Hyperstretching in elongational flow of densely grafted comb and branch-on-branch model polystyrenes

Abstract

Strain hardening of long-chain branched polymers in elongational flow occurs due to the stretch of the backbone chain between branch points. With an increasing number of side arms, the length of the backbone chain segment between two branch points of a comb decreases. Of particular interest is the case when the number Nb of arms per entanglement length of the polymer is larger than one. This leads not only to larger strain hardening but also to hyperstretching, i.e., the elongational stress growth shows an enhanced increase with strain. We consider elongational data reported by Abbasi et al. [Macromolecules 50(15), 5964–5977 (2017)] and Faust et al. [Macromol. Chem. Phys. 224(1), 2200214 (2023)] on a series of comb and branch-on-branch polystyrene (PS) melts with the average number Nb of branches per entanglement segment of the backbone ranging from Nb = 0.2 to Nb = 9.5. In addition, we present measurements of the elongational viscosity of two PS combs with Nb = 4.7 as well as of blends consisting of 5 to 50 wt. % of a PS comb and a monodisperse linear PS. Analysis by the hierarchical multimode molecular stress function model shows that while backbone chains of loosely grafted combs with Nb < 1 are stretched affinely in elongational flow, backbone chains of more densely grafted combs with Nb > 1 show increasing hyperstretching with increasing Nb. The elongational data of the comb/linear blends confirm that hyperstretching is an intrinsic property of the comb macromolecule with Nb > 1, independent of its concentration in the blend. While this is of considerable interest from a modeling point of view, hyperstretching causing an enhanced increase of the elongational stress growth can also have a significant impact on the processability of polymers, and quantification of this effect is, therefore, important.