Nematoelastic crawlers

A propagating “beam” triggering a local phase transition in a nematic elastomer sets it into a crawling motion, which may morph due to buckling. We consider the motion of the various configurations of slender rods and thin stripes with both uniform and splayed nematic order in cross-section and detect the dependence of the gait and speed on flexural rigidity and substrate friction.

Figure 1

Successive configurations of an inflexible rod or a hollow cylinder (a) and of a walker with five sequentially actuated conical legs (b) on a substrate with a very high friction under a beam propagating from the left. Vertical lines mark the original positions of the ends.

Figure 2

(a) A twisted yarn in the isotropic state (above) and after nematic transition (below). (b) Snapshots of the contact line of a twisted yarn on a substrate with a very high friction under a beam propagating from the left, starting from the nematic state (side view). Vertical lines mark the original positions of the ends. (c) Cross-sectional director orientation in a splayed nematic.

Figure 3

(a, b) Successive shapes and positions of a flexible stripe with uniform $\left(\lambda =1.4,h=0.03\right)$ and splayed $\left(\lambda =1.01,h=0.05\right)$ director orientation; $\eta =0.1$. Vertical lines mark the original position of the ends. Shaded regions mark instantaneous beam positions. (c, d) Shapes of films of different thickness at a central beam position.

Figure 4

Bifurcation lines of translational and bending transitions, marked, respectively, by triangles and squares for uniform (above) and splayed (below) director orientation. Shading shows the values of displacement per beam passage $\mathrm{\Sigma }$.

Figure 5

Dependence of the displacement per beam passage $\mathrm{\Sigma }$ on the film thickness at selected values of $\eta$ for uniform (above) and splayed (below) director orientation.

Figure 6

Above: dependence of the crawling speed $\mathrm{\Sigma }/T$ on the characteristic beam passage time $T$ for uniform and splayed director orientation at $h=0.05,\eta =0.1$. Below: dependence of $\mathrm{\Sigma }/T$ on the stripe thickness at $\eta =0.1$ and selected values of $T$ for uniform director orientation.

Figure 7

(a) Successive shapes and positions of a translating strip with splayed director orientation under a beam inclined by the angle $\pi /4$ to the director. (b) Dependence of velocities along (squares) and across (triangles) the director on the inclination angle $\phi$ of the “illuminated” strip relative to the director. Parameters: $\lambda =1.01,h=0.035,\eta =0.1$.

Figure 8

Above: Snapshots of a stripe with uniform director orientation $\left(h=0.05\right)$ moving on the border of substrates with different surface mobilities $({\eta }_1=0.1$ on the lower and ${\eta }_2=0.01$ on the upper part of the picture) during the first, third, and seventh passage of the beam. Frames show the original position. Below: Average energy along the edges in contact with high friction (squares) and low friction (triangles) substrates vs. time (measured in the number of beam passages).