The application of distance distribution functions to structural analysis of core-shell particles

The structure of core–shell latex particles of polymethylmethacrylate (the core) and polyurethane (the shell) have been investigated by methods of small-angle X-ray scattering (SAXS) and atom-force microscopy. A set of SAXS patterns has been obtained using contrast variation method. Indirect methods have been used to follow the evolution of distance distribution functions from SAXS for lattices in various sucrose solutions over a range of solution density, yielding structural parameters of the particles such as core size, shell thickness and density of the polymers including density deviations within the particle’s core and shell. A model for an ensemble of core–shell particles with a normal distribution of average electron density of both the core and the shell has been developed to fit the distance distribution functions using a random search algorithm. The effects of nanophase separation in the polyurethane is estimated using Monte Carlo simulations of the distance distribution functions where the phase-separated polyurethane is represented by spherical truncated cones in a shell simulating the location of hard and soft polyurethane blocks, respectively.