Index of content:
Volume 60, Issue 6, November 2016

Viscoelasticity of entangled random polystyrene ionomers
View Description Hide DescriptionUsing literature data for entangled polystyrene ionomers, a sticky double reptation model is developed and tested that effectively accounts for distributions in both chain length and number of ionic groups per chain. The model predicts that if there are more ionic groups than entanglements, the classic Leibler double plateau will be observed, with modulus from ion associations plus entanglements transitioning to that of just entanglements, beyond the association lifetime. Whereas at low enough ion content, there are more entanglements than ionic groups, resulting in a single plateau, with modulus from ion associations and entanglements, that persists until the sticky reptation time of the chains.

Large amplitude oscillatory shear of hardsphere colloidal dispersions: Brownian dynamics simulation and Fouriertransform rheology
View Description Hide DescriptionBrownian dynamics simulations of large amplitude oscillatory shear (LAOS) in freely draining, hardsphere colloidal dispersions are performed. The time varying stress and microstructure under LAOS are measured, and the relationship between microstructural deformation and rheological response is explored. The shear stress, first and second normal stress differences are analyzed by Fouriertransform rheology for dispersions with two volume fractions . Highly nonlinear microstructural perturbations are identified and correlated with the magnitude of the stress response. The first departures from linearity in the shear and normal stresses are compared to recent theoretical predictions of the same, and agreement with scaling predictions in the limit of high frequency oscillation is found. Higher order nonlinearities in the stress response are found in the regime of rapid oscillation with order unity strain amplitude. These derive from symmetry breaking through shear induced ordering of the dispersion. These results confirm that LAOS responses outside of the weakly nonlinear, lowfrequency oscillation regime are a highly sensitive probe of interactions between microscopic constituents in complex fluids.

High frequency viscoelastic measurements using optical tweezers on wormlike micelles of nonionic and cationic surfactants in aqueous solutions
View Description Hide DescriptionLinear viscoelasticity of two kinds of wormlike micelles in aqueous solutions, one is nonionic surfactants and the other one is cationic surfactant with organic salt, was measured over a wide frequency range with Brownian motion tracking microrheology (BMTR) using optical tweezers and a conventional rheometer. In BMTR measurements, the Brownian motion of a small particle embodied in the sample is traced and the complex modulus is calculated from the trajectory. The wideband linear viscoelastic spectra thus obtained for each of wormlike micelles were classified into the following three relaxation types as already known. Type A is similar to the spectrum of the nonentangle polymer solutions, type B similar to that of the entangle polymer systems, and type C has a single Maxwell relaxation at low frequencies. In the highfrequency region, spectra of all types showed a common powerlaw relaxation, which reflects the reorientation of the viscoelastic segment of the wormlike micelles, indicating that the dynamics of wormlike micelles is identical with that of the ordinary polymeric systems. For type A solutions, the molar mass of wormlike micelles was estimated by fitting the beadsspring models to the viscoelastic spectra. For type B solutions, the molar mass was estimated by using the universality of entangled system. For the case of nonionic micelles, thus determined molar mass is in good agreement with the reported result with the light scattering measurement.

Modeling interactions in carbon nanotube suspensions: Transient shear flow
View Description Hide DescriptionTransient shear flow data of untreated multiwalled carbon nanotubes (MWCNTs) dispersed in a Newtonian epoxy matrix are analyzed. A sequence of shearing and rest steps was applied to characterize the transient responses of the suspensions. Stress overshoots appeared at very small deformation during forward and reverse flow experiments and their intensity increased with rest time between two consecutive flows, during which the suspension structure was reconstructed. The transient behavior of the MWCNT suspensions is explained with the help of a recently proposed model [G. Natale et al., AIChE J. 60(4), 1476–1487 (2014)]. The MWCNTs are described as rigid rods dispersed in a Newtonian matrix, and the evolution of the system is controlled by hydrodynamics, rodrod interactions, and Brownian motion. The force due to the interactions is modeled as a nonlinear lubrication force and the total stress tensor is evaluated introducing a fourthorder interaction tensor. The Fokker–Planck equation is numerically solved for transient simple shear flow using a finite volume method, avoiding the need of closure approximations. The model predictions show that interactions slow down the orientation evolution of the rods. For the first time, the effect of shear rate is directly accounted by the model, which predicts that a critical shear rate is necessary to break down the structure and let the rods orient in the flow direction. In addition, we confronted the model predictions with the rheological data of a glass fiberfilled polybutene [M. Sepehr et al., 48(5), 1023–1048 (2004)], demonstrating its ability to describe the behavior of micro and nanoscale particle suspensions.

