Modeling, Analysis and Applications of Coupled Elasticity and Liquid Crystal Effects

University Of Minnesota-Twin Cities, Minneapolis MN

Investigators

Abstract

Calderer DMS-0909165 This project deals with modeling and analysis of ferroelectric liquid crystals and hydrogels, with the goal of studying switching and hysteresis of devices made of such materials. The project on liquid crystals focuses on newly discovered bent core ferroelectric phases that are capable of sustaining polarization fields of just one order of magnitude below that of traditional solid ferroelectric compounds. The goal of the work on hydrogels is to model a cyclic membrane appropriate for application to the design of pulsating drug delivery devices. Such types of elastic membranes are also very relevant to the study of fuel cells and filtrating devices. Both problems share distinctive phenomenology and mathematical issues, such as presenting a first order phase transition behavior between two distinguished states. In ferroelectric liquid crystals, they correspond to the oppositely polarized states with distinct optical properties; a main goal is to optimize the switching speed between them. Understanding and controlling hysteresis may help achieve optimal switching. This also requires a good understanding of the rheology of bent core liquid crystal flow. Mathematical issues involve non-convexity, metastability, and coupling of Maxwell's equations with fluid flow and elasticity. Overall, ferroelectricity is an area of liquid crystals rich in phenomenology, modeling, and mathematical challenges that remain largely unexplored. It is often the case that seemingly disparate problems of science and technology have common mathematical underpinnings. In this project, the investigator addresses two of these problems, with applications in pharmacology and fuel cells as well as in optical devices, such as video and high speed Internet switching. The underlying idea is the modeling and mathematical study of "switching," with the goal of designing faster and more efficient devices. In pharmaceutical applications, a switch connects the two relevant states: release and non-release of the drug to be administered. A goal of the investigator is to model a cyclic drug delivery membrane. Such periodically releasing devices are believed to be especially relevant in hormone therapies, where matching the natural body hormone cycle is perhaps as important as the replacement hormone itself. In proton exchange membrane fuel cells, positive hydrogen ions produced at the anode travel through the membrane, separating from the fuel and yielding electrons. A ferroelectric switch connects optically distinct states. In these examples, energy loss is a common feature of switching dynamics, together with cycle lengthening in periodic devices. This phenomenon, known as hysteresis, occurs in many mechanical and magnetic systems. The investigator harnesses the mathematical knowledge of hysteresis in other fields as an approach to understanding pharmacological and liquid crystal devices. Mentoring of graduate and undergraduate students as well as other educational activities is intertwined and integrated with the research aspects of the work.