Thermodynamic and scattering properties of dense fluids of monodisperse isotropic particles : an information theory approach

(Received 5 April 1993, accepted 10 June 1993)

Abstract
The purpose of this paper is to use (X-ray or neutron) scattering spectra to assess the degree of order - more precisely, translational entropy - in a fluid of monodisperse isotropic particles, avoiding to rely on microscopic models and on computer simulations. The mathematical approach, borowed from information theory, is based upon an ideal stochastic process : a particle is cast in a box containing a known number of particles, with a probability density corresponding to the distribution 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 straightforward function of the radial distribution function of the interparticle 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 thermodynamic properties of the system is discussed. By way of illustration, the treatment is applied to neutron scattering experiments performed on Ar and Kr : the agreement of the entropy determined by the thermodynamic and the scattering procedures is quite satisfactory. The validity of the treatment, and more generally the very possibility of determining the function g(r) from the scattering data is shown to require that the function [ g(r)-1] have a finite support.