Nematic liquid crystal in the wedge and edge geometry in the case of homeotropic alignment

Wetting of Nematic Liquid Crystals on Crenellated Substrates: A Frank–Oseen Approach

We revisit the wetting of nematic liquid crystals in contact with crenellated substrates, studied previously using the Landau–de Gennes formalism. However, due to computational limitations, the characteristic length scales of the substrate relief considered in that study limited to less than 100 nematic correlation lengths. The current work uses an extended Frank–Oseen formalism, which includes not only the free-energy contribution due to the elastic deformations but also the surface tension contributions and, if disclinations or other orientational field singularities are present, their core contributions. Within this framework, which was successfully applied to the anchoring transitions of a nematic liquid crystal in contact with structured substrates, we extended the study to much larger length scales including the macroscopic scale. In particular, we analyzed the interfacial states and the transitions between them at the nematic–isotropic coexistence.

Pattern-induced anchoring transitions in nematic liquid crystals

In this paper we revisit the problem of a nematic liquid crystal in contact with patterned substrates. The substrate is modelled as a periodic array of parallel infinite grooves of well-defined cross-section sculpted on a chemically homogeneous substrate which favours local homeotropic anchoring of the nematic. We consider three cases: a sawtooth, a crenellated and a sinusoidal substrate. We analyse this problem within the modified Frank-Oseen formalism. We argue that, for substrate periodicities much larger than the extrapolation length, the existence of different nematic textures with distinct far-field orientations, as well as the anchoring transitions between them, are associated with the presence of topological defects either on or close to the substrate. For the sawtooth and sinusoidal cases, we observe a homeotropic to planar anchoring transition as the substrate roughness increases. On the other hand, a homeotropic to oblique anchoring transition is observed for crenellated substrates. In this case, the anchoring phase diagram shows a complex dependence on the substrate roughness and substrate anchoring strength.

Generalized Berreman's model of the elastic surface free energy of a nematic liquid crystal on a sawtoothed substrate

In this paper we present a generalization of Berreman's model for the elastic contribution to the surface free-energy density of a nematic liquid crystal in presence of a sawtooth substrate which favors homeotropic anchoring as a function of the wave number of the surface structure q, the tilt angle α, and the surface anchoring strength w. In addition to the previously reported nonanalytic contribution proportional to -q ln q, due to the nucleation of disclination lines at the wedge bottoms and apexes of the substrate, the next-to-leading contribution is proportional to q for a given substrate roughness, in agreement with Berreman's predictions. We characterize this term, finding that it has two contributions: the deviations of the nematic director field with respect to a reference field corresponding to the isolated disclination lines and their associated core free energies. Comparison with the results obtained from the Landau-de Gennes model shows that our model is quite accurate in the limit wL>1, when strong anchoring conditions are effectively achieved.

Scaling of the elastic contribution to the surface free energy of a nematic liquid crystal on a sawtoothed substrate

We characterize the elastic contribution to the surface free energy of a nematic liquid crystal in the presence of a sawtooth substrate. Our findings are based on numerical minimization of the Landau-de Gennes model and analytical calculations on the Frank-Oseen theory. The nucleation of disclination lines (characterized by non-half-integer winding numbers) in the wedges and apexes of the substrate induces a leading order proportional to q ln q to the elastic contribution to the surface free-energy density, with q being the wave number associated with the substrate periodicity.