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A model is presented to predict the linear viscoelastic rheology of hydrophobically modified adhesive soft particle glasses in an aqueous solution. The hydrophobes on the surfaces of particles in contact preferentially associate with each other, creating an adhesive force between particles. The extent of this adhesive force depends on the number of associating or physically bonded hydrophobes and the strain on the bonds. The model is first presented for two horizontal surfaces with hydrophobes attached to them. The force required for oscillatory movement between these adhesive surfaces exhibits a Maxwellian behavior with a single relaxation time that is about the time for hydrophobe dissociation. The model is extended to predict the storage and loss moduli of adhesive soft particle glasses in ordered cubic lattices. In addition to the adhesive force, the particles also exhibit repulsive elastic and elastohydrodynamic interparticle forces. For situations where there is no adhesive force between particles, the storage modulus is independent of frequency, and the loss modulus is a linear function of frequency. The storage and loss moduli as functions of frequency are richer with adhesive forces. The storage modulus exhibits two plateaus, one at low and one at high frequency. The loss modulus exhibits a local maximum in frequency that occurs at approximately the dissociation rate of the hydrophobes.

Until the advent of the novel Enders catalysts, the nonlinear rheological characterization of polyethylene (PE) blends, containing up to 50 wt. % of ultra-high molecular weight PE (UHMWPE, with weight average molecular weight Mw > 106 g/mol) was unattainable. In this study, by melt blending of a commercially available high-density PE (polymer matrix) and PE-reactor-blends (RBs), multimodal PE blends were prepared, and their nonlinear viscoelastic properties were investigated. The experiments revealed how extraordinarily high amount of UHMWPE content and ultra-broad molecular weight distribution characterized by well separated molecular weight modes influence the nonlinear viscoelasticity. Furthermore, in order to evaluate the strain hardening ability of the multimodal PE, an approach was proposed allowing to objectively analyze and quantify the nonlinear response of the investigated samples. Analyzing the “state diagram” of the extended specimens, which captures the melt behavior and flow instabilities during uniaxial extensional measurements, unveiled that the observed SH of multimodal PE blends, at temperatures notably higher than their melting temperature, is controlled by the stretched chains of the 2nd well separated UHMWPE molecular weight mode. Moreover, it was found that, in order to highly stretch the PE chains, a characteristic strain must be applied.

Linear and nonlinear viscoelastic approaches are used to study multiphase biobased blends of poly(lactic acid), poly(amide 11), poly(ether-b-amide) (PEBA), and poly(ethylene oxide) (PEO) in a wide range of compositions. The novelty of this work resides in (a) the study of hybrid quaternary blends with droplet-matrix as well as cocontinuous morphology, (b) the effect of the PEO and PEBA blend components on the rheological properties, and (c) the investigation of the nonlinear viscoelastic regime for complex hybrid blends. Correlations are established between blend morphology and rheological behavior. Among the different linear rheological approaches, i.e., elastic modulus, complex viscosity, yield stress, Cole–Cole plots, Han plots, and Mavridish–Shroff or Booij–Palmen plots, the latter is the most sensitive allowing extraction of a relaxation time from the plot. The results correlate reasonably well with the different morphologies of the blends. Both, linear and nonlinear methods lead to compatible results, distinguishing among blends with droplet-matrix, partially continuous dispersed phase and fully cocontinuous morphologies. Moreover, for the first time, the analysis of the nonlinear parameter, Q0, allows a qualitative comparison of the interfacial areas of blends with a dispersed phase-matrix morphology at different continuity levels and those with cocontinuous morphology.

The dynamics of model colloidal gels under a steady shear flow is studied by means of a Brownian dynamics (BD) simulation while applying orthogonal superposition rheometry, which superimposes a small amplitude oscillatory flow orthogonal to the main flow direction. Orthogonal dynamic frequency sweep (ODFS) curves are obtained at various magnitudes of the main flow, which shows shear thinning behavior of the colloidal gel. The viscoelastic spectra of the ODFS can be superimposed onto a master curve by the horizontal shift factor, which is equivalent to particle viscosity. That is, the shear rate controls a single master clock for all viscoelastic spectra of the ODFS in the form of a time–shear rate superposition, which bears an analogy with the time–temperature superposition of polymeric systems. In the low-frequency region of the master curve, both orthogonal moduli are well superimposed onto a single master curve, whereas the loss modulus deviates slightly from the master curve in the high-frequency region, which coincides with the experimental findings. We observe spatial and time-varying structural properties in both low- and high-frequency regions on the ODFS curves by decomposing the pair distribution function. It is verified that each flow condition shifted onto the same stress level on the master curve shows identical spatial orthogonal moduli at all radial distances despite the differences in the aggregate size and average particle connectivity.

