Index of content:
Volume 57, Issue 2, March 2013

Parallel plate geometry at narrow gaps allows one to perform rheology at high shear rates and with small volumes of fluid. The results from this analysis have to be corrected for a systematic error in the actual gap between the plates. We review the statistical and error analysis methodology for such applications and demonstrate that the process for estimating the gap error significantly impacts the overall accuracy of the analysis at narrow gaps. It is shown that the standard linear regression approach to the estimation of the gap correction is unsound and must not be used in practice. We highlight alternative methods and illustrate their accuracy with typical examples from narrow gap rheology.

Review of algorithms for estimating the gap error correction in narrow gap parallel plate rheology
View Description Hide DescriptionParallel plate geometry at narrow gaps allows one to perform rheology at high shear rates and with small volumes of fluid. The results from this analysis have to be corrected for a systematic error in the actual gap between the plates. We review the statistical and error analysis methodology for such applications and demonstrate that the process for estimating the gap error significantly impacts the overall accuracy of the analysis at narrow gaps. It is shown that the standard linear regression approach to the estimation of the gap correction is unsound and must not be used in practice. We highlight alternative methods and illustrate their accuracy with typical examples from narrow gap rheology.

Comparative study of interphase viscoelastic properties in polyethylene/polyamide blends compatibilized with clay nanoparticles or with a graft copolymer
View Description Hide DescriptionThe linear viscoelastic properties of immiscible polyethylene/polyamide blends filled with clay nanoparticles or compatibilized by a copolymer, exhibiting identical nodular morphologies, have been studied. The apparent compatibilizing effect of clay nanoparticles, exclusively located at the interface, was evidenced and compared to the more classical organic compatibilization due to the formation of a macromolecular interphase. The results show that there are some analogies between the two types of compatibilization, but mainly highlight significant differences in rheological properties of the two types of interphase involved in the compatibilization mechanisms. The major differences in interphase viscoelastic properties were evidenced not only directly from the experimental data but also indirectly by using the Palierne's model for different clay or compatibilizer contents.

Melt fracture and wall slip of metallocenecatalyzed bimodal polyethylenes in capillary flow
View Description Hide DescriptionThe melt fracture and wall slip behaviors of three metallocenecatalyzed bimodal polyethylene (PE) resins and one unimodal PE resin were investigated and critically compared. By comparing the flow curve observed by capillary rheology measurements with the linear viscoelastic (LVE) data, it was observed that the apparent slip increased with content of low molecular weight (MW) component. The bimodal resins that had higher content of low MW component first showed a matte surface at lower stresses. The matte surface remained until the extrudate converted to a wavy appearance before the stickslip transition as shear rates were increased. The plateau modulus estimated from the LVE data decreased with the increase in low MW content. It was observed that the onset stress of the matte surface (or sharkskin) melt fracture was proportional to the plateau modulus. It was proposed that the distinct separation of the two modes of the bimodal PE resin and the high content of small chains could cause the significant wall slip and the unusual melt fracture behaviors.

Linear viscoelastic properties of ethylene–octene copolymer/nanosilica composites investigated over a broad range of frequencies
View Description Hide DescriptionThe interrelations between microstructure and rheology of melt compounded poly(ethylenecooctene) (EOC) based nanocomposites containing low amounts of silica (SiO_{2}) nanoparticles were studied. In the presence of a maleated EOC compatibilizer, hydrogen bonds are established between the silanol groups located on the surface of the particles and the succinic anhydride functionality of the compatibilizer, resulting in improved filler dispersion during compounding and the formation of a bound layer of polymer surrounding the particles. This layer alters the interface between the bulk polymeric matrix and the particles, influencing the linear viscoelastic (LVE) response. The compatibilized composites exhibited a more stable response in time sweeps and a higher critical strain for the onset of nonlinearity, compared to their noncompatibilized counterparts. Superposition of small angle oscillatory shear and creep/creep recovery experiments revealed enhancements in the LVE functions in the absence of a compatibilizer, which are attributed to the increased hydrodynamic effect due to increased propensity for particle aggregation, and to the direct interactions between the polymer chains and the surface of the filler. On the contrary these effects were moderated in the case of the compatibilized composites, due to the presence of the bound layer of polymer surrounding the particles.

