Characterisation of Water-containing Reversed Micelles by Viscosity and Dynamic Light Scattering Methods BY ROBERT A. DAY? AND BRIAN H. ROBINSON* Chemical Laboratory, University of Kent, Canterbury CT2 7NH AND JULIAN H. R. CLARKE AND JANE v. DOHERTY Chemistry Department, UMIST, Manchester M60 1 QD Received 31st May, 1978 The size and aggregation number of reversed micelles formed by the system aerosol-OT+H20+ organic solvent have been determined by viscosity and dynamic light scattering methods. For the viscosity method, a procedure for deriving values of the aggregation number from particles of variable density is described. Measurements were made in cyclohexane, toluene and chlorobenzene. The dynamic light scattering method, based on photon correlation spectroscopy, yields single exponential correlation functions from which values of the translational diffusion coefficient and the micelle radius can be derived.The droplet size was found to depend primarily on the ratio of surfactant to water concentrations, but was essentially independent of solvent and concentration at a fixed surfactant to water concentration ratio. Satisfactory agreement was obtained among the two methods discussed in this paper and one (sedimentation ultracentrifugation) described previously. Aerosol-OT (sodium bis-2-ethylhexylsulphosuccinate) or AOT (fig. 1) is an anionic surfactant capable of solubilising very large amounts of water in organic solvents. For example, in n-heptane, a 0.1 mol dm-3 solution of AOT can solubilize up to 10 % water. We have determined the size and aggregation number of the reversed micelles (or water-in-oil microemulsion droplets) formed by the three component system (fig.l), by the application of viscosity and dynamic light scattering methods. Such systems are of considerable topical interest, which, from our point of view, include the study of the properties of the heterogeneous water present in the aqueous core of the droplets and the mechanism of reversed micellar catalysis and of novel synthesis at interfaces. The nature of the water in reversed micelles has been recently investigated by n.m.r. spectroscopy.1° These studies indicate that when only small amounts of water are present, the solubilised water is highly immobilised. Bulk water properties are not observed until the water content of the system exceeds 1 %.As a prelude to the detailed study of the kinetics of reactions in reversed micellar media, it is necessary to determine the size and aggregation number of the droplets as a function of the concentrations of added AOT and water. Viscosity measure- ments have the advantage of being quick and easy to perform and the system is only mildly perturbed during measurement. Dynamic light scattering is a promising technique for measuring size parameters, and it has already been demonstrated ' 9 that by analysing scattered light intensity fluctuations using photon correlation spectroscopy (PCS) it is possible to study translational diffusive motions of macro- molecules and micelles suspended in aqueous s~lution.~ It is of interest, therefore, t Present Address : Department of Chemistry, University of Sheffield.132R . A . DAY, B . H . ROBINSON, J . H . R . CLARKE AND J . v. DOHERTY 133 to investigate whether the similar motions of reversed micelles could be measured using this technique. If the Stokes-Einstein equation is assumed to be valid for the reversed micelles, average micellar radii can then be derived from the measured diffusion coefficients. EXPERIMENTAL Using this device the kinematic viscosity is obtained, which is a measure of the volume fraction of solution taken up by the dispersed droplets. Considerable care is required when deriving values of the aggregation number from such data when the droplet has regions of different density. Measurements were made in cyclohexane, toluene and chlorobenzene over a range of R values (1-8) where R is defined as the molar concentration ratio (= [H,O]/[AOT]) in a given solvent.Measurements were performed at 293.3 K for cyclohexane and chloro- benzene and 294.7 K for toluene. Viscosity measurements were made by means of an Ubbelohde viscometer. ‘ZH5 I + / \ I \ / \ / 0 0 CH C H 2 CH3 C CH2 CH2 CH2 \ - -?-Y - - ” - 8 - - - - - - - - ‘rn ‘H20 I aerosol-OT structure of a reversed-micelle FIG. 1.