Rapid, nonlinear diffusiophoretic swelling of chemically responsive hydrogels

Chemicaly responsive hydrogels can store and release chemical signals, such as polyacrylic acid (PAA) gels storing copper or calcium divalent ions and freeing them upon adding acid. While the PAA hydrogel interface is fully permeable to the released ions and acid, interactions between the free ions and the gel polymer network lead to a diffusiophoretic gel actuation at a rate faster than the characteristic poroelastic deformation rate. We have recently shown this effect theoretically and experimentally by focusing on linear deformations [1]. However, in light of potential applications such as hydrogel-based soft robotics and drug delivery, comprehending large diffusiophoretic deformations in hydrogels is imperative for increased strain rates and power output. We present a continuum nonlinear poroelastic theory to model large diffusiophoretic gel swelling, induced by high acid concentrations or by steady stimulus flow at arbitrary rates. The theory incorporates the interplay between nonlinear poroelasticity, variable hydrogel permeability, and the diffusiophoretic swelling along with the transport dynamics of chemical agents within the gel. With tunable diffusiophoretic interaction strength between the free ions and the gel backbone, we theoretically show that a wide array of chemically induced nonlinear hydrogel deformations are attained.