Mechanical properties of mono-domain side chain nematic elastomers

We investigate the behavior of the shear rigidity modulus G = G' + iG" of three mono-domain side chain liquid-crystalline elastomers composed of side chain polysiloxanes cross-linked by either flexible or rigid cross-linkers. The measurements were taken in a frequency domain ranging from approximately 0.02 Hz to approximately 10(4) Hz applying the shear in a plane perpendicular to or containing the director. The measurements as a function of temperature show an anisotropy of G' which appears around T(NI), when decreasing the temperature, and which is due to the expected lowering of G'(//) coming from the coupling between the shear and the director. The measurements as a function of frequency show that G has two components for both geometries, in both the isotropic phase and in the nematic phase around the phase transition. One reflects the network behavior in its hydrodynamic regime ( G' is constant and G'' is approximately f, where f is the frequency), the other which appears at higher frequencies is characterized by a scaling law behavior (G' is approximately G" is approximately f(0.5)) of the Rouse type. We discuss the results in the framework of available theories and show that the three elastomers present a non-soft behavior, even for the elastomer for which the contrary was claimed, and that there is no separation of time scales between the director and the network. We also present data on a poly-domain sample and a non-mesomorphic one which complement these results.