Modeling elongational viscosity and brittle fracture of 10 polystyrene Pom-Poms by the hierarchical molecular stress function model
Valerian Hirschberg, Max G. Schußmann, Marie‐Christin Röpert, Manfred Wilhelm, Manfred H. Wagner
Abstract
Abstract A Pom-Pom polymer with q a side chains of molecular weight M w,a at both ends of a backbone chain of molecular weight M w,b is the simplest branched polymer topology. Ten nearly monodisperse polystyrene Pom-Pom systems synthesized via an optimized anionic polymerization and a grafting-onto method with M w,b of 100 to 400 kg/mol, M w,a of 9 to 50 kg/mol, and q a between 9 and 22 are considered. We analyze the elongational rheology of the Pom-Poms by use of the hierarchical multi-mode molecular stress function (HMMSF) model, which has been shown to predict the elongational viscosity of linear and long-chain branched (LCB) polymer melts based exclusively on the linear-viscoelastic characterization and a single material parameter, the so-called dilution modulus G D . For the Pom-Poms considered here, we show that G D can be identified with the plateau modulus $${G}_{N}^{0}={G}_{D}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>G</mml:mi> <mml:mrow> <mml:mi>N</mml:mi> </mml:mrow> <mml:mn>0</mml:mn> </mml:msubsup> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>D</mml:mi> </mml:msub> </mml:mrow> </mml:math> , and the modeling of the elongational viscosity of the Pom-Poms does therefore not require any fitting parameter but is fully determined by the linear-viscoelastic characterization of the melts. Due to the high strain hardening of the Pom-Poms, brittle fracture is observed at higher strains and strain rates, which is well described by the entropic fracture criterion. Graphical abstract