Director reorientation and order reconstruction: competing mechanisms in a nematic cell

We propose a model to explore the competition between
two mechanisms possibly at work in
a nematic liquid
crystal confined within a flat cell with strong uniaxial planar
conditions on the bounding plates and subject to an external field.
To obtain an electric field perpendicular to the plates,
a voltage is imposed across the cell; no
further assumption is made on
the electric potential within the cell, which is therefore calculated together
with the nematic texture.
The Landau-de Gennes
theory of liquid
crystals is used to derive the equilibrium nematic order
tensor Q.
When the voltage applied is low enough,
the equilibrium texture is nearly homogeneous.
Above a critical voltage,
there exist two different possibilities for adjusting the order
tensor to the applied field within the cell:
plain director reorientation,
i.e., the classical Freedericksz transition,
and order reconstruction.
The former mechanism entails
the rotation of the eigenvectors of Q
and can be described essentially
by the orientation of the ordinary uniaxial
nematic director, whilst the latter mechanism implies a
significant variation of the eigenvalues of Q within the cell,
virtually
without any rotation of its eigenvectors,
but with the intervention of
a wealth of biaxial states.
Either mechanism can actually
occur, which yields different
nematic textures,
depending on material parameters, temperature, cell
thickness and the applied potential. The equilibrium phase diagram
illustrating the prevailing mechanism
is constructed for a significant set of parameters.