We study the viscoelastic solid properties of cohesive particulate suspensions using creep and constant rate tests in a vane-in-large-cup geometry. A cup-to-vane diameter ratio larger than 4 is used to ensure that wall effects are minimized. In both the creep and constant rate tests, the modulus becomes nonlinear at strains consistent with scaled interparticle bond distances. Yielding and subsequent flow do not occur until strains of order 1, corresponding to a cage melting or particle crowding failure mechanism. In between the bond and cage melting strains, the modulus shows power-law softening with an index of approximately −0.8, corresponding to progressive bond breakage. The observed behavior in creep correlates with constant rate experiments and demonstrates that strain softening of the modulus prior to yielding is an important component of the rheology of particulate gels and suspensions. The assumption of linear behavior up to yielding appears to be inappropriate. We observe that the transient creep behavior initially shows power-law or Andrade creep that transforms to an exponential decay at long times. For creep stresses that show time-dependent yield, the break time decreases exponentially with stress.

The yield stress behavior of colloidal gels with embedded active particles is studied with three experiments: start-up of steady shear, oscillatory strain amplitude sweep, and creep testing. Activity is generated by Janus particles with a platinum hemisphere; these particles undergo self-diffusiophoretic and self-electrophoretic motion in hydrogen peroxide solutions. The free particle active motion of the Janus colloids is consistent with an active energy of 25 times thermal energy at the highest hydrogen peroxide concentration studied. Consistent with prior work, the gels with embedded active particles display enhanced microdynamics and a reduction in linear viscoelastic moduli. Furthermore, at the activity levels studied, the yield stress decreases by as much as threefold for gels with an active-to-passive particle ratio of only 1:1200. We additionally find the yield strain is independent of activity. The significant reduction in yield stress at a very low active-to-passive particle ratio is modeled by combining the theory of how activity changes the spring constant of interparticle bonds in the gel with an argument that the number of active fractal clusters in the gel—rather than the number of active particles—drives the activity-induced softening of rheological properties. We estimate that 1 in 40 fractal clusters in the gel is active due to the presence of an active particle. This approach explains how an extremely small fraction of active particles causes a substantial change in both linear and nonlinear rheological properties. The results and modeling are potentially useful for the creation of gels with multistate mechanical properties.

The paraffin molecules in crude oil crystalize and precipitate out as the oil cools, resulting in a sharp increase in oil viscosity and further the gelation of the oil. The waxy crude oil gel exhibits complex rheological behaviors, such as viscoelasticity, yield stress, and thixotropy, posing challenges to the flow assurance of pipelines. Previous studies have verified that applying a high-voltage electric field to a flowing liquid oil can significantly reduce its viscosity. In this work, the electrorheological behaviors of waxy crude oil gel are explored by a stress-controlled rheometer equipped with in situ DC electric field manipulation. It is reported for the first time that the gel structure can be significantly weakened upon the application of an electric field for a duration of not less than 10 s, with the yield stress, storage modulus, loss modulus, and apparent viscosity reduced by up to 90%. In addition, the gel structure fracture is observed to transit from brittle-like to ductile-like. A stronger structure weakening effect can be obtained at a higher field strength and lower temperature. The structure weakening effect induced by the electric field can be maintained for a certain period of time after the removal of the electric field, with a recovery of yield stress and moduli less than 10% in 48 h. We hold the view that the electrorheological behaviors of waxy oil should be attributed to the weakened attraction between wax particles induced by the electric field.

We found an anomalous nonlinear behavior under large amplitude oscillatory shears, where the amplitude stress deviates strongly from the linear dependence of strain, while the time dependence of stress remains sinusoidal. This phenomenon is usually accompanied with the Payne effect of filled rubbers. In order to understand the molecular details regarding this unusual behavior, we examined a series of polybutadiene/tetradecane solutions filled with carbon black. Our results show that there is a previously unrecognized transition in the system as the matrix polymer concentration ϕ approaches and passes through a characteristic polymer concentration ϕc. Below ϕc, the system typically shows the classic nonlinearity, where the storage modulus G′ decreases as the strain amplitude γ0 increases and the resulting stress waveforms are distorted from sinusoidal waves. Above ϕc, the system displays an anomalous nonlinearity, where the stress responses at any given strain remain surprisingly sinusoidal regardless of the drop in the storage modulus G′. The critical concentration ϕc is about an order of magnitude greater than the entanglement polymer concentration ϕe. The degree of entanglement in the matrix apparently determines the occurrence of this unusual rheological event and plays a key role here. Increasing the polymer molecular weight enhances this transition.

