Strain-rate Frequency Superposition Research Articles

Structure-rheology relationship in monoolein liquid crystals

Hypotheses: Monoolein liquid crystals find use in foods and pharmaceuticals. Our hypotheses were: (a) liquid crystal symmetry dominates yielding and large deformation, and (b) strain rate frequency superposition (SRFS) may be used to determine mesophase long and short relaxation times.Experiments: Liquid crystal microstructure and rheology were characterised as a function of temperature and composition. Their structure was assessed using small angle X-ray scattering (SAXS) and polarised light microscopy. Small and large deformation rheology was characterised using frequency and amplitude sweeps, large amplitude oscillatory shear tests, and SRFS.Findings: We have contributed to the structure-rheology relationship governing the properties of the lamellar, cubic, and hexagonal mesophases. Initially, we characterised a number of monoolein-water binary phase transitions, which showed similar behaviour with earlier efforts. Frequency sweeps revealed that the cubic phases had the highest elasticity followed by the lamellar and hexagonal phases. The stiffening and thickening ratios, extracted from the Lissajous-Bowditch plots, were used to quantify intra-cycle non-linearities. The cubic phases displayed abrupt yielding with more pronounced stiffening and thinning behaviour compared to the others. Each liquid crystal phase displayed unique rheological behaviour upon large deformation and, by linking rheology with SAXS and composition, we show that their symmetry defined their rheology.

Influence of the Carrier Fluid Viscosity on the Rotational and Oscillatory Rheological Properties of Ferrofluids.

This work mainly presents a comprehensive experimental study on the magnetorheological behavior of ferrofluids with carrier fluids of different viscosities. Three lubrication oil based ferrofluids of different viscosities and similar saturation magnetization values were prepared and characterized. Static and dynamic rheological tests of the three ferrofluids were performed using an advanced rotational rheometer with a magnetic field generating module. According to the experimental results, the magneto viscous effect, yield stress and storage modulus increase with the viscosity of carrier fluid, indicating that the structures of ferrrofluids tend to be larger and more stable in a carrier fluid with larger viscosity. The emergence and growth of "crossover" region with the increase in carrier fluid viscosity was observed using the strain-rate frequency superposition method, which were explained according to the microscopic mechanism of magnetorheology. These findings contribute to a better understanding of the microscopic mechanism of magnetorheology and provide guidance for practical applications.

Rheological analysis of core-stabilized Pluronic F127 by semi-interpenetrating network (sIPN) in aqueous solution

A poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) triblock copolymer (Pluronic F127) micelle system was stabilized using an ultraviolet-induced semi-interpenetrating network (sIPN). The sIPN structure within the micelle cores was found to stabilize the micelles against low temperatures, but affected the resulting material properties. In this study, the rheological properties of Pluronic F127 with sIPN (F127-sIPN) and without sIPN (F127) were compared. The presence of the sIPN structure increased the gelation temperature (Tgel) at the same concentration, and unlike F127, F127-sIPN exhibited strong heating rate dependent and thermodynamically irreversible behaviors. Hard gels containing various concentrations of F127-sIPN and F127 were investigated at 40 °C. At concentrations above 18 wt. %, both F127-sIPN and F127 exhibited similar linear viscoelastic properties due to the tight, ordered core–shell micelles packing, but the two systems exhibited different behaviors below 18 wt. % concentration. To investigate this difference, hard gels with 16 wt. % F127-sIPN and F127 were selected, and two types of nonlinear rheological tests were conducted, i.e., large amplitude oscillatory shear (LAOS) and strain-rate frequency superposition (SRFS) tests. The cage modulus of F127-sIPN obtained from LAOS testing showed it maintained its elastic contribution over the large deformation region meaning that a loose core network still existed. The relaxation time spectrum of F127-sIPN obtained by SRFS testing indicated it had two relaxation modes (fast and slow) whereas that for F127 had only a fast mode. The slow relaxation mode of F127-sIPN is associated with crosslinking of the sIPN. Since these behaviors were not observed in linear rheological tests, it was concluded that nonlinear rheological tests provide more structural information about hard gels.

