The driving force of density fluctuation of amorphous polymer films under annealing processes was evaluated synthetically in terms of thermodynamics on the basis of the logarithmic light intensity as a function of annealing time. The time dependence of $\mathcal{l}n\left(I\right)$ of polyethylene (terephthalate) (PET) as an example for characterizing an amorphous state was classified into three stages: the first stage (stage I), where $\mathcal{l}n\left(I\right)$ showed insignificant changes with time; the second stage (stage II), where $\mathcal{l}n\left(I\right)$ increased linearly; and the third stage (stage III), where the intensity deviated from the linear relationship and tended to level off. The density fluctuation by chain diffusion, termed quasi-spinodal decomposition, in stage II was analyzed in terms of an increase of trans-conformation of an amorphous chain in stage I. To provide conclusive evidence, the orientation function of chain segments was calculated by using a lattice model that accounts for entropic and energetic characters. The former character is associated with segmental orientation due to the effect of chain stiffness of Kuhn segments characterized by a rod with a relatively large length-to-width ratio $x$, whereas the latter is associated with thermotropic systems with anisotropic polarizabilities. By using the theoretical orientation function, Hv light scattering patterns were calculated by a statistical approach in which the optical axis of a PET chain segment was chosen along the direction perpendicular to the benzene ring. This selection was justified by comparison of the three principal refractive indexes of a PET chain. The calculated patterns provided a clear $X$-type lobe, when the correlation between optical elements concerning the rotational fluctuation became stronger. The calculated patterns were in good agreement with the patterns observed in stage III. The series of experimental and theoretical results indicated that the conversion from gauche- to trans-conformation plays an important role to derive the density fluctuation of amorphous polymer chains associated with the initiation of crystallization.

• Received 8 October 2008

DOI:https://doi.org/10.1103/PhysRevE.79.041801