Optical penetration depth and periodic motion of a photomechanical strip

Liquid crystal elastomers (LCEs) containing light-sensitive molecules exhibit large reversible deformation when subjected to illumination. Here, we investigate the role of optical penetration depth on this photomechanical response. We present a model of the photomechanical behavior of photoactive LCE strips under illumination that goes beyond the common assumption of shallow penetration. This model reveals how the optical penetration depth and the consequent photomechanically induced deformation can depend on the concentration of photoactive molecules, their absorption cross-sections, and the intensity of illumination. Through a series of examples, we show that the penetration depth can quantitatively and qualitatively affect the photomechanical response of a strip. Shallow illumination leads to monotone curvature change while deep penetration can lead to non-monotone response with illumination duration. Further, the flapping behavior (a cyclic wave-like motion) of doubly clamped and buckled strips that has been proposed for locomotion can reverse direction with sufficiently large penetration depth. This opens the possibility of creating wireless light-driven photomechanical actuators and swimmers whose direction of motion can be controlled by light intensity and frequency.