Elasticity of rubber with smectic microstructure

Using a physically motivated continuum model for the free energy of an elastomer with a smectic or lamellar microstructure, we examine the effects of coupling between the smectic and the rubber-elastic degrees of freedom on measurements of the layer structure and elastic moduli. In agreement with experiment, we find that the elastic response to stretching along the layer normal is greatly increased by the smectic layering, while the modulus parallel to the layers is unchanged. We show that Landau-Peierls instability of fluctuations in the layer structure of ordinary smectic liquid crystals is removed by the elastic matrix. Consequently one sees Bragg peaks in the diffraction pattern of a solid with one-dimensional order and we calculate the Debye-Waller factors for these.