Molecular investigation of polyelectrolyte hydrogel under mechanical deformation

Abstract

Polyelectrolyte hydrogels are fascinating materials that can produce electromechanical responses when they are electrically or mechanically deformed. However, the accurate molecular origins of such phenomenon are still unknown, even though it is often ascribed to the change in condensation of counterion levels or alteration of ionic conditions in the pervaded volume of the hydrogel. We used all-atom molecular dynamics (MD) simulations to investigate this behavior by utilizing a polyacrylic acid (PAA) hydrogel immersed in an explicit polar solvent as our model system. In the atomistic MD simulation, we investigated the swelling behavior of polyelectrolyte hydrogels, traditionally computed through the equilibrium of chemical potential and pressure between the system and reservoir. However, we discovered that achieving the equilibrium swelling state was non-trivial, as faster relaxation of the simulation box resulted in lower swelling ratios, while slower relaxation led to larger swelling ratios. To address this challenge, we employed theoretical calculations with a Gaussian state as the reference to estimate the hydrogel’s swelling ratio effectively. In our computational study, we investigated the response of PAA polyelectrolyte hydrogel from weak to highly swollen (i.e., between 60 to 90% solvent content) when subjected to uniaxial mechanical compression and extension. Our primary aim is to compute the condensed counterions at different deformations at the microscopic level. We found out that condensation of counterion shows highly non-monotonic behavior when they are mechanically deformed, with an overall increase in total counterion condensation when the PAA hydrogel is uniaxially compressed or stretched. However, this effect diminishes for weakly swollen gel because a large fraction of counterions are already condensed on the polyelectrolyte polymer. Upon closer examination, we found that counterion condensation increases along the stretched chains in the hydrogel. on the one hand, this increase reaches to maximum value for certain deformation ratios after that, we see a decline in the condensation of counterions when the hydrogel chains are stretched further. On the other hand, we see a very minimal increase in condensation when the hydrogel is compressed, and chains are collapsed state. We also analyzed the single polyelectrolyte chains, which also displayed a qualitatively similar response. This observation gives us insight that polymer chain conformations affect the distribution of counterions in the gel. We further investigated the counterion condensation behavior for polyelectrolyte solutions at their critical concentration level. However, we don’t see any deformation-dependent counterion condensation. This suggests the importance of hydrogel topology, which constrains the polyelectrolyte chain ends and leads to the observed behavior. These extensive molecular dynamics simulations shed light on the interesting and heterogeneous behavior of counterion condensation when the hydrogel is deformed, showing a rich electrostatic response behavior. These findings contribute significantly to the understanding of the underlying behavior of mechanically deformed polyelectrolyte hydrogels.