Effect of Different Network Topologies on Swelling and Mechanical Properties of Polyelectrolyte Hydrogels

Elastic modulus, <i>G</i>, and equilibrium swelling ratio, <i>Q</i> _V, are two properties of hydrogels, which are linked by the scaling law <i>G</i> ∼ <i>Q</i> _V ^β, where β = -1 and -9/4 in the low- and high-salt limits, respectively. Tuning them independently would enable the optimization of the material design for a wide variety of distinct applications. In this work, we investigate several possibilities to achieve this using various network heterogeneities. We employ implicit solvent coarse-grained molecular dynamics simulations to explore mechanical, structural, and thermodynamic properties of hydrogels with varying topologies in comparison to a regular reference gel. We explore regular gels with tetrafunctional cross-linkers arranged in a diamond-lattice fashion, which we take as a reference gel, together with bottlebrush gels, gels with dangling ends, and gels coexisting with floating chains. We observe that incorporating dangling ends changes the swelling ratio and bulk modulus following the relation obtained from the regular reference gel, whereas the bottlebrush and floating-chain gels show stronger deviations. Specifically, floating-chain gels resulted in higher moduli and higher swelling ratios, while bottlebrush gels resulted in lower moduli and lower swelling ratios than the regular counterparts. Concomitantly, a clear change in salt partitioning was observed for various hydrogel architectures. Our results show new ways to optimize the elastic modulus of gels with respect to their swelling behavior and allow for the optimization and on-demand design of hydrogels.