J. Phys. Chem. 1983, 87, 7737-1744
trend of decreasing lifetime as energy difference decreases exists. Since the present state of theory cannot support exact calculations of back-intersystem-crossing rates, we need to assess whether chemical reaction could provide an equally plausible mechanism for the principle pathway for deactivation of the doublet state and explain the observed variations in lifetime. The answer is, of course, that one might (again in the absence of rigorous theory) simply assume that the observed lifetimes are caused by chemical reaction and end the argument. But is there any basis for expecting the observed pattern? The only basis on which one can answer that question is to use relative reactivities of ground-state molecules of the same configuration as models. Because substitution reactions on the ground state of C P complexes decrease with an increase in ligand field strength, and because this latter parameter also controls the energy gap, if there is a correlation between lifetime and energy gap there will be one between lifetime and anticipated substitution rate constant. But if we use the ground-state molecule as the basis for our comparison, then there are some unsettling features in an attempt to quantify this correlation. All trans-substituted bis(ethy1enediamine) complexes lose ethylenediamine at a nearly constant rate in thermal reactions37 independent of the axial ligand. Yet the excited-state lifetimes for truns-Cr(en),(NCS),+,trans-Cr(en),NCS(F)+, and tr~ns-Cr(en),F(H,O)~+ span two orders of magnitude. Further, the 1,3-propanediaminecomplexes do not lose a coordinated amine nearly as rapidly, yet trans-Cr(37) Linck, R. G. Inorg. Chem. 1977, 16, 3143.
1737
(tn),NCS,+ and trans-Cr(en),(NCS),+ have nearly equal lifetimes. In addition, cis complexes are more labile thermally than trans ones are, yet exactly the opposite result is found in the excited-state lifetimes. In some of these cases, the photochemical products of aquation and the thermal products are identical, suggesting that similar parameters should be at work in determining cis/trans reactivity. For most of the complexes studied, the presence of a coordinated water makes correlation between ground-state chemistry impossible, for we have no knowledge, in general, of the rate of loss of water. The chemical reaction hypothesis would leave us with a possible yet unlikely correlation, but most importantly, an untestable one. Quite apart from the details of the correlation, we, at least, would be surprised to find chemical reaction proceeding at rates near lo9 s-l in a d3 system of t2: configuration. The fact that our data do not "level off" earlier than they do at short lifetimes is itself an argument against the chemical reaction hypothesis. On the other hand, nothing in our data or our model precludes invoking chemical reaction to explain, more or less generally, the deviations in lifetimes at long times and large energy gaps. Acknowledgment. This work was supported in part by the National Science Foundation. Data analysis was made possible by a facility of the National Institutes of Health, Division of Research Resources. Registry No. 1, 29845-02-1; 2, 72982-93-5; 3, 24407-74-7; 4, 62106-77-8; 5, 85167-07-3; 6, 28101-89-5; 7, 25078-44-8; 8, 25125-60-4; 9, 85201-84-9; 10, 38985-25-0; 11, 38985-24-9; 12, 25078-41-5; 13, 22432-36-6; 14, 14873-01-9; 15, 85167-08-4; 16, 29830-76-0.
Examination of the Lamellar Phase of Aerosol OT/Water Using Pulsed Field Gradient Nuclear Magnetic Resonance P. T. Callaghan" and 0. Sodermant Department of Physics, University of British Columbia, Vancouver, V6T 2A6 Canada (Received: August 26, 1982; In Final Form: December 8, 1982)
The diffusion of water in randomly oriented lamellae of Aerosol OT (AOT)/watersolutions has been measured by using the pulsed field gradient nuclear magnetic resonance (PFG Nh4R) method. Three concentration regimes are identified and the transitions between them correspond with transitions in both the X-ray repeat distances and solution conductivity. By varying the diffusion observation interval we observe the displacement of water within a single domain or two and more domains. Diffusive barriers are indicated within each domain and a model is proposed which is consistent with both the pulsed field gradient NMR results and the X-ray and conductivity data.
Introduction Aerosol OT (bis(2-ethylhexyl) sodium sdfosuccinate) is an amphiphilic lipid possessing bulky side groups on the methylene chains. The structure of Aerosol OT and the phase diagram'-3 of the amphiphile/water systemare
* Address corremondence to this author at the following address: Department of Chemistry, Biochemistry, and Biophysics, Massey University, Palmerston North, New Zealand. Department of Physical Chemistry 11, Chemical Center, S-220 07 Lund, Sweden. 0022-365418312087-1737$01.50/0
shown in Figure 1. The phase behavior is unusual in that the lamellar mesophase covers a wide concentration and temperature regime and, despite having been studied by a variety of techniques, the properties of this particular phase have several curious features which have raised unanswered questions concerning the molecular organization. In particular, there exists conflicting evidence3,* (1) J. Rogers and P. A. Winsor, Nature (London), 216, 477 (1967). (2) P. A. Winsor, Chem. Rev., 68, 1 (1980). (3) P. A. Winsor, Mol. Cryst. Liq. Cryst., 12, 141 (1971).
