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The dynamic modulus of polymer solutions and melts can be expressed as a universal function of reduced frequency when the modulus is scaled by a characteristic value according to the scaling theory of polymer physics. Although the plot of the scaled modulus as a function of the scaled frequency supports the theory, it suffers from considerable scattered distribution of data points around the hypothetical master curve. Compared with the master curve of the time–temperature superposition (TTS) of polymer melts, the master curve of polymer solutions has poor quality. Furthermore, the scale factors of polymer solutions may not show a clear dependency on molecular weight and concentrations. Experimental errors and molecular weight distribution appear to enhance the inaccuracy of the master curve. Therefore, we apply a global optimization for the superposition of the viscoelastic data of polymer solutions with various molecular weights and concentrations. The global optimization resulted in the superposition of data as accurate as that of TTS. Furthermore, the numerically determined shift factors, which were relative scale factors, showed clear dependences on molecular weight and concentrations. We compared our global optimization with previous scaling methodologies. [ABSTRACT FROM AUTHOR]

The trade-off between hardness and stretchability is a cornerstone of materials science. Balancing this trade-off is important in the molecular design of both chemical and physical networks. In this study, we report the quantitative trade-off at the molecular level for physical networks. Namely, we analyze, based on the reversible gelation model, a scaling relationship between the characteristic terminal relaxation modulus Gc in linear viscoelasticity and the stretch ratio λmax at the stress overshoot during the nonlinear elongation flow for unentangled randomly associative polymers, i.e., λmax ∼ Gc−0.17 and λmax ∼ Gc−0.33 in the mean-field and critical-percolation regimes, respectively. We use sulfonated polystyrene having different alkali counterions as a model system to test the relationship. The exponent of λmax ∼ Gc−0.25 seen in the experiment is in between the two theoretical values. We also discuss the quantitative deviation with respect to the size distribution of the network strands. [ABSTRACT FROM AUTHOR]

Mixtures of polymers of varying topologies and stiffnesses display complex emergent rheological properties that often cannot be predicted from their single-component counterparts. For example, entangled blends of ring and linear polymers have been shown to exhibit enhanced shear thinning and viscosity, as well as prolonged relaxation timescales, compared to pure solutions of rings or linear chains. These emergent properties arise in part from the synergistic threading of rings by linear polymers. Topology has also been shown to play an important role in composites of flexible (e.g., DNA) and stiff (e.g., microtubules) polymers, whereby rings promote mixing while linear polymers induce demixing and flocculation of stiff polymers, with these topology-dependent interactions giving rise to highly distinct rheological signatures. To shed light on these intriguing phenomena, we use optical tweezers microrheology to measure the linear and nonlinear rheological properties of entangled ring-linear DNA blends and their composites with rigid microtubules. We show that linear viscoelasticity is primarily dictated by microtubules at lower frequencies, but their contributions become frozen out at frequencies above the DNA entanglement rate. In the nonlinear regime, we reveal that mechanical response features, such as shear thinning and stress softening, are mediated by entropic stretching, threading, and flow alignment of entangled DNA, as well as forced dethreading, disentanglement, and clustering. The contributions of each of these mechanisms depend on the strain rate as well as the entanglement density and stiffness of the polymers, leading to nonmonotonic rate dependences of mechanical properties that are most pronounced for highly concentrated ring-linear blends rather than DNA-microtubule composites. [ABSTRACT FROM AUTHOR]

We provide a canonical introduction to dual-junction-functionality associative polymer networks, which combine high and low functionality (f) dynamic cross-link junctions to impart load-bearing, dissipation, and self-repairing ability to the network. This unique type of network configuration offers an alternative to traditional dual-junction networks consisting of covalent and reversible cross-links. The high-f junctions can provide load-bearing abilities similar to a covalent cross-link while retaining the ability to self-repair and concurrently confer stimuli-responsive properties arising from the high-f junction species. We demonstrate the mechanical properties of this design motif using metal-coordinating polymer hydrogel networks, which are dynamically cross-linked by different ratios of metal nanoparticle (high-f) and metal ion (low-f) cross-link junctions. We also demonstrate the spontaneous self-assembly of nanoparticle-cross-linked polymers into anisotropic sheets, which may be generalizable for designing dual-junction-functionality associative networks with low volume fraction percolated high-f networks. [ABSTRACT FROM AUTHOR]

Existing single-chain models for unentangled associating polymers account for the association by assigning the sticky junctions a large value of the monomeric friction coefficient, which prevents them from moving in space unless stickers effectively dissociate. With such an assumption, comparison of model predictions with linear viscoelastic data is not fully successful in the intermediate range of frequency. In this work, we improve agreement with data by developing a single-chain model where sticky junctions are allowed to quickly move in space without dissociating. We also account for a random distribution of the stickers but differently from the recent model by Jiang et al. [Macromolecules 53, 3438–3451 (2020)]. Predictions of the model are successfully compared with unentangled melt data for two different copolymer chemistries and different sticker concentrations. Particularly significant are the data by Cui et al. [J. Rheol., 62, 1155–1174 (2018)] of melts of polymers with only two stickers per chain, revealing that sticky junctions are in fact also endowed with fast mobility. [ABSTRACT FROM AUTHOR]

