We present a comprehensive experimental rheological dataset for purified entangled ring polystyrenes and their blends with linear chains in nonlinear shear and elongation. In particular, data for shear stress growth coefficient, steady-state shear viscosity, and first and second normal stress differences are obtained and discussed as functions of shear rate as well as molecular parameters (molar mass, blend composition and decreasing molar mass of linear component in blend). Over the extended parameter range investigated, rings do not exhibit clear transient undershoot in shear, in contrast to their linear counterparts and ring-linear blends. For the latter, the size of the undershoot and respective strain appear to increase with shear rate. Universal scaling of strain at overshoot and fractional overshoot (ratio of maximum to steady-state shear stress growth coefficient) indicates subtle differences in the shear-rate dependence between rings and linear polymers or their blends. The shear thinning behaviour of pure rings yields a slope nearly identical to predictions (-4/7) of a recent shear slit model and molecular dynamics simulations. Data for the second normal stress difference are reported for rings and ring-linear blends. While is negative and its absolute value stays below that of , as for linear polymers, the ratio is unambiguously larger for rings compared to linear polymer solutions with the same number of entanglements (almost by factor of two), in agreement with recent non-equilibrium molecular dynamics simulations. Further, - exhibits slightly weaker shear rate dependence compared to at high rates, and the respective power-law exponents can be rationalized in view of the slit model (3/7) and simulations (0.6), although further work is needed to unravel the molecular original of the observed behaviour. The comparison of shear and elongational stress growth coefficients for blends reflects the effect of ring-linear threading which leads to significant viscosity enhancement in elongation. Along the same lines, the elongational stress is much larger than the first normal stress in shear, and their ratio is much larger for rings and ring-linear blends compared to linear polymers. This conforms the interlocking scenario of rings and their important role in mechanically reinforcing linear matrices.

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 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.

Viscoelastic shear properties of human vocal fold tissues were previously quantified by the shear moduli ( and ). Yet these small-strain linear measures were unable to describe any nonlinear tissue behavior. This study attempted to characterize the nonlinear viscoelastic response of the vocal fold lamina propria under large-amplitude oscillatory shear (LAOS) with a stress decomposition approach. Human vocal fold cover and vocal ligament specimens from eight subjects were subjected to LAOS rheometric testing with a simple-shear rheometer. The empirical total stress response was decomposed into elastic and viscous stress components, based on odd-integer harmonic decomposition approach with Fourier transform. Nonlinear viscoelastic measures derived from the decomposition were plotted in Pipkin space and as rheological fingerprints to observe the onset of nonlinearity and the type of nonlinear behavior. Results showed that both the vocal fold cover and the vocal ligament experienced intercycle strain softening, intracycle strain stiffening, as well as shear thinning both intercycle and intracycle. The vocal ligament appeared to demonstrate an earlier onset of nonlinearity at phonatory frequencies, and higher sensitivity to changes in frequency and strain. In summary, the stress decomposition approach provided much better insights into the nonlinear viscoelastic behavior of the vocal fold lamina propria than the traditional linear measures.

The rheological properties of a particle suspension can be substantially altered by adding a small amount of a secondary fluid that is immiscible with the bulk phase. The drastic change in the strength of these capillary suspensions arises due to the capillary forces, induced by the added liquid, leading to a percolating particle network. Using rheological scaling models, fractal dimensions are deduced from the yield stress and from oscillatory strain amplitude sweep data as function of the solid volume fraction. Exponents obtained using aluminum-oxide-based capillary suspensions, with a preferentially wetting secondary fluid, indicate an increase in the particle gel's fractal dimension with increasing particle size. This may be explained by a corresponding relative reduction in the capillary force compared to other forces. Confocal images using a glass model system show the microstructure to consist of compact particle flocs interconnected by a sparse backbone. Thus, using the rheological models two different fractal dimensionalities are distinguished - a lower network backbone dimension ( = 1.86-2.05) and an intrafloc dimension ( = 2.57-2.74). The latter is higher due to the higher local solid volume fraction inside of the flocs compared to the sparse backbone. Both of these dimensions are compared with values obtained by analysis of spatial particle positions from 3D confocal microscopy images, where dimensions between 2.43 and 2.63 are computed, lying between the two dimension ranges obtained from rheology. The fractal dimensions determined via this method corroborate the increase in structural compactness with increasing particle size.

The crystallization of a polymer melt is characterized by dramatic structural and mechanical changes that significantly impact the processing conditions used to generate industrially-relevant products. Relationships between crystallinity and rheology are necessary to simulate and monitor the effect of processing conditions on the properties of the final product. However, separate measurements of crystallinity and rheology are difficult to correlate due to differences in sample history, geometry, and temperature. Recently, we have developed a rheo-Raman microscope for simultaneous rheology, Raman spectroscopy, and polarized reflection-mode optical measurements of soft materials, which allows for quantitative crystallinity measurements through features in the Raman spectrum. In this work, we apply this technique to monitor the isothermal crystallization of polycaprolactone to probe the relationship between structure, crystallinity, and rheology. Both crystallinity and the shear modulus vary over comparable timescales, but the birefringence increases much earlier in the crystallization process. We directly plot rheological parameters as a function of crystallinity to probe a range of suspension-based and empirical models relating the complex modulus to crystallinity, and we find that the previously developed models cannot describe the crystallinity-modulus relationship over the crystallization process. By developing a suspension-based model we can fit the complex modulus over the crystallization range. The crystallization process is characterized by a critical percolation fraction and a single scaling exponent.

