Breakdown of conventional hydrodynamics for smectic-A, hexatic-B, and cholesteric liquid crystals

We present a detailed analysis of anharmonic effects on the viscous and elastic properties of various systems with one-dimensional order. We show that the nonlinear coupling of the velocity field to thermally excited undulation modes causes four of the five viscosities in these uniaxial systems (including one, ${\eta }_2$, governing shear flow in the layers) to diverge as $\frac{1}{\omega }$ when measured at small frequencies $\omega$. As a result, sound attenuations scale as $\omega$, rather than ${\omega }^2$ as in most materials. A simple algebraic relation between the divergent parts of three of the viscosities is derived. We argue that the divergence in ${\eta }_2$ leads to strongly non-Newtonian flow in the liquid layers of these materials. The calculations here extend the previous work of the authors to include an analysis of irreducible graphs to all orders in perturbation theory in the temperature. Some new results on the nonlinear elastic theory of these systems are also obtained, extending earlier work by Grinstein and Pelcovits. The existing experimental evidence for our predictions is discussed, and additional experiments are suggested.