This study examines the linear viscoelasticity of double-associative ionomers based on poly(hexyl methacrylate). The ionomer samples are unentangled and contain a fixed number of ionic stickers per chain, f ion ≅ 4 , but a varied number of hydrogen-bonding stickers per chain, fH = 5.5–27. Increasing fH has distinct effects on the glassy and rubbery dynamics. On the one hand, the glassy relaxation mode distribution broadens, and the glassy-to-rubbery transition region delays significantly with increasing fH. On the other hand, the delay of the ionic dissociation and, accordingly, the terminal relaxation (activated by continuous ionic dissociations) are much weaker. This contrast suggests that the ionic dissociation is not only activated by the segmental motion of the main backbone but is also partly activated by the motion of the side chains that is less dependent on fH. [ABSTRACT FROM AUTHOR]

A thorough study is made of the dependences on salt concentration and polymer chain lengths of the low-frequency plateau of coacervates of poly (diallyl dimethyl ammonium chloride), PDADMAC, and poly (sodium 4-styrenesulfonate), PSS. The reliability and reproducibility of these measurements are carefully checked by determining the frequency-dependent stress limits of the rheometer through the use of reference fluids and by repeat experiments with coacervates. Long-time frequency sweeps show that coacervates with less salt are more repeatable than those with higher salt. A low-frequency plateau reliably appears only below a critical salt concentration, and the magnitude of the plateau depends strongly on salt concentration and chain lengths of both polycation and polyanion. It is only present for the molecular weight of the polycation, PDADMAC, higher than 100 kDa, but the magnitude of the plateau is more strongly influenced by the chain length of the polyanion, PSS. Possible causes of the low-frequency plateau are discussed. [ABSTRACT FROM AUTHOR]

Although bead microrheology experiments are routinely used to characterize the viscoelasticity of complex matter, their simulation analog—probe rheology molecular simulations—has been scarcely used since the system characteristics required for its robust implementation are not established in the literature. We address this issue by analyzing an active probe rheology simulation setup consisting of a probe particle that is subjected to an external oscillatory force and a harmonic trapping force. We identify a set of eight conditions of the system properties that must be satisfied for the successful implementation of the probe rheology technique in molecular simulations. Among these criteria, the two most important are as follows: (1) The spring force constant for the trapping force should be sufficiently large such that the peak in the Fourier transform of the probe displacement occurs at the same frequency as that of the applied force. (2) System parameters should be chosen such that the magnitude of the external force used to drive the probe motion should be comparable to the magnitude of the hydrodynamic friction force experienced by the probe particle in the viscoelastic medium. Furthermore, a scaling relation that can be used to determine the frequency at which inertial effects set in for a given probe size is also established. The validity of our procedure is demonstrated by applying it to determine the viscoelastic properties of a weakly entangled polymer melt system. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We derive new analytical solutions for the nonaffine Johnson–Segalman/Gordon–Schowalter (JS/GS) constitutive equation with a general relaxation kernel in medium-amplitude oscillatory shear (MAOS) deformation. The results show time-strain separable (TSS) nonlinearity, therefore providing new physically meaningful interpretation to the heuristic TSS nonlinear parameter in MAOS [Martinetti and Ewoldt, Phys. Fluids 31, 021213 (2019)]. The upper-convected, lower-convected, and corotational Maxwell models are all subsets of the results presented here. The model assumes that the microscale elements causing stress in the material slip compared to the continuum deformation. We introduce a visualization of the nonaffine deformation field that acts on stress-generating elements to reinforce the physical interpretation of the JS/GS class of models. Finally, a case study is presented where previously published results, from fitting TSS models to MAOS data, can be reinterpreted based on the concept of nonaffine motion of the JS/GS framework. [ABSTRACT FROM AUTHOR]

Asphaltenes are a class of high molecular weight aromatic compounds found in crude oil. They adsorb onto toluene-water interfaces and induce a spontaneous emulsification phenomenon, whereby stable water-in-oil emulsions form without the need of an external energy input. This work aims to control and understand the factors affecting spontaneous droplet formation in the presence of asphaltene adsorption. This is particularly useful for crude oil refining, where the presence of a stable emulsion hampers the efficiency of downstream processing operations. We explore the effect of the addition of copolymers designed as crude oil flow improvers as a means to control the extent of emulsion formation. We find that the polymers competitively adsorb onto the toluene-water interface and diminish spontaneous emulsification. We also conduct fluorescence microscopy experiments and measurements of the interfacial energy to determine the mechanism of spontaneous emulsification in asphaltene systems. We conclude that an emulsion forms via the diffusion of molecular water into the oil phase and subsequent binding with asphaltene aggregates, leading to the nucleation of micrometer-sized water droplets. We find that the polymer forms complexes with the dissolved asphaltenes, possibly hampering the ability of diffused water to bind to the asphaltenes and reducing the extent of spontaneous emulsification. Finally, we investigate the role of interfacial shear and dilatational viscoelasticity to better understand which fundamental interfacial properties are important in the emulsification of asphaltene-laden systems. We find that the rate of formation of an interfacial microstructural network is inversely correlated with the extent and rate of spontaneous emulsification. [ABSTRACT FROM AUTHOR]

