Free Energy of Rigid Rods: Contribution of Rotational Entropy to Frank Elasticity

We apply the density functional formalism developed by the present authors [J. Fukuda and H. Yokoyama: J. Chem. Phys. 115 (2001) 4930] for the calculation of the free energy of rigid rods as a functional of the compositional scalar order parameter φ and the orientational order parameter of second-rank tensor Q_ij We model rigid rods as semiflexible wormlike chains with infinite bending elasticity and the exact expression for the entropic part of the free energy up to the second order in the gradients can be obtained. Discussion is devoted to the contribution of rotational entropy to Frank elasticity. Although none of the previous molecular theories for the Frank elasticity of liquid crystals has taken rotational entropy into account, our results indicate that rotational entropy can give a non-negligible contribution to Frank elasticity.