Elongational rheology of bacterial biofilms in situ
View Description Hide DescriptionBacterial biofilms are able to resist a broad range of chemical challenges as well as mechanical stress. The mechanical properties of natively grown biofilms, however, remain largely unknown. This is mostly due to a lack of suitable experimental setups which are capable of quantifying the mechanical properties of those biofilms in their naturally grown state, i.e., without harvesting and transferring the biofilm material into a measuring device. Here, we present a customized device which allows measuring material parameters of bacterial biofilms in situ. Parameters that can be obtained from our stretching experiments include the tensile strength and rupture energy of native and chemically treated biofilms. Although the example measurements shown here have all been conducted with biofilms formed by the apathogenic soil bacterium B. subtilis B1, the setup should be applicable to a broad range of bacterial biofilms or other viscoelastic materials.

A magnetic rod interfacial shear rheometer driven by a mobile magnetic trap
View Description Hide DescriptionThe magnetic rod interfacial shear rheometer has been successfully used over the past years to measure mechanical properties of fluidfluid interfaces. However, the resolution is limited due to the finite system compliance and the probe mass and size. Here, we propose a new design that modifies the way in which the magnetic force is imposed on the probe by substituting the usual coils by a pair of small permanent magnets forming a magnetic trap. Suitably displacing the magnet pair imposes a longitudinal force on the probe that depends on the probetrap displacement. We show that the relative importance of the surface drag to the rest of the forces acting on the probe is increased, allowing more precise measurements. We have checked our dynamical model on a clean airwater interface, showing that the device response depends only on the elastic constant of the magnetic trap. We have made a full characterization of the performance of several trapprobe combinations showing that the new configuration yields a null system compliance and a stable probe positioning. We have checked the rheometer performance on silicone oil thin films and pentadecanoic acid Langmuir monolayers, showing that surface viscosities as low as are measurable.

On the use of continuous relaxation spectra to characterize model polymers
View Description Hide DescriptionThere 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.

Mixing of polar and nonpolar molten olefinic copolymer with polar liquids in conditions of very low viscosity ratio: Shear dominated flows
View Description Hide DescriptionThis work analyzes the dispersion conditions of polar liquids with low viscosities into polymer melts. For this purpose, the curve of the critical capillary number in shear as a function of the viscosity ratio for low viscosity liquids dispersed into polymer melts was built. To obtain this curve, the disperse phase and matrix were chosen to have large polarity and viscosity differences (viscosity ratio between 10^{−7} and 10^{−2}). To this end, polyethylene glycols with various molecular weights, ethylene glycol, glycerol or water were mixed with olefinic copolymers in an internal mixer assumed to generate mostly shear. Concentrations of dispersed phase were low enough to prevent coalescence. In combination with viscosity data and measured interfacial tension, the critical capillary number was calculated from the droplet size in equilibrium conditions and the variation with viscosity ratio was compared with theoretical equations from the literature.

Flow of a Boger fluid around an isolated cylinder
View Description Hide DescriptionThe flow around an isolated cylinder with a Boger fluid was studied experimentally by partially immersing a small vertical cylinder in a test fluid contained in an annular tank slowly rotating on a turntable. To approximate isolation, the ratio of the tank width to cylinder diameter varied from 40/1 to 300/1, and Reynolds numbers ranged from 10^{−5} to 0.5. Drag was measured by a custommade mechanical/optical system and the flow field was mapped using particle image velocimetry (PIV). The experimental liquids were two Newtonian fluids and two polyisobutylene/polybutene Boger fluids, and the cylinders had various diameters. The Newtonian drag data, corrected for end and wall effects, agree with Kaplun's lowRe asymptotic formula. Elasticity increased the drag, starting at a Deborah number of 0.6, by 50% at a De of 2.5, and by more at higher Deborah numbers. PIV measurements were made around a cylinder—upstream, downstream, and transversely—and at 180° from it. The velocity measurements showed that the wake increased with De, among other findings. To relate the increased drag to fluid elasticity, normal stresses due to elasticity were found from deformation rates derived from the PIV data, but these stresses appear to be insufficient to account for the effect.

