Widom insertion method

Abstract: Methods and intermolecular potentials apt for the molecular simulation of solubilities of solids in supercritical fluids are briefly reviewed. As an illustrative example, the solubilities of naphthalene in supercritical carbon dioxide at 328.15 K are studied using an isotropic multipolar potential model. Upon using the Widom insertion method, a quantitative prediction of the experimental data is obtained. A further look at the calculations shows that the customary implementation of the method is tainted by the use of experimental information about the vapor pressure and density of the solid. If the actual properties (obtained via simulation) of the model solid are used, the equilibrium is, in this example, poorly described. Full-scale molecular dynamic simulations, which include both the solid and fluid phases, confirm the results. It is shown how an accurate description and modeling of the solute solid-phase properties is a prerequisite for the determination of the solubilities of solids in supercritical...

Abstract: The chemical potential of lattice polymers is calculated in two alternative ways: by the Widom insertion method using the Rosenbluth and Rosenbluth sampling technique and by the modified Widom method, based on the insertion of one segment to an existing polymer chain. In the first part of this paper we present a detailed derivation of the modified Widom technique for lattice systems. We then proceed to calculate the chemical potential for chains of up to 50‐mers in monomeric and polymeric solvents. We observe marked odd‐even effects on the chemical potential. The density dependence of the chemical potential is found to vary with chain length. For most temperatures and densities studied the chemical potential of chain molecules in a fixed environment becomes linear in chain length for molecules longer than 10–20 segments. The results are compared to the classical lattice theories, which are found to be best at high densities, as expected based on previous investigations.

Abstract: Hard sphere three-body distribution functions predicted by the recently developed Excluded-Volume-Anisotropy (EVA) model are compared with Monte Carlo computer simulation measurements. Two types of simulations, both based on the Widom insertion method, are performed as a function of solvent density (0.1⩽ρσ3⩽0.8), solute structure (linear, triangular, and bent 3-bead chain), and solute–solvent sphere diameter ratio (0⩽σ/σS⩽3). Comparisons of these results with those of previous studies illustrate the accuracy of the EVA model in predicting multi-body distribution functions near contact separations (and inside of contact), where the Kirkwood-Superposition-Approximation is least accurate.