Theory and observations of polymer crystal thickening

Abstract

The thickening of polymer crystals during isothermal annealing is usually observed to be an irreversible process. Phenomenological laws that govern such processes take the form of simple proportionalities—flux being proportional to force. For polymer crystals, a thermodynamic force capable of driving the thickening phenomenon arises from the unequal free energies of the fold and lateral surfaces. By analogy with other irreversible phenomena, the rate of crystal thickening is taken to be proportional to the derivative of the surface free energy with respect to crystal thickness. After certain assumptions, integration yields an equation in which three parameters characterize the system: an initial thickness l0, an equilibrium thickness l*, and a relaxation time τ which is a function of the ``undercooling''. The theory provides a basis for considering the effects of parameters such as time, temperature, thermal history, pressure, and liquids on the thickening rate. In particular, the theory adequately describes the time and temperature dependence of crystal thickening in random copolymers of tetrafluoroethylene and hexafluoropropylene which exhibit thickening behavior completely analogous to that of homopolymers. During thickening, the unit cell dimensions of these quenched-crystallized copolymers decrease in a manner that is consistent with the concept of complete comonomer inclusion upon crystallization.