The linear viscoelasticity of coacervates formed by oppositely charged polyelectrolytes in the salt solution is reviewed, with a focus on time-temperature, time-salt, time-pH, and time-hydration superpositions, and on fundamental relaxation mechanisms. A variety of polyelectrolyte pairs are covered, showing the frequent, but not universal, success of the time-salt superposition. Master curves in many cases are similar to those for neutral polymers, including Rouse and reptation theories. However, in some cases, solidlike, as opposed to fluidlike, response is observed at low frequencies, especially at low salt concentrations. Some coacervates seem to fit “sticky diffusion” theory reasonably well, wherein relaxation is controlled by the breakage rate of ion pairs; the dependence of the “sticker” lifetime on salt concentration has been explored but is not well understood as yet. It is also possible that local relaxation is not controlled by breakage of ion pairs but by cooperative, “glassy,” relaxation of monomers, salt ions, and water molecules. Compilation and comparison of different datasets and suggested formulas for rheological time constants are presented, and some suggestions are given for future directions.

Rheological models based on fractional order derivatives have been applied to characterize the linear viscoelasticity of asphalt cements for a long time. Such models provide continuous spectra which are fundamentally related to the molecular characteristics and facilitate analytical investigations as compared to discrete representations. With the increasing complexity in asphalt composition to satisfy various purposes, however, the inadequacy of existing fractional models has been noted. This paper proposed a generalized fractional Maxwell-dashpot (GFMD) model as a general framework for describing the modulus behaviors of asphalt cements. The generalized fractional Voigt (GFV) model was considered the counterpart for the compliances. The material functions given by each model are primarily the superposition of its constituent fractional Maxwell-dashpot or fractional Voigt (FV) elements. Geometric features of these elements were investigated such that a proper initial guess of model parameters can be obtained graphically with relative ease. For computational efficiency, the continuous spectra were discretized to provide the Prony representations of the material functions. To demonstrate the model capability, the dynamic mechanical data of a neat asphalt showing the typical behavior and a heavily polymer-modified asphalt exhibiting strong cross-linking were utilized. For the typical behavior, the GFMD and GFV models containing two fractional elements yielded excellent descriptions. A third fractional unit was necessitated in both models to account for the cross-linking mechanism for the modified asphalt. A relaxation/retardation mode density of two points equidistantly per decade produced material functions with negligible waviness and almost the same accuracy as compared to the use of the continuous spectra.

Blood-derived products, particularly platelet-rich plasma (PRP), have received increased attention in the past several years due to their great potential as a therapy for osteoarthritis and tendon injuries. Therefore, characterizing the mechanical properties of PRP becomes important to better understand its therapeutic efficacy. This paper aims to investigate the rheological properties of PRP in order to provide further insight into its mechanism of action. The PRP samples in our study may have higher erythrocyte count than the average PRP reported in the literature. Flow-sweep, small amplitude oscillatory shear (SAOS), large amplitude oscillatory shear (LAOS), and thixotropy tests have been performed at room and physiological temperatures to characterize the non-Newtonian properties of PRP samples. Flow-sweep tests reveal shear-thinning behavior, with higher apparent viscosity observed at a lower temperature. Rheological models such as Carreau, Casson, power-law, and Herschel–Bulkley have been fitted to flow-sweep data with the latter showing the closest agreement. Over the acceptable narrow range of frequency in SAOS tests, the loss modulus appears to be slightly larger than the storage modulus with both moduli decreasing at higher temperature. The nonlinear viscoelastic properties are furthermore quantified through the static and dynamic LAOS analyses. For a given strain and angular frequency, the former identifies strain-softening and shear-thinning, while the latter discloses a range of other transient behavior within an oscillation cycle. Lastly, peak-hold tests have revealed consistent thixotropy in PRP solutions.

Here, we report for the first time that resonance in dynamic-mode cantilever sensors persists in hydrogels and enables the real-time characterization of hydrogel viscoelastic properties and the continuous monitoring of sol-gel phase transitions (i.e., gelation and dissolution processes). Real-time tracking of piezoelectric-excited millimeter cantilever (PEMC) sensor resonant frequency (fair = 55.4 ± 8.8 kHz; n = 5 sensors) and quality factor (Q; Qair = 23.8 ± 1.5) enabled continuous monitoring of high-frequency hydrogel shear storage and loss moduli (G′f and G″f, respectively) calculated by sensor data and fluid–structure interaction models. Changes in the sensor phase angle, quality factor, and high-frequency shear moduli obtained at the resonant frequency (G′f and G″f) correlated with low-frequency moduli obtained at 1 Hz using dynamic mechanical analysis. Characterization studies were performed using physically and chemically crosslinked hydrogel systems, including gelatin hydrogels (6–10 wt. %) and alginate hydrogels (0.25–0.75 wt. %). The sensor exhibited a dynamic range from the rheological properties of inviscid solutions to hydrogels with high-frequency moduli of 80 kPa and low-frequency moduli of 26 kPa. The sensor exhibited a limit of detection of 260 Pa and 1.9 kPa for changes in hydrogel storage modulus (E′) based on the sensor’s phase angle and quality factor responses, respectively. We also show that sensor data enable quantitative characterization of gelation process dynamics using a modified Hill model. This work suggests that cantilever sensors provide a promising platform for the sensor-based characterization of hydrogels, such as quantification of viscoelastic properties and real-time monitoring of gelation processes.

