Explore the vast range of titles available.

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.

We analyse shear stress and normal stress data obtained by cone-partitioned-plate (CPP) shear rheometry in recent years. The data sets of Schweizer et al. (Rheol. Acta 47, 943–957, 2008 ) and Costanzo et al. (Macromolecules 49, 3925–3935, 2016; & Fluids 4, 28, 2019 ) on nearly monodisperse polystyrene melts and solutions are considered to be among the most reliable shear data available. The Doi-Edwards independent alignment (DEIA) model (J. Chem. Soc., Faraday Transactions 2: Molecular and Chemical Physics 74, 1802–1832, 1978a , b ) allows for quantitative description of the steady-state values of shear viscosity η ( γ ̇ ) and first normal stress coefficient ψ 1 ( γ ̇ ) , while it underpredicts the stress overshoot of the stress growth coefficient of the shear stress, η + ( t ), and fails in predicting a stress overshoot of the stress growth coefficient of first normal stress difference, ψ 1 + t . On the other hand, the extended interchain pressure (EIP) model (J. Rheol. 64, 95–110, 2020 ) provides an excellent prediction of the stress overshoots of both shear stress and first normal stress difference, while overpredicting the steady-state shear viscosity and the first normal stress coefficient. We demonstrate that the shear stress overshoot is the result of a combination of orientational stress overshoot and stretch overshoot, while the normal stress overshoot depends solely on the overshoot of the stretch. Based on these considerations, we propose a novel constitutive approach consisting of a combination of the DEIA and the EIP model, and predictions of this approach are found to be in quantitative agreement with the data sets of Schweizer et al. and Costanzo et al. within experimental accuracy.

A consistent model of the rheology of polymer melts and concentrated solutions is presented, based on the idea that the pressures exerted by a polymer chain on the walls of an anisotropic confinement are anisotropic (Doi and Edwards. The Theory of Polymer Dynamics , Oxford University Press, 1986 ). In a tube model with variable tube diameter, chain stretch and tube diameter reduction are related, and at deformation rates larger than the inverse Rouse time τ R , the chain is stretched and its confining tube becomes increasingly anisotropic. Tube diameter reduction leads to an interchain pressure in the lateral direction of the tube (Marrucci and Ianniruberto. Macromolecules 37:3934-3942, 2004 ). Chain stretch is balanced by interchain tube pressure in the lateral direction, which is proportional to the third power of stretch, and by a spring force in the longitudinal direction of the tube, which is linear in stretch. Analyzing elongational viscosity data of Huang et al. (Macromolecules 46:5026-5035, 2013a ; ACS Macro Letters 2:741-744, 2013b ) shows that dilution of polystyrene by oligomeric styrene does not change the relative interchain tube pressure. Based on this extended interchain pressure concept, scaling relations for linear viscoelasticity and elongational viscosity of polystyrene melts and concentrated solutions of polystyrene in oligomeric styrene are presented based exclusively on the relaxation modulus of a reference polymer melt, the volume fraction of polymer in the solution, and the time-molar-mass shift as well as the time-temperature shift caused by the reduction of the glass transition temperature T g of the polymer in a solution relative to T g of the melt.

Elongational viscosity data of four well-characterized blends consisting of 10% mass fraction of monodisperse polystyrene PS-820k (molar mass of 820 kg/mol) and 90% matrix polystyrenes with a molar mass of 8.8, 23, 34, and 73 kg/mol, respectively, as reported by Shahid et al. Macromolecules 52: 2521–2530, 2019 are analyzed by the extended interchain pressure (EIP) model including the effects of finite chain extensibility and filament rupture. Except for the linear-viscoelastic contribution of the matrix, the elongational viscosity of the blends is mainly determined by the high molar mass component PS-820k at elongation rates when no stretching of the lower molar mass matrix chains is expected. The stretching of the long chains is shown to be widely independent of the molar mass of the matrix reaching from non-entangled oligomeric styrene (8.8 kg/mol) to well-entangled polystyrene (73kg/mol). Quantitative agreement between data and model can be obtained when taking the interaction of the long chains of PS-820k with the shorter matrix chains of PS-23k, PS-34k, and PS-73k into account. The interaction of long and short chains leads to additional entanglements along the long chains of PS-820k, which slow down relaxation of the long chains, as clearly seen in the linear-viscoelastic behavior. According to the EIP model, an increased number of entanglements also lead to enhanced interchain pressure, which limits maximal stretch. The reduced maximal stretch of the long chains due to entanglements of long chains with shorter matrix chains is quantified by introducing an effective polymer fraction of the long chains, which increases with the increasing length of the matrix chains resulting in the excellent agreement of experimental data and model predictions.

