Student Research Project
Olga Stulov is a double major in Mathematics and Electrical Engineering. This summer she did a research project at George Mason University, using differential equations and other techniques to model the structure of chemical polymers. Here’s what she says about her work:
The research investigated a mathematical model for the equilibrium states of "diblock-copolymers" in one dimension. These are essentially chains of two kinds of monomers, A and B, covalently joined together as blocks of A's and B's such as: ...A-A-A-A-B-B-B-B-B-A-A-A-B-B-B-B-A-A-A-A...
During the process of chemical synthesis, varying the sizes and relationships of these blocks gives block copolymers many useful and desirable properties. The ability to design materials with certain properties is of great technological importance. Finding the properties experimentally is a challenging task due to the complexity of the chemical reactions.
However, these practical difficulties can be avoided by studying the patterns of diblock copolymers through a mathematical model. Using partial differential equations, linear algebra and numerical methods allowed for solutions of the homogeneous and inhomogeneous equilibria. Physically, homogeneous equilibrium is the moment in which the substances involved are in the same phase of matter. Meanwhile, inhomogeneous equilibrium is a mixture between several phases. For simplicity the mathematical model was analyzed in one dimension and time independently. In future work, the next step of this project is to find the time varying solutions and explore the system in higher dimensions (2 and 3 D), making this research fully applicable.