Víctor H. Rolón-Garrido

Analysis of medium amplitude oscillatory shear data of entangled linear and model comb polymers

Studying the mechanical response of nearly monodisperse linear and comb polystyrene (PS) melts to medium amplitude oscillatory shear (MAOS), Hyun and Wilhelm [Macromolecules 42, 411 (2009)] identified two important scaling relations: (1) The relative intensity I3/1 of the third harmonic compared to the first harmonic scales with the strain amplitude according to γ02. Consequently, a new nonlinear coefficient Q≡I3/1/γ02 as well as the so-called intrinsic nonlinearity Q0≡limγ0→0 Q was introduced. (2) In the terminal relaxation regime, the intrinsic nonlinearity Q0(ω) scales with ω2 and was found to be a very sensitive measure regarding molecular topology by identifying and separating relaxation processes in model branched polymers. A constitutive analysis based on a general single integral constitutive equation, which includes the Doi–Edwards model without (DE) and with (DE IA) independent alignment assumption as well as the molecular stress function (MSF) model, confirms both scaling relations. We show tha...

Modeling non-Gaussian extensibility effects in elongation of nearly monodisperse polystyrene melts

Elongational viscosity and birefringence of two nearly monodisperse polystyrene melts with molar mass MW of 206000gmol−1 (PS206k) and 465000gmol−1 (PS465k), respectively, were measured simultaneously by Luap et al. [Rheol. Acta. 45, 83–91 (2005)]. The samples did not follow the stress optical rule (SOR). Elongational viscosity data can be modeled quantitatively by the molecular stress function (MSF) model of Wagner et al. [J. Rheol. 49, 1317–1327 (2005)], which is based on the assumption of a strain-dependent tube diameter and the interchain pressure term of Marrucci and Ianniruberto [Macromolecules 37, 3934–3942 (2004)], and which is modified here to account for non-Gaussian chain extension using the Pade approximation of the inverse Langevin function. The tube diameter relaxation time scales with MW2. While the transient elongational viscosity shows a small dependence on finite extensibility, the predicted steady-state elongational viscosity is not affected by non-Gaussian effects. The power-law exponen...

Verification of branch point withdrawal in elongational flow of pom-pom polystyrene melt

According to tube model ideas, chain stretch at deformation rates below the inverse Rouse time of the chain, is only possible for polymer topologies with two or more branch points. The basic topologies, which embody this idea, are the H molecule with two side chains, and the pom-pom molecule with q>2 side chains at each end of the backbone. According to the pom-pom hypothesis, maximum chain stretch of the backbone is limited by branch point withdrawal, i.e., the side chains are drawn into the tube of the backbone as soon as the relative tension in the backbone reaches a value of q. This hypothesis, which has never been verified before, can now be tested by considering recent elongational experiments by Nielsen et al. [Macromolecules 39, 8844–8853 (2006)] on a nearly monodisperse polystyrene pom-pom melt with q=2.5. The analysis presented is based on the original integral version of the pom-pom model, and on the molecular stress function (MSF) model with strain-dependent tube diameter. The material strain ...

A constitutive analysis of transient and steady-state elongational viscosities of bidisperse polystyrene blends

The transient and steady-state elongational viscosity data of three bidisperse polystyrene blends were investigated recently by Nielsen et al. [J. Rheol. 50, 453–476 (2006)]. The blends contain a monodisperse high molar mass component (ML=390kg∕mol) in a matrix of a monodisperse small molar mass component (either MS=103kg∕mol or MS=52kg∕mol at two different weight fractions). The experimental data are analyzed in the framework of the molecular stress function model of Wagner et al. [J. Rheol. 49, 1317–1327 (2005)], which is based on the assumption of a strain-dependent tube diameter and the interchain pressure term of Marrucci and Ianniruberto [Macromolecules 37, 3934–3942 (2004)]. The dilution of the long chains in the matrix of the short chains is identified as the origin of a drastic increase in the tube-diameter relaxation time of the long chains, leading to a large stretching potential of the long-chain component and an increasing steady-state elongational viscosity with increasing strain rate. In ad...

The molecular stress function (MSF) model in rheology

The molecular stress function (MSF) model is an integral constitutive equation introduced more than two decades ago. It is based on the time-deformation separability principle. The time contribution encloses the linear viscoelastic information, which can be provided by the phenomenological models or any molecular theory. The deformation contribution is defined in the MSF model as a strain measure describing the orientation and the stretch of the strands of the chain as independent processes. The orientation is described by the second-order tensor of the Doi-Edwards model, considering the independent alignment assumption. The stretch is taken into account by the molecular stress function, the main characteristic being that it is included inside the integral and it is the solution of an evolution equation. Since its proposal, the MSF model has been used to describe quantitatively the non-linear rheology of a broad variety of materials such as rubbers, linear and long-chain branched polymer melts and blends of polydisperse samples relevant to the industry. Nearly, monodisperse systems in solution and melt states have also been studied in samples with different structures like linear, bidisperse blends with linear components, combs and pom-pom molecules. Predictions have been obtained for a variety of deformations like uniaxial, equibiaxial and planar extensional flow as well as for steady, medium and large amplitude oscillatory and exponential shear flow. The quantitative description of polymer melts in transient elongation is crucial for numerical simulations. Therefore, the MSF model has been applied to perform finite element simulations for different processes and freesurface deformations, due to its flexibility, reliability and reduced number of material parameters. The integral constitutive equation and its physical interpretation remains the same since it was first published. The evolution equation of the molecular stress function is material dependent because it considers different molecular mechanisms occurring in different structures. Given its importance to rheology, it is the objective of this contribution to review the antecedents, physical basis and applications of the MSF model.

