Diffusion of spherical macromolecules at finite concentration

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Abstract
An expression for the concentration‐dependent diffusion coefficient is derived which accounts for both hydrodynamic and long‐range potential interactions between rigid spherical macromolecules in solution. A self‐consistent field approach is taken, based on the Smoluchowski equation for a single Brownian particle in an external force field. The external force contribution to particle flux is replaced by a configurational average which includes the effects of both interparticle forces and hydrodynamicfriction for each configuration; this term gives rise to a concentration‐gradient‐induced migration. The purely diffusive contribution to particle flux is computed from an analysis of two‐particle viscousinteractions assuming uncoupled pressure fluctuations on each particle. Since only binary hydrodynamicinteractions between particles are considered, the resulting expression for the diffusion coefficient is valid only to order φ, the volume fraction of particles in the solution. This expression is evaluated for several types of interparticle potentials. For the hard sphere case, these calculations show fair agreement with published experimental data for diffusion at finite concentrations. The model predicts that tracer and mutual diffusion coefficients for hard spheres should be equal, in agreement with these data. The general relation between diffusivity and particle concentration derived here differs from the classical one, which views the driving force as the gradient in chemical potential. The difference is due to the manner in which the hydrodynamicinteractions are averaged.