Three-body distribution functions in hard sphere fluids. Comparison of excluded-volume-anisotropy model predictions and Monte Carlo simulation

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.

Pressure and temperature-dependent gauche-trans isomerization of 1-bromopropane: Raman measurement and statistical thermodynamic analysis

“…36 The sensitivity of the PHF model to solute anisotropy ͑⌬͒ comes from the fact that the chemical potential of each solute depends on anisotropy ͑as dictated by the EVA model and confirmed by Monte Carlo simulation results͒. 28,29,36 In retrospect, it should not be surprising that the best fit anisotropy values are not exactly the same as those derived for the excluded volumes and areas of the solutes ͑see Appendix and Table II͒. This is because the EVA model is only strictly intended to model cavity formation energies for solute molecules dissolved in hard sphere fluids.…”

“…28,29 The present work, and previous solvation free energy calculations, 10 illustrate applications of the EVA model to molecular liquid thermodynamic calculations. In order to perform such calculations reliably, it is very important to choose an appropriate effective hard sphere diameter for the solvent.…”

Chemical Potentials of Hard-Core Molecules by a Stepwise Insertion Method

“…We validated the proposed stepwise insertion Monte Carlo method through the calculation of residual chemical potentials of highly dilute trimers in spheres. The trimers are composed of identical spheres whose centers form an equilateral triangle with side length equal to one spherical diameter, so that we could reproduce the results of Ben-Amotz et al (1997). The simulation box contained 256 spheres and the diameter ratio d 1 = σ 1 /σ S varied from 0.1 to 0.9 at the reduced densities of 0.1, 0.5, and 0.8.…”

“…Results are presented in Figure 6 and were compared with those of Ben-Amotz et al (1997), who calculated the chemical potential with two different methodologies, both based on the Widom insertion method. One can observe an increase of residual chemical potential with the increase of the diameter ratio.…”

Assessment of Three-Dimensional Distribution Functions and Triplet Distribution Functions for Hard Spheres Calculated Using a Three-Dimensional Ornstein–Zernike Equation with Hypernetted-Chain Closure

“…Therefore, an assessment of the triplet correlation is our second purpose. Some molecular simulations have been used to obtain triplet distribution functions for a hard-sphere fluid [19][20][21][22][23]. However, the results are not adequate for our study, because we wish to examine the distribution function of a system that has the same packing fraction as water.…”