PATTERN-FORMATION AT THE TRAVELING LIQUID-CRYSTAL TWIST GRAIN BOUNDARY SMECTIC-A INTERFACE

Pattern formation at phase boundaries moving in a temperature gradient is one of the major areas of nonequilibrium physics attracting consid erable attention. While most of the early work concentrated on the mov ing solid-liquid interface, now the focus has changed to phase transit ions characterized by broken continuous symmetry. Most recently we inv estigated 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 t wist grain boundary (TGB) phase. The TGB state is analogous to the vor tex lattice in Type-II superconductors predicted by de Gennes' analogy between the nematic (N)-smectic A (A) transition and the normal-super conducting transition. In this analogy, a cholesteric A transition is analogous to the normal-superconducting transition in an external magn etic field and a theory has been developed for its analogous vortex la ttice, the TGB phase, when this transition is Type II. We study patter ns formed at the traveling TGB-A phase boundary. Different patterns ar e 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 dire ctional melting (i.e. TGB growing into A). As these patterns have a br oad 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 thes e traveling interfaces. Two lengths emerged from this analysis: a long er one set by sample thickness and a shorter one set by the smallest T GB 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 sec ond-order TGB-cholesteric phase transition so it is eventually squeeze d out leaving behind a direct cholesteric-A transition.