Mesophase Growth

Abstract

I review experimental and theoretical studies of the shape instabilities that occur during the free and directional growth of liquid crystals. The observed instabilities are due ultimately to the same mechanisms that cause snowflakes in freezing water and dendrites in freezing metals. However, the material parameters of liquid crystals are very different from those of solids, and there are physical effects, such as anisotropic elasticity, that are peculiar to the phase being studied. For these reasons, the details of the shape instabilities of liquid crystals differ greatly from those in solids. Here, I focus on the two types of interfaces — nematic-isotropic and discotic-isotropic — that have been most extensively explored, while observations from other systems are summarized more briefly. I also summarize the approach and results of the major lines of theoretical analysis that have so far been attempted. Some of the more notable studies to date have been the quantitative analysis of the first instability of a flat interface in directional solidification and of a circular interface in free growth; the analysis of free dendritic growth and comparison to microsolvability theory; and the exploration of secondary instabilities in directional solidification, including notably a parity-breaking instability that leads to drifting cellular patterns. Recent theories suggesting the existence of many more secondary and tertiary instabilities, along with the existence of spatiotemporally chaotic states (observed so far only in passing, with no detailed study), imply that many interesting results are still to come.