Molecular Stress Function Model Research Articles

Prediction of the Bubble Growth Behavior by Means of the Time-, Temperature-, Pressure- and Blowing Agent Concentration-Dependent Transient Elongational Viscosity Function of Polymers.

Bubble growth processes are highly complex processes, which are not only dependent on the foaming process parameters (temperature, pressure and blowing agent concentration) but also on the type and structure of the polymer used. Since the elongational viscosity at the bubble wall during bubble growth also depends on these influencing factors, the so-called transient elongational viscosity plays a key role in describing the gas bubble growth behavior in polymer melts. The model-based description of the transient elongational viscosity function is difficult due to its dependence on time, Hencky strain and strain rate. Therefore, representative viscosities or shear viscosity models are usually used in the literature to predict the bubble growth behavior. In this work, the transient equibiaxial elongational viscosity function at the bubble wall during bubble growth is described holistically for the first time. This is achieved by extending the so-called molecular stress function (MSF) model by superposition principles (temperature, pressure and blowing agent concentration) and by using the elongational deformation behavior (Hencky strain and strain rate) at the bubble wall during the initial, and thus viscosity-driven, bubble growth process. Therefore, transient uniaxial elongational viscosity measurements are performed and the non-linear MSF model parameters of the two investigated polymers PS (linear polymer chains) and PLA (long-chain branched polymer chains) are determined. By applying the superposition principles and by changing the strain mode parameter to the equibiaxial case in the MSF model, the transient equibiaxial viscosity master curve is obtained and used to describe the bubble growth process. The results show that the extended MSF model can fully predict the transient equibiaxial elongational viscosity function at the bubble wall during bubble growth processes. The bubble growth behavior over time can then be realistically described using the defined transient equibiaxial elongational viscosity function at the bubble wall. This is not possible, for example, with a representative viscosity and therefore clearly demonstrates the influence and importance of knowing the transient deformation behavior that prevails at the bubble wall during bubble growth processes.

Modeling Elongational Rheology of Model Poly((±)-lactide) Graft Copolymer Bottlebrushes

The shear and elongational rheology of graft polymers with poly(norbornene) backbone and one poly((±)-lactide) side chain of length Nsc = 72 per two backbone repeat units (grafting density z=0.5) was investigated recently by Zografos et al. [Macromolecules 56, 2406–2417 (2023)]. Above the star-to-bottlebrush transition at backbone degrees of polymerization of Nbb>70, increasing strain hardening was observed with increasing Nbb, which was attributed to side-chain interdigitation resulting in enhanced friction in bottlebrush polymers. Here we show that the elongational rheology of the copolymers with entangled side chains and an unentangled backbone can be explained by the Hierarchical Multi-mode Molecular Stress Function (HMMSF) model, which takes into account hierarchical relaxation and dynamic dilution of the backbone by the side chains, leading to constrained Rouse relaxation. In nonlinear viscoelastic flows with larger Weissenberg numbers, the effect of dynamic dilution is increasingly reduced leading to stretch of the backbone chain caused by side chain constraints and resulting in strain hardening. If the backbone is sufficiently long, hyperstretching is observed at larger strain rates, i.e. the stress growth is greater than expected from affine stretch.

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

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.

Effect of thermal-oxidative and mechanical degradation of recycled LDPE on foaming

In this study, we investigated the effect of recycling process on the molecular structure, viscoelasticity and foaming behavior of low density polyethylene (LDPE). A series of LDPE samples with different recycling process was prepared by multiple extrusion using a twin-screw extruder. The molecular weight distribution (MWD) was characterized by gel permeation chromatography (GPC). Wider MWD indicated the generation of higher molecular weight products. Small-amplitude oscillation rheology showed reduced loss factors, indicating that the chain entanglement was more difficult to relax. Moreover, nonlinear viscoelasticity was investigated using elongational rheology and molecular stress function (MSF) model. The results showed a steeper strain hardening exhibited in recycled LDPE. The correlated parameter β in the MSF model indicated that the recycling did not significantly change the branches regularity in LDPE, while the increasing [Formula: see text], the other correlated parameter, indicated that the chain entanglement was enhanced, which was corresponded to the improvement of high molecular weight component. The foaming results revealed that the recycled LDPE had finer cellular structure and higher nucleation density. Moreover, despite adding PP and active CaCO3 to simulate the impurities, the foamability loss of these mixed samples was well restricted and still valuable. Recycled LDPE is instead better than its corresponding virgin one in foaming performance, exhibiting the application potential for further developments.

