We have modified the full-chain stochastic tube (XDS) model developed by Xu et al. [J. Rheol. 50, 477-494 (2006)] to simulate the rheology of entangled melts and solutions of linear monodisperse polymers. The XDS model, which has a single adjustable parameter that is equivalent to the Rouse time, successfully describes steady and transient shear and normal stress data at low to moderate rates, but the results deviate systematically from experimental data at high rates. The algorithm for re-entanglement was revised, and a configuration- dependent friction coefficient (CDFC), as originally proposed by Giesekus, was incorporated to account for microstructural change of the tube away from equilibrium. The simulation results from the modified model significantly reduce the deviation from the experimental data in shear, and they also agree well with extensional data for entangled solutions, including an initial -0.5-power dependence of the steady extensional viscosity on extension rate. We also applied the CDFC to the molecular model developed by Mead et al. [Macromolecules 31, 7895-7914 (1998)] and obtained improved predictive performance at high deformation rates, reinforcing the idea that there is a structural change in the tube far from equilibrium that accelerates relaxation processes. Finally, noting that molecular models make fundamentally different assumptions about the effect of the deformation on the entanglement density but give essentially equivalent rheological predictions, we explored the effect of the dynamics of the entanglement density by changing the entanglement assumptions in the stochastic model.


Chemical and Biochemical Engineering


National Science Foundation (U.S.)


This work was supported by NSF Grant No. 0625072.

Keywords and Phrases

Adjustable Parameters; Deformation Rates; Entangled Polymeric Liquids; Entangled Polymers; Experimental Data; Extensional Viscosity; Friction Coefficients; High Rate; Microstructural Changes; Microstructure Modifications; Modified Model; Monodisperse Polymers; Normal Stress; Power Dependence; Predictive Performance; Steady and Transient; Stochastic Simulations; Structural Change; Tube Model; Deformation; Molecular Modeling; Rheology; Stochastic Models; Tubes (Components); Polymers

International Standard Serial Number (ISSN)

0148-6055; 1520-8516

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2012 American Institute of Physics (AIP), All rights reserved.

Publication Date

01 Sep 2012