Dynamic shear rheology and structure kinetics modeling of a thixotropic carbon black suspension

The rheological characterization of a model, nearly ideal thixotropic carbon black suspension first proposed by Dullaert and Mewis (JNNFM 139: 21–30, 2006) is extended to include large amplitude oscillatory shear (LAOS) flow, shear flow reversal, and unidirectional LAOS flow (UD-LAOS). We show how this broader data set is useful for validating and improving constitutive models of thixotropy. We apply this new data to further test a recently developed structure-kinetics model, the Modified Delaware Thixotropy Model (Armstrong et al., J Rheol. 60: 433–450, 2016a), as well as to better understand the microstructural basis and validity of strain-rate superposition methods proposed for soft solids. This comparison identifies the limitations of models based on a scalar description of microstructure, which cannot fully capture the reversal of flow directionality inherent in LAOS flow. Further, we use the model to identify a possible microstructural justification for the hypothesized technique of strain-rate frequency superposition in soft solids.

Superposed nonlinear rheological behavior in filled elastomers

In the present work, the rheological properties of a number of filled elastomers under oscillatory shear conditions are investigated. In both linear and nonlinear regimes, the relationships between moduli (G′ and G″) and strain amplitude (γ0) in response to the frequency change display constant shifts along the vertical direction, leading to a striking superposition of the curves. We show that this superposition via a change of its independent-variables can directly lead to a strain-rate frequency superposition. The underlying principle is that the measured dynamical properties can be separated into a linear viscoelastic frequency-dependent part and a nonlinear strain-dependent part. This frequency-deformation separability is experimentally valid for various rubber compounds that differ widely in the polymer structure, the chemical composition, and the type of the filler as well as the shape, the average size, and the distribution of the particles.

A revisit of strain-rate frequency superposition of dense colloidal suspensions under oscillatory shears

Strain-rate frequency superposition (SRFS) is often employed to probe the low-frequency behavior of soft solids under oscillatory shear in anticipated linear response. However, physical interpretation of an apparently well-overlapped master curve generated by SRFS has to combine with nonlinear analysis techniques such as Fourier transform rheology and stress decomposition method. The benefit of SRFS is discarded when some inconsistencies of the shifted master curves with the canonical linear response are observed. In this work, instead of evaluating the SRFS in full master curves, two criteria were proposed to decompose the original SRFS data and to delete the bad experimental data. Application to Carabopol suspensions indicates that good master curves could be constructed based upon the modified data and the high-frequency deviations often observed in original SRFS master curves are eliminated. The modified SRFS data also enable a better quantitative description and the evaluation of the apparent structural relaxation time by the two-mode fractional Maxwell model.

Dynamics and Rheology of Soft Colloidal Glasses.

The linear viscoelastic (LVE) spectrum of a soft colloidal glass is accessed with the aid of a time-concentration superposition (TCS) principle, which unveils the glassy particle dynamics from in-cage rattling motion to out-of-cage relaxations over a broad frequency range 10-13 rad/s < ω < 101 rad/s. Progressive dilution of a suspension of hairy nanoparticles leading to increased intercenter distances is demonstrated to enable continuous mapping of the structural relaxation for colloidal glasses. In contrast to existing empirical approaches proposed to extend the rheological map of soft glassy materials, i.e., time-strain superposition (TSS) and strain-rate frequency superposition (SRFS), TCS yields a LVE master curve that satisfies the Kramers-Kronig relations which interrelate the dynamic moduli for materials at equilibrium. The soft glassy rheology (SGR) model and literature data further support the general validity of the TCS concept for soft glassy materials.