Elongational viscosity data of well-characterized solutions of 3–50% weight fraction of monodisperse polystyrene PS-820k (molar mass of 820,000 g/mol) dissolved in oligomeric styrene OS8.8 (molar mass of 8800 g/mol) as reported by André et al. (Macromolecules 54:2797–2810, 2021) are analyzed by the Extended Interchain Pressure (EIP) model including the effects of finite chain extensibility. Excellent agreement between experimental data and model predictions is obtained, based exclusively on the linear-viscoelastic characterization of the polymer solutions. The data were obtained by a filament stretching rheometer, and at high strain rates and lower polymer concentrations, the stretched filaments fail by rupture before reaching the steady-state elongational viscosity. Filament rupture is predicted by a criterion for brittle fracture of entangled polymer liquids, which assumes that fracture is caused by scission of primary C-C bonds of polymer chains when the strain energy reaches the bond-dissociation energy of the covalent bond (Wagner et al., J. Rheology 65:311–324, 2021).

The data set of steady and transient shear data reported by Santangelo and Roland Journal of Rheology 45: 583–594, ( 2001 ) in the nonlinear range of shear rates of an unentangled polystyrene melt PS13K with a molar mass of 13.7 kDa is analysed by using the single integral constitutive equation approach developed by Narimissa and Wagner Journal of Rheology 64:129–140, ( 2020 ) for elongational and shear flow of Rouse melts. We compare model predictions with the steady-state, stress growth, and stress relaxation data after start-up shear flows. In characterising the linear-viscoelastic relaxation behaviour, we consider that in the vicinity of the glass transition temperature, Rouse modes and glassy modes are inseparable, and we model the terminal regime of PS13K by effective Rouse modes. Excellent agreement is achieved between model predictions and shear viscosity data, and good agreement with first normal stress coefficient data. In particular, the shear viscosity data of PS13K as well as of two polystyrene melts with M = 10.5 kDa and M = 9.8 kDa investigated by Stratton Macromolecules 5 (3): 304–310, ( 1972 ) agree quantitatively with the universal mastercurve predicted by Narimissa and Wagner for unentangled melts, and approach a scaling of Wi −1/2 at sufficiently high Weissenberg numbers Wi . Some deviations between model predictions and data are seen for stress growth and stress relaxation of shear stress and first normal stress difference, which may be attributed to limitations of the experimental data, and may also indicate limitations of the model due to the complex interactions of Rouse modes and glassy modes in the vicinity of the glass transition temperature. Graphical abstract

Startup shear stress data of a well-defined set of binary polystyrene blends consisting of monodisperse blend components were reported recently by Parisi et al. (J Non-Newtonian Fluid Mech 315:105028, 2023 ). They presented convincing evidence that in the fast flow of melts with narrow molar mass distribution, shear stress undershoot is observed after the overshoot and before approaching the steady state. For blends with broad relaxation time spectra, no undershoot was found. We analyze this data set by comparison with predictions of the rotation zero stretch (RZS) model (Wagner et al. Rheol Acta 63:573–584, 2024 ), which is generalized here to the multi-mode MRZS model for polymer blends. We confirm that the steady-state shear viscosity of the monodisperse blend components as well as of the binary blends agrees with the viscosity predicted by the Doi-Edwards independent alignment model. As long as there is no undershoot, the RZS model (monodisperse melts) and the MRZS model (binary blends) result in a quantitative description of the full startup curve of the shear stress growth σ 12 + ( γ ˙ , t ) including overshoot and steady state, based solely on the linear viscoelastic characterization. The shear stress undershoot observed at higher shear rates in melts with narrow molar mass distribution is not described by the RZS or MRZS model. However, the analysis of the experimental data shows clear evidence that undershoot occurs only if after the overshoot, the decreasing shear stress at a higher shear rate undercuts the shear stress at lower rates, i.e., only if ∂ σ 12 + ( γ ˙ , t ) / ∂ γ ˙ < 0 . For blends with broad relaxation time spectra, ∂ σ 12 + ( γ ˙ , t ) / ∂ γ ˙ ≅ 0 and no undershoot is observed. The hypothesis is made that undershoot is due to transient shear banding, which is initiated in shear stress regimes characterized by ∂ σ 12 + ( γ ˙ , t ) / ∂ γ ˙ < 0 and which disappears at larger strains when the shear stress growth σ 12 + ( γ ˙ , t ) approaches the steady state σ 12 ( γ ˙ ) with ∂ σ 12 ( γ ˙ ) / ∂ γ ˙ > 0 . Graphical Abstract

