Time-concentration Superposition Research Articles

Critical-Like Gelation Dynamics in Cellulose Nanocrystal Suspensions.

We use time-resolved mechanical spectroscopy to offer a detailed picture of the gelation dynamics of cellulose nanocrystal (CNC) suspensions following shear cessation in the presence of salt. CNCs are charged, rodlike colloids that self-assemble into various phases, including physical gels serving as soft precursors for biosourced composites. Here, a series of linear viscoelastic spectra acquired across the sol-gel transition of CNC suspensions are rescaled onto two master curves that correspond to a viscoelastic liquid state prior to gelation and to a soft solid state after gelation. These two states are separated by a critical gel point, where all rescaling parameters diverge in an asymmetric fashion yet with exponents that obey hyperscaling relations consistent with previous works on isotropic colloids and polymer gels. Upon varying the salt content, we further show that these critical-like dynamics result in both time-connectivity and time-concentration superposition principles.

Microrheological characterisation of Cyanoflan in human blood plasma

Naturally occurring polysaccharidic biopolymers released by marine cyanobacteria are of great interest for numerous biomedical applications, such as wound healing and drug delivery. Such polymers generally exhibit high molecular weight and an entangled structure that impact the rheology of biological fluids. However, biocompatibility tests focus not so much on rheological properties as on immune response. In the present study, the rheological behaviour of native blood plasma as a function of the concentration of a cyanobacterium biopolymer is investigated via multiple particle tracking microrheology, which measures the Brownian motion of probes embedded in a sample, and cryogenic scanning electron microscope microstructural characterisation. We use Cyanoflan as the biopolymer of choice, and profit from our knowledge of its chemical structure and its exciting potential for biotechnological applications. A sol–gel transition is identified using time-concentration superposition and the power-law behaviour of the incipient network's viscoelastic response is observed in a variety of microrheological data. Our results point to rheology-based principles for blood compatibility tests by facilitating the assignment of quantitative values to specific properties, as opposed to more heuristic approaches.

Time–Concentration Superposition for Linear Viscoelasticity of Polymer Solutions

The concentration dependence of linear viscoelastic properties of polymer solutions is a well-studied topic in polymer physics. Dynamic scaling theories allow qualitative predictions of polymer solution rheology, but quantitative predictions are still limited to model polymers. Meanwhile, the scaling properties of non-model polymer solutions must be determined experimentally. In present paper, the time-concentration superposition (TCS) of experimental data is shown to be a robust procedure for studying the concentration scaling properties of binary and ternary polymer solutions. TCS can not only identify whether power law scaling may exist or not, and over which concentration range, but also unambiguously estimate the concentration scaling exponents of linear viscoelastic properties for a range of non-model polymer solutions.

Concentration Scaling on Linear Viscoelastic Properties of Cellular Suspensions and Effects of Equilibrium Phase Behavior.

Concentration scaling on linear viscoelastic properties of cellular suspensions has been studied by rheometric characterisation of Phormidium suspensions and human blood in a wide range of volume fraction under small amplitude oscillatory shear experiments. The rheometric characterisation results are analysed by the time-concentration superposition (TCS) principle and show a power law scaling of characteristic relaxation time, plateau modulus and the zero-shear viscosity over the concentration ranges studied. The results show that the concentration effect of Phormidium suspensions on their elasticity is much stronger than that of human blood due to its strong cellular interactions and a high aspect ratio. For human blood, no obvious phase transition could be observed over the range of hematocrits studied here and with respect to a high-frequency dynamic regime, only one concentration scaling exponent could be identified. For Phormidium suspensions with respect to a low-frequency dynamic regime, three concentration scaling exponents in the volume fraction Region I (0.36≤ϕ/ϕref≤0.46), Region II (0.59≤ϕ/ϕref≤2.89) and Region III (3.11≤ϕ/ϕref≤3.44) are identified. The image observation shows that the network formation of Phormidium suspensions occurs as the volume fraction is increased from Region I to Region II; the sol-gel transition takes place from Region II to Region III. In combination with analysis of other nanoscale suspensions and liquid crystalline polymer solutions reported in the literature, it is revealed that such a power law concentration scaling exponent depends on colloidal or molecular interactions mediated with solvent and is sensitive to the equilibrium phase behaviour of complex fluids. The TCS principle is an unambiguous tool to give a quantitative estimation.

