Application of the MLD “toy” model to extensional flows of broadly polydisperse linear polymers: Part I – Model development

Abstract

When no relative tube stretch is present, all topological entanglements are equivalent in their impact on the dynamics of nearby, primary chain segments independent of molecular weight, molecular architecture, position along the chain or flow conditions. In this no relative tube stretch limit, the average lifetime of an entanglement is its only distinguishing feature [1]. However, when tube stretch commences and non-homogeneous chain tension is present, two rational bases for entanglement discrimination manifest themselves. One is based upon the entanglement orientational relaxation time relative to the test chain stretch relaxation time and the other on the relative tension (incremental moduli) of the test chain and the entangling chain. In this paper we focus on the first criteria for entanglement discrimination and demonstrate its fundamental importance in predicting the transient extensional stresses of broadly polydisperse polymer systems typical of commercial resins. Entanglement microstructure modification, i.e. reduction of the number of viable “stretch” entanglements for a given MWD component, determined by the underlying MWD is critical to properly predicting transient and steady material properties in extensional (stretching) flows (Mishler et al. (2000) [2]; Mishler (2001) [3]). A new molecular model is created incorporating these new ideas along with the new extensional rheometry experimental results of Auhl et al. into the polydisperse MLD model structure at the “toy” level [1–4]. Multiple fundamental length scales in polydisperse melts are predicted by the new model, a fundamental paradigm shift from the original Doi–Edwards model. An alternative model for diluted tube stretch and orientation proposed by Auhl et al. has also been cast into the generalized MLD format for polydisperse systems [4]. Predictions of the Auhl et al. model and the new diluted stretch tube MLD polydispersity model proposed in this paper are in close accord for model bidisperse systems but disagree for systems with general polydispersity such as the data of Minegishi et al. [5–7]. The origins of the differences between the two models can be traced to the distinction between mean field tube descriptions of the entanglement effect used by Auhl et al. and the pair wise discrete description of entanglement constraints used in the MLD model. These seemingly subtle differences in interpretation of the entanglement effect become important when stress is calculated in polydisperse systems.