Modeling flow induced crystallization in film casting of polypropylene

Abstract

Data from iPP film casting experiments served as a basis to model the effect of flow on polymer crystallization kinetics. These data describe the temperature, width, velocity and crystallinity distributions along the drawing direction under conditions permitting crystallization along the draw length.

In order to model the effect of flow on crystallization kinetics, a modification of a previously defined quiescent kinetic model was adopted. This modification consisted in using a higher melting temperature than in the original quiescent model. The reason for the modification was to account for an increase of crystallization temperature due to entropy decrease of the flowing melt. This entropy decrease was calculated from the molecular orientation on the basis of rubber elasticity theory applied to the entangled and elongated melt. The evolution of molecular orientation (elongation) during the film casting experiments was calculated using a non-linear dumbbell model which considers the relaxation time, obtained from normal stress difference and viscosity functions, to be a function of the deformation rate.

The comparison between experimental distributions and model based crystallinity distributions was satisfactory.

Appendix

Comparison between Eq. (24) and the data of Fig. 5 shows that at gradients larger than 0.1 s⁻¹ the relaxation time becomes proportional to $\dot{\gamma }^{{ - a_{2} }}$; at these gradients, according to Eqs. (25) and (26), n _m becomes about proportional to $\dot{\gamma }^{{a_{2} /\beta }}$. Considering the order of magnitude of the terms of Eq. (6) one can say that, when time derivative is negligible, a _xx =λ²−1 becomes about proportional to $\dot{\gamma }\tau$ and thus, for high deformation rates, to $\dot{\gamma }^{{1 - a_{2} }}$.

The entropy change by effect of flow, which according to Eq. (19) is proportional to the ratio between (a _xx +2/λ−2) and n _m , for high deformation rates is, thus, essentially proportional to $\dot{\gamma }^{{1 - a_{2} {\left( {1 + \frac{1} {\beta }} \right)}}}$.