Tensor representation of Oseen-Frank strain energy in uniaxial cholesterics

de Gennes gave a three-parameter representation of strain energy in a cholesteric liquid crystal that is second order on the Q tensor, and hence in order parameter. He discarded a term involving an elastic constant K₂₄ which is relevant at surfaces and disclinations. The splay and bend elastic constants K₁₁ and K₃₃ are alike in the second-order theory. The complete Oseen-Frank expression in terms of a director has five parameters, including K₂₄. If uniaxiality, which is implicit in the director theory, is imposed on the Q tensor, five independent third-order tensor functions are found. These differentiate between K₁₁ and K₃₃ and show the third-order dependence of the Oseen-Frank elastic constants on order parameter. Numerical values of these second- and third-order elastic coefficients of 4-methoxybenzylidene-4{'}-n-butylaniline (MBBA), p-azoxyanisole (PAA), and E-7 (British Drug House designation of a cyano-biphenyl mixture) are obtained from published values of the dependence of Oseen-Frank elastic constants and various anisotropies on temperature, and from a relation of Nehring and Saupe.