Experimental test of a fluctuation-induced first-order phase transition: The nematic–smectic-Atransition

Abstract

In 1974, Halperin, Lubensky, and Ma (HLM) [Phys. Rev. Lett. 32, 292 (1974)] predicted that the nematic–smectic-A transition of pure compounds and their mixtures should be at least weakly first order. One way to obtain such a prediction is to treat the smectic order parameter as a constant and integrate out the director fluctuations. The coupling between the director fluctuations and the smectic order parameter then generates a cubic term in the effective free energy for the nematic–smectic-A(N–Sm-A) transition, which tends to drive the transition first order. So far, however, there has not been clear experimental evidence in support of this prediction: Some materials appear to exhibit a first-order transition but others a second-order transition. In this paper we introduce two new approaches to test the predictions of HLM. First, we note that if a cubic term in the effective free energy for the smectic order parameter is present, its effect is dominant near the Landau tricritical point (LTP), where the quartic term in the free energy vanishes.