1116
Langmuir 1995,11, 1116-1121
Characterization of the Lamellar Phase Aerosol OTMrater System by NMR Diffusion Measurements L. Coppola, R. Muzzalupo,* G. A. Ranieri, and M. Terenzi Chemistry Department, Universita della Calabria, Rende (CS) 1-87036, Italy Received July 11, 1994. In Final Form: November 23, 1994@ Different studies on the Aerosol AOT/water system have shown that the liquid crystal lamellar phase is strongly influenced by mechanical stresses. The effects of stirring or mechanical manipulations may relax within days or weeks. In this work pulsed field gradient spin echo-NMR water self-diffusion,D20NMR lineshape, and optical microscopy have been used to characterize the lamellar microstructures of the liquid crystal phase. In order to understand the effects of different mechanical stresses, water selfdiffusion has been interpreted using simulation procedures in which water molecules moved randomly in defective lamellar aggregates with a variable macroscopic time scale. Such a procedure gives values of about 50 and 17pm for the size of the lamellar domains in the relaxed and perturbed samples,respectively.
Introduction Mesomorphic phases appear in a variety of surfactant systems.l v 2 With increasing Surfactant concentration most systems exhibit the hexagonal-cubic-lamellar phase progression, sometimes with additional phases occurring in the narrow concentration interval separating the three classical phases. Lyotropic lamellar phases are particularly interesting because of their importance in biological science and in a number of scientific and technological applications. The lamellar structure occurring in surfactant systems has been visualized by different techniques as being composed of infinitely large bilayers of amphiphilic molecules alternating with water layers. However recent studies314 have pointed out that different defects can coexist with the ideal lamellar structure; they produce some changes in the mesophase properties, decrease its stability causing the onset of a different phase, and reduce the liquid crystalline long-range order. Ionic and nonionic surfactant systems exhibit phase diagrams with lamellar phases differently located. For example, in binary mixtures of nonionic surfactant this phase is present in a large concentration range and at comparativelylow temperature. For ionic surfactantsthe concentration range of the lamellar phases is reduced, whereas they are stable up to relatively high temperature. Typical double-chain ionic surfactants such as Aerosol OT (sodium bis(2-ethylhexyl) sulfosuccinate, AOT), dialkyldimethylammonium halides, and many phospholipids including lecithin are less hydrophilic than the corresponding single-chainionic surfactant. Although the short-double-chain surfactants for normal micelles in a diluted solution, most compounds in this class form lamellar liquid crystals even in highly diluted solution. This behavior is in accordance with predictions based on geometrical packing of hydrophobic chains. The AOT/water binary system, for example, is dominated by a large lamellar liquid crystalline phase D, as is shown in Figure l.5-7 In addition, a t high surfactant Abstract published in Advance ACS Abstracts, March 1,1995. (1)Tiddy, G.J. T. Phys. Rep. 1980,57,1. (2) Luzzati, V. Biological Membranes; Chapman, D., Ed.; Academic Press: New York, 1968;Vol. 1. (3)Kekicheff, P.;Cabane, B.; Rawiso, M. J. Phys. Lett. 1984,45, L-813. (4) Di Meglio, J. M.; Paz, L.;Dvolaitzky, M.; Taupin, C. J. Phys. Chem. 1984,88,6036. ( 5 )Rogers, J.; Winson, P. A. Nature 1967,216,477. (6)Winson, P. A. Chem. Rev. 1968,68,1. (7)Fontell, K.J. Colloid Interface Sci. 1973,44, 318. @
150n
0 e
100-
I=
50-
20
40
6-0
8'0
AOT w t % Figure 1. Phase diagram for the binary system AOT/water from ref 18: D, lamellar; I;, viscous isotropic; F, reverse hexagonal; L1, isotropic liquid solution. content, a bicontinous cubic phase, hexagonal phase, F, are formed.
