Positive definite distortion term of the extended Landau-de Gennes model

Abstract

The issue of the extended Landau-de Gennes model of nematic liquid crystals is revisited. To satisfy the condition that the elastic free energy density be positive definite a new scheme of expansion is put forward. The scheme displays a number of interesting features among which the most nontrivial one is the implication of the lower bound of 6/5 for the ratio $L_2/L_1.$