When injected through a contraction, high molecular weight polymer solutions exhibit a sharp increase in apparent viscosity, which originates from stretching polymer chains above a critical extension rate. This chain stretching can also induce polymer scission, which then decreases the extensional viscosity. In practice, the two phenomena are difficult to separate. Moreover, these phenomena are often observed in situations where flow instabilities appear. In order to disentangle the two effects, we have measured the pressure-flow rate relation for polymer solutions passing through a hyperbolic contraction. The ratio of the pressure drop to that of the (Newtonian) solvent exhibits a maximum due to the competition between polymer extension and scission. We find a geometry-dependent relation between the flow rates at which the maximum occurs for successive passages in a given contraction, which appears to be independent of molecular weight, concentration, solvent quality, and viscosity and can be used to predict the scission under successive passes. [ABSTRACT FROM AUTHOR]

A new polydisperse "toy" constitutive model is derived and developed from fundamental principles and ideas governing the nonlinear rheology of linear flexible polymers [Mead et al., J. Rheol. 59, 335-363 (2015)]. Specifically, the new model is comprised of four fundamental pieces. First, the model contains a simple differential description of the entanglement dynamics of discrete entanglement pairs. Second, the model contains a differential description of the ij entanglement pair orientation tensor dynamics. Third, following a similar development by Mead and Mishler [J. Non-Newtonian Fluid Mech. 197, 61-79 and 80-90 (2013).], a diluted stretch tube is constructed to describe the relative stretch of each component in the molecular weight distribution (MWD). Fourth, a description of configuration dependent friction coefficients is generated by generalizing the monodisperse formulation of Ianniruberto et al. [Macromolecules 45, 8058-8066 (2012)]. The polydisperse stress calculator is developed from the orientation, stretch and entanglement density and is fundamentally different from other molecular models that assume a constant entanglement density. The resulting model is comprised of three differential evolution equations and is simple to code and fast to execute. The model can simulate arbitrary fast nonlinear flows of arbitrary MWD's. In the slow flow linear viscoelastic limit, the model collapses to the double reptation model. This welcome result has positive implications with respect to our model parameter determination [Ye et al., J. Rheol. 47, 443-468 (2003); Ye and Sridhar, Macromolecules 38, 3442-3449 (2005)] for making quantitative calculations. [ABSTRACT FROM AUTHOR]

We here extend to integral constitutive equations of the Doi-Edwards type the analysis of shear banding instabilities during shear startup recently performed by Moorcroft and Fielding [J. Rheol. 58, 103-147 (2014)]. Shear banding is the instability encountered in simple shear flows, whereby different shear rates coexist along the sample thickness, so that the velocity profile departs from the usually assumed linear profile. Results of both linear and nonlinear stability analysis mostly confirm those obtained by Moorcroft and Fielding [J. Rheol. 58, 103-147 (2014)] with the Rolie-Poly equation [Likhtman, A. E., and R. S. Graham, J. Non-Newtonian Fluid Mechan. 114, 1-12 (2003)] (which is an approximate differential counterpart of the Doi-Edwards integral one "[The Theory of Polymer Dynamics (Clarendon, Oxford, 1986)]"), but some significant differences are also found. Features that coincide with those predicted by the Rolie-Poly equation include: (i) For the nonmonotonic flow curve of the original Doi-Edwards equation, the viscous instability classically predicted in the decreasing part of the flow curve is preceded during startup by an elastic instability in the region of the stress overshoot; (ii) to the right of the flow-curve minimum, a region of metastability is found, whereas, to the left of the maximum, attempts at finding metastability have failed; and (iii) when convective constraint release (CCR) is accounted for, and a monotonic flow curve is obtained, transient banding instabilities of elastic origin in the shear-rate range of the quasiplateau region are again found close to the overshoot. On the other hand, the integral Doi-Edwards equation appears not to predict transient elastic instabilities to the left of the maximum of the flow curve, differently from what found by Moorcroft and Fielding [J. Rheol. 58, 103-147 (2014)] with the Rolie-Poly equation. Also, for the case where CCR generates a monotonic flow curve, the shear-rate range in the plateaulike region where elastic instabilities are found comes out much narrower than for the Rolie-Poly. All considered, the integral Doi-Edwards equation appears to predict fewer instabilities than its differential counterpart, which is perhaps more in line with the contradictory experimental results on banding of entangled polymers reported by different authors. [ABSTRACT FROM AUTHOR]

