Solvent diffusion in ordered macrofluids: A stochastic simulation study of the obstruction effect

Abstract

An off-lattice random-flight simulation procedure is described which accurately predicts the obstruction factors for self-diffusion of small molecules in macrofluids. The simulation procedure, employing a continuous step length distribution that ensures rapid and accurate convergence, was validated by comparison with exact results for cylindrical and spherical obstructions on 2D and 3D lattices. The exact results were computed with Rayleigh’s multipole method, which also was used to derive a new analytical formula for the obstruction factor of parallel cylinders on a hexagonal lattice, of much higher accuracy than the commonly used approximations. Random-flight simulations were used to assess the accuracy of existing mean-field approximations for the obstruction factors of orientationally ordered nonspherical objects. Due to a near-cancellation of errors, the mean-field result accurately describes the obstruction effect on the trace of the diffusion tensor, as measured in isotropic systems, up to moderately high volume fractions. In contrast, the diffusion anisotropy, a sensitive indicator of microstructure in anisotropic fluids, is accurately predicted by mean-field theory only at low volume fractions.