Anisotropy of the Nematic-Smectic a Phase Transition

Abstract

Critical behavior at the transition from the nematic phase to the smectic A phase in liquid crystals has been of interest for over two decades. Discussions about the nature of the transition, its analogy to the superconducting transition, and the degree of anisotropy present in the critical exponents have been extensive during this time. This review article concentrates on the question of anisotropy at the nematic-smectic A transition. The experimental and theoretical work related to this question is summarized and compared. While progress has been made, there are many interesting questions related to this transition that remain for investigators to answer.

Smectic Vortex Phase in Optimally DopedYBa2Cu3O7Thin Films

“…For a nematic to smectic-A transition s 1 ÿ 3 ÿ 1 [2,32]. Measured values for the nematic-smectic-A correlation-length exponent in liquid crystals range from 0.37 to 0.83 [33], implying 0:1 < s < 1:5, in accordance with the values of s that we find. The fact that s is similar at higher temperatures for H k ab and at all temperatures for other angles suggests a common origin of the melting This change in the dynamic response of the vortex liquid near the liquid-solid transition is also observed in the vortex solid through J c measurements, where the nonlinear nature of the response upon exceeding the critical current changes abruptly for T < 80 K and H k ab [34].…”

Effect of Aerosil Gels on de Gennes Nematic−Smectic Coupling

“…Unfortunately, the effect of fluctuations in the phase φ of the smectic order parameter due to coupling to director fluctuations is an extremely challenging and as yet unsolved theoretical problem. An excellent review of the theoretical situation has been given by Andereck, and perhaps the most useful theory for a discussion of experimentally observed N-SmA critical behavior is the self-consistent one-loop model of Patton and Andereck. , This model predicts an extremely wide and gradual crossover between the isotropic XY fixed point with ν ∥ = ν ⊥ to a new fixed point characterized by strong critical anisotropy with ν ∥ = 2ν ⊥ . The predicted crossover occurs over a range of 14 decades from 10 6 to 10 −8 in a theoretical variable a / a 30 that is proportional to t +γ , but experimental data are obtained over a much more limited t range of ∼3 decades or less.…”

“…Note that nematic orientational order is described by a second-rank, symmetric and traceless, tensor Q ij that can be characterized by the scalar magnitude S on short length scales and a “head-less” vector n on longer length scales . Unfortunately, the detailed consequences of δ n- φ coupling are still not theoretically established …”