Coupling between elasticity in a nematic phase and front dynamics for a moving nematic-isotropic boundary

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Abstract
During growth or melting of the nematic phase at the expense of the isotropic one caused by pulling the sample from a hot into a cold thermal contact, or vice versa (directional ordering or melting), the two-phase front undergoes a morphological instability on the mesoscale at a critical pulling speed, known under the name of the Mullins-Sekerka instability. Their original work [J. Appl. Phys. 35, 444 (1964)] focused on the diffusive nature of the instability: it is driven by impurity diffusion. At large speeds—where the destabilizing diffusion length is small enough—the front restabilizes into a planar one due to surface tension. The anchoring of the liquid crystal molecules on both the front and the plates within which the sample is confined causes strong distortions of the molecules, which react on front dynamics. In this paper, we present a general formulation for the coupling between elasticity in a nematic phase and front dynamics during growth or melting of the nematic phase. As an exploitation of this model, we confine ourselves to a simplistic geometry of the director configuration in the linear regime (where the front depletion is small). We find that both during growth and melting, the coupling leads to a drift of the pattern along the two-phase front. During melting, and at large enough growth velocities (which are experimentally accessible and lie in the range 100–200 μm/s), the coupling is stong and leads to a large shift of the restabilization speed. We present the results in a physically appealing picture. Speculation and outlook for new lines of physical inquiries are presented.