Relationship between the Frank elastic constant anisotropy measured from the lamellar director and that of the molecular director around disclinations in main chain liquid crystalline polymers

The transmission electron microscope technique enables direct visualization of disclination core structure of main chain liquid crystalline polymers. Generally, the lamellar structure, that is a function of type of polymer and molecular length, and of which the thickness is 10-200 nm, can be observed. In terms of distortions in the director field produced by a disclination, the elastic anisotropy, ε, can easily be calculated. However, the ε does not indicate the molecular distortion produced by the disclination. Continuum mechanics is used to describe the relationship between the elastic anisotropy, ε_a, measured from the lamellar director and that, ε_b, of the molecular director in main chain liquid crystalline polymers. The relationship is ε_a = -ε_b, indicating that lamellar distortion is completely different from the molecular distortion.