Linear and Extensional Rheology of Model Branched Polystyrenes: From Loosely Grafted Combs to Bottlebrushes

Monodisperse comb polystyrenes (comb-PS) with loosely to densely grafted architectures up to loosely grafted bottlebrush structures were synthesized via anionic polymerization. This comb-PS series, named PS290- N br -44, had the same entangled backbone, M w,bb = 290 kg/mol, corresponding to a number of entanglements along the backbone Z bb ≅ 20, and similar branch length, M w,br ≅ 44 kg/mol or Z br ≅ 3, but varied in the number of branches per molecule, N br, from 3 to 190 branches. Consequently, the average number of entanglements between two consecutive branch points along the backbone (branch point spacing), Z s, ranged from well entangled, Z s ≅ 5, to values that were far less than one entanglement, Z s ≅ 0.1. Linear viscoelastic data including the zero-shear rate viscosity, η 0, diluted modulus, G N,s 0, and a new diluted modulus extracted from the van Gurp–Palmen plot, | G *| at δ = 60°, were analyzed as a function of the M w of the combs. Scaling of η 0 versus M w revealed three different regions for increasing N br or decreasing Z s: (1) loosely grafted combs with Z br < Z s and η 0 ∼ exp( M w ), (2) densely grafted combs with 1 < Z s < Z br and η 0 ∼ M w –3.4 followed by η 0 ∼ M w –1 for 0.2 < Z s < 1, and (3) loosely grafted bottlebrushes with Z s < 0.2 and η 0 ∼ M w 5 . The relative maximum in η 0 corresponded to a comb-PS with Z s ≅ Z br, and the relative minimum resulted from a comb-PS with Z s ≅ 0.2, which displayed almost the same η 0 as the linear PS290. Strain hardening factors, SHF ≡ η E,max /η DE,max, measured in extensional experiments increased with increasing N br and reached SHF > 200 for Hencky strains below ε H = 4, which is tremendously high and has to the best of our knowledge not been observed yet. Such a high strain hardening is of great fundamental and technical importance in extensional processes, e.g., foaming, film blowing, or fiber spinning.