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Flow-fields are typically used to intimately mix large μm-sized particles with polymer melts. Here we show, using rheology, X-ray scattering, and electron microscopy, that shear flows do not improve the spatial dispersion or ordering of spherical nanoparticles (NP) grafted with polymer chains over the ranges of flow fields realizable in our experiments in the melt state. In the absence of flow, grafted NPs robustly self-assemble into a variety of superstructures when they are added to a homopolymer matrix with the same chemistry as the NP grafts. We find that isolated particles and spherical NP clusters remain dispersed but do not flow align. On the other hand, anisotropic NP assemblies initially break and their constituent building blocks (strings or sheets) flow-align locally. At very large strains, they coarsen into large aggregates, reflecting the dominance of interparticle attractions over flow fields and thermal energy.

We report on the unusual response of a well-characterized entangled comb polymer in simple shear flow. The polymer with highly entangled backbone (about 16 entanglements) and on average 29 long branches (about 3 entanglements each) has been extensively characterized by interaction chromatography and its rheology carefully studied under controlled conditions using a special cone partitioned-plate geometry. We observe that the start-up shear stress becomes roughly rate independent above a certain critical rate, related to the relaxation time of the branches. Within the rate-independent region, the start-up shear stress displays a double overshoot. We interpret these observations in light of tube-based pompom dynamics. The key idea is that for sufficiently long branches the main stress overshoot, which reflects backbone stretching and orientation, is preceded by the withdrawal of branches into the backbone tube. The excellent quantitative comparison between the simulations and experiments supports the proposed mechanism of the double stress overshoot.

We present an experimental investigation of the curing kinetics and viscoelasticity for a number of “vitrimers” recently developed by Leibler and coworkers.1-3 Vitrimers are covalently crosslinked networks that can relax stress at elevated temperatures due to thermoreversible bond-exchange reactions. The chosen formulations are composed of diglycidyl ether of bisphenol A, commercial fatty acid mixtures and an appropriate catalyst. The effects of the catalyst and functionality of the curing agents on the kinetics of the curing reactions were systematically investigated using rheometry. The curing kinetics followed the Arrhenius law and the catalyst drastically accelerated the reactions. Time-temperature superposition was used to construct master curves of the small-strain amplitude oscillatory shear moduli over wide ranges of frequencies for the cured networks. Terminal relaxation was not reached in oscillatory experiments for temperatures up to 130 °C and creep and stress relaxation experiments were used to probe the long-time relaxation. The shift factors displayed a Williams-Landel-Ferry dependence on temperature which could be divided into two regions, one above 70 °C, where the dynamics appeared to be controlled by the catalyst, and one below, controlled by the monomeric friction and the free volume of the network. The moduli of the vitrimers obeyed the classical rubber theory well, indicating that the curing reactions proceeded to completion. Furthermore, we systematically and reproducibly observed a double relaxation behavior for the vitrimers, i.e. next to the rubbery plateau at high frequencies, the storage modulus displayed a secondary plateau at lower frequencies before reaching terminal relaxation at even lower frequencies. Interestingly, 70 °C was found to be the transition point in agreement with the shift factors. To the best of our knowledge, the double relaxation behavior has not been previously reported in experimental works and recent theories do not incorporate an explanation for this behavior. Consequently, future investigations concerning the viscoelasticity of other “vitrimer-chemistries” are important to assess if the double relaxation is a universal fingerprint for vitrimers or if it is specific to the here-investigated formulations based on commercial fatty acid mixtures. © The Royal Society of Chemistry.

