Elastic contribution to the free energy of a nematic in presence of a structured substrate: beyond Berreman's approach
Romero-Enrique, J.M.1
1Universidad de Sevilla, Spain
The behaviour of liquid crystals close to structured
surfaces has attracted much attention on the last years due to their potential
applications, such as bistable LCDs
[1]. The presence of microstructured surfaces can
frustrate the long-ranged orientational ordering of a
nematic phase. Associated to the deformation of the
director field of a nematic phase we can identify an elastic
contribution of the free energy, which may play an important role in the
interfacial behaviour of nematic phases. If the
director field deformation is smooth, Berreman’s
approach [2] or its generalizations [3] account for the elastic contribution.
In some cases topological defects also appear in the nematic
phase. The presence of defects –with complex structure and dynamics– is a new
ingredient and an additional source of surface inhomogeneity,
not present in the adsorption of simple liquids. Indeed, colloidal particles
dispersed in bulk nematics are known to give rise to complex
nematic-mediated colloidal interactions, in which
topological defects play an important role [4]. The inteplay
between defects and surface structure is not still well understood.
We have considered a nematic
phase in contact with a saw-shaped substrate of period L with favours (local) homeotropic alignment. We assume that the nematic phase can be described by the Landau-de Gennes free-energy, and the equilibrium order parameter
profile is obtained by using the Finite Element Method (FEM) with adaptive
meshing [5]. The analysis of the nematic free energy
and its dependence on the periodicity of the substrate shows that under strong
anchoring conditions (i.e. large L) the elastic contribution is not described
by Berreman approach, but it has a
geometry-dependent, log(L) contribution. Using a
modified Frank-Oseen elastic Hamiltonian approach, we
ascribe this elastic contribution to the appearance of non-half-integer topological
defects on the cusps (edges and wedges) of the substrate [6]. This non-Berreman elastic contribution explains the large deviations
of the wetting transition parameters with respect to the Wenzel law prediction
[7], and it may lead to novel nematic-mediated
interactions between prism-like colloidal particles [8].
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