Spherulite growth in polymers

Quantitative mesoscale kinetic simulations of structure and topology evolution during polymer solidification and amorphous-to-spherulite crystallization phenomena is an important issue in the field of advanced polymer processing. Among the various structural phenomena involved, crystallization and related phase transformation phenomena play a major role in that context. In the field of polymer solidification, mesoscopical simulation methods which are discrete in space and time are particularly valuable since spherulite growth during crystallization occurs mostly under inhomogeneous mechanical and thermal boundary conditions.
Earlier approaches to the modelling of crystallization and sperulite growth processes in polymers were suggested and discussed in detail by various groups. For instance, Koscher and Fulchiron studied the influence of shear on polypropylene crystallization experimentally, and also in terms of a kinetic model for crystallization under quiescent conditions and under the influence of shear. Their approach was based on a classical topological Avrami–Johnson–Mehl–Kolmogorov (AJMK) model for isothermal conditions and on related statistical models such as those of Nakamura and Ozawa for non-isothermal conditions. The authors found in part excellent agreement between these modelling results and their own experimental data. For predicting crystallization kinetics under shear conditions, Koscher and Fulchiron used an AJMK model in conjunction with a formulation for the additional number of shear-induced nuclei. They related the increase in the density of nuclei to the first normal stress difference. The authors justified this approach by suggesting that the first normal stress difference includes the effects of the elastic portion of the rheological behaviour of the material. They assumed that the systematic shear and alignment of certain preferred molecular orientations may predispose and, thereby, favour oriented clustering of molecular segments initiating additional nucleation. The latter part of the approach was based on an earlier study of Eder who expressed the number of activated nuclei as a function of the square of the shear rate which provides the possibility of predicting the thickness of threadlike precursors. A related approach was published by Hieber who used the Nakamura equation to establish a direct relation between the Avrami and the Ozawa crystallization rate constants.
AJMK-based transformation models have been applied to polymers with great success in cases where the underlying assumption of material homogeneity is reasonably fulfilled. It is, however, likely that further progress in understanding and tailoring polymer microstructures can be made by the use of cellular automata. These approaches are designed to cope with more realistic situations in terms of the heterogeneity of the material and of the boundary conditions encountered. Our approach to the study of mesoscale kinetic simulations of structure and topology evolution during polymer solidification and amorphous-to-spherulite growth phenomena, therefore, is to use a three-dimensional probabilistic cellular automaton model for the prediction of the kinetics and topology of spherulite growth during crystallization. The model can use experimental and theoretical input parameters which can be adopted together with the corresponding experimental data on the topology and kinetics of the polymer under consideration.