Modeling elongational viscosity of polystyrene Pom-Pom/linear and Pom-Pom/star blends

The elongational rheology of blends of a polystyrene (PS) Pom-Pom with two linear polystyrenes was recently reported by Hirschberg et al. (J. Rheol. 2023, 67:403-415). The Pom-Pom PS280k-2x22-22k with a self-entangled backbone (M-w,M-bb = 280 kg/mol) and 22 entangled sidearms (M-w,M-a = 22 kg/mol) at each of the two branch points was blended at weight fractions from 75 to 2 wt% with two linear polystyrenes (PS) having M-w of 43 kg/mol (PS43k) and 90 kg/mol (PS90k), respectively. While the pure Pom-Pom shows strong strain hardening in elongational flow (SHF > 100), strain hardening (SHF > 10) is still observed in Pom-Pom/linear blends containing only 2 wt% of Pom-Pom. The elongational start-up viscosities of the blends with Pom-Pom weight fractions above 10 wt% are well described by the Molecular Stress Function (MSF) model, however, requiring two nonlinear fit parameters. Here we show that quantitative and parameter-free modeling of the elongational viscosity data is possible by the Hierarchical Multi-mode Molecular Stress Function (HMMSF) model based on the concepts of hierarchical relaxation and dynamic dilution. In addition, we investigated the elongational viscosity of a blend consisting of 20 wt% Pom-Pom PS280k-2x22-22k and 80 wt% of a PS star with 11 arms of M-w,M-a = 25 kg/mol having a similar span molecular weight as PS43k and similar M-w,M-a as the Pom-Pom. This work might open up possibilities toward polymer upcycling of less-defined polymers by adding a polymer with optimized topology to gain the intended strain hardening, e.g., for film blowing applications.