Fracture of Polymer Networks Containing Topological Defects

Abstract

The failure properties of a polymer network, including toughness, ultimate strain, and ultimate stress, are some of the most critical properties for network performance. The polymer networks often contain various topological defects, such as primary loops and dangling ends, which have a noticeable effect on these properties. This work focuses on understanding the effect of these defects on the fracture strength of a material by expanding the classical Lake−Thomas theory to account for such defects under the assumption that each defect is unaffected by the presence of other defects in its environment. A Flory−Stockmayer gel point criterion is combined with the improved theory to identify the incipience of fracture. The predictions demonstrate that although the presence of defects weakens the material by reducing the tearing energy, the overall network elongation depends strongly on the primary loop fraction. Specifically, a transition from a low ultimate-strain to a significantly high ultimate-strain behavior is predicted. The addition of a kinetic theory for bond scission predicts that the sharpness of this transition is a strong function of the strain rate. To experimentally test these predictions, a series of poly(ethylene glycol) (PEG) gels with previously characterized primary loop fractions were synthesized. Remarkably, the measured tearing energies agree quite well with the theoretical predictions and also suggest the onset of the low to high extensibility transition.

Fracture of model end-linked networks

“…G c measurements display a trend where the classic Lake–Thomas theory underestimates the experimental measurements. This trend is consistent with previous observations and is often attributed to an underestimation of the size scale of dissipation, which many compensate for with an enhancement factor ( 33 , 34 ).…”

“…Our model, while qualitatively similar, has several key differences from the models recently proposed by Arora et al. ( 34 ) and Lin and Zhao ( 51 ). First, Arora et al.…”

“…As discussed in SI Appendix , similar reasoning also led Arora et al. ( 34 ) to use a value of U that was significantly less than the BDE.…”

“…Arora et al. ( 34 ) recently attempted to address this discrepancy by accounting for loop defects; however, different assumptions were used when inputting U to calculate Lake–Thomas theory values that again required the use of an enhancement factor to achieve quantitative agreement. In this work we demonstrate that refining the Lake–Thomas theory to account for loop defects while using the full bond dissociation energy to represent U yields excellent agreement between the theory and both simulation and experimental data without the use of any adjustable parameters.…”

Why is Mechanical Fatigue Different from Toughness in Elastomers? The Role of Damage by Polymer Chain Scission

“…However, DN elastomers suffer from strain-dependent damage under cyclic loading, developing a zone of accumulated and delocalized damage at high applied energy release rates G which is prone to sudden localization and fast crack growth. This dependence of damage on the applied load serves as experimental evidence to refine current molecular models of fracture, like that of Lake and Thomas (6) and Olsen and co-workers (33), where the contribution of damage to the fracture energy results only from scission of stretched polymer chains in a damage zone of mesh-size.…”