Viscoelasticity of a homeotropic nematic slab

The viscoelastic behavior of a homeotropic nematic slab is studied when it is subjected to a (dilation-compression) sinusoidal deformation of small amplitude (linear regime). I show that the nematic phase behaves as an isotropic liquid of viscosity η(c) (ν(3)) at low (high) frequency, where η(c) is the third Miesowicz viscosity and ν(3) a smaller viscosity first introduced by Martin, Parodi, and Pershan. The crossover frequency f(☆) between these two asymptotic regimes scales as h(2)/D, where h is the sample thickness and D=K(3)/γ(1) is the orientational diffusivity (with K(3) the bend constant and γ(1) the rotational viscosity). Between these two limits the sample behaves as a viscoelastic fluid whose elastic and loss moduli G' and G" are calculated. These predictions are tested experimentally with a piezoelectric rheometer.