The long-wavelength hydrodynamics of the Renn-Lubensky twist grain boundary phase with grain boundary angle 2πα, α irrational, is studied. We find three propagating sound modes, with two of the three sound speeds vanishing for propagation orthogonal to the grains, and one vanishing for propagation parallel to the grains as well. In addition, we find that the viscosities ${\mathrm{\eta }}_1$, ${\mathrm{\eta }}_2$, ${\mathrm{\eta }}_4$, and ${\mathrm{\eta }}_5$ diverge like 1/‖ω‖ as frequency ω→0, with the divergent parts Δ${\mathrm{\eta }}_{\mathit{i}}$ satisfying Δ${\mathrm{\eta }}_1$Δ${\mathrm{\eta }}_4$=(Δ${\mathrm{\eta }}_5$${)}^2$, exactly. Our results should also apply to the predicted decoupled lamellar phase.

• Received 19 November 1992

DOI:https://doi.org/10.1103/PhysRevLett.70.2090