Exploring the elastic-plastic behavior of hydrogen bond cross-linked polymers, based on the principle of minimum energy and the slide of non-covalent cross-linking

Hydrogen bond cross-linked polymers exhibit remarkable toughening, yet the molecular origin of their sliding and plasticity remains unclear. The changes in the mechanical behavior of polymers caused by the sliding of microscopic polymer chains have not yet been effectively understood. We develop a minimum free energy model for forced sliding of non-covalent cross-links and derive a closed-form expression for sliding free energy density by treating electrostatic and repulsive contributions on equal footing. This model predicts two distinct sliding states governed by the ratio of initial electrostatic energy to repulsive energy. The strong electrostatic interaction manifests as a conventional resistance-dependent sliding process, whereas the weak electrostatic interaction under applied load initially promotes hydrogen bond formation. We couple this sliding energy with conformational free energy obtained from Langevin chain statistics and the tube model to yield a total stress–strain response. Uniaxial tensile data for three material families are predicted with correlation coefficients. The theory quantitatively captures yield, necking, strain hardening, and the transition from entropy-dominated elasticity to slide-governed plasticity. The free energy generated by sliding of hydrogen bond cross-linking and the corresponding engineering stress. (a) Analytical results of sliding energy-microscopic stretching curves of hydrogen bond cross-linked polymers with various W e 0 / W r 0 . (b) Analytical results of engineering stress-elongation ratio curves of hydrogen bond cross-linked polymers with various W e 0 / W r 0 . (c) At given W e 0 / W r 0 =1.2, analyzing the sliding mechanism of hydrogen bonds based on energy and stress curves. (d) At given W e 0 / W r 0 =0.9, analyzing the sliding mechanism of hydrogen bonds based on energy and stress curves. • Two molecular mechanisms of hydrogen bond cross-linking sliding were proposed, and the corresponding free energies were given. • The elasticity and plasticity of hydrogen bond cross-linked polymers were analyzed. • A constitutive and free energy model was proposed to analyze the complex mechanical behavior of polymers.