No abstract

We study a class of models for bent-core molecules using low density version of Local Density Functional Theory. Arms of the molecules are modeled using two-and three Gay-Berne (GB) interacting units of uniaxial and biaxial symmetry. Dipole-dipole interactions are taken into account by placing a dipole moment along the C 2 symmetry axis of the molecule. The main aim of the study is to identify molecular factors that can help stabilizing the biaxial nematic phase.The phase diagrams involving isotropic (I), uniaxial (N U ) and biaxial (N B ) nematic phases are determined at given density and dipole strength as function of bent angle. For molecules composed of two uniaxial arms a direct I − N B phase transition is found at a single Landau point, which moves towards lower bent angles with increasing dipole magnitude. For the three-segment model strengthening of the dipole-dipole interaction results in appearance of a line of Landau points.There exists an optimal dipole strength for which this line covers the maximal range of opening angles. Interestingly, the inclusion of biaxial GB ellipsoids as building blocks reveals the direct I − N B transitions line even in a non-polar, two-arms model. The line is shifted towards higher opening angles as compared to the uniaxial case.

A minimal coupling model exhibiting isotropic, uniaxial, and biaxial nematic phases is analyzed in detail and its relation to existing models known in the literature is clarified. Its intrinsic symmetry properties are exploited to restrict the relevant ranges of coupling constants. Further on, properties of the model are thoroughly investigated by means of bifurcation theory as proposed by Kayser and Raveché [Phys. Rev. A 17, 2067 (1978)] and Mulder [Phys. Rev. A 39, 360 (1989)]. As a first step toward this goal, the bifurcation theory is applied to a general formulation of density functional theory in terms of direct correlation functions. On a general formal level, the theory is then analyzed to show that the bifurcation points from the reference, high-symmetry equilibrium phase to a low-symmetry structure depend only on the properties of the one-particle distribution function and the direct pair correlation function of the reference phase. The character of the bifurcation (whether spinodal, critical, tricritical, isolated Landau point, etc.) depends, in addition, on a few higher-order direct correlation functions. Explicit analytical results are derived for the case when only the leading L=2 terms of the potential (mean-field analysis) or of the direct pair correlation function expansion in the symmetry-adapted basis are retained. Formulas are compared with the numerical calculations for the mean-field, momentum L=2 potential model, in which case they are exact. In particular, bifurcations from the isotropic and uniaxial nematic to the biaxial nematic phases are discussed. The possibility of the recently reported nematic uniaxial-nematic biaxial tricritical point [A. M. Sonnet, E. G. Virga, and G. E. Durand, Phys. Rev. E 67, 061701 (2003)] is analyzed as well.