Ultra-small-angle neutron scattering: A tool to study packing of relatively monodisperse polymer spheres and their binary mixtures

We measured ultra-small-angle neutron scattering (USANS) from polymethylmethacrylate spheres tamped down in air. Two slightly polydisperse pure sphere sizes (1.5 and 7.5 mu m diameters) and five mixtures of these were used. All were loose packed (packing fractions of 0.3-0.6) with nongravitational forces (e. g., friction) important, preventing close packing. The USANS data are rich in information on powder packing. A modified Percus-Yevick fluid model was used to parametrize the data-adequately but not well. The modifications required the introduction of small voids, less than the sphere size, and a parameter reflecting substantial deviation from the Percus-Yevick prediction of the sphere-sphere correlation function. The mixed samples fitted less well, and two further modifying factors were necessary. These were local inhomogeneities, where the concentration of same-size spheres, both large and small, deviated from the mean packing, and a factor accounting for the presence within these "clusters" of self-avoidance of the large spheres (that is, large spheres coated with more small spheres than Percus-Yevick would predict). The overall deviations from the hard-sphere Percus-Yevick model that we find here suggest that fluid models of loose packed powders are unlikely to be successful but lay the ground work for future theoretical and computational works.