# Self-Diffusion in Two-Dimensional Colloidal Systems: A Computer Simulation Study

## TL;DR

This study uses computer simulations to explore how mobility changes in dense two-dimensional colloidal systems over short and long timescales.

## Contribution

A novel thermal model and Monte Carlo simulations were used to analyze the relationship between short- and long-time diffusion in colloidal systems.

## Key findings

- Reduced solvent mobility in short time correlates with reduced colloid mobility in long time.
- Solvent diffusion in long time is affected by colloid concentration but not directly linked to short-time behavior.
- DLL algorithm enabled detailed analysis of cross-ratios of diffusion coefficients.

## Abstract

The dynamics of dense colloidal systems are not fully understood. In the study of these types of systems, computer simulations based on the so-called hard sphere model play a significant role. In the presented work, we consider a system of hard spheres of the same size but different mobilities (molecules with high mobility correspond to solvent molecules, while molecules with reduced mobility are colloid particles) at varying concentrations. For this purpose, a two-dimensional lattice and an thermal model of such systems was designed. In order to determine the properties of such systems, a Monte Carlo computer simulation was used, employing the Dynamic Lattice Liquid (DLL) algorithm. Our main aim was to determine how the dynamic behavior of the system in the short time affects the long-time behavior. For this purpose, we investigated the cross-ratios of the diffusion coefficients in the short and long time of the considered system elements. It was found that the reduction in the solvent mobility with increasing concentration of colloidal particles in a short time leads to a very similar reduction in the mobility of the colloid particles in a long time, but we do not observe such behavior in the case of the solvent, i.e., there is a decrease in the value of the solvent diffusion coefficient in the long time with the change in the concentration of colloid particles, but it is difficult to connect it in a simple way with the decrease in the diffusion coefficient in the short time.