Scaling relations for brittle fracture of entangled polystyrene melts and solutions in elongational flow

The criterion for brittle fracture of entangled polymer liquids [Wagner et al., J. Rheol. 62, 221-223 (2018)] is extended by including the effects of finite chain extensibility and polymer concentration. Crack initiation follows from rupture of primary C-C bonds, when the strain energy of entanglement segments reaches the energy of the covalent bond. Thermal fluctuations will concentrate the strain energy on one C-C bond of entanglement segments, leading to bond scission and rupture of polymer chains followed by crack initiation and fast crack growth. In start-up flows, entanglement segments characterized by long relaxation times, i.e., predominantly those in the middle of the polymer chain, will be the first to reach the critical strain energy and will fracture. Recent experimental data of Huang [Phys. Fluids 31, 083105 (2019)] of fracture of a monodisperse polystyrene melt and of several solutions of monodisperse polystyrenes dissolved in oligomeric styrene are in agreement with the scaling relations for critical Weissenberg number as well as Hencky strain and stress at fracture derived from this fracture criterion and the extended interchain pressure model [Narimissa, Huang, and Wagner, J. Rheol. 64, 95-110 (2020)].