Step Strain Experiments Research Articles

Effects of the Polydispersity on Rheological Properties of Entangled Polystyrene Solutions

Previous studies on extensional properties of entangled solutions have mainly dealt with monodisperse polymers. To investigate the effect of polydispersity on rheological properties of entangled polystyrene solutions, a polydisperse blend with an average molecular weight of 2.65 × 106 was made by mixing 18 components of nearly monodisperse polystyrene. The effect of polydispersity is illustrated by comparing the rheological behavior of this blend with that of a solution of monodisperse polymer with the same average molecular weight and at the same concentration. Shear, small-amplitude sinusoidal flow, step strain in shear, and uniaxial extension are used in this study. The multicomponent system has a much broader relaxation spectrum and a slightly smaller zero-shear-rate viscosity than the solution of monodisperse polymer. The shear thinning behavior of the two solutions are very similar except that the polydisperse system shows an earlier onset of shear thinning. In step strain experiments, the polydispe...

A critical evaluation of step strain flows of entangled linear polymer liquids

A critical evaluation of step strain flow experiments on entangled, linear polymer liquids is performed. Roughly one-half of the published shear stress relaxation modulus data for these systems are consistent with the predictions of the well-known tube model. A model of step strain flow experiments is developed to determine whether the remaining published data, which are qualitatively different from tube model predictions, are simply artifacts caused by slip, an imperfect strain step strain history, or transducer compliance. Modeling results suggest that these factors are capable of producing the types of behavior observed in experiments deemed anomalous. New criteria based on the retraction time τR, or longest Rouse relaxation time, for avoiding anomalies caused by imperfect strain step strain history and transducer compliance are proposed. These simple criteria are, in a majority of cases, found to be capable of predicting the type of observed stress relaxation behavior for 60 published step strain experiments on entangled, linear polymer liquids.

Discrete Relaxation Spectrum and K-BKZ Constitutive Equation for PVC, NBR and Their Blends

Abstract Frequency sweep experiments were performed on poly(vinyl chloride) (PVC) and acrylonitrile butadiene rubber (NBR) as well as their miscible blends PVC/NBR (70/30), PVC/NBR (50/50), and PVC/NBR (30/70) in oscillatory shear. The samples were prepared by mechanical blending at 160˚C. In order to investigate the validity of time temperature superposition (TTS) principle the loss angle δ versus the logarithm of the absolute value of the complex modulus, G*, were plotted. It was shown that the TTS principle is not valid for the above-mentioned polymer materials and therefore they are not thermorheologically simple. Master curves of PVC, NBR, and PVC/NBR (50/50) blend were therefore obtained approximately. Using a nonlinear regression method, discrete relaxation spectra were determined for PVC, NBR, and PVC/NBR (50/50). To study non-linear viscoelasticity behavior, the experiments of steady shear, start up steady shear, and step strain were carried out. The damping function was determined by the step strain experiments. Using K-BKZ constitutive equation, the shear viscosity and the shear stress growth function were calculated from the discrete relaxation spectra and the damping function and then compared to experimental data. The K-BKZ constitutive equation provides very good prediction over the entire range of experimental results.

Step-strain stress relaxation of carbon black-loaded natural rubber vulcanizates

Step-strain stress relaxation experiments were performed on natural rubber vulcanizates of various carbon black (HAF) concentrations by subjecting the samples to a very rapid strain and fixing its length at the deformed state. Time–temperature superposition in the viscoelastic region was evaluated to investigate the effect of temperature on the relaxation times of the rubbery composites. Remarkably, it was observed that, at higher HAF concentrations, increasing the temperature had a lesser effect on decreasing the overall stress values. That was attributed to the lower number of elastomeric chains per unit volume due to the agglomeration of the carbon black particles. The energy barrier resulting from the adsorption of the rubbery chains on the filler particles was insufficient to drastically reduce the diffusion and rearrangement of the polymer chains. The activation energy of the rubber-like deformation calculated from the time–temperature superposition was shown to be independent of temperature. Interestingly, the viscosity coefficients showed a large increase with a modest addition of the carbon black. This is due to the long-range nature of the temporary bonds formed between the polymer molecules and the surface-active carbon black. The stress–strain of the rubbery composites was shown to behave in a Gaussian manner in accordance with the Mooney–Rivlin relationship. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 3387–3393, 2004

