Journal
BRAZILIAN JOURNAL OF PHYSICS
Volume 46, Issue 1, Pages 26-34Publisher
SPRINGER
DOI: 10.1007/s13538-015-0375-2
Keywords
Elastic constants; Liquid crystals; Lattice models; Pseudo-molecular method
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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 rodlike 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, rodlike 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.
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