MOLECULAR THEORY FOR THE LESLIE VISCOSITIES OF NEMATICS

Simple analytic expressions for all six Leslie viscosities for nematics are obtained from the molecular theory for rigid prolate molecules. The theory relates the viscosities to the second and fourth moments, P-2 and P-4, Of the molecular distribution function, the aspect ratio a of the molecules, and an isotropic viscosity that accounts for the effects of orientation-independent momentum transport. The theory is obtained by using expressions derived from a molecular theory by Kuzuu and Doi, as well as an approximate formula for the 'tumbling parameter' lambda in terms of P-2 and P-4; this approximate formula agrees well with data for many small-molecule nematics. Using the Maier-Saupe potential to compute P-2 and P-4, we find that the temperature dependencies of all six Leslie viscosities are in surprisingly good agreement with measurements of these viscosities for MBBA.