Dynamic Monte Carlo algorithm for out-of-equilibrium processes in colloidal dispersions

Colloids have a striking relevance in a wide spectrum of industrial formulations, spanning from personal care products to protective paints. Their behaviour can be easily influenced by extremely weak forces, which disturb their thermodynamic equilibrium and dramatically determine their performance. Motivated by the impact of colloidal dispersions in fundamental science and formulation engineering, we have designed an efficient Dynamic Monte Carlo (DMC) approach to mimic their out-of-equilibrium dynamics. Our recent theory, which provided a rigorous method to reproduce the Brownian motion of colloids by MC simulations, is here generalised to reproduce the Brownian motion of colloidal particles during transitory unsteady states, when their thermodynamic equilibrium is significantly modified. To this end, we investigate monodisperse and bidisperse rod-like particles in the isotropic phase and apply an external field that forces their reorientation along a common direction and induces an isotropic-to-nematic phase transition. We also study the behaviour of the system once the external field is removed. Our simulations are in excellent quantitative agreement with Brownian Dynamics simulations when the DMC results are rescaled with a time-dependent acceptance ratio, which depends on the strength of the applied field. Further generalising our DMC algorithm to processes displaying significant density fluctuations, such as nucleation and growth, where the MC acceptance ratio is expected to depend on both time and space, is currently under investigation.