Nonlinear statistical mechanics drives intrinsic electrostriction and volumetric torque in polymer networks

Statistical mechanics is an important tool for understanding polymer electroelasticity because the elasticity of polymers is primarily due to entropy. However, a common approach for the statistical mechanics of polymer chains, the Gaussian chain approximation, misses key physics. By considering the nonlinearities of the problem, we show a strong coupling between the deformation of a polymer chain and its dielectric response, that is, its net dipole. When chains with this coupling are cross linked in an elastomer network and an electric field is applied, the field breaks the symmetry of the elastomer's elastic properties and, combined with electrostatic torque and incompressibility, leads to intrinsic electrostriction. Conversely, deformation can break the symmetry of the dielectric response, leading to volumetric torque and asymmetric actuation. Both phenomena have important implications for designing high-efficiency soft actuators and soft electroactive materials, and the presence of mechanisms for volumetric torque, in particular, can be used to develop higher degree of freedom actuators and to achieve bioinspired locomotion.

Figure 1

Dielectric elastomer actuator with dimensions of length $\ell$ in the ${\widehat{\mathit{e}}}_1$ and ${\widehat{\mathit{e}}}_2$ directions and thickness $t$ in the ${\widehat{\mathit{e}}}_3$ direction, where $t\ll \ell$: (a) undeformed configuration and (b) a voltage difference is applied across the electrodes on the top and bottom surfaces and, as a result, the actuator contracts across its thickness and expands in the plane orthogonal.

Figure 2

Electrostriction of a DEA with a fixed bottom surface and an applied traction, ${\mathbf{t}}_{\mathbf{0}}$, to the top surface of the actuator that is equal and opposite to the Coulomb attraction (inset). Stretch across the thickness, ${\lambda }_E$, as a function of $\kappa =E^2\mathrm{\Delta }\chi /2kT$.

Figure 3

Shear-mode actuation of a DEA constrained to only undergo shear deformation (inset). The film is prestressed, with ${\tilde{t}}_0=0.1,0.5$, and 1.0, and then an electric field is applied. Misalignment of the polarization with the field causes an electrostatic shear stress which increases the deformation for DEs with FD chains (i.e., $E^2\mathrm{\Delta }\chi /2kT=\kappa >0$) and decreases the deformation for elastomers with FA chains (i.e., $\kappa <0$). The efficiency of the electrically induced deformation increases with ${\tilde{t}}_0$.

Figure 4

Shear-mode actuation of a DEA constrained to only undergo shear deformation. The electromechanical actuation (normalized by the initial deformation) is shown for applied tractions of ${\tilde{t}}_0=0.1,0.5$, and 1.0. The curves collapse onto each other after normalization. Thus, the deformation appears to be proportional to the initial deformation, $s_0$.