflected radiation as it reaches the upper surface again. This gives rise to an interference pattern whose spacing is determined by the film thickness. Pynn25 has within the Distorted Wave Born Approximation derived an expression for such diffuse scattering, and has shown that under such circumstances for a single thin film the diffuse scattering can be expressed as
dσ ) (4πFf)2|1 + Rf(k1z)|2|1 + dΩ Rf(k2z)|2e-qz σ
∫dx ∫dy e-ik.FC(F)
2 2
(6)
where Ff is the scattering length density of the film, qz ) k1z + k2z, and C(F) is the height-height correlation function (see eq 4). The structure of the diffuse scattering mimics that of the specular reflectivity as a function of k1z and k2z through the reflection coefficients Rf(kiz). The constant qz1 (wavelength) fringes are clearly visible, but weak, whereas the constant qz2 fringes are almost coincident with the constant qz fringes and are not distinguishable in the qxqz plots. Newton’s interference fringes are usually faint and difficult to observe, and Pynn23 has suggested that, for example, the enhancement associated with a polymer multilayer structure with surface islands may well make such fringes observable with neutrons. This is because the reflectance is enhanced at the Bragg wave vectors, and strong diffuse scattering can be expected because the (1 + Rf) will be large. Prominent Newton interference fringes have been observed in some well ordered multilayers and magnetic multilayer structures.24 This is essentially what is observed here, where the ordered AOT lamellae provide the multilayer enhancement. This would imply that there is a surface roughness contribution, with
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Figure 6. (a) Relative intensities (at qz ∼ 0.07 Å-1) of specular (2) and off-specular scattering (4) for 2% h-AOT-D2O at the liquid-solid interface as a function of temperature. (b) Ratio of data in part a. (c) Variation of in-plane correlation length, from the analysis described in the text, as a function of temperature.
a lateral length scale on the order of microns to obtain the structure in the measured qx range. This is most likely to arise from incomplete surface coverage, with the surface monolayer in the form of islands with lateral dimensions on the order of microns. The visibility of the Newton interference fringes is still fairly poor, and the range of data available in qx and qz in the region of the fringes is insufficient to extract reliable quantitative information. However, the observation of Newton fringes is indicative of the formation of surface islands on a length scale greater than or equal to micrometers, and they appear to be present at both the air-water and liquid-solid interfaces. They are less visible for the 5% data than for the 2% data, and at 2% their visibility increases with temperature
(being most evident at 35-40 °C.) These changes may be associated with changes in surface coverage and in the distribution of island sizes, or may simply correlate with the increased order in the lamellar multilayer. From our data it is difficult to distinguish between the two. Discussion From our previous work1,2 it was shown that the surface d spacing was systematically lower than the bulk spacing, and its variation with temperature was less pronounced. This is consistent with the interface suppressing fluctuations. However, it is expected that the fluctuations should increase with increasing temperature. If the van der Waals attraction and curvature moduli are constant with tem-
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Figure 7. Schematic diagram of the surface of an AOT solution at the air-solution interface, showing the adsorbed monolayer at the interface, and the undulating bilayers with conformality, or partial conformality (approximate dimensions are shown). Only two bilayers are shown in the representation, whereas the data indicate that the structure extends ∼4000 Å into the solution (see Figure 2).
perature, then the steric repulsion should increase with increasing temperature and hence the d spacing should also increase. However, the d spacing decreases with increasing temperature, and this is contrary to that expectation, as discussed previously.2 This would imply that the curvature modulus increases with temperature. Although also counter-intuitive, we see that the variations in specular and off-specular intensities and of the in-plane correlation length with increasing temperature are consistent with the observed variation in d spacing with temperature. That is, there is enhanced structure with increasing temperature, and an increase in the inplane correlation length with temperature. In contrast, Freyssingeas et al.27 have reported an increase in d spacing and bending modulus, κ, with increasing temperature for the lamellar phase of C12EO5. They attribute the increase in κ as due to an increase in membrane thickness, associated with extension of the EO5 headgroup due to dehydration; and they propose this as the mechanism responsible for the increase in d spacing with temperature. Salamat et al.31 have observed lamellar ordering at the liquid-solid interface in a different but related system, a mixture of pentaethylene glycol n-dodecyl ether and sodium decyl sulfate. They analyzed the specular reflectivity with an analytical expression for a damped undu(26) Thompson, P.; Cox, D. E.; Hastings, J. B. J. Appl. Crystallogr. 1987, 20, 79. (27) Freyssingeas, E.; Nallet, F.; Roux, D. Langmuir 1996, 12, 6028. (28) Skouri, M.; Marignan, J.; May, R. Colloid Polym. Sci. 1991, 269, 929. (29) Mitchell, D. J.; Ninham, B. W. J. Chem. Soc., Faraday Trans. 2 1981, 77, 609. (30) Li, Z. X.; Lu, J. R.; Thomas, R. K.; Penfold, J. Prog. Colloid Polym. Sci. 1995, 98, 243. (31) Li, Z. X.; Lu, J. R.; Fragneto, G.; Thomas, R. K.; Penfold, J.; Binks, B. P.; Fletcher, P. D. I. Colloids Surf., A 1998, 135, 277.
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lating bilayer. From this analysis they extracted an estimate of the lamellar undulations, which decreased with increasing ionic to nonionic molar ration of surfactant. This was interpreted, using the theory of deVries,33 to indicate that their salf-free lamellar phase was stabilized by unscreened electrostatic repulsions rather than by Helfrich fluctuations. As previously reported,2 the Debye length for AOT at its cmc is ∼60 Å (this can hence be taken as a maximum value), and so it is unlikely that the OAT lamellae are stabilized by electrostatic repulsions. Furthermore, the pronounced temperature dependence of the d spacing and of the structure would not be consistent with such an interpretation. A change in the internal structure of the membrane with increasing temperature can at least qualitatively explain the trends that are reported here for AOT. At low concentrations of AOT (in the regime of these measurements) the L1 micellar and LR lamellar phases coexist,28 becoming a pure lamellar phase for phase volumes > 15%. We assume that increasing temperature will result in a change in headgroup conformation arising from, for example, a progressive dehydration of the AOT headgroup. Significant changes in the molecular conformation of the AOT with coverage at the air-water interface have been reported.30-32 Consistent with the simple geometrical arguments of Mitchel and Ninham,29 this decrease in area/ headgroup will result in a reduction in curvature and a trend toward an increasing fraction of lamellar phase, and hence a reduction in the d spacing. Such conformational changes are consistent with an increase in the membrane rigidity, and a decrease in the steric repulsion between bilayers, further enhancing the likelihood of a decrease in d spacing. This is also consistent with the increase in structural order observed with increasing temperature. This could also imply that the in-plane distribution would become more structured and long ranged, consistent with the enhanced correlation length with temperature observed in the analysis of the offspecular scattering. Summary A quantitative analysis of the specular and off-specular scattering from the ordered multilayered structure formed by a concentrated AOT solution at the air-water and liquid-solid interfaces has been made. The analysis of both contributions to the surface or interfacial scattering is consistent with increasing structural order at the interface with increasing temperature. This provides an explanation for the unexpected variation of lamellar spacing with temperature. LA010211X (32) Li, Z. X.; Lu, J. R.; Thomas, R. K.; Penfold, J. J. Phys. Chem. B 1997, 101, 1615. (33) DeVries, R. Phys. Rev. E 1997, 56, 1879.