The evolution of viscoelastic properties near the sol-gel transition is studied by performing oscillatory rheological measurements on two different types of systems: a colloidal dispersion and a thermoresponsive polymer solution under isothermal and non-isothermal conditions. While undergoing sol-gel transition, both the systems pass through a critical point. An approach to the critical point is characterized in terms of divergence of zero-shear viscosity and the subsequent appearance of the low-frequency modulus. In the vicinity of the critical gel state, both the viscosity and the modulus show a power-law dependence on the relative distance from the critical point. Interestingly, the longest relaxation time has been observed to diverge symmetrically on both sides of the critical point and also shows a power-law dependence on relative distance from the critical gel point. The critical (power-law) exponents of the zero-shear viscosity and modulus are observed to be related to the exponents of the longest relaxation time by the hyperscaling laws. The dynamic critical exponent has also been calculated from the growth of the dynamic moduli. Remarkably, the critical relaxation exponent and dynamic critical exponent predicted from the scaling laws precisely agree with the experimental values from the isothermal as well as non-isothermal experiments. The associated critical exponents show remarkable internal consistency and advocate the universality of scaling relations for different kinds of systems undergoing the sol-gel transition.

To predict the nonlinear viscoelastic behavior of polymer melts and solutions under medium amplitude oscillatory shear (MAOS) flow, we summarized known analytical MAOS material functions and derived new analytical solutions from several continuum- or molecular-based constitutive models [Johnson–Segalman, Phan-Thien–Tanner, Leonov, Larson, Pom-Pom, coupled double-convection-reptation with chain stretch (cDCR-CS), and Rouse linear entangled polymers (Rolie-Poly)]. All constitutive models discussed in this study were classified as time-strain separable or inseparable models. Whereas linear viscoelastic behavior of all constitutive models under small amplitude oscillatory shear flow was identical, the frequency-dependent signatures of four MAOS moduli (first-harmonic elastic and viscous MAOS moduli and third-harmonic elastic and viscous MAOS moduli) were model-specific, though all analytical solutions exhibited negative first-harmonic elastic MAOS moduli. In particular, tube-based constitutive models displayed a sign change in first-harmonic viscous MAOS modulus when chain retraction of the models after deformation was not instantaneous. In addition, two models for entangled linear polymers, that is, the Rolie-Poly and cDCR-CS models, displayed a second sign change in third-harmonic elastic MAOS modulus when finite chain extensibility was introduced. These results suggest that chain relaxation dynamics can be reflected in signatures of MAOS moduli. We extended single-mode predictions into multimode versions to predict the behavior of weakly or moderately entangled polystyrene solutions (effective entanglement number

A new mathematical representation for nonlinear viscoelasticity is presented based on application of the Volterra series expansion to the general nonlinear relationship between shear stress and shear strain history. This theoretical and experimental framework, which we call Medium Amplitude Parallel Superposition (MAPS) Rheology, reveals a new material property, the third order complex modulus, which describes completely the weakly nonlinear response of a viscoelastic material in an arbitrary simple shear flow. In this first part, we discuss several theoretical aspects of this mathematical formulation and new material property. For example, we show how MAPS measurements can be performed in strain- or stress-controlled contexts and provide relationships between the weakly nonlinear response functions measured in each case. We show that the MAPS response function is a super-set of the response functions that have been previously reported in medium amplitude oscillatory shear and parallel superposition rheology experiments. We also show how to exploit inherent symmetries of the MAPS response function to reduce it to a minimal domain for straightforward measurement and visualization. We compute this material property for a few constitutive models to illustrate the potential richness of the data sets generated by MAPS experiments. Finally, we discuss the MAPS framework in the context of some other nonlinear, time-dependent rheological probes and explain how the MAPS methodology has a distinct advantage over these others because it generates data embedded in a very high dimensional space without driving fluid mechanical instabilities, and is agnostic to the flow protocol., Comment: 29 pages, 10 figures