0 1983 American Chemical Society
1738
Callaghan and Soderman
The Journal of Physical Chemisfty, Vol. 87, No. 10, 1983 a
0 II
c2H5
I
CH,CM,CH,CH,CH-CH, CH,CH2CH,CH,CH-CH,
0-C-CH, I
0--C-CHSOqNa J
II 0
1 c2’H5
120 -
g
.
Fundamental repeat distance
o
Conductivity
. 0
80-
*.
L
r ul
0 C
)
0
-
Q
A
v
..
40 -
0
0
0
0 1
I
10
20
30 Aerosol
I
50
40
OT
I
1
60
(‘10)
Figure 2. Variation of interlamellar repeat distance and conductivity for the lamellar phase of Aerosol OT/water. The data shown are taken from ref 5 and 6. The intermediate-concentrationregion gives a weak singleorder X-ray diffraction pattern for which the interlamellar spacing is approximately half that expected from onedimensional swelling. Ekwall et report some samples at around 40% Aerosol OT concentration with “normal” repeal distances and Fontel15reports finding erratic samples in the intermediate regime.
-
T
-
b
150 OC
100
50
Water Aerosol O T Figure 1. (a) Structure and (b) phase diagram of Aerosol OT/water taken from ref 1-3 and 8 D, lamellar liquid crystal; I, viscous isotropic cubic phase: F, reversed hexagonal phase; L, isotropic liquid solution.
as to the one-dimensionalnature of swelling over the entire concentration region of the lamellar phase although the most recent and precise measurements5 suggest that one-dimensional swelling, consistent with lamellar organization, is obeyed but with a central concentration regime where the X-ray repeat distances are anomalous. Furthermore, the electrical conductivity of the lamellar phase shows an order of magnitude increase over yet another range of concentration.6 Finally, both birefringence7and Raman scattering intensities8show significant changes at (4) P. Ekwall, L. Mandell, and K. Fontell, J. Colloid Interface Sci., 33, 215 (1970). (5) K. Fontell, J . Colloid Interface Sci., 44, 318 (1973). (6) I. Lundstrom and K. Fontell, Chem. Phys. Lipids, 15, 1 (1975). (7) J. Rogers and P. A. Winsor, J. Colloid Interface Sci., 30, 247 (1969).
certain concentration values within the lamellar phase, the latter results indicating a reorientation of some of the methylene chains in the region where X-ray anomalies have been observed. To date, no molecular arrangement has been proposed which can explain the confusing array of data concerning the lamellar phase of Aerosol OT/water. It was the purpose of this study to approach the problem with a technique sensitive to the lateral motion of the interlamellar water. We have used pulsed field gradient nuclear magnetic resonance (PFG NMR) to probe the magnitude, symmetry, and range dependence of the water molecule self-diffusion as a function of concentration within the lamellar phase and have found regimes of behavior with concentration boundaries which coincide with those for which transitions occur in X-ray, conductivity, and Raman data. On the basis of the diffusion measurements we are able to propose a model for the local molecular organization which is consistent with all three sets of measurements. Review of Lamellar Mesophase Properties. Figure 2 shows the relevant Aerosol OT/water X-ray repeat distances obtained by F ~ n t e l l .This ~ author observed that the uptake of water takes place under one-dimensional swelling at both high and low water contents and that the thickness of the amphiphilic bilayer remains constant at 20 while the mean interfacial area per polar head group is constant at 65 Hi2. The anomalous central region from 33% to 40.5% of Aerosol OT has only one weak reflection whereas two orders are apparent in the adjoining regions. The corresponding interplanar repeat distances are approximately half that obtained by interpolation from the adjoining regions and, while the apparent swelling remains one-dimensional albeit halved, the dimensions are completely inconsistent with the average bilayer area per head group obtained in the “well-behaved” regions. Indeed, there is nothing in the liquid crystalline morphology which suggests a sudden compression of the bilayer structure. A feature of the anomalous X-ray region was the scatter observed by Fontell among specimens made from the same (8) R. Faiman, I. Lundstrom, and K. Fontell, Chem. Phys. Lipids, 18, 73 (1977).