Microrheological study of single chain dynamics in semidilute entangled flexible polymer solutions: Crossover from Rouse to Zimm modes

The dynamics of polymer chains in entangled semidilute solution have been of theoretical and experimental interest. Among a number of characteristic lengths and times of the polymer in solution, those of the correlation blob are the key to understand the applicability of the Rouse and Zimm models to rheology of the semidilute solution. Direct rheological measurements of Rouse and Zimm modes are limited as the corresponding time scale is out of the range of classical rheological techniques. We investigated the single chain dynamics of entangled poly(ethylene oxide) in semidilute aqueous solutions by high-frequency micro-rheology based on diffusing-wave spectroscopy compared to classical shear macro-rheology. Concentration dependence of the three characteristic times of the entangled polymer chains, reptation time, entanglement time, and correlation time, was studied with the help of the time-concentration superposition. At the low frequency range, dynamic moduli measured by macro-rheology and micro-rheology showed a good agreement without adjustable parameters. At the higher frequency range, we found the Rouse regime in the mean square displacement of the probe particles and in the magnitude of the complex specific viscosity of the solution. We propose a simple method to estimate the boundary of the Rouse regime. Finally, at the high frequency range, we demonstrate that the contribution of the solvent to the solution viscosity needs to be subtracted to observe the power-law behavior of the Zimm mode.

Determination of the molecular weight distribution of ultrahigh molecular weight polyethylene from solution rheology

We investigate the linear rheology of ultrahigh molecular weight polyethylene (UHMWPE) solutions with the aim of determining the molecular weight distribution of the polymer. The UHMWPE is dissolved in oligo-ethylene in order to avoid issues related to unfavorable interactions with the solvent. To prepare the solutions, UHMWPE, solvent, and a fixed amount of antioxidants are mixed by means of a corotating twin-screw microcompounder. All prepared solutions are within the concentrated regime, as confirmed by the scaling laws of the main rheological parameters (plateau modulus, relaxation time, and zero-shear viscosity) with concentration. Based on the viscoelastic response of the solutions, we adopt a heuristic approach to extrapolate the linear viscoelastic behavior of the melt, according to a time-concentration superposition principle. Such a technique allows us to span many decades of angular frequency, eventually attaining the terminal relaxation regime. The latter is difficult to achieve by direct measurements in the molten state because of experimental issues such as extremely long experimental times and thermal limits. The viscoelastic spectrum of the melt is used to obtain the molecular weight distribution (MWD) according to the time-dependent diffusion/double reptation model. The MWD of UHMWPE evaluated by using this approach agrees well with data obtained from gel permeation chromatography.

Impact of structural flexibility in the adsorption of wheat and sunflower proteins at an air/water interface

Food transition requires the replacement in human diet of animal-based proteins by alternative sources of proteins including plant-based proteins. This calls for a detailed knowledge of the functional properties of plant-based proteins, including their surface activity. In this framework, we provide here a comparative study of the interfacial properties of two plant proteins, extracted respectively from wheat and sunflower. We combine time- and concentration-dependent measurements of the surface tension and the surface rheology, as measured with a pendant-drop set-up, and of the surface excess concentration, as measured by ellipsometry, of plant protein interfacial films. We demonstrate a time-concentration superposition principle for the surface pressure and surface excess concentration, showing that the kinetics for the building of the interfacial films is essentially governed by the diffusion of the proteins from the bulk to the interface. We find that the rheological and structural properties of the interfacial protein films show markedly different behaviors for the two classes of protein, which is encoded in the structural features of the individual proteins: wheat proteins are more surface active than sunflower proteins, are keen to compress and re-arrange at an air-water interface, whereas sunflower proteins do not. This work provides qualitative and quantitative analysis of the comparative interfacial behavior of flexible and rigid plant proteins extracted respectively from wheat and sunflower, and demonstrates that a combination of several experimental techniques is necessary to obtain insightful information on the interfacial properties of any species.

