Colloidal liquids of yolk-shell particles

In this paper we develop statistical mechanical tools to describe the intermediate- and long-time collective- and self-diffusion properties of a liquid of strongly-interacting hollow spherical particles (shells), each bearing a smaller solid sphere (yolk) in its interior. To decouple two complex effects we assume that the hydrodynamic interactions can be accounted for through the effective short-time self-diffusion coefficients $D^0_s$ and $D^0_y$ that describe the short-time Brownian motion of the yolk and the shell particles, and develop a self-consistent generalized Langevin equation theory to describe the intermediate- and long-time effects of the direct shell-shell, yolk-shell and yolk-yolk interactions. In a concrete application, we consider the simplest yolk-shell model system involving purely repulsive hard-body interactions between all (shell and yolk) particles. Using a softened version of these interparticle potentials we perform Brownian dynamics simulations to determine the mean squared displacement of both types of particles, as well as the intermediate scattering function of the yolk-shell complex. We compare the theoretical and simulation results between them, and with the results for the same system in the absence of yolks. We find that the yolks, which have no effect on the shell-shell static structure, influences the dynamic properties in a predictable manner, fully captured by the theory.