Observation of Two Diffusive Relaxation Modes in Microemulsions by

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Observation of Two Diffusive Relaxation Modes in Microemulsions by Dynamic Light Scattering Anuj Shukla,*,† Heinrich Graener,† and Reinhard H. H. Neubert‡ Department of Physics, Optics Group, Martin-Luther-University Halle-Wittenberg, 06099 Halle/Saale, Germany, and Department of Pharmacy, Institute of Pharmaceutics and Biopharmaceutics, Martin-Luther-University Halle-Wittenberg, 06120 Halle/Saale, Germany Received May 6, 2004. In Final Form: July 11, 2004 Water-in-oil microemulsions stabilized by AOT and dispersed in n-alkane oils with a constant molar water-to-surfactant ratio were studied by dynamic light scattering. A dilution series (in the range of volume fraction of water plus surfactant, φ ∼ 0.02-0.52) was used, which allowed us to extract information about droplet sizes, diffusion coefficients, interactions, and polydispersity from experimental data. We report the observation of two diffusive relaxation modes in a concentrated microemulsion (0.20 < φ < 0.5) due to density (collective diffusion) and concentration or polydispersity (self-diffusion) fluctuations. Below this concentration it was difficult to resolve two exponentials unambiguously, and in this case one apparent relaxation mode was observed. It was found that for a given composition self-diffusion is more pronounced in apparent relaxation mode for a shorter chain length alkane. The concentration dependence of these diffusion coefficients reflects the effect of hard sphere and the supplementary attractive interactions. It was observed that the attractive part becomes more pronounced in the case of a large alkane chain oil at a given temperature. This explains the shift of the region of microemulson stability to lower temperatures for higher chain length alkanes. Increase in hydrodynamic radius, Rh, obtained from the diffusion coefficient extrapolated to infinite dilution was observed with increase of alkane chain length. The polydispersity in microemulsion systems is dynamic in origin. Results indicate that the time scale for local polydispersity fluctuations is at least 3 orders of magnitude longer than the estimated time between droplet collisions.

Introduction Microemulsions are thermodynamically stable fluids composed of water and oil domains that are separated by a layer of surfactant molecules. The surfactants, which are molecules with a hydrophilic head and a hydrophobic tail, serve to stabilize the fluid and prevent it from macroscopic phase separation into water and oil. As the size of the water and oil domains is much smaller than the wavelength of visible light, the solutions appear optically isotropic and clear. These thermodynamically stable and optically isotropic systems have a wide range of applications in various industrial processes such as oil recovery, cosmetics, pharmaceuticals, food, and medicine.1 Because of many interesting properties involved in the microemulsion systems, considerable efforts (both experimentally and theoretically) have been devoted to their studies.2,3 The structure of microemulsions has been extensively studied using NMR, fast freeze-fracture, cryo-electron microscopy, and electrical birefringence.1 These experiments show that a microemulsion can form a variety of phases that depend on its composition and on the values of the state variables.2 The single-phase water-in-oil (W/ O) microemulsion of interest in this study is normally * Corresponding author. Phone: +49 (345) 5525313. Fax: +49 (345) 5527221. E-mail: [email protected]. † Department of Physics, Optics Group. ‡ Department of Pharmacy, Institute of Pharmaceutics and Biopharmaceutics. (1) For a review, see: Handbook of microemulsion science and technology; Kumar, P., Mittal, K. L., Eds.; Marcel Dekker: New York, 1999. (2) Chen, S. H.; Rouch, J.; Sciortino, F.; Targagilia, P. J. Phys.: Condens. Matter 1994, 6, 10855. (3) Dawson, K. A. In Structure and dynamics of strongly interacting colloids and superamolecular aggregates in solution; Chen, S. H., et al., Eds.; Kluwer Academic: Dordrecht, 1992.

