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.
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