We report upon the characterization of the steady-state shear stresses and first normal stress differences as a function of shear rate using mechanical rheometry (both with a standard cone and plate and with a cone partitioned plate) and optical rheometry (with a flow-birefringence setup) of an entangled solution of asymmetric exact combs. The combs are polybutadienes (1,4-addition) consisting of an H-skeleton with an additional off-center branch on the backbone. We chose to investigate a solution in order to obtain reliable nonlinear shear data in overlapping dynamic regions with the two different techniques. The transient measurements obtained by cone partitioned plate indicated the appearance of overshoots in both the shear stress and the first normal stress difference during start-up shear flow. Interestingly, the overshoots in the start-up normal stress difference started to occur only at rates above the inverse stretch time of the backbone, when the stretch time of the backbone was estimated in analogy with linear chains including the effects of dynamic dilution of the branches but neglecting the effects of branch point friction, in excellent agreement with the situation for linear polymers. Flow-birefringence measurements were performed in a Couette geometry, and the extracted steady-state shear and first normal stress differences were found to agree well with the mechanical data, but were limited to relatively low rates below the inverse stretch time of the backbone. Finally, the steady-state properties were found to be in good agreement with model predictions based on a nonlinear multimode tube model developed for linear polymers when the branches are treated as solvent.

We present a detailed study of self-assembled hydrogels of bundled and cross-linked networks consisting of positively charged amyloid-like nanofibers and a triblock copolymer with negatively charged end blocks as a cross-linker. In a first step small oligopeptides self-assemble into macrocycles which are held together by reversible disulfide bonds. Interactions between the peptides cause the macrocycles to assemble into nanofibers, which form a reversible hydrogel. The physical properties of the hydrogel are tuned using various methods such as control over the fibre length, addition of a cross-linking copolymer, and addition of salt. We establish a relationship between the bulk mechanical properties, the properties of the individual fibers and the hydrogel morphology using characterization techniques operating at different length scales such as rheology, atomic force microscopy (AFM) and cryo transmission electron microscopy (Cryo-TEM). This allows for a precise control of the elastic behaviour of these networks.

Functionalization of xanthan hydrogels is of interest for biomaterial applications. The authors report characterization of electrostatic complexation of xanthan with a recombinant collagen-inspired triblock protein polymer. This polymer has one charged polylysine end-block that can bind to xanthan by electrostatic interactions, and another end-block that can self-assemble into thermosensitive collagen-like triple helices; the end-blocks are connected by a neutral, hydrophilic, mostly inert random coil. The protein modifies the xanthan/protein composite hydrogels in three ways: (a) a significant increase in storage modulus, (b) thermosensitivity, and (c) a two-step strain softening in nonlinear rheology.

We report on a novel synthetic route to synthesize relatively large quantities of polystyrene (PS) star polymers with targeted arm functionality and molar mass and their theological properties in the molten state. The synthetic route involves grafting styrene monomers onto a modified (aliphatic, alternating) polyketone backbone with a specific number of initiating grafting sites using controlled atom transfer radical polymerization (ATRP). Several polyketone precursors were used. This resulted in a large array of star polystyrenes with nonspherical cores and varying average arm length and number of arms. Their linear viscoelasticity was investigated and discussed in the context of the known response of anionically synthesized stars. Using a powerful characterization toolbox, including state-of-the-art interaction chromatography, rheometry, and tube modeling via the branch-on-branch (BoB) algorithm, we have assessed the viscoelasticity of these star polymers quantitatively. In particular, we have demonstrated a variability in molecular structure, which differs substantially from their anionically synthesized counterparts. Hence, whereas this new family of star polymers is not recommended for fundamental studies of polymer physics such as the molecular origin of relaxation mechanisms without prior extensive fractionation, they could be used in studies of mixtures as well as industrially relevant processing operations that require large amounts of polymeric stars.