Increase of long-chain branching by thermo-oxidative treatment of LDPE: Chromatographic, spectroscopic, and rheological evidence

Low-density polyethylene was thermo-oxidatively degraded at 170 °C, i.e., degraded in the presence of air, by a one thermal cycle (1C) treatment during times between 30 and 90 min, and by a two thermal cycles (2C) treatment, i.e., after storage at room temperature, an already previously degraded sample was further degraded during times between 15 and 45 min. Characterization methods include gel permeation chromatography (GPC), Fourier transform infrared (FTIR) spectroscopy, as well as linear and nonlinear rheology. A reduction of molar mass was detected for all degraded samples by GPC, as well as an increase of the high molar mass fraction of the 1C sample degraded for the longest time. Intrinsic viscosity measurements indicate also a reduction of molar mass with increasing degradation times for both 1C and 2C samples. Thermo-oxidation is confirmed for 1C and 2C samples by analyzing specific indices in FTIR. Linear viscoelasticity seems to be in general only marginally affected by thermo-oxidative exposur...

Constant force elongational flow of polymer melts: Experiment and modelling

Characterizing elongational behavior of polymer melts in constant elongation rate or constant tensile stress experiments is hampered by the onset of “necking” instabilities according to the Considere criterion: For an elastic filament, homogeneous uniaxial extension is not guaranteed for strains larger than the strain at which a maximum occurs in the force versus extension curve. Although simulations and experiments seem to indicate that in viscoelastic fluids viscosity effects delay the onset of necking to higher strains, integral measurements of elongational viscosities in Meissner- or Munstedt-type elongational rheometers are often affected by inhomogeneous deformations. A simple means of avoiding the consequences of the Considere criterion consists in operating at constant tensile force, but little attention has been paid so far to constant force elongational rheometry since the pioneering work of Raible et al. [J. Non-Newtonian Fluid Mech. 11, 239 (1982)]. Constant force elongation is also of great i...

Elongational rheology and cohesive fracture of photo-oxidated LDPE

It was found recently that low-density polyethylene (LDPE) samples with different degrees of photo-oxidation represent an interesting system to study the transition from ductile to cohesive fracture and the aspects of the cohesive rupture in elongational flow. Sheets of LDPE were subjected to photo-oxidation in the presence of air using a xenon lamp to irradiate the samples for times between 1 day and 6 weeks. Characterisation methods included Fourier transform infrared spectroscopy, solvent extraction method, and rheology in shear and uniaxial extensional flows. Linear viscoelasticity was increasingly affected by increasing photo-oxidation due to crosslinking of LDPE, as corroborated by the carbonyl index, acid and aldehydes groups, and gel fraction. The molecular stress function model was used to quantify the experimental data, and the nonlinear model parameter β was found to be correlated with the gel content. The uniaxial data showed that the transition from ductile to cohesive fracture was shifted to...

Recent Advances in Constitutive Modeling of Polymer Melts

The pressures exerted by a polymer chain on the walls of an anisotropic confinement are anisotropic. In a tube model with variable tube diameter, this leads to an evolution equation for the chain stretch with an interchain pressure term, which is inverse proportional to the 3rd power of the tube diameter a and is characterized by a tube diameter relaxation time τa [1, 2]. The tube diameter relaxation time in the evolution equation of the Molecular Stress Function (MSF) model [2] is shown to be equal to 3 times the Rouse time in the limit of small chain stretch. From this result an advanced version of the MSF model is proposed allowing modelling of the transient and steady‐state elongational viscosity data of two monodisperse polystyrene melts without using any nonlinear parameter, i.e. solely based on the linear‐viscoelastic characterization of the melts. The same approach is extended to model experimental data of two polybutadiene solutions [3] in shear flow. Thus for monodisperse polymer melts and solut...

A hierarchical multi-mode MSF model for long-chain branched polymer melts part I: elongational flow

A novel hierarchical multi-mode molecular stress function (HMMSF) model for long-chain branched (LCB) polymer melts is proposed, which implements the basic ideas of (i) the pom-pom model, (ii) hierarchal relaxation, (iii) dynamic dilution and (iv) interchain pressure. Here, the capability of this approach is demonstrated in modelling uniaxial extensional viscosity data of numerous broadly distributed long-chain branched polymer melts with only a single non-linear parameter, the dilution modulus.