12,
and a reversed
The lamellar microstructure of the system AOT/water has been subjected to different analyses in the past years. Unusual results were observed, like the modification of the optical sign of the birifrangence in the range between 30 and 40 wt % AOT,6 the discontinuity of the electrical conductivity, and the anomalies from the X-ray datagy9 that divided the lamellar mesophase in three different ranges. Two of them show an ideal swelling behavior and are separated by a nonswelling one. Callaghan and Sodemanlo examined water diffusion in the lamellar phase of this system interpreting results in the light of X-ray data.7 They suggested that (a)at low AOT content, since the diffusion is particularly small, the interlayer spacing should contain curved barriers which restrict the solvent and (b) the intermediate range phase should be characterized by a certain amount of interlamellar bilayer disk within the water gap. ( 8 ) Park, D.; Rogers, J.;Toft, R. W.; Winsor, P. A. J.ColloidZnterface Sci. 1970,32,81. (9) Lundstrom, I.; Fontell, K. Chem. Phys. Lipids 1975,15,1. (10)Callaghan, P. T.; Soderman, 0. J. Phys. Chem. 1983,87,1737.
0743-7463/95/2411-1116$09.00/0 1995 American Chemical Society
Lamellar Microstructures
Langmuir, Vol. 11, No. 4, 1995 1117
Table 1. Composition of Analyzed Samples sample a b C
d e f
g
AOT wt % 15.26 19.76 24.83 29.40 32.96 38.80 45.16
sample h i j
k 1 m
AOT wt % 48.08 54.89 59.40 62.40 64.50 70.30
Recently Chidichimo et al.11J2 have inferred other observations about the lamellar AOT/water and AOTl1hexanelwater systems, by means of D20-NMR lineshape and H20-NMR self-diffusion experiments. They have observed that the systems were strongly influenced by mechanical stresses which force the lamellae to assume defective configurations analyzed in terms of a ripple model: the defective aggregate consists of rippled lamellae, similar to those reported for some phospholipid bilayer membranes. New water self-diffusion data, by means of pulsed field gradient spin-echo (PGSE)NMR experiments, have been collected in this present study. Particular attention has been directed to the analysis of water diffusion behavior, in the full lamellar range, on samples subjected to mechanical stresses. The previous and new results have finally been analyzed using different self-diffusion simulation procedures in which water molecules move in different defective lamellar structures. The comparison of experimental and simulated diffusion data has confirmed that the mechanical stresses do not modify considerably the geometry of the microaggregates, but it reduces the macroscopic dimensions of the lamellar domains. Microscopy and D20-NMR lineshape data have also been interpreted in this direction.
Experimental Methods Sample Preparation. The surfactant (sodium bis(2-ethylhexyl) sulfosuccinate), from Carlo Erba, was dissolved in hot methanol. The resulting solution was filtered, cooled, and vacuum-dried. The product was dissolved in hexane, filtered, and vacuum-dried. The whole procedure was repeated twice. The final product was a white waxy paste, birenfringent under a polarizing microscope. The surfactant was stored in a drybox until used. Water was bidistilled, deionized,and degassed;heavy water, 99.7% isotopically enriched, was from Merck. Methanol and hexane were high-purity products (Merck). Samples were prepared by weighting proper amounts of the components in glass tubes, which were centrifuged, sealed off, heated at 150 "C for 1 h and kept at 40 "C until equilibrium was obtained. The viscosity of the system increases enormously when a sample, kept at rest for a long time, is shaken or centrifuged and also the D20-NMR spectra were strongly affected by these mechanical treatments. For these reasons the lyotropic mixtures prepared, Table 1, have been investigated under two different experimental conditions. Self-diffision measurements and DzONMR spectra were realized from "relaxed" samples, that is after 1month from preparation, and from "perturbed" samples which were shaken and centrifuged for 2 min,just before measurements. PGSE-NMR Diffusion Measurements. Water, in lyotropic mixtures, is like a probe whose mobility depends on the structure of the amphiphilic aggregates, on their spatial orientation, and on the composition of the sample. The PGSE NMR method is particularly suitable in studying the water mobility in lyotropic systems (where the diffusion coefficient is of the order of 10+ cm2/s). The method monitors the water displacement over macroscopic distances (several micrometers) as to be sensitive to aggregate size and obstruction effects, yieldingdirect and easily interpretable data pertaining to the microstructure. (11)Chidichimo, G.; La Mesa, C.; Ranieri, G. A.; Terenzi, M. Mol. Cryst. Liq. Cryst. 1987,150b,221. (12)Chidichimo, G.; Imbardelli, D.; Golemme, A,; Ranieri, G. A.; Romeo, G. Mol. Cryst. Liq. C y s t . 1991,201, 125.
