Monte Carlo estimation of the structure factor for hard bodies in small-angle scattering

The structure factor and the effect of deviation from spherical symmetry are studied for elongated particles with axial ratios between 0.1 and 10. This is done using Monte Carlo simulation of the excluded-volume distance distribution function for ellipsoids of revolution, for cylinders and for cylinders with hemispherical end caps. The method suggested is general and is applicable to particles of any shape. The results of the calculations are compared with the Percus–Yevick formula [Percus & Yevick (1958), Phys. Rev.110, 1–13] for hard spheres. The comparisons indicate that the Percus–Yevick formula should only be used for axial ratios close to 1. For larger deviations from spherical symmetry it is often better to use the excluded-volume distance distribution function for the particle, in combination with the single-particle distance distribution function, for the calculation of the structure factor.