J . Chem. Soc., Furaday Trans. I, 1989, 85(4), 917-928 3 4 5 6 7 8 3' 4' 5' 6' 7' 8' IH and 13C Longitudinal and Transverse Relaxation in Aerosol OT in Methanol Solution and Inverted Microemulsions in Benzene Frank Heatley Department of Chemistry, University of Manchester, Manchester MI3 9PL 'H and 13C longitudinal and transverse relaxation in inverted micro- emulsions of Aerosol OT (AOT) in deuterated benzene has been studied as a function of composition and resonance frequency. Except at high AOT concentrations (> 2 mol AOT per kg C6D6) and low water content [AOT/ H,O mole ratio ( R ) < 21 the frequency dependence of T,, T, and the nuclear Overhauser effects can be satisfactorily interpreted in terms of the two-step correlation function of Wennerstrom et al. (H. Wennerstrom, B.Lindman, 0. Soderman, T. Drakenberg and J. B. Rosenholm, J. Am. Chem. Soc., 1979, 101, 6860). The slow correlation time decreases as the water content increases up to R x 3 and thereafter is constant. This behaviour suggests that the slow process is loss of AOT from the aggregate into the hydrocarbon phase. Relaxation of AOT in dilute methanol solution has been used to determine the relaxation mechanism. 917918 Relaxation in Aerosol OT Inverted microemulsions of Aerosol OT [AOT, sodium bis(2-ethylhexy1)sulpho- succinate, 11 in p-xylene have been studied using 13C & and NOE data.8 For the head- group nuclei C-1 and C-1', z, and 2 , were of the order of 10-l' and s, respectively, while S varied from ca. 0.8 at an H,O/AOT mole ratio (R) of 3.8, to ca.0.6 at an R value of 34. However, the C-1' linewidth (i.e. T,) was not consistent with the motional parameters extracted from the and NOE data, and a third process slower than z, was postulated. In view of the uncertainties associated with determining from the linewidths of lH decoupled spectra, it was thought appropriate to test the validity of eqn (1) more reliably by combining 13C and NOE data with the 13C T, data determined using the spin-echo technique. This paper reports such an investigation focussing on the AOT head-group in C,D, microemulsions. In addition 'H & and T, relaxation has been investigated for comparison with 13C relaxation, and relaxation in unaggregated AOT in methanol has been studied in order to obtain a comparison with unrestricted motion. Experiment a1 'H Data at 80 (TJ, 300 (q, T,) and 500 MHz (q) were obtained using Bruker Spectrospin WP-80, AC-300E and AM-500 spectrometers, respectively. The WP-80 and AC-300E instruments also provided 13C data at 20.1 (q, NOE) and 75.5 MHz (&, T,, NOE), respectively.T, measurements were performed using the (~-2-n/2) inversion recovery sequence, and T, measurements using the Carr-Purcell-Meiboom-Gill (CPMG) spin-echo sequence with an interval of 1 ms between z pulses. 'H decoupling was not applied during the 13C experiments at 75.5 MHz in order to avoid heating problems with the large decoupling fields necessary. l4 Nuclear Overhauser enhancements were measured using the gated decoupling method with relaxation intervals of at least 5 T,, for the enhanced and 8 T,, for the unenhanced spectrum.AOT was obtained from Sigma Chemical Company, St. Louis, U.S.A. and was used without further purification. [This procedure is justified in ref. (1 5).] Deuteriated solvents were obtained from CEA, France, and were used as received. Solutions were not degassed; trial degassing of a few samples showed that the AOT relaxation was essentially unaffected. Relaxation Theory T,, & and the NOE depend on a spectral density function J(w), which is related to the correlation function (1) by (1 -s")z, 9 2 , G(z)exp(imz)dz = +- 1 +m22,2 1 +m2g I3C Relaxation For a 13CH, group where the 13C is relaxed entirely by dipole4ipole interaction with the attached protons, the 'H-decoupled and the NOE are expressed in terms of the spectral density for motion of the C-H bond, JCH(w), by where Q = (3/10) o10/4~)2y,2yc2~2/rcH6.yx is the magnetogyric ratio and w, is the