Anisotropic thermal conduction in polymer melts in uniaxial elongation flows
View Description Hide DescriptionAnisotropic thermal conduction was measured in two amorphous polymers that were quenched immediately after being subjected to uniaxial elongation in the molten state. The quenching is performed so that the flowinduced orientation is retained and the samples are essentially in a stressfree state. A novel optical technique based on forced Rayleigh scattering is used to measure the two independent components of the thermal diffusivity tensor as a function of strain and strain rate. The thermal diffusivity is found to increase in the direction parallel, and decrease in the direction perpendicular, to the direction of elongation. Thermal diffusivity data along with measurements of the tensile stress at the point of quenching were used to evaluate the stressthermal rule, which is analogous to the wellknown stressoptic rule. The stressthermal rule was found to be valid for both polymers over a range of strains and strain rates. Since the quenched samples have orientation only, it appears that the primary source of anisotropy in thermal conductivity is the anisotropy of polymer chain orientation.

High frequency linear rheology of complex fluids measured from their surface thermal fluctuations
View Description Hide DescriptionWe characterize the linear viscoelastic properties of complex fluids using a new technique, based on the measurement of surface fluctuations: surface fluctuation specular reflection (SFSR) spectroscopy. The thermally excited waves propagating on a free surface are measured through the deflection of a laser beam specularly reflected from that surface. Elastic and loss moduli of the complex fluids are inferred from the measured power spectrum density of thermal noise, with the implicit use of Kramers–Kronig relations. The technique, besides being noninvasive, provides rheological data in a large frequency range and at vanishing strains. It is therefore especially well suited for the rheological characterization of complex fluids. We present measurements of the viscoelastic modulus of supramolecular polymer solutions in a frequency range extending up to six decades. We compare the SFSR measurements with rheometric data at low and high frequencies, and show that they are in good agreement. Using supramolecular polymer solutions of different natures, exhibiting or not surface viscoelasticity, we furthermore show that SFSR provides a characterization of the bulk properties of the fluids. In addition, we discuss the accuracy of the measurements.

Stress development, relaxation, and memory in colloidal dispersions: Transient nonlinear microrheology
View Description Hide DescriptionThe motion of a single Brownian particle in a complex fluid can reveal material behavior both at and away from equilibrium. In active microrheology, a probe particle is driven by an external force through a complex medium and its motion studied in order to infer properties of the embedding material. Most work in microrheology has focused on steady behavior and established the relationship between the motion of the probe, the microstructure, and the effective microviscosity of the medium. Transient behavior in the nearequilibrium, linearresponse regime has also been studied via its connection to lowamplitude oscillatory probe forcing and the complex modulus; at very weak forcing, the microstructural response that drives viscosity is indistinguishable from equilibrium fluctuations. But important information about the basic physical aspects of structural development and relaxation in a medium is captured by startup and cessation of the imposed deformation in the nonlinear regime, where the structure is driven far from equilibrium. Here, we study theoretically and by dynamic simulation the transient behavior of a colloidal dispersion undergoing nonlinear microrheological forcing. The strength with which the probe is forced, , compared to thermal forces, kT/b, governs the dynamics and defines a Péclet number, , where kT is the thermal energy and b is the colloidal bath particle size. For large Pe, a boundary layer (in which unsteady advection balances diffusion) forms at particle contact on the time scale of the flow, a/U, where a is the probe size and U its speed, whereas the wake forms over O(Pe) diffusive time steps. Similarly, relaxation following cessation occurs over several time scales corresponding to distinct physical processes. For very short times, the time scale for relaxation is set by a boundary layer of thickness , and so , where is the relative diffusivity between the probe of size a and a bath particle. Nearly all stress relaxation occurs during this time. At longer times, the Brownian diffusion of the bath particles acts to close the wake on a time scale set by how long it takes a bath particle to diffuse laterally across it, . Although the majority of the microstructural relaxation occurs during this wakehealing process, it does so with little change in the stress. Also during relaxation, the probe travels backward in the suspension; this recovered strain is proportional to the free energy stored in the compressed particle configuration, an indicator that the stress is proportional to the free energy density stored entropically in the microstructure. Theoretical results are compared with Brownian dynamics simulation where it is found that the dilute theory captures the correct behavior even for concentrated suspensions. Two modes of forcing are studied: Constant force and constant velocity. Results are compared to analogous macrorheology results for suspensions undergoing simple shear flow.

