Communication: relative diffusion in two dimensions: breakdown of the standard diffusive model for simple liquids.

Abstract

Using molecular dynamics simulations for a liquid of identical soft spheres we analyze the relative diffusion constant DΣn(r) and the self diffusion constant Dn where r is the interparticle distance and n = 2, 3 denotes the dimensionality. We demonstrate that for the periodic boundary conditions, Dn is a function of the system size and the relation: DΣn(r = L/2) ≅ 2Dn(L), where L is the length of the cubic box edge, holds both for n = 2 and 3. For n = 2 both DΣ2(r) and D2(L) increase logarithmically with its argument. However, it was found that the diffusive process for large two dimensional systems is very sensitive to perturbations. The sensitivity increases with L and even a very low perturbation limits the increase of D2(L → ∞). Nevertheless, due to the functional form of DΣ2(r) the standard assumption for the Smoluchowski type models of reaction kinetics at three dimensions:DΣn(r) ≈ 2Dn leads to giant errors if applied for n = 2.