Ordering effects in electric splay Freedericksz transitions

We analyze the interaction between a nematic liquid crystal and an electric field, in a cell in which splay Freedericksz geometry is enforced. Equilibrium configurations are explored both close to the Freedericksz threshold and in the limit of strong applied voltages. We frame within de Gennes' order-tensor theory, which allows us to detect the effects of a variable degree of orientation on critical fields and bifurcation shapes. The applied voltage induces nontrivial effects on the degree of orientation as well. Up to the Freedericksz transition, the degree of orientation decreases, whereas ordering is recovered when the applied voltage drop increases. We also stress the role played by the dielectric anisotropy. In particular, the limit in which the dielectric anisotropy approaches the dielectric permittivities deserves attention, since the order-tensor theory regularizes some of the critical phenomena exhibited by classical Frank solutions.