resonance frequency of nucleus X. rCH is the C-H bond length, taken to be 109 pm. TheF. Heatley 919 NOE is the ratio of the enhanced and unenhanced l3C intensities. For the CH, groups, eqn (3) and (4) do not take into account cross-correlation spectral densities which appear in rigorous density-matrix relaxation theory.16 However, eqn (3) does apply to the initial relaxation rate, while cross-correlation effects on the NOE are small compared to experimental errors and the limits of fitting data to eqn (2). Transverse 13C relaxation measurements in this work were performed without ‘H decoupling. In CH, groups, cross-correlation terms manifest themselves in different relaxation rates for the outer and centre lines of the 13C triplet.” However, they can be eliminated by taking the average of the two rates. For a 13CH, group, the average transverse relaxation time i d 4 ‘H Relaxation The H-1 proton (X) and H-1’ protons (A and B) form a coupled relaxation system. Although in C,D, microemulsions A and B are strongly spin-spin coupled,15 conventional first-order coupled longitudinal relaxation theory1* has been applied. This is felt to be acceptable because the AB multiplet is so broadened that only the total AB intensity was observable, and relaxation of this signal is dominated by the strong AB geminal interaction.The time dependence of the intensity of proton i, Si, is given by dS, - = - (& - sg) (p* + 2 Pij) - 2 Oij(s, - Si”) d t j i where The superscript O indicates equilibrium values, and the parameter p* represents relaxation by other mechanisms such as intra- and inter-molecular interactions with other protons.For the purpose of calculating relaxation times, since only the total AB intensity, designated SAB, is measured, it is convenient to combine the three equations governing SA, % and ,!& into two equations expressing the evolution of SAR and J;(. Eqn (7a) and (7b) give biexponential relaxation for SAB and &. In practice, the recovery of SAB was effectively exponential, although the recovery of S;E was in some systems distinctly not so. Further details are described in the Results section below. To calculate NOE values correctly, the three equations (6) were retained. The resulting expressions are AX + 0nx XA+PXB+P* NOEx(AB) = 1 +920 Relaxation in Aerosol OT Table 1.'H and 13C relaxation data at 22 "C for AOT in CD30Da concentrationb frequency parameter nucleus /MHz 0.24 2.1 T,, c- 1 75.5 c-1' 75.5 NOE C-1 75.5 c-1' 75.5 T H H-1' 300 H- 1 300 T , H H-1' 80 T2H H- 1 ' 300 0.77 0.22 0.44 0.13 2.94 1.96 2.93 2.06 0.55 2.0 0.52 0.52 a Relaxation times in s, uncertainty+_ 5 %. mol (kg CD,OD)-l. NOEJj} is the ratio of the i intensity with j saturated, relative to the unperturbed intensity. For lH transverse relaxation, only the AB peak has been studied. Because of the dominance of the geminal AB interaction TfB is given to good approximation by the expression for a pair of protons with additional contributions from other protons: where T,* represents external contributions.Results CD,OD Solutions The purpose in studying relaxation in methanol solution is to examine a system of unassociated molecules with all correlation times meeting the extreme-narrowing limit (W;Z: 6 1). In this regime is independent of resonance frequency and equal to q, and l3C(lH)NOE values for entirely dipolar relaxation with protons reach their maximum of 2.988. By these criteria, solutions of AOT in CD,OD containing 0.24 mol (kg CD, OD)-' met the desired objective (table 1). At a concentration of 2.1 mol (kg CD,OD)-l, however, the 13C values are much lower and the 13C NOE values are significantly less than maximal. Evidently, aggregation can occur in methanol as well as in water and hydrocarbons, although at a much higher concentration.Data are analysed only for the former solution. All relaxation curves were exponential within experimental error over a decade recovery. values for C-1 and C-1' is not quite 2, as expected for isotropic rotation. From eqn (2) and (3), setting S2 = 0, we obtain effective correlation times of 4.8 x lo-" and 5.5 x s for C-1 and C-l', respectively. It has been shown15 that AOT exists predominantly in conformation (111) in fig. 1 . Assuming tetrahedral bond angles and exact staggering, and defining A to be the H-1' trans to H-1, we calculate r,, = 178 pm, rA, = 306 pm and rBx = 249 pm. Eqn (7a) and The ratio of the 13CF. Heatley 92 1 SO” s 0, CO, R Fig. 1. Head-group conformations of AOT.