Alignment of columnar phase confined in polydimethylsiloxane microchannels
ABSTRACTThe alignment of a discotic liquid crystal confined in polydimethylsiloxane (PDMS) channels with a rectangular cross-section is studied. The microchannels were produced in PDMS using the mold-replica technique. In the PDMS channels, the disc-like molecules of the disogen were found to adopt an edge-on anchoring at the PDMS surface, and macroscopically, the discogen layer is planarly aligned. Using Newton colour scale technique it was revealed that discotic columns were aligned parallel to the channels.
We study multiple orthogonal polynomials of Meixner-Pollaczek type with respect to a symmetric system of two orthogonality measures. Our main result is that the limiting distribution of the zeros of these polynomials is one component of the solution to a constrained vector equilibrium problem. We also provide a Rodrigues formula and closed expressions for the recurrence coefficients. The proof of the main result follows from a connection with the eigenvalues of block Toeplitz matrices, for which we provide some general results of independent interest. ::: The motivation for this paper is the study of a model in statistical mechanics, the so-called six-vertex model with domain wall boundary conditions, in a particular regime known as the free fermion line. We show how the multiple Meixner-Pollaczek polynomials arise in an inhomogeneous version of this model.