Start-up Shear Research Articles

Nonlinear rheology and dynamics of supramolecular polymer networks formed by associative telechelic chains under shear and extensional flows

Nonequilibrium computer simulations have been applied to study the shear and extensional flow behavior of supramolecular polymer networks (SPNs) formed by unentangled and weakly entangled associative telechelic chains and their nonassociative polymer melt counterparts. The reversible bonding of the associative end monomers or stickers leads to the formation of percolated transient networks and consequently stronger mechanical properties of the SPNs than their melt counterparts. In startup shear, the transient shear viscosities η ( t ) and first normal stress coefficients Ψ 1 ( t ) of both the SPN and melt systems show overshoot behavior, but only the SPNs demonstrate transient strain hardening at high shear rates. In startup planar extensional flows, all systems demonstrate the characteristic extensional strain hardening behavior. The transient extensional viscosities η E ( t ) of the SPNs undergo a small overshoot before entering the steady state, which was not observed in the nonassociative polymer melts. For both types of polymer systems with unentangled and weakly entangled chain lengths, the steady-state shear viscosities show typical shear-thinning behavior, while the steady-state extensional viscosities demonstrate extension hardening, which are consistent with published simulation and experimental works. The observed flow behavior can be well understood from the flow-induced non-Gaussian chain stretching and segment orientation in all polymer systems studied, as well as the additional relaxation mechanisms in the SPNs, including the flow-induced reduction in the density of elastically active strands, the increment in the probability for the stickers to exchange their associated partners, and the reduction in the average sticky bond lifetimes at high strain rates.

Structural relaxation in amorphous materials under cyclic tension-compression loading

The process of structural relaxation in disordered solids subjected to repeated tension-compression loading is studied using molecular dynamics simulations. The binary glass is prepared by rapid cooling well below the glass transition temperature and then periodically strained at constant volume. We find that the amorphous system is relocated to progressively lower potential energy states during hundreds of cycles, and the energy levels become deeper upon approaching critical strain amplitude from below. The decrease in potential energy is associated with collective nonaffine rearrangements of atoms, and their rescaled probability distribution becomes independent of the cycle number at sufficiently large time intervals. It is also shown that yielding during startup shear deformation occurs at larger values of the stress overshoot in samples that were cyclically loaded at higher strain amplitudes. These results might be useful for mechanical processing of amorphous alloys in order to reduce their energy and increase chemical resistivity and resistance to crystallization.

Coupled nonhomogeneous flows and flow-enhanced concentration fluctuations during startup shear of entangled polymer solutions

A new type of transient shear banding in entangled polymer solutions observed in Taylor-Couette flow is reported. A novel combination of rheo-particle-tracking-velocimetry and rheo-microscopy reveals that the banded structure correlates with spatial variations in shear-enhanced concentration fluctuations. The results suggest that local concentration fluctuations, enhanced by shear, lead to extra dissipation within the fluid, which increases the effective fluid viscosity that can drive large flow nonuniformities when such dissipation varies spatially within the flow.

Characterization of velocity fluctuations and the transition from transient to steady state shear banding with and without pre-shear in a wormlike micelle solution under shear startup by Rheo-NMR

AbstractRheo-NMR velocimetry was used to study shear banding of a 6 wt.% cetylpyridinium chloride (CPCl) worm-like micelle solution under shear startup conditions with and without pre-shear. 1D velocity profiles across the fluid gap of a concentric cylinder Couette shear cell were measured every 1 s following shear startup for four different applied shear rates within the stress plateau. Fitting of the velocity profiles allowed calculation of the shear banding characteristics (shear rates in the high and low shear band, the interface position and apparent slip at the inner rotating wall) as the flow transitioned from transient to steady state regimes. Characteristic timescales to reach steady state were obtained and found to be similar for all shear banding characteristics. Timescales decreased with increasing applied shear rate. Large temporal fluctuations with time were also observed and Fourier transform of the time and velocity autocorrelation functions quantified the fluctuation frequencies. Frequencies corresponded to the elastically driven hydrodynamic instabilities,i.e.vortices, that are known to occur in the unstable high shear band and were dependent upon both applied shear rate and the pre-shear protocol.

