Molecular dynamics studies of transport phenomena in fluids via generalized Langevin equation

Abstract

The dynamics of translational motion and rotational motion were investigated by analyzing the fundamental fluid systems which are simple fluid and diatomic molecular fluid. The properties of correlation functions and transport coefficients were analyzed via generalized Langevin equation (GLE). The GLEs for the fluid systems were formulated for whole degrees of freedom including rotation, which lead to the matrix form of time-correlation and memory kernel.

The superdiffusive behavior of two-dimensional simple fluid was studied. We found the evidences of superdiffusivity from various physical properties such as the distribution function of squared displacements, mean squared displacement (MSD), velocity autocorrelation (VACF), and the time-dependent transport coefficients. Generalized Corngold relation was suggested. The relation showed considerable consistency in superdiffusive fluid. The consistency of Einstein relation is checked by the deviation between both sides of the relation. The deviation showed algebraic decay for both fluids in two dimension and three dimension, however much gradual decay was observed in two-dimensional fluid. In order to expand the Einstein relation for anomalous diffusion condition, the generalized version of Einstein relation was derived by Tauberian theorem. The self-consistency relation was derived based on linearized hydrodynamic equations for the fluid conditions of finite size and bulk limit. Then the analytical form of the VACF, the time-dependent diffusion coefficient, and the MSD was derived from the self-consistency relation in bulk limit via the form of ordinary differential equation. We compared the MD result and the analytical expression to verify the excellent agreement.

The modification of the superdiffusivity is analyzed. The two types of finite-size effect were analyzed with MD result. They are relevant to the exponential decay and the additional peaks in the VACF, respectively. The regions of superdiffusivity, normal diffusion, and subdiffusion were determined for two-dimensional fluid on the two-dimensional plane of number density and temperature. The tracer particle mass of superdiffusive fluid was gradually increased toward the Brownian limit, which resulted in the weakening of the superdiffusivity. This was observed by the enhanced decay of algebraic tail of the VACF and the memory kernel.

The diatomic molecular fluids were investigated. We checked the consistency of the GLE by analyzing fluctuation-dissipation theorem for fluid systems which are the diatomic molecule in the sea of ideal simple particle (DSSi) and real simple particle (DSS). The off-diagonal components of the correlation matrix and memory kernel matrix were negligible for the DSS fluid. The VACFs of the DSSi fluid and the DSS fluid showed analogous behavior to corresponding simple fluids. The exponential decay of the AVACF was observed for both diatomic molecular fluids. The faster exponential decay was observed in higher density. The orientational correlation functions (OCF) of both fluids basically exhibited Gaussian decay in low densities and exponential decay in high densities. Translation-rotation coupling (TRC) was calculated by using the function suggested by Balucani et al.. The value of the function was negligible when two atoms of diatomic molecule had identical mass, however the function showed the distinct peak when the mass symmetry of the molecule was broken.