Temperature dependence of aging kinetics of hectorite clay suspensions

The aging of salt-free hectorite suspensions with different concentrations (cL=2.9, 3.2 and 3.5wt%) stored for 2days or 4days was studied by rheology at different temperatures. The evolution of storage and loss moduli G′ and G″ during aging followed aging time–temperature superposition. The temperature dependence of the shift factor aT, which reflected the aging kinetics, was interpreted by the reaction-limited colloidal aggregation (RLCA) mechanism with counterion condensation in calculating the double-layer interaction of the charged clay particles. Temperature dependence of the plateau modulus and yield stress of the suspension aged for 800s was modeled with the soft glassy rheology (SGR) theory. The estimated noise temperature x indicated that the sample aged at higher temperature corresponded to a deeper quench in the nonergodic state. Under larger amplitude of oscillatory shear, the suspension exhibited a strain rate-frequency superposition (SRFS). The shearing eliminated the effects of aging and heating.

Effect of Pre-Stress on the Dynamic Tensile Behavior of the TMJ Disc

Previous dynamic analyses of the temporomandibular joint (TMJ) disc have not included a true preload, i.e., a step stress or strain beyond the initial tare load. However, due to the highly nonlinear stress-strain response of the TMJ disc, we hypothesized that the dynamic mechanical properties would greatly depend on the preload, which could then, in part, account for the large variation in the tensile stiffnesses reported for the TMJ disc in the literature. This study is the first to report the dynamic mechanical properties as a function of prestress. As hypothesized, the storage modulus (E′) of the disc varied by a factor of 25 in the mediolateral direction and a factor of 200 in the anteroposterior direction, depending on the prestress. Multiple constant strain rate sweeps were extracted and superimposed via strain-rate frequency superposition (SRFS), which demonstrated that the strain rate amplitude and strain rate were both important factors in determining the TMJ disc material properties, which is an effect not typically seen with synthetic materials. The presented analysis demonstrated, for the first time, the applicability of viscoelastic models, previously applied to synthetic polymer materials, to a complex hierarchical biomaterial such as the TMJ disc, providing a uniquely comprehensive way to capture the viscoelastic response of biological materials. Finally, we emphasize that the use of a preload, preferably which falls within the linear region of the stress-strain curve, is critical to provide reproducible results for tensile analysis of musculoskeletal tissues. Therefore, we recommend that future dynamic mechanical analyses of the TMJ disc be performed at a controlled prestress corresponding to a strain range of 5–10%.

Yielding and structural relaxation in soft materials: Evaluation of strain-rate frequency superposition data by the stress decomposition method

Rheological properties of soft materials are often investigated in oscillatory shear and characterized by the storage and loss modulus, G' and G'', respectively. Unfortunately, the relaxation dynamics of most soft materials is too slow to be directly probed by commercial rheometers. Recently, it was shown by Wyss et al. [Phys. Rev. Lett. 98, 238303 (2007)] that the application of an oscillating strain-rate drives such soft materials and shifts the structural relaxation to higher times. They called this experimental technique strain-rate frequency superposition (SRFS). The great benefit of SRFS is the extremely extended frequency range. As viscoelastic measures, Wyss et al. proposed the familiar storage and loss modulus. Using these moduli results in a serious drawback: When the material yields, nonlinearities appear and the physical interpretation of the storage and loss modulus breaks down. Thus, SRFS as proposed by Wyss et al. is limited to the linear regime and the benefit of the extended frequency regime vanishes. In the present work, we validate an alternative data analysis technique, recently established as the stress decomposition method [K. S. Cho et al., J. Rheol. 49, 747 (2005); R. H. Ewoldt et al., J. Rheol. 52, 1427 (2008)], for combination with SRFS. Use of the stress decomposition method provides a physical interpretation of linear and nonlinear SRFS data in terms of strain stiffening and softening as well as shear thickening and thinning.