Application of graphene oxide nanosheets and HPAM aqueous dispersion for improving heavy oil recovery: Effect of localized functionalization

Using efficient methods to recover heavy oil is crucial for economic success. Polymer flooding is a very efficient way to sweep oil reservoirs at both macroscopic and microscopic scales by increasing the viscosity of injected water. Recently, it was shown that addition of nanomaterials to polymer solutions may improve the flooding performance and recovery. In this work, two different types of graphene oxide (GO) nanofillers with different different location of OH group functionalization (functionalization mainly on basal plane (S-GO) and functionalization mainly on the edges (E-GO)) were synthesized to improve the rheological behavior and oil recovery efficiency of a partially hydrolyzed polyacrylamide (HPAM) solutions. To characterize the chemical structure of both GOs, thermogravimetric analysis (TGA) and Raman spectroscopy were employed. Frequency sweep, creep, creep recovery, shear start-up, and strain sweep tests were also utilized to evaluate the viscoelastic behavior of HPAM solutions, with or without the nanofillers in both linear and nonlinear viscoelastic regions. Cryo-SEM images of the hybrid dispersion of HPAM/GOs were captured to assess the dispersion state of all systems. A core flooding set up was used to evaluate the effectiveness of all dispersions in improving the viscous oil recovery by polymer injection. Rheological properties showed that addition of 0.2 wt% of both GOs reduced dynamic moduli. However, due to the better dispersion of S-GO in a HPAM solution, incorporation of 0.2 wt% of S-GO to the HPAM solution, improved the oil recovery by 7.8% compared to the HPAM solution.

Analyzing onset of nonlinearity of a colloidal gel at the critical point

In this work we study onset of nonlinear rheological behavior of a colloidal dispersion of a synthetic hectorite clay, Laponite, at the critical gel state while undergoing sol-gel transition. When subjected to step strain in the nonlinear regime, the relaxation modulus shifts vertically to the lower values such that the deviation from linearity can be accommodated using a strain dependent damping function. We also perform creep-recovery and start-up shear experiments on the studied colloidal dispersion at the critical gel state and monitor deviation in response as the flow becomes nonlinear. A quasi-linear integral model is developed with the time-strain separable relaxation modulus to account for the effect of nonlinear deformation. Remarkably, the proposed model predicts the deviation from linearity in the creep-recovery and start-up shear experiments very well leading to a simple formulation to analyze the onset of nonlinear rheological behavior in the critical gels. We also analyze the energy dissipation during the nonlinear deformation and validate the Bailey criterion using the developed viscoelastic framework.

Elucidating the Molecular Rheology of Entangled Polymeric Fluids via Comparison of Atomistic Simulations and Model Predictions

The startup and steady shear flow properties of an entangled, monodisperse linear polyethylene liquid (C1000H2002) were investigated via virtual experimentation using nonequilibrium molecular dynam...

Analysis of anisotropic rotary diffusion models for fiber orientation

Anisotropic rotary diffusion (ARD) has proved useful for modeling fiber orientation in molding of discontinuous-fiber composites. A number of ARD models have been proposed, but it has been difficult to compare models or understand the effects of each model’s parameters. We cast the framework laid out by Phelps and Tucker (JNNFM, 2009) into a new form that reveals the scalar magnitude and tensorial “direction” of rotary diffusion for each model. Existing models are compared in this framework. We illustrate the parameter values needed by each model to fit a steady-state orientation in simple shear flow and briefly discuss the behavior of the fitted models in planar elongational flow. The transient overshoot of flow-direction orientation at startup of simple shear varies considerably; however, the transient of the fourth-order component that governs shear stress is very similar among ARD models. Maps of achievable orientation states in steady simple shear are presented; these maps provide first-order estimates of the model parameters needed to fit experimental data.

Rheological signatures of aging in hard sphere colloidal glasses

Colloidal glasses are out-of-equilibrium in nature. When such materials are quenched from a shear-melted state into a quiescent one, their structure freezes due to entropic caging of the constituents. However, thermal fluctuations allow slow structural evolution, a process known as aging, in favor of minimizing free energy. Here, we examine the rheological signatures of aging, in a model system of nearly hard sphere colloidal glass. Subtle changes in the linear viscoelastic properties are detected with the age of the colloidal glass where viscous modulus shows a decrease with aging whereas the elastic modulus remains unaffected. This is associated with the slowing-down of long-time out-of-cage dynamics as the glass ages. On the contrary, nonlinear rheological measurements such as start-up shear flow, stress relaxation, and creep experiments show a strong dependence on sample age. Moreover, creep and stress relaxation experiments show ample evidence of avalanche type processes that occur during aging of colloidal glasses. Finally, comparison of creep and start-up shear flow measurements indicate that the latter is more energy efficient in inducing flow in colloidal glasses irrespective of aging dynamics.

Unveiling Temporal Nonlinear Structure-Rheology Relationships under Dynamic Shearing.