The Journal of Physical Chemistry, Vol. 87, No. 10, 1983
Lamellar Phase of Aerosol OT/Water
preparation. It is characteristic of this lipid/water system that samples show a slow equilibration at certain concentrations, an effect particularly apparent in the present PFG NMR study. Faiman et al.8 have observed Raman spectroscopic band variations within the lamellar phase, most noticeably around 33% and 50% Aerosol OT content. Such changes, as noted by these authors, are unique to this particular amphiphile. It is noteworthy that the concentrations associated with Raman intensity changes correspond with the transition to anomalous X-ray spacings and the point of highest conductivity, respectively. Significantly these changes occur for Raman lines from the methylene chains but not those due to the sulfate group or the water. The authors conclude that the changes occurring are due to reorganization or separation of chains, rather than a change in the organization of the water layers. Figure 2 also shows the electrical conductivity data of Lundstrom and Fontell.6 Fontell has suggested5that the remarkable increase observed between 45% and 60% Aerosol OT concentration could be due to a significant movement of the ions of the polar amphiphile surfaces and to the displacement as a whole of the aqueous layers. Puked Field Gradient NMR. PFG NMR uses the label of the nuclear Larmor frequencies to follow the diffusive motion of the molecular host. The experiment is sensitive to the spatial displacements of the nuclei because an applied magnetic field gradient imparts a spatial tag to the Larmor spectrum. The time scale of the diffusion measurement is determined by the separation of two gradient pulses applied respectively before and after the 180' refocusing rf pulse of a Hahn echo sequence. Irreversible decay of the nuclear magnetization due to spin-spin relaxation limits the time over which such measurements are possible and in practice confines the observation to molecules whose nuclei have, on a local molecular scale, a "liquidlike" isotropic reorientational behavior. The protons attached to the Aerosol OT of the lamellar bilayers experience a significant residual interproton dipolar interaction due to the nonisotropic molecular reorientation. This has the effect that their corresponding NMR free induction decay (fid) drops in a rapid, "solidlike" manner, making no contribution to the Hahn echo. In contrast, the protons of the water molecules have their dipolar interactions averaged to zero by a combination of molecular tumbling and rapid chemical exchange. In the case of the Aerosol OT/water system the entire contribution to the proton Hahn echo in the millisecond regime arises from the water protons. In following the diffusive motion of water, PFG NMR has the useful property that, by altering the spacing between the magnetic field gradient pulses, the root mean square (rms) distance traveled by the molecules can be determined as a function of observation time and in consequence the dimensions of diffusive barriers can be probed. Furthermore, because the technique is sensitive only to displacements in excess of lo00 A, the diffusion of water in a layer some 10-100 A thick appears ideally two-dimensionaland so the method presents an opportunity to examine the symmetry of the water organization.
Theory The pulsed field gradient technique has been described in detail else~here.~JOIf two gradient pulses of magnitude G, duration of 6, and separation A are applied respectively during the dephasing and rephasing periods (7) of the (9)E.0.Stejskal and J. E. Tanner, J. Chem. Phys., 42, 288 (1965). (10)E.0.Stejskal, J. Chem. Phys., 43, 3597 (1965).
1739
Hahn echo rf pulse sequence, 90~-~180y-~-echo, then the resulting echo attenuation may be written, in the short gradient pulse limit, as A(G,A) = I m P ( z , A )cos (y6Gz) dz -m
(1)
where z represents the nuclear spin displacement along the field direction and &,A) is the normalized probability that a spin is displaced by z after a time delay A. For an ensemble of uniformly distributed spins undergoing Brownian motion in three dimensions, &,A) has the Gaussian form &,A)
= T ' / ~ uexp(-z2/u2)
(2)
where a2 =
or
4DA
(34
-
z2 = 2DA
Thus, relabeling the echo attenuation, A(G,A), by the symbol R, one obtains
R = exp(-y262G2DA)
(4) An exact expression for 6 finite has been given by Stejskal and Tanner,g namely R = exp(-y2J2G2D(A- 6/3)) (5) so that A - 6/3 may be regarded as the effective diffusion time in the experiment. It should be noted that for all the experiments performed here 6 is sufficiently less than A that the approximate equation 1gives a good description. In practice 2 is required to be >(lo00 A)2 for significant attenuation to be observed in the Hahn echo. For water trapped in the space between the lamellar bilayers only two dimensions are available for displacements on this scale. Furthermore, the orientation of these free dimensions will be distributed randomly with respect to the laboratory field axis in a polycrystalline sample. The case of diffusion in a randomly oriented array of elements, each with an axis of cylindrical symmetry, has been treated previously." Consider a displacement (z ',y ',z') in the element coordinate system. Only the displacement along z , the laboratory field axis, can influence the PFG NMR experiment and for all azimuthal orientations
- -
+
z2 = z n cos2 8 7sin2 0 (64 where 8 is the polar angle between the z and z'axes. In general, we may write
-
z2 = 2Dll(A- 6/3) cos2 8
+ 2D,(A
-
6/3) sin2 8
(6b)
where Dlland D, are the self-diffusion coefficients applying to motion parallel and perpendicular to the element director axis, z'. In the case of water layers between lamellae, Dll= 0 and D, = D, the bulk self-diffusion coefficient of the water molecules. While the echo attenuations for spins residing in a given element will be Gaussian, the powder average will not. It is simple to show, by averaging the element orientations over all solid angle, that 1
R = exp(-kD,)j 0 exp(-k(D,, - D,)x2) dx
(7)
k = y262G2(A- 6/3)
(8)
where
(11) P. T.Callaghan,K. W. Jolley, and J. Lelievre, Biophys. J., 28,133 (1979).