Rheological study of semidilute aqueous solutions of a thermoassociative copolymer

In this paper, the linear and nonlinear rheological behavior of semidilute aqueous solutions of a recently synthesized thermoassociative graft copolymer was investigated, as a function of temperature and polymer concentration. The polymer, namely CMC–g–PNIPAM, is based on a carboxymethylcellulose (CMC) backbone bearing thermosensitive poly(N-isopropylacrylamide) (PNIPAM) sidechains. The samples have been submitted to steady shear, oscillatory shear, and step-strain experiments, mainly at temperatures above the threshold temperature Tassoc to observe thermothickening. The linear and nonlinear rheological data clearly show the existence of two temperature regimes, separated by a transition temperature T′ > Tassoc. At temperatures below T′, the solutions behave like a soft critical gel, corresponding to weak PNIPAM segregation. At temperatures above T′, the solutions behave like a stiff critical gel, corresponding to strong PNIPAM segregation.

Evaluation by means of stress relaxation (after a step strain) experiments of the viscoelastic behavior of polymer melts in uniaxial extension

As is widely acknowledged, morphology in most materials is far more sensitive to extensional than to shear deformations but, unfortunately, due to the experimental difficulties involved, there are no non-destructive, morphology probing techniques in such flows, i.e., the equivalent of stress relaxation and oscillatory experiments in shear flows. This paper tries to overcome some of those drawbacks by proposing an experimental technique that allows stress relaxation experiments after a step strain in uniaxial extension to be performed. The benefits of this technique are twofold: (a) while the deformation is small enough for the response to be in the linear viscoelastic regime it constitutes a probe of the microstructure of the material and (b) it allows the departure to the non-linear regime to be studied, useful, for example, for the definition of the damping function in uniaxial extensional flow or for the study of the response of materials to fast transient flows with a strong extensional component, such as contraction flows.

Viscoelastic Properties of Physical Gels Formed by Associative Telechelic Polyelectrolytes in Aqueous Media

We report on the viscoelastic response of a physical gel formed in aqueous solutions of poly(sodium acrylate) end-capped with short polystyrene (PS) blocks. Above a percolation threshold (cgel = 0.2 wt %) a transient network is formed constituted of PS hydrophobic domains (cross-links) interconnected via fully charged polyelctrolyte chains. Oscillatory shear and step-strain experiments were employed to study the viscoelastic properties. The stretched conformation of the charged middle blocks (bridges) and the high hydrophobicity of the PS ends have fundamental consequences on the various viscoelastic parameters: (1) The linear viscoelastic behavior is only observed at very small strains, indicating that the telechelic polyelectolytes form weak gels. (2) The magnitude of the plateau modulus, in the unentangled regime, is very high due to the stretched conformation of the polyelectrolyte chains that limits the formation of elastically inactive loops. (3) The lifetimes of the physical cross-links are influenced by the high hydrophobicity of the PS ends, compensated largely by the stretching of the polyelectrolyte chains which increases the disengagement probability. The final result is that slow mode relaxation phenomena predominate (relaxation times of the order of 102−103 s).