Creating an entry vortex growth simulation to show viscous and elastic fluid behaviors has always been a major challenge for the computational rheology of well-characterized polymer melts with extension thickening. For one thing, it is difficult to ensure stable convergence and reliable solutions via the viscoelastic constitutive equations at a relatively high Deborah number. From a revisitation of the generalized Newtonian fluids (GNFs), deriving the weighted viscosity is natural with the coexistence of shear and extensional flow; it is called the eXtended GNF (GNF-X) model. Herein, 3D contraction flow simulations incorporating the GNF-X weighted viscosity were significantly carried out over a wide range of Deborah numbers. Numerical results regarding changes in vortex sizes exhibit the same trend of experimental observations, while the predictive accuracy is enhanced for a quantitative comparison. More importantly, the vortex formation, in terms of the weighted viscosity and the extensional flow, is demonstrated with supporting evidence.

A particulate molecular model in which the solvent particles are considered explicitly is developed for studying the linear viscoelasticity of nanocolloidal suspensions using molecular dynamics simulations. Nanocolloidal systems of volume fractions ranging from 0.10 to 0.49 are studied. The hydrodynamics in these model systems are governed by interparticle interactions. The volume fraction dependence of the relative zero shear viscosity exhibited by this molecular model is consistent with that reported in the literature experiments and simulations. Over the range of frequencies studied, the relative dynamic viscosity values follow the same qualitative trend as that seen in the literature experiments. The time-concentration superposition (TCS) principle is successfully applied to construct the viscoelastic master curves that span nine decades of frequency in the case of the elastic modulus and more than four decades of frequency in the case of the loss modulus. The TCS principle was observed to fail at high volume fractions that are near the glass transition concentration; this finding is consistent with the literature experimental and simulation observations. The volume fraction dependence of the shift factors used in the construction of the viscoelastic master curves is in good quantitative agreement with that of the viscosity of the nanocolloidal systems. Our results demonstrate that molecular simulations in conjunction with an explicit solvent model can be used to quantitatively represent the viscosity and the viscoelastic properties of nanocolloidal suspensions. Such particulate models will be useful for studying the rheology of systems whose properties are governed by specific chemical interactions.

Rheological properties of polymer melts are significantly dependent on molecular structure and external parameters. While numerous experimental data of the dependence of the rheological behavior on stress, shear rate, and temperature are available in the literature, much less is known on the effect of hydrostatic pressure. This article reviews the knowledge about the pressure dependence of rheological properties of polymer melts. The different experimental devices for measurements under pressure are described, and the methods of determining the pressure coefficients of viscosity are critically analyzed. Very few investigations of the pressure dependence of viscoelastic properties are addressed. A comparison of the pressure coefficients of commercial polymers obtained by various authors from viscosity measurements with different methods shows the deficits in getting exact data. It can be said, however, that the pressure coefficients increase in the order of high density polyethylene, linear low-density polyethylene, low-density polyethylene, polypropylene, and polystyrene. For amorphous polymers and, particularly, for polystyrene, it is shown how the pressure coefficients decrease with growing temperature. For polyolefins, this dependency is less significant. The free volume concept is discussed with respect to an interpretation of the experimental findings. Results of using the hole fraction theory for describing the pressure dependence of viscosity are presented and critically assessed.

The rheological properties (viscosity, plasticity, viscoelasticity, and elasticity) of noncolloidal suspensions with varying concentrations of a solid phase (Al powder) in oligomeric polyethylene glycol have been studied in the shear mode of deformation. All typical types of rheological behavior have been observed. In the concentration range up to approximately 30%, suspensions are Newtonian liquids, while at a certain concentration, non-Newtonian and viscoelastic effects appear. With further increases in concentration, the flow curves become a power-law type, though the yield stress can be found only for suspensions with a high solid phase content. The elasticity of the suspensions can be detected at concentrations in the order of 55%. In a narrow range of concentrations, the rheological state of the suspensions can be treated as viscoplastic, wherein they preserve fluidity and become elastic. This concentration threshold, determined by the change in various rheological characteristics including the loss tangent, corresponds to the gelation or “colloid” glass transition. The most detailed experiments were devoted to the concentration range of 60–70 vol. %, which are treated as highly concentrated suspensions (HCSs). A concentration of 70% is the upper limit, because mixtures with higher concentrations do not keep their continuity and crumble. The rheological state of HCSs corresponds to the elastoplastic type of behavior. The separation of the total deformation into plastic and elastic components showed that plastic deformations (but not the flow) in the shearing of HCSs are small. Repeated shearing in the loading-unloading mode has been performed. In this case, a decrease in the elastic deformation and a remarkable growth of the shear elastic modulus was observed. This effect is presumably explained by the orientation of the particles and shear-induced anisotropy. A stress-concentration diagram of the physical states of suspensions has been proposed. The concentration range somewhat below that of the HCS state is of special interest for the powder injection molding technology, which is limited by the domain of plasticity.