Rheology of cellulose nanofibers suspensions: Boundary driven flow
View Description Hide DescriptionCellulose nanofibers (CNFs) are an exciting new renewable material produced from wood fibers. Even at low solids content, CNFwater suspensions have a complex rheology that includes extreme shearthinning as well as viscoelastic properties and a yield stress similar to other suspensions of nanoscale particles. When characterizing the rheology of CNF suspensions, the measurement method may influence the results due to a water layer expected at the boundary, but it is unclear how the behavior near walls influences the measurement method. Parallelplate, Couette, and vane geometries were used to compare yielding and flow of CNF suspensions obtained by steadystate shear and oscillatory rheological measurements. Five different techniques were compared as methods to obtain a yield stress. Cone and plate geometries were found to lead to sample ejection at low shear rates: Flocfloc interactions can explain this ejection. The suspensions violated the CoxMerz rule by a significant amount; this behavior has been explained in the past as weak gel structures that break down in shear, but for this material it seems that the acting mechanism involves the formation of a waterrich layer near the solid boundaries in steady shear, while for oscillatory tests, these layers do not form. For suspensions lower than 3% solids, the yield stress measured by different procedures was within 20% of each other, but for high solids suspensions, differences between the methods could be as large as 100%; the waterrich layer formation likely is the cause of these results. Oscillatory methods are suggested as a method to obtain yield stress values for this type of material. The Couette geometry data were below the powerlaw lines fitted to the parallelplate geometry data from steadyshear measurements perhaps again attributable to different waterrich layers that form in these different geometries.

Nonlinear rheological behavior of multiblock copolymers under large amplitude oscillatory shear
View Description Hide DescriptionThe nonlinear responses of olefin multiblock copolymers (OBCs) melts were investigated under large amplitude oscillatory shear (LAOS) using FourierTransform rheology in this work. Timetemperature superposition (TTS) was examined using linear viscoelastic functions, as well as nonlinear viscoelastic functions like the intrinsic Q factor (Q 3,0) and the dynamic moduli of the third harmonic ( and ). It is found that the intrinsic Q factor (Q 3,0) exhibits similar TTS behavior as those of storage moduli and loss moduli. However, the deviation from typical liquidlike behavior of homogeneous melt in Q 3,0 is much more evident than that in the storage moduli, indicating more sensitive of Q 3,0 to the microstructure than linear viscoelastic functions. In addition, we suggested a new plot, the intrinsic phase angle at third harmonic (δ3,0) versus the intrinsic complex moduli at third harmonic (), which is named as the vGP3 plot. Using the vGP3 plot, the much weaker mesophase separation can be distinguished from the homogeneous state successfully. The high sensitivity of vGP3 to the failure of TTS makes it a new candidate in studying the thermorheological behaviors of complex fluids. Finally, the frequency dependency of intrinsic nonlinearity under LAOS was modeled by combining the molecular stress function (MSF) model and emulsion model. The MSF model can describe the experiment data of linear dynamic moduli and Q 3,0 quite satisfactorily for homogeneous OBCs. For heterogeneous melt, the MSF model and the simple emulsion model account for the homogeneous contribution and the interfacial contribution, respectively. The predictions of the combined model agree quite well with the frequency dependency of the experimental data for both linear storage moduli and intrinsic Q factor (Q 3,0).

