Statistical thermodynamics of convex molecule fluids

Abstract

A theoretical study of the statistical mechanical description of systems composed of non-spherical convex molecules is made. Thermodynamic functions of one-component and multicomponent systems of particles interacting via the pair potential of the Kihara core type are expressed by integrals over the minimum distance between two interacting convex bodies and three angles characterizing the convex body geometry. The approach is applied to the hard convex body system where the averaged contact correlation function is introduced. Exploiting ideas of the scaled particle theory the approximate expressions for the averaged correlation functions are given in terms of the geometric functionals of hard convex bodies.

Molecular Fluids and Liquid Crystals in Convex-Body Coordinate Systems

“…(8b) has been obtained by us [21] in a simple manner but the same thing had first been derived by Curtiss and Dahler [12] through heavy algebra. The expression for ζ ex had also been obtained by Boublik [14], and by Allen et al [15] through consideration of the geometry of space outside the surface of the body (A + B).…”

“…It is further found that the dynamical properties of the rigid ellipsoidal systems are conveniently described in convex-body (CB) coordinates ( , θ, φ), where is the surfaceto-surface separation of a pair of ellipsoidal molecules, and θ and φ are the polar and azimuthal angles that = k makes with respect to a Cartesian frame fixed in the laboratory. It is imperative that unlike the case of spherical molecules, the geometries of (A + B) are quite different inside [12,13] and outside [13][14][15] its surface if constituent molecules A and B are oval shaped; the CB coordinates inside the surface will be described later on. The seemingly noncartesian nature of the CB system has been creating bottlenecks in many of its applications; in fact, many things remain to be done in this fascinating area of statistical physics.…”

Hard Convex Body Fluids

“…For a system comprised of hard smooth particles, the force can be replaced by [14] PFl2 = I~( s -0') (2.11) where I is the outward surface normal from particle 1 to particle 2 and s is the surface-to-surface separation measured along I. Accordingly, Eq (2.10) becomes P P = p + (1/6)p2 /dr12 dill dlL2rl2 .I6(s -O+)g(l, 2) (2.12)…”

Reminiscences about Tomáš Boublík, Ivo Nezbeda and the Liblice Meetings on the Statistical Mechanics of Liquids

“…No doubt, he is one of the most highly cited scientists of the Czech Republic of his generation that started their careers in the early fifties. His papers on the EOS of hard-body systems will be very useful well into the future [1,[10][11][12][13][14]. Carlos remembers: 'It was a pleasure and an honour to know Tomáš, and for me he was always an example to follow.…”