Stochastic Simulations of Diffusion and Relaxation in Heterogeneous Materials

This project focused on creating random-walk simulations of diffusion processes that could be used to predict results from NMR pulsed-field gradient (PFG) experiments, thereby giving insights to whether or not a particular NMR experiment might yield useful results. Initial simulations involved no boundaries that would impede the motion of the material. The results from this simulation confirmed the linear relationship between the root-mean-square displacement and the square root of time. From there, the simulations were improved to include reflective walls in which the molecules would be reflected back into the region it came from. The walls were then made to be reactive, which caused some of the molecules which hit it to no longer exist, or “die out”. This simulation showed how a boundary could ensure that the molecules move only a certain distance away from each other. In order to get results that could be used to analyze real experiments, the simulation was improved so that the cell had two different regions that were connected by a permeable wall. Periodic boundary conditions allowed the simulations to handle walks of arbitrary duration by making it seem that there were an infinite number of cells.