denoted as a L2 phase. For temperature below 40 °C and above 15 °C the L2 microemulsions can be well represented as a collection of surfactant-coated spherical droplets of water dispersed in a homogeneous medium of oil.4 The volume fraction of these droplets can be varied continuously from 0.02 to 0.52 without being interrupted by the lamellar phase. The size of W/O microemulsion droplets is highly dependent on the concentration of each constituent solubilized in the microemulsion;1 however, it is recognized that the aggregate size is dominantly characterized by the [H2O]/[AOT] molar ratio, defined as µ, rather than the actual concentration.5 The dynamical behavior of droplet phases in the diluted regime has been studied using both light and spin-echo neutron scattering.1 Comparatively, much less effort was spent to study experimentally the dynamical behavior of concentrated microemulsions. It has been shown by Weissman6 and Pusey et al.7 that in concentrated colloidal dispersions with a slight size polydispersity, two distinct diffusional modes (one is due to collective and another due to self-diffusion) should appear in dynamic light scattering (DLS). These two diffusion modes have been observed in several DLS measurements on concentrated (or strongly interacting) systems such as microemulsions,8-10 silica spheres,11,12 (4) Mays, H.; Ilgenfritz, G. J. Chem. Soc., Faraday Trans. 1996, 92, 3145. (5) Robinson, B. H.; Toprakcioglu, C.; Dore, J. C.; Chieux, P. J. Chem. Soc., Faraday Trans. 1 1984, 80, 13. (6) Weissman, M. J. Chem. Phys. 1980, 72, 231. (7) Pusey, P. N.; Fijnaut, H. M.; Vrij, A. J. Chem. Phys. 1982, 77, 4270. (8) Peter, U.; Roux, D.; Sood, A. K. Phy. Rev. Lett. 2001, 86, 3340. (9) Clarke, H. R.; J. Nicholson, D.; Regan, K. N. J. Chem. Soc., Faraday Trans. 1 1985, 81, 1173. (10) Yan, Y. D.; Clarke, J. H. R. J. Chem. Phys. 1990, 93, 4501. (11) Kops-Workhoven, M. M.; Fijnaut, R. J. Chem. Phys. 1982, 77, 2242.

10.1021/la048883l CCC: $27.50 © 2004 American Chemical Society Published on Web 08/21/2004

Diffusive Relaxation Modes in Microemulsions

and dispersion of latex particles.13,14 In diluted systems the two exponentials are not well resolved. Analyzing the obtained functions by a single exponent gives an apparent diffusion. With a very small difference in refractive index of particles and solvent, the self-diffusion part becomes more pronounced in apparent diffusion.11 Quite frequently, the apparent diffusion coefficient in a dilute regime is identified with either collective diffusion15 or self-diffusion.9 Moreover, the concentration dependence of collective and self-diffusion coefficients reflects the effect of direct and hydrodynamic interaction, for which several theories exist for hard sphere potential.16,17 To estimate the magnitude of the attraction and repulsion giving rise to the concentration dependence of diffusion coefficients, the measured value is generally compared to the hard sphere repulsion. Collective and self-diffusion coefficients have opposite concentration dependence for a hard sphere potential. Therefore the identification of an apparent diffusion coefficient as either collective or self-diffusion, while apparent diffusion as the “coupled combination” of both, may lead to a wrong conclusion for the interaction potential. One object of these studies has been to establish a relationship among the collective diffusion and self-diffusion coefficients observed at high concentrations and the apparent diffusion coefficient observed in a dilute regime. In the present study, detailed analysis of the correlation function data of water/AOT/n-alkane (n ) 7 and 8) microemulsions is reported over the large range of φ (0.020.52) at µ ) 45 and T ) 25 °C, for which two relaxation modes can be clearly characterized for high volume fractions. The oil has been varied to show the dependence of some general features of systems on chain length of n-alkane. The aim of this investigation is to present results on the diffusion dynamics of microemulsion droplets over a large concentration range. Experimental Section Materials and Sample Preparation. AOT (purity 98%), n-heptane (purity 99+%), and n-octane (purity 99+ %) were purchased from sigma-Aldrich, Germany. Water used was of bidistilled quality. The basic microemulsion consists of a ternary mixture of oil (n-heptane or n-octane), surfactant (AOT), and water. These basic microemulsions were diluted with the continuous phase (oil), keeping constant the molar water-tosurfactant ratio (µ ) 45) to preserve a constant droplet radius. Microemulsions are considered as a priori formed objects: the water core and surfactant film form a single entity, immersed in a continuous oil phase. Therefore, the volume fraction (φ) of the microemulsion droplets can be defined as φ ) φw + φAOT. All samples were prepared below the percolation threshold φ ∼ 0.55 predicted for water/AOT/n-alkane microemulsions at T ) 25 °C.18 All samples were analyzed in the single-phase microemulsion, normally denoted as the L2 phase (lower phase separation or solubilization temperature Tl ) 22.2 and 17.3 °C and upper phase separation temperature Tu ) 62.4 and 55.3 °C for microemulsion droplets in heptane and octane).4,19 Prior to the measurements the samples were filtered through a 0.45 µm pore size filter into dust-free sample cells. The (12) van Veluwen, A.; Lekkerkerker, H. N. W.; de Kruif, C. G.; Vrij, A. J. Chem. Phys. 1988, 89, 2810. (13) Pusey, P. N. J. Phys. A 1978, 11, 119. (14) Ottewill, R. H. Langmuir 1989, 5, 4. (15) Kim, M. W.; Dozier, W. D.; Klein, R. J. Chem. Phys. 1986, 84, 5919. (16) Cichocki, B.; Felderhof, B. U. Phys. Rev. A 1990, 42, 6024. (17) Felderhof, B. U. J. Phys. A: Math. Gen. 1978, 11, 929. (18) D’Aprano, A.; D’Arrigo, G.; Paparelli, A.; Goffredi, M.; Liveri, V. T. J. Phys. Chem. 1993, 97, 3614. (19) Rouch, J.; Safouane, A.; Tartaglia, P.; Chen, S. H. J. Chem. Phys. 1989, 90, 3756.

