Evaluation on the degrading behavior of melt polyolefin elastomer with dicumyl peroxide in oscillatory shear flow by Fourier transform rheology

The degradation of melt polyolefin elastomer (POE) at the presence of dicumyl peroxides (DCP) was estimated at elevated temperature in oscillatory shear flow. Large amplitude oscillatory shear (LAOS) experiments followed by Fourier transform rheology (FTR) were carried out to detect and evaluate the branching architecture of the products. The third complex harmonic (I₃^∗) and other two parameters, small strain elastic shear modulus (M) and large strain elastic shear modulus (L), which describe the nonlinearity and elasticity of a material obtained from FTR, are mainly used to characterize the topological structure of polymer chains. The results indicate the degradation appeared just after a large amount of the long chain branches (LCB) created rather than as soon as the reaction started when the strain was applied within the linear viscoelastic regime of the original POE at high frequencies. This is different from our previous result that the dominant reaction was coupling in linear shear flow. The threshold strain for degradation decreased with the oscillatory frequency, and the frequency owned a different acting mechanism from the strain amplitude to cause the degradation reaction. Moreover, there is a kind of selectivity of shear rate on the polymer chains for degradation. Low frequency results in short linear scission segments and a long branched chain suffers from degradation more than once. At high frequency, the possibility of degradation at the sites near the branching points of LCB increases.     

Selection of geometry for nonlinear rheology using large amplitude oscillatory shear: Poly (vinyl alcohol) based complex network systems

Oscillatory rheology is a common technique to characterize the linear and nonlinear mechanical response of complex materials. The present work studies two crosslinked systems of poly(vinyl alcohol) (PVA): physically crosslinked PVA-Borax, and glutaraldehyde (GA) based chemically crosslinked PVA-hyaluronic acid (HA) gel. Both exhibit nonlinear viscoelasticity with characteristic intracycle mechanisms during large amplitude oscillatory shear (LAOS), owing to H-bonding (physical) and covalent (chemical) interactions respectively, unlike PVA solutions/vinyl polymer melts. Parallel plate (PP) geometry is commonly utilized for rheology of crosslinked systems due to flexible gaps, and ease to retain exact material shapes. Unlike the widely employed cone and plate (CP) geometry for LAOS analysis, the inherent deformation and flow fields are not uniform in PP, which manifests as qualitative difference in the response of the material within the two geometries. A quantitative dissimilarity in the response of PVA based crosslinked systems is demonstrated in this work. Three approaches for PP correction from literature are explored to obtain a geometry independent response of the systems. Therein, the true stresses are computed from the apparent stresses via torque balance, their harmonics, and harmonic ratios based single-point correction. The first two are shown to have limited application, owing to their implicit assumption of geometry independence in the linear regime. The third approach is found to be effective upto medium strain amplitudes. We outline these shortcomings, and present guidelines to analyze PP LAOS results for the two PVA systems. The analysis can be generalized for the broader class of complex network systems' nonlinear rheology.     

Effect of large amplitude oscillatory shear (LAOS) on the dielectric response of 1,4-cis-polyisoprene

The dielectric response of 1,4-cis-polyisoprene under applied mechanical oscillatory shear with various shear amplitudes was investigated. For this purpose, a special setup was constructed which enables to measure dielectric spectra under the influence of large amplitude oscillatory shear (LAOS); the setup is explained in detail. A strong influence of the shear amplitude on the dielectric relaxation strength was observed if the dielectric normal mode was mechanically affected. With increasing amplitude the relaxation strength decreased while the mean relaxation time, the width and asymmetry basically remained unchanged. We interpret this process as an orientational phenomenon of the end-to-end-vectors which results in a decreasing fluctuation amplitude of the polarization fluctuations.     

Effect of oscillatory shear on the interfacial morphology of a reactive bilayer polymer system