(7b) with p* = 0 then yield TAB = 0.66 s and T,, = 4.74 s, compared with experimental values of 0.55 f 0.02 s and 2.0 0.1 s, respectively. The discrepancy between the calculated and experimental values, particularly Tx, is outside reasonable uncertainties in the internuclear distances and correlation times, and indicates a significant contribution to relaxation from sources other than interaction between H-1 and H-1’. These ‘ external ’ interactions are either intermolecular (including dissolved oxygen) or intramolecular with protons in the alkyl chains. In both cases, the H-1 and H-1’ signals are probably essentially equally affected, but the relative effect on H-1’ is less than on H-1 because of the comparatively short geminal AB distance. If p* is set equal to (pAX +psx + oAx + o,,), the calculated relaxation times are TAB = 0.60 s and Tx = 2.2 S, in good agreement with experiment.To support this analysis, the NOE of H-1 on irradiation of H-1’ was examined. The experimental NOE was 0.23f0.03, in good agreement with the value 0.2 calculated using this value of p*. Thus it appears that H-1 is relaxed as effectively by ‘external’ interactions as by interactions with H-1’. In the analysis of lH relaxation in microemulsions, p* was therefore incorporated using the same relationship p* = pAX +pBx + oAX + oBx. To obtain the same correction for relaxation of the H- 1’ protons, 1/T: in eqn (9) was set equal to ((IAx KAX + Q, KBx). The effect of these ‘external’ contributions on H-1’ relaxation is small. ‘’C Relaxation in Microemuisions Relaxation of C-1 and C-1’ in microemulsions of varying composition was studied at 307 K.Results are given in table 2. It is found that T, and the NOE depend on the resonance frequency, that T, is considerably less than and that the NOE is less than maximum. The participation of a slow motion (w:zt 2 1) in the relaxation process is therefore indicated. Note that if C-1 and C-1’ experienced identical motions, the relaxation times of C-1 should be twice those of C-l’, In fact the difference is less than a factor of 2. Qualitatively, the increase in and the NOE with increasing water content922 Relaxation in Aerosol OT Table 2. 13C relaxation data at 307 K in AOT microemulsions in C,D,* frequency/MHz 75.5 20.1 concentrationb Rc nucleus Tl T, NOE NOE 2.19 0.37 C-1 c-1’ c-1’ 2.1 1 2.9 C-1 c-1’ 2.1 1 11.0 c-1 c-1’ 0.222 0.98 C-1 c-1’ 0.2 14 12.1 c-1 c-1’ 2.16 0.78 C-1 0.220 0.129 0.187 0.093 0.198 0.120 0.306 0.169 0.164 0.102 0.288 0.163 0.043 0.027 0.07 1 0.042 0.120 0.077 0.182 0.122 0.112 0.071 0.23 1 0.141 1.27 1.31 1.38 1.42 1.73 1.80 2.3 1 2.37 1 S O 1.62 2.37 2.43 0.046 1.58 0.030 1.69 0.047 1.77 0.031 1.79 0.073 2.25 0.043 2.31 0.147 2.46 0.087 2.59 0.065 2.42 0.043 2.53 0.198 2.49 0.125 2.51 a Relaxation times in s, uncertainty f 5 %.mol (kg C6D6)-I. H,O/AOT molar ratio. and decreasing concentration indicates an increasing contribution from the faster motions. In order to test the validity of eqn (2), data were first analysed for those solutions where values were available at two resonance frequencies.The data set thus comprised five items: at 20.1 and 75.5 MHz, T, at 75.5 MHz and the NOE at 20.1 and 75.5 MHz. A computer search was performed for the values of S2, z, and z, giving the best fit to this data set, the best fit being defined as the minimum value of the quantity 2, given T,exptl is the experimental and the calculated value of parameter y. Data for carbons C-1 and C-l’-were analysed independently, with the