Elongational rheology of 2, 3 and 4 polymer stars connected by linear backbone chains

We consider the elongational rheology of model polystyrene topologies with 2, 3 and 4 stars, which are connected by one (2-star or “Pom-Pom”), two (3-star) and three (4-star) linear backbone chains. The number of arms of each star varies from $q_a$ = 3 to 24, the molecular weight of the arms from $M_w,_a$ = 25 kg/mol to 300 kg/mol, and the backbone chains from $M_w,_b$ = 100 kg/mol to 382 kg/mol. If the length of the arm is shorter than the length of the backbone, i.e. $M_w,_a$ < $M_w,_b$, and despite the vastly different topologies considered, the elongational stress growth coefficient can be modeled by the Hierarchical Multi-mode Molecular Stress Function (HMMSF) model, based exclusively on the linear-viscoelastic characterization and a single nonlinear parameter, the dilution modulus. If the length of the arms of the stars is similar or longer than the length of the backbone chain ($M_w,_a$ ≥ $M_w,_b$) connecting two stars, the impact of the backbone chain on the rheology vanishes and the elongational stress growth coefficient is dominated by the star topology showing similar features of the elongational stress growth coefficient as those of linear polymers.