Monte Carlo simulations solid-fluid equilibrium

A review of Monte Carlo and molecular dynamics simulation methods for studying solid-fluid equilibrium ... 

Molecular Simulations Molecular simulations are useful for predicting properties of bulk fluids and solids. Molecular dynamics (MD) simulations solve Newton s equations of motion for a small number (on the order of 10 ) of molecules to obtain the time evolution of the system. MD methods can be used for equilibrium and transport properties. Monte Carlo (MC) simulations use a model for the potential energy between molecules to simulate configurations of the molecules in proportion to their probability of occurrence. Statistical averages of MC configurations are useful for equilibrium properties, particularly for saturated densities, vapor pressures, etc. Property estimations using molecular simulation techniques are not illustrated in the remainder of this section as commercial software implementations are not generally available at this time. 

Chemical equilibrium in an inhomogeneous fluid requires that the local chemical potential p(r) be independent of r. For a fluid in a canonical ensemble (either molecular dynamics or Monte Carlo), one considers a particular configuration of N molecules. An additional molecule is inserted at Ri this molecule interacts with the N molecules and the solid initially there but does not affect the simulated molecular configuration in any way. If the energy of this interaction is denoted by y(l, N), where the added particle is at 1 and the A particles are at positions denoted by / .v, it can be shown that [14]... 

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