UNDULATION INSTABILITY IN SMECTIC-A LIQUID SINGLE-CRYSTAL ELASTOMERS

We present a macroscopic model for the behavior of smectic A liquid si ngle 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 lambda(c), of the expected undulation pattern is given by an expression quite similar to that obtained for LMW smect ic A phases. This result provides a possible explanation for the stron g light scattering (high turbidity) observed by Nishikawa et al. very recently in thick samples of a smectic A LSCE above a certain threshol d stress applied parallel to the layer normal in the experiments. We f ind that, in contrast to the critical wavelength lambda(c),, the thres hold dilatation epsilon(c), is dominated by the elastic properties of the smectic LSCE. Thus - as observed in the experiments by Nishikawa e t al. -epsilon(c), is found to be several orders of magnitude higher t han in the LMW case.