Fresh concrete is composed of aggregates and cement paste, which itself is a dense suspension that exhibits a yield stress and serves as a binder that solidifies through cement hydration. Although there is relatively little reaction during the fresh state (i.e., before setting), there is still the formation of early hydration products that will influence the paste rheology. Nonzero stress at rest widely exists in concrete practice, e.g., interruption during pumping, static formwork casting, and 3D concrete printing, but its impact on eventual viscoelastic properties is not well understood. In this study, we investigated the influence of different levels of applied shear stress at rest on fresh cement pastes and show that it dramatically alters the eventual solid performance (i.e., static yield stress and stiffness). With increasing applied shear stress at rest, the cement paste exhibited increasing static yield stress and increasingly elastic behavior, where the origin was tied to the progression of hydration. Cement pastes were compared against magnesium oxide suspensions, which served as an inert model system, and an accelerated rate of static yield stress increase over time was observed in the former but not in the latter. This highlights the role of early cement hydration on the solidification behavior of fresh cement pastes in the presence of nonzero shear stress at rest. We further support this by showing that the structural evolution of cement paste under applied stress can primarily be attributed to an enhanced elastic limit, which is associated with early hydration. The influence of two common viscosity modifying admixtures, nanoclay and diutan gum, on these properties was also examined. This work demonstrates the importance of taking the shear stress at rest into consideration for laboratory rheological experiments and industrial concrete applications, as it can substantially impact the eventual solidification behavior.

Melt compounding of ultrahigh molecular weight polyethylene (UHMWPE) with high density polyethylene (HDPE) promises to be an alternative route to prepare bimodal polyethylene grades. However, complete dissolution of UHMWPE in HDPE cannot be guaranteed during melt compounding. Indeed, in an earlier work [K. Chaudhuri et al., Polym. Eng. Sci. 59, 821–829 (2019)], it was shown that a fully entangled UHMWPE did not mix well with commercial HDPE. However, a disentangled UHMWPE (dPE) could be melt-mixed in the same HDPE as evidenced qualitatively by rheological measurements. The present work is focused on quantifying the extent of dissolution of dPE in HDPE. The proposed method involves fitting rheological models for linear viscoelasticity of entangled bimodal blends of polydisperse polymers to dynamic oscillatory shear data and extracting information on the extent of dissolved species. The time-dependent diffusion model of des Cloizeaux is used along with the theory of double reptation (DR) to describe the dynamics of polydisperse homopolymers and also to extract the molecular weight distribution of the UHMWPE sample. A quadratic mixing rule, consistent with the DR model, is used to describe the dynamics of bimodal blends. Melt-mixed dPE/HDPE blends were prepared and characterized for their linear viscoelastic response by frequency sweep tests. The blends showed complex behavior with multiple crossover points, especially for the higher content of dPE. The bimodal model was then fit to the experimental frequency sweep data to determine the only unknown parameter, namely, the extent of dissolved dPE. It was found that a considerable fraction of dPE is dissolved in HDPE during melt compounding.Melt compounding of ultrahigh molecular weight polyethylene (UHMWPE) with high density polyethylene (HDPE) promises to be an alternative route to prepare bimodal polyethylene grades. However, complete dissolution of UHMWPE in HDPE cannot be guaranteed during melt compounding. Indeed, in an earlier work [K. Chaudhuri et al., Polym. Eng. Sci. 59, 821–829 (2019)], it was shown that a fully entangled UHMWPE did not mix well with commercial HDPE. However, a disentangled UHMWPE (dPE) could be melt-mixed in the same HDPE as evidenced qualitatively by rheological measurements. The present work is focused on quantifying the extent of dissolution of dPE in HDPE. The proposed method involves fitting rheological models for linear viscoelasticity of entangled bimodal blends of polydisperse polymers to dynamic oscillatory shear data and extracting information on the extent of dissolved species. The time-dependent diffusion model of des Cloizeaux is used along with the theory of double reptation (DR) to describe the dyn...