-Formula of aerosol-OT (AOT) and postulated structure of a reversed micelle. The light scattering measurements were performed using a 24-channel digital clipped correlator (Precision Devices “ Malvern ” correlator) utilising 488 nm polarised radiation from an argon ion laser (Spectra-Physics Model 165). Samples of the microemulsions were contained in 1 cm2 cross-section clear glass cells.Each sample was centrifuged for x 18 h to remove suspended dust particles and finally allowed to stand for a further 24 h at which stage they were entirely clean and homogeneous. The optical aperture defining the scattering angle was located M 15 cm from the scattering source, and was 1 mm in diameter to minimise the coherence area.2 Scattered light further passed through a pinhole 8 cm behind the aperture and was detected by a photomultiplier (ITT FW130). Correlation functions were obtained for a series of angles with the scattering observed through either the front or side faces of the cells. Optical masks were used to minimise spurious light at the detector. It was necessary to make corrections for the large refractive index of the micro- emulsion to obtain the true angle of scattering.Aerosol-OT was a Fluka purum reagent ; reversed micelle solutions were prepared simply by adding water from a microsyringe to a solution of AOT in the organic solvent. An optically clear solution was formed after shaking for < 1 min. ANALYSIS OF VISCOSITY DATA We assume the droplets are spherical (as has been suggested previ~usIy)~ with a structure similar to that shown in fig. 1. In an ideal solution of non-interacting dispersed spheres the134 CHARACTERISATION OF REVERSED MICELLES volume fraction of the solution taken up by solute, 4, is related to the specific viscosity, qsp, by the Einstein equation : qsp = 2.54. (1) Cheng and Schachman ' tested the following extended empirical relationship (due to Guth and Simha)6 for values of q5 up to -0.10 and found it to hold well for dispersions of moderate concentration : qsp = 2.56+ 14.14'.(2) At the concentrations employed in our work it is necessary to use eqn (2). In the absence of added water it can easily be shown that if all the dispersant is associated in micellar form, 4 = (N[AOT]V&/(1000E) (3) where V, is the volume of a reversed micelle, 5 is the average aggregation number (number of AOT molecules per micelle) and N is Avogadro's number. 3 . 0 - 0 8 10 9 2 4 r, [H*Ol/[AOTl FIG. 2.-Dependence of 4 on [H20] for AOT in toluene from viscosity measurements T = 294.7 K ; [AOT] = 0.1 moldm-3. When water is added, the total micellar volume, Vm, is made up of a contribution from the water core ( VH~O) and the surfactant coat ( Vs).That is : Vm = VH,,+ V, and VHzo = SH20 iiR (4) where SH~O is the specific volume of a water molecule in the micelle. of the surfactant coat (fig. 1) : If rm is the total micellar radius, ~ H , O is the radius of the water core and I is the thickness Hence Values for SH~O and I (required for the calculation of 5 and YH~O) can be derived from experimental viscosity measurements by the following procedure. A plot of 4 against [H20] at constant AOT concentration has the form shown in fig. 2.R . A . DAY, B . H . ROBINSON, J . H . R . CLARKEAND J . v. DOHERTY 135 Above a certain value of R(#3), there is a linear dependence of 4 on [H20]. This suggests that : (i) the initially added water has a density which is apparently different from water added later.(ii) For R values >3, the density of the added water is found to be constant with respect to increasing water concentration. Furthermore, in cyclohexane and toluene, the slope of the line in fig. 2 is found to be 1.8 % mol-1 H2O indicating a water density of 1.0 kg dm-3 (i.e., as bulk water). A value for the surfactant contribution to the total solute volume, &, can be obtained from the extrapolated intercept on fig. 2. The high values of 4 at low R then suggest a more open or less dense structure of the aggregate. It is difficult to distinguish between effects due to surfactant or added water, for example there may be some restructuring of the surfactant region as the water content of the micelles increases and they become larger.However, if it is assumed that the surfactant density does not change, then derived values for the apparent densities of the water core for R < 3 are < 1.0 kg dm-3. is 1.1 nm, and the sulphonate head group is likely to be partially located in the water pool. An analysis of the intercept value of q5s suggests values for the density, pmic, of AOT of 1.3 kg dm-3 compared with a value of 1.14 kg dm3 obtained for the density (p) by direct pyknometry in the absence of added water in cyclohexane and ben~ene.