Step Shear Experiments Research Articles

A thermodynamic framework for modelling thixotropic yield stress fluids: Application to cement pastes

In this paper, a Helmholtz-potential-based thermodynamic approach was developed for modelling fluids that exhibit both yielding and thixotropic behavior. The yielding behavior was captured using a framework of multiple natural configurations. The thixotropy was described using a structural parameter. The Helmholtz potential is made a function of a structural parameter and a stretch quantity, and the rate of dissipation was made to depend on the rate of change of the natural configuration and the time derivative of the structural parameter. The final constitutive equations were obtained by maximizing the rate of dissipation with the reduced dissipation equation as a constraint. For experimental corroboration of the model, steady-shear and step-shear experiments were performed using cement paste. The predictions from the model were found to match well with the experimental data. Finally, the different model variants that can also be obtained using the presented framework are discussed.

Shear induced crystallization of bimodal and unimodal high density polyethylene

In-situ step-shear experiments by synchrotron X-ray techniques were performed to study shear-induced crystallization of bimodal (BM1) and unimodal (UM1) high-density polyethylene (HDPE). The BM1 sample consisted of a bimodal molecular weight (MW) and composition distribution with the low MW components having less short chain branches (SCBs), or hexene co-monomer, and the high MW components having more SCBs. The average molecular weight of BM1 was higher than that of UM1, where both BM1 and UM1 covered the same molecular weight range. The UM1 sample contained a unimodal but broad molecular weight distribution (MWD) with a constant SCB value between those of the low and high MW components in BM1. Discrete primary and secondary lamellae were found in BM1 and UM1, whereas UM1 exhibited faster secondary lamellar growth. Shear-induced crystallization resulted in higher lamellar orientation in UM1, but higher crystallinity in BM1. The large fraction of medium high MW components in UM1 was found to be effective in crystallization under deformation, leading to stronger shear-induced crystalline orientation.

Flow Activation Volume in Composites of Polystyrene and Multiwall Carbon Nanotubes with and without Functionalization

A new experimental protocol for the evaluation of the flow activation volume is proposed. It is based on step-shear experiments carried out on polymer melts. The flow activation volume evaluated agrees with the volume of a tube confining the chain, and is the same for the polymer melt and its composites with as received and functionalized carbon nanotubes. The functional groups bonded to the carbon nanotubes surface facilitate the polymer melt flow, eliminating the solid-like behavior in the high temperature flow region. A model for the morphology of polymer melts with carbon nanotubes is discussed. Polymer–nanotube interaction energies are discussed and the relaxation time of these interactions is estimated. The link between the solid-like behavior at the flow region and the strong shear thinning observed for the carbon nanotube composites is explained analyzing the different response to shear flow of each of the three networks considered by a model for the morphology of these composites.

What is the flow activation volume of entangled polymer melts?

We evaluate the flow activation volume in polymer melts of isotactic polypropylene and atactic polystyrene with step-shear experiments at different melt temperatures. The melt is initially sheared with constant shear rate until the attainment of a melt state with nearly constant viscosity. Perturbations to this experiment, involving shear steps in short-time intervals with decreasing rates, are induced next. Measurements of the shear stress value at each shear rate step allow the evaluation of an experimental (apparent) flow activation volume. The true flow activation volume is evaluated by extrapolating the experimental data to infinite shear stress values. The value obtained is larger than the physical volume of the chain and agrees with the volume of a tube confining chains with a molecular weight between M n and M w. Besides supporting the validity of tube model, experiments based on this protocol may be used on model polymer samples, in composites with nanoparticles and in polymer blends to access the validity of mechanisms considered by flow models.

Re-entrant Phase Behavior of a Concentrated Anionic Surfactant System with Strongly Binding Counterions

The phase behavior of the anionic surfactant sodium dodecyl sulfate (SDS) in the presence of the strongly binding counterion p-toluidine hydrochloride (PTHC) has been examined using small-angle X-ray diffraction and polarizing microscopy. A hexagonal-to-lamellar transition on varying the PTHC to SDS molar ratio (alpha) occurs through a nematic phase of rodlike micelles (Nc) --> isotropic (I) --> nematic of disklike micelles (N(D)) at a fixed surfactant concentration (phi). The lamellar phase is found to coexist with an isotropic phase (I') over a large region of the phase diagram. Deuterium nuclear magnetic resonance investigations of the phase behavior at phi = 0.4 confirm the transition from N(C) to N(D) on varying alpha. The viscoelastic and flow behaviors of the different phases were examined. A decrease in the steady shear viscosity across the different phases with increasing alpha suggests a decrease in the aspect ratio of the micellar aggregates. From the transient shear stress response of the N() and N(D) nematic phases in step shear experiments, they were characterized to be tumbling and flow aligning, respectively. Our studies reveal that by tuning the morphology of the surfactant micelles strongly binding counterions modify the phase behavior and rheological properties of concentrated surfactant solutions.

