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.

Dr. Panagiotou’s grant is entitled Computational Methods for Measuring Topological Entanglement in Polymers. The project aims to investigate the effects of polymer entanglement and architecture on material properties using computational and mathematical techniques. Entangled polymer physics are a subject of study since Edwards’ original model in the 60’s which is still under examination. Under some conditions we can see polymer chains as mathematical curves in space and measure their topological complexity. However, the use of topological entanglement for the study of polymer entanglement has not been fully explored, due to the difficulty of bridging the two notions, requiring background from topology and polymer physics and engineering.

 

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.

This study advances knowledge at the area of topology and geometry, by defining and studying new tools for measuring the geometrical/topological complexity of open curves in space and also advances computational infrastructure, by designing and prototyping algorithms in reusable code that in particular studies aspects in entangled polymer simulations (such as fluid-structure interactions for such systems and topological interactions). This work also extends SCFT simulations to account for topological aspects of polymers in a way that it is computationally feasible, which is presently absent in SCFT simulations. This holistic approach will thoroughly study entanglement in polymers of varying architecture that are currently of great interest in materials and manufacturing and nanotechnology, with the potential of immediate impact of our results to practical manufacturing. The results also provide valuable tools for studying biopolymers with potential impact in biotechnology. This project has educational objectives including strong impact on undergraduate research with a commitment in promoting underrepresented groups in STEM.

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