Force-induced length-change effect of macromolecular chains undergoing mechanochemical coupling and mechanical behaviors under uniaxial tension in soft hydrogels

Study on length-change effect in macromolecular chains is of critical importance for understanding mechanical behaviors of soft hydrogels, but mechanisms of force-induced transitions in macromolecular chains in soft hydrogels have not been fully understood due to their complex thermodynamics and kinetics. Herein, a globule-coil transition model is proposed to describe the force-induced length-change effect in macromolecular chains, of which the rubber elasticity and stiffening principles in hydrogels are investigated. A molecular model is firstly formulated to capture the microscopic physical mechanisms of the length-change effect based on the renormalized blob theory, and a free-energy equation is then proposed to characterize the globule-coil transition of macromolecular chains and rubber elasticity of polymer networks, based on the Flory-Huggins theory, entropic elasticity model, tube model and linear spring model. A kinetic equation for the force-induced globule-coil transition in macromolecular chains is further developed to describe the length-change effect, solved by finite difference method (FDM). Finally, quantitative comparisons have been conducted and good agreements have been achieved between the analytical results of proposed model and experimental data reported in literature. Our study provides a new perspective towards fully understanding of the length-change effect in macromolecular chains, rubbery elasticity, and stiffening principles in soft hydrogels undergoing mechanochemical coupling.