Brownian motion is a subject of renewed interest since the development of photon correlation spectroscopy (PCS) in the last decade. The dynamic properties of microemulsions and colloidal systems is studied by measuring the relaxation of concentration fluctuations, [1,2]. The relaxation time of the fluctuations can be expressed in a diffusion coefficient, which is called the collective diffusion coefficient (D_c), in the limit of infinite dilution. The study of the collective diffusion coefficient of microemulsion is an interesting topic in soft matter physics. The microemul- sions are thermodynamically stable mixtures of water, oil, and surfactant with nano-metric size of droplets to the solvents (H₂O or Oil). In the case of water/surfactants (droplet) to the nanopolar solvents (oil), microemulsions have L₂ phase and oil/surfactant inside the water solutions is L₁ phase of microemulsions. In our samples, the composition of each system is determined by the molar ratio X of water to surfactant molecules.

and the droplet mass fraction (mf),

which varies by the respective mass of the components water (), decane (m_Dec), and AOT. In this work, the microemulsion system is located in the L₂ region at studied temperatures and compositions investigated. Most works on collective diffusion coefficient of droplets and interactions of droplets have been done mainly on charged macromolecules, [3-15], for example bimolecular, [3-10], as DNA, proteins and amino acids, micelles, [11], and polymer latexes, [15], in water (as polar solvent) at low ionic strength. The strong, long range electrostatic interactions between the particles or droplets in these systems lead to remarkable structure effects. Only in the higher number densities or droplet concentration of microemulsions where the inter-particle separation is in the order of the particle dimensions hydrodynamic interactions can be observed.

In previous study of the collective diffusion coefficient in C₁₂E₅/H₂O/Decane microemulsion, the collective diffusion coefficient as function of droplet mass fraction has positive slop at the low droplet mass fraction (dilute regime mass fraction below 0.1) that describes an attractive interaction between droplets. It is well known that C₁₂E₅/- H₂O/Decane microemulsion at constant surfactant-oil mass ratio of 1.08 with the different mass fractions has shown behaviors as the hard sphere droplets, [16-20]. The Collec- tive diffusion coefficient as function of mass fraction in the C₁₂E₅/H2O/Decane microemulsion has positive behavior and only depends to the inter-particle interaction of hard sphere droplet. The mixture of PEG with C₁₂E₅/H₂O/- Decane microemulsion shown that addition of PEG causes slow down of the collective diffusion coefficient D_c. The measured D_c data for the droplets in the presence of PEG are modeled using the Asakura-Oosawa theory of depletion, [20], but D_c in the AOT/H₂O/Decane microemulsions has different behavior. Structure and phase behavior of AOT microemulsions are well investigated of a liquid of droplets on a nanometer scale, [21]. A study shown, for AOT/H₂O/Decane microemulsion, at the low droplet mass fractions (0.01 < mf < 0.1 transition from dilute to semi-dilute regime) and molar ratio 40 the collective diffusion coefficient has a linear function of mass fraction. It is well known that at high water concentration with the molar ratio of X = 40 the collective diffusion coefficient D_c depends on the droplet mass fraction (droplet concentration) due to inter-particle interactions, [22]. This study is an attempt to understand the collective diffusion coefficient behavior of AOT/H₂O/Decane microemulsion at low water concentration (molar ratio, X = 6.7). The most study in this range of water concentration that shown droplet of the microemulsion has spherical behavior, [23,24]. In the present work, we studied the behavior of the collective diffusion coefficient at the molar ratio 6.7 and low mass fraction (0.01 < mf < 0.08), by means of DLS and SAXS techniques. Also, we study effect of TBAC on the D_c in the AOT/H₂O/Decane microemulsion.

Microemulsions were formulated by mixing AOT with water and n-Decane at the fixed molar ratio of water to AOT (X = 6.7) at the different mass fraction (0.01 < mf < 0.07 dilute regime). The dynamic behavior of the AOT/- H₂O/Decane microemulsion was probed with dynamic light spectroscopy. The correlation function of the scattered light intensity showed a single exponential decay at all concentrations, Figure 1. (A). All the correlation functions in this work were fitted by a single stretched exponential function, [1,2].

That and the collective diffusion coeffi- cient D_c was extracted as a function of the droplet mass fraction as shown in Figure 1(b). 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 with two different molar ratio of TBAC (0.0 and 0.049 molar/l). In the Figure 1, the collective diffusion coefficient show a liner behavior with negative slop between 0.01 < mf < 0.07. By increasing TBAC content relaxation time decreases, Figure 1(a) and the diffusion coefficient increases, Figure 1(b).

In this experiment, SAXS is used for the determination of the structure of AOT/H₂O/Decane microemulsions at 293.15 K. The SAXS methods are useful for studies the structure of reverse micelles. This is because the scattering of X-rays of wavelengths of a few angstroms through small angles provides a Q range (as defined by Equation 2) which is particularly appropriate for the determination of both

the size of discrete reverse micelles and their interactions. From the angular dependence of the scattered X-ray intensity we have

where

Q is the wavelength and θ is the scattering angle. is referred to the form factor, which gives information on the dimensions of an individual reverse micelle, and is the structure factor, which provides information on inter-micelle interaction. We will consider the nature of the interactions between micelles. Information on interactions can be obtained from structure factor. The scattered intensity as a function of Q from samples presented in the Figure 2, which the lines are fits to a power law,

, with properties of a cylindrical object. At small Q, the scattering is only sensitive to the overall dimension of the scattering particles, and we expect from Guinier’s law, , where ξ is correlation length. The microemulsions with molar ration 6.7 and different droplet mass fractions were collected for these experiments. The SAXS data is measured from the high concentration sample (mass fraction 0.1) to the dilute sample. Figure 2 shows the small angle X-ray scattering intensities for AOT/H₂O/Decane as a function of Q at the molar ratio 6.7 and different mass fraction.

Figure 2, depict that intensity as a function of Q at the high droplet mass fraction (mf = 0.1) and Q range of 0.02 < Q (1/Å) < 0.1 has linear behavior. At low Q, we used Guinier’s law, , that results presented in the Figure 3" target="_self"> Figure 3. Our results show, the correlation length change from 23 Å to 50 Å with the increase of droplet mass fraction (Figure 3). The most important observation from Figure 2 is increasing of the correlation length with the increase of droplet mass fraction. We also study the effect of adding TBAC to the AOT/H₂O/Decane microemulsion with SAXS experiment. The correlation length change from 50 Å to 30 Å with adds TBAC to the AOT/H₂O/Decane microemulsion, Figure 3.