The PGSE NMR technique13consists of two rfpulses, HahnEcho sequence, with two identical magnetic field gradient pulses, the first applied between the 90" and 180"rfpulse and the second after the 180"rfpulse but before the echo. Following the usual notation, the magnetic field pulses have magnitude g, duration 6, and separation A. The significant quantity measured in this experiment is the "echo attenuation", that is the ratio between the echo amplitude in presence and in absence of a gradient pulse. Two good features of the PGSE experiment are that the mean molecular displacement is monitored in a well-defined time and the pulsed magnetic field orientation defines the direction in which motion is measured. The analysis of water diffision coefficients in lyotropic mesophases is particularly complex. These systems can be considered to be like polydomain samples, composedof a random oriented array of large single crystals, and the self-diffision coefficient, according t o the two site model,14must be considered as an average value
+
D = (1- Pb)Do P,,Db
(1)
where DOand Db are the free and bounded water self-diffusion coefficients,while pb is the water fraction bound to the aggregates. Callaghan et al.15J6 have derived different expressions for the echo attenuation due t o solvent self-diffision in lamellar and capillary structure ofnegligiblerepeat distance in polycrystalline samples. They have pointed out that an anisotropic lamellar structure can show an opportune curvature in the attenuated echo signals, in accordance to
Equation 2 is strictly useful in ideal lamellar structures (large domains) and it cannot be used for studying structure where the solvent motion is restricted (small domains) or where the aggregates are defective. In several papers17J8it was pointed out that for polydomain lyotropic mesophase a PGSE experiment can be conveniently represented in terms of an apparent self-diffusion coefficient, Dapp,obtained by the simple equation
(3) which holds in the experimental limit (y6g)2DoA5 1. A is the effective diffusion time of the measurement. Equation 3 is very similar to echo attenuation for an unrestricted and isotropic motion, where the average coefficient is replaced by the apparent one, related to the former one by the equation Dapp=fD. The apparent diffusionhas been interpreted, for different systems, in terms of an "obstruction factor",f ,which accounted for the loss of mobility of the solvent and is a very useful parameter in the investigation of mesophase structures and defectiveness. Simple considerations, supported by experimental results,lg gave for f a value of 2/3 in polydomain ideal lamellar structures. Here the analysis of the lamellar system AOT/water has been performed using self-diffusionstudies by the apparent diffusion coefficient, eq 3, and the obstruction factor. PGSE experiments were carried out in the its original time-domain form by a homebuilt pulsed spectrometer, working at 16 MHz. Due to the very short AOT TZrelaxation times, the echo decay was exclusively due to the water protons and a good signahoise ratio was also observed in all mixtures. For all the measurements here reported, we have used a diffusion time of 15 ms, pulse strength of 100 G/cm, and the length of the gradient pulse was varied in an opportune range to assure the condition (ydg)2ADo C. 1,in order 288. (13)Stejskal, E . 0.;Tanner, J. E. J.Phys. Chem. 1966,42, (14)Nilsson, P.G.; Lindman, B.J. Phys. Chem. 1983,87, 4756. P. T. Aust. J . Phys. 1984, 34, 359. (15)Callaghan, (16)Callaghan, P.T.; Jolley, K. W.; Leliervre, J. Biophys. J. 1979, 28. 133. (17)Stejskal, E.0.Adu. Mol. Rel. Proc. 1972,3,27. (18)Celebre, G.; Coppola, L.; Ranieri, G. A. J.Chem. Phys. 1992,97, 7781. (19) Chidichimo,G.; De Fazio, D.; Ranieri, G. A.; Terenzi, M. Chem. Phys. Lett. 1986,117, 514.
Coppola et al.
