Model for Photoresponsive Nematic Elastomers

TL;DR

This paper analyzes the equilibrium shapes of photoresponsive nematic elastomer ribbons, revealing a non-monotonic deformation response to light intensity, a first-order shape transition, and a critical length below which no deflection occurs.

Contribution

It provides a continuum mechanics model predicting complex deformation behaviors, including hysteresis and critical length effects, based on statistical mechanics principles.

Findings

Deformation first increases then decreases with light intensity.

Identifies a critical light intensity causing a shape transition.

Determines a critical length below which no deflection occurs.

Abstract

We study the equilibria of a photoresponsive nematic elastomer ribbon within a continuum theory that builds upon the statistical mechanics model put forward by Corbett and Warner [Phys. Rev. E 78, 061701 (2008)]. We prove that the spontaneous deformation induced by illumination is not monotonically dependent on the intensity $I$. The ribbon's deflection first increases with increasing $I$, as expected, but then decreases and abruptly ceases altogether at a critical value $I_\mathrm{e}$ of $I$. $I_\mathrm{e}$, which is enclosed within a hysteresis loop, marks a first-order shape transition. Finally, we find that there is a critical value of the ribbon's length, depending only on the degree of cross-linking in the material, below which no deflection can be induced in the ribbon, no matter how intense is the light shone on it.