results shown in table 3. With the exception of sample 1, the data are represented within the experimental error of ca. 5 % by eqn (2). It is not always necessary to invoke8 a slower process to reconcile and T,. It is difficult to quote an uncertainty in the motional parameters because they are highly covariant, as was found in a study of relaxation in micellar sodium 0ctan0ate.l~ Taking as an example C-1 of the system containing 2.16 mol AOT (kg C,D,)-’ and R = 0.78, if two of the three motional parameters are kept fixed at their best-fit values and only the third allowed to vary, the ranges giving an r.m.s.difference of 5 % or less are S2 = 0.66-0.76, z, = 3.1 to 3.9 ns and z, = 36 to 170 ps. However, if for example z, and z, are readjusted to give the best-fit for S2 = 0.66, their best-fit values are z, = 3.7 ns and z, = 110 ps with an r.m.s. difference of 4.1 YO. For S2 = 0.76 the best-fit parameters are z, = 3.3 ns and z, = 58 ps with an r.m.s. difference of 4.5%. In general, the trend on increasing water content is a large decrease in the order parameter, together with a smaller decrease in 2,.z, appears to increase slightly, but the effect is marginal. For both C-1 and C-1’ in the sample with R = 0.37, the r.m.s. deviation for the five-F. Heatley 923 Table 3. Best-fit motional parameters [eqn (2)] from the 13C relaxation data in table 2 concentra- tion‘ R‘ nucleus S2 zJns q/ps dev.O 2.19 0.37 C-1 c-1’ 2.16 0.78 C-1 c-1’ 2.11 2.9 C-1 c-1’ 2.11 11.2 c - 1 c-1’ 0.222 0.98 C-1 c-1’ 0.214 12.1 C-1 c-1’ 0.79 5.6 0.63 5.4 0.70 3.5 0.61 3.1 0.46 2.3 0.39 2.1 0.15 3.4 0.14 2.2 0.66 1.6 0.50 1.5 0.09 2.6 0.065 2.4 85 8.9 54 11.6 90 1.8 87 1.7 130 2.7 93 4.4 140 6.4 110 4.4 84 2.0 78 3.4 150 4.3 130 5.1 a See table 2. and experimental parameters. R.m.s. percentage difference between calculated item data set is significantly larger than the experimental error of ca.5 %, suggesting that eqn (2) is inaccurate in this case. In order to examine the form of deficiency, a four-item data set of and NOE values only was fitted, yielding the following parameters for C-1 (C-1’): S2 = 0.70(0.55), z, = 4.2 (3.7) ns, z, = 33 (23) ps, r.m.s. percentage deviation = 0.8 (1.3). With these motional parameters, the expected T, values are 65 ms for C-1 and 46 ms for C-1’. Both of these are some 50 O h larger than the experimental values. The same discrepancy was noted by Carnali et aL8 for a more concentrated [6.08 mol (kg solvent)-’] solution of AOT in p-xylene using & estimated from linewidths. ‘H Relaxation in AOT in Microemulsions The most reliable ‘H relaxation data are those for the H- 1’ protons, since their relaxation is dominated by their mutual geminal interaction. This leads to two important advantages in interpreting the data.First the magnitude of the dipolar interactions is known more accurately than for H-1, since it depends less on such variables as the dihedral angle in the head-group conformation and the contribution from intermolecular interactions. Secondly H-1’ relaxation is exponential over more than a decade and can therefore be characterised by a time constant. In contrast, for H-1 it was found that the spin-lattice relaxation recovery curves were frequently non-exponential, particularly in those systems of high-order parameter. The illustration of this behaviour in fig. 2 shows that the instantaneous relaxation ‘ time’ decreases as the relaxation proceeds.This can be understood in terms of the coupled equations (7a) and (7b). Immediately after the n pulse, which inverts both H-1 and H-1’, the relaxation ‘time’ of H-1 (i.e. &) is (pXA +pXB +p* +oAX +oBx). Because the H-1’ protons relax some three times more quickly than H-1, in the later stages of H-1 relaxation, the condition SAB z SABo holds, and the relaxation ‘time’ of H-1 is (pXA+pXH+p*). In the less mobile systems the correlation times are such that +Jj(wi - w j ) > 24(wi + mi). Hence oAX and oBX are negative, and the initial relaxation ‘time’ is less than the