Fluctuations and Long-Range Order in Smectic Elastomers

In a crosslinked polymer network, which has a lamellar or liquid crystalline smectic-A order, layer deformations are penalized by an underlying rubber elasticity. By integrating out phonon modes of the network, we obtain an effective smectic-A elastic free energy in which there is an energy cost for rotating smectic layers relative to the elastic network. As a result, there is long-range translational smectic order with true Bragg peaks in the X-ray scattering intensity with Debye-Waller factors depending on the crosslink density of the network. There is also a very anisotropic diffuse scattering.