On the scaling of molecular weight distribution functionals

When formulating a constitutive equation model or a mixing rule for some synthetic or biological polymer, one is essentially solving an inverse problem. However, the data will not only include the results obtained from simple step strain, oscillatory shear, elongational, and other experiments, but also information about the molecular weight scaling of key rheological parameters (i.e., molecular weight distribution functionals) such as zero-shear viscosity, steady-state compliance, and the normal stress differences. In terms of incorporating such scaling information into the formulation of models, there is a need to understand the relationship between various models and their molecular weight scaling, since such information identifies the ways in which molecular weight scaling constrains the choice of possible models. In Anderssen and Mead (1998) it was established formally that the members of a quite general class of reptation mixing rules all had the same molecular weight scaling. The purpose of this paper is to first introduce the concept of a generalized reptation mixing rule, which greatly extends the class examined by Anderssen and Mead, and then show that all such rules have the same molecular weight scaling. The proof is similar to that given by Anderssen and Mead, but uses the implicit function theorem to establish the uniqueness of the mean values which arise when invoking various integral mean-value representations for the molecular weight distribution functionals considered. The rheological significance of the new generalized two-parameter mixing rule, proposed in this paper, is examined in some detail in the conclusions. In particular, it is used to established how one must construct a mixing rule for a general polydispersed polymer where the molecular dynamics involves some single, some double and some higher levels of multiple reptation. The work of Maier et al. (1998) and Thimm et al. (2000) is then utilized to illustrate and validate this proposal.

Nonlinear rheology of immiscible polymer blends: Step strain experiments

Relaxation experiments after simple shear flow were performed on (50/50) PB/PDMS poly(1-butene)/polydimethylsiloxane immiscible model blends and the results were compared to the predictions of the Doi–Ohta and Lee–Park models. Three situations of flow were examined: (i) first the variation of stress relaxation was followed in time at various step strain amplitudes, (ii) variation of stress relaxation as a function of the amplitude of preshear rate at a fixed strain, and (iii) at a fixed strain and preshear rate, the relaxation of the stress was studied as a function of the time elapsed between the end of the preshear and the step strain. After application of step strains of various magnitudes, the stress relaxation modulus G(t,γ) at short times was found to obey the Wagner time-strain separability [Wagner (1976)]. It was possible to separate linear effects from the nonlinear ones via a damping function h(γ) of sigmoidal form. After cessation of steady shear flow of different magnitudes, the linear stress ...

Percolation in a Model Transient Network: Rheology and Dynamic Light Scattering

Step strain experiments and dynamic light scattering measurements are perfomed to characterize the dynamic behavior of an o/w droplet microemulsion into which is incorporated a telechelic polymer. At sufficient droplet and polymer concentrations, above the percolation threshold, the system is viscoelastic and its dynamic structure factor shows up two steps for the relaxation of concentration fluctuations: the fast one is dominated by the diffusion but the slower one is almost independent of the wave vector. The terminal time of the stress relaxation tR and the slow time of the dynamic structure factor tS are both presumably controlled by the residence time of a sticker in a droplet: consistently, tR and tS are of the same order, they both vanishes at the percolation threshold according to power laws but with different exponents. We discuss these features in terms of deviations at the transition, from the usual mean field description of the dynamics of transient networks.

A transient network of telechelic polymers and microspheres: structure and rheology

We study the structure and dynamics of a transient network composed of droplets of microemulsion connected by telechelic polymers. The polymer induces a bridging attraction between droplets without changing their shape. A viscoelastic behaviour is induced in the initially liquid solution, characterized in the linear regime by a stretched-exponential stress relaxation. We analyse this relaxation in the light of classical theories of transient networks. The role of the elastic reorganizations in the deformed network is emphasized. In the non-linear regime, a fast relaxation dynamics is followed by a second one having the same rate as that in the linear regime. This behaviour, in step strain experiments, should induce a non-monotonic behaviour in the elastic component of the stress for a constant shear rate. However, we obtain in this case a singularity in the flow curve very different from the one observed in other systems, that we interpret in terms of fracture behaviour.