Viscoelastic measurements made with a stress-controlled rheometer are affected by system inertia. Of all contributors to system inertia, motor inertia is the largest. Its value is usually determined empirically and precision is rarely if ever specified. Inertia uncertainty has negligible effects on rheologic measurements below the coupled motor/plate/sample resonant frequency. But above the resonant frequency, G' values of soft viscoelastic materials such as dispersions, gels, biomaterials, and non-Newtonian polymers, err quadratically due to inertia uncertainty. In the present investigation, valid rheologic measurements were achieved near and above the coupled resonant frequency for a non-Newtonian reference material. At these elevated frequencies, accuracy in motor inertia is critical. Here we compare two methods for determining motor-inertia accurately. For the first (commercially-used) phase method, frequency responses of standard fluids were measured. Phase between G' and G" was analyzed at 5-70 Hz for motor inertia values of 50-150% of the manufacturer's nominal value. For a newly-devised two-plate method (10 mm and 60 mm parallel plates), dynamic measurements of a non-Newtonian standard were collected. Using a linear equation of motion with inertia, viscosity, and elasticity coefficients, G' expressions for both plates were equated and motor inertia was determined to be accurate (by comparison to the phase method) with a precision of ± 3%. The newly developed two-plate method had advantages of expressly eliminating dependence on gap, was explicitly derived from basic principles, quantified the error, and required fewer experiments than the commercially used phase method.

We present experimental data and numerical modeling of a nonlinear phenomenon in active magnetic microbead rheology that appears to be common to entangled polymer solutions (EPS). Dynamic experiments in a modest range of magnetic forces show: 1. a short-lived high viscosity plateau, followed by 2. a bead acceleration phase with a sharp drop in apparent viscosity, and 3. a terminal steady state that we show resides on the shear-thinning slope of the steady-state flow curve from cone and plate data. This latter feature implies a new protocol to access the nonlinear steady-state flow curve for many biological EPS only available in microliter-scale volumes. We solve the moment-closure form of the Rolie-Poly kinetic model for EPS hydrodynamics, together with a decoupling approximation that obviates the need for a full 3D flow solver, and show that the model qualitatively reproduces the dynamic experimental sequence above. In this way, we explain the phenomenon in terms of entangled polymer physics, and show how the nonlinear event (acceleration and termination on the shear-thinning response curve) is tunable by the interplay between molecular-scale mechanisms (relaxation via reptation and chain retraction) and magnetic force controls. The experimental conditions mimic movement of cilia tips, bacteria, and sperm in mucus barriers, implying a physiological relevance of the phenomenon, and compelling further development of the fully coupled, 3D flow-microstructure model to achieve quantitative accuracy.

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.

Polymer crystallization occurs in many plastic manufacturing processes, from injection molding to film blowing. Linear low-density polyethylene (LLDPE) is one of the most commonly processed polymers, wherein the type and extent of short-chain branching (SCB) may be varied to influence crystallization. In this work, we report simultaneous measurements of the rheology and Raman spectra, using a Rheo-Raman microscope, for two industrial-grade LLDPEs undergoing crystallization. These polymers are characterized by broad polydispersity, SCB and the presence of polymer chain entanglements. The rheological behavior of these entangled LLDPE melts is modeled as a function of crystallinity using a slip-link model. The partially crystallized melt is represented by a blend of linear chains with either free or crosslinked ends, wherein the crosslinks represent attachment to growing crystallites, and a modulus shift factor that increases with degree of crystallinity. In contrast to our previous application of the slip-link model to isotactic polypropylene (iPP), in which the introduction of only bridging segments with crosslinks at both ends was sufficient to describe the available data, for these LLDPEs we find it necessary to introduce dangling segments, with crosslinks at only one end. The model captures quantitatively the evolution of viscosity and elasticity with crystallization over the whole range of frequencies in the linear regime for two LLDPE grades.

The rheology of crystallizing polymers is critical to polymer processing, but our current understanding of how crystallinity affects rheology during crystallization is lacking. The challenge is twofold: first, we must measure rheology simultaneously with crystallinity, and then we must develop models that can describe those measurements as well as prior phenomenological observations. Here, we further develop a generalized effective medium model to describe the frequency-dependent shear modulus of a crystallizing polymer. Through a simple model system, we show that the percolation transition in the effective medium model recovers the relaxation dynamics of a critical gel with a relaxation spectrum that can be approximated as the power mean of the initial melt and final semicrystalline material. We demonstrate the success of this model on the isothermal crystallization of polycaprolactones. From the generalized effective medium model, we can calculate the percolation fraction and power law relaxation exponent at the critical point, even when the measurement frequency range is dominated by shear thinning of the melt phase.

The viscosity of a shear-banding wormlike micelle solution at high shear rates is investigated using capillary rheology and particle streak velocimetry. Measurements of the flow profile and pressure gradient show an extended entrance region, which exceeds a length to diameter ratio of 100, to reach a fully developed flow. We characterized this entrance region for capillaries with different cross-sections and use the results to select a downstream portion of the capillary where viscosity measurements can be made on fully developed flow. Measurements from this portion of the channel show a shear-thinning power-law behavior for all channel geometries from shear rates of 1000 to 120000 . Varying the surfactant concentration shows two distinct power-law behaviors that depend on both shear rate and concentration and are an indication of change in micelle length.