Linear Viscoelastic Measurements Research Articles

Viscoelastic and Birefringence Relaxation of Individualized Cellulose Nanofibers in the Dilute and Semidilute Regions.

Viscoelastic relaxation mechanisms of individualized cellulose nanofibers (iCNFs) dispersed in glycerol in the dilute and semidilute regions were investigated by linear viscoelastic and dynamic birefringence measurements. The birefringence relaxation of the iCNFs was described by the orientational and curvature modes of an existing viscoelastic theory for ideal semiflexible polymers (Shankar-Pasquali-Morse theory). However, the Shankar-Pasquali-Morse theory could not fully describe the iCNF viscoelastic relaxation at high frequencies. Considering the results for birefringence relaxation, the experimental tension mode of the iCNFs was evaluated to be higher than the theoretical value. These results show that the viscoelastic relaxations of the iCNFs are different from those of ideal semiflexible polymers, in contrast to cellulose nanocrystals (CNCs). As the iCNF concentration increased, the orientational mode dramatically slowed, which was more drastic than other semiflexible polymers, including CNCs. This anomalous behavior is likely due to the nonideal nature of iCNFs.

A simple rheological method for the experimental assessment of the fiber percolation threshold in short fiber biocomposites

The identification of the percolation threshold (Φc) in short fiber composites is a challenging problem in Composite Science. Above Φc the fibers form a continuous network that causes substantial changes in mechanical and transport properties. Besides, percolation of natural fibers in biodegradable polymer matrices allows water and other pro-degradative species to access the inner parts of the material from the external environment, accelerating biodegradation. Whether such a speeding up is desired or not, assessing Φc in composites is of utmost importance. Unfortunately, natural fibers are not conductive and exhibit highly variable shape and physical properties. This prevents the use of many experimental and theoretical approaches for the estimate of Φc. Here we propose an original rheological approach borrowed from the viscoelastic modelling of polymer nanocomposites. The method was applied to two systems made of poly(lactic acid) filled with hemp or kenaf fibers (average length <500 μm, average length-to-diameter ratio <5). The estimate of Φc (∼10.1 and 19.5 vol% for the hemp- and kenaf-based composite, respectively) required a single set of simple linear viscoelastic measurements, and the computed values were in good agreement with those obtained through time-consuming (measurement times >3 weeks) dielectric spectroscopy analyses (∼10.1 and 18.5 vol%).

Ionic Conduction and Dielectric Response of Nanoparticle-Coupled Hydrogel Network Polymer Electrolytes

The molecular level understanding of ion and polymer dynamics in nanoparticle-coupled hydrogel network polymer electrolytes is investigated by linear dielectric and viscoelastic measurements covering broad ranges of frequency and temperature. We prepare hydrogel polymer electrolytes (HPEs), composed of Li+ conducting hydrophilic poly(lithium acrylate) (PLiA) as the HPE matrix and vinyl-functionalized silica nanoparticles (NPs) as cross-linking points, via radical polymerization and sol–gel reaction. The NP content variation leads to changes in ionic conductivity (σDC), dielectric constant (εs), relaxation frequency, and elastic modulus, which are important characteristic factors for understanding ion transport. From the physical model of electrode polarization (EP), allowing for the determination of the number density of simultaneously conducting ions and their mobility, the NP-containing HPEs (HPE-NP) have simultaneously higher conducting ion concentration (p) and mobility (μ), resulting in higher ionic conductivity (σDC ∼ pμ), compared to the HPE without NPs. The temperature dependence of p and μ follows Arrhenius (thermally activated) and Vogel–Fulcher (segmentally driven) temperature dependences, respectively. In addition to the lower frequency EP, the HPEs show higher frequency relaxation (α2), attributed to ions rearranging. NP incorporation leads to faster α2 relaxation and higher static dielectric constant εs (shorter Bjerrum length lB). Time–temperature superposition (tTS) works well for these electrolytes and is applied to construct master curves of viscoelasticity and in-phase conductivity. In the end, the NP-containing HPE-based supercapacitor is fabricated using carbon nanotube yarn (CNTY) electrodes and shows stable electrochemical performance, demonstrating that our HPE can be a solid-state polymer electrolyte for energy storage devices.