We present unique nonlinear rheological data of well-defined symmetric Cayley-tree poly(methyl methacrylates) in shear and uniaxial extension. Earlier work has shown that their linear viscoelasticity is governed by the hierarchical relaxation of different generations, whereas the segments between branch points are responsible for their substantial strain hardening as compared to linear homopolymers of the same total molar mass at the same value of imposed stretch rate. Here, we extend that work in order to obtain further experimental evidence that will help understanding the molecular origin of the remarkable properties of these highly branched macromolecules. In particular, we address three questions pertinent to the specific molecular structure: (i) Is steady state attainable during uniaxial extension? (ii) What is the respective transient response in simple shear? and (iii) How does stress relax upon cessation of extension or shear? To accomplish our goal, we utilize state-of-the-art instrumentation, i.e., filament stretching rheometry and cone-partitioned plate shear rheometry for polymers with 3 and 4 generations, and complement it with state-of-the-art modeling predictions using the branch-on-branch (BoB) algorithm. The data indicate that the extensional viscosity reaches a steady state value, whose dependence on extensional rate is identical to that of entangled linear and other branched polymer melts. Nonlinear shear is characterized by transient stress overshoots and the validity of the Cox-Merz rule. Remarkably, nonlinear stress relaxation is much broader and slower in extension compared to shear. It is also slower at higher generation, and rateindependent for rates below the Rouse rate of the outer segment. For extension, the relaxation time is longer than that of the linear stress relaxation, suggesting a strong "elastic memory" of the material. These results are described by BoB semiquantitatively, both in linear and nonlinear shear and extensional regimes. Given the fact that the segments between branch points are less than three entanglements long, this is a very promising outcome that gives confidence in using BoB for understanding the key features. Moreover, the response of the segments between generations controls the rheology of the Cayley trees. Their substantial stretching in uniaxial extension appears responsible for strain hardening, whereas coupling of stretches of different parts of the polymer appears to be the origin of the slower subsequent relaxation of extensional stress. Concerning the latter effect, for which predictions are not available, it is hoped that the present experimental findings and proposed framework of analysis will motivate further developments in the direction of molecular constitutive models for branched and hyperbranched polymers. [ABSTRACT FROM AUTHOR]

There have been many more papers published on methods for inferring a continuous relaxation spectrum from linear viscoelastic data than have been published on the use of such methods for polymer characterization. But a continuous spectrum can reveal key details of the relaxation process that are not evident from plots of the storage and loss moduli, particularly in the case of model polymers prepared for research. In particular there are sharp peaks in the spectrum where Rouse relaxation is complete and further relaxation is inhibited by entanglements in the plateau zone and at the entry to the terminal zone where molecules have escaped their tubes. Examples of continuous spectra that reveal these relaxation phenomena are presented. [ABSTRACT FROM AUTHOR]

Nonlinear oscillation shear has become an important method to study the complex fluids. However, choosing the suitable material functions is not as simple as that in linear viscoelasticity. A framework is suggested in this work to account for the stress-strain and stress-strain rate relationship based on the concept of mean stress and mean strain (rate) in the Lissajous curves. The applications of such framework in an imposed oscillatory shear strain and an imposed oscillatory shear stress are clearly demonstrated. The intracycle nonlinear modulus and viscosity are defined from the slope of the stress-strain curve and the stress-strain rate curve, respectively. The intercycle nonlinear behaviors are obtained from the strain (rate) amplitude dependence of the zero mean strain (rate) modulus or viscosity. We justify the strain-hardening/softening and shear-thickening/thinning behaviors of nonlinear moduli and viscosities by using typical constitutive models like Bingham model and the Maxwell model. It is found that the modulus (viscosity) defined from the stress-mean strain (rate) curves is the most physical reasonable quantity. In addition, we apply the new analysis method to two yield stress fluids, which reveals critical balance between aging and shear rejuvenation. [ABSTRACT FROM AUTHOR]

A stochastic constitutive model has been developed that explicitly acknowledges the nanometer size dynamic heterogeneity of glassy materials, where the distribution of the viscoelastic relaxation times emerges naturally as a result of the dynamic heterogeneity. A set of stochastic differential equations for local stresses and entropy describing behavior of a mesoscopic domain are developed, and the observed macroscopic response of the material is obtained as an average of an ensemble of domains. The stochastic constitutive model naturally predicts and provides a mechanism for the postyield stress softening and its dependence on physical aging that is observed during constant strain rate uniaxial deformations. [ABSTRACT FROM AUTHOR]

