A constitutive model for entangled polymers incorporating binary entanglement pair dynamics and a configuration dependent friction coefficient

Following recent work [e.g., J. Park et al., J. Rheol. 56, 1057–1082 (2012); T. Yaoita et al., Macromolecules 45, 2773–2782 (2012); and G. Ianniruberto et al., Macromolecules 45, 8058–8066 (2012)], we introduce the idea of a configuration dependent friction coefficient (CDFC) based on the relative orientation of Kuhn bonds of the test and surrounding matrix chains. We incorporate CDFC into the “toy” model of Mead et al. [Macromolecules 31, 7895–7914 (1998)] in a manner akin to Yaoita et al. [Nihon Reoroji Gakkaishi 42, 207–213 (2014)]. Additionally, we incorporate entanglement dynamics (ED) of discrete entanglement pairs into the new Mead–Banerjee–Park (MBP) model in a way similar to Ianniruberto and Marrucci [J. Rheol. 58, 89–102 (2014)]. The MBP model predicts a deformation dependent entanglement microstructure which is physically reflected in a reduced modulus that heals slowly following cessation of deformation. Incorporating ED into the model allows “shear modification” to be qualitatively captured. ...