The microemulsions were prepared by mixing of surfactants AOT, H₂O, and oil (Decane and Cyclohexane) waiting for several minutes until the samples were single phase and optically clear. Sodium-2-diethylhexyl sulfosuccinate, or AOT 99% (an Alfa product) and Decane 99% (Aldrich) and Cyclohexane was obtained from Sigma-Aldrich. The composition of the AOT/H₂O/Oil microemulsion is given by the two parameters X and mf.

The experimental solutions were prepared by weighting appropriate amounts of AOT dissolving in decane or Cyclohexane and adding water into the solution. Finally, all samples were filtered by using 0.2-pm Teflon filters (Gelman).

Microemulsions were formulated by mixing AOT with water and n-Decane or cyclohexane at the fixed molar ratio of water to AOT (X = 6.7) at the different mass fraction (0.01 < mf < 0.07 dilute regime). Dynamic behavior of the AOT/H₂O/Decane or AOT/H₂O/Cyclohexane microemulsion was probed with photon correlation spectroscopy methods. The correlation function showed a single exponential decay at all concentrations, Figure 1 and Figure 2. In the photon correlation spectroscopy experiments, the normalized intensity time correlation function g₂(q, t) was measured [13,14],

where I(q, t) is the scattered intensity at a given q and time t. The g₂(q, t) function is related to the normalized electrical field correlation function g₁(q, t) by the Siegert relation assuming that the system is an ergodic media

where B is the coherence factor of the equipment. All the correlation functions in this work were fitted by a single stretched exponential function [15].

The stretched exponential function describes the decay processes that have a distribution of relaxation times (t). The parameter β (0 ≤ β ≤ 1) measures the width of the distribution function. The results of the correlation function as function of delay time for AOT/H₂O/Decane at X = 6.7 at different mass fraction shown in the Figure 1. The correlation function as function of delay time for AOT/ H₂O/Cyclohexane at X = 6.7 is presented in the Figure 2.

The mean value of the relaxation time is given by

where Γ is the gamma function. Where the collective diffusion coefficient is calculated from Dc = 1/(q₂<τ>). All the correlation functions in this work were fitted by a single stretched exponential function, Equation (4). The collective diffusion coefficient Dc were extracted as the function of the droplet mass fraction and illustrated in Figure 3. The collective diffusion coefficient measurements were carried out on dilution series of microemulsion samples at fixed temperature 293.15 K and molar ratio 6.7. In the Figure 3, the collective diffusion coefficient show a liner behavior with negative slop between 0.01 < mf < 0.07. The light scattering experiments revealed that the collective diffusion coefficient of the system decreases with increasing droplet mass fraction, which indicates the attractive interactions between droplets.

In this work, SAXS was used for the determination of the structure of AOT/H₂O/Decane and AOT/H₂O/Cyclohexane microemulsion at 293.15 K. The scattered intensity as a function of q for AOT/H₂O/Decane and AOT/ H₂O/Cyclohexane with molar ration 6.7 and mass fractions 0.1 were collected for these experiments is presented in the Figure 4, which the lines are fits to a power law, I(q) ≈ q – 1, with properties of a cylindrical object. At small q, the Guinier’s law, I(q) ≈ exp(–(qξ)^2/3), is used for analyzing the data, where ξ is a correlation length.

Results show that the correlation length (ξ) is changing from 45Å to 23Å and cylindrical to spherical transition with changing oil from decane to cyclohexane. We know that spherical droplet with lower size can diffusion better that the cylindrical shape with bigger size. So, the change of size and shape can describe the different between the collective diffusion coefficient at AOT/H₂O/Decane and AOT/H₂O/Cyclohexane microemulsion. For analyzing the data, we applied a model for a mixture of core-shell spheres with an added depletion attraction due to dissolved non-adsorbing polymer. The scattering intensity as function of the scattering vector I(q) of spherical, monodisperse particles can be describe with a form factor component F(q), which is proportional to the scattering of a single particle, and a structure factor S(q), which describes the interaction effect:

c being a prefactor, which contains the number density of scattering particles. For the general case of n shells around a spherical droplet core the form factor reads.

where R_i is the radius of the ith shell or, respectively, the core R₀ and ∆ρ_i is the electron density contrast between the shells i and i + 1 with ρn + 1 and ρ₀ being the electron density of the solvent and the core, respectively. So, for a simple core-shell micelle n = 1. The structure factor is the Fourier transform of the pair correlation function g(r).

The pair correlation function gives the probability to find another particle at a distance r from the center of a given particle, relative to the probability to find a particle at this distance in an ideal gas. It is closely related to the total correlation function h(r) = g(r) − 1 and it can by means of the Ornstein-Zernike equation [16,17]. The results of the fit of SAXS experiment with hard sphere model and hard sphere model with core radius 25 and core-shell radius 30 with polydispersity 0.19 are presented in the Figure 5.