Study of cage effect and subdiffusion in Pickering emulsions from Molecular Dynamics simulations

In this work, we study the diffusion laws 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 Dynamics 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, α (between 0 and 1). This exponent and the generalized diffusion coefficient are computed varying the relevant parameters (surface charge, density, salt-concentration). We remark that the subdiffusion is significant only for strong surface charges and densities, and low-salt concentrations. The existence of a cage effect is shown 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, with the exponent α − 2. To validate our simulation data, we propose a memory diffusion theory that is based essentially on a generalized Langevin equation. Finally, we demonstrate that the results from simulations are in good agreement with the predictions of the elaborated theory.