Molecular dynamics and analytical Langevin equation approach for the self-diffusion constant of an anisotropic fluid

Abstract

We carried out a molecular-dynamics (MD) study of the self-diffusion tensor of a Lennard-Jones-type fluid, confined in a slit pore with attractive walls. We developed Bayesian equations, which modify the virtual layer sampling method proposed by Liu, Harder, and Berne (LHB) [P. Liu, E. Harder, and B. J. Berne, J. Phys. Chem. B 108, 6595 (2004)]. Additionally, we obtained an analytical solution for the corresponding nonhomogeneous Langevin equation. The expressions found for the mean-squared displacement in the layers contain naturally a modification due to the mean force in the transverse component in terms of the anisotropic diffusion constants and mean exit time. Instead of running a time consuming dual MD-Langevin simulation dynamics, as proposed by LHB, our expression was used to fit the MD data in the entire survival time interval not only for the parallel but also for the perpendicular direction. The only fitting parameter was the diffusion constant in each layer.

The generalized Langevin equation revisited: Analytical expressions for the persistence dynamics of a viscous fluid under a time dependent external force

“…where g(z 0 ) is the one-particle radial distribution function of the fluid, normalized in the slab [0, L]. In the virtual layer model simulations [4,22] the external mean force is assumed to be a constant within the slab, so the potential of mean force is W (z 0 ) ∼ = −F z 0 and in terms of the parameter Pe 0…”

“…To the best of our knowledge, all attempts to study a fluid diffusing within absorbing barriers are based on the Smoluchowski or high friction approximation [4,32,33,37,38] which can be obtained as a particular case of our general equations. As λ → ∞ we get the static Langevin approximation, using αχ LE (t) = (α t − 1 + e −α t )/α, while as αt ≫ 1 we get the Smoluchowski limit, using αχ SE (t) = t and D z (t) = D(t) = D 0 .…”

“…For zero force, the sums appearing in Eqs. (115) and (116) become the Riemann type, namely, ∞ n=1 [1 − (−1) n ] sin(nπz 0 /L)/n 3 = π 3 (L − z 0 )z 0 /4L 2 and ∞ n=1 [1 − (−1) n ] /n 4 = π 4 /48, so we get the well known results [32,38,39] To test the above equations, we used the MD simulation data for LJ-argon fully described elsewhere [4]. In Fig.…”

“…The static LE can be solved by a double integration or alternatively, through the solution of a second order differential equation [1,3]. In fact, an analytical solution for a confined fluid has been previously given [4].…”

Extracting work from a single reservoir in the non-Markovian underdamped regime

“…The Generalized Fokker-Planck Equation follows (subject to analytical tractability) from which the procedures in this paper can be used. This is already feasible fot the case treated here of a particle confined in a harmonic potential but more general relations have been obtained for smoothly varying external potential which can include anharmonicities [34]. The authors in Ref.…”