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Callaghan and Soderman
The Journal of Physical Chemistty, Vol. 87, No. 10, 1983
For lamellar diffusion one obtains
R2 = exp(-kD)J
1
exp(kDx2)dx
(9)
while for capillary and unrestricted motion one obtains respectively
R1 =
J' exp(-kDx2) dx
(10)
R3 = exp(-kD) (11) in accordance with eq 5 . Of course, R3 corresponds to a Gaussian distribution of displacements for the entire ensemble which, in view of the Fourier transform nature of eq 1, leads to R3 being Gaussian in G, the field gradient magnitude. Equations 9-11 endow their spin echo attenuation plots ( R vs. G') with a curvature which provides a signature to the symmetry of the water organization. A lamellar phase can thus be recognized provided that the observed spin echo attenuation shape for the entrapped water follows eq 9. Diffusion between Domains. It should be noted that the derivation of eq 9 assumes that each spin is confined to an element of unique director orientation. This will indeed be the case provided that the rms displacements within the lamellae (4DA)'/2 are less than the lateral dimensions of the domains of parallel bilayers for which common director orientations can be ascribed. For water at 25 "C where D = 2.25 X m2 s-' this dictates that the domain size be the order of micrometers if A is in the millisecond regime. It is relevant to this study to treat the case where the experimental time scale is sufficient for each spin to diffuse over several domains, thus changing director orientation several times. At first sight it would appear that, because a three-dimensional random walk would result, eq 11 should now apply. In fact this is not so. The motion is still confined to two-dimensional elements but now along a curvilinear path. Consider the case of N such changes in element orientation along the path. This problem, in one-dimensional form, is well-known in polymer physics where a polymer chain diffuses in a curvilinear tube formed by the surrounding chains.12 We define a total rms curvilinear path length A comprised of N domain displacements of rms length A. For two-dimensional curvilinear diffusion A2 = 4DA (12) where A =
NX
For the case of N sufficiently large that the central limits theorem applies we may write the mean square end-to-end length of the path
-
r2 = NX2
(14)
= 4(DN-')A
(15)
z 2 = 2(y3DN-')A
(16)
-
For N large the array of displacements for the ensemble of spins over the elements, each with r oriented at 0 to the z axis, is once again Gaussian and we may write lim R 2 ( N ) = e~p(-k(2/~DN-'))
hi- =
(17)
Comparison with 3 and 11 shows that, while the echo (12) P. G. de Gennes, Macromolecules, 9, 596 (1976).
attenuation plot has the Gaussian behavior of three-dimensional diffusion, the effective diffusion coefficient is Thus, in the large N limit attenuated by a factor of 2/fl-'. Deff= 2/,DX(4DA)-'12
(18)
Note that throughout this discussion we use A as the observation time. For narrow but finite gradient pulses we can always substitute A - 6/3 to good approximation. For convenience though, we retain the infinitesimal 6 expressions. The case of N small but greater than 1 is difficult. to treat exactly but the approximate form may be gained intuitively. When N = 1we have eq 9, for which it should be noted that the limiting form of G small is exp(-2/3kD). The initial slope thus yields an "apparent threedimensional" self-diffusioncoefficient attenuated by 2 / 3 N - 1 . It is reasonable then to write for the case of N small 1
R2(N) = exp(-kDN-')i
0
exp(kDN-'x2) dx
(19)
Equation 19 has the correct limiting form for N large and for N = 1 and reflects the large-N property that the observed diffusion coefficient is inversely proportional to the number of domains sampled by each spin.
Experimental Section Nominally 1005% bis(2-ethylhexyl)sodium sulfosuccinate was obtained from BDH. Chemical analysis showed that some Na,SO, impurity was present. A small amount of ultrapure material was prepared and used to make a 30% w/w Aerosol OT/water sample. The PFG NMR result was the same as that obtained by using the BDH Aerosol OT without further purification. Samples were prepared by mixing with distilled water, sealed in glass vials, heated to 50 "C, and centrifuged back and forth to ensure mixing. Concentrations are quoted in Aerosol OT content w/w. Samples were left to equilibrate at 20 f 3 "C for at least 3 days before running and, in most cases, a check was made for equilibration behavior by remixing and leaving for 14 days before carrying out PFG NMR measurements. All PFG NMR experiments were carried out at 90 MHz with the Bruker SXP 4-100 NMR spectrometer in the University of British Columbia Physics Department. Temperature was controlled with a thermocouple/ hot air feedback system and all measurements were performed at 25.0 f 0.5 "C. The home-built pulsed field gradient probe incorporated a quadrupolar gradient coil of 0.194 T m-l A-l and the metal parts of the probe were cut in a comb pattern to reduce eddy gradients. Current pulses were generated from computer logic output using a circuit identical with that given in ref 13. The phase alternating technique was used for all echo accumulations and, to compensate for any slight phase distortions, the true echo amplitude was taken from the rms value of the two quadrature detection channels. All pulse conditions used in this study were applied to a pure water sample and gave the correct self-diffusion coefficient14within experimental errors (Figure 3). To test for the presence of free amphiphiles or the influence of any potentially slowly relaxing amphiphilic proton signal, we examined some samples made up with D 2 0 for a proton Hahn echo at the shortest 7 value used of 15 ms. No detectable signals were observed, indicating that the only contribution to the Hahn echo in the Aerosol OT/water samples came from the interlamellar water. I _ _
._____I_
I _ _ _
(13) P. T. Callaghan, C. M. Trotter, and K. W. Jolley, J . Magn. Reson , 37, 247 (1980). (14! R. Mills, J . Phys. Chem., 77, 68'7 (1973).
