From loop probability of self-avoiding walk to constitutive models of hydrogels for thickness, strain-softening and hardening effects

Abstract

A novel self-avoiding walk (SAW) chain with loop probability model is proposed, incorporating parameters with clear physical meanings at the microscopic scale. By contrasting it with the phenomenally described Gent model, this research not only discovers the physical foundations of the Gent model assumed purely empirical previously but also provides insights into the stiffness-toughness conflict as well as the thickness effect of hydrogels. Coupled with the physically based Arruda-Boyce model, the proposed model empowers the Kuhn length with the ability to shorten or elongate, allowing for modelling strain-softening and hardening effects for both soft regular and highly entangled hydrogels. The proposed model is validated through comparisons with published experiments on stress-stretch curves of ultrathin hydrogel films and both soft regular and highly entangled hydrogels.