~ If part of the AOT molecule is in contact with water in the core, Pmic/p N LIZ. In this way, values of 0.9 and 0.95 nm were derived in toluene and cyclohexane, respectively. By means of these values of SH20, I and 4 estimates for n' were computed using eqn (3), (4) and (6).From these, all the micelle size parameters were derived. A value for I of 0.9 nm can be estimated since the formal length (L) of the AOT molecule ANALYSIS OF LIGHT SCATTERING DATA In the PCS technique, the correlation function of the fluctuating photocurrent at the light detector (n(t)n(t+z)) is measured directly, where n(t) is the number of photodetections in a sample time interval from (t-At/2) to (t+A.t/2) and < . . .) indicates a statistical average over time origins. For signals with gaussian statistics it is sufficient (and more practical) to determine the single clipped correlation function (nq(t)n(t+z)) where q is a clipping level chosen to be close to the average number of photodetections in the sample time Ar.For a single-clipped correlator nq = 1 if n ( t ) > q and nq = 0 if n(t) < q. Under these conditions it can be shown that after taking N samples, the recorded correlation function is given by : where CE(Z) is the correlation function of the scattered electric field at the detector and Yq can be regarded as an empirically determined parameter. For scattering from particles executing translational diffusion CAT) is given by C&) cc exp (- &k2z) where k is the scattering wave vector and DT is the translational diffusion coefficient of the scattering species. The parameter k can be expressed in terms of the scattering angle 8, the incident light wave vector ko and the sample refractive index n, using the equation : k = 2nk0 sin (0/2).(9) For our particular case, the theory predicts that the correlation function is a single exponential, with a relaxation time ZD = (2&k2)-l, superimposed on a continuous back- ground, as given by eqn (7). Complications will arise if there is a range of independently diffusing species (arising from polydispersity) or if there are other dynamic processes coupled to diffusion. These may lead to non-exponential correlation functions and/or the inverse relaxation time may no longer be a simple linear function of k2. An additional problem encountered for suspensions in organic liquids such as toluene is the substantial intensity of Rayleigh scattering from the dispersing medium itself. (This136 CHARACTERISATION OF REVERSED MICELLES problem does not arise for aqueous suspensions due to the small scattering cross-section of water).Thus for a suspension 1 .O mol dm3 in H20 and 0.1 mol dm-3 in AOT the scattering intensity attributable to solvent was about the same as that originating from the suspended reversed micelles. Whilst relaxation processes involving the solvent occur at much shorter times and are assumed to be uncoupled to diffusion of micelles, this scattering contributed substantially to the background intensity and hence affected the statistical accuracy of the correlation functions. Satisfactory data were obtained, therefore, only for samples with R values >3. No correlation functions were observed for AOT solutions containing no added water. RESULTS Viscosity data obtained for pH o, ii and rH as a function of the water-to-surfactant ratio are shown in table 1, and the dependence of ii on the concentration of micelles at fixed R is shown in table 2.A typical correlation function and a plot of the reciprocal relaxation time against sin2 (0/2) are shown in fig. 3. Within the limits of statistical precision, the correlation functions could all be fitted to single exponentials, and it is seen that 76' shows a simple linear dependence on sin2 (0/2) (and hence k2). There was no evidence for the existence of substantial reversed micelle size fluctuations TABLE 1 .-SUMMARY OF RESULTS DERIVED FROM VISCOSITY MEASUREMENTS solvent ( E ) cyclohexane (2.02) toluene (2.38) chlorobenzene temp/K 293.3 294.7 (5.7 1)-293.3 N= [HzOl/[AOTl) P H ~ O ii r H 2 0 P E Z O n rE20 P E ~ O n rHZo 0.75 27 0.64 0.97 36 0.81 1.00 47 1.00 1.01 59 1.19 1.01 72 1.37 1.01 86 1.54 1.01 101 1.71 1.02 114 1.86 0.36 0.65 0.86 0.99 0.99 0.99 0.99 0.99 41 0.93 44 0.99 49 1.07 56 1.18 68 1.35 82 1.52 97 1.70 112 1.87 0.60 25 0.67 0.75 34 0.87 0.77 46 1.09 0.77 59 1.30 0.78 73 1.50 0.80 85 1.66 0.82 99 1.82 0.86 108 1.93 [AOT] = 0.10 mol dm-3 for all measurements.rH2O in nm, PH20 in kg dm-3. Likely error in E + &lo %. which should give rise to an additional k-independent scattering component. Such components might be manifest in non-exponential correlation functions and a non- zero intercept in the inverse time axis at zero scattering angle.2* However, such features are only observable if there is an appreciable permittivity change accompany- ing the size fluctuations.* The measured diffusion coefficients and mean micelle radii (calculated assuming the Stokes-Einstein relation DT = kT/6nyrm) are included in table 3.On subtracting the thickness of the surfactant coat (obtained from the viscosity data), rH20 is obtained. TABLE 2.-DEPENDENCE OF fi ON [AOT] IN TOLUENE AS SOLVENT AT 293.3 K. R = 5.4 [AOT]/mol dm-3 rHzo/nm ii 0.005 1.22 46 0.01 1.39 69 0.02 1.34 61 0.05 1.33 60 0.07 1.34 62 0.10 1.37 66R . A . DAY, B . H. ROBINSON, J . H . R . CLARKE AND J . v. DOHERTY 137 sin2 (8/2) FIG. 3.