Modeling the Field Control of the Surface Electroclinic Effect near Continuous and First Order Smectic-A*-Smectic-C* Transitions

We present and analyze a model for the combination of bulk and surface electroclinic effects in the smectic-A* (Sm-A) phase near a Sm-A*--Sm-C* transition. As part of our analysis we calculate the dependence of the surface tilt on external electric field and show that it can be eliminated, or even reversed from its zero-field value. This is in good agreement with previous experimental work on a system (W415) with a continuous Sm-A*--Sm-C* transition. We also analyze, for the first time, the combination of bulk and surface electroclinic effects in systems with a first order Sm-A*--Sm-C* transition. The variation of surface tilt with electric field in this case is much more dramatic, with discontinuities and hysteresis. Near each type of Sm-A*--Sm-C* transition we obtain the temperature dependence of the field required to eliminate surface tilt. Additionally, we analyze the effect of varying the systems enantiomeric excess, showing that it strongly affects the field dependence of surface tilt, in particular, near a first order Sm-A*--Sm-C* transition. In this case, increasing enantiomeric excess can change the field dependence of surface tilt from continuous to discontinuous. Our model also allows us to calculate the variation of layer spacing in going from surface to bulk, which in turn allows us to estimate the strain resulting from the difference between the surface and bulk layer spacing. We show that for certain ranges of applied electric field, this strain can result in layer buckling which reduces the overall quality of the liquid crystal cell. For de Vries materials, with small tilt-induced change in layer spacing, the induced strain for a given surface tilt should be smaller. However, we argue that this may be offset by the fact that de Vries materials, which typically have Sm-A*--Sm-C* transitions near a tricritical point, will generally have larger surface tilt.