Dr. Eleni Panagiotou, Assistant Professor in Mathematics in the UTC Department of Mathematics, has been awarded a 3-year, $125,000 Research in Undergraduate Institutions (RUI) grant from the National Science Foundation (NSF). The NSF RUI program supports faculty in research that engages them in their professional fields, builds capacity for research, and supports the integration for research and undergraduate education.

The project consists of an inter-disciplinary effort with researchers from Mathematics and Chemical Engineering to solve the problem of quantifying the effects of topological entanglement and polymer architecture to material properties of polymers. The contribution is an innovative approach that integrates analytical, computational and experimental methods to solve a problem at the interface of polymer physics, topology and geometry. Understanding how microscopic properties affect material properties will lead not only to the smart manufacturing of new materials, but also to the understanding of living matter.

In order to understand and quantify the interplay between microstructure and macroscopic properties of polymers, this project proposes to use mathematical concepts from topology and investigate properties of polymers at different length-scales through computer simulations. The results will be complemented and validated by experimental data and the proposed works can be summarized as follows: (1) the creation of new methods to account for polymer entanglement in Self-Consistent Field Theory (SCFT) simulations, (2) the development of new partitioned algorithms to simulate the fluid-structure interaction for entangled polymers (3) the development of new computational user-packages for measuring topological entanglement of open curves and (4) the combined application of all the above mentioned tools to understand the self-assembly, organization and viscoelastic properties of polymer melts of varying architecture using simulations and experiments.

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