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We model the behavior of a single colloid embedded in a cross-linked polymer gel, immersed in a viscous background fluid. External fields actuate the particle into a periodic motion, which deforms the embedding matrix and creates a local microcavity, containing the particle and any free volume created by its motion. This cavity exists only as long as the particle is actuated and, when present, reduces the local density of the material, leading to swelling. We show that the model exhibits rich resonance features, but is overall characterized by clear scaling laws at low and high driving frequencies, and a pronounced resonance at intermediate frequencies. Our model predictions suggest that both the magnitude and position of the resonance can be varied by varying the material's elastic modulus or cross-linking density, whereas the local viscosity primarily has a dampening effect. Our work implies appreciable free-volume generation is possible by dispersing a collection of colloids in the medium, even at the level of a simple superposition approximation.

Recently, three distinct, well-separated transient regimes were discovered in the dynamics of the volume expansion of shape-shifting liquid crystal network films in response to the switching on of an alternating electric field [Van der Kooij et al., Nat. Commun., 2019, 10, 1]. Employing a spatially resolved, time-dependent Landau theory that couples local volume generation to the degree of orientational order of mesogens that are part of a viscoelastic network, we are able to offer a physical explanation for the existence of three time scales. We find that the initial response is dominated by overcoming the impact of thermal noise, after which the top of the film expands, followed by a permeation of this response into the bulk region. An important signature of our predictions is a significant dependence of the three time scales on the film thickness, where we observe a clear thin-film-to-bulk transition. The point of transition coincides with the emergence of spatial inhomogeneities in the bulk of the film in the form of domains separated by regions of suppressed expansion. This ultimately gives rise to variations in the steady-state overall expansion of the film and may lead to uncontrolled patterning. According to our model, domain formation can be suppressed by (1) decreasing the thickness of the as-prepared film, (2) increasing the linear dimensions of the mesogens, or (3) their degree of orientational order when cross-linked into the network. Our findings provide a handle to achieve finer control over the actuation of smart liquid crystal network coatings.

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 timescale 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 crosslinked 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.

Liquid crystal networks combine the orientational order of liquid crystals with the elastic properties of polymer networks, leading to a vast application potential in the field of responsive coatings, e.g., for haptic feedback, self-cleaning surfaces, and static and dynamic pattern formation. Recent experimental work has further paved the way toward such applications by realizing the fast and reversible surface modulation of a liquid crystal network coating upon in-plane actuation with an AC electric field [Liu, Tito, and Broer, Nat. Commun. 8, 1526 (2017)10.1038/s41467-017-01448-w]. Here, we construct a Landau-type theory for electrically-responsive liquid crystal networks and perform molecular dynamics simulations to explain the findings of these experiments and inform on rational design strategies. Qualitatively, the theory agrees with our simulations and reproduces the salient experimental features. We also provide a set of testable predictions: the aspect ratio of the nematogens, their initial orientational order when cross-linked into the polymer network, and the cross-linking fraction of the network all increase the plasticization time required for the film to macroscopically deform. We demonstrate that the dynamic response to oscillating electric fields is characterized by two resonances, which can likewise be influenced by varying these parameters, providing an experimental handle to fine-tune device design.