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

Abstract

A theory recently proposed characterizes effective two-body interactions in gases by molecular sizes and energies plus effective measures of the nonconformality between the exact potential and a spherical reference. This theory provides a procedure to construct effective potentials which reproduce the second virial coefficients B(T) of the substance of interest and allows us to express B(T) in simple and compact form. In this paper we test the applicability of the theory to a variety of nonspherical modelssspherocylinders, ellipsoids, Lennard-Jones polyatomics, square-well chains, and Stockmayer moleculessand show that their virial coefficients are accounted for accurately by the theory. The theory is used to study the effects of molecular geometry, particularly the elongation of linear molecules, on the angle averaged molecular parameters and on the effective potential. The effective potentials of the models considered are obtained, and the effects of size and geometrical shape are discussed.

Accurate Effective Potentials and Virial Coefficients in Real Fluids. 1. Pure Noble Gases and Their Mixtures

“…We have shown that the potentials u ( r , Ω) and u 0 ( r ) may be related by introducing a relative measure of the difference between their profiles in a u vs r 3 plot. When the nonconformality between both potentials is such that it can be described by a constant parameter S , we have further shown that the virial coefficients B ( T ) and B 0 ( T ) are explicitly and very simply related. , Although there are pairs of potentials u ( r ,Ω) and u 0 ( r ) for which S is strictly constant and for them this NC theory is exact, the study of a great variety of widely used model systems, both spherical and nonspherical, has shown that assuming S to be constant leads to approximate results of high accuracy . We refer to this as the approximate nonconformal (ANC) theory, which in general allows us to use two values, S R and S A , of the softness parameter to describe the repulsive and attractive parts of the u vs r 3 profile, respectively.…”

“…18,20 Although there are pairs of potentials u(r,Ω) and u 0 (r) for which S is strictly constant and for them this NC theory is exact, the study of a great variety of widely used model systems, both spherical and nonspherical, has shown that assuming S to be constant leads to approximate results of high accuracy. 19 We refer to this as the approximate nonconformal (ANC) theory, which in general allows us to use two values, S R and S A , of the softness parameter to describe the repulsive and attractive parts of the u vs r 3 profile, respectively.…”

“…These parameters, and in particular the softness S , are derived from a given true pair potential within well-prescribed approximations. In a second paper we widened the scope of the treatment to explicitly deal with gases comprising nonspherical, and particularly linear, model molecular systems. In these nonspherical cases, the effective parameters ε, r m , and S are defined by the appropriate angle averages so that the potential reproducing B ( T ) works as an “effective” spherical potential.…”

Comparison of molecular models of carbon monoxide for calculation of vapor-liquid equilibrium

“…Within the simpler non-polar models are those that represent the CO molecule as a spherical Lennard-Jones site without charges (1CLJ), developed mainly from viscosity data [6][7][8] or the second virial coefficient [9][10][11], although in recent years, these models have also been used to study the separation of CO and H 2 on carbon nanotubes [12]. Another model proposes a rigid molecule composed of two equal L-J centers (2CLJ) located at each atom [13], which has been used to study the thermal conductivity of liquid CO [14] and its solubility in ionic liquids [15].…”

Ecuación de estado virial de esferas suaves

“…La ec. (1.22) se cumple con muy buena aproximación para moléculas de gases nobles, diatómicas no polares o poco polares, alcanos, perfluoroalcanos y percloroalcanos, entre otras [17].…”