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Polymers 2018, 10(8), 848; https://doi.org/10.3390/polym10080848

The Chain Distribution Tensor: Linking Nonlinear Rheology and Chain Anisotropy in Transient Polymers

1
Department of Mechanical Engineering, University of Colorado Boulder, Boulder, CO 80309, USA
2
Materials Science and Engineering Program, University of Colorado Boulder, Boulder, CO 80309, USA
*
Author to whom correspondence should be addressed.
Received: 15 June 2018 / Revised: 27 July 2018 / Accepted: 30 July 2018 / Published: 1 August 2018
(This article belongs to the Special Issue Mechanics of Emerging Polymers with Unprecedented Networks)
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Abstract

Transient polymer networks are ubiquitous in natural and engineered materials and contain cross-links that can reversibly break and re-form. The dynamic nature of these bonds allows for interesting mechanical behavior, some of which include nonlinear rheological phenomena such as shear thickening and shear thinning. Specifically, physically cross-linked networks with reversible bonds are typically observed to have viscosities that depend nonlinearly on shear rate and can be characterized by three flow regimes. In slow shear, they behave like Newtonian fluids with a constant viscosity. With further increase in shear rate, the viscosity increases nonlinearly to subsequently reach a maximum value at the critical shear rate. At this point, network fracture occurs followed by a reduction in viscosity (shear-thinning) with a further increase in shear rate. The underlying mechanism of shear thickening in this process is still unclear with debates between a conversion of intra-chain to inter-chain cross-linking and nonlinear chain stretch under high tension. In this paper, we provide a new framework to describe the nonlinear rheology of transient polymer networks with the so-called chain distribution tensor using recent advances from the transient network theory. This tensor contains quantitatively and statistical information of the chain alignment and possible anisotropy that affect network behavior and mechanics. We investigate shear thickening as a primary result of non-Gaussian chain behavior and derive a relationship for the nonlinear viscosity in terms of the non-dimensional Weissenberg number. We further address the criterion for network fracture at the critical shear rate by introducing a critical chain force when bond dissociation is suddenly accelerated. Finally, we discuss the role of cross-linker density on viscosity using a “sticky” reptation mechanism in the context of previous studies on metallo-supramolecular networks with reversible cross-linkers. View Full-Text
Keywords: shear thickening; nonlinear rheology; polymer mechanics; supramolecular polymers; associative polymers; transient network theory; dynamic bond shear thickening; nonlinear rheology; polymer mechanics; supramolecular polymers; associative polymers; transient network theory; dynamic bond
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Lalitha Sridhar, S.; Vernerey, F.J. The Chain Distribution Tensor: Linking Nonlinear Rheology and Chain Anisotropy in Transient Polymers. Polymers 2018, 10, 848.

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