Dynamical Landau-de Gennes theory for electrically-responsive liquid crystal networks

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.