Order parameter and temperature dependence of the hydrodynamic viscosities of nematic liquid crystals

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Abstract
A theoretical analysis of the order parameter and temperature dependence of the complete set of five independent viscosities of incompressible nematic liquid crystals is presented. It is an extension of a previous theory by the authors on the thermal dependence of the twist viscosity in nematics (Port. Phys. 9 (1975) 129 and Mol. Cryst. Liq. Cryst. 66 (1981) 133) and develops from the concept of free volume and the theory of rate pro-cesses. Theoretical expressions are derived for each of the five viscosities in terms of the order parameter S(T), the current temperature T, eight parameters which depend on molecular properties, and some fixed temperature T0 below which viscous molecular motion is not possible due to the lack of enough free volume. These expressions are contrasted with the experimental data available for M.B.B.A. and all of them are found to be in good agreement with the data, over the full nematic range of this material