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

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.

6 pages, 3 figures

Cited by in corpus (17)

• Tuning density profiles and mobility of inhomogeneous fluids
• Phase equilibria and fractionation in a polydisperse fluid
• Solid-liquid coexistence of polydisperse fluids via simulation
• Phase behaviour of polydisperse spheres: simulation strategies and an application to the freezing transition
• Finite-size scaling and particle size cutoff effects in phase separating polydisperse fluids
• Accurate simulation estimates of cloud points of polydisperse fluids
• Phase behaviour and particle-size cutoff effects in polydisperse fluids
• A polydisperse lattice-gas model
• Influence of polydispersity on the critical parameters of an effective potential model for asymmetric hard sphere mixtures
• Liquid-gas coexistence and critical point shifts in size-disperse fluids
• Polydisperse hard spheres at a hard wall
• Implications of the effective one-component analysis of pair correlations in colloidal fluids with polydispersity
• Effect of polydispersity on the relative stability of hard-sphere crystals
• Solid-solid transition of the size-polydisperse hard-sphere system
• Liquid-vapor interface of a polydisperse fluid
• Elasticity of a polydisperse hard-sphere crystal
• Accurate simulation estimates of phase behaviour in ternary mixtures with prescribed composition