  Due to elastic anisotropy, two-dimensional patterning of substrates can
promote weak azimuthal alignment of adjacent nematic liquid crystals. Here, we
consider how such alignment can be achieved using a periodic square lattice of
circular or elliptical motifs. In particular, we examine ways in which the
lattice and motif can compete to favor differing orientations. Using Monte
Carlo simulation and continuum elasticity we find, for circular motifs, an
orientational transition depending on the coverage fraction. If the circles are
generalised to ellipses, arbitrary control of the effective alignment direction
and anchoring energy becomes achievable by appropriate tuning of the ellipse
motif relative to the periodic lattice patterning. This has possible
applications in both monostable and bi-stable liquid crystal device contexts.

Soft Condensed Matter