New determination of the thermophysical properties of argon gas considering nuclear spin and symmetry effects

Context

Since statistical physics and quantum mechanics were first successfully combined thanks in part to the work of Chapman and Cowling and Hirschfelder. Extensive theoretical and experimental research has been dedicated to understanding the kinetics of gases and gas mixtures. This integration has, among other achievements, theoretically established a direct link between the macroscopic properties of gases whether measured or calculated and the quantum characteristics of their constituent particles. This model successfully established straightforward mathematical relationships linking the microscopic interactions between the atomic and/or molecular components of a gas to measurable transport properties, such as diffusion and viscosity coefficients. It also provided explanations for how these properties vary and how they are influenced by thermodynamic parameters like pressure, density, and temperature.

Methods

The potential data available to us are either obtained from ab initio calculations or experimental measurements. The ab initio values of the potential V(R) are derived from a quantum-theoretical approach to the molecular problem. Typically, these methods provide the potential energy at discrete values of the internuclear distance R within a specified range. To build the potential energy curve corresponding to the fundamental interactions, we will rely on ab initio data. Knowing this potential allows for the numerical solution of the radial wave equation using Numerov’s method, ultimately enabling the calculation of the phase shifts \(\eta \left( E\right) \). From the elastic collision phase shifts, we derive the self-diffusion coefficient D, viscosity \(\eta \), and thermal conductivity \(\lambda \) using the Chapman-Enskog model. For diffusion and viscosity, we perform calculations both with accounting for the symmetry and spin effects associated with the identical nature of the colliding particles. We then examine how these transport coefficients vary with temperature and propose a straightforward computational approach to obtain analytical expressions for D(T), \(\eta (T)\), and \(\lambda (T).\)