In this chapter we note that solution scattering data can be divided into four regions. At zero scattering angle, the scattering provides information on molecular weight of the particle in solution. Beyond that, the scattering is influenced by the radius of gyration. As the scattering angle increases, the scattering is influenced by the particle shape, and finally by the interface with the particle and the solution. There are a number of important invariants that can be calculated directly from the data including molecular mass, radius of gyration, Porod invariant, particle volume, maximum particle dimension, particle surface area, correlation length, and volume of correlation. The meaning of these is described in turn along with their mathematical derivations.
Microscopic investigation into liquefaction resistance of pre-sheared sand: Effects of particle shape and initial anisotropy