Molecular simulation of nanocolloid rheology: Viscosity, viscoelasticity, and time-concentration superposition

A particulate molecular model in which the solvent particles are considered explicitly is developed for studying the linear viscoelasticity of nanocolloidal suspensions using molecular dynamics simulations. Nanocolloidal systems of volume fractions ranging from 0.10 to 0.49 are studied. The hydrodynamics in these model systems are governed by interparticle interactions. The volume fraction dependence of the relative zero shear viscosity exhibited by this molecular model is consistent with that reported in the literature experiments and simulations. Over the range of frequencies studied, the relative dynamic viscosity values follow the same qualitative trend as that seen in the literature experiments. The time-concentration superposition (TCS) principle is successfully applied to construct the viscoelastic master curves that span nine decades of frequency in the case of the elastic modulus and more than four decades of frequency in the case of the loss modulus. The TCS principle was observed to fail at high volume fractions that are near the glass transition concentration; this finding is consistent with the literature experimental and simulation observations. The volume fraction dependence of the shift factors used in the construction of the viscoelastic master curves is in good quantitative agreement with that of the viscosity of the nanocolloidal systems. Our results demonstrate that molecular simulations in conjunction with an explicit solvent model can be used to quantitatively represent the viscosity and the viscoelastic properties of nanocolloidal suspensions. Such particulate models will be useful for studying the rheology of systems whose properties are governed by specific chemical interactions.

High shear capillary rheometry of cellulose nanocrystals for industrially relevant processing

A microcapillary rheometer was employed to study the rheological characteristics of CNCs at temperatures between 15 °C and 50 °C and aqueous concentrations between 1.5 wt% and 12.1 wt%, at rates up to 8 × 105 s−1. Time-temperature and time-concentration superposition were applied to analyze the data. A master curve of shear rate sweeps at temperatures between 15 °C and 50 °C was successfully generated to a reference temperature of 25 °C with the shift factor plot suggesting an Arrhenius relationship over the entire measured temperature range. Concentration-dependent data indicate a high shear Newtonian plateau at the limit of low concentration. Repeated testing of the same sample volume was implemented to represent extended times at elevated stress, with repeated experiments leading to a permanent decrease in viscosity. Atomic force microscopy (AFM) suggests sensitivity of the CNC geometry to moderate stress in a flow field.

Reinforcement and Payne effect of hydrophobic silica filled natural rubber nanocomposites

Nanoparticles significantly reinforce rubber and enhance nonlinear rheological behaviors while the underlining mechanisms are not yet clear. Herein a time-concentration superposition (TCS) principle is employed for constructing master curves of high-frequency linear rheology of hydrophobic silica filled natural rubber compounds with reference to the matrix. The effect of dynamics retardation of the matrix disclosed by the TCS principle is explained by the time-dependent diffusion double reptation model that predicts linear rheology well covers the TCS mater curves in the nonterminal region. With aid of the convective constrain release model, the Payne effect of the compounds is shown to originate mainly from the filler-promoted disentanglement of chains in the matrix whose local strain amplitude is amplified by the filler. Furthermore, the filler is shown to be able to enhance both the elastic and viscous nonlinearities of compounds under large strain amplitudes.

Relaxation Dynamics and Underlying Mechanism of a Thermally Reversible Gel from Symmetric Triblock Copolymer

We report a novel thermally responsive system from poly(butyl methacrylate)-b-poly(methacrylic acid)-b-poly(butyl methacrylate) (PBMA-b-PMAA-b-PBMA) triblock copolymer in dimethylformamide (DMF) solvent. This system shows a sol–gel transition by cooling below a critical temperature Tc. The network relaxation times of these gels rightly fall in the typical rheological experiment window, permitting us to investigate the relaxation dynamics and underlying mechanism, with a combination of linear rheology, time-resolved small-angle X-ray scattering (SAXS), and temperature-elevated nuclear magnetic resonance (NMR) measurements. Both time–temperature superposition (TTS) and time–concentration superposition (TCS) are well held in this system. The relaxation dynamics at temperatures below and above Tc are quite different, giving two different activation energies E1a and E2a, respectively. The E1a, being polymer concentration independent, is related to micelle formation of end-blocks, while the concentration depend...

A study on time-concentration superposition of dilatational modulus and foaming behavior of sodium alkyl sulfate

The oscillatory dilatational flow of interfacial rheology is a useful tool to unveil the motion of molecules and the interaction between adsorbed molecules at the interfacial layers. Despite its usefulness, it is difficult to analyze the dilatational moduli because they are functions of both the frequency and concentration. In this study, we adopted superposition behavior to investigate the diffusive transport of sodium alkyl sulfate surfactant based on the interfacial rheology under oscillatory dilatational flow. We found that the time-concentration superposition is valid for dynamic dilatational moduli. The shifting factors for superposition on time-axis exponentially decrease as concentration increases due to the molecular exchange between interface and bulk. It is found that the concentration dependence of the shift factors decreases as the size of the hydrophilic and hydrophobic groups increases. It is worth noting that the concentration dependence of the shift factors is related to the foaming speed of the surfactant solutions: As the concentration-dependence of shifting factors increases, the foaming speed increases. It is expected that the time-concentration superposition can be a new tool to study the dynamic dilatational rheology.

