Gradient diffusion coefficients — theory and experiment

Abstract

The concentration dependence of the gradient diffusion coefficient of electrostatically stabilised colloidal particles has been investigated, both experimentally and theoretically, as a function of the physicochemical parameters. Dynamic light scattering experiments were used to measure the gradient diffusion coefficient of the electrostatically stabilised protein bovine serum albumin (BSA). A theoretical analysis based on the calculation of the thermodynamic and hydrodynamic coefficients which appear in the generalised Stokes–Einstein equation has been developed. Determination of these coefficients was based on a fundamental calculation of the colloidal interactions between particles which accounts for multiparticle electrostatic interactions, dispersion forces and configurational entropy effects. The thermodynamic coefficient was determined via (i) dilute limit calculations, (ii) solution of the Ornstein–Zernike equation with the hypernetted-chain (HNC) closure or (iii) cell model calculations. Further, the hydrodynamic interaction coefficient was computed via (i) dilute limit calculations (with two different forms for the radial distribution function) or (ii) a combination of perturbation theory and the results of an exact numerical solution for an ordered system. These coefficients were then combined to allow comparison between theory and experiment. It was shown that of the different theoretical approaches investigated, the best methods for calculation of the gradient diffusion coefficient are: (a) HNC approximation in disordered suspensions (high ionic strength and/or low particle concentration) and (b) cell model in ordered suspensions (low ionic strength and/or high particle concentration). Good quantitative agreement between theory and experiment was found.