  Liquid crystal networks exploit the coupling between the responsivity of
liquid-crystalline mesogens, e.g., to electric fields, and the (visco)elastic
properties of a polymer network. Because of this, these materials have been put
forward for a wide array of applications, including responsive surfaces such as
artificial skins and membranes. For such applications, the desired functional
response must generally be realized under strict geometrical constraints, such
as provided by supported thin films. To model such settings, we present a
dynamical, spatially-heterogeneous Landau-type theory for electrically-actuated
liquid crystal network films. We find that the response of the liquid crystal
network permeates the film from top to bottom, and illustrate how this affects
the time scale associated with macroscopic deformation. Finally, by linking our
model parameters to experimental quantities, we suggest that the permeation
rate can be controlled by varying the aspect ratio of the mesogens and their
degree of orientational order when cross-linked into the polymer network, for
which we predict a single optimum. Our results contribute specifically to the
rational design of future applications involving transport or on-demand release
of molecular cargo in liquid crystal network films.
