A non-equilibrium Monte Carlo approach to potential refinement in inverse problems

TL;DR

This paper introduces a non-equilibrium Monte Carlo method to efficiently determine interparticle potentials in inverse problems for polydisperse systems, improving computational robustness at high densities and polydispersity.

Contribution

The paper presents a novel non-equilibrium simulation approach for accurately and efficiently finding the chemical potential distribution in polydisperse inverse problems.

Findings

Method successfully computes chemical potentials for polydisperse fluids.

Approach is robust at high densities and polydispersity levels.

Demonstrated on a log-normal particle size distribution.

Abstract

The inverse problem for a disordered system involves determining the interparticle interaction parameters consistent with a given set of experimental data. Recently, Rutledge has shown (Phys. Rev. E63, 021111 (2001)) that such problems can be generally expressed in terms of a grand canonical ensemble of polydisperse particles. Within this framework, one identifies a polydisperse attribute (`pseudo-species') $\sigma$ corresponding to some appropriate generalized coordinate of the system to hand. Associated with this attribute is a composition distribution $\bar\rho(\sigma)$ measuring the number of particles of each species. Its form is controlled by a conjugate chemical potential distribution $\mu(\sigma)$ which plays the role of the requisite interparticle interaction potential. Simulation approaches to the inverse problem involve determining the form of $\mu(\sigma)$ for which $\bar\rho(\sigma)$ matches the available experimental data. The difficulty in doing so is that $\mu(\sigma)$ is (in general) an unknown {\em functional} of $\bar\rho(\sigma)$ and must therefore be found by iteration. At high particle densities and for high degrees of polydispersity, strong cross coupling between $\mu(\sigma)$ and $\bar\rho(\sigma)$ renders this process computationally problematic and laborious. Here we describe an efficient and robust {\em non-equilibrium} simulation scheme for finding the equilibrium form of $\mu[\bar\rho(\sigma)]$. The utility of the method is demonstrated by calculating the chemical potential distribution conjugate to a specific log-normal distribution of particle sizes in a polydisperse fluid.