Mechanical deformation affects the condensation of counterions in highly swollen polyelectrolyte hydrogels.

Polyelectrolyte gels can generate electric potentials under mechanical deformation. While the underlying mechanism of such response is often attributed to the changes in counterion-condensation levels or alterations in the ionic conditions in the pervaded volume of the hydrogel, exact molecular origins are still unknown. By using all-atom molecular dynamics simulations of a polyacrylic acid hydrogel in explicit water as a model system, we simulate the uniaxial compression and uniaxial stretching deformations of a highly-swollen (i.e., $>$90\% solvent content) hydrogel network and calculate the microscopic condensation levels of counterions around the gel chains. The counterion condensation is highly non-monotonic, and both compression and stretching increase the overall counterion condensation in the hydrogel with deformation. The effect weakens for weakly swollen hydrogels. The condensation profiles around the chains of the deformed hydrogel are highly anisotropic; the condensation tends to increase for the stretched chains of the hydrogel. However, this increase reaches a maximum and decreases as the chains are strongly stretched under uniaxial extension. Under compression, the condensation around the chains perpendicular to the deformation direction increases. For the same reason, the hydrogel chains in the constrained and unconstrained (deformation-free) directions exhibit opposing condensation behaviors. Further, the deformation-induced counterion condensation does not occur in a semi-dilute polyelectrolyte solution, suggesting the role of hydrogel topology constraining the chain ends in this phenomenon. Our results indicate that counterion condensation in a deforming polyelectrolyte hydrogel can be highly heterogeneous and depends on the conformations of constituting chains.