Emergence of biaxial nematic phases in solutions of semiflexible dimers.

We investigate the isotropic, uniaxial nematic and biaxial nematic phases, and the transitions between them, for a model lyotropic mixture of flexible molecules consisting of two rigid rods connected by a spacer with variable bending stiffness. We apply density-functional theory within the Onsager approximation to describe strictly excluded-volume interactions in this athermal model and to self-consistently find the orientational order parameters dictated by its complex symmetry, as functions of the density. Earlier work on lyotropic ordering of rigid bent-rod molecules is reproduced and extended to show explicitly the continuous phase transition at the Landau point, at a critical bend angle of 36^{∘}. For flexible dimers with no intrinsic biaxiality, we find that a biaxial nematic phase can nevertheless form at a sufficiently high density and low bending stiffness. For bending stiffness κ>0.86k_{B}T, this biaxial phase manifests as dimer bending fluctuations occurring preferentially in one plane. When the dimers are more flexible, κ<0.86k_{B}T, the modal shape of the fluctuating dimer is a V with an acute opening angle, and one of the biaxial order parameters changes sign, indicating a rotation of the directors. These two regions are separated by a narrow strip of uniaxial nematic in the phase diagram, which we generate in terms of the spacer stiffness and particle density.