A dynamical test of phase transition order: New things in old places or old wine in new bottles

We first discuss nonlinear aspects of phase transition theory applied to a particular liquid crystal phase transition. A simple derivation is given to show how two coupled Goldstone modes (one appearing as gauge fluctuations of the ordered phase) can force a phase transition, against all expectations, to take place discontinuously (theory of Halperin, Lubensky, and Ma)-but the discontinuity may be immeasurably small. Then, we describe a new dynamical test of phase transition order, developed by Cladiset al., that turns out to be more sensitive than x-ray diffraction and adiabatic calorimetry. Quantitative data found by this new method are in excellent agreement with the measurements of adiabatic calorimetry and x-ray diffraction as well as expectations implicit in the predictions of HLM.This is the text of an after-banquet talk given at the CNLS Workshop on the Dynamics of Concentrated Systems.     

Study of Liquid Crystals in Flow: I. Conventional Viscometry and Density Measurements

Using the technique of conventional viscometry (Haake-Hoeffler Falling Ball and Ostwald-Poiseuille viscometers), we have measured the temperature dependence of the apparent viscosity of three liquid crystals: methoxybenzylidene butylaniline (MBBA), hexyloxybenzylidene amino benzonitrile (HBAB) and cyanobenzylidene octyloxyaniline (CBOOA). The measurements with the falling-ball show a small discontinuity in the apparent viscosity of (HBAB) at ～ 91°C, where the flow properties of this compound have been found to change from one flow regime in which the “classical” molecular alignment with the flow can be observed (T > 91°C) to another regime in which this alignment cannot be observed (T < 91°C). However, in spite of this small discontinuity, the apparent falling-ball viscosity which we measured for (HBAB) is still very close to the Miesowicz viscosity, η_B, obtained by constraining the director n to remain parallel to the velocity vector during the measurements. Measurements performed with the Ostwald-Poiseuille viscometer show: (i) that the apparent viscosity and the viscous heat of the nematic and smectic-A mesophases depend upon the radius of the capillary; (ii) that the apparent viscosity, in both the flow-alignment and the non-flow-alignment regimes, is very close to η_B and (iii) that there is no convincing evidence of a discontinuity in the apparent viscosity of (HBAB) at 91°C.

Our measurements of the temperature dependence of the density of the mesophases show that the isobaric coefficients of thermal expansion for (HBAB) and (CBOOA) are different in the flow alignment and in the non-flow-alignment regimes. This is consistent with the hypothesis that there is a greater degree of molecular association in the non-flow-alignment regime.     

First Truly Ferroelectric Liquid Crystal

The first faroelectric liquid crystalline phase (in 8SI* (ΔS-(+)-(4-(2′methylbuty1) phenyl-4′-n-octylbiphenyl-4 carboxylate) is reported and its physical properties are discussed. The close connection between the phase sequences of 8SI* and its racemate are established. Both compounds show a number of smectic phases above the newly discovered ferroelectric phase and its analogue in the racemate. These phases (CI and G') are tilted in the racemate 8SI and tilted with a helicoidal structure in 8SI*. In the truly ferroelectric phase, X, the director of the molecules can be oriented in a bistable way in an electric field Furthermore when the field is turned off the director orientation remains unchanged. This behaviar is fundamentally different from that in bulk smectic phases which support the helix structure in the absence of external forces. A model far ‘racemates’ in higher smectic phases like G, G', H’ etc as well as a the newly discovered ferroelectric phase is presented. The response of cholesteric blue phases of 8SI* to an external field is discussed in an appendix.     

Splay-bend textures involving tetrahedratic order

We show that defect-free splay-bend textures are less energetic compared to uniform states in liquid-crystalline phases that possess both quadrupolar (nematic) and octupolar (tetrahedratic) order. This is because, in such systems, there is a symmetry-allowed linear gradient term in the energy. Another unusual feature of these splay-bend textures is the fact that they have a non-homogeneous, space-dependent free-energy density. These results may help clarify some mysterious features noted for the B7 liquid-crystal phase formed by achiral banana-shaped molecules.     

Pattern formation at the traveling liquid-crystal twist grain boundary-smectic a interface

Summary Pattern formation at phase boundaries moving in a temperature gradient is one of the major areas of nonequilibrium physics attracting considerable attention. While most of the early work concentrated on the moving solid-liquid interface, now the focus has changed to phase transitions characterized by broken continuous symmetry. Most recently we investigated consequences to interfacial patterns of a chirality-induced equilibrium length. Here we study patterns at another chiral interface where one of the phases has a chirality-induced defect lattice, the twist grain boundary (TGB) phase. The TGB state is analogous to the vortex lattice in Type-II superconductors predicted by the Gennes’ analogy between the nematic (N)-smectic A (A) transition and the normal-superconducting transition. In this analogy, a cholesteric A transition is analogous to the normal-superconducting transition in an external magnetic field and a theory has been developed for its analogous vortex lattice, the TGB phase, when this transition is Type II. We study patterns formed at the traveling TGB-A phase boundary. Different patterns are observed depending on whether TGB grows into A or A into TGB. Indeed, this maybe the first time a steady-state pattern is observed in directional melting (i.e. TGB growing into A). As these patterns have a broad band of wavelengths, they are difficult to characterize physically. Thus, we introduced a novel analysis (most simply but not rigorously described as) measuring the fractal dimension of the patterns at these traveling interfaces. Two lengths emerged from this analysis: a longer one set by sample thickness and a shorter one set by the smallest TGB unit that can grow into an oriented smectic A phase. We invoke our old dynamic arguments to account for why TGB cannot propagate at a second-order TGB-cholesteric phase transition so it is eventually squeezed out leaving behind a direct cholesteric-A transition. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

A prepared pattern with wavelength selection in directional solidification

As crystal growth is a vital link in the long chain of processes leading to state-of-the-art technological devices, a great deal is known about patterns formed at the solid-liquid interface of a growing crystal. However, some basic questions are still unanswered concerning macroscopic features exhibited by a moving solid-liquid interface. Even for the first instability, the cellular instability, a unique steady-state wavelength does not emerge from theory. Furthermore, while wavelength selection is observed in many different materials, its origin is still to be discovered. By breaking continuous rotational symmetry of the flat solid-liquid interface about the pulling direction v, we prepared a cellular pattern with a well-defined wavelength by front propagation into the unstable uniform state. The material is succinonitrile and the rectangular interface geometry is formed by loading it into a flat capillary. The capillaries are chosen to provide a sample thicknessy ₀ = 100n , and width 10y ₀ and 20y ₀. We use a high-resolution directional solidification apparatus and grow the crystal from grain-boundary-free seed crystals. Surprisingly, the shape of the groove next to the uniform state is initially well-described by nearly self-similar Gaussians. This suggests that the initial perturbation of the interface is localized to a region /2 around a groove. A pattern with a well-defined wavelength is established when the half-width of the Gaussians ₀16m is small compared to 80m so there is little overlap between a groove and its predecessor or successor. When overlap is significant, the pattern is time-dependent. These results suggest that wavelength selection in this prepared pattern is a consequence of front propagation of a localized perturbation.