The effects of temperature and environmental moisture on the viscoelastic behavior of polyurethane foams were investigated both theoretically and experimentally. It was shown that the effect of the environmental parameters can be explained in terms of a variation of the free volume of the solid fraction of the foams, thus allowing the use of the superposition principle to predict their influence on the viscoelastic behavior of the materials. Dynamic mechanical analyses were performed to measure the dependence on frequency, temperature, and relative humidity of the complex modulus of two different polyurethane foams, differing in terms of their glass transition temperature. The time-temperature-humidity superposition principle was proved to be applicable for the tested materials. Next, the relaxation spectra and their dependence on the relative humidity were adopted to assess its effects on the large strain behavior of the foams.The effects of temperature and environmental moisture on the viscoelastic behavior of polyurethane foams were investigated both theoretically and experimentally. It was shown that the effect of the environmental parameters can be explained in terms of a variation of the free volume of the solid fraction of the foams, thus allowing the use of the superposition principle to predict their influence on the viscoelastic behavior of the materials. Dynamic mechanical analyses were performed to measure the dependence on frequency, temperature, and relative humidity of the complex modulus of two different polyurethane foams, differing in terms of their glass transition temperature. The time-temperature-humidity superposition principle was proved to be applicable for the tested materials. Next, the relaxation spectra and their dependence on the relative humidity were adopted to assess its effects on the large strain behavior of the foams.

The elongational viscosity data of Bach et al. [Macromolecules 36, 5174–5179 (2003)] and Huang et al. [ACS Macro Lett. 2, 741–744 (2013); Macromolecules 48, 4158–4163 (2015); Macromolecules 46, 5026–5035 (2013)] on monodisperse polystyrene melts and concentrated polystyrene solutions in oligomeric styrene represent a unique benchmark for improving the tube model of Doi and Edwards with respect to its predictive capabilities of nonlinear viscoelasticity and especially chain stretch. By relaxing one of the basic assumptions of the original tube model of Doi and Edwards [J. Chem. Soc., Faraday Trans. 2 Mol. Chem. Phys. 74, 1802–1817 (1978); J. Chem. Soc., Faraday Trans. 2 Mol. Chem. Phys. 74, 1818–1832 (1978)], i.e., the assumption of a constant tube diameter, and assuming that chain stretch is inversely proportional to a deformation-dependent tube diameter, the extended interchain pressure (EIP) theory [Wagner and Rolon-Garrido, AIP Conf. Proc. 1152, 16–31 (2009); Wagner and Rolon-Garrido, Korea Aust. Rheol. J. 21, 203–211 (2009)] allowed a parameter-free modeling of the elongational viscosity of monodisperse polystyrene melts. Here, we demonstrate that when the dependence of the interchain pressure effect on polymer concentration and molar mass of the oligomeric solvent is considered, the EIP model agrees with experimental evidence that at low Weissenberg numbers W i R = e ˙ τ R < 1 melts and solutions show extension thinning behaviors, while at W i R ≅ 1 solutions switch to extensional thickening or show a more or less constant steady-state elongational viscosity and melts continue with extension thinning behavior with a scaling of η E ∝ W i R − 0.5. We explain quantitatively the effects of molar mass of solvent and of polymer concentration on the elongational viscosity in the investigated concentration range from 10% to 100% (melt), based solely on the linear-viscoelastic characterization. For polystyrene dissolved in oligomeric styrene with molar mass larger than a quarter of the entanglement molar mass of the melt, M o s ≥ M e m / 4 = 3.3 kg / mol, we predict a universal relation for the steady-state elongational stress at W i R ≫ 1, which is independent of polymer concentration and molar mass of the solvent, while the stretch potential of polystyrene dissolved in oligomeric styrene with M o s < 3.3 kg / mol increases with decreasing molar mass of solvent and decreasing polymer concentration in agreement with available experimental evidence.The elongational viscosity data of Bach et al. [Macromolecules 36, 5174–5179 (2003)] and Huang et al. [ACS Macro Lett. 2, 741–744 (2013); Macromolecules 48, 4158–4163 (2015); Macromolecules 46, 5026–5035 (2013)] on monodisperse polystyrene melts and concentrated polystyrene solutions in oligomeric styrene represent a unique benchmark for improving the tube model of Doi and Edwards with respect to its predictive capabilities of nonlinear viscoelasticity and especially chain stretch. By relaxing one of the basic assumptions of the original tube model of Doi and Edwards [J. Chem. Soc., Faraday Trans. 2 Mol. Chem. Phys. 74, 1802–1817 (1978); J. Chem. Soc., Faraday Trans. 2 Mol. Chem. Phys. 74, 1818–1832 (1978)], i.e., the assumption of a constant tube diameter, and assuming that chain stretch is inversely proportional to a deformation-dependent tube diameter, the extended interchain pressure (EIP) theory [Wagner and Rolon-Garrido, AIP Conf. Proc. 1152, 16–31 (2009); Wagner and Rolon-Garrido, Korea Aust. Rheol...