1118 Lungmuir, Vol. 11,No. 4, 1995
'ri J i 1600H=
Figure 2. Textures of sample b, by a optical microscope with crossed polarizers: relaxed sample on the right; perturbed sample on the left. to obtain the apparent diffusion coefficient. The volume of the sample was kept a t about 300 pL in a 5-mm NMR tube in order to minimize unwanted signals. The gradient was calibrated by measuring the known self-diffusion of pure water a t the same temperature which was kept a t 35 "C, measured and controlled within 0.1 "C or better. The apparent diffusion coefficients were obtained by fitting the experimental data to eq 3, using a nonlinear least-squares routine. The accuracy of Dappwas typically of the order of 5 to 10%. DeuteriumNMR Spectroscopy. D20-NMR spectra can be a very powerful tool in probing the structure of the liquid crystal materials. All information from the static lineshape is contained in the quadrupole frequency given by20 OQ = 0d2((3cos2
6 - 1) + q sin2 6 COS 24)
condition; right-hand side, spectra in perturbed condition.
n
-
o
g \
1.5
Results A preliminary analysis of the lamellar structure in the system AOT/water has been performed by direct observations using polarized microscopy. In mixtures at low AOT weight percent (samples a-i) observations show a clear difference of the size of the lamellar domains between relaxed and perturbed samples. Examples of the textures observed in the two conditions are reported in Figure 2, for mixture b. The size of the lamellar domains appears polydispersed but it is evident that we can observe smaller domains in the perturbed conditions than in the relaxed ones. In mixtures at high AOT weight percent (samples j-k) a remarkable difference was not observed after mechanical treatments. Microscopicobservations did not show liposome-like textures as hypothesized by other authors. (20)Abragram, A. The Principles of Nuclear Magnetism;Oxford University Press: London, 1961. (21)Blum, F. D.; Franses,E. I.; Kenneth, D. R.; Bryant, R. G.; Miller,
I
:
5 ;
v
1.0
y,
-
I
0 .
-
n
: -
-
o"0.5
0.0
(4)
where 8 and 4 are the spherical polar angles that specify the orientation of the HOfield with respect to crystal axes, 00 is the quadrupole frequency for 8 = 0,and q the asymmetry parameter (of the crystal-frame electric field gradient tensor). In an ideal lamellar mesophasewe have q =0 and for powder samples spectra consist of a broad absorption curve with two marked peaks (quadrupole splitting). Deuterium quadrupole line profiles were recorded by a FTNMR Bruker W M 300 spectrometer, operating on deuterium a t about 46 MHz. The analysis was performed by observing a small percentage of D20, purposely added to the mixtures. The quadrupole echo technique was used for data akquisition and a typical experimental setup was 400-1000 transients and 1 s repetition. The working temperature was about 35 "C.
W. G. Langmuir 1987,3,448.
Figure 3. Deuterium NMR spectra of samples b, f, and j of Table 1recorded at 35 "C: left-hand side, spectra in relaxed
-lo
AOT w t 48 Figure 4. Apparent water self-diffusion coefficients in perturbed (A)and relaxed (0) conditions as a function of AOT w t %, at 35 "C. The solid line shows the expected self-diffusion in the ideal lamellar structure characterized by an obstruction factor f = 0.66.
D20-NMR spectra were recorded in relaxed and perturbed conditions in AOT/water mixtures. Mechanical stresses induce a reduction of the quadrupole splitting and an asymmetry of the electric field gradient tensor. In addition, in samples subjected to stress, the lineshape changes with time; yet no modification is observed after 1 month on samples kept at 40 "C.We can consider this time as the mean relaxation time for mechanical perturbations. The spectral lineshape recorded as function of the AOT concentration distinguishes clearly between lyotropic aggregates with uniaxial and biaxial structure. In fact, samples in relaxed conditions give spectra with a biaxial lineshape when the AOT concentration is in the range 10-40 w t %; at higher concentration they became uniaxial. The biaxial character in perturbed conditions even extends to mixtures with 60 wt % in AOT; beyond this point the spectra look uniaxial. Samples in relaxed and perturbed conditions give powder spectra with the same uniaxial character for AOT concentration higher than 60%in weight. Some of this evidence is sketched in Figure 3. The apparent water self-diffusion coefficients, Dapp,as a function of AOT composition are shown in Figure 4. The lower and the upper trends respectively refer to measurements in relaxed and perturbed samples. At low concentrations, self-diffusion coefficients are strongly influenced by mechanical stresses while this difference decreases with the increasing of the surfactant amount. For the two experimental conditions, we finally observe
Lamellar Microstructures
Langmuir, Vol. 11, No. 4, 1995 1119
Table 2. Obstruction Factor for Lamellar Mixtures Using Equation 7 in Reference 19 ~~~
obstruction factor
(f,
sample combination
relaxed
perturbed
a-b c-d e-f
0.30 0.21 0.34
0.05 0.18
8"
0.50
k-1
0.34 0.44 0.62
1-m
0.65
1-J
j-k
0.12 0.32
0.10 0.15 0.63 0.66
similar behaviors when the surfactant compositionis more than the 60 wt %. Here the high values of the system viscosity probably reduce the effect in the aggregate microstructure or in the size of the lamellar domains. Calculation of the obstructionfactor due to the reduction of the solvent mobility by the surfactant aggregates was realized using the apparent self-diffusion data and eq 7 obtained in ref 19. The AOT composition dependence of these parameters is shown in Table 2. The obstruction factors refer to both relaxed and perturbed mixtures.