We investigated, via atomic force microscopy and transmission electron microscopy, the effect of oscillatory shearing amplitude (γ₀) and frequency (ω) on the interfacial morphology of a reactive bilayer polymer system composed of end-functionalized polystyrene with carboxylic acid (PS-mCOOH) and poly(methyl methacrylate-ran-glycidylmethacrylate) (PMMA-GMA). It has been observed that in the absence of oscillatory shearing (or at very small values of γ₀ and ω), the roughness of the interface increased with reaction period, while at large values of γ₀ and ω it became less than that observed in the absence of oscillatory shearing. This observation may be attributable to the possibility that oscillatory shearing might have hindered the diffusion of polymer chains, which are located away from the interface, to the interface of the layers. However, the effect of γ₀ and ω on the roughness of the interface of (PS-mCOOH)/(PMMA-GMA) bilayer is found to be quite different. Specifically, when a large γ₀ was first applied to the bilayer, followed by application of a low γ₀, the reactive polymer chains diffused into the interface of the (PS-mCOOH)/(PMMA-GMA) bilayer; and then the roughness of the interface increased. However, when a high ω of oscillatory shear flow was first applied to a specimen, followed by application of a low ω of oscillatory shear flow to the same specimen, a relatively low degree of roughness of the interface was observed. This is attributable to the fact that the oscillatory shear with a large ω generated a multilayer microstructure consisting of PS and PMMA layers, which apparently played the role of an obstacle (or diffusion barrier) that hindered the diffusion of both reactive polymer chains to the interface for chemical reactions.     

Correlations in rheological behavior between large amplitude oscillatory shear and steady shear flow of silica-filled star-shaped styrene-butadiene rubber compounds: Experiment and simulation

The large amplitude oscillatory shear (LAOS) and steady shear behavior of star-shaped SSBR/silica 60 phr (21 vol%) compounds with various filler surface areas was measured and simulated. An SBR gum and SBR compounds containing four different silicas with surface areas of 55, 135, 160, and 195 m²/g were utilized. Rheological behavior indicated clear correlation with surface area. LAOS tests showed an increase in dynamic moduli, shear stress, and higher order harmonic contributions with surface area. Elastic and viscous Lissajous figures showed significant distortion at intermediate and higher strain amplitudes. Additionally, ratios of third and fifth order stress harmonics to the first stress harmonic (I_3/1 and I_5/1 , respectively) showed a ''bump'' at intermediate strain amplitudes for the three highest surface area compounds. With regards to steady shear, all materials showed strong shear thinning behavior, and an increase in shear viscosity with surface area. The Cox-Merz rule was shown to be valid for the SBR gum but not for the filled compounds. However, the complex viscosity as a function of shear rate amplitude at various frequencies at high strain amplitudes and the steady shear viscosity as a function of shear rate coincided. This correlation, referred to as the Philippoff approach, has important ramifications for the rubber industry, providing quick data for predicting processing behavior. The Simhambhatla-Leonov model was successfully employed to simulate rheological behavior for the SBR gum and the lowest surface area silica compound, but the model yielded mixed results for the higher surface area silica compounds.     

Synthesis and electrorheological characteristics of titanate nanotube suspensions under oscillatory shear

In this study, titanate nanotubes (TNTs) were synthesized by hydrothermal treatment of TiO₂ powders (P25) in a NaOH solution. The as-synthesized TNTs exhibit high surface area and large aspect ratio. Rheological properties of TNTs suspensions were then investigated under oscillatory shear. The TNTs fluid shows the viscoelastic behavior and the dynamic moduli (G′, G″) increase significantly by about 4 orders of magnitude as the electric field strength is up to 2.0 kV/mm. Transient response under dynamic shear reveals different changes in the microstructure of TNTs fluid from steady shear. The complex modulus of TNTs fluids is sensitive to temperature while that of P25 fluid become insensitive at higher temperature. Dynamic viscoelastic behavior suggests that structure of P25 to TNTs transition merits the enhancement of ER activity of TNTs fluid.     

Modeling the strain dependence of torque harmonics as measured through large‐amplitude oscillatory shear rheometry

Data describing the stress response to large‐amplitude oscillatory shear can be considered as the nonlinear viscoelastic signature of polymer materials. How such data can be fitted with an appropriate equation is a problem of prime importance because (1) it allows results gathered in a large strain window to be summarized in a small number of representative parameters and (2) it permits a physical significance to be sought for equation parameters. This article analyzes and discusses several mathematical relationships that were proposed in the literature to fit harmonics vs. strain data, and probes their relative merits with various sets of experimental results. A simple four‐parameter model is shown to encompass all the other approaches and to yield parameters that correctly describe not only material behavior in the linear‐to‐nonlinear transition region but also in the asymptotic high‐strain range. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Elongational,hysteresis, and oscillatory flows of complex fluids

The simple model proposed earlier to describe te rheological properties of complex fluids is used to calculate (a) the extensional viscosity, (b) the hysteresis loops, and (c) the complex viscosity. It has been found that the rheological properties predicted by the model agree with experimental observations. It is shown that for some viscoelastic fluids the extensional viscosity is always finite and for some other fluids the extensional viscosity tends t infinity at finite extensional rate. In the latter case, steady flow is not attainable. The shape of the hysteresis loops depends on the maximum shear-rate. It also depends on the material properties. In a small amplitude oscillatory flow, our model reduces t a linear viscoelastic fluid.     

