Volume fraction of hard particles from small-angle scattering experiments

The paper deals with possibilities for the calculation of the total volume fraction, c, of a single phase of hard, disconnected particles from scattering data. The diversity of particle arrangements is far reaching. Explicit formulas demand special assumptions. se was selected and analyzed more in detail: Hard particles, the centres of which are described by a pair correlation function g(r). proved, for any isotropic arrangement of hard particles, that c can be detected based on the relative scattering intensity I(h) from the small-angle scattering correlation function γ(r) operating with the first derivative in the origin. Let γ0′(0) be the first derivative of the correlation function of the single particles. Then c is given by c=1−γ0′(0)/γ′(0). This is explained for a so-called dead leaves model, where γ(r) is known analytically, and for experimental examples.