Cholesteric elastomers in external mechanical and electric fields

In our studies, we focus on the reaction of cholesteric side-chain liquid single-crystal elastomers (SCLSCEs) to static external mechanical and electric fields. By means of linearized continuum theory, different geometries are investigated: The mechanical forces are oriented in a direction either parallel or perpendicular to the axis of the cholesteric helix such that they lead to a compression or dilation of the elastomer. Whereas only a homogeneous deformation of the system is found for the parallel case, perpendicularly applied mechanical forces cause either twisting or untwisting of the cholesteric helix. This predominantly depends on the direction in which the director of the cholesteric phase is anchored at the boundaries of the elastomer, and on the sign of a material parameter that describes how deformations of the elastomer couple to the relative rotations between the elastomer and the director. It is also this material parameter that leads to an anisotropy of the mechanical reaction of the system to compression and dilation, due to the liquid crystalline order. The effect of an external electric field is studied when applied parallel to the helix axis of a perfect electric insulator. Here an instability arises at a threshold value of the field amplitude, where the latter results from a competition between the effects of the external electric field on the one hand and the influences of the boundaries of the system, the cholesteric order, and the coupling between the director and the polymer network on the other hand. The instability is either homogeneous in space in the directions perpendicular to the external electric field and includes homogeneous shearing, or, for certain values of the material parameters, there arise undulations of the elastomer and the director orientation perpendicular to the direction of the external electric field at onset. This describes a qualitatively new phenomenon not observed in cholesteric systems yet, as these undulations are due to the coupling of the director orientation to the deformations of the elastomer. Furthermore, we find that theoretically it should be possible to synthesize cholesteric and nematic SCLSCEs in which the director can be reoriented by an external electric field without macroscopically distorting the sample; the latter applies for one specific set of values for the material parameters involved. We also propose ways of experimental access to the material parameters in the general situation.