Scaling of Langevin and molecular dynamics persistence times of nonhomogeneous fluids

Abstract

The existing solution for the Langevin equation of an anisotropic fluid allowed the evaluation of the position-dependent perpendicular and parallel diffusion coefficients, using molecular dynamics data. However, the time scale of the Langevin dynamics and molecular dynamics are different and an ansatz for the persistence probability relaxation time was needed. Here we show how the solution for the average persistence probability obtained from the backward Smoluchowski-Fokker-Planck equation (SE), associated to the Langevin dynamics, scales with the corresponding molecular dynamics quantity. Our SE perpendicular persistence time is evaluated in terms of simple integrals over the equilibrium local density. When properly scaled by the perpendicular diffusion coefficient, it gives a good match with that obtained from molecular dynamics.

Water self-diffusion at the surface of silica glasses: effect of hydrophilic to hydrophobic transition

“…The method we use is similar to a published method [25], but instead, we use a realistic model for liquid and wall. Another difference is the inclusion of reflective boundary conditions, as explicited later.…”

“…This method we use for the definition of normal diffusion which is based on the Smoluchowski equation cannot be valid at short times and at short distances. This difficulty has been considered extensively [24,25,39]. The difficulty is that particle enters in diffusion mode after an average relaxation time, after moving of an average minimal distance.…”

“…p i (x, t) is the integral over x 0 inside the ith layer of the conditional probability p i (x, t|x 0 , 0). Introducing the forward Smoluchowski operator L in its factorised form, the derivative of the conditional probability with respect to time can be expressed as [25] …”

“…This method neglects the external force and it can be applied far away from the interface where the density is uniform and the PMF is negligible. Another strategy [25] consists of fitting the survival probabilities (SPs) calculated by Brownian dynamics simulations (at the Langevin level of approximation) with the external force: in that case the normal diffusion coefficient is the one for which the SP calculated from Brownian dynamics compares well with the one calculated from molecular dynamics (MD). Recently Olivares-Rivas [25] has determined diffusion processes of a 12-6 Lennard-Jones model fluid, with a model wall by a similar approach.…”

“…A simple method [24][25][26] consists of calculating autocorrelation functions of the eigenfunction of the diffusion equation. This method neglects the external force and it can be applied far away from the interface where the density is uniform and the PMF is negligible.…”