Understanding how microscopic rearrangements manifest in macroscopic flow responses is one of the central goals of nonlinear rheological studies. Using the sequence-of-physical-processes framework, we present a natural 3D structure–rheology space that temporally correlates the structural and nonlinear viscoelastic parameters. Exploiting the rheo-small-angle neutron scattering (rheo-SANS) techniques, we demonstrate the use of the framework with a model system of polymer-like micelles (PLMs), where we unveil a sequence of microscopic events that micelles experience under dynamic shearing across a range of frequencies. The least-aligned state of the PLMs is observed to migrate from the total strain extreme toward zero strain with increasing frequency. Our proposed 3D space is generic, and can be equally applied to other soft materials under any sort of deformation, such as startup shear or uniaxial extension. This work therefore provides a natural approach for researchers to study complex out-of-equilibrium structure–rheology relationships of soft materials.

Rheology of Concentrated Polymer/Ionic Liquid Solutions: An Anomalous Plasticizing Effect and a Universality in Nonlinear Shear Rheology.

An anomalous plasticizing effect was observed in polymer/ionic liquid (IL) solutions by applying broad range of rheological techniques. Poly(ethylene oxide)(PEO)/IL solutions exhibit stronger dynamic temperature dependence than pure PEO, which is in conflict with the knowledge that lower-Tg solvent increases the fractional free volume. For poly(methy methacrylate)(PMMA)/IL solutions, the subtle anomaly was detected from the fact that the effective glass transition temperature Tg,eff of PMMA in IL is higher than the prediction of the self-concentration model, while in conventional polymer solutions, Tg,eff follows the original Fox equation. Observations in both solutions reveal retarded segmental dynamics, consistent with a recent simulation result (Macromolecules, 2018, 51, 5336) that polymer chains wrap the IL cations by hydrogen bonding interactions and the segmental unwrapping delays their relaxation. Start-up shear and nonlinear stress relaxation tests of polymer/IL solutions follow a universal nonlinear rheological behavior as polymer melts and solutions, indicating that the segment-cation interaction is not strong enough to influence the nonlinear chain orientation and stretch. The present work may arouse the further theoretical, experimental, and simulation interests in interpreting the effect of complex polymer-IL interaction on the dynamics of polymer/IL solutions.

Individual Molecular Dynamics of an Entangled Polyethylene Melt Undergoing Steady Shear Flow: Steady-State and Transient Dynamics.

The startup and steady shear flow properties of an entangled, monodisperse polyethylene liquid (C1000H2002) were investigated via virtual experimentation using nonequilibrium molecular dynamics. The simulations revealed a multifaceted dynamical response of the liquid to the imposed flow field in which entanglement loss leading to individual molecular rotation plays a dominant role in dictating the bulk rheological response at intermediate and high shear rates. Under steady shear conditions, four regimes of flow behavior were evident. In the linear viscoelastic regime (), orientation of the reptation tube network dictates the rheological response. Within the second regime (), the tube segments begin to stretch mildly and the molecular entanglement network begins to relax as flow strength increases; however, the dominant relaxation mechanism in this region remains the orientation of the tube segments. In the third regime (), molecular disentangling accelerates and tube stretching dominates the response. Additionally, the rotation of molecules become a significant source of the overall dynamic response. In the fourth regime (), the entanglement network deteriorates such that some molecules become almost completely unraveled, and molecular tumbling becomes the dominant relaxation mechanism. The comparison of transient shear viscosity, , with the dynamic responses of key variables of the tube model, including the tube segmental orientation, , and tube stretch, , revealed that the stress overshoot and undershoot in steady shear flow of entangled liquids are essentially originated and dynamically controlled by the component of the tube orientation tensor, rather than the tube stretch, over a wide range of flow strengths.

Molecular dynamics simulations of crystal nucleation in entangled polymer melts under start-up shear conditions.

Understanding the flow induced crystallisation process is necessary due to its technological relevance to polymer processing. Polymer crystallisation controls the morphology of semi-crystalline polymers and hence the properties of the end product. We perform molecular dynamics simulations of polymer melts consisting of sufficiently entangled linear chains under shear flow. We determine the Rouse relaxation time (τR) for linear polymer chains using an established rheological model at different temperatures and fit the simulation data with the Arrhenius and Williams-Landel-Ferry equations. We simulate the crystallisation induction times for different values of the Rouse-Weissenberg number (WiR=γ̇τR) at different temperatures. We observe that the level of strain and stretch required to induce crystallisation increases with temperature. We find that the induction times follow a power law in shear rate and observe a more pronounced effect of flow rate for higher temperatures than at lower temperatures. Moreover, we determine that nucleation events occur relatively early in the shear transient and at a stretch value that is smaller than its steady state value. We also report the values of strain at which the occurrence of a nucleation event is most likely to happen.

