Derivation of Variable Soft Sphere Model Parameters in Direct-Simulation Monte Carlo Method Using Quantum Chemistry Computation

Abstract

A practical procedure for deriving parameters of the variable soft sphere (VSS) molecular model for the Lennard–Jones potential of gas species in the direct-simulation Monte Carlo (DSMC) method is introduced. Intermolecular potential energy is fitted through the Lennard–Jones (L–J) potential, which is obtained by quantum chemistry computation. Computed L–J potentials are then used to compute viscosity and diffusivity coefficients for like and unlike molecules, respectively, based on gas kinetics theory. Related parameters of the VSS molecular model are derived by fitting these computed coefficients to those derived from the VSS model. Test results for O2–H2 mixtures using this procedure are in good agreement with existing data. VSS parameters for silicon-based species frequently encountered in the chemical vapor deposition process are derived as an example to illustrate the importance of this procedure in extending the applicability of the DSMC computation to gas species other than air-related species.