Competing alignments of nematic liquid crystals on square-patterned substrates

Abstract

A theoretical analysis is presented of a nematic liquid crystal confined between substrates patterned with squares that promote vertical and planar alignment. Two approaches are used to elucidate the behavior across a wide range of length scales: Monte Carlo simulation of hard particles and Frank-Oseen continuum theory. Both approaches predict bistable degenerate azimuthal alignment in the bulk along the edges of the squares; the continuum calculation additionally reveals the possibility of an anchoring transition to diagonal alignment if the polar anchoring energy associated with the pattern is sufficiently weak. Unlike the striped systems previously analyzed, the Monte Carlo simulations suggest that there is no "bridging" transition for sufficiently thin cells. The extent to which these geometrically patterned systems resemble topographically patterned substrates, such as square wells, is also discussed.

Independent control of polar and azimuthal anchoring

“…This figure shows as well a schematic illustrating these different states and their relationship to the microscopy image. This diagonal alignment behavior in VV regions is predicted by continuum model calculations [26] if the polar anchoring energy promoted by the surface is rather weak.…”

“…The second item of note from these snapshots is that the surface patterns do not "bridge" across the film. As with square patterns [26], this is presumably due to the different interfacial stabilities that would pertain at the resultant twistlike and bendlike domain boundaries.…”

“…In Ref. [26], we saw that the azimuthal angle cannot be effectively controlled using square-patterned substrates, degenerate alignment being seen between the two edge directions. Here, though, for both R values investigated, clear orientational pinning was apparent.…”

“…Experimental studies on SAM-based square-patterned systems have shown that, for feature sizes of 30 μm, the favored alignment runs along the diagonals of the planar-promoting squares [22]. When the patterning length scale is reduced to that accessible to particle-based simulation, however, the preferred orientations run along the pairs of opposite edges of the squares [26]. An anchoring transition between these arrangements is then predicted for, e.g., a sufficiently weak polar anchoring condition.…”

“…The model used is essentially that described in Ref. [26]. Briefly, interparticle interactions have been modeled through the hard Gaussian overlap (HGO) potential [27], which can be seen as equivalent to the well-known Gay-Berne model [28], stripped of its attractive interaction.…”