Numerical simulation results of the nonlinear coefficient Q from FT-Rheology using a single mode pom-pom model

In previous experimental observations, Hyun and Wilhelm [Macromolecules 42, 411–422 (2009)] proposed a nonlinear coefficient Q (≡ I 3/1/γ 0 2) that was determined from Fourier transform rheology experiments under dynamic oscillatory shear flow. Additionally an intrinsic zero-strain nonlinearity, Q 0 ( ≡ lim γ 0 → 0 Q ), was defined. It was found that this nonlinear coefficient Q(ω,γ 0), also given as Q 0(ω), is a very promising parameter to quantify nonlinear mechanical properties that are highly affected by polymer topology, e.g., branched structures. In this study, we systematically investigated the effect of polymer topology on the nonlinear parameters Q(ω,γ 0) and Q 0(ω) with a single mode differential pom-pom model. A number of parameters are affecting the topology of a pom-pom polymer, such as the number of dangling arms (q) and the dimensionless molecular weight of both the backbone (s b) and the arms (s a). In the here presented work, the linear viscoelastic properties G′(ω) and G″(ω) were compared with the nonlinear viscoelastic property Q 0(ω) for variety of molecular parameters. The intrinsic nonlinearity Q 0(ω) displayed two distinct relaxation processes for pom-pom architectures even though G′(ω) and G″(ω) could not distinguish two relaxation processes. Furthermore, the behavior of Q(γ 0) as a function of strain amplitude was also investigated in detail. From the results of these numerical simulations, it was concluded that polymer topology had a stronger influence on the nonlinear viscoelastic properties Q and Q 0 than on the linear viscoelastic properties.