A Quantitative Hofmeister Framework for Hydrogen-Bonded Hydrogel Relaxation Dynamics

Abstract

The Hofmeister series provides an empirical description of ion-specific effects, yet a quantitative framework connecting ion-specific hydration to polymer relaxation has remained elusive. Here, we establish such a framework for hydrogen-bonded hydrogels by introducing the dimensionless parameter Bc (the product of the Jones–Dole viscosity B coefficient and salt concentration c) as a quantitative descriptor of the hydration environment. Using poly(methacrylamide) (PMAm) hydrogels as a model system, we show that the effects of ion identity and salt concentration on polymer relaxation can be quantitatively correlated through Bc. Within the water-abundant regime (Bc < 0.2), polymer relaxation follows the scaling relationship ln(τp) ∼ Bc, whereas this scaling gradually deviates as the system enters the water-depleted regime (Bc > 0.2). This deviation suggests that polymer relaxation becomes progressively less dependent on hydration-mediated processes as the hydration environment becomes increasingly constrained. The resulting Bc framework provides a quantitative correspondence among ion identity, salt concentration, and temperature through their effects on polymer relaxation. This framework provides a quantitative basis for tuning hydrogel viscoelasticity and shape-memory actuation through salt-mediated modulation of the hydration environment. More broadly, the framework extends the Hofmeister effect from an empirical ion ordering to a quantitative description of relaxation behavior for hydrogen-bonded polymer networks by linking the hydration environment with polymer dynamics.