Experimental validation of the hierarchical multi-mode molecular stress function model in elongational flow of long-chain branched polymer melts

Experimental validation of the hierarchical multi-mode molecular stress function model in elongational flow of long-chain branched polymer melts

Modeling elongational viscosity of polystyrene Pom-Pom/linear and Pom-Pom/star blends

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 (Mw,bb = 280 kg/mol) and 22 entangled sidearms (Mw,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 Mw 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 Mw,a = 25 kg/mol having a similar span molecular weight as PS43k and similar Mw,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

Fracture in elongational flow of two low-density polyethylene melts

Samples of two commercial low-density polyethylene melts were investigated with respect to their fracture behavior in controlled uniaxial extensional flow at constant strain rate in a filament stretching rheometer. In order to assess the possible influence of grain boundaries on fracture, the samples were prepared by three different types of pre-treatment: by compression molding of (1) virgin pellets used as received, (2) pellets homogenized in a twin-screw extruder, and (3) pellets that were milled into powder by cryogenic grinding under liquid nitrogen. The elongational stress growth data were analyzed by the Extended Hierarchical Multi-mode Molecular Stress Function (EHMMSF) model developed by Wagner et al. (Rheol. Acta 61, 281-298 (2022)) for long-chain branched (LCB) polymer melts. The EHMMSF model quantifies the elongational stress growth including the maximum in the elongational viscosity of LDPE melts based solely on the linear-viscoelastic relaxation spectrum and two nonlinear material parameters, the dilution modulus GD and a characteristic stretch parameter {overline{lambda}}_m. Within experimental accuracy, model predictions are in excellent agreement with the elongational stress growth data of the two LDPE melts, independent of the preparation method used. At sufficiently high strain rates, the fracture of the polymer filaments was observed and is in general accordance with the entropic fracture criterion implemented in the EHMMSF model. High-speed videography reveals that fracture is preceded by parabolic crack opening, which is characteristic for elastic fracture and which has been observed earlier in filament stretching of monodisperse polystyrene solutions. Here, for the first time, we demonstrate the appearance of a parabolic crack opening in the fracture process of polydisperse long-chain branched polyethylene melts.

Time-Resolved Extensional Rheo-NMR Spectroscopy for Investigating Polymer Nanocomposites under Deformation

Understanding the microstructure change of polymer nanocomposites (PNCs) under elongation deformation at the molecular level is the key to coupling structure-property relationships of PNCs. In this study, we developed our recently proposed in situ extensional rheology NMR device, Rheo-spin NMR, which can simultaneously obtain both the macroscopic stress-strain curves and the microscopic molecular information with the total sample weight of ∼6 mg. This enables us to conduct a detailed investigation of the evolution of the interfacial layer and polymer matrix in nonlinear elongational strain softening behaviors. A quantitative method is established for in situ analysis of (1) the fraction of the interfacial layer and (2) the network strand orientation distribution of the polymer matrix based on the molecular stress function model under active deformation. The results show that for the current highly filled silicone nanocomposite system, the influence of the interfacial layer fraction on mechanical property change during small amplitude deformation is quite minor, while the main role is reflected in rubber network strand reorientation. The Rheo-spin NMR device and the established analysis method are expected to facilitate the understanding of the reinforcement mechanism of PNC, which can be further applied to understand the deformation mechanism of other systems, i.e., glassy and semicrystalline polymers and the vascular tissues.

Modeling elongational viscosity and brittle fracture of 10 polystyrene Pom-Poms by the hierarchical molecular stress function model

A Pom-Pom polymer with qa side chains of molecular weight Mw,a at both ends of a backbone chain of molecular weight Mw,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 Mw,b of 100 to 400 kg/mol, Mw,a of 9 to 50 kg/mol, and qa 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 GD. For the Pom-Poms considered here, we show that GD 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

Complex polymer topologies in blends: Shear and elongational rheology of linear/pom-pom polystyrene blends

The shear and elongational rheology of linear and pom-pom shaped polystyrene (PS) blends was investigated experimentally and modeled using constitutive models such as the Doi–Edwards and the molecular stress function (MSF) model. The pom-pom molecule is the simplest topology to combine shear thinning with strain hardening in elongational flow. A PS pom-pom with a self-entangled backbone (Mw,bb = 280 kg mol−1) and 22 entangled sidearms (Mw,a = 22 kg mol−1) at each star was blended with two linear PS with weight average molecular weights of Mw = 43 and 90 kg mol−1 and low polydispersities (Ð < 1.05). A semilogarithmic relationship between the weight content of the pom-pom, ϕpom-pom, and the zero-shear viscosity was found. Whereas the pure pom-pom has in uniaxial elongational flow at T = 160 °C strain hardening factors (SHFs) of SHF ≈100, similar values can be found in blends with up to ϕpom-pom = 50 wt. % in linear PS43k and PS90k. By blending only 2 wt. % pom-pom with linear PS43k, SHF = 10 can still be observed. Furthermore, above ϕpom-pom = 5–10 wt. %, the uniaxial extensional behavior can be well-described with the MSF model with a single parameter set for each linear PS matrix. The results show that the relationship between shear and elongational melt behavior, i.e., zero-shear viscosity and SHF, can be uncoupled and customized tuned by blending linear and pom-pom shaped polymers and very straightforwardly predicted theoretically. This underlines also the possible application of well-designed branched polymers as additives in recycling.

