Geometric approach to the Miesowicz coefficients at the region of the crystalline-nematic transition and a universal relation for their ratio.

In this work the ratios between the Miesowicz coefficients of rigid calamitic nematic liquid crystals will be studied. It will be shown that the microscopic theory that describes these coefficients, the kinetic theory [M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Oxford Press, New York, 1986)], suggests that some ratios between the Miesowicz coefficients would have a universal character, that does not depend on the nematic material being examined. A set of experimental data has been collected from the liquid crystal literature and, once these data are rescaled in a common temperature scale, they point to the existence of such a universality. Nevertheless, only in the neighborhoods of the nematic-isotropic transition, do the theoretical calculations of the kinetic theory and the experimental data predict the same profile for this universality; when the region of the crystalline-nematic transition is approached theory and experiment present severe discrepancies. The reason for this disagreement is studied and it is proposed that it results from the fact that the kinetic theory does not take into account the packing properties of the nematic medium. A different approach to the calculation of these ratios is proposed and it is shown that it describes the experimental data for all temperatures.