Langmuir, Vol. 20, No. 20, 2004 8527 cylindrical sample cells are made of Suprasil quartz glass by Hellma, Muellheim, Germany, and have a diameter of 10 mm. DLS Experiments. Dynamic light scattering experiments were performed on a standard commercial apparatus (ALV) using a green Nd:YAG DPSS-200 mW laser emitting vertically polarized light at a wavelength of 532 nm. The thermostated sample cell (temperature controlled to (0.1 °C) is placed on a motor-driven precision goniometer ((0.01°) which enables the photomultiplier detector to be moved from 20° to 150° scattering angle. The light-scattering process defines a wave vector q ) 4πn/λ sin(θ/2), where λ is the wavelength of the incident light in a vacuum, θ is the scattering angle, and n is the refractive index of miroemulsion. The value of n was measured for each sample using an Abbe refractometer. The intensity-time autocorrelation functions g2(τ) are recorded with an ALV-5000E multiple tau digital correlator with a fast option. The minimal sampling time of this correlator is 12.5 ns. If the scattered field obeys Gaussian statistics, the measured correlation function g2(τ) can be related to the theoretically amenable first-order field correlation function g1(τ) by the Siegert relationship20 g2(τ) - 1 ) β|g1(τ)|2, where β is the coherence factor of the experiment and ideally should be 1. The coherence factor of the setup was proven to be better than 0.9. The intensitytime autocorrelation function corresponding to one set of experimental parameters has been measured five times, and data used for fitting are averaged over these five measurements. All dynamic light scattering measurements were made at three different scattering angles, 50°, 55°, and 60°, at 25 °C. In all cases the decay of g2(τ) - 1 was followed up with values of τ large enough to reach the baseline. Analysis of the Dynamic Light Scattering Data. The picture that emerges from this investigation is that the correlation function for concentrated microemulsions exhibits two relaxation modes. The fast mode may be associated with collective diffusion and slow modes with self-diffusion. We analyzed the correlation data with two exponentials

g1(τ) ) Afaste-Γfastτ + Aslowe-Γslowτ

(1)

where Ai values are the amplitudes and Γi values are the characteristic relaxation rate of mode i. Equation 1 also arises in a natural way from the theoretical treatment of Weissman et al.,6 Pusey et al.,7 and Milner et al.21 In the diluted region the difference between Γfast and Γslow is expected to be small. Therefore, resolution in the diluted region of the measured autocorrelation function by a sum of two exponents will be difficult. Analyzing the obtained functions in the low concentration region by a single exponent gives an apparent relaxation rate Γapp, which can be related to Γfast and Γslow using an expansion for both exponents of eq 1

lim Γapp(q) ) τf0

AfastΓfast(q) + AslowΓslow(q) Afast + Aslow

(2)