Discussion A simple and direct structural analysis can be conducted for mixtures at high surfactant concentrations (>60 wt %). According to data analyzed in the previous section, the lamellar structure here is ideal and no difference between relaxed and perturbed samples has been found. In this concentration range the viscosity of the system is very high and the modifications induced by mechanical stresses are for this reason nullified. The Dz0-NMR lineshapes are nice powder patterns whereas water selfdiffision obstruction factors are close to 2/3, confirming an ideal structure of the lamellar domain, as already pointed out in a previous work.zz For AOT/water mixtures at low surfactant concentrations ( ~ 6 wt 0 %) we have found different results that justify the presence of an anomaly of the lamellar structure. In particular the shape of Dz0-NMR spectra is strongly biaxial and the mechanical effects in the structure can be considered relevant. The self-diffusion obstruction factor due to the reduction of the solvent mobility is far from the value expected for a ideal lamellar structure. Chidichimo et al. have demonstrated that quadrupolar NMR lineshapes in the 10-60 wt % AOT range are compatible with rippled lamellar aggregates, with an averaged curvature angle A84 between 25 and 40°, for perturbed mixtures.'l Some explanation was also made on the self-diffusion behavior. As seen in Table 2, the apparent water self-diffision coefficientsgive, in mixtures with compositionhigher than 60 wt %, obstruction factors which are compatible with a ideal lamellar mesophase. These data can be utilized to obtain the expected self-diffision coefficientsfor lamellar mixtures at low concentrations in the hypothesis of ideal structures. We recall here a stoichiometric model of some years ag0,19,23 which can be used in a lyotropic phase assuming that the hydration does not change with the composition of the mixtures and the structure always remains ideal. at In this way, if we consider two mixtures (a and different composition, it is possible to describe the respective apparent self-diffusioncoefficients(D,and Dp)by the equations (22)Coppola, L.;La Mesa, C.; Ranieri, G. A,; Terenzi, M. J. Chem. Phys. 1993,98,5087. (23)Chidichimo, G.; De Fazio, D.; Ranieri, G. A.; Terenzi, M. Mol. Cryst. Liq. Cryst. 1986,135,223.