Unexpected Slow Relaxation Dynamics in Pure Ring Polymers Arise from Intermolecular Interactions.

Ring polymers have fascinated scientists for decades, but experimental progress has been challenging due to the presence of linear chain contaminants that fundamentally alter dynamics. In this work, we report the unexpected slow stress relaxation behavior of concentrated ring polymers that arises due to ring-ring interactions and ring packing structure. Topologically pure, high molecular weight ring polymers are prepared without linear chain contaminants using cyclic poly(phthalaldehyde) (cPPA), a metastable polymer chemistry that rapidly depolymerizes from free ends at ambient temperatures. Linear viscoelastic measurements of highly concentrated cPPA show slow, non-power-law stress relaxation dynamics despite the lack of linear chain contaminants. Experiments are complemented by molecular dynamics (MD) simulations of unprecedentedly high molecular weight rings, which clearly show non-power-law stress relaxation in good agreement with experiments. MD simulations reveal substantial ring-ring interpenetrations upon increasing ring molecular weight or local backbone stiffness, despite the global collapsed nature of single ring conformation. A recently proposed microscopic theory for unconcatenated rings provides a qualitative physical mechanism associated with the emergence of strong inter-ring caging which slows down center-of-mass diffusion and long wavelength intramolecular relaxation modes originating from ring-ring interpenetrations, governed by the onset variable N/ND, where the crossover degree of polymerization ND is qualitatively predicted by theory. Our work overcomes challenges in achieving ring polymer purity and by characterizing dynamics for high molecular weight ring polymers. Overall, these results provide a new understanding of ring polymer physics.

Linking Processing Parameters and Rheology to Optimize Additive Manufacturing of k-Carrageenan Gel Systems.

Additive manufacturing—in particular, three-dimensional (3D) printing—has been introduced since the late 1980s, offering a novel paradigm for engineering design and manufacturing, as it allows the fabrication of very complex structures. Additive manufacturing of hydrogels is a very popular method to produce scaffolds to be used in tissue engineering and other biomedical applications, as well as in other advanced technological areas. When printing a thermoreversible physical hydrogel, a subtle balance between thermal and rheological parameters exists. The characteristic times of the sol–gel transition, regulated by a well-defined thermal history, must be optimized with respect to the characteristic processing times. In this work, we use this thermo-rheological approach to the additive manufacturing of a physical hydrogel. A low-cost desktop 3D printer for thermoplastic polymers was suitably modified to print a 1.5 wt% solution of k-carrageenan. The thermal behavior of the printer was determined by performing experimental measurements of the temperature–time evolution during the different processing steps, from solution loading, to the extrusion of the incoming gel, to the final solidification stage. In parallel, linear viscoelastic oscillatory shear measurements were performed in a rotational rheometer under thermal histories as close as possible to those previously measured in the printing process. The comparison between the rheological results and the quality of printing under different thermal histories is presented and discussed, highlighting the main relations between rheological and processing behavior, which are helpful in the assessment and optimization of the printing conditions.

Flow of gluten with tunable protein composition: From stress undershoot to stress overshoot and strain hardening

Understanding the origin of the unique rheological properties of wheat gluten, the protein fraction of wheat grain, is crucial in bread-making processes and has raised questions of scientists for decades. Gluten is a complex mixture of two families of proteins, monomeric gliadins and polymeric glutenins. To better understand the respective role of the different classes of proteins in the supramolecular structure of gluten and its link to the material properties, we investigate here concentrated dispersions of gluten proteins in water with a fixed total protein concentration but variable composition in gliadin and glutenin. Linear viscoelasticity measurements show a gradual increase in the viscosity of the samples as the glutenin mass content increases from 7 to 66%. While the gliadin-rich samples are microphase-separated viscous fluids, homogeneous and transparent pre-gel and gels are obtained with the replacement of gliadin by glutenin. To unravel the flow properties of the gluten samples, we perform shear startup experiments at different shear-rates. In accordance with the linear viscoelastic signature, three classes of behavior are evidenced depending on the protein composition. As samples get depleted in gliadin and enriched in glutenin, distinctive features are measured: (i) viscosity undershoot suggesting droplet elongation for microphase-separated dispersions, (ii) stress overshoot and partial structural relaxation for near-critical pre-gels, and (iii) strain hardening and flow instabilities of gels. We discuss the experimental results by analogy with the behavior of model systems, including viscoelastic emulsions, branched polymer melts, and critical gels, and provide a consistent physical picture of the supramolecular features of the three classes of protein dispersions.

