Generalized mean-field potential description for ferroelectric ordering in nematic liquid crystals.

Ferroelectric ordering in a nematic liquid crystal system is described using a generalized mean-field potential including effective potentials for both axial and polar interactions. From a self-consistent numerical analysis, a complete phase diagram is obtained as a function of the axial and polar interaction potential strengths. The obtained phase diagram exhibits not only the usual isotropic-nematic phase transition but also nematic-ferroelectric nematic and direct isotropic-ferroelectric nematic phase transitions with a tricritical point among the phases. The phase transition behaviors and the angular orientational distribution function of the molecules were investigated by studying the dependence of the polar and the axial order parameters on the reduced temperature. Moreover, the other polar order parameters responsible for second-harmonic generation (SHG) were also investigated in the generalized mean-field potential description. As a concrete example, we performed a quantitative analysis of the SHG signal reported previously in a lyotropic poly L-glutamate system, detailing the relationship between the angular distribution function and the order parameters based on our potential model. This clarifies the nature of the ferroelectric phase responsible for SHG in nematics.