For a unit nematic director, the bulk elastic density is . The three positive moduli penalize nematic splay, nematic twist, and nematic bend. Boundary elastic terms, chirality, or varying nematic order require additional contributions.
For a laterally uniform nematic director , its divergence is and its twist invariant is . Thus and . A normal electric field contributes . The Euler-Lagrange equations for two fields are and .
Nematic bend curves the integral lines of the nematic director. For a unit field, , so the bend energy measures curvature along those lines.
Nematic twist rotates the nematic director around an axis perpendicular to it. The helix has zero nematic splay and nematic bend, and twist density .
Nematic splay describes local spreading or convergence of the nematic director field. Its leading elastic cost is quadratic in the divergence and invariant under the head-tail identification .
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Distortion free energy density is a concept from materials science and thermodynamics, particularly in the study of phase transitions and elasticity in materials. It typically relates to the energy required to deform a material without introducing additional defects or fluctuations in its internal structure. In the context of crystal structures and phase transitions, "distortion" refers to any deviation of the crystal lattice from its ideal, symmetrical arrangement.