Mechanical response and yielding transition of silk-fibroin and silk-fibroin/cellulose nanocrystals composite gels

We investigated the mechanical properties of gels formed by silk fibroin and silk fibroin/cellulose nanocrystal mixtures. Viscosity and linear viscoelasticity measurements showed that the addition of cellulose nanocrystals induces a speed-up of the gelation kinetics and leads to moderately stiffer gels. Combining continuous shear tests and large amplitude oscillatory shear (LAOS) measurements we additionally characterized the shear-induced solid-fluid transition. Continuous shear tests indicated a larger yield stress for the silk fibroin/cellulose nanocrystal gel, confirming thus the stiffening effect. They also revealed that the yield strain of the gels becomes smaller at higher shear rates, possibly as a result of shear-induced compaction. The detailed analysis of the full anharmonic response in LAOS measurements additionally evidenced that the fluidization of the gels is a broad and gradual transition, which is characterized by two different yield strains: one corresponding to the onset of solid melting and one to the complete fluidization of the system.

Hydrolytic Degradation of 3D-Printed Poly (Lactic Acid) Structures

Hydrolytic degradation of commercially available 3D printing filament, i.e. poly (lactic acid) with broad molecular weight distribution was induced by incubating 3D-printed parts in deionized water at 3 temperatures. Small changes in orthogonal dimensions occurred due to relaxation of printing stresses, but no mass or volume loss were detected over the time-frame of the experiments. Molecular weight decreased while polydispersity remained constant. The most sensitive measure of degradation was found to be nondestructive, small-amplitude oscillatory tensile measurements. A rapid decay of tensile storage modulus was found with an exponential decay time constant of about an hour. This work demonstrates that practical monitoring of commercially available PLA degradation can be achieve with linear viscoelastic measurements of modulus.

Composites ofABSwithSEBS‐g‐MAand copper microparticles modified by mussel‐bioinspired polydopamine: A comparative rheological study

AbstractCharacterizing and understanding composite polymeric systems' rheological behavior is essential to tune their melt flow in polymer processing machinery. Also, rheological tests are suitable tools to evaluate the microstructure and interface adhesion of polymeric composites, which are relevant parameters on the composite performance in their applications. Poly(acrylonitrile‐co‐butadiene‐co‐styrene) (ABS) and its composites are essential materials used to manufacture consumer goods necessary to maintain the quality of life of human beings. In this work, we report on polymer systems based on ABS and poly(styrene‐block‐ethylene‐co‐butylene‐block‐styrene)‐graft‐maleic anhydride (SEBS‐g‐MA) as polymer matrix containing dispersed copper microparticles (ABS:SEBS‐g‐MA:Cu). Polydopamine, a bioinspired polymer, was applied as a filler‐matrix interface compatibilizer of the composites. The linear viscoelastic rheological measurements evidence a shear‐thinning behavior for the composites, and the polydopamine coating affects the polymer phase's relaxation time. The cohesive energy density (Ec) and SEM micrographs indicate good adhesion between copper and ABS:SEBS‐g‐MA due to polydopamine interfacial adherence.

Influence of age on molecular characteristics and rheological behavior of nopal mucilage.

Nopal mucilages are of interest due to a variety of potential applications, which include their use as thickeners and rheological modifiers. In this work, changes in molecular characteristics of nopal mucilages with their age and its influence on the rheological behavior of their solutions were analyzed by light scattering, high performance liquid chromatography, a colorimetric method, and linear viscoelastic rheometrical measurements. For this, mucilages obtained from cladodes from Opuntia ficus‐indica with different ages, namely 20, 80, and 600 days, respectively, were extracted using water as solvent and then subjected to freeze‐drying. The weight‐average molecular weight (M w) of the mucilages was found to increase along with the age; meanwhile, the concentration of uronic acids increased and the galactose, rhamnose, and xylose contents decreased. Increasing M w with age resulted in enhanced viscoelastic behavior of solutions, namely, higher viscosity and elasticity at lower mucilage concentrations. Also, along with increasing M w, decrease in neutral sugar contents and increase of pectic compounds (uronic acids) and Ca+ cations in mucilages with age promoted formation of weak gels. Overall, the molecular weights and rheological behaviors reported in this work for nopal mucilages are comparable to those of widely used thickeners such as xanthan and guar gums, which suggest their use in similar applications regarding its age.

