Collaborative Research: FRG: Ferroelectric phenomena in soft matter systems

In this Focused Research Group project the investigators

study the behavior of a class of soft materials characterized by

strong 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 and

actuators -- based on the electro-mechanical coupling. One goal

is to determine the conditions that enhance the combined effects

of the soft-elasticity modes of elastomers and their ferroelectric

response by application of external electric fields. In these

studies the investigators combine mathematical analysis, modeling,

computer simulations, physical experiments, and application of the

three-dimensional visualization techniques. These mathematical

problems are analytically modeled by highly nonlinear elliptic,

parabolic, mixed hyperbolic-parabolic and stochastic systems of

partial differential equations, including the equations of

nonlinear elasticity, viscoelastic flow, and Maxwell's equations

of electrodynamics. Partial differential equation methods for

phase transitions, modeling, and numerical tools such as spectral

methods and adaptivity to simulate the solutions are among the

techniques employed.

The project is a comprehensive effort towards modeling and

development of soft matter actuator and sensor devices used in a

vast array of applications, including ultra-fast optic and video

switching, artificial muscles, biological membranes, and

filaments. Increase of switching speeds and size reduction of the

device are two relevant technological goals at the heart of the

investigation. One type of materials to investigate, liquid

crystal elastomers, can be thought of as rubber networks that

require very little energy to be deformed along special

directions. This property, coupled with the efficient response of

the material to electric fields, may offer optimal ingredients for

developing high speed devices able to provide very large

mechanical deformations with the application of electric or

magnetic fields of small magnitude. These are highly desirable

properties, for instance, in the design of artificial muscles for

robots. The investigators carry out the studies by combining

mathematical analysis, computer simulations, and physical

experiments. Use of three-dimensional visualization techniques is

important in both conducting the work and disseminating the

results. Many of the problems present modeling challenges that

call for a synergistic effort of mathematicians and physicists. A

central principle in this endeavor is close cross-disciplinary

interaction among the applied and numerical analysts and the

physicists of the group. A major component of the project is the

interdisciplinary training of post-docs and graduate students,

including the organization of a summer school, development of new

courses, and summer research opportunities for undergraduate

students. Interdisciplinary conferences, group workshops, and

seminars devoted to the FRG project at each institution are also

planned.