The long wavelength hydrodynamics of films with unidirectional translational order adsorbed on fluid surfaces (as in a Langmuir monolayer) is formulated. We find the hydrodynamic frequencies ω(q)∝(± √3 -i)${\mathit{q}}^{14/9}$ ${\cos }^{4/3}$θ ${\sin }^{14/9}$θ where q≡‖q‖ and π/2-θ is the angle between the direction of propagation and the direction of translational order. We also obtain the dynamic structure factor. Our results apply to nematic polymers adsorbed onto a fluid surface and to striped phases of Langmuir monolayers, and provide an experimentally accessible probe of the anomalous elasticity predicted for two-dimensional smectics by Golubović and Wang.

• Received 1 February 1993

DOI:https://doi.org/10.1103/PhysRevLett.70.2443