Small-angle scattering from collections of interacting hard ellipsoids of revolution studied by Monte Carlo simulations and other methods of statistical thermodynamics

Computer simulations using Monte Carlo methods are used to investigate the effects of interparticle correlations on small-angle X-ray and neutron scattering from moderate or highly concentrated systems of ellipsoids of revolution. Both oblate and prolate ellipsoids, of varying eccentricities and concentrations, are considered. The advantage with Monte Carlo simulation is that completely general models, both regarding particle shapes and interaction potentials, can be considered. Equations are also given that relate the nonideal part of the chemical potential, βμⁿⁱ, with the scattering at zero angle, I(0), and the compressibility factor, z. The quantity βμⁿⁱ can be obtained during the Monte Carlo simulations by using Widom's test-particle method. For spherical particles, the simulations are compared with approximation formulas based on the Percus–Yevick equation. A method is also suggested for the calculation of both βμⁿⁱ and z from experimental values of I(0) recorded as a function of concentration.