Mass-diffusion and self-diffusion properties in systems of strongly charged spherical particles

Abstract

Using the Fokker–Planck equation as the basic description, various collective and single-particle properties of highly charged spherical macroparticles in solution are derived. The dynamic structure factor S(k,t) for finite k is found to be non-exponential in t due to the viscoelastic properties of the liquid of interacting macroions. By using a mode-coupling procedure the dynamical properties can be completely reduced to the static structure factor S(k), which is calculated according to the method developed by Hansen and Hayter. At short times the system exhibits elastic behaviour and the corresponding high-frequency elastic moduli have been calculated. The bulk modulus is found to increase with c², where c is the concentration. With regard to the single-particle properties, the velocity autocorrelation function is calculated and from it are obtained the mean-square displacement and the self-diffusion coefficient D_s as a function of concentration and of the coupling strength between macroions.