Comparison of shear viscosity and normal stress measurements by rotational and on-line slit rheometers with tube model predictions

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.

Mechanical and rheological properties and CO2-foaming behavior of reactively modified TPEE with controlled chain entanglement

Thermoplastic polyether ester elastomer (TPEE) foams can be fabricated using supercritical carbon dioxide (CO2) as an environment-friendly blowing agent. In this study, we investigated the effect of chain entanglement on the mechanical properties, viscoelasticity, and CO2-foaming behavior of TPEE. A series of branched TPEE samples with controlled chain entanglement were prepared by reactive extrusion using modifiers with epoxy groups. The gel-permeation chromatography–intrinsic viscosity (GPC-IV) methodology was employed to determine branch density. The junction point of chain entanglement was obtained; it increased at higher branch densities. The tensile behavior revealed that the branched TPEE samples became more rigid and poorer ductility, with stronger chain entanglement. Small-amplitude oscillation rheology showed enhanced shear thinning and zero-shear viscosity, reduced loss factor, and slower relaxation; these parameters indicated an improvement in linear viscoelasticity. Furthermore, nonlinear viscoelasticity was studied using elongational rheology, and the results were analyzed in combination with molecular stress function (MSF) model. The experimental results revealed that strain hardening was steeper with stronger chain entanglement, as proved by increasing value of free parameters fmax2 and β from MSF model. The reactively modified TPEE samples exhibited a larger expansion ratio than that of raw TPEE during the CO2-foaming process. Additionally, broader foaming temperature window to fabricate high-fold TPEE foams at CO2-foaming process enable the reactively modified TPEE to be used in the industrial production of TPEE foam with stable quality like bead and molded foaming.

3D simulation of the hierarchical multi-mode molecular stress function constitutive model in an abrupt contraction flow

• First simulation of the hierarchical multi-mode molecular stress function model. • The model is compared to experiment for a 3D contraction flow of Lupolen LDPE. • Striking agreement shown for vortex opening angles over a large range of flow rates. • Simulated and experimental birefringence show very good correspondence. • Variation of apparent stress optical coefficient with flow rate shown to be low. A recent development of the Molecular Stress Function constitutive model, the Hierarchical Multi-Mode Molecular Stress Function (HMMSF) model has been shown to fit a large range of rheometrical data with accuracy, for a large range of polymer melts. We develop a 3D simulation of the HMMSF model and compare it to experimental data for the flow of Lupolen 1840H LDPE through an abrupt 3D contraction flow. We believe this to be the first finite element implementation of the HMMSF model. It is shown that the model gives a striking agreement with experimental vortex opening angles, with very good agreement to full-field birefringence measurements, over a wide range of flow rates. A method to give fully-developed inlet boundary conditions is implemented (in place of using parabolic inlet boundary conditions), which gives a significantly improved match to birefringence measurements in the inlet area, and in low stress areas downstream from the inlet. Alternative constitutive model parameters are assessed following the principle that extensional rheometer data actually provides a ‘lower bound’ for peak extensional viscosity. It is shown that the model robustly maintains an accurate fit to vortex opening angle and full-field birefringence data, provided that both adjustable parameters are kept such that both shear and extensional data are well fitted.

Modelling elongational viscosity overshoot and brittle fracture of low-density polyethylene melts

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 {overline{lambda }}_{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 {overline{lambda }}_{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.

A new slit‐radial die for simultaneously measuring steady state shear viscosity and first normal stress difference of viscoelastic liquids via capillary rheometry

AbstractA new slit‐radial die capable of simultaneously obtaining steady state shear viscosity and the average first normal stress difference coefficient via capillary rheometry has been developed. The steady state shear viscosity and average first normal stress difference coefficient are calculated in the slit part and radial part of the die, respectively. The steady state shear viscosity from the slit part of the slit‐radial die is compared to shear viscosities obtained from a capillary die and also the magnitude of the complex viscosity obtained from oscillatory shear experiment. The average value of first normal stress difference coefficient which is calculated in the radial part of the slit‐radial die is compared to first normal stress difference coefficient obtained from transient shear experiment in a cone‐plate geometry and the molecular stress function model predictions. The effect of variation of power law fitting parameters (consistency index, k and power law index, n) on average value of the first normal stress difference coefficient obtained from the radial part of the slit‐radial die is discussed. As this die has the shape of the city map of Karlsruhe it is named as Karlsruhe die.

Modelling of Elongational Flow of HDPE Melts by Hierarchical Multi-Mode Molecular Stress Function Model.

