A geometrical relation between the Miesowicz's coefficients

Abstract

In this work, it will be shown that the Miesowicz's viscosity coefficients of the nematic liquid crystals are not independent, but connected by the effective geometry that the nematic molecules/micelles acquire under random oscillatory vibration. This result follows from a straightforward application of the Onsager reciprocal relation to a recent proposed generalisation of the conformal transformation approach of the nematic rheology [1], where it had been assumed that the nematic dissipative process is not driven by a unique initial isotropic viscosity term, but by two; a rotational term has been added. As a consequence of the application of the Onsager relation, these two viscosity terms become related by the effective eccentricity of the nematic grain, leading to a connection between the Miesowicz's coefficients. Known experimental data of nematic compounds are used to test this prediction, resulting in its confirmation, which gives to the conformal transformation approach a predictive vigour that is not found in any other nematic viscosity theory.

Keywords:

• liquid crystals
• rheology
• nematic viscosity
• nematic liquid crystals

Acknowledgements

We are grateful to the Brazilian Agencies CAPES, CNPq, and Fundação Araucária (PR) for the financial support given to this work.