Phase Field Crystals as a Coarse-Graining in Time of Molecular Dynamics

TL;DR

This paper demonstrates how phase field crystals can be derived as a time coarse-graining of molecular dynamics, enabling simulations of material dynamics at mesoscopic time scales using a free energy approach.

Contribution

It introduces a method to interpret PFC as a coarse-grained version of MD, linking free energy forms to microscopic density fields through classical density functional theory.

Findings

PFC can be derived from MD via time coarse-graining.

The PFC free energy matches the structure factor of coarse-grained MD.

Application to protein membrane systems demonstrates practical relevance.

Abstract

Phase field crystals (PFC) are a tool for simulating materials at the atomic level. They combine the small length-scale resolution of molecular dynamics (MD) with the ability to simulate dynamics on mesoscopic time scales. We show how PFC can be interpreted as the result of applying coarse-graining in time to the microscopic density field of molecular dynamics simulations. We take the form of the free energy for the phase field from the classical density functional theory of inhomogeneous liquids and then choose coefficients to match the structure factor of the time coarse-grained microscopic density field. As an example, we show how to construct a PFC free energy for Weber and Stillinger's two-dimensional square crystal potential which models a system of proteins suspended in a membrane.