Pe. Cladis et al., PATTERN-FORMATION AT THE TRAVELING LIQUID-CRYSTAL TWIST GRAIN BOUNDARY SMECTIC-A INTERFACE, Nuovo cimento della Societa italiana di fisica. D, Condensed matter,atomic, molecular and chemical physics, biophysics, 16(7), 1994, pp. 765-770
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.