Results and Discussion Interpretation of Correlation Function. Figure 1 shows the normalized correlation function data (at a scattering angle of 60°) at five different concentrations for the water/AOT/n-octane system. Below φ ) 0.25, systems show single exponential correlation functions as is clearly seen in Figure 1 (semilog correlation function could be well fitted to a straight line). However, above φ ) 0.25, the correlation function clearly becomes two exponentials as can be seen in Figure 2 for the water/ AOT/n-octane system with φ ) 0.51 and θ ) 60°. Figure 2B also shows the residuals obtained when fitted to a stretched exponential as has been done by Chen et al.22 for concentrated microemulsions. As can be seen, the residuals for the fit to two exponentials are substantially (20) Siegert, A. J. F. MIT Radiat. Lab. Rep. No. 1943, 465. (21) Milner, S. T.; Cates, M. E.; Roux, D. J. Phys. (Paris) 1990, 51, 262. (22) Chen, S. H.; Huang, J. S. Phys. Rev. Lett. 1985, 55, 1888.

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Figure 1. Concentration dependence of the correlation function g2 - 1(τ) for the microemulsion system AOT/water/n-octane at a fixed scattering angle of 60°. Only part of the experimental data is shown for the sake of clarity. Note that, while increasing the droplet concentration, two relaxation modes are observed. The full line represents the single-exponential fit.

Figure 2. (A) Concentration between one of the experimental correlation functions and the fits to two exponentials and a single exponential. The distribution of relaxation times obtained from the CONTIN is also shown. (B) Residuals obtained from the fits single, two, and stretched exponentials. The data correspond to the system AOT/water/n-octane at a fixed scattering angle of 60°. Only the second point of the autocorrelation data is plotted.

smaller than that for a stretched exponential or singleexponential fit. Alternatively, the data can be analyzed using the inverse Laplace transfom program CONTIN,23 which better accounts for a continuous distribution of relaxation rates A(Γ). There is a fundamental difference between describing the correlation function with two exponentials or with CONTIN. In effect, while in the first case two relaxation processes are assumed, in the second one, two distributions of relaxation rates are taken into account. However, it must be remarked that the CONTIN method leads, in our results, to distributions of relaxation rates Γ ()1/τ) that are centered at the values of Γ obtained when using eq 1. Therefore, for the sake of simplicity, above φ ) 0.25 concentration, we fitted g1(τ) with eq 1 as did Peter et al.,8 Yan et al.,10 and Kops-Werkhoven et al.11 for concentrated microemulsions. Below this concentration it was difficult to resolve the two exponentials unambiguously, in these cases g1(τ) was fitted to the second-order (23) Provencher, S. W. Comput. Phys. Commun. 1982, 27, 229.

Shukla et al.

Figure 3. Scattering wave vector (q) dependence of the characteristic decay rates Γapp, Γc, and Γs.