We present a critical assessment of the range of validity of the empirical Cox-Merz rule for a wide range of model entangled polymer samples with a well-defined molecular structure, from linear monodisperse and polydisperse polymers, to branched model polymers (i.e. stars, H-polymers, and combs) and blends of linear polymers of the same chemistry. We focus on melts and concentrated solutions. Overall, we find that the simple empirical rule is obeyed rather well for the investigated cases. As often reported in the literature, relatively small systematic failures occur with the steady viscosity being below the complex one at high rates for most polymers, with linear polydisperse polymers (with a polydispersity index of about 2) being a notable exception. For the latter polymers, the rule is obeyed identically within experimental error. More unusual failures, with the steady shear viscosity being higher than the complex viscosity, are found for branched polymers with more than one branch point. More specifically, these unusual failures are observed at very high branching levels, when the backbone of the polymer is being stretched at low rates due to the motion of the branch points. The extra stress coming for the stretch renders the steady viscosity higher than the complex one. Due to the well-characterized nature of the combs, we can state that failures of the latter type are only apparent when the branches comprise more than 70 % of the molecular structure of the comb. This estimation could serve as a rough guideline in applications, although it is only a necessary and not sufficient condition for these failures to occur.

The structure and linear viscoelastic behavior of four different model star polymer melts were investigated experimentally. The star polymers were prepared via different synthetic routes based on atom transfer radical polymerization (ATRP). Stars with small elongated (linear backbone) cores exhibited slight differences in the asymmetry of the core, which however did not affect the rheological properties significantly. The relaxation behavior of these stars with an asymmetric core was well-described by available tube models. On the other hand, stars with large cross-linked cores exhibited a core–shell morphology and their stress relaxation was dominated by a power-law decay over about 8 decades, akin to gel-like soft systems. This behavior reflected their liquid-like ordering and small intercore distances, and bares analogueies to that of interpenetrating soft colloids and microgels.

We report on a detailed rheological investigation of well-defined symmetric entangled polymer stars of low functionality with varying number of arms, molar mass of the arms, and solvent content. Emphasis is placed on the response of the stars in simple shear, during start-up, and for relaxation upon flow cessation. To reduce experimental artifacts associated with edge fracture (primarily) and wall slip, we employ a homemade cone-partitioned plate fixture which was successfully implemented in recent studies. Reliable data for these highly entangled stars could be obtained for Weissenberg numbers below 300. The appearance of a stress overshoot during start-up with a corresponding strain approaching a value of 2 suggests that in the investigated shear regime the stars orient but do not stretch. This is corroborated by the fact that the empirical Cox–Merx rule appears to be validated, within experimental error. On the other hand, the (shear) rate dependent steady shear viscosity data exhibit a slope smaller t...

We report on the shear flow start-up and the relaxation upon flow cessation of anionically synthesized comb polymers of different chemistries. The experimental data, obtained with a cone partitioned-plate geometry in order to avoid artifacts, showed that the start-up shear flow of combs exhibits systematic dependencies on the branching structure. They were interpreted by invoking dynamic dilution and hierarchical relaxation, which are known to control the linear viscoelastic response. For all combs studied here, the backbones remained entangled after dynamic dilution due to branch relaxation. We combined the important molecular parameters (i.e., the number and molar mass of the branches) into a single parameter, the number of entanglements of the dynamically diluted backbone, ZBBDIL., which we found to be the main scaling parameter for the observed nonlinear flow behavior. The steady viscosities as function of Weissenberg number were less shear-thinning compared to linear analogues, and the higher the amo...

A cone-partitioned-plate fixture for the ARES rheometer (TA instruments, DE) has been designed, implemented, and validated. This geometry allows measuring the nonlinear shear flow properties of samples, which display edge fracture in regular cone-and-plate geometries, such as polymer melts and concentrated solutions. Reliable bulk shear flow data can be obtained with these systems at high rates and strains, using very small sample quantities. Measurements can be performed at temperatures ranging from at least − 50 °C up to over 200 °C in a controlled nitrogen environment. An extensive set of start-up shear measurements on moderately entangled linear monodisperse polyisoprene (60 kg/mol) and polystyrene (182 kg/mol) melts to validate the design are presented and discussed with focus on the Cox–Merz rule and the characteristics of the stress overshoot. With this new geometry, the range of artifact-free data is extended by a decade in Weissenberg number (WiD). It is shown that the obtained results compared w...

