Dynamic light scattering from concentrated water-in-oil microemulsions: The coupling of optical and size polydispersity

Abstract

Dynamic light scattering from highly concentrated colloidal systems with a narrow distribution of particle sizes can be interpreted in terms of the sum of two independent modes due, respectively, to collective diffusion and polydispersity fluctuations; a general formalism has been presented for calculating the relative mode amplitudes for hard spheres in the Percus–Yevick approximation [Pusey, Fijnaut, and Vrij, J. Chem. Phys. 77, 4270(1982)]. This work extends the relative mode amplitude calculation to the general case where optical (i.e., refractive index) and size polydispersity are completely coupled such as in water-in-oil microemulsions. To develop the theory a concentric core-shell hard sphere model is adopted, in which particles possess a continuous variation in the core sizes but have constant shell thickness, thus giving rise to a distribution in the particle refractive indices. A new ‘‘measured’’ static structure factor SM(0) is derived, and applied to the calculation for the relative amplitude of the slow mode, A2/(A1+A2), as a function of solvent refractive index n0. A strong enhancement of the slow mode is predicted as the optical matching point is approached. The theory also shows that the dependence of A2/(A1+A2) on n0 is very sensitive to the extent of polydispersity, but rather insensitive to the distribution function used. Neglect of the nonuniformity in particle refractive index can cause a substantial overestimate of the size polydispersity. We have used our extended treatment to interpret the dynamic light scattering data from concentrated water-in-oil microemulsions formed from H2O, AOT, and apolar solvents using solvent composition to control the contrast in refractive index. It is found that the AOT-stabilized water microemulsion droplets have a size polydispersity of about 6.5%, which is smaller than previously thought.