Viscometric functions for noncolloidal sphere suspensions with Newtonian matrices
View Description Hide DescriptionWe present the results of measuring the three viscometric functions [the relative viscosity , and the first ( ) and second ( ) normal stress differences] for nominally monosize sphere suspensions in a silicone fluid, which is nominally Newtonian. The measurements of and were made with a parallelplate rheometer, while we used the open semicircular trough method to give directly. With the trough method measurements of could be made down to a 10% concentration ( ); measurements were continued up to 45% concentration. The trough surface shows visually that is directly proportional to the shear stress τ, and the measurements of agree quite well with the results of Zarraga et al. [J. Rheol. 44, 185–220 (2000)] in the range where concentrations overlap (0.3–0.45) and with those of later investigators. The results for show greater scatter. In the range , our best estimate of is and that of is . Hence, the magnitude of is much greater than that of . Measurement uncertainties are given in the text—they depend on φ. We have also compared the new experiments with two sets of numerical simulations. There is considerable divergence, which remains to be explained, between some of the simulations and the experiments. However, agreement between experiment and some of the simulations of Bertevas et al. [Rheol. Acta 49, 53–73 (2010)] is reasonable.

Role of linear viscoelasticity and rotational diffusivity on the collective behavior of active particles
View Description Hide DescriptionA linear dynamics scheme has been used to quantify the impact of viscoelasticity of the suspending fluid on the collective structure of active particles, including rotational diffusivity. The linear stability examines the response near an isotropic state using a meanfield theory including farfield hydrodynamic interactions of the swimmers. The kinetic model uses three possible constitutive models, the OldroydB, Maxwell, and generalized linear viscoelastic models inspired by fluids like saliva, mucus, and biological gels. The perturbation growth rate has been quantified in terms of wavenumber, translational diffusivity, rotational diffusivity, and material properties of the fluids. A key dimensionless group is the Deborah number, which compares the relaxation time of the fluid with the characteristic timescale of the instability. An advantage of the model formalism is the ability to calculate some properties analytically and others efficiently numerically in the presence of rotational diffusion. The different constitutive equations examined help illustrate when and why the dispersion relation can have a peak at a particular wavenumber. The fluid properties can also change the role of rotational diffusion; diffusion always stabilizes a system in a Newtonian fluid but can destabilize a system in a Maxwell fluid.

Approximations of the discrete sliplink model and their effect on nonlinear rheology predictions
View Description Hide DescriptionThe discrete sliplink model (DSM) was developed to describe the dynamics of flexible polymer melts. The model is able to predict linear viscoelasticity of monodisperse linear, polydisperse linear, and branched systems. The model also shows good agreement with dielectric relaxation experiments, except for the single data set available for bidisperse linear systems with a small volume fraction of long chains. In this work, both shear and elongational flow predictions obtained using the DSM without parameter adjustment are shown. Model predictions for shear flow agree very well with experimental results. The DSM is able to capture the transient response as well as the steadystate viscosity. However, for elongational flow, agreement is unsatisfactory at large strains. The DSM captures the onset of strain hardening, but after a Hencky strain between 2 and 3, it predicts transient strain softening, whereas experiments show only monotonic growth. We explore a number of assumptions and approximations of the model and their effect on flow predictions. The approximations are related to the neglect of these phenomena, which are expected to be more sensitive in elongational flow: finite extensibility, convective constraint release, and deformation of dangling ends. We indeed find that shear flow predictions are insensitive to these approximations, but elongational flow is affected. However, none of these effects is able to bring prediction in line with experiments. We conclude that the currently accepted view of entanglement dynamics is incomplete.

Necking in extrusion film casting: The role of macromolecular architecture
View Description Hide DescriptionExtrusion film casting (EFC) is used on an industrial scale to produce several thousand tons of polymer films and coatings. While significant research has been carried out on necking of films of viscoelastic melts in EFC, the influence of macromolecular chain architecture on the necking behavior is not yet fully understood. In the present research, we have explored experimentally and theoretically the effects of long chain branching and molecular weight distribution on the extent of necking during EFC. Polyethylenes of essentially linear architecture but having narrow and broad molecular weight distributions, and polyethylenes having long chain branching were used for experimental studies. The EFC process was analyzed using the onedimensional flow model of Silagy et al. [Polym. Eng. Sci. 36(21), 2614–2625 (1996)] in which multimode molecular constitutive equations namely the “extended pompom” equation (for long chain branched polymer melts) and the “Rolie–Poly (Rouse linear entangled polymers)” equation (for linear polymer melts) were incorporated. We show that the model qualitatively captures the salient features of the experimental data thereby elucidating the role of chain architecture on the extent of necking.