Direct conversion of creep data to dynamic moduli
View Description Hide DescriptionThe conversion of creep compliance to dynamic moduli is one of the promising ways to overcome the limitation of the dynamic measurements for wide range of frequency. Remarkable algorithms were developed by Evans et al. [Phys. Rev. E 80, 012501 (2009)] and Kim et al. [J. Rheol. 59, 237–252 (2015)]. Although the former is independent of any model of creep compliance, it suffers from the instability for experimental error. On the other hand, although the latter is a stable algorithm based on the model of Havriliak and Negami [Polymer 8, 161–210 (1967)], it has a problem of parameter identification. This paper is an effort to improve the approach of Kim et al. [J. Rheol. 59, 237–252 (2015)] by suggesting new approximate functions for the Laplace transform of creep compliance. We compared our algorithm with the two previous ones.

The effect of pressure on the viscosity of two different nanocomposites based on a PS matrix: A case of piezorheological complexity
View Description Hide DescriptionThe pressure dependence of viscosity of two nanocomposites with a polystyrene (PS) matrix that contains, respectively, multiwalled carbon nanotubes (MWCNTs) and graphene, was investigated. Two procedures were used: (a) Pressurevolumetemperature (PVT) results to obtain the pressure coefficient β0 for Newtonian viscosity and (b) measurements in a pressure chamber in a capillary rheometer, to obtain the pressure coefficient at constant shear rate, β′ and the pressure coefficient at constant shear stress, β″. PVT results revealed that the most significant differences between the samples concerned the variation of the glass transition with pressure, dTg/dP, which was concomitant with the number of polymer chains fixed on the surface of the nanofillers. Pressure chamber results showed that the pressure coefficient β″ was similar for PS and the nanocomposites, at the shear rates involved in processing. For the first time, the piezorheological complexity of nanocomposites was analyzed, together with the thermorheological complexity. PS/MWCNT nanocomposite was thermorheologically complex in the linear viscoelastic regime, but thermorheologically and piezorheologically simple in the shear thinning flow region. Nevertheless, PS/graphene nanocomposite was thermorheologically and piezorheologically complex in the linear viscoelastic regime and the shear thinning regime. This was due to the high capacity of graphene 2D platelets to retain polymer chains anchored to its surface.

Application of a generalized Oldroyd model to a suspension of spheroids subject to Brownian rotations
View Description Hide DescriptionA new approach to constitutive modeling for nonNewtonian liquids is presented, with a particular application to a dilute suspension of spheroids (prolate and oblate) subject to Brownian rotations at finite Péclet numbers, but with a general framework that can be applied to other complex fluids, including concentrated suspensions and emulsions. A generalized traceless Oldroyd model is used for the particle contribution to the stress, with five material parameters as functions of one instantaneous flow invariant: the intrinsic energy dissipation rate. All five parameters are found from simultaneously fitting the model to numerical results for two base flows at arbitrary flow intensities: planar extensional flow and simple shear flow. Precise numerical solutions of the FokkerPlanckSmoluchowski equation for the orientation distribution function are used to prepare the database rheological functions, and also to validate the resulting model in flows with arbitrary kinematics. The present work also verifies the accuracy of various closure models in the literature for dilute suspensions of spheroids in several test flows. Although these closure models give excellent results and are often more accurate than the present approach in the test cases, they are relevant specifically to fiber suspensions, and it is not clear how to generalize the closure approach to other types of nonNewtonian, microstructurally complex liquids. In contrast, the present approach to constitutive modeling is more general and does not hinge on a particular microstructure; it can be applied to various systems with strong hydrodynamical interactions (highly concentrated suspensions, emulsions, etc.).