Ordering induced by shear flow can be used to direct the assembly of particles in suspensions. Flow-induced ordering is determined by the balance between a range of forces, such as direct interparticle, Brownian, and hydrodynamic forces. The latter are modified when dealing with viscoelastic rather than Newtonian matrices. In particular, 1D stringlike structures of spherical particles have been observed to form along the flow direction in shear thinning viscoelastic fluids, a phenomenon not observed in Newtonian fluids at similar particle volume fractions. Here we report on the formation of freestanding crystalline patches in planes parallel to the shearing surfaces. The novel microstructure is formed when particles are suspended in viscoelastic, wormlike micellar solutions and only when the applied shear rate exceeds a critical value. In spite of the very low volume fraction (less than 0.01), particles arrange themselves in 2D crystalline patches along the flow direction. This is a bulk phenomenon because 2D crystals form throughout the whole gap between plates, with the gap thickness being much larger than the particle size. Shear flow may hence be an easy method to drive particles into crystalline order in suspensions with viscoelastic properties. The crystalline structure reported here could be used to design new materials with special mechanical, optical, thermal, or electric properties.

We briefly review the recent advances in the rheology of entangled polymers and identify emerging research trends and outstanding challenges, especially with respect to branched polymers. Emphasis is placed on the role of well-characterized model systems, as well as the synergy of synthesis-characterization, rheometry and modeling/simulations. The theoretical framework for understanding the observed linear and nonlinear rheological phenomena is the tube model which is critically assessed in view of its successes and shortcomings, whereas alternative approaches are briefly discussed. Finally, intriguing experimental findings and controversial issues that merit consistent explanation, such as shear banding instabilities, multiple stress overshoots in transient simple shear and enhanced steady-state elongational viscosity in polymer solutions, are discussed, whereas future directions such as branch point dynamics and anisotropic monomeric friction are outlined., Comment: 25 pages, accepted for publication in Journal of Physics Condensed Matter (August 2015)

We report the design, production and characterization of a biosynthetic asymmetric triblock copolymer which consists of one collagen-like and one cationic block spaced by a hydrophilic random coiled block. The polymer associates into micelles when a polyanion is added due to the electrostatic interaction between the cationic block and the polyanion. The collagen-like block self-assembles into thermo-responsive triple helices upon cooling. When both end blocks are induced to self-assemble, a physical gel is formed via thermo-responsive association of the charge-driven micelles. The self-assembly of both end blocks and the effects of salt and temperature thereon were characterized by light scattering and rheology.

The ability to purify cyclic polymers with liquid chromatography at the critical condition and the recent advances in theoretical modeling and advanced simulations have opened the route for determining and understanding their rheological properties, and hence resolving a nearly 30-years old controversy. In the unentangled regime, the zero-shear viscosity of cyclic polymers is half that of their linear counterparts and their rheology conforms to the Rouse model. The behavior of entangled rings conforms to the lattice animal configuration and is characterized by a self-similar stress relaxation with a power law exponent of about 0.4 extending over 3 decades in time. No entanglement plateau is observed. Their viscosity remains much smaller in comparison to linear polymers. Tiny amounts of linear chain contaminants (of the order of 0.1%, below their overlap concentration) dramatically alter the rheology of rings as they entropically penetrate them, forming a transient network of linear chains bridged by rings. Despite the significant progress, many outstanding challenges lie ahead and make this topic fascinating.