Practical application of thixotropic suspension models

The practical implementation of several thixotropic rheological models has been evaluated for a prototypical industrial application. We have studied the ability of the models to predict both steady and transient rheology of a suspension of alumina particles and the suitability of those models for full transient finite element calculations. The constitutive models for thixotropic materials examined include the Carreau-Yasuda model and first and second-order indirect structure models. While all of these models were able to predict the shear-thinning behavior of the steady viscosity, the first and second-order structure models were also able to capture some aspects of the transient structure formation and fluid history. However, they were not able to predict some more complex transient behavior observed in step shear experiments. For most thixotropic suspensions, the time constant required to form structure is longer than the time constant to break it down. For this suspension, the time constant at a given shear rate was also dependent on the previous shear rate. If the previous shear rate was high, the time required to reach equilibrium was longer than if the previous shear rate was lower. This behavior was not captured by the simple initial structure dependence in the previous models. By adding an additional dependence on the initial suspension structure, the prediction of the transient rheology was substantially improved while maintaining an excellent agreement with the steady shear viscosity. Finite element results are presented for extrusion of a suspension to form a fiber. This model two-dimensional problem contains many of the same complexities as practical three-dimensional mold filling simulations (i.e., nonviscometric and mobile free surface). Our results show that these direct structure models exhibit oscillations near the stick-slip point in finite element calculations similar to many polymeric constitutive equations, but are otherwise suitable for implementation in complex industrial modeling applications.

Shear rheology of a cell monolayer

We report a systematic investigation of the mechanical properties of fibroblast cells using a novel cell monolayer rheology (CMR) technique. The new technique provides quantitative rheological parameters averaged over ∼106 cells making the experiments highly reproducible. Using this method, we are able to explore a broad range of cell responses not accessible using other present day techniques. We perform harmonic oscillation experiments and step shear or step stress experiments to reveal different viscoelastic regimes. The evolution of the live cells under externally imposed cyclic loading and unloading is also studied. Remarkably, the initially nonlinear response becomes linear at long timescales as well as at large amplitudes. Within the explored rates, nonlinear behaviour is only revealed by the effect of a nonzero average stress on the response to small, fast deformations. When the cell cytoskeletal crosslinks are made permanent using a fixing agent, the large amplitude linear response disappears and the cells exhibit a stress stiffening response instead. This result shows that the dynamic nature of the cross-links and/or filaments is responsible for the linear stress-strain response seen under large deformations. We rule out the involvement of myosin motors in this using the inhibitor drug blebbistatin. These experiments provide a broad framework for understanding the mechanical responses of the cortical actin cytoskeleton of fibroblasts to different imposed mechanical stimuli.

Nonquiescent Relaxation in Entangled Polymer Liquids after Step Shear

Large step shear experiments revealed through particle tracking velocimetry that entangled polymeric liquids display either internal macroscopic movements upon shear cessation or rupturelike behavior during shear. Visible inhomogeneous motions were detected in five samples with the number of entanglements per chain ranging from 20 to 130 at amplitudes of step strain as low as 135%.

Shear-induced crystallization of isotactic poly(1‐butene)

In the present work the kinetics of the isothermal quiescent crystallization of the isotactic Poly(1-butene) (i-PB) is analyzed by means of rheological measurements and is used as an internal reference to study the effects of the shear flow. In particular, the flow-induced crystallization of two i-PB samples with different molecular weight is investigated by step-shear experiments at the crystallization temperature, Tc, of 95°C. Indeed, with step-shear experiments the effects of the applied shear rate and shear strain on the crystallization kinetics can be separately analyzed. In all the cases the overall-crystallization rate constant, k, defined as the inverse of the half-time of crystallization (t 0.5 ) has been evaluated. The results show that a critical shear rate (at a constant shear strain) and a critical shear strain (at a constant shear rate) are necessary to obtain the enhancement of k. These results significantly depend on the molecular weight revealing a stronger sensitivity to flow for the higher molecular weight sample. On the contrary, in the quiescent experiments no evidence of relevant molecular weight effects is detected. The in-situ optical analysis has shown that faster growth rates and a strong enhancement of nucleation density are observed in the step-shear experiments compared to the quiescent case.

