Light scattering of a concentrated multicomponent system of hard spheres in the Percus–Yevick approximation

A formalism for light scattering (or small angle x-ray or neutron scattering) from a (concentrated) multicomponent system of spherical (colloidal) particles dispersed in a low-molecular weight solvent is derived in terms of direct correlation functions introduced by Ornstein and Zernike and also in terms of Q functions introduced by Baxter. These functions, which characterize the interparticle interactions, are often theoretically much more accessible than the more familiar pair-distribution functions. The formalism is applied to a multicomponent system of hard spheres treated in the Percus–Yevick approximation. For zero scattering angle, a rather simple, exact expression can be formulated containing mean products of particle diameter and particle scattering amplitude. Some limiting cases are treated in more detail. A series expansion in the particle concentration is given up to the order for which the PY approximation is exact. The influence of polydispersity on light scattering is illustrated for a (generalized) exponential size distribution for cases in which the scattering amplitude is proportional to the second and third power of the particle diameter. The reliability of the PY approximation for hard spheres is discussed.