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. The MBP model is tested against experimental data in steady and transient extensional and shear flows. The MBP model captures the monotonic thinning of the extensional flow curve of entangled monodisperse polystyrene (PS) melts [A. Bach et al., Macromolecules 36, 5174-5179 (2003)] while simultaneously predicting the extension hardening found in PS semidilute solutions where CDFC is diluted out [P. K. Bhattacharjee et al., Macromolecules 35, 10131-10148 (2002)]. The simulation results also show that the rheological properties in nonlinear extensional flows of PS melts are sensitive to CDFC but not to convective constraint release (CCR) while those for shear flows are influenced more by CCR. The monodisperse MBP toy model is generalized to arbitrary polydispersity.
D. W. Mead et al., "A Constitutive Model for Entangled Polymers Incorporating Binary Entanglement Pair Dynamics and a Configuration Dependent Friction Coefficient," Journal of Rheology, vol. 59, no. 2, pp. 335 - 363, American Institute of Physics (AIP), Mar 2015.
The definitive version is available at https://doi.org/10.1122/1.4905921
Chemical and Biochemical Engineering
Keywords and Phrases
Aluminum; Deformation; Friction; Macromolecules; Convective Constraint Release; Entanglement Dynamics; Friction Coefficients; Monodisperse Polystyrene; Relative Orientation; Rheological Property; Semidilute Solutions; Steady and Transient; Shear Flow
International Standard Serial Number (ISSN)
Article - Journal
© 2015 American Institute of Physics (AIP), All rights reserved.
01 Mar 2015