Instabilities in nematic elastomers in external electric and magnetic fields

In this paper we study the macroscopic behavior of nematic side-chain liquid single crystal elastomers exposed to an external electric or magnetic field. For this purpose we use the framework of a continuum model. The geometries investigated comprise the bend and the twist geometry known from the classical Frederiks transition in low molecular weight liquid crystals. For the bend geometry we find a laterally homogeneous and a two-dimensional undulatory instability, which may compete at onset. In the case of the twist geometry three instabilities can occur at onset, two of which are two dimensional and clearly show undulations. As a major result we propose how the values of the twist coefficient K-2 and the values of the material parameters D-1 and D-2 connected to relative rotations between the director field and the polymer network can be determined from experimental observations. In addition, we explain why a twist experiment is probably the most suitable set-up in order to measure the material parameter D-1.