  We study the possibility of the spinodal decomposition in the induction
period of the polymer crystallization. This phenomenon was first reported in an
X-ray scattering experiment, and has still been controversial due to various
experiments and theories that support or deny the phenomenon. In this article,
we explain the condition for the spinodal decomposition to occur in polymer
melts by deriving a Ginzburg-Landau model of the free energy as a functional of
the density and the orientation of the segments, where we introduce the
excluded volume and the nematic interactions through a combination of the
random phase approximation and the transfer matrix for the polymer
conformation. We show that, upon elimination of the degrees of freedom of the
orientation, the nematic interaction reduces to an effective attraction whose
strength increases with the stiffness of the polymer chain. Such an attraction
induces spinodal decomposion especially for stiff polymer chain case.