Hydrophobically modified poly(vinyl alcohol) using alkoxy-substituted methyl gallate: Synthesis and rheology

Hydrophobically modified poly(vinyl alcohol) (HMPVA) polymers were synthesized by potassium t-butoxide-catalyzed reaction of PVA with methyl 3,4,5-tris(n-octyloxy) benzoate (MGC 8 )/3,4,5-tris(n-dodecyloxy) benzoate (MGC 12 ) and 1,3-propane sultone. The concentration of 1,3-propane sultone was kept constant at 10 mol % and that of MGC 8 (2, 3, and 4 mol %)/MGC 12 (2 and 3 mol %) was varied to obtain HMPVAs with different hydrophobic contents. The incorporation of MGC 8 /MGC 12 and 1,3-propane sultone onto HMPVA was confirmed by NMR spectroscopy. Rheological properties of aqueous solutions also confirmed the presence of hydrophobic and charged functional groups on HMPVAs. In the semidilute regime, the specific viscosity of HMPVAs followed concentration scaling that is typical of polyelectrolytes. At higher concentrations, the HMPVA solutions with 3 and 4 mol % of MGC 8 exhibited large increase in specific viscosity. Oscillatory experiments on these solutions exhibited gel-like behavior at polymer concentrations of 40-50 g/L. Confocal microscopy images of HMPVA with 4 mol % of MGC 8 clearly indicated the existence of microgels. The tendency of formation of microgels further increased with increasing chain length of the hydrophobe, that is, with MGC 12 . These samples exhibited rheological behavior that is typical of soft solids and was therefore probed by the strain-rate frequency superposition technique reported recently in the literature. HMPVAs with improved rheological properties show potential applications as thickeners in cosmetic creams, lotions and as drug carriers in pharmaceutical formulations.

Strain-rate frequency superposition in large-amplitude oscillatory shear

In a recent work, Wyss [Phys. Rev. Lett. 98, 238303 (2007)] have noted a property of "soft solids" under oscillatory shear, the so-called strain-rate frequency superposition. We extend this study to the case of soft solids under large-amplitude oscillatory shear (LAOS). We show results from LAOS studies in a monodisperse hydrogel suspension, an aqueous gel, and a biopolymer suspension and show that constant strain-rate frequency sweep measurements with soft solids can be superimposed onto master curves for higher harmonic moduli with the same shift factors as for the linear viscoelastic moduli. We show that the behavior of higher harmonic moduli at low frequencies in constant strain-rate frequency sweep measurements is similar to that at large strain amplitude in strain-amplitude sweep tests. We show surface plots of the harmonic moduli and the energy dissipation rate per unit volume in LAOS for soft solids and show experimentally that the energy dissipated per unit volume depends on the first harmonic loss modulus alone, in both the linear and the nonlinear viscoelastic regime.

Examining the validity of strain-rate frequency superposition when measuring the linear viscoelastic properties of soft materials

A strain-rate frequency superposition (SRFS) technique, recently proposed to analyze the low-frequency behavior of soft materials, is evaluated. The application of SRFS to an emulsion and multiarm star polymer solution produces master curves that, while promising in appearance, do not match the anticipated linear response as they seem inconsistent with dynamic frequency sweep data and the Kramers–Kronig relation. While the raw unscaled frequency sweep data are well described using the generalized Maxwell model, strong discrepancies appear when the same procedure is applied to SRFS data. These inconsistencies appear to be generic and are observed in other materials as well. An examination of Lissajous curves obtained from large amplitude oscillatory strain shows that nonlinear contributions, such as solvent-mediated convective flow, strongly affect SRFS master curves. Based on these findings, SRFS should be approached with caution when applied to soft materials.

Shearing particle monolayers: Strain-rate frequency superposition

We report surface shear rheological measurements on monolayers of silica nanoparticles at the air-water interface. We have used the method of strain-rate frequency superposition (SRFS) to characterize the structural relaxation. We show that the rheological properties of the layers have the same universal linear and nonlinear behavior as three-dimensional soft materials. We also discuss the original healing properties of these monolayers.

Strain-Rate Frequency Superposition: A Rheological Probe of Structural Relaxation in Soft Materials

The rheological properties of soft materials often exhibit surprisingly universal linear and nonlinear features. Here we show that these properties can be unified by considering the effect of the strain-rate amplitude on the structural relaxation of the material. We present a new form of oscillatory rheology, strain-rate frequency superposition (SRFS), where the strain-rate amplitude is fixed as the frequency is varied. We show that SRFS can isolate the response due to structural relaxation, even when it occurs at frequencies too low to be accessible with standard techniques.