Miscibility studies of two twist-bend nematic liquid crystal dimers with different average molecular curvatures. A comparison between experimental data and predictions of a Landau mean-field theory for the NTB-N phase transition

We report a calorimetric study of a series of mixtures of two twist-bend liquid crystal dimers, the 1 '',7 ''-bis(4-cyanobiphenyl)-4l-yl heptane (CB7CB) and 1 ''-(2',4-difluorobiphenyl-4'-yloxy)-9 ''-(4-cyanobiphenyl-4'-yloxy) nonane (FFO9OCB), the molecules of which have different effective molecular curvatures. High-resolution heat capacity measurements in the vicinity of the N-TB-N phase transition for a selected number of binary mixtures clearly indicate a first order N-TB-N phase transition for all the investigated mixtures, the strength of which decreases when the nematic range increases. Published theories predict a second order N-TB-N phase transition, but we have developed a self-consistent mean field Landau model using two key order parameters: a symmetric and traceless tensor for the orientational order and a short-range vector field which is orthogonal to the helix axis and rotates around of the heliconical structure with an extremely short periodicity. The theory, in its simplified form, depends on two effective elastic constants and explains satisfactorily our heat capacity measurements and also predicts a first-order N-TB-N phase transition. In addition, as a complementary source of experimental measurements, the splay (K-1) and bend (K-3) elastic constants in the conventional nematic phase for the pure compounds and some selected mixtures have been determined.