Shear Alignment and Instability of Smectic Phases

We consider the shear flow of well-aligned one-component smectic phases, such as thermotropic smectics and lamellar diblock copolymers, below the critical region. We show that, as a result of thermal fluctuations of the layers, parallel $\left(c\right)$ alignment is generically unstable and perpendicular $\left(a\right)$ alignment is stable against long-wavelength undulations. We also find, surprisingly, that both $a$ and $c$ alignments are stable for a narrow window of values for the anisotropic viscosity.