A thermodynamic strategy of hydrogels with pearl-necklace-like chains towards excellent hyperelasticity

Polyelectrolyte hydrogels, characterized by their charged networks, exhibit exceptional deformability and biocompatibility, making them ideal platforms for realizing multifunctional and intelligent material systems, yet the molecular origin of their pearl-necklace-like chains remains controversial. Here we develop a thermodynamic unbinding framework that treats the necklace as an assembly of compact polymeric blobs connected by worm-like spacers. The total free-energy density is decomposed into three additive contributions: (i) conformational entropy of the worm-like chains, (ii) electrostatic interaction, and (iii) interfacial unbinding of the blobs, the latter being modeled through a constrained-junction model that captures non-affine micro-deformation. Conceptualizing the pearl necklace as an assembly of distinct polymer blobs and connecting chains, this approach facilitates a detailed examination of its microstructure and complex mechanical response. Closed-form stress-elongation ratio relations are derived for arbitrary three-dimensional loading. The proposed blob-unbinding strategy offers a universal platform for rationalizing the mechanochemistry of polyelectrolyte networks. The uniaxial tensile data of 50 times deformed hyperelastic hydrogels, regular PAM hydrogels, and ring cross-linked hydrogels, and the planar extension data of PTHF hydrogels were analyzed to illustrate the effectiveness of the proposed model.