Dissipative particle dynamics modeling of low Reynolds number incompressible flows
View Description Hide DescriptionThis paper is concerned with the numerical modeling of a slow (creeping) flow using a particlebased simulation technique, known as dissipative particle dynamics (DPD), in which the particles' mass is allowed to approach zero to simultaneously achieve a high sonic speed, a low Reynolds number, and a high Schmidt number. This leads to a system of stiff stochastic differential equations, which are solved efficiently by an exponential time differencing (ETD) scheme. The ETDDPD method is first tested in viscometric flows, where the particle mass is reduced down to 0.001. The method is then applied for the modeling of rigid spheres in a Newtonian fluid by means of two species of DPD particles, one representing the solvent particles and the other, the suspended particle. Calculations are carried out at particle mass of 0.01, with corresponding Mach number of 0.08, Reynolds number of 0.05, and Schmidt number of . Stokes results are used to determine the DPD parameters for the solventsphere interaction forces. The method obeys equipartition and yields smooth flows around the sphere with quite uniform farfield velocities.

Uniaxial extensional rheology of wellcharacterized comb polymers
View Description Hide DescriptionWe present a detailed systematic investigation of the transient uniaxial extensional response of a series of wellcharacterized, 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 longchain branched polyolefins.

Apparent elongational yield stress of soft matter
View Description Hide DescriptionApparent elongational yield stresses of soft matter including polymer gels, highly concentrated emulsions, and aggregated suspensions have been determined from step stretch experiments. Materials display apparent shear yield stresses in the range 1–100 Pa and large but finite shear relaxation times t_{R}. For all investigated fluids, the Laplace pressure within the stretched filaments is essentially constant during an initial period of time after the step strain. Then, it increases rapidly and finally the filaments break. Filament lifetime t_{f} strongly increases with decreasing stretching ratio ε. The apparent elongational yield stress is identified as the initial value of the Laplace pressure obtained at a critical stretching ratio ε_{c} corresponding to a Deborah number De = t_{R} /t_{f} = 1. For all fluids, the ratio of this elongational yield stress to shear yield stress is in agreement with the von Mises plasticity criterion, irrespective of the physical nature of structural breakdown. Elongational experiments performed at different ε or t_{f} covering Deborah numbers between 0.1 and 100 reveal a universal relationship between the initial plateau value of the Laplace pressure normalized to the shear yield stress and De. This stress ratio varies between 0.5 and 5, and equals only for De ≈ 1.

Fixedpoint iteration for relaxation spectrum from dynamic mechanical data
View Description Hide DescriptionAn algorithm was developed for the continuous spectrum of linear viscoelasticity. The algorithm is free from the possibility of negative relaxation intensity whereas most previous algorithms suffer from the problem. The algorithm is not only simpler than the nonlinear regularization of Honerkamp and Weese [Rheol. Acta 32, 65–73 (1993)] but is also as accurate as the nonlinear regularization. The basic concept of the algorithm is to use a fixedpoint iteration, which transforms the initial spectrum to a new one that is closer to the leastsquare solution. The iteration algorithm regularizes the errors in data in a different manner of conventional regularization.

Power series approximations of dynamic moduli and relaxation spectrum
View Description Hide DescriptionWe suggest a new algorithm for relaxation time spectrum, which is based on the power series approximation of dynamic modulus and relaxation time spectrum. Through the regression of dynamic modulus as a polynomial of the logarithm of frequency, the method converts the coefficients of the modulus to those of relaxation time spectrum. The algorithm provides relaxation time spectrum as stable as regularization method.

Viscoelastic characterization of wood: Time dependence of the orthotropic compliance in tension and compression
View Description Hide DescriptionThis study is concerned with the viscoelastic behavior of wood. The time dependency of the orthotropic compliance for beech wood is investigated by performing tensile (Te) and compressive (Co) creep experiments in all wood's orthotropic directions. Time evolution of the creep strain in the axial and lateral directions is recorded using the digital image correlation technique, to determine the time dependent Young's moduli and the Poisson's ratios needed for the calculation of the diagonal and nondiagonal elements of the viscoelastic compliance matrix. The results of this study demonstrate the viscoelastic character of wood, revealing the significant time influence on the mechanical behavior. The unequal time dependency of the Young's moduli and the Poisson's ratios obtained for the individual directions highlights the orthotropic nature of the viscoelastic compliance. Differences between the time dependent behavior for the compliance determined in Te and Co further indicate that the viscoelastic behavior of wood depends on the loading modality. Supported by the unequal evolution of the Te and Co creep strain, the results suggest that the time dependent stress–strain relationship of wood is essentially different in Te and Co. Poisson's ratio values, which are shown to increase with time in Te and decrease in Co, demonstrated this fact. The substantially different time dependency of the nondiagonal elements of the compliance matrix further emphasizes the complexity of the viscoelastic character of wood. Visualized by the time evolution of the corresponding nondiagonal elements ratio, differences between the Te and Co viscoelastic behavior become particularly visible in the time dependency of the orthotropic compliance asymmetry.