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Register a new userThe Smectic $A$-$C$ Phase Transition in Biaxial Disordered Environments
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We study the smectic $A$-$C$ phase transition in biaxial disordered environments, e.g. fully anisotropic aerogel. We find that both the $A$ and $C$ phases belong to the universality class of the XY Bragg glass, and therefore have quasi-long-ranged translational smectic order. The phase transition itself belongs to a new universality class, which we study using an $epsilon=7/2-d$ expansion. We find a stable fixed point, which implies a continuous transition, the critical exponents of which we calculate.
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We study theoretically the smectic A to C phase transition in isotropic disordered environments. Surprisingly, we find that, as in the clean smectic A to C phase transition, smectic layer fluctuations do not affect the nature of the transition, in spite of the fact that they are much stronger in the presence of the disorder. As a result, we find that the universality class of the transition is that of the Random field XY model (RFXY).
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.
We develop a theory of Smectic A - Smectic C phase transition with anomalously weak smectic layer contraction. We construct a phenomenological description of this transition by generalizing the Chen-Lubensky model. Using a mean-field molecular model, we demonstrate that a relatively simple interaction potential suffices to describe the transition. The theoretical results are in excellent agreement with experimental data.
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.
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.
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