Phase equilibrium, Monte Carlo simulations

By virtue of their simple stnicture, some properties of continuum models can be solved analytically in a mean field approxunation. The phase behaviour interfacial properties and the wetting properties have been explored. The effect of fluctuations is hrvestigated in Monte Carlo simulations as well as non-equilibrium phenomena (e.g., phase separation kinetics). Extensions of this one-order-parameter model are described in the review by Gompper and Schick [76]. A very interesting feature of tiiese models is that effective quantities of the interface—like the interfacial tension and the bending moduli—can be expressed as a fiinctional of the order parameter profiles across an interface [78]. These quantities can then be used as input for an even more coarse-grained description. 

A sequence of successive configurations from a Monte Carlo simulation constitutes a trajectory in phase space with HyperChem, this trajectory may be saved and played back in the same way as a dynamics trajectory. With appropriate choices of setup parameters, the Monte Carlo method may achieve equilibration more rapidly than molecular dynamics. For some systems, then, Monte Carlo provides a more direct route to equilibrium structural and thermodynamic properties. However, these calculations can be quite long, depending upon the system studied. 

The energy landscape approach can elucidate such general properties of molecular recognition as the nature of the thermodynamic phases and barriers on the ligand-protein association pathway [127,128]. This method evaluates equilibrium thermodynamic properties of the system from Monte Carlo simulations of the system at a broad temperature range with the aid of the optimized data analysis and the weighted histogram analysis technique [148-153],... 

Pioneering grand canonical Monte Carlo simulations by Schoen et al, [176,183,184] examined the equilibrium behavior of a film of spherical molecules between two commensurate walls. As h and the lateral translation x of the top wall were varied, the film underwent transitions between fluid and crystalline states. The crystal was stable when the thickness was near an integral multiple of the spacing between crystalline layers and when the lateral translation was also consistent with the crystalline repeat. In this case, the ordering influences of the two walls interfered constructively and provided a strong ordering influence. Other values of h and x led to destructive interference and stabilized the fluid phase. 

In Monte-Carlo simulations, the energy of the molecular system is minimized by randomly moving the molecules in accordance with a desired probability distribution. After each move, the energy of each molecule is computed. When the total energy is reduced, the move is accepted and the molecules are redistributed. Moves are continued until equilibrium is achieved. As for molecular dynamics simulations, potential functions are provided. After convergence, the thermophysical properties, at equilibrium, are computed by averaging. Monte-Carlo methods, which are particularly effective for the calculation of thermophysical properties, including phase equilibria, are considered in detail by Rowley (1994). 

This chapter discusses the form and parameterization of the potential energy terms that are used for the atomistic simulation of polymers. The sum of potential terms constitutes a molecular force field that can be used in molecular mechanics, molecular dynamics, and Monte Carlo simulations of polymeric systems. Molecular simulation methods can be used to determine such properties as PVT data, selfdiffusion coefficients, modulus, phase equilibrium, x-ray and neutron diffraction spectra, small molecule solubility, and glass transition temperatures with considerable accuracy and reliability using current force fields. Included in the coverage of Chapter 4 is a review of the fundamentals of molecular mechanics and a survey of the most widely used force fields for the simulation of polymer systems. In addition, references to the use of specific force fields in the study of important polymer groups are given. 

The grand canonical ensemble simulations model systems in which the chemical potential (/x), the volume and temperature are held fixed while the number of particles changes. The approach is very useful for simulating phase behavior which requires a constant chemical potential. Grand Canonical Monte Carlo simulation has been used to calculate sorption isotherms for a number of difierent microporous silicate systems. The simulations are used to model the equilibrium between zeolite and sorbate phases and, as such, it provides a natural way of simulating sorption isothermsl ... 

Gibbs ensemble Monte Carlo simulation is predominantly used to simulate phase equilibrium for fluids and mixtures. Two fluid phases are simulated simultaneously allowing for particle moves between each phasel . 

Monte Carlo simulation techniques have been extensively used to study solvent effects on molecular properties and equilibrium points. Jorgensen has summarized theoretical work of condensed-phase effects on conformational equilibria [63]. 

---