By considering the rotationality of shear flow, we distinguish between tube segments created by reptation before the inception of shear flow and those created during flow. Tube segments created before inception of shear flow experience both stretch and orientation, while tube segments created after inception of flow are not stretched, but are only aligned in the flow direction. Based on this idea, the Rotation Zero Stretch (RZS) model allows for a quantitative description of the start-up of shear flow and stress relaxation after step-shear strain experiments, in agreement with data of polystyrene long/short blends and corresponding polystyrene 3-arm star polymers investigated by Liu et al. (Polymer 2023, 281:126125), as well as the shear viscosity data of poly(propylene carbonate) melts reported by Yang et al. (Nihon Reoroji Gakkaishi 2022, 50:127–135). In the limit of steady-state shear flow, the RZS model converges to the Doi-Edwards IA model, which quantitatively describes the steady-state shear viscosity of linear polymer melts and long/short blends. The assumption of “non-stretching” of tube segments created during rotational flow is therefore in agreement with the available experimental evidence. Three-arm star polymers behave in a similar way as corresponding blends of long and short polymers confirming the solution effect of the short arm in asymmetric stars. The analysis of step-shear strain experiments reveals that stress relaxation is at first dominated by stretch relaxation, followed at times larger than the Rouse stretch relaxation time by relaxation of orientation as described by the damping function of the Doi-Edwards IA model. The RZS model does not require any nonlinear-viscoelastic parameter, but relies solely on the linear-viscoelastic relaxation modulus and the Rouse stretch relaxation time. Graphical Abstract

In fast elongational flows, linear polymer melts exhibit a monotonic decrease of the viscosity with increasing strain rate, even beyond the contraction rate of the polymer defined by the Rouse time. We consider two possible explanations of this phenomenon: (a) the reduction of monomeric friction and (b) the reduction of the tube diameter with increasing deformation leading to an Enhanced Relaxation of Stretch (ERS) on smaller length scales. (Masubuchi et al. ( 2022 ) reported Primitive Chain Network (PCN) simulations using an empirical friction reduction model depending on segmental orientation and could reproduce the elongational viscosity data of three poly(propylene carbonate) melts and a polystyrene melt. Here, we show that the mesoscopic tube-based ESR model (Wagner and Narimissa 2021 ) provides quantitative agreement with the same data set based exclusively on the linear-viscoelastic characterization and the Rouse time. From the ERS model, a parameter-free universal relation of monomeric friction reduction as a function of segmental stretch can be derived. PCN simulations using this friction reduction relation are shown to reproduce quantitatively the experimental data even without any fitting parameter. The comparison with results of the earlier PCN simulation results with friction depending on segmental orientation demonstrates that the two friction relations examined work equally well which implies that the physical mechanisms of friction reduction are still open for discussion.

Reactive extrusion with pyromellitic dianhydride (PMDA) and tetraglycidyl diamino diphenyl methane (TGDDM) was conducted to create long-chain branched poly(ethylene terephthalate) (LCB-PET). The mechanical and molecular properties were analyzed by linear and non-linear viscoelastic rheology in the melt state and by size-exclusion chromatography measurements with triple detection. The two tetra-functional chain extenders lead to strong viscosity increases, increasing strain hardening effects, and increasing LCB with increasing chain extender concentration. Molecular stress function model predictions show good agreement with the elongational data measured and allowed a quantification of the strain hardening. Analysis of SEC triple detection data shows a strong increase of the average molar mass, polydispersity, radius of gyration, and hydrodynamic radius with increasing chain extender concentration. Branching was confirmed by a decreasing Mark-Houwink exponent, and the analysis of the contraction of the molecule revealed either star-like, comb-like, random tree-like or hyperbranched structures depending on concentration and type of chain extender.