Karl Saunders

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*) transitions, 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 changes in birefringence and layer spacing are shown to scale quadratically with the induced tilt angle.

Hydrodynamics of polar liquid crystals.

Starting from a microscopic definition of an alignment vector proportional to the polarization, we discuss the hydrodynamics of polar liquid crystals with local C infinity v symmetry. The free energy for polar liquid crystals differs from that of nematic liquid crystals (D infinity h) in that it contains terms violating the n --> -n symmetry. First we show that these Z2-odd terms induce a general splay instability of a uniform polarized state in a range of parameters. Next we use the general Poisson-bracket formalism to derive the hydrodynamic equations of the system in the polarized state. The structure of the linear hydrodynamic modes confirms the existence of the splay instability.

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.

Biaxial smectic-A ∗ phase and its possible misidentification as a smectic-C α * phase

The biaxial smectic-A∗ (Sm-AB) phase, appearing in the phase sequence Sm-A –Sm-AB–SmC∗, 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-AB–SmC∗ 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∗ α phase . As such, it is possible that the Sm-A ∗ B phase could be misidentified as a Sm-C∗ α phase. Ways to distinguish the two phases are discussed.

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.

Modeling the field control of the surface electroclinic effect near continuous and first-order smectic-A* to 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, as demonstrated in 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. With regard to technological, e.g., display, applications, this could be a feature to be avoided or potentially exploited. 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.