Undulation instability in smecticA liquid single crystal elastomers

We present a macroscopic model for the behavior of smectic A liquid single crystal elastomers (LSCEs) under an external dilatory stress thus investigating the elastomeric analogue of the undulation instability in low molecular weight (LMW) smectic A liquid crystals. We show that the critical wavelength λc of the expected undulation pattern is given by an expression quite similar to that obtained for LMW smectic A phases. This result provides a possible explanation for the strong light scattering (high turbidity) observed by Nishikawa et al. very recently in thick samples of a smectic A LSCE above a certain threshold stress applied parallel to the layer normal in the experiments. We find that, in contrast to the critical wavelength λc, the threshold dilatation εc is dominated by the elastic properties of the smectic LSCE. Thus – as observed in the experiments by Nishikawa et al. −εc is found to be several orders of magnitude higher than in the LMW case.