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Register a new userMolecular model for de Vries type smectic A - smectic C phase transition in liquid crystals
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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.
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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.
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.
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Leiming Chen (College of Science
, The China University of Mining andn Technology
, Xuzhou
2011
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.
A high-resolution calorimetric study has been carried out on nano-colloidal dispersions of aerosils in the liquid crystal 4-textit{n}-pentylphenylthiol-4-textit{n}-octyloxybenzoate ($bar{8}$S5) as a function of aerosil concentration and temperature spanning the smectic-textit{C} to nematic phases. Over this temperature range, this liquid crystal possesses two continuous XY phase transitions: a fluctuation dominated nematic to smectic-textit{A} transition with $alpha approx alpha_{XY} = -0.013$ and a mean-field smectic-textit{A} to smectic-textit{C} transition. The effective critical character of the textit{N}-Smtextit{A} transition remains unchanged over the entire range of introduced quenched random disorder while the peak height and enthalpy can be well described by considering a cut-off length scale to the quasi-critical fluctuations. The robust nature of the textit{N}-Smtextit{A} transition in this system contrasts with cyanobiphenyl-aerosil systems and may be due to the mesogens being non-polar and having a long nematic range. The character of the Smtextit{A}-Smtextit{C} transition changes gradually with increasing disorder but remains mean-field-like. The heat capacity maximum at the Smtextit{A}-Smtextit{C} transition scales as $rho_S^{-0.5}$ with an apparent evolution from tricritical to a simple mean-field step behavior. These results may be generally understood as a stiffening of the liquid crystal (both the nematic elasticity as well as the smectic layer compression modulus $B$) with silica density.
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).
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