The effect of using a viscoelastic suspending medium, on the;in-plane hydrodynamic interaction between two equally sized spheres in shear flow is studied experimentally to understand flow-induced assembly behavior (i.e., string formation). A counterrotating device equipped with a Couette geometry is used together with quantitative videomicroscopy. To evaluate the effects of differences in rheological properties of the suspending media, fluids have been selected that highlight specific constitutive feature's. These include a reference Newtonian fluid (N), a,constant-viscosity, high-elasticity Boger fluid (BF), a wormlike micellar surfactant solution with a, single dominant relaxation time (WMS), and a broad spectrum shear-thinning elastic polymer solution (ST). As expected, the trajectories are symmetric in the Newtonian fluid. In the BF, the midpoints. of the spheres are observed to remain in the same plane before and after,the interaction, as in the Newtonian fluid, although the path lines are in this case no longer symmetric. Interactions in the, ST and WMS are highly asymmetric. Two, fundamentally different kinds of path lines are Observed in the WMS and ST: reversing and Open trajectories: The type of trajectory depends on the initial Configuration of the spheres with respect to:each,other and on the shear rate. On the basis of the obtained results, shear-thinning of the viscosity seems to be the key rheological parameter that determines the overall nature of, the interactions rather than the relative magnitude of the normal stress differences.

The intrinsically coupled effects of the curvature of the flow-field and of the viscoelastic nature of suspending medium on the cross-stream lateral migration of a single non-Brownian sphere in wide-gap Couette flow are studied. Quantitative videomicroscopy experiments using a counterrotating device are compared to the results of 3D finite element simulations. To evaluate the effects of differences in rheological properties of the suspending media, fluids have been selected which highlight specific constitutive features, including a reference Newtonian fluid, a single relaxation time wormlike micellar surfactant solution, a broad spectrum shear-thinning elastic polymer solution and a constant viscosity, highly elastic Boger fluid. As expected for conditions corresponding to Stokes flow, migration is absent in the Newtonian fluid. In the wormlike micellar solution and the shear-thinning polymer solution, spheres are observed to migrate in the direction of decreasing shear rate gradient, i.e. the outer cylinder, except when the sphere is initially released close to the inner cylinder, in which case the migration is towards it. The migration is enhanced by faster relative angular velocities of the cylinders. Shear-thinning reduces the migration velocity, showing an opposite behavior as compared to previous results in planar shear flow. In the Boger fluid, within experimental error no migration could be observed, likely due to the large solvent contribution to the overall viscosity. For small Deborah numbers the migration results are well described by an heuristic argument based on a local stress balance.

When particles are dispersed in viscoelastic rather than Newtonian media, the hydrodynamics will be changed entailing differences in suspension rheology. The disturbance velocity profiles and stress distributions around the particle will depend on the viscoelastic material functions. Even in inertialess flows, changes in particle rotation and migration will occur. The problem of the rotation of a single spherical particle in simple shear flow in viscoelastic fluids was recently studied to understand the effects of changes in the rheological properties with both numerical simulations [D’Avino et al., J. Rheol. 52 (2008) 1331–1346] and experiments [Snijkers et al., J. Rheol. 53 (2009) 459–480]. In the simulations, different constitutive models were used to demonstrate the effects of different rheological behavior. In the experiments, fluids with different constitutive properties were chosen. In both studies a slowing down of the rotation speed of the particles was found, when compared to the Newtonian case, as elasticity increases. Surprisingly, the extent of the slowing down of the rotation rate did not depend strongly on the details of the fluid rheology, but primarily on the Weissenberg number defined as the ratio between the first normal stress difference and the shear stress. In the present work, a quantitative comparison between the experimental measurements and novel simulation results is made by considering more realistic constitutive equations as compared to the model fluids used in previous numerical simulations [D’Avino et al., J. Rheol. 52 (2008) 1331–1346]. A multimode Giesekus model with Newtonian solvent as constitutive equation is fitted to the experimentally obtained linear and nonlinear fluid properties and used to simulate the rotation of a torque-free sphere in a range of Weissenberg numbers similar to those in the experiments. A good agreement between the experimental and numerical results is obtained. The local torque and pressure distributions on the particle surface calculated by simulations are shown.

