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Over the past 25 years, IRIS has become an integral resource in materials laboratories around the world, bringing together stimulating communities of rheology experimentalists and theoreticians, rheological experts, and experts from other fields, and even making rheology accessible to non-rheologists. The calculational tools of IRIS interface data from different experimental findings with predictions from rheology theories. Since its beginning, many theory groups used IRIS to share their original codes for rheology predictions. We demonstrate this in two examples, (1) the detailed analysis of small amplitude oscillatory shear data (SAOS) and predictions thereof and (2) a theory, newly implemented in IRIS, that elegantly unites dynamical quantities from small amplitude oscillatory shear (SAOS) with data from filament stretching rheometry and predictions of transient shear. IRIS supports this convergence with a standardizing data (Dealy et al., J Rheol 39:253-265, 1995 ), which makes data sharing easy and independent of instrument brand-specific and laboratory-specific coding.

The study of commercial low-density polyethylenes (LDPEs) has always focused on the effects of the molecular architecture of the polymer on its shear and extensional rheological properties due to their direct influence on manufacturability. However, the complex morphology of industrial-grade LDPEs also affects the crystallization kinetics and dynamic mechanical properties of the polymers, which are key to the processibility and applications. Therefore, a comprehensive investigation was conducted into the areas of crystallization kinetics, crystallinity, dynamic mechanical, and linear and non-linear shear rheological properties of two industrial-grade LDPEs to build a cohesive insight into the influence of morphology on these material properties. We further analyzed the steady-state and transient shear viscosity data obtained from the two LDPEs in comparison with constitutive model predictions using the hierarchical multi-mode molecular stress function (HMMSF) and found excellent agreement within experimental accuracy between predictions by the HMMSF model and shear stress as well as normal stress data of the LDPEs investigated.

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,bb = 280 kg/mol) and 22 entangled sidearms ( M w,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,a = 25 kg/mol having a similar span molecular weight as PS43k and similar M w,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. Graphical Abstract

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. Graphical Abstract

A Pom-Pom polymer with q a side chains of molecular weight M w,a at both ends of a backbone chain of molecular weight M w,b is the simplest branched polymer topology. Ten nearly monodisperse polystyrene Pom-Pom systems synthesized via an optimized anionic polymerization and a grafting-onto method with M w,b of 100 to 400 kg/mol, M w,a of 9 to 50 kg/mol, and q a between 9 and 22 are considered. We analyze the elongational rheology of the Pom-Poms by use of the hierarchical multi-mode molecular stress function (HMMSF) model, which has been shown to predict the elongational viscosity of linear and long-chain branched (LCB) polymer melts based exclusively on the linear-viscoelastic characterization and a single material parameter, the so-called dilution modulus G D . For the Pom-Poms considered here, we show that G D can be identified with the plateau modulus G N 0 = G D , and the modeling of the elongational viscosity of the Pom-Poms does therefore not require any fitting parameter but is fully determined by the linear-viscoelastic characterization of the melts. Due to the high strain hardening of the Pom-Poms, brittle fracture is observed at higher strains and strain rates, which is well described by the entropic fracture criterion. Graphical abstract

The Hierarchical Multi-mode Molecular Stress Function (HMMSF) model predicts the elongational and multiaxial extensional viscosities of polydisperse linear polymer melts based exclusively on their linear viscoelastic characterization and a single nonlinear material parameter, the so-called dilution modulus G D . For long-chain branched (LCB) polymer melts such as low-density polyethylene (LDPE), the HMMSF model describes quantitatively the elongational stress growth coefficient up to the maximum of the elongational viscosity but fails to predict the existence of the maximum and the following steady-state viscosity. By taking into account branch point withdrawal in elongational flow of LCB melts, we extend the HMMSF model and show that the maximum of the elongational viscosity can be characterized by a single additional parameter, the characteristic stretch λ ¯ m , while the steady-state tensile stress and the elongational viscosity depend only on the dilution modulus G D as in the case of linear polydisperse melts. Comparison of predictions of the Extended Hierarchical Multi-mode Molecular Stress Function (EHMMSF) model to experimental data of 5 LDPE melts with widely different molecular weights, polydispersities and densities, and a model polystyrene pom-pom polymer shows good agreement within experimental accuracy in constant elongational-rate flow as well as stress relaxation after steady and reversed elongational flow. For the LCB melts considered, we report differences in the specific Hencky strain at the maximum of the tensile stress as quantified by the characteristic stretch λ ¯ m , and we discuss correlations between polydispersity, dilution modulus G D , and strain hardening potential of the LDPE melts. We also extend the fracture criterion for brittle fracture of monodisperse polymer melts to the case of polydisperse polymers and find reasonable agreement with experimental evidence.

In-extruder measurements of shear viscosity and normal stresses are important as these measurement techniques allow determining the rheological state of the polymer melt at processing conditions up to high shear rates. However, validation of viscosity and normal stress data obtained by in-line slit rheometers at high shear rates is difficult due to a lack of overlap of the in-line data and the off-line measurements by rotational rheometers limited to lower shear rates. Here, shear viscosity and normal stress data measured in-line at large shear rates during extrusion and off-line at low shear rates are compared to predictions of the Doi-Edwards model and the Hierarchical Multi-Mode Molecular Stress Function (HMMSF) model using linear-viscoelastic off-line small amplitude oscillating shear data of two polystyrenes and a low-density polyethylene as input parameters. For polystyrene, the results of this investigation do not only validate the experimental data obtained by rotational as well as slit-die rheometry, but also demonstrate the agreement between experiments and models up to very high shear rates, which were not experimentally accessible earlier. The low-density polyethylene shows a more complex behaviour, which follows the HMMSF model at low shear rates, but approaches the Doi-Edwards model at high shear rates.

The transient elongational data set obtained by filament-stretching rheometry of four commercial high-density polyethylene (HDPE) melts with different molecular characteristics was reported by Morelly and Alvarez [Rheologica Acta 59, 797–807 (2020)]. We use the Hierarchical Multi-mode Molecular Stress Function (HMMSF) model of Narimissa and Wagner [Rheol. Acta 54, 779–791 (2015), and J. Rheology 60, 625–636 (2016)] for linear and long-chain branched (LCB) polymer melts to analyze the extensional rheological behavior of the four HDPEs with different polydispersity and long-chain branching content. Model predictions based solely on the linear-viscoelastic spectrum and a single nonlinear parameter, the dilution modulus GD for extensional flows reveals good agreement with elongational stress growth data. The relationship of dilution modulus GD to molecular characteristics (e.g., polydispersity index (PDI), long-chain branching index (LCBI), disengagement time τd) of the high-density polyethylene melts are presented in this paper. A new measure of the maximum strain hardening factor (MSHF) is proposed, which allows separation of the effects of orientation and chain stretching.