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 for extensional flows reveals good agreement with elongational stress growth data. The relationship of dilution modulus to molecular characteristics (e.g., polydispersity index (PDI), long-chain branching index (LCBI), disengagement time ) 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.

Modeling of nonlinear extensional and shear rheology of low‐viscosity polymer melts

AbstractThe hierarchical multi‐mode molecular stress function (HMMSF) model developed by Narimissa and Wagner [Rheol. Acta 54, 779–791 (2015), and J. Rheol. 60, 625–636 (2016)] for linear and long‐chain branched (LCB) polymer melts were used to analyze the set of transient elongational and shear viscosity data of two LCB low‐density polyethylenes (1840H and 2426 k), and a linear poly‐(ethylene‐co‐α‐butene), PEB A‐780090 as reported by [Li et al. J. Rheol. 64, 177 (2020)], who had developed a new horizontal extensional rheometer to extend the lower limits of elongational viscosity measurements of polymer melts. Comparison between model predictions and elongational stress growth data reveals excellent agreement within the experimental window, and good consistency with shear stress growth data, based exclusively on the linear‐viscoelastic relaxation spectrum and only two nonlinear model parameters, the dilution modulus GD for extensional flows, and in addition a constraint release parameter for shear flow.

Analysis of bubble coalescence and determination of the bubble radius for long‐chain branched poly(ethylene terephthalate) melt foaming with a pressure balanced bubble‐growth model

AbstractA pressure balanced bubble‐growth (PBB) model was proposed to analyze bubble coalescence and determine the bubble radius for the melt foaming of long‐chain branched poly(ethylene terephthalate) (LCB‐PET). The key for the PBB model calculation was to determine the bubble inner pressure composed of additional pressure induced by interface tension, and molecular stress, that is, the biaxial tensile stress of the polymer cell wall calculated with the molecular stress function model. LCB‐PET was generated by reactive extrusion, and the molecular structure and viscoelasticity were well characterized. Batch melt‐foaming experiments with CO2 were conducted for the LCB‐PET. The critical coalescence radius curve was calculated with the PBB model to dynamically describe the bubble coalescence and evaluate the melt foamability. The PBB model was also used to determine the bubble size of LCB‐PET foam. Both the evaluation of the melt‐foamability and the determination of the bubble radius agreed well the experimental results.

Analysis of high melt‐strength poly(ethylene terephthalate) produced by reactive processing by shear and elongational rheology

Three grades of poly(ethylene terephthalate) (PET) produced by different synthesis routes and with different molar masses were reactively extruded with two tetra‐functional chain extenders, i.e., pyromellitic dianhydride (PMDA) and tetraglycidyl diamino diphenyl methane (TGDDM). The preferred reactivity of the coupling agents led to different long‐chain branched (LCB) structures, which can be related to different hydroxyl and carboxyl end group concentrations of the PET grades investigated. The complex viscosity and the transient elongational viscosity increased by up to two decades. Both the activation energy of flow and the loss angle indicate long‐chain branching. A more quantitative assessment of the extent of strain hardening was achieved by application of the molecular stress function (MSF) model. The two material parameters of the model revealed different behaviors depending on the chain extender used. The initial molar mass of PET and the concentration of end groups, i.e., hydroxyl and carboxyl, determine the structure of the polymer molecules. PMDA proved to be an excellent coupling agent for industrial processing which induces reproducibly either a star‐like, comb‐like, or randomly branched structure depending on the concentration of coupling agent added and the hydroxyl concentration of the PET employed. TGDDM led to a hyperbranched structure. POLYM. ENG. SCI., 59:396–410, 2019. © 2018 Society of Plastics Engineers

Review of the hierarchical multi‐mode molecular stress function model for broadly distributed linear and LCB polymer melts

We developed a novel Hierarchical Multi‐mode Molecular Stress Function (HMMSF) model for linear and long‐chain branched (LCB) polymer melts implementing the basic ideas of (1) hierarchical relaxation, (2) dynamic dilution, (3) interchain tube pressure, and (4) convective constraint release. With a minimum number of nonlinear free parameters and remarkable quantitative predictions of the rheology of polymer melts, this model is an outstanding option for the simulation of different processing operations in the polymer industry. The excellent predictions of this model were demonstrated in uniaxial, equibiaxial, and planar extensional deformations for linear and LCB melts, as well as in shear flow for a LCB polymer, with a minimum number of adjustable free nonlinear material parameters, that is, one in the case of extensional flows, and two in shear flow. In this contribution, we review the development of the HMMSF model and present a reduced number of well‐defined constitutive relations comprising the rheology of both linear and LCB melts. We also extend the comparison of model and data to cover the shear flow of a linear polymer melt. POLYM. ENG. SCI., 59:573–583, 2019. © 2018 Society of Plastics Engineers