Extensive study of cage effect and subdiffusion in Pickering emulsions using molecular dynamics simulations

In this work, we aim at an extensive study of the diffusion phenomenon of oil-droplets dispersed in water onto which are strongly adsorbed charged point-like particles (Pickering emulsions). This diffusion that originates from multiple collisions with the molecules of water, is anomalous, due to the presence of relatively strong correlations between the moving oil-droplets. Using Molecular Dynamic simulation, with a pair-potential of Sogami-Ise type, we first observe that the random walkers execute a normal diffusion, at intermediate time, followed by a slow diffusion (subdiffusion) we attribute to the presence of cages, formed by the nearest neighbors (traps). In the cage-regime, we find that the mean-square-displacement increases according to a time-power law, with an anomalous diffusion exponent between 0 and 1. The existence of a cage effect is shown also by computing the velocity auto-correlation function of the random walker. It is found that, in a cage, this function is governed by an underdamped (oscillatory) behavior, for strong densities and surface charges, and low-salt concentration. In the inverse situation, however, we observe that this correlation-function is rather overdamped (non-oscillatory). In the two cases, at large-time, this function fails according to a time-power law.