A fundamental rule: Determining the importance of flow prior to polymer crystallization

Abstract

A continuum-level model for nonisothermal polymer crystallization following a complex flow is presented, along with a fundamental rule that may be employed to determine if the flow will influence the ensuing crystallization dynamics. This rule is based on two dimensionless parameters: the (Rouse) Weissenberg number and an inverse Deborah number defined by the ratio between the time taken to cool and the melting point vs the stretch relaxation time, which determines the time available for flow-enhanced crystallization. Moreover, we show how the time to reach the melting point can be derived semianalytically and expressed in terms of the processing conditions in the case of pipe flow - ubiquitous in polymer processing. While the full numerical model is required to quantitatively predict induction times and spherulite-size distributions, the proposed fundamental rule may be used practically to ensure, or eliminate, flow-enhanced structures by controlling the processing conditions or material properties. We discuss how flow-enhanced structures may be revealed only after postprocessing annealing and finally examine previous works that have successfully applied the model to extrusion-based three-dimensional printing.