Geometrical content of Leslie coefficients

In this work, we will study how the effective geometry acquired by nematic molecules under thermal vibration contribute to the determination of the Leslie coefficients. To do this, we will divide this work in two sections. In the first section, we present the geometrical fundamentals of the so-called Hess-Baalss (HB) approach [D. Baalss and S. Hess, Phys. Rev. Lett. 57, 86 (1986)] where we show that its basic assumptions can be understood as a geometrical interpretation of de Gennes' passage from the microscopic to the macroscopic order parameter. In the second section, we use an extended version of the HB approach [M. Simões, K. Yamaguti, and A. J. Palangana, Phys. Rev. E 80, 061701 (2009)] to obtain the geometrical contribution to each Leslie coefficient. Our results will be compared with experimental data, and we will show that the Miesowicz's coefficients are connected as long as the ratio α(3)/α(4) between these Leslie coefficients can be considered small.