-Plot of inverse correlation time, T - ~ , against sin2 (8/2) obtained by photon correlation spectroscopy for micelle suspensions with R 21 10 in toluene at 20°C. 8 is the scattering angle (corrected for refractive index effects).Inset is a semi-log plot of a typical correlation function for R 2: 10, 8 = 88". TABLE 3 .-DERIVED VALUES FROM DYNAMIC LIGHT SCATTERING MEASUREMENTS IN TOLUENE AT 293 K (0 = STANDARD DEVIATION) R D~/lO-lo m2.s -1 a/10-11 rn2 s-1 rm/nm m20/nm 3.36 3.85 4.78 5.83 7.50 8.34 8.97 9.56 1.79 1.66 1.63 1.47 1.37 1.35 1.22 1.20 1.69 0.79 1.21 1.85 0.95 1.38 1.92 1.02 1.15 2.07 1.19 0.86 2.25 1.35 1.43 2.30 1.40 0.64 2.45 1.55 0.49 2.48 1.58 DISCUSSION Fig. 4 summarises results for the overall micelle diameter obtained by the two methods reported in this paper, together with data obtained by sedimentation ultracentrifugation for AOT-stabilised reversed micelles in heptane. Reasonable agreement is obtained using the three different methods. The data allow us to draw the following conclusions regarding the structure and stability of reversed micelles : (i) the average aggregation number increases rapidly as the [H,O]/[AOT] ratio increases.This is true for all solvents studied. (ii) The droplet size remains essentially constant when the concentration of AOT is varied at a fixed value of [H,O]/[AOT]. The primary factor which determines micellar stability in these systems is thus the ratio of water to surfactant rather than total concentrations or the solvent. (iii) The aggregation number (and hence m.w.) varies very little with the nature of the solvents used. (iv) The droplet systems are thermo- dynamically stable over long periods at room temperature. Although kinetic138 CHARACTERISATION OF REVERSED MICELLES evidence suggests that an inelastic collision process between droplets leads to the transient formation of dimer-type species, no evidence for such reactions was obtained by the dynamic light scattering method.(v) At high concentrations of added water, the water pool density is similar to that of bulk water, but for R values less than three, low apparent values are obtained. This probably indicates only partial occupancy of the core by added water ; possibly there is some " clustering " of solvated water molecules. (vi) The data in chlorobenzene indicate some differences in behaviour compared with the other solvents. Water solubilisation is more difficult in this solvent, and the maximum density of the water core is only 0.800 kg dm-3, indicating a more open structure.This is probably due to the reduced coulombic interactions 0.0 2.0 4.0 6.0 8.0 10.0 12.0 R = [H,O]/[AOT] FIG. 4.-Droplet diameter, dm, as a function of R. Open symbols are viscosity data for solvents A , toluene ; 0, chlorobenzene ; 0, cyclohexane ; + , ultracentrifuge data using n-heptane solvent, @, dynamic light scattering using toluene solvent. in chlorobenzene. It seems that the solubilising power of the different solvents is closely related to their permittivity values. (vii) The apparently simple form of the observed correlation functions does not necessarily indicate the absence of some polydispersity, only that the size distribution is rather small. For example, it is extremely difficult to resolve exponentials with relaxation times that differ by less than a factor of two even if the amplitudes are comparable.We can, therefore, only put an upper limit of x 50 % for the variance of the micelle size distribution. The light scattering and ultracentrifuge methods give excellent agreement in terms of weight-averaged values, but these are lower than those measured by the viscosity method. This difference may be significant in the interpretation of the results; e.g. it may give some indication of the extent of polydispersity. We especially thank Shell Research, Thornton for a CASE award (to R. A. D.) and the provision of the viscometer, and Mr. Peter Barlow of Shell for his guidance, encouragement, and interest in the work. We thank the S.R.C. for the provision of equipment associated with this project.R. A . DAY, B. H. ROBINSON, J . H. R . CLARKE AND J . v. DOHERTY 139 B. J. Berne and R. Pecora, Dynamic Light Scattering (Plenum, N.Y., 1975). Specialist Periodical Report, 1975), vol. 11. N. A. Mazer, G. B. Benedek and M. C. Carey, J. Phys. Chem., 1976, 80, 1075. M. B. Mathews and E. Hirschhorn, J. Colloid Sci., 1953, 8, 86. P. Y. Cheng and H. K. Schachman, J. Polymer Sci., 1955, 16, 19. E. Guth and R. Simha, KoZloidZ., 1936, 74,266. J. H. R. Clarke, G . J. Hills, C. J. Oliver and J. M. Vaughan, J. Chem. Phys., 1974, 61, 2810. B. H. Robinson, D. C. Steytler and R. D. Tack, J.C.S. Faraday I, 1979,75, in press. ’ P. N. Pusey and J. M. Vaughan, in Dielectric and Related Phenomena (Chemical Society ’ P. Eckwall, L. Mandell and K. Fontell, J. Colloid Interface Sci., 1970, 33, 215. lo M. Wong, J. K. Thomas and T. Nowak, J. Amer. Chem. SOC., 1977, 99,4730. (PAPER 8/1010)