Effect of the Coupling Between Director and Mass Density Fluctuations on the Paranematic–Nematic Transition Temperature: A Mean-field Treatment

Abstract

It has experimentally verified that the variation of the paranematic–nematic transition temperature follows the relation $\Delta T_{PN}^{}=m E$ for low electric fields. Values of the coefficient m are found to be positive and negative. Previous work, on the basis of a simple physical model supplemented by dimensional argument, attributed this behavior to the quenching of long-wavelength director fluctuations due to the field. In this paper, we show that the Landau–de Gennes theory predicts $\Delta T_{PN}^{}\propto E^2$ even when the quenching of director fluctuations is considered. Based on a recent generalization of the Landau–de Gennes theory that incorporates mass density fluctuations, we give a mean-field treatment of the coupling between director and mass density fluctuations and calculate the contribution of this mechanism to the Helmholtz free energy. Interestingly, the expression we obtain for $\Delta T_{PN}^{}$ is in good quantitative agreement with what is experimentally observed. In particular, it explains why m takes values of both signs.