University of Ontario Institute of Technology

Purpose

Even conceptually simple problems can be difficult to solve. To motivate this project, consider a system of particles of type A and type B that are thoroughly mixed in a closed box. They are moving around at a rate dictated by the temperature (ie, diffusion). At some time, the type A particles start to bond together to form chains (ie, polymers). The question is: what does the system look like after a long time? It turns out that there are several answers to this question. If the particles move around a rate much faster than the polymerization rate, then as the polymers of type A are formed the type B monomers will move away from the polymers. Hence, after a long time, the monomers of type B will be in a separate section of the box than the type A polymers. Conversely, if the polymerization rate is fast compared to the rate of diffusion, then type B monomers can be trapped in the network of type A polymers. Computer simulations are ideally suited to solve such problems since the system can be evolved in time as dictated by known physical laws and particular sets of parameters (e.g., diffusion/ polymerization rates). The end simulation state can be analyzed and characterized. For example, we can quantify the purity of the separation of A and B particles. Performing the simulation and analysis across different parameters then allows us to reveal trends of how the final state depends on those parameters. This knowledge can be used to guide experiments that desire to achieve a particular final state. In this project, this fundamental knowledge will contribute to a larger project of designing new materials with particular properties.