Viscosity in molecular dynamics with periodic boundary conditions

TL;DR

This paper introduces a new Helfand-moment method for calculating viscosity in molecular dynamics with periodic boundary conditions, aligning with Green-Kubo and Alder's approaches, and verifies it with hard disk simulations.

Contribution

A novel Helfand-moment definition for viscosity that accounts for periodic boundaries and aligns with existing methods, validated through hard disk simulations.

Findings

Method agrees with Green-Kubo and Alder's approaches.

Viscosity values match Enskog's theory for small systems.

Effective in systems with periodic boundary conditions.

Abstract

We report a study of viscosity by the method of Helfand moment in systems with periodic boundary conditions. We propose a new definition of Helfand moment which takes into account the minimum image convention used in molecular dynamics with periodic boundary conditions. Our Helfand-moment method is equivalent to the method based on the Green-Kubo formula and is not affected by ambiguities due to the periodic boundary conditions. Moreover, in hard-ball systems, our method is equivalent to the one developed by B. J. Alder, D. M. Gass, and T. E. Wainwright [{\it J. Chem. Phys.} {\bf 53}, 3813 (1970)]. We apply and verify our method in a fluid composed of $N\geq 2$ hard disks in elastic collisions. We show that the viscosity coefficients already take values in good agreement with Enskog's theory for N=2 hard disks in a hexagonal geometry.