A comparison of some models for describing polymer crystallization at low deformation rates

There is now in the literature a number of mathematical models of the effects of flow on crystallization of polymers, and here we compare the performance of various models in slow simple shearing and sinusoidal strain (oscillatory) flows. We compare the model predictions to the experiments of Wassner and Maier [E. Wassner, R.-D. Maier, Shear-induced crystallization of polypropylene melts. in: D.M. Binding, et al. (Ed.), Proceedings of the XIII International Congress on Rheology, Cambridge, 2000, pp. 1-183] on isotactic polypropylene. Both the Kolmogorov [A.N. Kolmogorov, On the statistics of the crystallization process on metals. Bull. Akad. Sci. USSR, Class Sci., Math. Nat. 1 (1937) 355-359] and Nakamura et al. [K. Nakamura, T. Watanabe, K. Katayama, T. Amano, Some aspects of non-isothermal crystallization of polymers I, J. Appl. Polym. Sci. 16 (1972) 1077-1091] crystallinity formulations are discussed, and the advantages of the former are emphasized. For the cases considered, we see that strain-based crystallinity enhancement formulations appear to give results close to the experiments at the low flow rates which were studied, although they have some drawbacks. Several other ideas also lead to acceptable results; a new formulation based on both strain and strain-rate appears to give the best overall fit.