Critical elastic constants and viscosities above a nematic-smectic a transition of second order

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Abstract
Abstraet. — The fluctuations of the local order parameter above a second order nematic-smetic A phase transition give rise to singularities in the elastic constants and the viscosities of a nematic. In the hydrodynamic regime qξ << 1, the critical behaviour of the elastic constants has already been calculated by de Gennes. Based on the same assumptions, we derive a singularity of the critical viscosities proportional to (T - Tc) -0.33. As theoretical framework we use linear response theory and the fluctuation-dissipation theorem. We treat also the general case of arbitrary wave numbers. In the critical regime qξ >> 1, we find a critical spectrum of the director modes ωS ∼ q3/2, in agreement with a recent suggestion of F. Brochard based on a dynamical scaling argument