Phase properties of nematics confined by competing walls

The consequences of confinement on the isotropic-nematic (IN) transition are investigated for a slab geometry with walls that compete in molecular alignment. We employ the Landau-de Gennes free energy with symmetrically opposing wall fields that favor random parallel and homeotropic orientations, respectively, at each wall, and describe the phase diagram with the use of the associated nonlinear dynamical-system phase portraits. The differences in phase behavior with respect to the bulk, or with the system confined by identical walls, are important: Depending on the wall separation L and the strength of the walls' field μs, the IN transition is either unaffected and its temperature TIN remains fixed, or, the transition disappears altogether. We find: (i) when μs < μsw (where μsw is the wall field value for the wetting transition of the semi-infinite system) the transition occurs for all wall separations, and (ii) when μs > μsw there is no transition for all wall separations above a given value Lqw(μs). The boundary Lqw(μs) between these two regions is identified as a shifted wetting transition in which IN phase coexistence is transformed into an interface-like state, and it is of the 1st order, tricritical and critical when μsw < μs < μstc, μs = μstc and μs > μstc, respectively. For temperatures in the neighborhood of TIN, Lqw(μs) is continued as a locus of shifted prewetting transitions. This behavior is equivalent, but manifests differently, to that already known for a magnetic slab under symmetrically opposing surface fields and vanishing surface coupling enhancement.