Influence of multipolar and induction interactions on the speed of sound

At large distances between molecules, the intermolecular forces are essentially attractive. They can be classified conveniently into three types, that is, multipolar, induction, and dispersion forces. We consider rigid nonlinear molecules with enough symmetry so those principal axes of the quadrupole tensor of the polarizibility coincide. Multipolar and induction interactions are calculated with the help of quantum mechanical calculations of the intermolecular energy function and the help of perturbation theory. The multipole expansion is terminated at the quadrupole term. The focus is on the development of a mathematical model for calculation of the influence of multipole and induction interactions on the speed of sound and other thermodynamic functions of state. For the calculation of the thermodynamic functions of state, perturbation theory with the Lennard-Jones potential as the reference is used. The thermodynamic and structural properties of the Lennard-Jones system are known from Monte Carlo and molecular dynamics computer simulations. All important contributions are featured (translation, rotation, internal rotation, vibration, intermolecular potential energy, and the influence of electron and nuclei excitation). The analytical results are compared with the experimental data and models obtained by classical thermodynamics and show relatively good agreement.

[1]  J. S. Rowlinson,et al.  The Third Virial Coefficients of Polar Gases , 1951 .

[2]  H. Nishiumi.  AN IMPROVED GENERALIZED BWR EQUATION OF STATE WITH THREE POLAR PARAMETERS APPLICABLE TO POLAR SUBSTANCES , 1980 .

[3]  S. Saito,et al.  AN IMPROVED GENERALIZED BWR EQUATION OF STATE APPLICABLE TO LOW REDUCED TEMPERATURES , 1975 .

[4]  D. Heinemann,et al.  Thermodynamic properties of fluid oxygen from the SSR-MPA potential , 1993 .

[5]  John A. Zollweg,et al.  The Lennard-Jones equation of state revisited , 1993 .

[6]  Sofia Calero,et al.  Description of alternative refrigerants with BACKONE equations , 1998 .

[7]  Koichiro Nakanishi,et al.  Generalized equation of state for Lennard-Jones fluids—I. Pure fluids and simple mixtures , 1988 .

[8]  S. G. Penoncello,et al.  A New Fundamental Equation for Thermodynamic Property Correlations , 1986 .

[9]  K. Gubbins,et al.  Thermodynamics of polyatomic fluid mixtures—II , 1978 .

[10]  K. Shukla.  Thermodynamic properties of binary mixtures of atoms and diatomic molecules from computer simulation and perturbation theory , 1997 .

[11]  John S. Rowlinson,et al.  Liquids and liquid mixtures , 1959 .

[12]  Jurij Avsec,et al.  Velocity of Sound of Binary Mixture R507 and Ternary Mixture R404A , 2001 .

[13]  K. Gubbins,et al.  Thermodynamics of polyatomic fluid mixtures—I theory , 1978 .

[14]  J. Fischer,et al.  Construction and application of physically based equations of state: Part II. The dipolar and quadrupolar contributions to the Helmholtz energy , 1992 .

[15]  W. B. Sediawan,et al.  Computer modeling of naphthalene , 1989 .

[16]  Y. Miyano,et al.  An equation of state for lennard-jones pure fluids applicable over a very wide temperature range , 1993 .

[17]  J. Fischer,et al.  Construction and application of physically based equations of state: Part III. Correlative and predictive application to the refrigerants R22 and R152a , 1994 .

[18]  K. Gubbins.  Applications of molecular simulation , 1993 .

[19]  W. Reynolds.  Thermodynamic properties in SI , 1979 .

[20]  D. J. Tildesley,et al.  Equation of state for the Lennard-Jones fluid , 1979 .

[21]  J. Prausnitz,et al.  Molecular thermodynamics for fluids at low and high densities. Part I: Pure fluids containing small or large molecules , 1986 .

[22]  J. S. Rowlinson,et al.  The Critical Constants of Polar Gases , 1951 .

[23]  Ming-Jer Lee,et al.  An Improved Model of Second Virial Coefficients for Polar Fluids and Fluid Mixtures , 1998 .

[24]  K. Lucas,et al.  Third virial coefficient of simple linear molecules , 1986 .

[25]  J. Barker,et al.  What is "liquid"? Understanding the states of matter , 1976 .

[26]  K. Shukla.  Phase equilibria and thermodynamic properties of molecular fluids from perturbation theory: I. Pure fluids , 1994 .

[27]  K. Gubbins,et al.  Integrals over pair- and triplet-correlation functions for the Lennard-Jones (12–6)-fluid , 1986 .

[28]  J. Prausnitz,et al.  Molecular thermodynamics for fluids at low and high densities. Part II: Phase equilibria for mixtures containing components with large differences in molecular size or potential energy , 1986 .

[29]  Johann Fischer,et al.  Backone family of equations of state: 1. Nonpolar and polar pure fluids , 1996 .

[30]  Y. G. D. Rio.  Thermodynamics of a square well octopolar fluid , 1996 .