Chain breaking in the statistical mechanical constitutive theory of polymer networks

Abstract

Elastomers are used in a wide range of applications because of their large strain to failure, low density, and tailorable stiffness and toughness. The mechanical behavior of elastomers derives mainly from the entropic elasticity of the underlying network of polymer chains. Elastomers under large deformation experience bonds breaking within the backbone chains that constitute the polymer network. This breaking of chains damages the network, can lead to material failure, and can be utilized as an energy dissipation mechanism. In the case of reversible bonds, broken chains may reform and heal the damage in the network. If the reversible bonds are dynamic, chains constantly break and reform and create a transient network. A fundamental constitutive theory is developed to model the mechanics of these polymer networks. A statistical mechanical derivation is conducted to yield a framework that takes in an arbitrary single-chain model (a Hamiltonian) and outputs the following: the single-chain mechanical response, the breaking and reforming kinetics, the equilibrium distribution of chains in the network, and the partial differential equations governing the deformationcoupled network evolution. This statistical mechanical framework is then brought into the continuum scale by using macroscopic thermodynamic constitutive theory to obtain a constitutive relation for the Cauchy stress. The potential-supplemented freely jointed chain (uFJC) model is introduced, and a parametric study of its mechanical response and breaking kinetics is provided. This single-chain model is then implemented within the constitutive framework, which we specialize and apply in two exemplary cases: the mechanical response and irreversible breakdown of a multinetwork elastomer, and the mechanical response of a dual crosslink gel. After providing a parametric study of the general constitutive model, we apply it to a hydrogel with reversible metal-coordination crosslinks. In several cases, we find that the breakdown of the network causes secondary physical mechanisms to become important and inhibit the accuracy of our model. We then discuss these mechanisms and indicate how our existing framework can be adjusted to incorporate them in the future.

Force-mediated molecule release from double network hydrogels

“…The model for small molecule release in the double network hydrogel was adapted from 62 to include an irreversible reaction (molecule release) that does not result in fracture of the polymer chains, in addition to a later irreversible scission of the chains. In brief, this model starts from the statistical mechanical description of a single polymer chain and predicts the stress response and mechanochemical response of the polymer network when subjected to mechanical deformation.…”

“…Κ and γscission were calibrated to the mechanical response of the material, while γrelease was then calibrated to the corresponding release percentage. 62 The model is stiffer than the experimental data at large strain primarily because we neglect the increase in contour length that results from the small molecule release.…”