Fracture of Polymer Networks Containing Topological Defects

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.