Pitch Contributions to the Cholesteric−Isotropic Interfacial Tension

Abstract

Phase transitions in lyotropic and thermotropic liquid crystalline systems are a topic of current fundamental and applied research. 1 An important feature that impinges on the kinetic, thermodynamic, and morpholical properties of biphasic systems involving order/disorder phases is the interfacial tension. The interfacial tension at the nematic-isotropic (N/I) phase transition has been studied extensively theoretically 2-6 and experimentally, 7,8 and its basic features are sufficiently well understood. On the other hand, the interfacial tension of the cholesteric-isotropic (Ch/I) interface has been experimentally characterized, 9 and as already pointed out by de Gennes and Prost, 10 it is difficult to analyze. One of the reasons is that cholesteric liquid crystals are layered materials that behave as nematic liquid crystals at length scales smaller than the layer spacing and as smectic liquid crystals at length scales longer than the layer spacing. A further complication is that the layer spacing, known as the pitch of the cholesteric helix, is a function of pressure, temperature, concentration, and the nematic scalar order parameter. 10,11,14 Since the pitch is a function of the scalar order parameter, at the cholesteric/isotropic interface, the gradients in the scalar order parameter lead to gradients in the pitch. It is then clear that the interfacial tension between isotropiccholesteric phases contains additional contributions not found in the nematic-isotropic interface, because nematics are positionally disordered materials while cholesteric are layered materials. Thus, a better understanding of layer spacing contributions to the interfacial tension is highly desirable.Recently the interfacial tension between the Ch/I interface was carefully studied theoretically and experimentally, 9 and it was found that several theories 2-4 that describe the N/I interface predict the correct molecular weight dependence of the interfacial tension but underpredict its magnitude. In addition, the experiments 9 clearly show pitch gradients in the direction normal to the interface, in agreement with the experimentally obeserved 14 and theoretically expected 14 pitch dependence on the scalar order parameter.The objective of this note is (i) to use the uniaxial version of Landau-de Gennes theory 12 to characterize the interfacial tension of the cholesteric-isotropic interface and (ii) to provide an analysis of the effect of cholesteric ordering on the interfacial tension of the Ch/I interface. It is possible that other mechanisms based on polydispersity also contribute to the interfacial tension. Fluctuations are not taken into account in this note. It should be noted that fluctuations at the nematic/ solid or gas interface have been proposed as the mechanism to explain the complex temperature dependence of γ. 13 Uniaxial cholesteric liquid crystals are chiral nematics 10 whose equilibrium structure in a rectangular coordinate system (x,y,z) is given by the following director field n 0 :where q 0 is the equilibrium wave vector, ...

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