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Gels made of telechelic polymers connected by reversible cross-linkers are a versatile design platform for biocompatible viscoelastic materials. Their linear response to a step strain displays a fast, near-exponential relaxation when using low-valence cross-linkers, while larger supramolecular cross-linkers bring about much slower dynamics involving a wide distribution of timescales whose physical origin is still debated. Here, we propose a model where the relaxation of polymer gels in the dilute regime originates from elementary events in which the bonds connecting two neighboring cross-linkers all disconnect. Larger cross-linkers allow for a greater average number of bonds connecting them but also generate more heterogeneity. We characterize the resulting distribution of relaxation timescales analytically and accurately reproduce stress relaxation measurements on metal-coordinated hydrogels with a variety of cross-linker sizes including ions, metal-organic cages, and nanoparticles. Our approach is simple enough to be extended to any cross-linker size and could thus be harnessed for the rational design of complex viscoelastic materials.
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Relaxation dynamics of supramolecular polymer networks with mixed cross-linkers
The linear rheological properties of supramolecular polymer networks formed by mixtures of two different bis-Pd(II) cross-linkers with poly(4-vinylpyridine) in dimethyl sulfoxide are examined. The changes in storage and loss moduli of the networks with mixed cross-linkers are compared to those of samples with a single type of cross-linkers. While the plateau moduli, and presumably network topology, of the networks remain equal regardless of the cross-link distribution, the relaxation time contributed by the faster cross-linkers is increased (by a factor of about 1.5 for the specific samples used in this work) by the presence of the slower cross-linkers, while the reverse influences are not significant. This effect can be explained by the fact that a certain fraction of the elastically effective strands cross-linked with fast cross-linkers is pinned on one end by slow cross-linkers, reducing by half the rate of fast chain relaxation. This effect is anticipated to be general for gels with two well-separated relaxation times.
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- Award ID(s):
- 2116298
- PAR ID:
- 10378362
- Publisher / Repository:
- Society of Rheology
- Date Published:
- Journal Name:
- Journal of Rheology
- Volume:
- 66
- Issue:
- 6
- ISSN:
- 0148-6055
- Page Range / eLocation ID:
- p. 1193-1201
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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