Kc@
W,(lOO - Wa> = Wa(10O - w,>
where DOis the pure water self-diffusion coefficient and Wa and Wp are the water fractions in weight percent for the mixtures a andp, respectively. The solid line in Figure 4 represents the average water self-diffision coefficient using this procedure and shows the expected behavior for an ideal lamellar structure in the whole concentration range. The experimental self-diffision results strongly differ from the expected data in mixtures at concentrations less than 60 wt %, and this happens at the same time for relaxed and perturbed samples. It is also important to observe that in this concentration range the diffusion coefficients are quite independent of the water content and for this reason we found obstruction factors much less than V3. Such low obstruction factors do not find justification in the frame of a ripple model of a lamellar phase. In such a structure, simple physical considerations suggest that the obstruction factor must range from f = 0.66 to f = 0.33 for a open (A6 = 0') and fully closed (A6 = 180")rippled structure, respectively. In different colloidalsystems (emulsion, microemulsion, vesicles)it has often been found that the root mean square displacement of the solvent (or continuous phase) is restricted by the colloidal structures with the result that the self-diffision coefficients are smaller than those in the pure phase. We believe that in order to understand the water diffusion data of our AOT/water system, we used some similar limitations on the lamellar domain; Callaghan and Soderman have already taken into consideration a similar hypothesis.'O The self-diffusion restriction due to small lamellar domains can be confirmed by PGSE experiments performed with different diffision times A. In Figure 5 is sketched the time dependence of spin-echo amplitude on the perturbed mixture 0. The spin-echo amplitudes exhibit different curvature and a clear dependence by the diffusion time. These findings confirm the presence of a restriction to the solvent motion due to small sizes of the lamellar domains dimensions. The microscope observations have pointed out that the lamellar domain sizes of the relaxed samples are sensibly larger than those of the perturbed ones; the same behavior is found in the water self-diffisiondata. In consequence of mechanical stresses, lamellar domains break into non-interconnected smaller domains which limit the water mobility, In the next section we concentrated in modeling the water self-diffisionin a liquid-crystallamellar mesophase. We analyzed the concentration dependence of the water diffusion and the reduction of the obstruction factor to low value, as a consequence of two different reasons. These are the ripple presence in the lamellar structure and water mobility restrictions due to small non-interconnected domains whose average size, d, is comparable to the root mean square displacement in the time A of PGSE experiment (r= (6DA)"). Theoretical considerations were omitted in this analysis, because it is too difficult to find the right displacement distribution function for our case. We prefer to study the problem by means of Brownian motion simulation techniques, which are able to provide self-diffusion coefficients in different structural condit i o n ~ . ~These * techniques consist of experiments carried out on computers where we can define, as we like, ideal (24)Coppola, L.;Di Gregorio, S.; Ranieri, G. A.; Rocca, G. Mol. Simulation 1991,7,241.
Coppola et al.
1120 Langmuir, Vol. 11, No. 4, 1995
' 3~
0.0
,
10
I
,
>
I
,
20
,
,
,
,
,
,
so
I
,
/
,
40
1
,
,
,
,
AOT w t Figure 6. Normalized water echo amplitude in (f) perturbed mixture as a function of (y6g)2Aover the maximum accessible range, at 35 "C. Experimentally g = 100 Glcm, 6 is changed from 0.2 to 3 ms, and A is equal t o 15 ms ( 0 )and 80 ms (U), respectively. Table 3. Thickness of Amphiphilic Layers = 20 4 Repeat Distance by Reference 7 and Other Simulation Parameters repeat
sample (AOTwt %)
distance(&
20 25 30 35 40 45 50 55 60 65 70
110 88 72 32 26 48 42 38 34 32 29
dlliP2 re1 pert 3.12 1.05 3.18 1.06 3.25 1.09 3.35 1.12 3.46 1.16 3.62 1.21 3.75 1.26 4.15 1.39 4.74 1.58 5.91 1.97 9.80 3.27
A0 (deg) pert
'
re1 32 24 16 8 0 0 0 0 0 0
72 64 56 48 40 32 24 16 8 0
0
0
or defective structures and subsequently compare these results with experimental data. The simulation procedure has already been described in previous ~ o r k . ~ The ~ simulation J ~ generates random displacements for a large number of solvent molecules with restricted motions among different geometrical structure. The interstitial solvent molecules travel a certain number, N , of mean free paths, all with the same length 1, at a random angle from random starting positions in the crystal unit cell. The self-diffision is only due to the motion of the solvent and the lyotropic aggregates are considered impenetrable and reflecting. For the present analysis we used two different lamellar structures: an ideal structure for samples characterized by uniaxial DzONMR spectra and a monodimensional rippled structure for mixtures where some biaxiality characters have been observed. Data are reported in Table 3. For the rippled lamellar structures the ripple period has been fixed, for all the simulations, equal to 60 A. In fact, the simulation procedure was independent of this parameter if it was much bigger than the mean free molecular path. The ripple angle A0 has been changed linearly with concentration) with the assumption that for perturbed mixtures at 40 and 65 wt % AOT the angles are A0 = 40" and A0 = 0" respectively, as observed by D2ONMR data (Table 3). The remaining simulation parameters are very similar to those of ref 18: the mean free cm (typical value for pure molecular path was 1 = 2 x water), the number of this displacement changes up to N = 1.5 x lo5 and the number of analyzed molecules was M = 3 x lo4. The domain size has been considered not dependent on the mixture composition; different domain sizes were introduced for sample in relaxed and perturbed
,
,
,
,
/
60
50
,
,
1
,
,
70
,
1
,
,
,
80
%
Figure 6. Comparison between simulated (full symbols) and experimental (empty symbols) apparent water self-diffision coefficients. Squares refer t o relaxed samples are triangles t o
perturbed ones.
