Landau–de Gennes theory of biaxial nematics reexamined

Abstract

Recent experiments report that the long-looked-for thermotropic biaxial nematic phase has been finally detected in some thermotropic liquid crystalline systems. Inspired by these experimental observations, we concentrate on some elementary theoretical issues concerned with the classical sixth-order Landau-de Gennes free energy expansion in terms of the symmetric and traceless tensor order parameter Q alpha beta. In particular, we fully explore the stability of the biaxial nematic phase giving analytical solutions for all distinct classes of the phase diagrams that theory allows. This includes diagrams with triple, critical, and tricritical points and with multiple (reentrant) biaxial and uniaxial phase transitions. A brief comparison with predictions of existing molecular theories is also given.

Generalized Liquid Crystals: Giant Fluctuations and the Vestigial Chiral Order ofI,O, andTMatter

“…1. The associated physics of the nematic phases can then be studied in terms of Landau-de Gennes theory, where an order parameter tensor is needed for each subgroup of O(3) [28][29][30][31][32][34][35][36][37]45]. Instead of the (3)].…”

“…After all, constructing the theory of three-dimensional orientational order should be a welldefined exercise in the Landau paradigm of spontaneous symmetry breaking. However, the Landau-de Gennes order parameter theory of more symmetric nematics generically involves a complicated high-rank tensor order parameter theory [28][29][30][31][32][33][34][35][36][37], making the physical ramifications basically unexplored, in spite of the identification of the general structure of point-group invariants [17,38]. In this sense, the problem represents one of the remaining frontiers of the Landau paradigm.…”

Energetic and Entropic Contributions to the Landau–de Gennes Potential for Gay–Berne Models of Liquid Crystals

“…Different from the standard expression, the coefficient of the fourth order term is slightly density-and temperature-dependent, due to the deviation of the mean internal energy from the Maier-Saupe expression for strong orientational ordering and nonlinear entropic effects. In order to describe stable biaxial phases, a sixth order expansion of the free energy was found to be necessary [35], which clearly is contained within our approach. Figure 6 shows the full Landau-de Gennes free energy F, Equation (14), as a function of the Maier-Saupe orientational order parameter S 2 for the model parameters of [30].…”

Statistical Theory of Biaxial Nematic and Cholesteric Phases

“…The order parameter tensor can be constructed by means of the anisotropic part of the diamagnetic susceptibility or, in some cases, by means of other macroscopic response functions [1]. In the absence of electric and magnetic fields the bulk free energy for the isotropic and the nematic phases in the Landau-de Gennes theory has the form [13] …”

“…The first idea to assess the macroscopic effects of molecular biaxiality was of Freiser [2,3]. Later, liquid crystals phases formed by biaxial molecules have been studied using molecular field treatments [4][5][6][7][8][9], the Landau-de Gennes theory [10][11][12][13], computer simulations of lattice models [14][15][16][17], an SU(3) representation [18,19]. It was shown that single-component models consisting of biaxial molecules and interacting by properly chosen continuous potentials, can produce a biaxial phase.…”