We present a detailed systematic investigation of the transient uniaxial extensional response of a series of well-characterized, anionically synthesized comb polystyrenes and polyisoprenes. The comb architecture consists of a linear chain backbone with multiple branches of equal molar mass, and represents an excellent model branched polymer. The linear viscoelastic response has been studied already in great detail. Our results indicate that the strain hardening becomes more important as the Hencky strain rate is increased. In general, the larger the number of entanglements of the segments between branches and/or of the branches, the stronger the strain hardening and the smaller the characteristic rate for its onset. The key molecular parameter appears to be the number of entanglements per branch. By varying it, one can tailor the amount and onset of strain hardening. This can be rationalized by accounting for the combined effect of backbone tube dilation and extra friction, brought about by the branches. In fact, we define an effective 'stretch time' of the comb as the timescale for stretch relaxation along the dilated backbone tube when accounting for the large friction that comes from the branches and suggest that extension hardening occurs at rates equal to or greater than its inverse. The good comparison of this prediction to experimental data is a promising guide toward a universal framework for understanding the effects of branches on extensional rheology, and hence providing some insight into the behavior of long-chain branched polyolefins. [ABSTRACT FROM AUTHOR]

The idea of incorporating multiple models of linear rheology into a superensemble, to forge a consensus forecast from the individual model predictions, is investigated. The relative importance of the individual models in the so-called multimodel superensemble (MMSE) was inferred by evaluating their performance on a set of experimental training data, via nonlinear regression. The predictive ability of the MMSE model was tested by comparing its predictions on test data that were similar (in-sample) and dissimilar (out-of-sample) to the training data used in the calibration. For the in-sample forecasts, we found that the MMSE model easily outperformed the best constituent model. The presence of good individual models greatly enhanced the MMSE forecast, while the presence of some bad models in the superensemble also improved the MMSE forecast modestly. While the performance of the MMSE model on the out-of-sample training data was not as spectacular, it demonstrated the robustness of this approach. [ABSTRACT FROM AUTHOR]

Some of the fluids routinely used in microfluidic devices have micro and nanostructures that can generate viscoelastic behavior. In this paper, an experimental technique is developed to estimate the extensional flow resistance of dilute polymer solutions using flow in a lubricated, converging, and microfluidic channel. The channel has a two-dimensional hyperbolic profile, and the viscous or viscoelastic core fluid is lubricated by a less viscous Newtonian fluid that is introduced through side channels upstream. Differences in flow patterns are observed between miscible and immiscible lubricants. Stable flows are achieved with an immiscible lubricant and with a suitable interfacial tension between the core fluid and the lubricant. Steady extensional flows are established at low Reynolds numbers (Re < 1 for the core fluid), at moderate Hencky strains (3 < &eh;H < 3.9), and over a wide range of Deborah numbers (0 < De < 20). Pressure drop and flow rate measurements are made, and the velocity field is characterized by particle image velocimetry and streak photography. The apparent extensional viscosity, as a function of strain rate, is estimated from the difference between the experimental pressure drop and the calculated pressure drop due to shearing in the core flow. Values of the Trouton ratio, for dilute solutions of high-molecular-weight polyethylene oxide, are O(103), consistent with literature values. [ABSTRACT FROM AUTHOR]

Non-linear correlations are found between the melt strength and fundamental shear flow properties such as low frequency loss tangent, crossover frequency, and zero-shear-rate viscosity for a series of polypropylene (PP) melts. The very good non-linear correlations suggest rheotens as a reliable rheological test to characterize extensional rheology relevant to fabrication, despite its non-homogeneous and non-isothermal flow kinematics. The rheotens model of Doufas [J. Rheol. 50, 749-769 (2006)] with a modified Giesekus (MG) viscoelastic constitutive equation is expanded to the case of PP melts. A single set of molecular parameters per material predicts the rheotens force curves very well over a wide range of processing conditions. The rheotens model is proposed as a tool for determination of rheological parameters of constitutive equations applicable to the simulation of complex polymer processes. Molecular considerations and predictions of the rheotens model are extensively discussed. A multi-mode MG model predicts the non-linear steady shear data (shear and first normal stresses) very favorably satisfying linear viscoelasticity. The oscillatory shear data and model predictions satisfy both the Cox-Merz [J. Polym. Sci. 28, 619-621 (1958)] and Laun [J. Rheol. 30, 459-501 (1986)] rules. The model exhibits stable numerical behavior without singularities or turning points in the prediction of steady shear viscosity even at quite high shear rates (e.g., on the order of 20 000 s-1), problems that have been reported for other constitutive equations. [ABSTRACT FROM AUTHOR]

In this manuscript, we extend the tube-based model that we developed for predicting the linear viscoelasticity of entangled polymers [van Ruymbeke et al., J. Non-Newtonian Fluid Mech. 128, 7-22 (2005)] to the prediction of the extensional rheology of monodisperse and bidisperse linear polymers and confront the results to experimental data. This model is based on the concepts of stretch-orientation separability [McLeish and Larson, J. Rheol. 42, 81-110 (1998)] and inter-chain pressure [Marrucci and Ianniruberto, Macromolecules 37, 3934-3942 (2004)]. In order to deal with polydisperse samples, a new mixing law is proposed. As it does not require knowledge of the full linear relaxation spectrum, the proposed model is a powerful predictive tool. Very good agreement is found between theoretical and experimental results. For bidisperse samples, the individual contribution of each component is determined, and it is shown that only few percent of long chains are enough to generate the strong strain hardening observed in the experimental data. Last, we discuss the value of the tube diameter relaxation time. For monodisperse samples, this parameter is found to scale with M2. However, for bidisperse samples, as it was already observed by Wagner et al. [J. Rheol. 52, 67-86 (2008)], the tube diameter relaxation time of the long component must be rescaled, which is contrary to the inter-chain pressure model and opens several new questions. [ABSTRACT FROM AUTHOR]

