The Chain Distribution Tensor: Linking Nonlinear Rheology and Chain Anisotropy in Transient Polymers
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 an...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-08-01
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| Series: | Polymers |
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| Online Access: | http://www.mdpi.com/2073-4360/10/8/848 |
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| author | Shankar Lalitha Sridhar Franck J. Vernerey |
| author_facet | Shankar Lalitha Sridhar Franck J. Vernerey |
| author_sort | Shankar Lalitha Sridhar |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T02:18:27Z |
| format | Article |
| id | doaj.art-bbb37e3987754d1cbd7afbeb65676c8d |
| institution | Directory Open Access Journal |
| issn | 2073-4360 |
| language | English |
| last_indexed | 2024-04-13T02:18:27Z |
| publishDate | 2018-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Polymers |
| spelling | doaj.art-bbb37e3987754d1cbd7afbeb65676c8d2022-12-22T03:07:04ZengMDPI AGPolymers2073-43602018-08-0110884810.3390/polym10080848polym10080848The Chain Distribution Tensor: Linking Nonlinear Rheology and Chain Anisotropy in Transient PolymersShankar Lalitha Sridhar0Franck J. Vernerey1Department of Mechanical Engineering, University of Colorado Boulder, Boulder, CO 80309, USADepartment of Mechanical Engineering, University of Colorado Boulder, Boulder, CO 80309, USATransient 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.http://www.mdpi.com/2073-4360/10/8/848shear thickeningnonlinear rheologypolymer mechanicssupramolecular polymersassociative polymerstransient network theorydynamic bond |
| spellingShingle | Shankar Lalitha Sridhar Franck J. Vernerey The Chain Distribution Tensor: Linking Nonlinear Rheology and Chain Anisotropy in Transient Polymers Polymers shear thickening nonlinear rheology polymer mechanics supramolecular polymers associative polymers transient network theory dynamic bond |
| title | The Chain Distribution Tensor: Linking Nonlinear Rheology and Chain Anisotropy in Transient Polymers |
| title_full | The Chain Distribution Tensor: Linking Nonlinear Rheology and Chain Anisotropy in Transient Polymers |
| title_fullStr | The Chain Distribution Tensor: Linking Nonlinear Rheology and Chain Anisotropy in Transient Polymers |
| title_full_unstemmed | The Chain Distribution Tensor: Linking Nonlinear Rheology and Chain Anisotropy in Transient Polymers |
| title_short | The Chain Distribution Tensor: Linking Nonlinear Rheology and Chain Anisotropy in Transient Polymers |
| title_sort | chain distribution tensor linking nonlinear rheology and chain anisotropy in transient polymers |
| topic | shear thickening nonlinear rheology polymer mechanics supramolecular polymers associative polymers transient network theory dynamic bond |
| url | http://www.mdpi.com/2073-4360/10/8/848 |
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