Steady shearing flow of a moderately entangled polyethylene liquid
View Description Hide DescriptionThe rheological properties and dynamical responses of a monodisperse polyethylene (PE) liquid, C700H1402, were examined using equilibrium molecular dynamics and nonequilibrium molecular dynamics simulations of the atomistically detailed molecules. Equilibrium structural and dynamical properties of the PE liquid, such as the disengagement time (), Rouse time (), entanglement time, (), reptation tube diameter, number of entanglements, and the distribution of the chain endtoend vector, each followed very closely the predictions of the Doi and Edwards theory. Under steady shear conditions, the rheological and dynamical responses exhibited starkly different behavior as functions of shear rate, which could be categorized within four distinct shear rate regions; namely, , , , and . In the first region, the topological properties of the liquid remained relatively unperturbed from quiescent conditions and the rheological characteristic functions remained constant throughout. Little in the way of chain orientation or stretching occurred, and reptation theory described very well the system properties. Within the second range, chain orientation became the dominant dynamical system response with only a slight degree of chain stretching being evident. Rheological characteristic functions displayed shearthinning behavior, and a plateau in the shear stress profile was observed. In the third range, significant chain stretching became apparent which led to a dramatic reduction in the number of entanglements, thereby enabling a rotational motion of the individual chain molecules in response to the vorticity of the shear field. A new timescale became evident that was associated with the period of the rotation/retraction cycles of the individual molecules. In the fourth region, the rotational motion of the chains became the sole relaxation mode of the system as the number of entanglements was gradually reduced to a level too low to support the conventional reptation theory. Furthermore, the individual molecular motions shared the same characteristics as those of similar chains in dilute and semidilute solution. Comparisons of the corresponding structural and dynamical properties of the C700H1402 liquid with those of the mildly entangled PE liquid C400H802 revealed how the properties of the liquids scaled with chain length.

Structuring of nonBrownian ferrite particles in molten polypropylene: Viscoelastic analysis
View Description Hide DescriptionThis paper focuses on the relation between the structure and the rheological properties of nonBrownian ferrite particles suspended in a molten polypropylene matrix with and without the addition of a dispersant agent. The studied filler levels were 2, 15, and 20 vol. %. Under low deformation, the measurement of the complex shear modulus over time showed that the material structure was not stable. Such evolution was, on the one hand, more visible at concentrations near the percolation threshold () and on the other hand, less visible when adding a dispersant agent. Oscillatory time sweep experiments were performed after a preshearing. It was shown that the kinetics of the evolution strongly depends on the applied deformation. Such evolution has also been highlighted by optical microscopy, in which an agglomeration phenomenon was clearly observed after few hours, again less visible for formulations with a dispersant agent. Under high deformations, no structure evolution was noticeable. Our results stress the important role of adding a dispersant into the formulation of highly filled materials. The dispersant agent acts therefore as a stabilizer and a lubricating agent. The origin of such structuring process has been attributed to a favorable entropy gradient from the polymer chains between the particles and the polymer chains in the bulk.

Customizable tool geometries by additive manufacturing for mechanical rheometry of soft matter
View Description Hide DescriptionThe advent of lowcost, customizable, additive manufacturing methods of 3D printing offers promise for applications in mechanical rheometry. By taking advantage of the high inplane resolution of a consumergrade fuseddeposition 3D printer and using solvent welding, we design and manufacture both standard and customized plastic tool geometries suitable for use in mechanical rheometers. In particular, 3Dprinted tools can be designed to match available sample volumes of soft materials, and, while these plastic tools can be reused in many cases, they can also be disposable, especially when certain materials can be very difficult to clean. Here, we demonstrate the versatility of this approach by designing and producing a raised annular parallel plate geometry, which offers a more uniform strain field and a higher torque than a standard parallel plate geometry. We also show that customized tool roughness can be directly printed, and we demonstrate that 3Dprinted roughened tools can provide a noticeable improvement over smooth metal tools in mechanical rheometry. Overall, selective design and use of consumergrade 3D printers opens up many exciting directions in mechanical rheometry.

High bandwidth noninvasive measurements of the linear viscoelasticity of collagen gels
View Description Hide DescriptionWe report measurements of the linear viscoelastic modulus of collagen gels. Collagen gels are crosslinked networks of bundles formed from the association of single filaments. Their structure is heterogeneous at microscopic length scales, and measurements of their viscoelasticity at a larger scale are required. We use a technique that we recently developed based on the measurement of surface thermal fluctuations and called surface fluctuation specular reflection [Pottier et al., Soft Matter 7, 7843–7850 (2011)] to characterize the linear viscoelastic properties of collagen gels for frequencies ranging from 1 Hz to 30 kHz. These properties are determined at a mesoscopic scale (∼100 μm) at which the gels are homogeneous. We further study the influence of both collagen origin and concentration in the light of previous findings on these systems.