Universal Polymeric-to-Colloidal Transition in Melts of Hairy Nanoparticles.

Two different classes of hairy self-suspended nanoparticles in the melt state, polymer-grafted nanoparticles (GNPs) and star polymers, are shown to display universal dynamic behavior across a broad range of parameter space. Linear viscoelastic measurements on well-characterized silica-poly(methyl acrylate) GNPs with a fixed core radius (Rcore) and grafting density (or number of arms f) but varying arm degree of polymerization (Narm) show two distinctly different regimes of response. The colloidal Regime I with a small Narm (large core volume fraction) is characterized by predominant low-frequency solidlike colloidal plateau and ultraslow relaxation, while the polymeric Regime II with a large Narm (small core volume fractions) has a response dominated by the starlike relaxation of partially interpenetrated arms. The transition between the two regimes is marked by a crossover where both polymeric and colloidal modes are discerned albeit without a distinct colloidal plateau. Similarly, polybutadiene multiarm stars also exhibit the colloidal response of Regime I at very large f and small Narm. The star arm retraction model and a simple scaling model of nanoparticle escape from the cage of neighbors by overcoming a hopping potential barrier due to their elastic deformation quantitatively describe the linear response of the polymeric and colloidal regimes, respectively, in all these cases. The dynamic behavior of hairy nanoparticles of different chemistry and molecular characteristics, investigated here and reported in the literature, can be mapped onto a universal dynamic diagram of f/[Rcore3/ν0)1/4] as a function of (Narmν0f)/(Rcore3), where ν0 is the monomeric volume. In this diagram, the two regimes are separated by a line where the hopping potential ΔUhop is equal to the thermal energy, kBT. ΔUhop can be expressed as a function of the overcrowding parameter x (i.e., the ratio of f to the maximum number of unperturbed chains with Narm that can fill the volume occupied by the polymeric corona); hence, this crossing is shown to occur when x = 1. For x > 1, we have colloidal Regime I with an overcrowded volume, stretched arms, and ΔUhop > kBT, while polymeric Regime II is linked to x < 1. This single-material parameter x can provide the needed design principle to tailor the dynamics of this class of soft materials across a wide range of applications from membranes for gas separation to energy storage.

Relationship between large amplitude oscillatory shear (LAOS) experiments and commercial pressure sensitive adhesives applications testing

Abstract Historically, analytical test methods on pressure sensitive adhesives (PSAs) have shown modest correlation to applications test results. Since applications tests such as peel strength and shear strength involve large deformations of the adhesive, large amplitude oscillatory shear (LAOS) experiments may correlate more strongly to the applications test results than typical linear viscoelastic measurements. Here we report some of the earliest LAOS measurements on commercial PSA films and compare them to the measured peel strength and shear strength. The parameters, G’M, Q, and e3/e1, showed a strong correlation to the peel and shear results while the parameters, S, T, and v3/v1, demonstrated weaker dependencies. While detailed molecular level interpretation of the LAOS results is not possible, these results indicate LAOS testing may provide a better indication of applications performance in a more efficient way than existing applications test protocols.

Rheological properties of sulfonated polystyrene ionomers at high-ion contents

Structure and dynamics are examined for unentangled randomly-sulfonated polystyrene ionomer samples with cesium as counterion, using the X-ray scattering, DSC, and linear viscoelasticity (LVE) measurements. The large size of cesium cation leads to low association energy, enabling the dynamics to be examined for the high-ion-content samples, i.e., samples having a fraction of ionized monomers p up to 19%. X-ray scattering data shows an ionic peak, indicating the formation of ion aggregates. DSC reveals the glass transition process that shifts to higher T and broadens significantly when the ion content p is higher than 10%. In accordance with this broadening, the glassy and rubbery regimes seen in the LVE merge into one broad process with a wide relaxation distribution. We propose that the transition occurs when the number of ionic groups per chain becomes comparable to that of Kuhn segments per chain so that the polymer strands between ionic groups become non-flexible.