We probed the viscoelastic behavior of polydisperse star/linear polymer blends with varying composition and average arm length. The linear viscoelastic behavior has been investigated over a wide range of frequencies using both oscillatory and long creep/recovery experiments. A method was developed for splitting the molar mass distributions of the blends into the contributions of different architectures. These results were used to implement a time-marching algorithm based on a parameter-free tube model for predicting the linear viscoelastic behavior. The model predictions were successfully validated with the experimental data, opening the route for designing blends with desired rheological properties. [ABSTRACT FROM AUTHOR]

Visco-elastic models are commonly used in modeling time dependent behavior of asphalts, polymers, and biomaterials (e.g., soft tissues). In order to ensure that these models are thermomechanically consistent, their stress-strain behavior has to be derived using a strain energy function. For a non-linear viscoelastic behavior, this appears to be a rather subtle problem: some quasi-linear viscoelastic energy formulations presented in the literature do not use the true energy functions for the stress-strain response attributed to these models, making their mechanical interpretation and validation of thermomechanical consistency difficult. This paper represents an attempt to propose an alternative framework, which would retain simplicity and convenience in numerical applications of the quasi-linear viscoelasticity, but would have a straightforward mechanical interpretation and guarantee the thermomechanical consistency. This is achieved by using a thermomechanical approach with internal kinematic variables, where both the energy and dissipation potentials have the same kind of non-linearity, leading to a general family of non-linear visco-elastic models. Within this context, a simple thermomechanically consistent non-linear hyperviscoelastic model with pressure dependent bulk stiffness is proposed, with an example modeling experimental data from laboratory tests on asphalts. [ABSTRACT FROM AUTHOR]

A strain-rate frequency superposition (SRFS) technique, recently proposed to analyze the low-frequency behavior of soft materials, is evaluated. The application of SRFS to an emulsion and multiarm star polymer solution produces master curves that, while promising in appearance, do not match the anticipated linear response as they seem inconsistent with dynamic frequency sweep data and the Kramers–Kronig relation. While the raw unscaled frequency sweep data are well described using the generalized Maxwell model, strong discrepancies appear when the same procedure is applied to SRFS data. These inconsistencies appear to be generic and are observed in other materials as well. An examination of Lissajous curves obtained from large amplitude oscillatory strain shows that nonlinear contributions, such as solvent-mediated convective flow, strongly affect SRFS master curves. Based on these findings, SRFS should be approached with caution when applied to soft materials. [ABSTRACT FROM AUTHOR]

We have studied stress overshoot behavior in startup shear of four monodisperse polymer melts with a range of chain entanglement from Z=24 to 160 entanglement points per chain. In the elastic deformation regime defined by γτR>1, where τR is the Rouse relaxation time, (i) the peak shear stress σmax scales with the time tmax at the peak to -1/2 power, in contrast to an exponent of -1/4 in the viscoelastic regime (for γτR<1), (ii) σmax changes linearly with the elapsed strain at the stress peak γmax, which scales with the applied shear rate as γ1/3, (iii) a supermaster curve collapses time-dependent shear stress growth curves up to the stress maximum at all shear rates for all the four styrene-butadiene rubber samples. [ABSTRACT FROM AUTHOR]

A procedure is described and analyzed for the determination of the relative placement of linear viscoelastic functions and their relative relaxation/retardation spectra for a commercial polycarbonate (LEXAN GE). The complete set of viscoelastic functions in creep and relaxation was obtained from two simple experimental data, namely the linear viscoelastic response in shear and the pressure volume temperature (PVT) behavior. The dimensionless bulk compliance was extracted from PVT data showing that it coincides with the memory function appearing in the Kovacs, Aklonis, Hutchinson, Ramos phenomenological theory [Kovacs, A. J., J. J. Aklonis, J. M. Hutchinson, and A. R. Ramos, J. Polym. Sci., Polym. Phys. Ed. 17, 1097 (1979)]. Our results are compared with the relevant literature data obtained on different polymers and show that polycarbonate fulfills simultaneously the responses features concerning the relative placement of the bulk and shear moduli [Kono, R. J., Phys. Soc. Jpn. 15, 4 (1960)], the shapes of the bulk and the shear retardation spectra [Bero, C. A., and D. J. Plazek, J. Polym. Sci., Part B: Polym. Phys. 29, 39–47 (1991)], the relative placement of the bulk and shear compliance [Deng, T. H., and W. G. Knauss, Mech. Time-Depend. Mater. 1, 33–49 (1997); Sane, S. B., and W. G. Knauss, Mech. Time-Depend. Mater. 5, 293–324 (2001)], the relative placement of bulk modulus and shear compliance [Meng, Y., and S. L. Simon, J. Polym. Sci., Part B: Polym. Phys. 45, 3375–3385 (2007)], the relative placement of the bulk compliance and the axial relaxation modulus [Knauss, W. G., and I. Emri, Polym. Eng. Sci. 27, 86–100 (1987)], and the shape of the Poisson’s ratio [Lakes, R. S., Cell. Polym. 11, 466–469 (1992); Von Koppelmann, J., Rheol. Acta 1, 20–28 (1958); Ferry, J. D., Viscoelastic Properties of Polymers, 3rd ed. (Wiley, New York, 1980)], and its scaling with the shear modulus [O’Brien, D. J., N. R. Sottos, and S. R. White, Exp. Mech. 47, 237 (2007)]. [ABSTRACT FROM AUTHOR]

