THERMODYNAMIC AND SCATTERING PROPERTIES OF DENSE FLUIDS OF MONODISPERSE ISOTROPIC PARTICLES - AN INFORMATION-THEORY APPROACH

The purpose of this paper is to use (X-ray or neutron) scattering spec tra to assess the degree of order - more precisely, translational entr opy - in a fluid of monodisperse isotropic particles, avoiding to rely on microscopic models and on computer simulations. The mathematical a pproach, borrowed from information theory, is based upon an ideal stoc hastic process : a particle is cast in a box containing a known number of particles, with a probability density corresponding to the distrib ution of interparticle distances defined by the scattering experiment. If the a priori probability density (i.e. before the X-ray scattering experiment) is uniform, then the information associated with the pair of probability densities can be determined : its expression is a stra ightforward function of the radial distribution function of the interp article distances, g(r). The information, moreover, is proportional to the derivative, with respect to concentration, of the (translational) entropy in excess over the perfect gas. The correlation with the ther modynamic properties of the system is discussed. By way of illustratio n, the treatment is applied to neutron scattering experiments performe d on Ar and Kr: the agreement of the entropy determined by the thermod ynamic and the scattering procedures is quite satisfactory. The validi ty of the treatment, and more generally the very possibility of determ ining the function g(r) from the scattering data is shown to require t hat the function [g(r)-1] have a finite support.