Walter Hess

Self-diffusion of spherical Brownian particles with hard-core interaction

The N-particle Smoluchowski equation is solved exactly for a system of spherical Brownian particles interacting through hard-core potentials to first order in the volume concentration φ. The self-diffusion coefficient is found to be given by Ds = D0(1−2φ), where D0 is the free diffusion constant. The hydrodynamic interaction is then taken into account in a perturbative way. Using the Oseen approximation, Ds = D0(1−0.09φ) is found, whereas the improved form for the hydrodynamic interaction due to Felderhof gives Ds = D0(1−1.89φ).

ON THE MEMORY FUNCTION FOR THE DYNAMIC STRUCTURE FACTOR OF INTERACTING BROWNIAN PARTICLES

It is shown that the memory function of concentration fluctuations M(k, t), derived from the generalized Smoluchowski equation, is not a one-particle irreducible quantity. A new function M(k, t), which is one-particle irreducible, is derived and the relation between both functions is established. The irreducible memory function M(k, t) can be interpreted as a dynamic viscosity. In contrast to earlier statements there is no discrepancy in the results, which are obtained from phase space approach (Fokker-Planck equation) and those obtained from the Smoluchowski equation.

The static structure factor of a dilute system of charged rods in solution

For a solution of charged rods the static structure factor is derived in a weak-coupling expression. The interaction between the rods is assumed to be a superposition of screened Coulomb interactions between point charges distributed along the rod. Screening arises from the counter ions as well as from salt in the solvent. The authors treat the case of an isotropic solution as well as the nematically ordered state.

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

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 Ds as a function of concentration and of the coupling strength between macroions.