Two Experimental Tests of the Halperin-Lubensky-Ma Effect at the Nematic–Smectic-APhase Transition

Abstract

We have conducted two quantitative tests of predictions based on the Halperin-Lubensky-Ma (HLM) theory of fluctuation-induced first-order phase transitions. First, we explore the effect of an external magnetic field on the nematic-smectic-A transition in a liquid crystal. Second, we examine the dependence of the first-order discontinuity as a function of mixture concentration in pure 8CB and three 8CB-10CB mixtures. We find the first quantitative evidence for deviations from the HLM theory. PACS numbers: 64.70.Md, 61.30.Gd, 64.60.Fr One of the most important advances made in our understanding of continuous phase transitions has been the modification of critical exponents, due to thermal fluctuations, from the values predicted by mean-field theory [1]. But thermal fluctuations have another effect, one that is less well understood theoretically and studied only to a limited extent experimentally: when two order parameters (or an order parameter and a gauge field) are simultaneously present and interact with each other, the fluctuations of one may drive the phase transition of the other first order. In high-energy physics, for example, an analogous situation occurs in the Higgs mechanism [1]. In condensed-matter physics, over two decades ago, Halperin, Lubensky, and Ma (HLM) [2] predicted that this could occur in two settings: the normal-superconducting phase transition in type-1 superconductors and the nematic-smectic-A (NA) transition in liquid crystals. At the NA transition [3-6], the first fluctuating field is the nematic order parameter Q ij S ° 3n i n j 2 d ij ¢ 2, while the other order parameter is the two-component smectic-A order parameter c. In principle, a complete theory must account for thermal fluctuations in the nematic order parameter magnitude S, the nematic directorˆndirectorˆ directorˆn, and the smectic-A order parameter c. The de Gennes-McMillan mechanism [3] takes into account S fluctuations but is mean field inˆninˆ inˆn and c. The HLM theory, in addition, considersˆnconsidersˆ considersˆn fluctuations but is mean field in c. Deviations from the de Gennes-McMillan mechanism have been quantitatively established by Anisimov et al. [7] and Cladis et al. [8]. Although their conclusions are consistent with the HLM mechanism, the experiments are at their resolution limits and the full implications of the HLM theory remain to be tested. In this paper, we conduct the first two quantitative tests of the HLM theory, both leading to significant discrepancies from HLM. (i) Mukhopadhyay et al. [9] have made a detailed prediction for the external-field dependence of the HLM effect; we look for this field effect experimentally in the cyanobiphenyl liquid crystal 8CB, as well as in mixtures of 8CB and 10CB. (ii) The first-order discon-tinuity implied by the HLM theory (which can be characterized by the number t 0 T NA 2 T T , where T NA is the transition temperature and T is the spinodal point) should also be sensitive to the mixture concentration x in the 8CB-10CB system. Here, we make a quantitative study o...

Kinked Focal Conic Domains in a SmA

“…(see [10]), where e ¼ c=a is the eccentricity, c ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi a 2 À b 2 p , a and b the semi-major and semi-minor ellipse axes respectively. The equation above shows that the decrease (increase) of the number of the dislocations, attached to the ellipse at constant eccentricity leads to the FIGURE 8 Temperature dependence of the ellipse longer diameter for nematogenic smectic 8OCB.…”

“…It turns out that the non-nematogenic and nematogenic smectics differ by their temperature dependence for the modulus B. For non-nematogenic smectics B is very weakly temperature dependent, while for the nematogenic smectics B decreases according to some critical exponent when approaching the phase transition to the nematic phase [7][8][9][10]. Therefore the replacement of the FCD texture by the distortions involving dislocations on heating approaching the phase transition to the nematic phase can be explained by the switching from the 'isometric deformation' regime, in which the layers are mostly affected by FIGURE 6 Temperature dependence of the ellipse major axis for nonnematogenic smectic 10CB.…”

Imperfections in focal conic domains: the role of dislocations

“…N phase transition has been the object of many investigations (for a review, see De Gennes and Prost [3]). The compression modulus, B, tends towards a value equal to or slightly different from zero, according to the author [4][5][6][7]; its variation is noticeable in a large temperature range (more than half a degree in the compounds that we have investigated). Notice that in this range, K 1 (the splay modulus) stays practically constant.…”

Effect of order parameter fluctuations on the Halperin-Lubensky-Ma first-order transition in superconductors and liquid crystals

“…(2) becomes positive, but the transition remains first order, in agreement with the HLM theory. At smaller concentrations, t continues to decrease, as expected, but there is a clear deviation from the HLM result [19]. To attempt to fit the data in the whole concentration range 0 < x < 0.65, we take the above parameters to set the initial values of the couplings, and then evolve t, e, and b according to Eqs.…”