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.

de Vries behavior of the electroclinic effect in the smectic-A* phase near a biaxiality-induced smectic-A* -- smectic-C* tricritical point

Using a generalized Landau theory involving orientational, layering, tilt, and biaxial order parameters we analyze the smectic-A* and smectic-C* (Sm-A* -- Sm-C*) transition, showing that a combination of small orientational order and large layering order leads to Sm-A* -- Sm-C* transitions that are either continuous and close to tricriticality or first order. The model predicts that in such systems the increase in birefringence upon entry to the Sm-C* phase will be especially rapid. It also predicts that the change in layer spacing at the Sm-A* -- Sm-C* transition will be proportional to the orientational order. These are two hallmarks of Sm-A* -- Sm-C* transitions in de Vries materials. We analyze the electroclinic effect in the Sm-A* phase and show that as a result of the zero-field Sm-A* -- Sm-C* transition being either continuous and close to tricriticality or first order (i.e for systems with a combination of weak orientational order and strong layering order) the electroclinic response of the tilt will be unusually strong. Additionally, we investigate the associated electrically induced change in birefringence and layer spacing, demonstrating de Vries behavior for each, i.e. an unusually large increase in birefringence and an unusually small layer contraction. Both the induced change in birefringence and layer spacing are shown to scale quadratically with the induced tilt angle.

The Surface Electroclinic Effect near the First Order Smectic-A*--Smectic-C* transition

We analyze the surface electroclinic effect (SECE) in a material that exhibits a first order bulk smectic-$A^*$ (Sm-$A^*$) -- smectic-$C^*$ (Sm-$C^*$) transition. The effect of a continuously varying degree of enantiomeric excess on the SECE is also investigated. We show that due to the first order nature of the bulk Sm-$A^*$ -- Sm-$C^*$ transition, the SECE can be unusually strong and that as enantiomeric excess is varied, a jump in surface induced tilt is expected. A theoretical state map, in enantiomeric excess - temperature space, features a critical point which terminates a line of first order discontinuities in the surface induced tilt. This critical point is analogous to that found for the phase diagram (in electric field - temperature space) for the bulk electroclinic effect. Analysis of the decay of the surface induced tilt, as one moves from surface into bulk shows that for sufficiently high surface tilt the decay will exhibit a well defined spatial kink within which it becomes especially rapid. We also propose that the SECE is additionally enhanced by the de Vries nature (i.e. small layer shrinkage at the bulk Sm-A* -- Sm-C* transition) of the material. As such the SECE provides a new means to characterize the de Vries nature of a material. We discuss the implications for using these materials in device applications and propose ways to investigate the predicted features experimentally.

The Biaxial Smectic-A* Phase -- A New Phase, Already But Unknowingly Discovered?

The biaxial smectic-A* (Sm-A_B*) phase, appearing in the phase sequence Sm-A*--Sm-A*_B--Sm-C*, is analyzed using Landau theory. It is found to possess a helical superstructure with a pitch that is significantly shorter than the pitch of the Sm-C* helical superstructure. The Sm-A_B*--Sm-C* transition can be either 1st or 2nd order, and correspondingly there will be either a jump or continuous variation in the pitch. The behaviors of the birefringence and electroclinic effect are analyzed and found to be similar to those of a Sm-C*_alpha phase. As such, it is possible that the Sm-A_B* phase could be misidentified as a Sm-C*alpha phase. Ways to distinguish the two phases are discussed.

De Vries Behavior in Smectics near a Biaxiality Induced Smectic A - Smectic C Tricritical Point

We show that a generalized Landau theory for the smectic A and C phases exhibits a biaxiality induced AC tricritical point. Proximity to this tricritical point depends on the degree of orientational order in the system; for sufficiently large orientational order the AC transition is 3D XY-like, while for sufficiently small orientational order, it is either tricritical or 1st order. We investigate each of the three types of AC transitions near tricriticality and show that for each type of transition, small orientational order implies de Vries behavior in the layer spacing, an unusually small layer contraction. This result is consistent with, and can be understood in terms of, the diffuse cone model of de Vries. Additionally, we show that birefringence grows upon entry to the C phase. For a continuous transition, this growth is more rapid the closer the transition is to tricriticality. Our model also predicts the possibility of a nonmontonic temperature dependence of birefringence.