Linear viscoelasticity of weakly cross-linked hydrogels

Chemically cross-linked polyacrylamide (PA) hydrogels have been studied extensively, but gels with a very low cross-linker ratio have received relatively little attention. In this paper, the rheology of bis-cross-linked PA hydrogels is examined with acrylamide concentrations ca approximately 10% w/v and cross-linker to acrylamide ratios cbis/ca in the range 0.2–0.9 mmol mol−1. Linear viscoelastic responses were measured during and following gelation. The effective cross-link formation rate increases with the cross-linker ratio, with a plateau modulus that is weakly quadratic in the cross-linker ratio. The gels exhibit distinctly different features from their counterparts in the literature with higher cross-linker ratios. Plateau regions in the dynamic moduli spectra are less pronounced, and the loss tangents are several orders of magnitude higher than for gels with a higher cross-linker ratio but a comparable plateau modulus. Time-temperature superposition of viscoelastic spectra furnishes a disentanglement activation energy that decreases with increasing temperature, from ≈25 to 6kBT. Time-concentration superposition for samples prepared above the percolation threshold furnishes a critical relaxation exponent Δ≈0.38, which is much smaller than previously reported for the universal sol-gel transition. These distinct features can be attributed to the predominance of entanglements. We show that a Wiechert model with a power-law distribution of relaxation times faithfully reproduces dynamic moduli spectra from the creep compliance. Together, the results provide a foundation with which to interpret acoustic and electroacoustic rheological responses (at MHz frequencies) and the linear viscoelasticity of DNA-cross-linked gels (to be reported elsewhere).

Exploring the validity of time-concentration superposition in glassy colloids: Experiments and simulations

Author(s): Peng, Xiaoguang; Wang, J Galen; Li, Qi; Chen, Dongjie; Zia, Roseanna N; McKenna, Gregory B

Linear and non-linear flow behavior of welan gum solutions

Rheological and microstructural properties of welan gum aqueous solutions were studied as a function of polymer concentration in the 0.2–0.6% (m/m) range at fixed temperature 20 °C. Welan gum is an exopolysaccharide produced by Sphingomonas sp. All the systems exhibited a shear thinning and weak gel–like behavior whose parameters were well adjusted to a power law with the concentration. Furthermore, time-concentration superposition methods were carried out to obtain two master curves, one from the flow curves and the other from the mechanical spectra, which made it possible to extend the accessible experimental range. The non-linear viscoelastic properties were also studied by means of parallel superposition tests. The superimposed shear stress induced a change from weak gel to entangled solution behavior. This latter flow behavior is characterized by a frequency crossover that has been shown to have a linear dependence on the superimposed steady-state shear rate. Finally, Cryo-SEM images revealed a network with numerous junction zones between polymer chains.

Linear and nonlinear rheological behaviors of silica filled nitrile butadiene rubber

Nanoparticles significantly reinforce rubber and enhance nonlinear mechanical behavior while the underlining mechanisms are not clear. Herein the effects of crosslinking, filler content and filler surface chemistry on the linear and nonlinear rheological responses of silica filled nitrile butadiene rubber are investigated. A time-concentration superposition principle is employed for constructing rheological master curves. While the strain amplification and dynamics retardation contribute to the high-frequency linear rheology of the compounds, the former is crucial for the vulcanizates with matrix of similar crosslinking degree. In both the compounds and vulcanizates, the Payne effect is initiated at a similar microscopic strain of the rubber phase. A weak overshoot of loss modulus appears in compounds containing hydrophilic silica and vulcanizates containing hydrophobic silica. It is suggested that the viscoelastic matrix is highly important for the rheological responses of the filled compounds and vulcanizates.

