Collaborative Research: FRG: Ferroelectric phenomena in soft matter systems

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In this Focused Research Group project the investigatorsstudy the behavior of a class of soft materials characterized bystrong coupling of electrical, optical, and mechanical properties. Such materials, which include some liquid crystals and elastomers,can be used to develop ultra-fast switches for video display --based on electro-optical coupling -- and miniature sensors andactuators -- based on the electro-mechanical coupling. One goalis to determine the conditions that enhance the combined effectsof the soft-elasticity modes of elastomers and their ferroelectricresponse by application of external electric fields. In thesestudies the investigators combine mathematical analysis, modeling,computer simulations, physical experiments, and application of thethree-dimensional visualization techniques. These mathematicalproblems are analytically modeled by highly nonlinear elliptic,parabolic, mixed hyperbolic-parabolic and stochastic systems ofpartial differential equations, including the equations ofnonlinear elasticity, viscoelastic flow, and Maxwell's equationsof electrodynamics. Partial differential equation methods forphase transitions, modeling, and numerical tools such as spectralmethods and adaptivity to simulate the solutions are among thetechniques employed. The project is a comprehensive effort towards modeling anddevelopment of soft matter actuator and sensor devices used in avast array of applications, including ultra-fast optic and videoswitching, artificial muscles, biological membranes, andfilaments. Increase of switching speeds and size reduction of thedevice are two relevant technological goals at the heart of theinvestigation. One type of materials to investigate, liquidcrystal elastomers, can be thought of as rubber networks thatrequire very little energy to be deformed along specialdirections. This property, coupled with the efficient response ofthe material to electric fields, may offer optimal ingredients fordeveloping high speed devices able to provide very largemechanical deformations with the application of electric ormagnetic fields of small magnitude. These are highly desirableproperties, for instance, in the design of artificial muscles forrobots. The investigators carry out the studies by combiningmathematical analysis, computer simulations, and physicalexperiments. Use of three-dimensional visualization techniques isimportant in both conducting the work and disseminating theresults. Many of the problems present modeling challenges thatcall for a synergistic effort of mathematicians and physicists. Acentral principle in this endeavor is close cross-disciplinaryinteraction among the applied and numerical analysts and thephysicists of the group. A major component of the project is theinterdisciplinary training of post-docs and graduate students,including the organization of a summer school, development of newcourses, and summer research opportunities for undergraduatestudents. Interdisciplinary conferences, group workshops, andseminars devoted to the FRG project at each institution are alsoplanned.