Molecular theory of elastic constants of liquid crystals. III. Application to smectic phases with tilted orientational order.

Using the density-functional formalism we derive an expression for the distortion free energy of systems with continuous broken symmetry and use it to derive an expression for the elastic constants of smectic phases in which the director is tilted with respect to the smectic layer normal. As in the previous papers of this series [Y. Singh, S. Singh, and K. Rajesh, Phys. Rev. A 45, 974 (1992); Y. Singh, K. Rajesh, V. J. Menon, and S. Singh, Phys. Rev. E 49, 501 (1994)], the expressions for the elastic constants are written in terms of order and structural parameters. The structural parameters involve the generalized spherical harmonic coefficients of the direct pair correlation function of an effective isotropic liquid. The density of this effective isotropic liquid depends on the nature and amount of ordering present in the system and is evaluated self-consistently. We estimate the value of elastic constants using reasonable guesses for the order and structural parameters.