Bending and Stretching in a Narrow Ribbon of Nematic Polymer Networks

TL;DR

This paper develops a theoretical model for the spontaneous bending of nematic polymer network ribbons due to temperature changes, revealing a complementarity relation between bending and stretching energies and identifying a thickness-independent deformation regime.

Contribution

The study introduces a comprehensive energy-based theory that captures the interplay of bending and stretching in nematic polymer ribbons, including a novel bleaching regime.

Findings

Energy components obey a complementarity relation during equilibrium.

Deformation becomes thickness-independent at high activation parameters.

The model explains out-of-plane bending induced by temperature changes.

Abstract

We study the spontaneous out-of-plane bending of a planar untwisted ribbon composed of nematic polymer networks activated by a change in temperature. Our theory accounts for both stretching and bending energies, which compete to establish equilibrium. We show that when equilibrium is attained these energy components obey a \emph{complementarity} relation: one is maximum where the other is minimum. Moreover, we identify a \emph{bleaching} regime: for sufficiently large values of an activation parameter (which measures the mismatch between the degrees of order in polymer organization in the reference and current configurations), the ribbon's deformation is essentially independent of its thickness.