The Journal of Physical Chemistry, Vol. 87,No. IO, 1983 1741
Lamellar Phase of Aerosol OT/Water
o
0.5
1.0 i5 x109
*8%
Figure 3. Echo attenuation of the proton NMR signal from pure water at 25 O C under applied magnetic field gradient pulses. The attenuation obeys eq 5 exactly over a wide range of G, A, and 6 variation. All such data are plotted as log ( R ) vs. y26’G2(A 6/3).
-
An attempt was made to produce an oriented sample by
smearing a 25% mixture on thin glass plates and forming a stack which was subsequently compressed. The rapidly decaying amphiphilic proton fid showed negligible “magic angle” effect and only a factor of 2 difference in H20 diffusion rate was noted for the stack aligned perpendicular and parallel to the laboratory field direction. It was concluded that the Aerosol OT/water lamellar phase could not be formed with a unique director orientation by using the glass plate method. All the results quoted in this work refer to randomly oriented polycrystalline arrays.
Results Dependence of Diffusionon Aerosol OT Concentration. In this section we present spin echo attenuation data for a wide range of concentration with the diffusive observation time, A, fixed at 15 ms, the shortest practicable with the existing apparatus. Three distinct concentration regimes are apparent and we deal with them in turn. Low-Concentration Regime. At the lower concentrations used here, from 16% to 31% AOT content, the spin echo attenuation plots exhibit a marked curvature. The data for 20.1% are typical and are shown in Figure 4a along with the best fits using the powder distribution curves for one- and two-dimensional diffusion as well as that for unrestricted three-dimensional Brownian motion (eq 10, 9, and 11,respectively). It is immediately obvious that the two-dimensional powder model provides an excellent fit, consistent with a randomly oriented array of lamellae but the self-diffusion coefficient obtained has the remarkably low value of 5.3 (1)X 10-lom2 s-l, a factor of 4 below that of free water. For all samples in this low-concentration regime, the two-dimensionalpowder model works well and in each case yields a value for D in the vicinity of 5 X 10-lo m2 s-l. The significance of these low D values will be examined later but their lack of dependence on the interlamellar water layer thickness strongly indicates that the inhibition of diffusion arises from somethingother than the influence of the amphiphile surfaces. The equilibration of the samples in the low-concentration regime was relatively rapid, all reaching final equilibrium within 3 days with the exception of the 24.8% sample which equilibrated a few days later. The data for 20.1 % shown in Figure 4a demonstrate the indistinguishability of experiments performed after 3 days and 3 months of equilibration. Intermediate-ConcentrationRegime. The diffusive behavior of the interlamellar water shows a distinct change
Flgure 4. Echo attenuations for the interlamellar water protons in Aerosol OT/water under the gradient pulse conditions A = 15 ms and 6 = 3 ms for (a) 20.1 % (low-concentration regime), (b) 32.2% (intermediate), and (c) 49.2% (high). The equilibration is rapid except in the intermediate regime. The calculated lines R , , R,, R , are best fits to the data using eq 10, 9, and 11, respectively.
