Work and Activation in a Nematic Polymer Network Ribbon

Abstract

We study spontaneous deformations of a ribbon made of nematic polymer networks and activated under the action of a mechanical load. We show that when such ribbons are activated appropriately, the deformations produced can pull back and perform work against the externally applied load. We perform two numerical experiments to demonstrate this effect: (1) the \emph{pulling} experiment, where the ribbon is pulled longitudinally by a point force, and (2) the \emph{bending} experiment, where the ribbon is bent out of plane by a terminally applied point force. We quantify the capacity of the ribbon to work against external loads, and compute its dependence on both the ribbon thickness and the imprinted nematic texture (that is, the distribution of the nematic directors across the ribbon's length). Finally, we compute the efficiency of the activation process. Building on the outcomes of our numerical explorations, we formulate two educated conjectures on how the activation efficiency can in general be improved by acting on both the applied load and the imprinted nematic texture.

Figures (6)

• Figure 1: Schematic of the reference configuration of a narrow, rectangular, nematic polymer network ribbon with width $2w$ and length $L$. The coordinate $s$ runs along the centerline, while the coordinate $t$ spans the ribbon's width along the material lines (marked in red) where the nematic director $\bm{q}_0$ has been imprinted prior to activation.
• Figure 2: Three distributions, governed by equation \ref{['eq:alpha_0']}, of nematic directors imprinted on a narrow rectangular NPN ribbon. The width of the ribbon has been exaggerated for clarity of presentation.
• Figure 3: The figure pertains to various results from the pulling experiment with $P=6\times 10^{-3}kL^2$. \ref{['fig:pulling_experiment_a']} Plots of the normalized displacement $\Delta r_3/L$ of the tip of the NPN ribbon as a function of the applied force $P/kL^2$ for various values of the thickness $h/L$. \ref{['fig:pulling_experiment_b']} Plots of $\Delta r_3/L$ as a function of the activation parameter $S$ (with $S_0=4.788$), obtained by activating the configurations which have been pulled. Panels \ref{['fig:pulling_experiment_c']}, \ref{['fig:pulling_experiment_d']} and \ref{['fig:pulling_experiment_e']} show deformed configurations of the ribbon of thickness $h/L=0.06$ for the cases $n=0$, $n=1$ and $n=2$, respectively.
• Figure 4: \ref{['fig:bending_experiment_a']} Plots of the normalized displacement $\Delta r_2/L$ of the tip against the applied transverse load $P=6\times 10^{-4} kL^2$ for various values of the thickness $h/L$. \ref{['fig:bending_experiment_b']} The transverse displacement $\Delta r_2/L$ plotted against the activation parameter $S$ (with $S_0 = 4.788$) obtained upon activating the configurations under mechanical bending. Panels \ref{['fig:bending_experiment_c']}, \ref{['fig:bending_experiment_d']} and \ref{['fig:bending_experiment_e']} show the deformed configurations of the ribbon of thickness $h/L=0.06$ in the bending experiment for the cases $n=0$, $n=1$ and $n=2$, respectively.
• Figure 5: Panels \ref{['fig:efficiency_a']} and \ref{['fig:efficiency_b']} show how the activation efficiency $\mathsf{e}$ of an NPN ribbon defined in \ref{['eq:tm_efficiency']} varies with the normalised thickness ($h/L$) for the pulling and bending experiment, respectively. Panels \ref{['fig:heat_c']} and \ref{['fig:heat_d']} show the amount of heat $\Delta Q_\mathrm{h}$ (scaled to $2kL^2 w$) as a function of the normalised thickness of the ribbon ($h/L$) in pulling and bending, respectively.