Theoretical modeling and scaling laws in hydrogels incorporating convoluted chain entropy and interchain repulsion

The macroscopic mechanical properties of hydrogels are primarily determined by their microscopic network architecture. However, current micromechanical models typically neglect interchain repulsive interactions, and their influence on macroscopic stresses within the network structure remains insufficiently clarified. This study develops a theoretical model that integrates polymer chain conformational entropy with interchain repulsive interactions, establishing scaling laws for model parameters across a range of polymer concentrations. Initially, the polymer reference interaction site model (PRISM) for polymer solutions is utilized to quantify interchain repulsive interactions, which captures the steric repulsion arising between polymer chains. Moreover, the model framework is established by characterizing the crosslinked and entangled chain components within the network structure using the classical eight-chain and tube-constraint framework, where power-law scaling relations are derived for each component. Finally, the proposed model is validated against the reported experimental data, thus providing a robust theoretical framework for the precise design of hydrogel network structures and their mechanical properties.