cumulants method.24 The apparent relaxation rate Γapp and size polydispersity index σs were deduced from first and second cumulants. The size polydispersity σs measured for all our systems using second cumulant suitably normalized by first cumulant is 0.25 with error (10%. It should be noted that this value lies on the higher side of the measured value from the contrast variation experiments.29 As already pointed out by some authors,10,25 the second cumulant (represents only small correction to the shape of the correlation function) overestimates the polydispersity of microemulsion droplets. As an example Figure 3 shows the decay rates of the apparent, fast, and slow modes for the samples corresponding to water/AOT/n-octane. In all cases, relaxation rates seem to be diffusive; i.e., the characteristic decay rate varies to a good agreement with the square of the wave vector, indicating a hydrodynamic origin of modes. The solid lines in Figure 3 represent a fit of Γi ) Diq2, where Di are the diffusion coefficients of a mode i. In the case of the hydrodynamic origin, the fast mode represents collective diffusion (number density fluctuations) and the slow mode represents self-diffusion (concentration or polydispersity fluctuations).26 In the following, the indexes c and s will stand for “collective” and “self”, respectively. Figure 4 shows a corresponding plot of diffusion coefficients obtained by the three types of relaxation rates. Each of three diffusion coefficients (Dc and Ds obtained from two exponentials and Dapp from the cumulant fit represented in Figure 4) should fit to the same value, D0, as φ f 0, so the use of two methods of data analysis permits this point to be fixed quite accurately. D0 can be identified with Dapp when φ f 0, which is used for the calculation of hydrodynamic radius. The mean droplet hydrodynamic radius Rh is obtained using the Stokes-Einstein equation, Rh ) kBT/6πηD0, where, kB is Boltzmann’s constant, T is the absolute temperature, and η is the coefficient of viscosity of the solvent (the continuous phase in the case of microemulsion). As shown in Table 1, Rh is slightly increases with increase of length of the n-alkane chain. Rh is larger in the larger chain alkane oil system because oil penetration into the surfactant tail region is smaller for larger chains, which causes a decrease in spontaneous curvature of the surfactant layer in comparison to a shorter (24) Koppel, D. E. J. Chem. Phys. 1972, 57, 4814. (25) Ricka, J.; Borkovec, M.; Hofmeier, U. J. Chem. Phys. 1991, 94, 8503. (26) Pusey, P. N.; Tough, R. J. A. In Dynamic Light Scattering; Pecora, R., Ed.; Plenum Press: New York, 1985; p 85.

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[

Rapp ) Rc +

Figure 4. Volume fraction (φ) dependence of diffusion coefficients Dc (O), Ds (4), and Dapp (0) in water/AOT/n-alkane microemulsions with µ ) 45 at 25 °C. D0 is the infinite dilution (extrapolated) value. Linear fits to Di according to eq 3 are plotted through solid lines.

chain. This result is consistent with the results obtained for AOT-stabilized microemulsions.27,28 Concentration Dependence of Diffusion Coeffients. As shown in Figure 4, the self-diffusion coefficient Ds decreases with increasing volume fraction, whereas Dc shows a small increase. This is consistent with the interpretation that Ds describes polydispersity fluctuations by self-diffusion and that Dc arises from mutual diffusion of microemulsion droplets. Mutual diffusion can be regarded as being driven by osmotic pressure and retarded by interdroplet friction, whereas for self-diffusion, the osmotic term is absent and the dominant effect is the increasing value of the friction coefficient with concentration, tending to reduce the diffusion coefficient.26 The influence of the optical contrast has been investigated by changing the oil. Refractive index matching point for droplets in n-heptane and n-octane can be obtained at µ ) 35 and 25, respectively.29 Therefore, droplets having µ ) 45 are close to refractive index matching point in n-heptane in comparison to n-octane. We expect that with decreasing the difference between the refractive indices of droplets and solvent (i.e., close to the matching point) part of self-diffusion mode will increase. This is indeed observed as shown in Figure 4. The behavior of Dapp is closer to Ds in the case of n-heptane in comparison to n-octane. This fact is interesting, since this explains why Kim et al.15 observed a collective diffusion mode in a dilute regime from AOT/water/ndecane systems having µ ∼ 41 (far from refractive index matching point), while Clarke et al.9 observed a selfdiffusion mode in a dilute regime from AOT/water/p-xylene systems having µ ) 10 (close to the refractive index matching point). As shown in Figure 4, the three diffusion coefficients fit satisfactorily to a linear equation

Di ) D0(1 + Riφ)

(3)

with Ri listed in Table 1. Using eqs 2 and 3, one can write (27) Visser, A. J. W. G.; Vos, K.; van Hoek, A.; Santema, J. S. J. Phys. Chem. 1988, 92, 759. (28) Eastoe, J.; Robinson, B. H.; Visser, A. J. W. G.; Steytler, D. C. J. Chem. Soc., Faraday Trans. 1991, 87, 1899. (29) Shukla, A. Characterization of Microemulsions using Small Angle Scattering Techniques. PhD Dissertation, Martin-Luther-University, Halle/Saale, Germany, 2003.

