Stretching response of a polymer chain with deformable bonds

The stretching response of polymer chains fundamentally determines the mechanical properties of polymer networks. Classical chain models capture conformational changes at small stretches but fail at large stretches where enthalpic bond deformations dominate. Here we present a model that, for the first time, integrates bond extension, bond angle deformation, and rotation hindrance into a unified statistical thermodynamic framework, using transfer matrix techniques to solve the partition function in the Gibbs ensemble. Our results show that bond extension and angle deformation markedly affect chain stiffness at large stretches, while rotation hindrance has a minor effect. Based on this, we develop a simplified model that neglects rotation hindrance and derive an interpolation formula for the force-extension relationship of freely rotating chains with uniform bond lengths and angles. We also construct a free energy expression to account for bond deformations, using energy minimization to find equilibrium bond parameters. The simplified model closely aligns with the statistical model, and both show strong agreement with experimental data on carbon chain stretching, especially at large stretches. This work lays the foundation for future studies on chain scission and network failure.