Experimental test of a fluctuation-induced first-order phase transition: The nematicsmectic-A transition

In 1974, Halperin, Lubensky, and Ma (HLM) [Phys. Rev. Lett. 32, 292 (1974)] predicted that the nematicsmectic-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 nematicsmectic-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. In a mean-field approximation, a universal scaling form of the latent heat can then be derived close to the LTP. Its form depends sensitively on the presence of the cubic term. By reanalyzing earlier calorimetric measurements near the LTP, we find that these data yield evidence for the presence of the cubic term predicted by HLM. The second new approach to experimentally determine whether a transition is weakly first order or second order is a dynamical method. This general method is based on the observation that when a transition is (weakly) first order, the dynamics of interfaces are symmetric about Tc, so that an interface can propagate into both phases, depending on whether the sample is undercooled or overheated (corresponding to melting and freezing). For a weakly first-order transition, a simple scaling relation for the interface speed can be derived. In contrast, the dynamics of propagating fronts close to a second-order transition are very asymmetric. Results of moving interfaces close to Tc in 8CB-10CB (where CB represents cyanobiphenyl) and 9CB-10CB mixtures are presented and shown to support both qualitatively as well as quantitatively the prediction that the transition is always at least weakly first order. For the N Sm-A transition in these compounds, our comparison finds that the dynamic experiments are more sensitive than the adiabatic calorimetry experiments by about one order of magnitude and more sensitive than the x-ray-diffraction experiments by about two orders in detecting the phase-transition order.