]

Aslow (R - Rc) Afast + Aslow s

(4)

Far from the refractive index matching point, Aslow f 0; Rapp f Rc, whereas in the refractive index matching point itself Afast f 0; Rapp f Rs. Substituting the value of Ri in eq 4, one can obtain Aslow/(Afast + Aslow) ) 0.86 and 0.56 for water/AOT/n-heptane and water/AOT/n-octane, respectively. These values are consitent with the interpretation that closer to the matching point (droplets in n-heptane) the major part of Dapp comes from the self-diffusion. Interdroplet Interaction. If we assume that the droplet size does not vary significantly over the concentration range, then the measured values Rc,s can be compared to Rc,s for a hard sphere repulsion. A proof of the constancy of droplet size can be found in Figure 4. The same D0 is obtained over a measured range of concentration, indicating that the droplet size remains constant over a measured range of concentration. A more complete proof of the constancy of droplet size can be found in neutron scattering experiments, which give also the gyration radius of the droplets for each concentration φ.29 The difference of the virial coefficient Rc,s obtained from collective and self-diffusion coefficients from its hard sphere value δRc,s ) Rc,s - (Rc,s)HS is negative if there are supplementary attractive interactions and positive in the case of additional repulsive interactions.16,17 For hard spheres, (Rc)HS ) 1.56 and (Rs)HS ) -1.83.16,17 Grenz et al.30 also predicted that attractive interaction becomes stronger as the negative value of δRs is increased. For studied systems, δRc,s is negative as expected for droplets interacting via hard sphere interaction with perturbation of attractive interaction. The values of Rc,s increase with increase of the chain length of alkane oil. This indicates that droplets in longer n-alkane chain length oil are more attractive than those in smaller n-alkane chain length at a given temperature. The origin of this attractive interaction is thought to be due to the fact that AOT molecules along with the interface of the microemulsion droplets allow penetration of the surfactant hydrophobic chains of the other droplets during collisions. The overlapping of the penetrable volume of the microemulsion droplets under dynamic motion gives rise to an attractive interaction. To estimate the depth and range of the interaction potential, following Kim et al.15 we modeled the interaction potential as a hard sphere which ensures the identity of microemulsion droplets plus an attractive square well which arises due to interpenetration of the surfactant tail. For such a potential, it has been shown that Dc is as follows15,31

[

15 8(1 + x) 9 75 369 (5) 3 4 256 64(1 + x) 256(1 + x)

δRc ) (e - 1) -8x3 - 18x2 - 12x +

]

where x and  are the range (scaled by the droplet diameter) and depth of the well (scaled by kBT). Taking x ) 3 Å/2Rcore to be constant (3 Å is the range of interaction determined by small angle neutron scattering (SANS)32 and Rcore ) (30) Grenz, U.; Dhont, J. K. J.; Klein, R. J. Chem. Phys. 1987, 87, 2990. (31) Finsy, R.; Devrise, A.; Lekkerkerker, H. J. Chem. Soc. Faraday Trans. 2 1980, 76, 767. (32) Huang, J. S.; Safran, S. A.; Kim, M. W.; Grest, G. S.; Kotlarchyk, M.; Quirke, N. Phys. Rev. Lett. 1984, 57, 592.

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Table 1. The Size, Interaction Energy, and the Related Parameters of the Microemulsion Droplets in n-Heptane and n-Octane at µ ) 45 and 25 °C interaction size two exponentials energy AOT + D0 Rh  water + (10-8 cm2/s) (nm) Rapp Rc Rs n-heptane n-octane

54.88 ( 0.64 41.80 ( 0.19

9.94 ( 0.12 10.40 ( 0.05

-1.54 ( 0.01 -0.76 ( 0.03

Figure 5. Volume fraction (φ) dependence of the ratio between amplitude of the fast and slow decay modes in water/AOT/nalkane microemulsions with µ ) 45 at 25 °C.

