Modeling of oriented crystallization kinetics of polymers in the entire range of uniaxial molecular orientation

Abstract

Closed-form analytical formulas describing kinetics of oriented crystallization under constant or variable amorphous orientation and isothermal or non-isothermal conditions are derived, valid in the whole range of orientation. Master relation for the deformation free energy vs. orientation factor, or tensile stress, is derived accounting for non-linear effects of finite chain extensibility. The Avrami-Evans model is expanded to account for the effects of orientation in thermodynamic driving force of nucleation and crystal growth.Involvement of predetermined and spontaneous nucleation varies strongly with the orientation and leads to domination of spontaneous nucleation at high orientations. Crystallization half-time involving separated or coexisting predetermined and spontaneous nucleation is discussed.A formula predicting equal contribution of both nucleation modes vs. orientation factor and temperature is derived and ranges of domination of the modes are discussed. Example computations illustrate the model predictions for an example polymer (PLLA) and are in good agreement with the experimental results.