Multistep building of a soft plant protein film at the air-water interface

Gliadins are edible wheat storage proteins well known for their surface active properties. In this paper, we present experimental results on the interfacial properties of acidic solutions of gliadin studied over 5 decades of concentrations, from 0.001 to 110 g/L. Dynamic pendant drop tensiometry reveals that the surface pressure Π of gliadin solutions builds up in a multistep process. The series of curves of the time evolution of Π collected at different bulk protein concentrations C can be merged onto a single master curve when Π is plotted as a function of αt where t is the time elapsed since the formation of the air/water interface and α is a shift parameter that varies with C as a power law with an exponent 2. The existence of such time-concentration superposition, which we evidence for the first time, indicates that the same mechanisms govern the surface tension evolution at all concentrations and are accelerated by an increase of the bulk concentration. The scaling of α with C is consistent with a kinetic of adsorption controlled by the diffusion of the proteins in the bulk. Moreover, we show that the proteins adsorption at the air/water interface is kinetically irreversible. Correlated evolutions of the optical and elastic properties of the interfaces, as probed by ellipsometry and surface dilatational rheology respectively, provide a consistent physical picture of the building up of the protein interfacial layer. A progressive coverage of the interface by the proteins occurs at low Π. This stage is followed, at higher Π, by conformational rearrangements of the protein film, which are identified by a strong increase of the dissipative viscoelastic properties of the film concomitantly with a peculiar evolution of its optical profile that we have rationalized. In the last stage, at even higher surface pressure, the adsorption is arrested; the optical profile is not modified while the elasticity of the interfacial layer dramatically increases with the surface pressure, presumably due to the film ageing.

Linear rheology of natural rubber compounds filled with silica, short nylon fiber or both

Engineered rubbery materials in practical applications usually contain nanoparticle and microscopic short fiber while no theories could describe the viscoelasticity of the compounds varying with these two kinds of fillers. We describe how the linear rheology of natural rubber compounds varies with the loading of precipitated silica, short nylon fiber, or both. We for the first time disclose a filler dimension-dependent hydrodynamic-to-non-hydrodynamic transition by applying the time-concentration superposition principle for accounting for the apparent liquid-to-solid transition related to filler composition and loading and the retarded dynamics of the matrix. A framework for simultaneous solving the reinforcement and dissipation of the multi-component compounds is suggested, providing a new perspective on understanding the filling effect for manufacturing high-performance rubber materials.

Self-healing hydrogels formed by complexation between calcium ions and bisphosphonate-functionalized star-shaped polymers.

Star-shaped poly(ethylene glycol) (PEG) chain termini were functionalized with alendronate to create transient networks with reversible crosslinks upon addition of calcium ions. The gelation ability of alendronate-functionalized PEG was greatly dependent on the number of arms and arm molecular weight. After mixing polymer and calcium solutions, the formed hydrogels could be cut and then brought back together without any visible interface. After 2 minutes of contact, their connection was strong enough to allow for stretching without tearing through the previous fracture surface. Oscillatory rheology showed that the hydrogels recovered between 70 and 100% of the original storage and loss modulus after rupture. Frequency sweep measurements revealed a liquid-like behavior at lower frequencies and solid-like at high frequencies. Shifting frequency curves obtained at different calcium and polymer concentrations, all data collapsed in a single common master curve. This time-concentration superposition reveals a common relaxation mechanism intrinsically connected to the calcium-bisphosphonate complexation equilibrium.

Fluxing as a new tool for bitumen rheological characterization and the use of time-concentration shift factor (ac)

The concept of temperature shift factor (aT) as defined by Doolittle, relating the free volume of a viscoelastic material at the current and reference states is briefly examined together with the resultant William-Landel-Ferry equation. This paper highlights the fact that change in free volume arise not only from temperature variations but can also result from the absorption of solvents and thus a generalized Doolittle relation may also be applied to a solvent concentration shift factor (ac). To validate this concept, a small scale laboratory investigation was carried out by blending 40/60 penetration grade bitumen with various proportions of one type of cooking oil and conducting dynamic shear rheometer frequency sweeps at a range of temperatures. By applying time-concentration superposition to each flux content, it was possible to shift horizontally (ac) each set of complex modulus data measured at each test temperature, so that all sets superimpose onto the master curve of the base bitumen at a preselected reference temperature. A direct relationship between conventional time-temperature shift and the proposed time-concentration shift factors was thus demonstrated using a sample of penetration grade bitumen and one type of vegetable oil. Further experimentation with other bitumen-flux combinations is necessary prior to recommending general adoption of the proposed tool.