Brownian dynamics simulation of interacting particles

The dynamics of the ions in an electrical double layer has been studied using stochastic dynamics simulation methods. The theory of a brownian particle in an external force field is discussed and a modified form of the fluctuation-dissipation theorem is derived. With slowly varying external forces the simulations can be restricted to configuration space and the correction term to the fluctuation-dissipation theorem, arising from the external force, can be neglected. It is shown that the diffusion coefficient of a brownian particle can be calculated from the force correlation function. In comparison with calculations from mean-square displacements the former way turns out to be much more efficient. Finally, a relation between the external force () and the random force () is derived such that <(0)(t)> = -2<(0)(t)>.