A statistical mechanics framework for polymer chain scission, based on the concepts of distorted bond potential and asymptotic matching
Abstract
To design increasingly tough, resilient, and fatigueresistant elastomers and hydrogels, the relationship between controllable network parameters at the molecular level to macroscopic quantities that govern damage and failure must be established. Constitutive models based upon statistical mechanics have used variants of the freely jointed chain (FJC) model with rigid links. However, since the free energy state of a polymer chain is dominated by enthalpic bond distortion effects as the chain approaches its rupture point, bond extensibility ought to be accounted for if the model is intended to capture chain rupture. To that end, a new bond potential is supplemented to the FJC model (as derived in the uFJC framework of Buche and colleagues), which we have extended to yield a tractable, closedform model that is amenable to constitutive model development. Inspired by the asymptotically matched uFJC model response, a simple, quasipolynomial, and anharmonic bond potential energy function is derived. Using this bond potential, approximate yet highlyaccurate analytical functions for bond stretch and chain force dependent upon chain stretch are established. Then, using this polymer chain model, a stochastic thermal fluctuationdriven chain rupture framework is developed. This framework is based upon a forcemodified tilted bond potential that accounts for distortional bond potential energy, allowing for the calculation of dissipated chain scission energy. The model is fit to singlechain mechanical response data collected from atomic force microscopy tensile tests for validation and to glean deeper insight into the molecular physics taking place. Due to their analytical nature, this polymer chain model and the associated rupture framework can be straightforwardly implemented in finite element models accounting for fracture and fatigue in polydisperse elastomer networks.
 Publication:

arXiv eprints
 Pub Date:
 August 2022
 arXiv:
 arXiv:2208.07352
 Bibcode:
 2022arXiv220807352M
 Keywords:

 Condensed Matter  Soft Condensed Matter;
 Condensed Matter  Statistical Mechanics