Influence of viscosity on the thermal vibrations of a lamellar liquid crystal

Abstract

The thermal vibrations of a lamellar liquid crystal are treated with due account taken of the bending elasticity of the bilayers, the bilayer interactions and of the viscosity of the intervening water layers. Employing the fluctuation–dissipation theorem the spectral density function of the thermal vibrations was derived. Our calculations show that the spectral function, J(k, q, ω), corresponding to each mode takes the usual Lorentzian form when the viscous friction is taken into account, i.e. it is practically constant within 0 ⩽ω⩽ω₀, where ω₀ is the inverse of the correlation time, and it drops rapidly to zero above ω₀. For a lone bilayer we find that ω₀=k_cq³/4η while, for a complete lamellar liquid crystal, ω₀ has a more complicated form.