Valence can control the nonexponential viscoelastic relaxation of multivalent reversible gels

Author:

Le Roy Hugo12ORCID,Song Jake34ORCID,Lundberg David5,Zhukhovitskiy Aleksandr V.67,Johnson Jeremiah A.6ORCID,McKinley Gareth H.8ORCID,Holten-Andersen Niels39ORCID,Lenz Martin110ORCID

Affiliation:

1. Université Paris-Saclay, CNRS, LPTMS, 91405, Orsay, France.

2. Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland.

3. Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA.

4. Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA.

5. Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA.

6. Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA.

7. Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA.

8. Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA.

9. Department of Bioengineering and Materials Science and Engineering, Lehigh University, Bethlehem, PA 18015, USA.

10. PMMH, CNRS, ESPCI Paris, PSL University, Sorbonne Université, Université de Paris, F-75005 Paris, France.

Abstract

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.

Publisher

American Association for the Advancement of Science (AAAS)

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