Simulations of Melting Colloidal Suspensions

Abstract

This paper discusses about approaches in identifying the mechanisms of melting through Monte Carlo simulations of colloidal suspensions. Utilizing the simulations we are able to create perfect crystals with the absence of surfaces through periodic boundary conditions. Following an experiment done by a research group at Harvard we create our crystal by modeling a soft inter-particle potential known as the Yukawa potential in the body-centered cubic (BCC) lattice and simulate it in an isothermal system. To help determine when the system has melted we utilize two melting criterion - the Lindemann parameter and the Born criterion. Throughout the simulation we calculate various quantities to measure the changes that occur that could possibly hint at the markers of melting. Furthermore, we translate some of the techniques done in the experiment throughout the simulation such as identifying particles with Lindemann parameter greater than 0:25 as "hot" particles. We do a cluster analysis on these "hot" particles in hopes of identifying whether or not our system has transitioned to a liquid via a percolation phase transition which is a second-order phase transition. Additionally, the shear elastic constant is tracked to see whether or not the melting of the crystal is suggestive of Born melting.