final relaxation ‘time’. The same phenomenon leads to ‘H NOE values of less than unity. Table 4 gives data for H- 1’ relaxation in a number of microemulsion systems. Because924 Relaxation in Aerosol OT “r--- 2 P 0 0.5 1.0 tlS 5 Fig.2. Inversion recovery curve of H-1 in a microemulsion containing 2.16mol (AOT) (kg C6D6)-l, R = 0.78, at 296 K and 300 MHz. The line is for eye guidance only. Go - &(t) is in arbitrary units. Table 4. H-1’ relaxation data in AOT microemulsions in C6D6a frequency/ MHz 500 300 80 concentra- tionb R b T/K T T T, T, 2.19 2.16 2.1 1 2.11 0.206 0.222 0.2 12 0.214 0.025 0.021 0.37 296 307 0.78 296 307 2.9 296 307 11.2 296 307 0.18 296 0.98 296 2.5 296 12.1 296 1.0 296 10.9 296 1.37 0.777 0.736 1.10 0.655 0.544 0.682 0.404 0.320 0.480 0.275 0.297 0.512 0.907 0.490 0.310 0.511 0.323 0.420 0.493 0.300 0.019 0.025 0.036 0.037 0.051 0.085 0.086 0.133 0.040 0.054 0.070 0.118 0.061 0.116 ~~ 0.140 0.109 0.107 0.093 0.083 0.087 0.105 0.140 0.076 0.077 0.079 0.122 0.074 0.1 14 a Relaxation times are in s, uncertainty & 5 YO.See table 2.F. Heatley 925 Table 5. Best-fit correlation parameters [eqn (2)] from the H-1' relaxation data in table 4" concen tra- tion' R b T/K S 2 t,/ns t,/ps dev.c 2.19 2.16 2.1 1 2.1 1 0.206 0.222 0.212 0.2 14 0.025 0.021 0.37 0.78 2.9 11.2 0.18 0.98 2.5 12.1 1 .o 10.9 296 0.76 6.6 307 0.80 4.8 296 0.69 3.7 307 0.71 3.5 296 0.61 2.6 307 0.48 1.6 296 0.34 2.2 307 0.20 1.8 296 0.79 2.8 296 0.71 2.3 296 0.59 1.8 296 0.31 1.6 296 0.68 1.9 296 0.32 1.5 190 1.3 190 98 1.5 160 180 2.2 150 180 3.6 130 220 110 1.3 150 110 4.4 130 120 4.6 a Where an r.m.s. deviation is entered, four relaxation times were fitted. For the other systems, three relaxation times were fitted exactly.See table 2. See table 3. of the much greater sensitivity of 'H n.m.r. compared to 13C, it was possible to investigate a wider range of systems, especially those of low AOT concentration. Qualitatively the 'H relaxation behaviour parallels that of 13C in that the AOT motion becomes less restricted as the water/AOT ratio increases. The 'H results also show that for a given water/AOT ratio the AOT motion becomes slightly less restricted as the concentration decreases. For some of the systems in table 3, four independent relaxation times were available, and an extended test of eqn (2) was possible using the same best-fit criterion as for the 13C analysis. The derived correlation parameters are given in table 5, with the r.m.s. deviation, The quality of the simulation is within experimental error.For the other systems, only three relaxation times were available which can be fitted exactly by a unique set of the three correlation parameters. The good quality of the overdetermined four-item fits justifies accepting these unchecked three-item fit parameters as reasonably accurate. This analysis was restricted to H-1' relaxation data because of the problems associated with H- 1 mentioned above. The numerical results confirm the qualitative conclusions described above. If the molecular dynamics can be represented as ' fast ' and ' slow ' processes, the values of zf and z, from lH and 13C relaxation should be reasonably consistent. This is so for those systems appearing in both tables 3 and 5, within the limits of the fitting procedure.Some variation in S 2 may be expected because S 2 depends on the range of orientations allowed to an internuclear vector by the fast process. S 2 for the H-1' geminal interaction tends to be larger than for the C-H interactions, particularly at the higher values of R. Comparing systems in table 5 with the same R value but different AOT concentrations, it appears that when R > 2, z, is independent of concentration, but at lower values of R, z, increases with increasing AOT concentration. z, is effectively independent of composition.926 Relaxation in Aerosol OT Table 6. Comparison of experimental and simulated (using parameters in table 5) values of relaxation parameters involving HXa T"ff NOE,.