Microstructural characterization of a star-linear polymer blend under shear flow by using rheo-SANS

We present an investigation into the dynamic relaxation mechanisms of a polybutadiene blend composed of a four-arm star (10 wt. %) and a linear polymer matrix in the presence of an applied shear flow. Our focus was the response of the star polymer, which cannot be unambiguously assessed via linear viscoelastic measurements since the signature of the star polymer can barely be detected due to the dominant contribution of the linear matrix. By utilizing small-angle neutron scattering (SANS) coupled with a Couette shear device and a deuterated matrix polymer, we investigated the dynamics of the minority star component of the blend. Our results confirm that the stars deform anisotropically with increasing shear rate. We have compared the SANS data with predictions from the well-established scattering adaptation of the state-of-the-art tube model for entangled linear polymer melts undergoing shear, i.e., Graham, Likhtman, Milner, and McLeish (GLaMM) approach, appropriately modified following earlier studies in order to apply to the star. This modified model, GLaMM-R, includes the physics necessary to understand stress relaxation in both the linear and nonlinear flow regimes, i.e., contour length fluctuations, constraint release, convective constraint release, and chain retraction. The full scattering signal is due to the minority star component and, although the contribution of the linear chains is hidden from the neutron scattering, they still influence the star polymer molecular dynamics, with the applied shear rate ranging from approximately 8 to 24 s−1, below the inverse relaxation time of the linear component. This study provides another confirmation that the combination of rheology and neutron scattering is an indispensable tool for investigating the nonlinear dynamics of complex polymeric systems.

Chemical modification of poly(1‐butene) resins through reactive processing

AbstractControlled‐rheology poly(1‐butene) resins have been produced by chemical modification of commodity poly(1‐butene) (PB‐1) resins through reactive processing with an organic peroxide. Using various amounts of peroxide, samples have been produced and have been analyzed in terms of their molecular and rheological properties. Molecular weight distributions (MWD) as determined by gel permeation chromatography (GPC) indicate that polydispersity (PDI) remains approximately constant but weight‐average molecular weight (Mw) decreases with increasing peroxide concentration. These trends are in agreement with predictions from a kinetic model previously developed for the production of controlled‐rheology polypropylene. Linear viscoelastic measurements indicate that the modified samples are thermorheologically simple and that zero‐shear viscosity decreases with increasing peroxide concentration while flow activation energy remains approximately constant. Finally, no significant variation in melting and crystallization properties was observed for the range of peroxide concentrations used. Based on these results, it is proposed that tailor‐made controlled‐rheology poly(1‐butene) resins can be produced easily through reactive extrusion operations similar to those used for the production of controlled‐rheology polypropylene (CRPP).

Melt Rheological Behavior and Morphology of Poly(ethylene oxide)/Natural Rubber-graft-Poly(methyl methacrylate) Blends.

The influence of morphology on the rheological properties of poly(ethylene oxide) (PEO) and natural rubber-graft-poly(methyl methacrylate) (NR-g-PMMA) blends in the melt was investigated. The blends were prepared at different blend compositions by a solution-casting method. Linear viscoelastic shear oscillations measurements were performed in order to determine the elastic and viscous properties of the blends in the melt. The rheological results suggested that the blending of the two constituents reduced the elasticity and viscosity of the blends. The addition of an even small amount of NR-g-PMMA to PEO changed the liquid-like behavior of PEO to more solid-like behavior. Morphological investigations were carried out by optical microscopy to establish the relationship between morphology and melt viscosity. Depending on the blend compositions and viscosities, either droplet–matrix or co-continuous morphologies was observed. PEO/NR-g-PMMA blends exhibited a broad co-continuity range, and phase inversion was suggested to occur at the PEO/NR-g-PMMA blend with a mass ratio of 60/40 (m/m), when NR-g-PMMA was added to PEO as a matrix.

Stress relaxation in symmetric ring-linear polymer blends at low ring fractions.