when the Aerosol OT content exceeds 31% . While the two-dimensional powder model still provides an excellent fit to the spin echo attenuation data for A = 15 ms, the self-diffusion coefficients are higher at -8 X 10-lom2 s-l. Figure 4b shows the data for 32% AOT content for two samples run respectively 3 and 14 days after mixing. A slower equilibration process was evident for these intermediate concentrations although the changes in reaching final equilibrium were generally small as seen in the 32% case for which the respective 3- and 14-day D values were 8.6 (3) X and 7.7 (4) X m2 s-l. In common with the X-ray experiments of Fontell we observed some erratic behavior in this concentration regime in that one sample, of 40.0% AOT concentration, had anomalously rapid water diffusion whereas its close “neighbor” at 41.1% was consistent with the rest of the intermediate-concentration group. High-Concentration Regime. A t 44.5% Aerosol OT content a dramatic change occurs in the water diffusion with a sharp transition to apparently three-dimensional behavior. The data for 49% are shown in Figure 4c and, while the unrestricted three-dimensional fit is not perfect, the spin echo attenuation is now almost Gaussian in the field gradient magnitude, indicating that the spins are no longer confined to single director orientations over the shortest available experimental time scale. The identity of the 3- and 14-day experiments evident in Figure 4c is common to all the samples with Aerosol OT concentration in excess of 45%, notwithstanding the fact that the spin echo attenuation behavior shows a continuous variation up to the very highest concentration used. The transition between intermediate- and high-concentration regimes is, however, clearly marked as is especially obvious in a “borderline” preparation of 44.5 % AOT content which shows an erratic switching in behavior from one regime to the other as demonstrated in Figure 5, where the spin echo attenuations observed span a range between two- and three-dimensional behavior in a reversible manner. In view of the imperfect fit given by the three-dimensional diffusion model in Figure 4c, it is difficult to accurately assign a local self-diffusion coefficient to the water. If the initial part of the attenuation plot is used, one obtains 8.6 (3) X m2 s-l and similar values are evident
1742
Caliaghan and Soderman
The Journal of Physical Chemistty, Vol. 87, No. 10, 1983
TABLE I 101oD,Q [Aerosol OT],7% 10'oD,Qm2 5-l m 2 s-l 4.0 ( 3 ) b 41.1 8.5 ( 4 ) b 44.5 9.7 ( 3 ) b 4.8 ( l ) b 5.3 (l)b 44.5 8 . 5 (3)' 4.3 ( 2 ) b 45.0 8 . 2 (3)' 4.2 ( 2 ) b 45.7 8 . 6 (3)' 5.6 ( 2 ) b 49.2 8 . 4 (3)' 4.0(3)b 53.1 7.0 (2)' 55.7 7.2 (3)' 4.5 ( 3 ) b 7.7 ( 4 ) b 59.2 7 . 0 ( 4 ) ' 12 ( l ) b 7.7 ( 4 ) b 65.4 6.8 ( 3 ) b 8.6 ( 4 ) b
[Aerosol OT], % 16.0 18.0 20.1 21.5 23.0 24.8 27.9 30.0 32.2 34.7 36.7
Obtained by using twoSelf-diffusion coefficient. dimensional fit (eq 9 ) . ' Obtained by using threedimensional fit (eq 11). (10' sm.>)
k
.
.
41
._ -.-:
140 K
lo'.?
x
o x
I"-.-,. ... .
,
7
0"
41
A
+
~
i?,(3)
. 1,(2) ~
5 O
s
o
n
Figure 6. Echo attenuation plots for higher concentrations in the high-concentration regime. A gradual return to two-dimensional curvature is apparent and this correlates with a return of the conductivity to low values.
up to around 60% Aerosol OT content. Owing to the model uncertainties in obtaining these coefficients, it is unwise to attach much significance to their similarity with those obtained by using the two-dimensional powder model in the medium-concentration regime. In fact the high concentrations display a gradual transition back to twodimensional water movement above 60% Aerosol OT content, a feature which correlates strongly with the conductivity behavior. This change is shown in Figure 6, where the 59% and 65% samples demonstrate the return of two-dimensionalspin echo attenuation curvature as the water content decreases. Because we use the criterion of a sharp transition to specify a diffusive regime for the interlamellar water, it seems reasonable to group together all the data from 45% to the highest Aerosol OT content studied. The A = 15 ms data so far discussed are summarized in Table I. Leaving aside for the moment the question of how the diffusive transitions correlate with the data from other measurements, we turn now to the use of the PFG NMR method to probe the observed water diffusion as a function of measurement time, A. Dependence of Water Diffusion on Observation Range. As pointed out in the Theory section of this paper, the ability to vary the PFG NMR parameter, A, enables one to probe the numbers of domains traversed by the water molecules over the experimental time scale. The ability in practice to increase A depends on the available Hahn
Flgure 7. Echo attenuation plots for a 24.8% sample of Aerosol OT/water showing the dependence of diffusive behavior as the effective observatlon tlme (A - 6/3)is varied over a wide range. For spins confined to one domain over the lifetime of the measurement the data should be coincident in accordance with eq 9. The theoretical curves for the cases where spins sample successively 1, 2, and then higher numbers of domains (eq 19) are shown with D values obtained by fitting to the A = 15 ms, 6 = 3 ms data, the case N = 1 (eq 9). (a) Result for equilibrated sample; (b) result for a sample with 3 days of equilibration.