Two-dimensional Fourier transform rheology

A two-dimensional Fourier transformation (FT) rheology experiment is presented that separates the relaxation dynamics of different contributions to the stress relaxation, here specifically for entangled polymers. This experiment has the overall form of discrete large amplitude oscillations and consists of multiple step shear experiments. It is called large amplitude step shear oscillations, LASSO. The time-dependent nonlinear material response follows the discrete periodic excitation and can therefore be Fourier transformed, which results in a spectrum of harmonics for each delay time between the steps. The FT is used here to correlate the different step shear experiments. The method was applied to a slightly entangled, polydisperse polyisobutylene solution where a small deviation of the time strain separation is detected, even at times exceeding the Rouse time by orders of magnitude. On the other hand, the time temperature superposition seems to work for all the harmonic decays within the spectrum. When the time window between the shear steps is reduced such that slow relaxation processes still possess memory of prior steps, an increase of the nonlinear contributions of the fast, completely relaxed, relaxation modes is observed. This is in qualitative agreement with reptation models where polymer stretching and orienting are considered coupled processes.

Shear-Induced Vesicle to Wormlike Micelle Transition

The present paper reports the first observation of a vesicle to wormlike micelle transition in the surfactant cetyltrimethyl ammonium 3-hydroxynaphthalene-2-carboxylate induced by shear. The structural aspects investigated by small angle neutron scattering indicate that the transition induced by shear, temperature, and added surfactant present similar aspects. Step-shear experiments indicate the presence of other shear-induced transitions with very long characteristic times.

Validity of separable BKZ model for large amplitude oscillatory shear

Large amplitude oscillatory shear (LAOS) is a useful tool for the study of nonlinear viscoelasticity in polymeric liquids. To concisely describe the response of a material to such a test, it is desirable to make use of a constitutive equation. In this way, the response can be described in terms of the parameters of the rheological model. We have found a separable BKZ model, e.g., Wagner’s equation, to be useful in this regard for LDPE IUPAC X. The damping function determined in step shear experiments does not lead to accurate predictions of the LAOS response. For a given low frequency, however, it is possible to fit the parameters of a simple damping function equation to the LAOS response at one strain amplitude and to use these parameter values to reliably predict the response at other strain amplitudes. Thus, the Wagner equation provides a basis for the concise description of the response of LDPE IUPAC X to large amplitude oscillatory shear experiments at low frequencies. Conversely, it was found that the response of a HDPE melt to large amplitude oscillatory shear cannot be concisely described by the Wagner equation.

Comparison of the rheology of polymer melts in shear, and biaxial and uniaxial extensions

The experimental properties of different polymer melts, polystyrene, high density polyethylene and low density polyethylene are compared for the first time in three different deformations: step shear, step biaxial extension and steady uniaxial extension. Properties of three other melts are also studied in step biaxial and shear experiments. For our comparative purposes some data of Laun and Winter from the literature are used, as well as new data reported here. In all the step strain experiments, the stresses can be factored into a time dependent relaxation modulus and a strain dependent damping function. The data are interpreted using a differential constitutive equation of Larson which satisfies this time-strain separability and has a single parameter that describes the strain softening character of the material. Results show that differences in the properties of the melts are most pronounced in uniaxial extension and least in biaxial extension. All melts follow the Doi-Edwards prediction relatively closely in biaxial extension. In uniaxial extension, the branched material shows a strong strain hardening effect although its shear and biaxial properties are similar to the other melts. The constitutive model gives a reasonably good fit to the data in all three deformations for unbranched materials for the same value of the adjustable parameter; the model, however, fails for the branched low density polyethylene.

Superposition of small strains on large deformations as a probe of nonlinear response in polymers

AbstractThe incremental response ΔG(t) obtained by superposing a deformation, Δγ, on a large deformation, γ1, has been determined in step shear experiments for a polyisobutylene solution and for a poly(methylmethacrylate) glass in torsion. For both systems ΔG(t) at γ1 was found to be smaller than the linear viscoelastic modulus, G(t), at zero prestrain. ΔG(t) was found to increase with increasing time, te, after imposition of the large deformation. It was also observed that the “apparent relaxation spectrum” associated with ΔG(t) narrows and shifts to shorter times when compared to the spectrum associated with the linear viscoelastic modulus, ΔG(t). The results for the solution art‐well described by the nonlinear constitutive equation of the BKZ elastic fluid theory. It is found that ΔG(t) for the glass falls between the behavior predicted by the BKZ theory and the linear viscoelastic behavior.