Exploring free energy density and rubber elasticity of hydrogels undergoing macromolecular crowding, based on extended flory-fisk thermodynamics

Abstract Hydrogels, with their unique properties between fluid and solid states, have attracted significant attention due to their unique constitutive relationships and extensive applications. However, the mechanical behavior of hydrogels becomes highly nonlinear with various enhancement strategies, making it challenging to understand the changes in their constitutive equations and polymer chain conformations. It is one of the difficult problems to solve the previously neglected crowding effect in hydrogel elasticity. To address this, based on extended Flory-Fisk thermodynamics and freely jointed chain model, a constitutive model is established to elucidate the conformational transformations and variations in end-to-end distances of chains within solution environments. The model considers the effects of excluded volume, swelling, solute–solvent interactions, and external loads on conformational equilibrium and interaction energies. The free energy model was validated through comparative analysis with experimental data from the literature. The results show that the proposed model can accurately predict the mechanical behavior of hydrogels under different conditions, providing a deeper understanding of their conformational changes and mechanical properties.