Transport and Helfand moments in the Lennard-Jones fluid. I. Shear viscosity

Abstract

The authors propose a new method, the Helfand-moment method, to compute the shear viscosity by equilibrium molecular dynamics in periodic systems. In this method, the shear viscosity is written as an Einstein-type relation in terms of the variance of the so-called Helfand moment. This quantity is modified in order to satisfy systems with periodic boundary conditions usually considered in molecular dynamics. They calculate the shear viscosity in the Lennard-Jones fluid near the triple point thanks to this new technique. They show that the results of the Helfand-moment method are in excellent agreement with the results of the standard Green-Kubo method.

Are pressure fluctuation-based equilibrium methods really worse than nonequilibrium methods for calculating viscosities?

“…All viscosities from equilibrium approaches are averages over a correlation time of 2-20. For the LJ fluid at the triple point: T ‫ء‬ = 0.722 and ‫ء‬ = 0.8442, our computed viscosity of 3.269Ϯ 0.002 matches well the most recent and accurate viscosity value reported by Viscardy et al, 15 3.291Ϯ 0.057.…”

Thermodynamic formalism for transport coefficients with an application to the shear modulus and shear viscosity

“…Measuring the average current as a function of driving strength then allows to extract the transport coefficient from the initial linear slope. Two drawbacks of this approach are: (i) the dependence on the finite size of the simulated system, which often requires some sort of extrapolation in order to determine bulk properties [7,8] and (ii) smaller fields lead to larger errors. In principle one can control either the field ("Thévenin" ensemble) or the current ("Norton" ensemble), but typically one of these two can be implemented more easily.…”

“…In some cases these fluxes can be rewritten as a total derivative, which allows the Green-Kubo formula to be recast in terms of an Einstein-Helfand relation [19]. Transport coefficients can then be determined either from moments evaluated at explicit boundaries [20] or in bulk implementing periodic boundaries [8,21].…”

Viscosity calculations at molecular dynamics simulations

“…Green and Kubo proved that the coefficients describing the transport properties of the system can be represented as integrals of autocorrelation functions [3]. The self-diffusion coefficient D is calculated using the formula:…”

“…Two basic methods for the transport coefficients calculation are applied. The first one uses the Green-Kubo formulas which relate the transport coefficient to the integrals of the autocorrelation functions [3]. Another method exploits the EinsteinHelfand expressions [3,4] which permit to obtain transport coefficients directly from the particle displacements and velocities.…”