Phenomenological model for the confined dynamics in semicrystalline polymers: the multiple alpha relaxation in cold-crystallized poly(ethylene terephthalate).

The segmental relaxation in poly(ethylene terephthalate), crystallized from either an isotropic or a cold-drawn glass, is investigated by means of dielectric spectroscopy. It is shown that there exist two distinct alpha relaxation modes: a slow one, characterized by a rather wide frequency interval, and a faster, much narrower one. A simple phenomenological model is developed in order to analyze the polarization autocorrelation functions phi(t)'s associated with these relaxation modes. The model is based on the idea that the growth of crystalline domains causes a progressive confinement of the amorphous regions where, eventually, the observed alpha processes take place. The mechanism of confinement is accounted for by applying to the case of constrained density fluctuations, well known concepts introduced by Adam and Gibbs [J. Chem. Phys. 43, 139 (1965)] concerning the relaxation dynamics in liquids close to the glass transition. Randomness on confining conditions is then introduced, leading to the derivation of analytical expressions which are used afterwards to fit the asymptotic behavior of the phi's for long-time tails. It is found that the slow, broad alpha process takes place in regions where the confining effect of crystals is strong, whereas the amorphous domains relaxing via the fast mode are those where the confinement effect of crystals is weak. The analysis of the phi's by means of this model allows us to relate the fitting exponents to the dispersion in the free energy associated with structural rearrangement.