59th Annual Report on Research 2014

The goal of this research is to better understand the mechanism of three dimensional melting by simulating the melting of colloid sphere suspensions near melting. During the past year we have developed computer programs to simulate the colloid system using a Yukawa program with both Monte Carlo and Molecular Dynamics(using the LAMMPS software from Sandia National Laboratories) algorithms. We have identified the metastable region where the melting occurs and have explored the behavior of the following quantities: energy per particle, pressure, specific heat, pair correlation function, elastic constants, and the Lindemann ratio. Following the suggestion of David Weitz's group at Harvard, which experimentally explored this system, we have identified so called `hot' particles which have a large Lindemann ratio. If two such 'hot' particles are within a nearest neighbor distance we say they are connected and then can form clusters. We do a cluster analysis computing the mean cluster size, the cluster size distribution, and the connectedness length, to see if the melting can be described by percolation theory.

Thus, far we have validated our programs using N = 250 and 2000 particles, and the results were promising. We are just beginning to do more careful runs on 20,000 particle systems, where we find that in the metastable region the system can remain in the BCC solid state for a very long time before the number of 'hot' particles starts to grow and then the system melts. All quantities such as the energy, pressure, elastic constants, and the Lindemann ratio change strongly when the system melts. Before melting the cluster distribution for the `hot' particles follow the power law plus an exponential cutoff behavior expected before the system percolates. We need to explore more densities to better estimate where the metastable region begins, and pin down the percolation quantities more accurately.

Our plans for the future include defining `hot' particles using the local spherical harmonic for each particle, carrying out simulations to estimate the free energy directly and thus determine the location of the thermodynamic metastable region, and exploring the relevance of elastic percolation theory to melting. 

There have been three students working on this project this year, Nicole Antoine, Jeric Derema, and Takumi Matsuzawa. The first two have graduated and will use their experiences from this project to help them further their education in a technical field. Takumi will be a junior this coming year, will continue working on the project, and plans a career in condensed matter physics. 

My own research is probably at the highest level of intensity in almost 15 years because during ten of those years I was editor of the American Journal of Physics. This work is attracting attention from my collaborators and their students. In particular, my long term collaborator Harvey Gould, is doing some work in support of the project. I have also found that my experience working with my students has been some of the most productive in my career at Kalamazoo College.