Collision Diameters, Interaction Potentials, and Virial Coefficients of Small Quasi-Spherical Molecules

Abstract

A recently introduced mapping approach to the equation of state of classical fluids is used to study the dilute gas phase. The approach introduces mean collision diameters σ(T) and R(T), which reflect the contributions to the pressure from the repulsive and attractive forces, respectively. The mean diameters are analyzed for a variety of molecules in the gas phase. The temperature dependence of σ(T) and R(T) is shown to be essentially dominated by two shape factors, S R and S A , characterizing the form of the repulsive and attractive parts of a the interaction, respectively. The method gives insight into the collision diameters and second virial coefficients, B(T), of model molecules, both spherical and nonspherical, including three-parameter potential functions and diatomic Lennard-Jones molecules. As a practical bonus, the theory provides a compact and highly accurate model for B(T) of model and real molecules. The theory also provides a route to reliable information on the effective intermolecular potential from a knowledge of B(T). The theory is applied to gaseous neon, argon, krypton, dinitrogen, dioxygen, difluorine, methane, and tetrafluoromethane, and their mean collision diameters and potential parameters are determined and analyzed.

Nonconformal Potentials and Second Virial Coefficients in Molecular Fluids. 1. Theory

“…16,18 More recently, the analysis of collision diameters in dilute gases has led to interesting applications and insights. 19,20 In the low-density limit, where σ and λ are functions of T only, the approach provides very simple expressions for the virial coefficients B(T) of many gases of interest, both model and real. In a previous publication, we have shown that σ 3 and λ 3 of two nonconformal gases can be linearly related to each other by means of two shape parameters S R and S A connected to the form of the potentials in their repulsive and attractive regions, respectively.…”

Nonconformal Potentials and Second Virial Coefficients in Molecular Fluids. II. Applications to Nonspherical Molecules

“…1 This theory provides an explanation of regularities in the behavior of second virial coefficients B(T) and mean collision diameters found previously. 2 We have shown that effective pair intermolecular potentials are characterized by two scale parameterssa distance r m and an energy sand two constants S R and S A describing the softness of the potential of interest in its repulsive and attractive regions with respect to a reference. The theory also provides closed and simple expressions for B(T) of many gases of interest, both model and real.…”

“…The approach provides a general and simple expression for B(T) and reliable effective pair interaction parameters for many substances, spherical and quasi-spherical, which reproduce the available data within estimated experimental errors. 2 In this paper, we apply the theory to more complex molecules. Effective potentials are obtained for a variety of nonspherical modelssspherocylindrical and ellipsoidal square wells, linear Kihara molecules, multicentered Lennard-Jones, square-well chains, and Stockmayer polar moleculessand the effects of geometrical shape are discussed in light of the theory.…”

Interaction potentials and thermodynamics of small polar molecules. The case of C1-Freons (halomethanes)

“…For u ANC (z; s) to be an accurate effective potential at low densities and with constant parameters equation (7) has to be satisfied by B exp (T ) data of the substance in question; as a matter of fact, many substances do so to a high degree of approximation [45]. This property is exhibited in figure 2 for four very dissimilar substances: Ar, CH 4 , HCl and H 2 O.…”