Controlling permeation in electrically deforming liquid crystal network films: A dynamical Landau theory

Abstract

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Transient response and domain formation in electrically deforming liquid crystal networks

“…To address this, we propose a dynamical Landau-de Gennes theory, based primarily on the state of the mesogens, rather than on the configuration of the polymer network; the motivation for this choice is that the liquid crystal network is extremely dense in mesogenic component, so as to effectively be liquid crystalline itself. In a series of recent papers, we already obtained promising qualitative agreement between the theory, molecular dynamics computer simulations, and experiments, and have also characterized how in a thin-film geometry, as is common in experiments, the response to a constant electric field permeates the liquid crystal network from top to bottom [31,48].…”

“…This boundary condition is slightly different from the one we used in Ref. [31]; we shall return to this point in Sec. IX.…”

“…Although, due to the generic nature of our model, it encompasses various underlying mechanisms, ranging from an electrically-driven glass transition to the collective motion of an array of coupled oscillators [31], for the purpose of this paper we shall illustrate it based on excluded-volume arguments. That is, upon application of the electric field, the pendant, dipolar mesogens reorient in response to it, whereas the crosslinked mesogens remain relatively immobile.…”

“…However, a relaxational term that increases monotonically with t suppresses any volume expansion if we wait long enough, rendering a dynamic steady state impossible in the long term. Thus, we require a more sophisticated relaxation function, τ (z 0 , t) [s], which locally keeps track of the deformation history of the liquid crystal network to determine how strongly a given volume element should relax [31]. This is a highly non-trivial component of the theory, and although it is not a true memory kernel, it fulfills a similar function.…”

“…In terms of the theory, the initial thickness of the liquid crystal network film enters only through the scaled square-gradient coefficients, κf and κη , which depend inversely on it. We shall focus on the former, since the model dynamics is primarily dictated by the population order parameter, f 2 [31]. In particular, the unscaled coefficient, κ f [ J/m], represents an energy scale, smeared over a microscopic length scale of the system.…”