This paper reports finite-element simulations of drop deformation in converging flows in an axisymmetric conical geometry. The moving interface is captured using a diffuse-interface model and accurate interfacial resolution is ensured by adaptive refinement of the grid. We have explored the effects of viscoelasticity on drop deformation when either the drop or the matrix is a Giesekus fluid. Contrary to the popular belief that viscoelasticity in the drop hinders deformation and that in the matrix enhances deformation, we predict a more complex picture in which viscoelasticity in either component may suppress or promote drop deformation depending on the capillary number Ca and the drop-to-matrix viscosity ratio β. Smaller Ca and β are conducive to the behavior mentioned above, while large Ca and β may produce the opposite effect. Both trends are explained by the reaction of the polymer stress to the inhomogeneous and transient deformation in the converging flow field. Finally, this understanding reconciles contradictory results in the literature as opposite limits in the parameter space. [ABSTRACT FROM AUTHOR]

This paper reports initial experimental flow birefringence studies of cross-slot flow for a range of molten polyethylenes using a multipass rheometer (MPR). An MPR was modified to accommodate a cross-slot center section insert thereby enabling small quantities of molten polymer to be evaluated in a near two-dimensional pure shear extensional flow. The results show that it was possible to obtain precise processing data for cross-slot flow using 10 g quantities of polymer. Experimental observations on different polyethylenes showed that in all cases the flow commenced from a Newtonian situation where the optical birefringent fringes around the central stagnation point were essentially symmetric. As the flow developed, the fringe pattern became progressively more asymmetric about the exit symmetry plane and the extent of the viscoelasticity of the polymer could be quantified by the observed level of anisotropy between the birefringence fringes on the entry and exit symmetry planes of the flow. The progressive development of anisotropy and stress with increasing extensional flow rate and type of polymer is presented for a number of flow conditions and it was found that increasing viscoelasticity of the polymer resulted in a progressive increase in viscoelastic center-line extensional stresses. The data provide benchmark large strain extensional flow experiments for certain polymer melts that can in the future be used to compare with numerical simulation. [ABSTRACT FROM AUTHOR]

The breakdown of finite element (FEM) computations for the steady symmetric two-dimensional flow of dilute and ultradilute Oldroyd-B fluids around a cylinder in a channel, at Weissenberg numbers Wi=O(1), is shown to arise due to a coil-stretch transition experienced by polymer molecules in the wake of the cylinder in the vicinity of the location of the stress maximum on the centerline. In dilute Oldroyd-B fluids, due to the modification of the flow caused by the presence of the polymer, the coil-stretch transition leads to the stress maximum diverging toward infinity at a finite value of Wi≈0.7. On the other hand, in ultradilute solutions, the stress maximum approaches infinity only as Wi→∞. In FENE-P fluids, the coil-stretch transition leads to the mean extension of the molecules saturating to a value close to the fully-extended length, with the maximum stress remaining bounded with increasing Wi. An estimation of the number of finite elements required to achieve convergence for ultradilute Oldroyd-B fluids reveals that obtaining solutions at Wi>1 is not feasible. [ABSTRACT FROM AUTHOR]

Single-step and three types of reversing double-step experiments were conducted on concentrated solutions of a linear and two dendritic (hyperbranched or arborescent) polyisobutylenes (PIBs). The results in reversing double-step experiments further confirm our previous findings on polyethylene melts that the K-BKZ theory provides better predictions for long chain branched polymers than linear ones. The short chain branched material looks more like the linear material in the present experiments. Isochronal derivatives of the strain potential function (W1 and W2) were calculated from torque (T) and normal force (N) responses in single-step parallel plate experiments. The damping function was extracted from W1 and W2 for both linear and branched PIBs. The damping function of the linear PIB falls between two versions of the Doi–Edwards model. The arborescent PIB with longer branches and lower branching frequency shows weak damping behavior, which is a specific behavior for long chain branched polymers. The arborescent PIB with shorter branches, higher branching frequency and low entanglement density, on the other hand, exhibits the same damping behavior as that of the linear PIB, which is consistent with the findings in the reversing double-step experiments in which it behaves more like a linear polymer. [ABSTRACT FROM AUTHOR]