Evidence of Nonlinear Chain Stretching in the Rheology of Transient Networks

We report on telechelic associating polymers in aqueous solutions that self-assemble into starlike flowers in the dilute regime and develop a fully connected network of flowers above some threshold concentration φ* (∼1 wt %). The peculiarity of these telechelics is that the end caps are partially fluorinated. Small-angle neutron scattering has been used to investigate the form and structure factors of the starlike aggregates, and linear rheology was performed in order to identify the viscoelastic features of the physically cross-linked network. Taking advantage of the long network relaxation times, we use step-strain experiments of amplitudes γ comprised between 0.01 and 3 to explore the nonlinear regime of shear deformations. In the linear regime, the stress relaxation function is well described by a stretched exponential of the form G(t) = G0 exp(−(t/τ0)α), where G0 is the elastic modulus, τ0 the relaxation time, and α an exponent close to 1 (α ∼ 0.8). With increasing deformations (γ > 0.4), the elastic...

Compressive stress relaxation of metallocene-based polyolefin foams: Effect of gamma-ray-induced crosslinking

Metallocene-based polyolefin (MPO) foams possess a closed-cell structure which is in contrast to the open-celled structure of polyurethane (PU) foams. In this study, we investigate the effects of gamma-irradiation on the mechanical behavior of MPO foams using PU foam behavior as a basis. Compressive step-strain experiments reveal a two-step relaxation process in MPO foams, dominated by polymer chain relaxation at short times and gas diffusion from the closed cells at longer times. On the other hand, the relaxation in PU foams is similar to fully crosslinked polymers with the relaxation modulus reaching an equilibrium value after an initial decay. The closed-celled structure of MPO foams lends to rapid stress relaxation and low structural recoverability upon application of compressive loads. Exposure to gamma radiation induces crosslinking in MPO foams and improves their resilience and recoverability. Stress relaxation tests reveal that nonradiated MPO foams show complete relaxation and structural loss at high temperatures. In contrast, radiated MPO foams show a significant retardation in relaxation kinetics and structural stability attributed to radiation-induced crosslinking. Dynamic rheology and solvent-extraction studies also support the results obtained from stress-relaxation experiments. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1045–1056, 1999

Synthesis and Relaxation Dynamics of Multiarm Polybutadiene Melts

We describe synthesis and nonlinear relaxation dynamics of various multiarm entangled polybutadiene molecules of the general type A3-A-A3. In low-amplitude oscillatory shear, entangled multiarm polymers display broader relaxation spectra than linear polybutadienes of comparable molecular weight. Dramatic slowing down of cross-bar (A) relaxation by the entangled arms (A) is believed to be the source of this behavior. In nonlinear step strain experiments the A arms have a rather remarkable effect on polymer dynamics. At a critical shear strain γ of around 6.0, 〈|E·u|〉 = 3.2, the nonlinear relaxation modulus G(t;γ) abruptly decreases in value but retains similar time dependence to G(t;γ) at strains below the critical value. The sudden drop in G(t;γ) is reflected in the damping function and appears to be a consequence of arm withdrawal into the tube confining the cross-bar. This behavior is in near perfect agreement with a recent theoretical proposal for branched polymer dynamics. That this proposal is based on the notion of tensile forces on individual macromolecules due to tube confinement supports the existence of such forces and provides new circumstantial evidence for the existence of a mean-field tube. For all multiarm polymers studied we find time−strain separability at all strains with a separability time λk that appears insensitive to the arm withdrawal process. This last finding is not in agreement with current descriptions of multiarm polymer dynamics.

Relaxation of stress and orientation in thermo-reversible networks

Abstract 4-(3,5-dioxo-1,2,4-triazolidin-4-yl) benzole (U4A) or -isophthalic acid (U35A) units randomly attached to a polybutadiene backbone form extended supramolecular hydrogen bond assemblies, which act as effective junction zones in unusual thermoreversible elastomer networks. The relaxation behavior of stress and the segmental orientation induced after a sudden strain, has been investigated by means of step-strain experiments and 2 H-NMR spectroscopy. The stress relaxation behavior can be described as a two-step process in which the first step is very sensitive to the stability of the supramolecular aggregates. About 20 s after reaching the initial strain, stress is reduced to a value comparable to the yield-stress in stress-strain cycles. The long-time relaxation behavior is interpreted as a reduction of the effective cross-link density due to a gradual breakdown of the hydrogen bond clusters. The relaxation data of the functionalized polybutadienes can be superimposed to give master curves, which are characteristic for the type of junction zone. The degree of aggregate degradation is estimated as a function of the initial stress. In the same type of step-strain experiment, the 2 H-NMR spectra show a decay of the line splitting as well as a change in the complete lineshape.