Nonlinear rheological study of magneto responsive soft gels

Swollen physical magnetorheological (MR) gels were obtained by self-assembly of triblock copolymers containing dispersed magnetic particles. We carry out a detailed investigation of the nonlinear rheological properties of MR gels under large amplitude oscillatory shear flow. A strong Payne effect is observed for strains above 0.05% which is the limit of linear viscoelastic region. The onset strain for the transition from linear to nonlinear viscoelastic behaviour is much smaller than in the absence of a magnetic field. We show that the magnetic Payne effect strongly depends on the magnetic flux density, the particle volume fraction, the sample's initial particle distribution and viscoelastic properties of the matrix.The rheological response of MR gels is strongly related to the ability for rearrangement of the particles in the presence of the magnetic field. Upon sudden application of a magnetic field, the particle network embedded in a soft matrix becomes more anisotropic than is the case in a hard matrix since the resistance of the matrix to particle rearrangement is smaller. The induced anisotropic particle network parallel to the field provides larger absolute rheological response.     

Linear viscoelasticity of discotic mesophases

The small-amplitude oscillatory capillary Poiseuille flow of uniaxial incompressible discotic nematic liquid crystals, representative of discotic mesophases, is characterized using analytical, computational, and scaling methods. Linear viscoelastic material functions are calculated and discussed in terms of fundamental anisotropic viscoelastic processes. The role of orientation to generate flow and store elastic energy is discussed. Viscoelastic behavior is found only at frequencies of similar magnitude to the single orientation relaxation time. In the terminal small-frequency zone the storage modulus scale as G^′∼ω², and the loss modulus as G^″∼ω, typical of viscous fluids. Comparisons between steady and oscillatory Poiseuille flow shows that the Cox-Merz rule is not obeyed, but that as expected the steady and complex viscosities in the terminal zone are identical. A remarkable and useful correspondence between the stored elastic energy under steady flow and the storage modulus G^′ has been discovered.     

A constitutive theory for polyolefins in large amplitude oscillatory shear

A versatile transient network theory has been used as a framework for the interpretation of large amplitude oscillatory behavior of polyolefin melts in terms of their entanglement kinetics. The model reasonably describes all previously published measurements of the large amplitude oscillatory shear behavior on melts. Seven polyolefins are examined, three new materials and four previously studied. A qualitative difference in the nonlinear behavior in large amplitude oscillatory shear has been identified between the polyethylenes examined and the two other polyolefins, polystyrene and polyisobutylene.     

Viscoelastic properties of polyamic acid solutions—precursors of polyimides

The rheology of polyamic acid (PAA) solutions, precursors of polyimides used in microelectronic device applications, has been investigated by dynamic (oscillatory) shear flow measurements. Frequency dependent storage and loss moduli and dynamic viscosity were measured in the frequency range 10^?1 to 10³ rad/s at 23°C. The storage modulus G′ (ω) and loss modulus G″ (ω) exhibited quadratic and linear dependence in frequency at low frequencies respectively, the viscoelastic fluid behavior commonly predicted for polymer solutions from many molecular theories. At high frequencies both dynamic moduli become proportional to ω^2/3. The results show that PAA solutions are very high loss viscoelastic fluids, judging from the loss tangent values which far exceed unity. It is suggested that dynamic viscoelastic properties could be used to monitor the degree of imidization since there is a gradual change from viscoelastic fluids to soft viscoelastic solids to hard viscoelastic solids as PAA is converted to polyimides. Onset of non-Newtonian flow as shown on the frequency dependent dynamic viscosity was in the range 30 to 200 rad/s. The viscoelastic constants, zero-shear rate viscosity η_o and steady-state compliance J_e⁰, where also determined from the dynamic data and compared to previous steady shear flow results.     

Soft Matter in a Tight Spot: Nanorheology of Confined Liquids and Block Copolymers

The linear frequency-dependent shear rheology and force–distance profiles of molecularly-thin fluids of very different structure were contrasted: a globular molecule octamethylcyclotetrasiloxane (OMCTS), branched alkanes (3-methylundecane and squalane), and a polymer brush in near-theta solution (polystyrene-polyvinylpyridine). In each case the data suggest a prolongation of the longest relaxation time (τ₁) with increasing compression. At frequencies ω > 1/τ₁ the shear response was “solid-like”, but at ω < 1/τ₁ it was “liquid-like”. OMCTS under mild compression exhibited seeming power-law viscoelastic behavior with G′(ω) = G″(ω) over a wide frequency range. Of the branched-molecule fluids, 3-methylundecane exhibited oscillatory force–distance profiles; this confirms prior computer simulations. But squalane (6 pendant methyl groups in an alkane chain 24 carbons long) showed one sole broad attractive minimum. Polymer brushes in a near-theta solvent exhibited changes qualitatively similar to those OMCTS, in particular, a smooth progression of longest relaxation time, generating a transition from “liquid-like” to “solid-like” shear rheology with decreasing film thickness. The common trend of shear response in these systems, in spite of important differences in molecular structure and force–distance profiles, is emphasized.     

