How liquid crystal networks work in theory

Liquid crystal networks, similar to nematic elastomers, are composite materials consisting of rod-like, liquid-crystalline mesogens crosslinked into a polymeric matrix. Their responsivity derives from these mesogens being aligned along some preferred orientation in the matrix, but that spontaneously reorient in response to external stimuli, such as light, temperature, or electric fields. This reorientation causes a mechanical deformation of the material through the polymer matrix. Actuating these materials in a controlled manner opens the door to a wide array of applications, ranging from haptic or self-cleaning surfaces to the controlled release of molecular cargo encapsulated in the material. Although in the case of nematic elastomers there exists a well-tested theoretical framework that has helped guide the development of such applications, we shall see that these conventional models are unsuitable to describing liquid crystal networks, which arguably provide for an even richer application potential. This is because recent experiments have shown that liquid crystal networks, which contain a significantly higher density of mesogenic component than their elastomeric counterpart, can in addition to the aforementioned responsivity also sustain steady-state volume changes upon actuation. To gain a better understanding of the underlying mechanics, we propose a phenomenological model that couples the excluded volume of the mesogens to the deformation of the liquid crystal network. We will discuss the qualitative agreement between the model, simulations and experiments, and identify the aspect ratio of the mesogens, their initial orientational order when cross-linked into the polymer network, and the cross-linking fraction of the network as the most important experimental control parameters.