Boundary-layer phase transition in nematic liquid crystals

Phase-transition properties of nematic liquid crystals aligned by a short-range, arbitrary-strength-substrate potential are examined in the framework of Landau—de Gennes theory. It is shown that the substrate potential, which can arise from surface treatment of liquid-crystal display cells, not only induces a boundary layer in which the order-parameter values can be significantly different from that of the bulk, but also introduces a new "boundary-layer phase transition" which occurs at temperatures higher than the bulk-transition temperature. This novel transition is found to take place only in a limited range of substrate potential strength. For 4-pentyl-4'-cyanobiphenyl (PCB), the limiting values of this range are computed to be ∼0.075 and ∼0.15 erg/${\mathrm{cm}}^2$. Calculations are performed for both the semi-infinite-sample case and the finite-thickness-sample case. Various phase diagrams are presented to show the effects of sample thickness and substrate potential on the bulk as well as the boundary-layer phase-transition temperatures. The paper concludes with a discussion of experimental possibilities.