Diffusion of Fractal Particles in a Fractal Fluid

TL;DR

This study investigates the anomalous diffusion behavior of fractal particles in a fractal fluid using Monte Carlo simulations, revealing sub-diffusive regimes and particle localization at high packing fractions.

Contribution

It provides new insights into the diffusion dynamics of fractal particles in fractal media, highlighting the effects of steric hindrance and particle localization.

Findings

Mean squared displacement follows a nonlinear power law with time.

Sub-diffusive behavior emerges at finite packing fractions.

Particle localization occurs over extensive timescales at high packing fractions.

Abstract

Anomalous short- and long-time self-diffusion of non-overlapping fractal particles on a percolation cluster with spreading dimension $1.67(2)$ is studied by dynamic Monte Carlo simulations. As reported in Phys. Rev. Lett. 115, 097801 (2015), the disordered phase formed by these particles is that of an unconfined, homogeneous and monodisperse fluid in fractal space. During particle diffusion in thermodynamic equilibrium, the mean squared chemical displacement increases as a nonlinear power of time, with an exponent of $0.96(1)$ at short times and $0.63(1)$ at long times. At finite packing fractions the steric hindrance among nearest neighbor particles leads to a sub-diffusive regime that separates short-time anomalous diffusion from long-time anomalous diffusion. Particle localization is observed over eight decades in time for packing fractions of $\sim 60\%$ and higher.