echo amplitude at long 7 values and hence on the waterproton T2. In the Aerosol OT/water samples the water T2values progressively decreased with increasing Aerosol OT concentration, so much so that, for the high-concentration samples, spin echoes could not practically be observed for T values in excess of a few tens of milliseconds. As a consequence of the ease of covering a wide range of T and A values for the low-concentration samples, and because of the importance of elucidating the barriers to diffusion which result in anomalously low D values, we have chosen to carry out detailed time-scale measurements on a 25% sample in the middle of the low-concentration regime. Figure 7a summarizes the echo attenuation data for eight magnitudes of A from 15 to 350 ms for the 24.8% sample after reaching equilibrium. The data are plotted as log (echo attenuation, R), vs. the parameter k which appears in the arguments for eq 9 and 19. For N fixed the data should coincide and, while that is indeed the case from A = 15 to A = 53 ms, a gradual change is apparent between 53 and 150 ms to a new "band" where the data once again merge. Beyond A = 200 ms the data appear to move to
Lamellar Phase of Aerosol OT/Water
higher curves. The discrete nature of these bands is remarkable and, while the theory is too primitive to give an exact description, we are strongly inclined to draw the conclusion that the spins traverse only a very small number of domains in these experiments. Indeed the coincidence of the data from 15 to 53 ms, Le., over a factor of 4 in A and hence 2 in the curvilinear rms displacement, can only be consistent with all the spins each residing in a single domain over this time for, if N were larger than 1,a doubling of the total rms displacement would clearly increase the number of domains sampled. As a check on this hypothesis we show the curves for N = 1,2, and 3 using eq 19 and taking our D value by fitting the case of N = 1to the A = 15 ms experiment. The evident agreement with the data must to a large extent be fortuitous in view of the simplistic nature of the theory for N > 1 and the imperfection of the fit to the exact N = 1 equation when k is very large. Nonetheless, the results suggest a scenario where the spins successively sample, on average, one, two, and then greater numbers of domains as A is increased. This particular sample (24.8%) was a little slower to equilibrate than the others of the low-concentration regime and a time-scale experiment was performed before final equilibration was achieved. The results are shown in Figure 7b and are remarkably similar except that the D values for the first domain confinement band is higher than that obtained from Figure 7a, indicating that fewer diffusive barriers have formed. From the time-scale experiments we can reasonably conclude that the A = 15 ms measurements occur over a time sufficiently short that practically all water molecules diffuse within lamellar layers with unique director orientation. We may also derive the average domain size for the 24.8% sample from the crossover time A when the single-domain criterion breaks down, namely, (40A)1/2. For breakdown at 50 ms we obtain an average domain size of 10 pm. The barriers to diffusion which result in highly attenuated D values must exist over a distance much smaller than the domain sizes. It is clear that the key to understanding the unusual properties of the lamellar phase of Aerosol OT/water lies in the details of the obstacles to water movement parallel to the amphiphile bilayers.
-
Hypothesis We now look for a relationship between the X-ray, conductivity, Raman, and water self-diffusion results and tentatively suggest an amphiphile organization which is consistent with them all. Figure 8 shows a superposition of the short-time-scale PFG NMR results, the X-ray interlamellar repeat distances, and the conductivity data as a function of Aerosol OT concentration. The three regimes of diffusive behavior closely correspond with the normal/anomalous/normal X-ray regimes and, in addition, the transition to high conductivity, and then back to low as Aerosol OT concentration is increased corresponds with the sudden change to three-dimensionrd diffusion and then the return of two-dimensional behavior. The coincidence of the various boundaries is not, of course, perfect. Nonetheless, the correspondence is sufficiently close that a one-to-one assignment can reasonably be made. It was alluded to previously that the independence of D on water layer thickness in the low Aerosol OT concentration regime precludes any inhibition of water diffusion due to viscosity changes caused by the polar amphiphile surfaces. This is supported by neutron scattering experiments on thin water layers in :aeolites15where ap(15) S. Olejnik and J. W. White, Nature (London),Phys. Sci., 236, 15 (1972).
The Journal of Physical Chemistry, Vol. 87,No.
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Fundamental repea: d s t a r x e
I
0 0 0
.. t to
20
30 Aerosol
50
40
OT
60
O'O)
Flgure 8. Superposition of the X-ray, conductivity, and selfdiffusion behavior for the lamellar phase of Aerosol OT/water as the amphiphile concentration is varied. A correspondence in behavioral regimes is apparent. Selfdiffusion coefficients are obtained by using the twoor three-dimensional models (eq 9 and 11) as indicated.
preciable surface influences on water diffusion are noticed only for layer thicknesses of less than 25 A whereas, in all except the highest concentration samples used here, the water layers are well in excess of this, namely, from 50 to 120 8, in the low-concentration regime. A recent study of the water interior of Aerosol OT inverted micelles by fluorescence polarization decay16 shows that the water viscosity drops to its bulk value beyond 20 A from the polar surface but is significantly increased within 10 A. This supports the view that some other mechanism exists to inhibit water diffusion parallel to the bilayer surfaces within the domains. A clue to the possible nature of these barriers is given by the bulky chain structure of Aerosol OT and the ease with which it forms small inverted micelles in nonpolar solvents and a reversed hexagonal phase for Aerosol OT/water at much lower amphiphile concentration than, for example, phospholipids. The ethyl side lobes tend to favor a natural packing curvature with the polar heads facing inward. This effect enables inverted micelle radii as small as 25 A.ls It is reasonable then to picture a lamellar structure for the Aerosol OT/water system in which some of the amphiphiles curve across the water layers to form, on a local scale, an admixed region of "hexagonal" phase. This is depicted in Figure 9a. The curved barriers need not extend far or contain any more than a small fraction of the amphiphiles for the water diffusion to be severely reduced. Thus, one-dimensional swelling would still be observed for such a molecular organization. The average distance between the obstacles must however be shorter than the rms displacement of the water molecules in the shortest time scale PFG NMR measurement, that is, less than a few micrometers. It is important to draw a sharp distinction between the neutron scattering and PFG NMR techniques in their determination of self-diffusion coefficients. Neutron scattering measures molecular displacements over a distance scale of the order of nanometers, some 3 or so orders of magnitude less than PFG NMR, and, in the present context, this method would be expected to probe the water molecule diffusion over a scale much shorter than the separation distance of the barriers proposed in the present model. One would therefore expect that neutron scattering would yield a water diffusion coefficient close to the unrestricted value. (16) P. E. Zinsli, J.Phys. Chem., 83, 3223 (1979).