Milligram Size Rheology of Molten Polymers

During laboratory practice, it is often necessary to perform rheological measurements with small specimens, mainly due to the limited availability of the investigated systems. Such a restriction occurs, for example, because the laboratory synthesis of new materials is performed on small scales, or can concern biological samples that are notoriously difficult to be extracted from living organisms. A complete rheological characterization of a viscoelastic material involves both linear and nonlinear measurements. The latter are more challenging and generally require more mass, as flow instabilities often cause material losses during the experiments. In such situations, it is crucial to perform rheological tests carefully in order to avoid experimental artifacts caused by the use of small geometries. In this paper, we indicate the drawbacks of performing linear and nonlinear rheological measurements with very small amounts of samples, and by using a well-characterized linear polystyrene, we attempt to address the challenge of obtaining reliable measurements with sample masses of the order of a milligram, in both linear and nonlinear regimes. We demonstrate that, when suitable protocols and careful running conditions are chosen, linear viscoelastic mastercurves can be obtained with good accuracy and reproducibility, working with plates as small as 3 mm in diameter and sample thickness of less than 0.2 mm. This is equivalent to polymer masses of less than 2 mg. We show also that the nonlinear start-up shear fingerprint of polymer melts can be reliably obtained with samples as small as 10 mg.

Cellulose nanocrystals in aqueous suspensions: rheology of lyotropic chiral liquid crystals

A thorough rheological study of the behavior of cellulose nanocrystals (CNC) in water was undertaken, focusing on the main characteristics of rod-like suspensions that allign under flow and can display liquid crystal behavior at rest, in at least a range of concentrations. The effect of adding a dispersing agent (gum arabic, GA) to the suspension was analyzed, and different surface treatments were also performed on the CNC using TEMPO, chloro(dodecyl)dimethylsilane and trimethoxysilyl propylmethacrylate, named as TCNC, DCNC and MCNC respectively. The CNC, TCNC and the suspensions prepared with added GA formed stable suspensions with a concentration range in which isotropic and anisotropic (self-organized) phases coexisted in equilibrium. On the other hand, the aqueous suspensions of the two silanized CNCs only displayed flow-induced ordering, with a similar type of rheological behavior to the other nanocrystal suspensions, although with obvious quantitative differences. These latter ones were not stable suspensions and precipitated after a few hours of rest. The rheological tests included steady shear, dynamic oscillations and start-up of steady shear that were performed for all the nanocrystals suspensions prepared at different concentrations. Differences observed were related to the crystals surface modifications or addition of the dispersing agent. A persistent periodic oscillation of the viscosity was measured in the start-up of steady shear tests and the periods of the oscillations were determined and related to the different types of crystals considered.

Rheological properties of ring and linear polymers under start-up shear by molecular dynamics simulations

We analyze the structure and rheological properties of ring and linear polymers under shear byusing the non-equilibrium molecular dynamics simulation. The simulation results show that compared with the ring chains, the linear polymers do not present prominent stress over shoot phenomenon. Since the overshoot reflects the maximum flow-induced deformation of the polymer, this qualitative observation already implies that the ring experience less deformation than its linear precursor in simple shear flow. This is consistent with the recent experimental result. In order to further study the molecular mechanism of this phenomenon, the segmental structure and orientation angle distribution as a function of strain under the different Weissenberg numbers are given in this study. The weak overshoot of the stretching of the ring polymers proves that the weak shear thinning and peak strain are due to the weak deformation of the segment chain of the ring in the shear flow. The rheological properties of linear and ring system are extracted from the stress-strain curves, can be used further to analyze the data. The peak strain <i>γ</i><sub>max</sub> as afunction of <i>Wi</i><sub>R</sub> follows a power-law with an exponent of 0.3 for linear polymer at <i>Wi</i><sub>R</sub>>1, however, for the ring system thepeak strain follows a power-law with an exponent of 0.1. The parameter <i>η</i><sub>max</sub>/<i>η</i><sub>steady</sub> is also the measure of the effective chain deformation at a steady state. The data show its progressive increase with <i>Wi</i><sub>R</sub> increasing, and follows a power-law with a scaling slop of 0.13 and 0.08 for linear and ring polymers, respectively. The peak stress <i>σ</i><sub>max</sub> as a function of <i>Wi</i><sub>R</sub> is also extracted from stress-strain curve. The two investigated systems both obey the scaling law with an exponent of 0.5. The normalized steady-state shear viscosity obeys a shear thinning slop of –0.86 for the linear polymer, the ring polymer obeysa shear thinning slop of –0.4. According to the gyration tensor and orientation angle, the power-law relationship between stretching and orientation is also given in this work.

