The object of study is modeling, simulation, and analysis of the ferroelectric phenomena in soft matter systems such as liquid crystals, elastomers, and gels. Of particular interest for ferroelectric phenomena are the interaction with electric fields in switching processes for display devices. It is desirable to having workable mathematical models. For traditional liquid crystal technology, such models exist. But, for the newer ferroelectric materials and potential technologies, the modeling is still in development.
The liquid crystals that have been around since the 1950s and 1960s rely on an externally applied electrical field for control--after all, nature does not tend to spontaneously generate electrical fields. What is special about the ferroelectric systems is that they have their own (internal) source of electric field.
The ferroelectric technology is quite new, and exists today mostly in laboratories. There are, however, some companies that have switchable films that can be used in viewfinders and display devices based on a ferroelectric liquid crystal phase that has been understood for some time.
The basic idea behind liquid crystal display in general is that the molecules in the liquid crystal tend to arrange themselves in specific patterns, and this affects how light passes through the crystal. We can affect the way that the crystals are patterned by
We want to better understand the arrangements of the crystals that affect the liquid crystal phenomena that we use in displays and viewfinders. These are not necessarily static arrangements, but involve fluid motion in certain molecular scale layers. Some of this is caused by intermolecular forces, and some by external force fields. Thus a probability distribution can be used to model the ferroelectric liquid crystals.
One big theme in this workshop was "switching". We want to understand both the switching for a liquid-like ferroelectric model and also the switching for a solid material with liquid features. Another theme was numerical simulation. We want to develop numerical techniques which are capable of capturing the complex interfacial dynamics associated with these ferroelectric models.
A big part of the activities for the week has been to examine various systems of partial differential equations that are supposed to model the physical phenomena. The modeling is tricky, because it involves certain approximations and simplifications. There is no model that is universally accepted for the systems of interest. In her Tuesday lecture, organizer Carme Calderer proposed one particular model that generated considerable discussion.
There are important issues of scale in the modeling process. Some models are valid only at the macroscopic level. Others work at the mesoscopic level. And still other models are molecular in scale. It is of particular interest to know what happens at the boundary between two of these scales.
The interaction of physicists and applied mathematicians over a broadly applicable problem of diverse interest generated a dynamic and lively workshop that produced many new ideas and spawned a number of new collaborations. Prospects for future developments in the field are bright.