The effect of the viscoelastic nature of the suspending medium on the rotation of spherical particles in a simple shear flow is studied experimentally using a counter-rotating device. To evaluate the effect of variations in rheological properties of the suspending media, fluids have been selected which highlight specific constitutive features. These include a reference Newtonian fluid, a constant viscosity, high elasticity Boger fluid, a single relaxation time wormlike micellar surfactant solution, and a broad spectrum shear-thinning elastic polymer solution. It is shown that particle rotation slows down, when compared to the Newtonian case, as elasticity increases, in qualitative agreement with computer simulation studies. Despite the variation in constitutive properties and the wide range of time scales of the fluids, it is found that the Weissenberg number suffices to scale the data: the dimensionless rotation speed of the spheres in the different fluids scales onto a single master curve as a function of the Weissenberg number. This indicates that the slowing down in rotation finds its main origin in (indirect) normal stress effects. ©2009 The Society of Rheology

The rotation speed of spherical particles in a shear flow is studied experimentally in rheologically different fluids. The fluids, selected to highlight specific constitutive features, include a Newtonian fiuid, a Boger fluid, a wormhke micellar surfactant solution, and a shear thinning elastic polymer solution. It is shown experimentally that particle rotation slows down, when compared to the Newtonian case, as elasticity increases. This is in qualitative agreement with TFEM simulation studies. Furthermore, the dimensionless rotation speed of the spheres in the different fluids as function of the elasticity of the medium scales onto a single curve. This scaling with the Weissenberg number was somewhat unexpected given simulation results for different rheological models, where significant differences are observed for selected single relaxation time differential models.

In inertialess suspensions of rigid particles, the rotational motion of each particle is governed by the so-called freely rotating condition, whereby the total torque acting on the particle must be zero. In this work, we study the effect of viscoelasticity of the suspending liquid on the rotation period of a sphere by means of three-dimensional finite element simulations, for conditions corresponding to a macroscopic shear flow. The simulation results capture the slowing down of the rotation, relative to the Newtonian case, which was recently observed in experiments. It is shown that such a phenomenon depends on the specific constitutive equation adopted for the viscoelastic liquid. Analysis of transients shows a clear correlation between rotation rate and the development of first normal stress difference.

An emerging challenge in polymer physics is the quantitative understanding of the influence of a macromolecular architecture (i.e., branching) on the rheological response of entangled complex polymers. Recent investigations of the rheology of well-defined architecturally complex polymers have determined the composition in the molecular structure and identified the role of side-products in the measured samples. The combination of different characterization techniques, experimental and/or theoretical, represents the current state-of-the-art. Here we review this interdisciplinary approach to molecular rheology of complex polymers, and show the importance of confronting these different tools for ensuring an accurate characterization of a given polymeric sample. We use statistical tools in order to relate the information available from the synthesis protocols of a sample and its experimental molar mass distribution (typically obtained from size exclusion chromatography), and hence obtain precise information about its structural composition, i.e. enhance the existing sensitivity limit. We critically discuss the use of linear rheology as a reliable quantitative characterization tool, along with the recently developed temperature gradient interaction chromatography. The latter, which has emerged as an indispensable characterization tool for branched architectures, offers unprecedented sensitivity in detecting the presence of different molecular structures in a sample. Combining these techniques is imperative in order to quantify the molecular composition of a polymer and its consequences on the macroscopic properties. We validate this approach by means of a new model asymmetric comb polymer which was synthesized anionically. It was thoroughly characterized and its rheology was carefully analyzed. The main result is that the rheological signal reveals fine molecular details, which must be taken into account to fully elucidate the viscoelastic response of entangled branched polymers. It is important to appreciate that, even optimal model systems, i.e., those synthesized with high-vacuum anionic methods, need thorough characterization via a combination of techniques. Besides helping to improve synthetic techniques, this methodology will be significant in fine-tuning mesoscopic tube-based models and addressing outstanding issues such as the quantitative description of the constraint release mechanism.