Mechanical strains and electric fields applied to topologically imprinted elastomers

We analyze and predict the behavior of a chirally imprinted elastomer under a mechanical strain and an electric field, applied along the helical axis. As the strain and/or field increases, the system is deformed from a conical or transverse imprinted state towards an ultimately nematic one. At a critical strain and/or field there is a first-order transition to a low imprinting efficiency state. This transition is accompanied by a discontinuous global rotation of the director toward the axis of the imprinted helix, measured by the cone angle, $\theta$. We show that the threshold electric field required for switching this transition can be conveniently low, provided an appropriate prestrain is imposed. We suggest that these properties may give rise to a “chiral pump.”

Figure 1

The director in spherical polars.

Figure 2

The physical value of the helix cone angle ${\theta }_m$ and also the effective chiral power $\alpha \left({\theta }_m\right)$ as a function of the stretch factor $T$ when $\kappa =1.8$, $r=2$, and ${\alpha }_0=0.49$.

Figure 3

The imprinting efficiency $e_0$ as a function of the stretch factor $T$ when $\kappa =1.8$, $r=2$, and ${\alpha }_0=0.49$.

Figure 4

The physical value of the helix cone angle ${\theta }_m$ and also the effective chiral power $\alpha \left({\theta }_m\right)$ as a function of the stretch factor $T$ when $\kappa =2.5$, $r=2$, and ${\alpha }_0=0.45$.

Figure 5

The physical value of the helix cone angle ${\theta }_m$ and also the effective chiral power $\alpha \left({\theta }_m\right)$ as a function of the dimensionless field $\delta$ when $\kappa =1.3$, $r=2$, and ${\alpha }_0=0.5$.

Figure 6

The physical value of the helix cone angle ${\theta }_m$ and also the effective chiral power $\alpha \left({\theta }_m\right)$ as a function of the dimensionless field $\delta$ when $\kappa =2.1$, $r=2$, and ${\alpha }_0=0.4$.

Figure 7

The physical value of the helix cone angle ${\theta }_m$ and also the effective chiral power $\alpha \left({\theta }_m\right)$ as a function of the dimensionless field $\delta$ when $\kappa =2.1$, $r=1.1$, and ${\alpha }_0=0.49$.

Figure 8

The physical value of the helix cone angle ${\theta }_m$ and also the effective chiral power $\alpha \left({\theta }_m\right)$ as a function of the dimensionless field $\delta$ when the sample is prestrained to $T=1.304$. The parameter values are $\kappa =2.5$, $r=2$, and ${\alpha }_0=0.4$.