The viscoelastic behavior of very concentrated and electrostatically stabilized suspensions of kaolinite particles has been investigated in the linear and nonlinear regime as a function of volume fraction, ionic strength and in the presence of polymer at various concentrations. Material properties such as linear viscoelastic moduli and cohesive energy density are extensively enhanced by either increasing volume fraction or decreasing ionic strength. Attention has been paid to the large amplitude oscillatory shear behavior of concentrated suspensions of plate-like particles, characterized by a hump in G″ curves. Rheological investigation shows the extreme sensitivity of the intensity of the strain hardening in G″ to excluded volume, electrostatic and steric interactions. A physical interpretation of this nonlinear behavior has been proposed. [ABSTRACT FROM AUTHOR]

We investigated the linear melt viscoelasticity and the crystallization kinetics of a series of model poly(ethylene oxide) stars with different functionalities (f=4–32 arms) and moderately entangled arms (their molecular masses ranging from 5.5 to 12 kg/mol). The limited data in the homogeneous state indicated that the zero-shear viscosity η0 was adequately described by the Milner–McLeish model for functionalities f<32, where the core effect is insignificant; a similar behavior was observed for the recoverable compliance Je0 which depended on both the molecular weight and the number of the arms. Below the melting point, the isothermal crystallization was measured with differential scanning calorimetry and rheology, and analyzed in terms of the Avrami theory, expanding over a wide range of temperatures. The results were supported by additional polarizing optical microscopy data and indicated a slower crystallization kinetics of the stars compared to their linear analogues. They showed a strong dependence of the crystallization rate on the arm molecular weight, whereas the available experimental evidence is suggestive of some functionality dependence as well. [ABSTRACT FROM AUTHOR]

A recent, nonlinear viscoelastic theory for predicting the thermomechanical response of glassy polymers has been shown to predict behaviors from enthalpy relaxation to temperature-dependent mechanical yield in various modes of deformation quite well. The foundation of this theory rests on a “material clock” that depends on the potential energy of the system. The molecular basis for the clock and the Rational Mechanics framework for the constitutive equation are briefly reviewed. The theory is then used to predict and explain much more complicated behavior of glassy polymers: the change in compressive yield stress during physical aging at different temperatures, the peculiar enthalpic response of glassy polymers previously compressed to different strains, “volumetric implosion” on samples subjected to tensile strains, and the dependence of the shift factor on aging time and applied stress. [ABSTRACT FROM AUTHOR]

Our previous, extensively validated, nonlinear viscoelastic formalism for glassy polymers is extended to include the effects of chemical reaction. Two modifications are necessary. First, the extent of reaction represents an additional degree of freedom that must be included in the free energy series expansion. Second, simultaneous reaction and deformation can lead to “compression set” that is represented by an evolving stress-free configuration in the cross-linked solid. The material clock, which is based on potential energy and must also incorporate these modifications, naturally predicts the increase in glass transition with cure. [ABSTRACT FROM AUTHOR]

The linear viscoelastic properties of binary blends of monodisperse linear polymers of various polymers, including polyisoprene, polybutadiene, and polystyrene, are compared with the predictions of the model of Park and Larson (2004), which is an extension of the Milner-McLeish model [Milner and McLeish (1998)]. For each polymer system the model parameters needed in the predictions of the binary blend are obtained from experimental data for monodisperse polymers. For well entangled blends of nearly monodisperse polymers, the model predictions are in good agreement with experimental data for a wide range of values of the Graessley parameter Gr, which is proportional to the ratio of the reptation time of the long chain in the undilated tube to the constraint-release Rouse time. Our results show that for polymers of multiple chemical types, the terminal behavior of the long chain is controlled by reptation in an undilated tube for small GrGrc, where Grc is around 0.06. For values of Gr near Grc, behavior intermediate between reptation in a dilated and an undilated tube is found. [ABSTRACT FROM AUTHOR]

We have developed a sensitive method to detect very low levels of long chain branching in sparsely branched polymers and applied it to high-density polyethylene samples with broad molar mass distribution obtained by Ziegler–Natta, Phillips, and metallocene catalysis. We compare experimental dynamic moduli with predicted values. The predicted moduli, which are only valid for truly linear chains, are computed from a known molar mass distribution by the application of a modified time-dependent diffusion reptation model described in [van Ruymbeke et al., Macromolecules 35, 2689 (2002)]. Discrepancies between experimental and predicted moduli are observed at branching levels below the usual detection limit of 13C nuclear magnetic resonance (about 1 branch per 10000 carbon atoms). Our method is easier to implement and the results more clearcut than those obtained by the zero-shear viscosity method. The sensitivity is comparable with the activation energy spectrum method described in [Wood-Adams et al., Macromolecules 33, 7489 (2000)]. The use of our method is however not restricted to thermorheologically complex polymers. The interest of polymer fractionation is also demonstrated for the detection of extremely low levels of long chain branching. [ABSTRACT FROM AUTHOR]