Structural response of nematic liquid crystals to weak transient shear flows

Using conoscopy, we have investigated the dynamic director response of nematics to oscillatory shear and step shear strain. In oscillation, the ratio of the amplitude of the director rotation to the strain amplitude and the phase difference between the director rotation and the applied strain are measured as functions of frequency for both 5CB and 8CB. Comparison with the Leslie–Ericksen theory allows extraction of several important material parameter ratios. In particular, data in the high frequency limit yield λ, the material parameter which indicates flow‐aligning (λ≳1) or tumbling (λ<1) behavior. For 5CB at 32.5 °C, λ≊1.03, while 8CB at 34 °C gives λ≊0.42. An analysis is presented for director field relaxation following distortion induced by a step strain. Step strain experiments on 5CB and 8CB provide an independent measurement of viscoelastic properties. Aside from confirming the flow classification of these model nematics, these new experimental methods establish a framework for the study of director dynamics in polymeric nematic liquid crystals.

A note on path-dependent strain measures and strain jumps in Isotropie simple materials

It is shown here that the method often used for evaluating the discontinuity in various path-dependent strain measures for the idealized step-strain experiment leads to a violation of certain universal relations for isotropic simple fluids and solids. It is further shown how this difficulty can be avoided by a proper description of such discontinuities.

Rheological characterization of the time and strain dependence for polyisobutylene solutions

The rheological response of polyisobutylene (PIB) solutions in Decalin and a related standard fluid S1 has been characterized in dynamic oscillatory flow, step strain, step-shear rate and steady shear using a Rheometrics RDSII rheometer. The time dependence represented as a discrete spectrum of relaxation times and the strain dependence characterized as an exponential damping function have been presented as a function of PIB concentration. The relaxation spectrum was calculated from the dynamic storage modulus and loss modulus. The damping function was determined from the non-linear relaxation modulus in a step-strain experiment. The Wagner integral viscoelastic model incorporated with the relaxation and the damping function has been used to predict the stress growth and the steady-shear behaviour, which were compared with the experimental data. A novel extensional rheotester was also used in this study to measure the stretching response of polymer solutions. The data gave a near single relaxation time for each solution, and this single relaxation time obtained from uniaxial extension was correlated to the relaxation spectrum obtained in simple shear.

The gel and rheological behaviour of radiation-crosslinked linear low-density polyethylene

Linear low-density polyethylene (LLDPE) was irradiated with electron beam radiation at room temperature and in the melt. It was found that the gel point, as measured by an insoluble fraction in boiling xylene, occurred at a slightly lower radiation dose for melt irradiated samples. The melt radiation-crosslinked samples showed different melt rheological properties from the room-temperature radiation-crosslinked samples, as exemplified by the stress relaxing more slowly in a step strain experiment (relaxation modulus) for the former at a given radiation dose. The relaxation modulus could be fitted to a power-law expression consisting of two parameters, which, when plotted against each other, resulted in a single master curve for both irradiation temperatures. The curve showed two distinct regions of differing slope, which intersect at a point argued to represent a pseudogel point.

Relaxation Dynamics of Bidisperse Temporary Networks

Simultaneous measurement of IR dichroism and birefringence is used to examine the component relaxation in bidisperse, fully entangled melts of polybutadienes with 1% of the repeating units modified with 4-phenyl-1,2,4-trixoline-3,5-dione (urazole) groups. Since the urazole groups are capable of forming interchain hydrogen bonds, the rheological properties of these materials differ significantly from those of the analogous polybutadiene melts without polar stickers. Samples with 30, 50, and 70% long chains are examined by step strain and oscillatory shear experiments. In addition, the step strain experiments are carried out at two temperatures