By use of a standard theoretical method, we arrive at a coarse-grained elastic energy density for twist-bend nematic (N
tb
) phases which features two fields, a director t designating the outer ...macroscopic optic axis and a variable cone angle
reflecting the inner heliconical microscopic structure. The theory describes the N
tb
phase through a nematic-like energy with an extra scalar order parameter. The coupling with an external field is similarly described at the same coarse-grained level and a field-induced transition to the ordinary nematic phase is also predicted to take place in a confined Frederiks cell, in the simplified setting where natural boundary conditions are prescribed on the cell's plates.
The bulk and the surface-like elastic constants of a nematic liquid crystal are calculated for an ensemble of particles interacting via anisotropic dispersion forces using the pseudo-molecular ...method. The geometrical anisotropy of the molecules is also taken into account in the calculations by choosing a molecular volume of ellipsoidal shape. Analytical expressions for the elastic constants are obtained as a function of the eccentricity in the molecular volume shape. The method allows one to explore the dependence on the molecular orientation with respect to the intermolecular vector by analyzing the magnitude and the behaviour of macroscopic elastic parameters defining the nematic phase.
•Liquid crystals elastic constants are calculated for anisotropic dispersion forces.•The Pseudo-molecular method furnishes analytical expressions of elastic constants.•The interaction and molecular volume are of ellipsoidal shape.•Bulk and surface-like elastic constants depend on the molecular volume shape.•Surface-like elastic constants become negative for a small region of parameters.
The pseudo-molecular method is employed to obtain analytical expressions for the elastic constants of an ensemble of anisotropic particles, in both disc-like and rod-like geometries. These particles ...interact via a phenomenological pair potential constructed from the non-spherical correction to the dispersion forces between two identical molecules. The molecular shape appears in the calculations of the elastic constants in two different cases. The first case considers a molecular volume of ellipsoidal shape continuously deformed from a positive (prolate spheroid, rod-like molecule) to large negative (oblate spheroid, disc-like molecule) values of a parameter describing some kind of eccentricity. The second one considers a molecular volume shape continuously deformed from a cylinder (calamitic molecule) to a plane disc by changing the ratio between the diameter of the cylinder and its long axis. The particular cases of Maier-Saupe and Nehring-Saupe interactions are obtained as simple limiting cases of the general pair potential interaction. These general results may be helpful to understand the limits of the pseudo-molecular method, and to understand the origin of elastic constants in discotic liquid crystals from a molecular perspective.