{W NOEX{ AB} 1x concentra- tionb Rb exptl calcd exptl calcd exptl calcd 2.19 0.37 0.69 0.67 0.43 0.22 1 .o 1.36 2.16 0.78 0.78 0.82 0.51 0.48 0.95 1.59 2.1 1 2.9 0.93 0.931 0.67 0.64 0.85 1.22 2.11 11.2 0.997 0.986 0.913 0.903 0.95 1.04 0.222 0.98 0.69 0.58 a All values are at 296 K and 300 MHz.See table 2. As a further check on the validity of this interpretation of the 'H relaxation, calculated values of relaxation parameters involving the H-1 proton have been compared with experiment. These parameters were NOE,,{X}, NOE,{AB} and an X longitudinal 'relaxation time'. Because of the non-exponential nature of the X longitudinal relaxation described above, a single relaxation time cannot be defined, nor is it easy to measure the initial or final slopes. For the purposes of this exercise, an effective 'relaxation time', Tf! was defined as the time constant obtained from the slope of a linear least-squares fit to a log(time) plot for the X recovery over a period of time equal to the AB relaxation time.This quantity is easily obtained experimentally and theoretically. The comparison is presented in table 6. There is excellent agreement between the calculated and experimental values of NOE,,{X), a parameter which depends principally on the relative A-B, A-X and B-X distances. It therefore appears that the geometrical assumptions are reasonable and that all three interactions have essentially the same correlation function. The agreement for the other parameters, NOE,{AB} and T;;, is less good, but these are more susceptible to uncertainties in the external relaxation contribution.Discussion We consider first the relatively poor quality of fit given by eqn (2) to the 13C data for the microemulsions with R = 0.37. There are two possible reasons for this deficiency. The first is that eqn (2) does not adequately represent the spectral density for both and q. The simplest modification, suggested by Carnali et al.,' is to add a third term to give a three-stage loss of correlation. If this third process is very slow (w:z," 9 1) it could make a significant contribution to T, without materially affecting T,, even if its contribution to averaging the dipolar interaction is very small. However, it is difficult to find an acceptable physical explanation for such a slow process. Those processes contributing to z, have been proposed as overall aggregate tumbling and molecular diffusion around the aggregate surface.' A further possibility is exchange either with free surfactant or with surfactant in other aggregates.All these processes would lead to complete loss of correlation, and any slower process would not be separately detectable. It is perhaps more likely that the form of the local motions is such that eqn (1) no longer represents the correlation function satisfactorily. It would be necessary to obtain further relaxation data over a greatly extended frequency range to test this possibility. The second explanation is that an additional relaxation mechanism contributes to q, such as exchange between states of different chemical shift. An example relevant to micelles is proton exchange between a carboxylic acid and carboxylate anion which has been shown to contribute to the T, relaxation of the methylene group adjacent to theF.Heatley 927 Table 7. Order parameters for rotation about an axis axis c,-c,, interaction C,-SO, bisector C,-H, 0.1 1 0.25 C,,-H, 0.1 1 0.25 C,,-H, 0.1 1 0.25 H,-H, 0.25 0.0 16 carbonyl in sodium octanoate micelles if the acid form is not suppressed by an excess of alkali.’