Recovery rheology via rheo-SANS: Application to step strains under out-of-equilibrium conditions

Stress relaxation from a step strain test provides important information about constituent dynamics, but if a material has experienced a complex shear history, the underlying physics is not straightforward to access. We use recovery rheology and rheo-small-angle neutron scattering to probe the nonlinear dynamics of an entangled wormlike micelle solution by applying step strains after complex shear histories enforced by large-amplitude oscillatory shear (LAOS) flow. We show that a universal relaxation modulus can be obtained from step strain tests with complex shear histories, as long as the modulus is defined in terms of the recoverable strain. The shear and normal stresses, as well as the alignment of micellar Kuhn segments, are shown to be positively correlated with the recoverable strain. We identify re-entanglement of polymeric chains after cessation of LAOS and show that this process occurs over the same timescales as linear-regime stress relaxation. This work, therefore, lays the foundation of how to accurately probe out-of-equilibrium rheology in a consistent manner.     

Characterisation of impeller driven and oscillatory mixing by spatial and temporal shear rate distributions

Computational fluid dynamics (CFD) technique was used to model spatial and temporal behaviour of flow patterns in an impeller-driven stirred vessel (IDSV) and in an oscillatory flow baffled vessel (OFBV). The spatial and temporal shear rate distributions were assessed for IDSV based on k-ε model, appropriate for classical mixing, while the distributions for OFBV were calculated based on large eddy simulation suitable for oscillatory flow mixing. In addition, the real parameters of the vessels such as geometry, physical dimensions, impeller speed, oscillation frequency and amplitude, and density and viscosity of the fluid (water), were taken into account. Under given operating conditions the spatial shear rate distribution appears to be quite distinct for two different methods of mixing. For OFBV, the volume-averaged shear rate was found to be of one order of magnitude larger than that of IDSV. In addition, a marked distinction between the temporal shear rate distributions was observed. In OFBV, the modelling shows that particles spend most of their residence time in the high shear regions, while in IDSV, particles reside mainly in the region of considerably lower shear rates.     

Effect of organoclay on non-linear rheological properties of poly(lactic acid)/poly(caprolactone) blends

The nonlinear viscoelastic properties of PLA/PCL blends with and without clay (montmorillonite, MMT) under large amplitude oscillatory shear (LAOS) flow were investigated. The G′ and G″ as a function of strain amplitude, Lissajous plots and FT-rheology methods were used to interpret nonlinear behavior of PLA/PCL blends with and without MMT. Additionally, scanning electron microscopy (SEM) images of PLA/PCL with MMT blends were taken to investigate the effects of clay on the internal structure of the PLA/PCL blends. A relationship between morphological changes and linear and nonlinear rheological properties was observed. SEM image analysis revealed that clay acted as a compatibilizer and then reduced the size of droplets in the PCL domain of the PLA matrix. As a result, nonlinear properties sensitively reflect morphological changes with increasing MMT amount. The nonlinear rheological properties of PLA/PCL/MMT/metallocene-LLDPE (mLLDPE) were also investigated when mLLDPE was used as an impact modifier to improve mechanical properties, and the nonlinear rheological properties of PLA/PCL/MMT and PLA/PCL/MMT/mLLDPE were also compared.     

The missing parameter in rheology: hidden solid‐like correlations in viscous liquids,polymer melts and glass formers

