First-order liquid crystal orientation transition on inhomogeneous substrates.

In a recent experiment, we uncovered an unconventional liquid crystal (LC) orientation transition on microtextured substrates consisting of alternating horizontal and vertical corrugations. When the period of alternation was decreased toward approximately 1 microm, the LC alignment underwent an abrupt transition from inhomogeneous planar to a more uniform configuration with a large pretilt angle ( approximately 40 degrees ). With the aid of a model based on the competition between the Frank-Oseen elastic energy and a phenomenological surface potential of the form W(theta,phi)=(1/2)W((2))(theta) sin(2) theta+(1/4)W((4))(theta) sin(4) theta+(1/2)W(phi) cos(2) theta sin(2) phi(x,y) (where theta and phi are, respectively, the pretilt and azimuthal angles of the LC director and W((2))(theta), W((4))(theta), and W(phi) are constants) that demonstrated good agreement with experiment, we investigated the microscopic origin of the observed transition. It was found that this transition comprises two steps. First, the LC director homogenizes toward the phi=45 degrees azimuthal direction in the plane to relax the elastic energy. The resulting rise in azimuthal anchoring energy subsequently drives the LC to adopt a finite pretilt. The values of the W's deduced from the model reveal that the polar anchoring energy is about approximately 1/10 of the typical values, with the sin(4) theta term dominating the sin(2) theta term. We present a possible explanation for this unexpected finding.