3vw/asµ + 3vH/as, where vw ) 29.9 Å3, vH ) 103 Å3, 33 and as ) 56 Å2 and 50 Å2 for AOT molecule in n-heptane and n-octane, respectively29), we obtained attractive interaction energy values, , using eq 5, and  values are listed in Table 1. As shown in the table, the value of  increases with increases of the chain length of oil. Droplets in longer n-alkane chain length are more attractive (more surfactant to surfactant attractive interaction) than those with smaller n-alkane chain length at constant temperature. This is consistent with the interpenetration mechanism because droplet size is larger in the larger alkane chain and hence overlapping the volume. It is also noted that  values are small in comparison to the value of  ) 3.83 for the water/AOT/n-decane system (µ ∼ 41, T ) 25 °C) obtained by SANS.32 This is consistent with the fact that droplets in n-heptane or n-octane are far from the percolation temperature in comparison to the droplets in decane at 25 °C. (Percolation temperatures for microemulsion droplets in n-heptane, n-octane, and n-decane are 42.3, 34.8, and 23.8 °C, respectively).4 This mechanism could also explain the shift of the region of microemulson stability to lower temperatures for higher chain length alkanes. Finally the experimental data Afast/Aslow can be compared with fact that Afast/Aslow is proportional to structure factor (S) divided by optical polydispersity (p).11 Figure 5 shows the volume fraction dependences of the Afast/Aslow. Assuming no change in the optical contrast with increasing volume fraction, we expect a decrease of Afast/Aslow with increasing volume fraction, due to the effect of the structure factor. This is indeed observed as shown in Figure 5. In addition, we have found that the values of Afast/Aslow decrease at a given concentration for droplets in n-heptane in comparison to droplets in n-ocatne. This is also consistent with the theoretical prediction that droplets (33) Kotlarchyk, M.; Stephens, R. B.; Huang, J. S. J. Phys. Chem. 1988, 92, 1533.

1.03 ( 0.07 0.85 ( 0.04

-1.96 ( 0.08 -2.03 ( 0.05

1.15 1.45

in n-heptane are closer to the refractive index matching point (i.e., larger p) and less attractive in comparison to droplets in n-ocatne (i.e., smaller S); both effects contribute to decreasing the value of Afast/Aslow. In interpreting the above results, it is useful to distinguish spatial and collision-induced concentrations or polydispersity fluctuations. The observation of the particle self-diffusion implies spatial fluctuations of polydispersity over distances of the order of q-1, with characteristic relaxation time τD ) (D0q2)-1 ∼ 10-5 s. In addition, however, the physical interaction of neighboring particles can give rise to local collision-induced polydispersity fluctuations, with characteristic relaxation time τI. If τD . τI, DLS observes slow fluctuations of macroscopic spatial extent and droplet self-diffusion would not be observed by DLS.34 Since the evidence discussed above strongly suggests that for φ > 0.20, self-diffusion is being measured. We conclude that τI > 10-5 s. For particles of diameter less than 1 µm, the binary collision rate due to Brownian motion is e10-8 s, indicating that the time scale for polydispersity fluctuations is at least 3 orders of magnitude slower than the particle collision frequency. This is in agreement with a previous estimate35 that 1 in 1000 to 10000 encounters results in solubilizate exchange. Conclusions We have studied the autocorrelation function of light scattered by W/O microemulsions. For concentrated suspension of microemulsion droplets, the measured autocorrelation function is composed of two groups of modes with well-separated decay times. Fast mode may be associated with collective diffusion and slow modes with self-diffusion. It was observed that a droplet has a slightly higher hydrodynamic radius in large chain alkane oil in comparison to short chain alkane oil. It was observed that near the so-called optical matching point, selfdiffusion is more pronounced in apparent relaxation mode. The concentration dependence of these diffusion coefficients reflects the effect of hard sphere and the supplementary attractive interactions. The attractive part becomes more pronounced in the case of large alkane chain oil at a given temperature. This explains the shift of the region of microemulson stability to lower temperatures for higher chain length alkanes. The polydispersity in microemulsion systems is dynamic in origin, characterized by a local fluctuation time τI > 10-5 s. Acknowledgment. The authors are indebted to Dr. Martin Janich for beneficial discussions. Financial support by the Deutsche Forschungsgemeinschaft is gratefully acknowledged. LA048883L (34) Pusey, P. N.; Tough, R. J. A. Adv. Colloid Interface Sci. 1982, 16, 143. (35) Fletcher, P. D. I.; Howe, A. M.; Robinson, B. H. J. Chem. Soc., Faraday Trans. 1 1987, 83, 985.