By using a field-theoretical treatment of semi-flexible polymers, Fukuda formulated the free energy of semi-flexible polymers as a functional of a compositional scalar order parameter φ (local density of polymers) and an orientational order parameter of second-rank tensor Sij . Fukuda also gave a set of dynamical equations that these two order parameters obey, based on the assumption that the order parameters are relaxed mainly through reptation motion of polymers [2,3,4]. Fukuda did some numerical calculations to demonstrate that the orientational order has a significant effect on the phase separation dynamics, and the phase-separated domains are highly elongated due to the anisotropic interfacial energy.
Fukuda also showed that, in the limit of infinite bending elasticity of polymer chaings, the free energy functional of polymers can be rigorously evaluated up to 2nd order in the gradients [5,6] (here "rigorous" means that the Taylor expansion in terms of the two order parameters can be carried out up to infinite order). The form of the free energy also implied that the configurational entropy of polymer chains contribute to the Frank elasticity, though none of the previous theoretical studies to determine Frank elastic constants on a microscopic basis had taken into account such contributions.