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b)
Figure 9. Proposed amphiphile organization for (a) low-concentration and (b) intermediate-concentration regimes in Aerosol OTIwater.
The limit to the formation of such obstacles will be the degree of curvature which the chain packing can withstand. Given the reluctance of Aerosol OT to form inverted micelles of less than 25 A, we may surmise that the critical water layer thickness where such structures will break up is about 50 A. Allowing for the bilayer thickness of 20 A, we might expect this to occur for a repeat distance of 70 A, almost exactly where the transition to anomalous X-ray spacings and more rapid two-dimensional water diffusion is indeed observed. Supposing that some of these trans water layer links are formed in the mixing of the intermediate-concentration regime samples only to subsequently break apart as the system approaches a uniform repeat distance, we might imagine that the free amphiphiles so released could gather within the water gap to form, locally, a disk of second bilayer as shown in Figure 9b. In consequence the transverse area of the obstacles to diffusion will be significantly reduced and to this extent the model is supported by the present study. An explanation for the anomalous X-ray data is also immediately obvious. With the trans water “bridges“ removed, the bilayers will have greater surface “waviness”except in the small regions where the second, interlamellar bilayer disks exist. Low-angle X-ray scattering is very sensitive to small fluctuations in repeat distance because the wavelength
Callaghan and Soderman
(around 1.5 8,) is so much less than the interplanar spacing. In the intermediate-concentration region we would therefore expect the X-ray orders from the bulk of the bilayer area to be smeared out and the low-angle X-ray scattering will be dominated by the more rigid regions where a repeat distance of exactly one-half the true average spacing prevails. A weak X-ray reflection at twice the angular separation of the expected value will result, in exact accord with the observation of Fontell. Of course, the limit to the formation of extra bilayer pockets is reached once the water layer spacings is less than 20 A, the average bilayer thickness, so that a total repeat distance of 40 8, should see the return of a “normal” arrangement. The restoration of the X-ray data to normal repeat spacings a t about 43% Aerosol OT concentration is entirely consistent with this picture. We now address the region where the conductivity data show a marked increase and the water self-diffusion exhibits a sudden change to three-dimensional behavior. The suggestion by Fontell that entire layer movement may be occurring is convincing. A likely explanation is that domain walls are in continual rapid reorganization, thus enabling water molecules to diffuse in a three-dimensional random walk among lamellar elements of different director orientation. The return at higher concentrations to twodimensional diffusion occurs at the same region where the conductivity drops and this enhances the notion that these effects are related to the same molecular phenomena. The mechanism for domain wall movement and its cessation a t high concentrations remains obscure. At least part of the reason for the inhibition of this effect may have to do with the rigidity of the water layer once the thickness reduces to -10 A. Other peculiarities of the lamellar phase of Aerosol OT/water can be understood. Clearly the Raman behavior with the observation of changes in the methylene chain scattering intensities in the concentration vicinity of the proposed local reorganization is consistent with the model. The slow equilibration behavior of the low- and especially the intermediate-concentration regime can be pictured in terms of the formation and breaking up of the crosswater-layer amphiphile structures. It should be emphasized that the model pictured in Figure 9 is highly speculative. It does however have the virtue of going some way toward explaining results which to date have been incomprehensible. In fact, a rather similar proposal of curved cross-water-layer amphiphile links has been made very recently by Van Venetie and Verklej17 for cardiolipin/phosphatidylcholine mixtures where freeze-fracture experiments show a slow transition from lamellar to reversed hexagonal phases. In the present case the pulsed field gradient NMR study has shown that the method offers a powerful tool in the study of the structural organization in liquid crystal systems.
Acknowledgment. We are indebted to Professor Myer Bloom for supporting this work and to Dr. Alex Mackay for valuable technical advice. We also acknowledge useful discussions with Dr. Pieter Cullis. Registry No. AOT, 577-11-7; H,O, 7732-18-5. (17) R. Van Venetie and A. J. Verkleij, Biochim. Biophys. Acta, 645, 262 (1981).