* The contribution to q from such a process is given by19 where PA and P, are the fractional populations of the two sites, 6v is the frequency difference between the sites, and k,, is the (first-order) rate constant for A+B. If such a process is responsible for the deviations in T,, the exchange contributions to T, may be obtained from the difference between the experimental q and that calculated using the motional parameters fitting the and NOE only.The exchange contributions were found to be 127 and 65 ms for C-1 and C-l’, respectively. That the exchange contribution is twice as great for C-1’ as for C-1 is difficult to interpret, since such a process is most likely to involve the SO, group, hence producing a larger 6v for C-1 than for C-1’. The fact that the deviations in T, are in the same ratio as the number of protons is perhaps not fortuitous, and supports the idea that eqn (2) inadequately represents the dipolar correlation function under certain conditions. and NOE data at 300 K for p-xylene microemulsions containing 6.08 mol AOT (kg p-xylene)-l and R = 3.7G33.8. Comparing the R values closest to those used here, for C-1 and C-1’ at R = 3.76 their analysis gave S 2 z 0.8, z, = 2.1 kO.25 ns and z, = 37+ 13 ps, while at R = 8.46 their analysis gave S2 x 0.8, z, = 0.9k0.1 ns and zf = 60+40 ps.The values of z, are comparable to those reported here, confirming the lack of any significant concentration dependence when R 2 2. However, the values of S 2 are rather larger and the values of zf rather smaller. Carnali et pointed out that their values of z, were not entirely compatible with expectations based on a model of aggregate tumbling plus monomer diffusion. The present results are also inconsistent with this interpretation. Note particularly that the decrease in z, with increasing R in table 3 runs counter to evidence from viscosity that the droplet radius increases with increasing R in toluene.20 It is easier to understand the behaviour of z, if the slow process originates in an ejection of a surfactant molecule from the aggregate into the hydro- carbon phase.In the free state the molecule undergoes several rotations, more or less isotropically, before rejoining an aggregate. The rate-determining step for the average loss of correlation will be the slower ejection step, which could well be independent of concentration or R as long as the surfactant molecules are not tightly bound in the aggregate. The increase in z, with decreasing R and the high values of S 2 when R is low are both consistent with a more rigid droplet structure. Even at high R, the values of S2 in these microemulsions are very much higher than those in normal m i c e l l e ~ ~ - ~ ” - ~ ~ (typically ca.0.05 at the head-group) indicating that the AOT local motions are much more restricted in amplitude. A simple model for the local Carnali et a1.8 have derived motional parameters from 13C928 Relaxation in Aerosol OT motion is diffusion within a cone of semi-angle a, for which S2 is given by21 S 2 = [cos a (cos a + 1)/212. (12) The order parameters in table 3 correspond to angles a ranging from ca. 25 to 60" according to water content. An alternative model is rotation about an axis, for which S 2 is given by21 where 9 is the angle between the internuclear vector and the rotation axis. On examination of the predominant conformation of AOT (I11 in fig. I), it appears that the most likely axes for such a rotation are either the C-SO, bond or the bisector of the C-2 and C-2' dihedral angle.The former would minimise disturbance of polar interactions while the latter would minimise resistance to motion of the alkyl chains. The order parameters calculated for rotation about these two axes are given in table 7, from which it can be seen that the order parameters for the C,-SO, axis are more consistent with the results for the systems of high R. S 2 = g3 COS2 8- (13) I am grateful to Prof. G. C. K. Roberts and Dr Ly-yun Lian of the University of Leicester Biological N.M.R. Centre for making the AM-500 spectrometer available, and to the S.E.R.C. for grants towards the other spectrometers, References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 H. Wennerstrom, B. Lindman, 0. Soderman, T. Drakenberg and J. B. Rosenholm, J. Am. Chem. SOC., 1979, 101, 6860. T. Ahlnas, 0. Soderman, C. Hjelm and B. Lindman, J. Phys. Chem., 1983, 87, 822. 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