BACKGROUND: Determination of dynamic relaxation consists of measuring the viscous and the elastic components of a material by generally applying a small (oscillatory) deformation. The shear stress is transmitted to the material via contact with a substrate. Dating at least back to Stokes, the no‐slip boundary condition between the fluid and the substrate is supposed to be fulfilled during this measurement. We show that the viscoelastic parameters of fluids are usually not determined under no‐slip boundary conditions and do not originate from the first linear regime. Viscous and viscoelastic fluids (entangled and unentangled polymers, glass formers) measured under no‐slip conditions exhibit a fundamentally different response with a dominant terminal solid‐like response. RESULTS: We show that the terminal behaviour of fluids such as liquid polymers or glass formers measured at the sub‐millimetre scale and far above the glass transition is not viscous but solid‐like. Instead of a viscoelastic behaviour scaling as ω and ω² (ω is the frequency) for the viscous and the elastic moduli, respectively, the dynamic response is simplified; for low gap thickness, both viscous and elastic moduli are invariant with respect to the frequency (with the elastic modulus being larger than the viscous modulus) and enhanced by two to four orders of magnitude compared to the conventional viscoelastic response. Over a critical strain amplitude, the solid‐like response decreases and is progressively replaced by the conventional viscoelastic behaviour. We discuss the implications of this observation and reconsider the assumptions inherent to a rheology measurement. CONCLUSION: The identification of so far neglected macroscopic elasticity in the fluidic state far above the glass transition temperature in entangled and unentangled polymers and glass formers shows that the liquid state is dominated by long range intermolecular interactions. This information is fundamental to understand and to foresee dynamic behaviour; it sheds further light on nonlinear phenomena such as large time scale relaxations, rheo‐thinning, violation of the no‐slip boundary condition and spectacular shear‐induced instabilities (spurt effect, ‘shark‐skin’ instabilities, gross melt fracture, etc.) that are unpredictable in the frame of the conventional viscoelastic approach. It also implies that the viscoelastic times (reptation, Rouse) in polymers are not the longest relaxation times of these materials. Copyright © 2009 Society of Chemical Industry     

Analysis of dynamic oscillatory rheological properties of PP/EVA/organo-modified LDH ternary hybrids based on generalized Newtonian fluid and generalized linear viscoelastic approaches

A comprehensive investigation was performed on single-step melt processed polypropylene (PP)/(ethylene vinyl acetate copolymer (EVA)/organo-modified layered double hydroxide (LDH) counterpart ternary hybrids to explore the effect of LDH loading on small-amplitude oscillatory shear (SAOS) rheological properties and to correlate the properties with microstructure. The rheological results were analyzed in detail from qualitative and quantitative perspectives. Using qualitative interoperation of storage modulus and complex viscosity alteration against LDH loading, and also quantitative analysis by viscosity models based on both the generalized Newtonian fluid (GNF) and generalized linear viscoelastic (GLVE) approaches, detailed predictions were carried out on the microstructure of samples and also partitioning of the organo-modified LDH particles and their intercalation and exfoliation extent within hybrids. By comparing the elasticity and relaxation spectrum of PP-rich/LDH with those of EVA-rich/LDH hybrids, it was predicted that organo-modified LDH platelets, in the case of PP-rich samples, have been located at the interface or within the EVA dispersed particles, while in the case of EVA-rich samples, they mainly localized within the matrix. In addition, the crossover frequency and slope of G′ and G″ curve at terminal region were correlated with the extent of intercalated and exfoliated structures of filler. The validity of these predictions on microstructure of the developed hybrids was confirmed visually using transmission electron microscope (TEM) micrographs.     

Shear thickening behavior of dilute poly(diallyl dimethyl ammonium chloride) aqueous solutions

Using dynamic light scattering (DLS) and capillary dynamic viscoelasticity (DVE) analyzer, we investigated dilute (0.5 mg/ml) poly(diallyl dimethyl ammonium chloride) (PDADMAC) aqueous solution properties for three different molecular weights of PDADMACs mixed with various concentrations of NaCl. The dependence of PDADMAC molecular chain conformations in aqueous solutions on polymer molecular weight and NaCl concentration were studied. By analyzing dynamic shear viscosity η′(ω), viscoelastic relaxation times t_r, and shear rate at tube wall ?_a(ω) of PDADMAC aqueous solutions in oscillatory flows, we proposed that polymer chain conformations varied with increasing shear frequency ω via the following steps: intra-polymer associations, dissociation of intra-polymer associations, stretching of polymer chains, inter-polymer aggregations, and dissociations of inter-polymer aggregations. The intra-polymer associations lowered the n′ exponent of storage modulus G′(ω) (G′(ω) ∼ ω^n′) with n′ < 2, and the polymer chain stretching and inter-polymer aggregations caused shear thickening (i.e. upturn of η′(ω)) of PDADMAC aqueous solutions. The behaviors of the lowering of n′ exponent with n′ < 2 and the shear thickening were favored by increasing ionic strength of solutions. By comparing η′(ω) data with DLS hydrodynamic radii (R_h) data, we also confirmed the possibility of inter-polymer aggregations in dilute solutions when polymer chains were stretched in oscillatory flows.