A longstanding goal in polymer rheology is to develop a physical picture that relates the growth of mechanical moduli during polymer crystallization to that of a structure. Here, we utilize simultaneous mechanical rheology and optical microscopy, with augmentation by deterministic reconstruction and stochastic simulations, to study isothermal crystallization in isotactic polypropylene. We observe the nucleation and growth of the surface and bulk spherulites, which are initially isolated and then impinge to form clusters and superstructures that eventually span the gap. We find that spherulitic superstructures play a critical role in the rheology, especially in the characteristic sharp upturn in moduli. Both the rheology and the spherulitic superstructures show pronounced gap dependencies, which we explain via finite-size effects in percolation phenomena and via surface-induced nucleation. The modulus-crystallinity relationship can be described through a general effective medium theory. It indicates that for thicker gaps, the viscoelastic liquid to solid transition can be described via percolation, whereas for our thinnest gap, it is best described by the linear mixing rule. We describe our results in terms of dimensionless nucleation rates and spherulite size, which enable the estimation of when gap-dependent superstructure effects can be anticipated.A longstanding goal in polymer rheology is to develop a physical picture that relates the growth of mechanical moduli during polymer crystallization to that of a structure. Here, we utilize simultaneous mechanical rheology and optical microscopy, with augmentation by deterministic reconstruction and stochastic simulations, to study isothermal crystallization in isotactic polypropylene. We observe the nucleation and growth of the surface and bulk spherulites, which are initially isolated and then impinge to form clusters and superstructures that eventually span the gap. We find that spherulitic superstructures play a critical role in the rheology, especially in the characteristic sharp upturn in moduli. Both the rheology and the spherulitic superstructures show pronounced gap dependencies, which we explain via finite-size effects in percolation phenomena and via surface-induced nucleation. The modulus-crystallinity relationship can be described through a general effective medium theory. It indicates that f...

Rheological measurements in which the applied stress or strain is oscillated are widely used to interrogate viscoelastic properties due to the independent control over the time scale and length scale afforded by changes in amplitude and frequency. Taking a nontraditional approach, we treat stress-controlled oscillatory tests as creep tests with transiently varying stress and apply an analysis typically used for steady creep and recovery experiments. Defining zero strain as the state prior to external shearing, it is shown that strain responses to small-amplitude oscillatory stressing are naturally shifted from the starting point by an amount proportional to the phase of the applied stress. The phenomenology is experimentally observed with entangled polymerlike micelles and polyethylene oxide solutions. A theory of strain shifting in the steady alternating state is provided based on recovery rheology, where differences between total strain and recoverable strains are acknowledged. User-controlled variables, such as the amplitude of the stress, the angular frequency, and the phase of the stress, as well a lone material parameter, the zero-shear viscosity, are shown to dictate the amount of shifting. A rapid and efficient approach of determining the zero-shear viscosity is, therefore, presented. We investigate the microstructural evolution via in situ small-angle neutron scattering when strain shifting appears. The microscopic orientation is shown to correlate to the recoverable strain independent of the shifting. Additional measurements are carried out on collagen, pluronic-hyaluronic acid, alginate gels, and polystyrene melts to show the generic nature of the strain shift phenomenon. In addition, we demonstrate that the strain-shift knowledge can be applied to determine the horizontal shift factor in time-temperature superposition, free of any numerical fitting procedures.

We report a systematic rheological analysis of perfluorosulfonic acid (PFSA) ionomer monolayers at the air/water interface. Equipped with a custom-designed double wall knife-edge interfacial rheometer, we measure both the linear and nonlinear viscoelasticity of various PFSA ionomer monolayers. Based on rheological measurements along with other static measurements, we find that the rheological properties of the PFSA ionomer monolayers mainly originate from the electrostatic interaction of negatively charged groups (SO3−) rather than direct interactions between backbones, as is typical of other polymeric monolayers. Although the rheological properties mainly come from the SO3− groups, equivalent weight (EW) and length of the side chain affect the rheological properties as well: (1) surface activity increases with EW, thereby a larger EW tends to have stiffer interfaces; (2) PFSA ionomer with longer side chains also has larger shear moduli at the same surface pressure (Π), presumably because the longer side chain has larger configurational entropy, thus leading to better closed packing. Moreover, it is found from Π dependent measurements that both the elastic and viscous moduli exhibit unusually weak dependence on Π compared with typical polymeric and surfactant monolayers. The weak Π dependence can be explained in terms of charged colloids with long-range repulsive interactions, as they are susceptible to shear stress but resistive to compressional stress. This rheology of ionomers and their underlying morphology at the interface are expected to provide useful information for various membrane applications where ultrathin membranes can be helpful, such as ion exchange membranes and fuel cell/flow battery membranes.

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., Comment: 4 figures