Time-dependent shear rate inhomogeneities and shear bands in a thixotropic yield-stress fluid under transient shear.

We study the rheological responses and shear-rate inhomogeneities and shear banding behaviors of a thixotropic fumed silica suspension in shear startup tests and flow reversal tests. We find that this suspension under transient shear exhibits not only viscoelasticity, yielding, kinematic hardening, and thixotropy, but also time-dependent shear inhomogeneities including bands when the apparent shear rate is below a critical value between 0.1 and 0.25 s-1. Through multiple shear startup tests and flow reversal tests, we find that thixotropy promotes flow heterogeneity while kinematic hardening suppresses it. We propose a simple thixo-plastic constitutive equation that can qualitatively predict the important features of the rheological response and banding dynamics in shear startup tests and flow reversal tests.

Energy Fluctuations in Slowly Sheared Granular Materials.

Here we show the first experimental measurement of the particle-scale energy fluctuations ΔE in a slowly sheared layer of photoelastic disks. Starting from an isotropically jammed state, applying shear causes the shear-induced stochastic strengthening and weakening of particle-scale energies, whose statistics and dynamics govern the evolution of the macroscopic stress-strain curve. We find that the ΔE behave as a temperaturelike noise field, showing a novel, Boltzmann-type, double-exponential distribution at any given shear strain γ. Following the framework of the soft glassy rheology theory, we extract an effective temperature χ from the statistics of the energy fluctuations to interpret the slow startup shear (shear starts from an isotropically jammed state) of granular materials as an "aging" process: Starting below one, χ gradually approaches one as γ increases, similar to those of spin glasses, thermal glasses, and bulk metallic glasses.

Effect of Shear Rate on the Orientation and Relaxation of a Vanillic Acid Based Liquid Crystalline Polymer

In this study, we report on the visco-elastic response during start-up and cessation of shear of a novel bio-based liquid crystal polymer. The ensuing morphological changes are analyzed at different length scales by in-situ polarized optical microscopy and wide-angle X-ray diffraction. Upon inception of shear, the polydomain texture is initially stretched, at larger strain break up processes become increasingly important, and eventually a steady state texture is obtained. The shear stress response showed good coherence between optical and rheo-X-ray data. The evolution of the orientation parameter coincides with the evolution of the texture: the order parameter increases as the texture stretches, drops slightly in the break up regime, and reaches a constant value in the plateau regime. The relaxation of the shear stress and the polydomain texture showed two distinct processes with different timescales: The first is fast contraction of the stretched domain texture; the second is the slow coalescence of the polydomain texture. The timescale of the orientation parameter’s relaxation matched with that of the slow coalescence process. All processes were found to scale with shear rate in the tested regime. These observations can have far reaching implications for the processing of liquid crystal polymers as they indicate that increased shear rates during processing can correspond to an increased relaxation rate of the orientation parameter and, therefore, a decrease in anisotropy and material properties after cooling.

Rheo-NMR of transient and steady state shear banding under shear startup

In this work, shear band formation following shear startup as a function of flow protocol is investigated in the wormlike micelle (WLM) system of 6 wt. % cetylpyridinium chloride and sodium salicylate in 0.5M NaCl brine in a Couette Rheo-nuclear magnetic resonance (NMR) shear cell. Many applications using WLM solutions occur under time dependent conditions; however, shear banding under time dependent flow protocols is not as well characterized. 1D velocity profiles across the 1 mm fluid gap are recorded every 1 s after shear startup using Rheo-NMR velocimetry and used to evaluate shear banding characteristics, including the shear rates in the low and high shear band, the interface position, and the apparent wall slip as a function of time. The velocity, and therefore the shear banding characteristics, exhibits large temporal fluctuations following an abrupt startup to 12 s−1. Data were decomposed into an average and fluctuation about the average in order to extract the characteristic time scales for the transition of the flow from transient to steady state. In addition, the Fourier transform of time autocorrelation functions was used to quantify the fluctuation frequencies themselves, which are related to the apparent slip at the inner rotating wall and the presence of flow instabilities. This analysis has the potential to allow a 1D measurement to provide information about the 3D flow. Shear startup experiments were also performed for flow protocols with and without preshear. Preshear resulted in different magnitudes of the timescales and a shift in the frequencies of the fluctuation of all shear banding characteristics, emphasizing the importance of shear history on the flow behavior of these WLM solutions.