Valence can control the nonexponential viscoelastic relaxation of multivalent reversible gels

Hugo Le Roy; Jake Song; David Lundberg; Aleksandr V Zhukhovitskiy; Jeremiah A Johnson; Gareth H McKinley; Niels Holten-Andersen; Martin Lenz

doi:10.1126/sciadv.adl5056

Valence can control the nonexponential viscoelastic relaxation of multivalent reversible gels

Sci Adv. 2024 May 17;10(20):eadl5056. doi: 10.1126/sciadv.adl5056. Epub 2024 May 15.

Authors

Hugo Le Roy^{1

2}, Jake Song^{3

4}, David Lundberg⁵, Aleksandr V Zhukhovitskiy^{6

7}, Jeremiah A Johnson⁶, Gareth H McKinley⁸, Niels Holten-Andersen^{3

9}, Martin Lenz^{1

10}

Affiliations

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.