Melted grain boundaries in smectic a under imposed bend: role of the anisotropy

Abstract

ABSTRACT The well-known de Gennes analogy between smectics and superconductors predicts two types of smectic A behaviour under imposed bend. In Type I smectics, the smectic order melts, expelling all of the bend in a bulk nematic region (3D ‘defect’). In Type II smectics, the order melts on 1D defects, edge dislocation lines, which form an Abrikosov-like lattice. Here, I discuss how the strong anisotropy of the smectic coherence lengths influence the smectic A behaviour under imposed bend distortion. I show analytically and numerically that, as proposed previously, a third type of behaviour is possible close to a second-order nematic–smectic A transition, with smectic order melting on the plane of the grain boundary (2D defects). This third kind of behaviour, Melted Grain Boundary (MGB), which has been previously reported experimentally in the smectic A material 9CB, is intermediate between the Type I and Type II behaviours and can be considered as Type ‘one-and-a-half’ smectic A. I define the domain of material parameters in which the planar MGB defect is energetically and topologically stable. I discuss also if similar planar defects may exist, or not, in other anisotropic materials, e.g. superconductors, chiral smectic A, cholesterics and twist-bend nematics.