conditions, as shown by the microscope observations. Simulation programs have been run changing the ratio dllIP2,which is equivalent to change the ratio d/(6DA)1/2 in the PGSE experiments. The D values are those extrapolated by eq 5 using the apparent self-diffusion coefficients for mixtures at higher AOT compositions. These simulation conditions have been chosen to obtain the maximum of simplicity in our structural model; the procedures were performed with the same accuracy of the experimental self-diffusion data. Using the simulation parameters in Table 3 we obtained the water diffision coefficients shown in Figure 6 , for relaxed and perturbed samples. Such results, with reference to real experimental parameters, are consistent with relaxed and perturbed samples in which the sizes of the lamellar domains were of 50 and 17 pm, respectively. Different simulations have been carried out with ripple angles up to 4 times less than those for the previous one; for example, a t 40 wt % AOT, A0 was 10". These new results are close to the ones shown in Figure 6,provided that the domain size, and consequently the d/1Nf2ratio, is chosen ca. 10%smaller. In short, the domain size is the parameter which drives mainly the simulation fitting; the water self-diffision coefficienthas a minimum dependence on the other simulation parameter (A0,ripple period, A0 slope vs concentration). The strong decrease observed in samples a t composition less than 60 w t % can be assigned to the restriction of small non-interconnected lamellar domains. Such an effect evidently increases with the increasing of the water concentration; in fact, in this situation, a larger number of molecules meet the wall of different domains.
Conclusions The microstructure of the lamellar phase of the system AOTlwater has been studied using optical microscopy) D20-NMR lineshapes and water apparent self-diffusion by means of PGSE-NMR experiments. The study was performed on relaxed and perturbed samples. The analysis by optical microscopy has pointed out in 0 t %) the mixtures at low AOT concentration ( ~ 6 w existence of a strong difference in the lamellar domain size between relaxed and perturbed samples. D20-NMR spectra recorded as a function of the surfactant concentration distinguished clearly between mixtures with uniaxial and biaxial structure. For a relaxed sample, the biaxial character was observed in the range 10-40 w t % AOT, while for perturbed sample it was extended up to 60 wt %. Mixtures at higher concentration showed powder
Langmuir, Vol.11,No. 4,1995 1121
Lamellar Microstructures pattern NMR spectra, typical of an ideal lamellar mesophase. Apparent self-diffusion coefficient measurement and calculation of the obstruction factor were performed by PGSE experiments. The obstruction factors, f, and the self-diffision data, Dapp,as a function of surfactant concentration confirmed the presence of an anomaly in the lamellar structure of this system. Low values f and were associated with a difference in domain change in Dapp size between relaxed and perturbed mixtures, as also seen by optical microscopy. In this work we also carried out a simulated study of water self-diffusionin ideal and defective lamellar structures having domains of different size. As a defective structure we simulated a ripple lamellar phase, as suggested by the study of Chidichimoet al.;llconsequently the study was realized by varying the two adjustable parameters d/lWi2and A8. The experimental and simulated findings were analyzed together. The fundamental evidence showed that the lamellar phase ofthe AOTIwater
system is constituted by small noninterconnected domains whose dimensions are comparable to the water root mean square displacement. The size of the lamellar domains, obtained by the simulated diffusion data, was ca. 50 and 17 pm in relaxed and perturbed mixtures, respectively. As observed above these findings are rather independent from the values of the structural parameter, entering in the simulation. The Brownian simulation analysis for the water selfdiffusion gave evidence that the diffusion coefficients are not distinguished between flat-ideal and rippled lamellar structure. Consequently, it was not possible to show a connection between the lineshape biaxiality of the deuterium spectra and the presence of a rippled structure.
Acknowledgment. Financial support was from CNR and MURST grants. LA940544C