We combine linear viscoelastic measurements and modelling in order to explore the dynamics of blends of the same-molecular-weight ring and linear polymers in the regime of the low volume fraction (0.3 or lower) of the ring component. The stress relaxation modulus is affected by the constraint release (CR) of both rings and linear components due to the motion of linear chains. We develop a CR-based model of ring-linear blends that predicts the stress relaxation function in the low fraction regime of ring component in excellent agreement with experiments. Rings trapped by their entanglements with linear chains can only relax by linear-chain-induced constraint release, resulting in much slower relaxation of rings than of linear chains. The relative viscosity of the blend with respect to the linear melt viscosity η L at ring overlap volume fraction increases proportionally to the square root of ring molecular weight . Our experimental results clearly demonstrate that it is possible to enhance the viscosity and simultaneously the structural relaxation time of linear polymer melts by adding a small fraction of ring polymers. These results not only provide fundamental insights into the physics of the CR process but also suggest ways to fine-tune the flow properties of linear polymers by means of adding rings.

The effect of aggregation of cured rubber particles on rheology of thermoplastic vulcanizates

AbstractIn this work, we study the effect of microstructure of rubber particle aggregates on linear and nonlinear viscoelastic properties of olefinic thermoplastic vulcanizates (TPVs) based on ethylene‐propylene‐diene rubber (EPDM) and polypropylene (PP). TPVs samples with identical rubber content and different extent of rubber particle aggregation are prepared through dynamic vulcanization of PP/EPDM blends (conventional method) with different compositions as well as dilution of PP/EPDM 40/60 TPVs. Morphological observations show larger aggregates of cured rubber particles in the diluted samples (D) compared to the ones prepared by conventional method (B). The difference between the microstructures of the two series of samples decreases with increasing rubber content. Linear viscoelastic measurements demonstrate higher elastic modulus and dynamic viscosity at low frequency for D samples compared to B ones, representing the effect of aggregation of the dispersed rubber phase. The higher extent of aggregation in D samples also leads to a lower percolation threshold and smaller linear viscoelastic region. From fitting of a structure‐dependent model on the stress growth results, longer characteristic relaxation times are obtained for D samples due to the presence of rubber aggregates. Additionally, A higher degree of orientation and less contribution of rubber aggregate destruction are found under shear flow in D samples.

Design, operation, and validation of a microrheology instrument for high-pressure linear viscoelasticity measurements

We report a passive microrheology experiment to measure the linear viscoelasticity of complex fluids at pressures of up to 200 MPa. The apparatus incorporates a sealed steel alloy sample chamber with dual sapphire windows into a diffusing wave spectroscopy (light-scattering) apparatus. We validate this high-pressure microrheology technique with 1-propanol–water mixtures and extend the measurement to hydraulic fracturing fluids containing poly(vinyl alcohol) polymer and borate as a transient, physical cross-linker. In the latter, the viscous modulus is higher than the elastic modulus at frequencies ω > 2 × 10 3 s − 1 at atmospheric pressure. The crossover of the viscous and elastic moduli shifts to lower frequencies as the storage modulus decreases with increasing pressure. The crossover shift indicates a decrease in the cross-link density, which is potentially detrimental for hydraulic fracturing fluid performance at down-hole conditions.

Improvement of Mechanical Properties of Anisotropic Glassy Polystyrene by Introducing Heat-Labile Reversible Bonds

Carboxylic acid groups were introduced into polystyrene, and the effect both on melt rheology and on mechanical properties of stretched and quenched anisotropic solids below the glass-transition temperature (Tg) was investigated. First, the facile preparation of well-defined copolymers of styrene (S) and 4-vinylbenzoic acid (A) by reversible addition–fragmentation chain-transfer polymerization was demonstrated. The evaluation of monomer reactivity ratios shows that the acid polymerizes faster than styrene but shows that block formation is suppressed under the applied conditions. Addition of acid groups leads to an increase in Tg, and this is documented by the detection of acid dimers in the glassy polymers. Importantly, linear viscoelastic measurements confirm that all the tested samples have a similar number of entanglements per chain (Z), which suggests that the acid groups do not form hydrogen bonds at temperatures above Tg. These are further confirmed by nonlinear extensional rheology of the samples i...