Application Of Time-temperature Superposition Research Articles

An investigation into the nonlinear rheological behavior of modified asphalt binders using large amplitude oscillatory shear rheology

ABSTRACT Asphalt binders have been studied extensively with respect to their linear viscoelastic properties. From these properties, performance metrics have been derived and used for specification purposes. However, these materials are used in asphalt concrete pavements where they may experience time-dependent loads in the nonlinear regime. In the past, the vast majority of asphalt binders exhibited strong correlations between their linear and nonlinear properties and so despite this mismatch in characterization and the actual use phase domains, a system based on linear properties could be reliably deployed. More recently though, novel binders and additives have been introduced with differing relationships between linear and nonlinear behaviors. As such there is a need to characterize the asphalt binder response under large strains and use specifications that more explicitly account for the binder nonlinearity. Here, an attempt has been made to characterize the nonlinear rheological properties of asphalt binder using large amplitude oscillatory shear. The response of a single terminal blend, crumb rubber modified binder under large strains is analyzed using Lissajous-Bowditch plots while the contribution of higher harmonics is evaluated using Fourier-transform rheology. Finally, the elastic and viscous contributions are obtained using stress decomposition to an orthogonal set of Chebyshev polynomials. It is found that the relative nonlinearity increases with increasing strain and frequency under the tested conditions. The asphalt binder evaluated in this study predominantly exhibits shear thinning and either strain stiffening or softening behavior depending upon the test conditions. The applicability of time-temperature superposition in the nonlinear regime for asphalt binders is also evaluated.

Center Impedance Method for Estimating Complex Modulus with Wide Frequency Range and Large Loss Factors

A simple method for determining viscoelasticity over a wide frequency range using the frequency response function (FRF) mobility obtained by the center impedance method is presented. As user data comprise the FRF between the velocity of the excitation rod and excitation force, it is challenging to separate the signal and noise. Our proposed method is based on the FRF obtained from the analytical solution of the equation of motion of the viscoelastic beam and relationship between the complex wavenumber (real wavenumber and attenuation constant) of flexural wave and viscoelasticity. Furthermore, a large loss factor can be handled over a wide frequency range without using the half-power bandwidth. In this study, actual FRF mobility data containing noise were processed using preprocessing, inverse calculation, and postprocessing. Preprocessing removed low-coherence data, compensates for the effects of instrument gain, and transformed the FRF into its dimensionless equivalent. Then, inverse calculations were used to solve the mobility equation and determine the complex wavenumber. In postprocessing, the complex wavenumber obtained by the inverse calculation was curve fitted using functions with mechanical significance. Consequently, the storage modulus based on the curve-fitted complex wavenumber was a monotonically increasing frequency function. The loss factor had a smooth frequency dependence such that it has the maximum value at a single frequency. The proposed method can be applied to composite materials, where the application of time-temperature superposition is challenging. We utilized the measured FRF mobility data obtained over a duration of several seconds, and this method can also be applied to materials with large loss factors of 1 or more.

Thermodynamics, Dynamics, and Rheology of Fuel Surrogates: Application of the Time–Temperature Superposition Principle in Molecular Dynamics Simulations

All-atom molecular dynamics (MD) simulation is used to determine the thermodynamics and rheological properties of fuel surrogates, which are modeled as a mixture of n-hexadecane and methyl laurate. The volumetric properties of the studied systems, namely, density and coefficient of thermal expansion, show an excellent agreement with experiments. The temperature dependence of translational and rotational diffusion of the molecules follows an Arrhenius-type behavior, which is consistent with the temperature dependence of the zero shear viscosity obtained from nonequilibrium simulations. At high shear rates, the molecules align in the flow direction that gives rise to the shear-thinning behavior for these fuel surrogates. The time–temperature superposition (TTS) principle is then successfully applied to collapse the shear viscosity and translational/rotational motion data in all systems. The application of TTS on the dynamics data obtained in equilibrium, which are readily accessible in the all-atom MD simulations, allows one to reduce the time scale gap between experiments and simulations and predict the rheological response of complex fluids, especially mixtures of short alkanes and fatty acid esters, which are of interest in fuel surrogates.

Linear shear and nonlinear extensional rheology of unentangled supramolecular side-chain polymers

Supramolecular polymers are important within a wide range of applications including printing, adhesives, coatings, cosmetics, surgery, and nano-fabrication. The possibility to tune polymer properties through the control of supramolecular associations makes these materials both versatile and powerful. Here, we present a systematic investigation of the linear shear rheology for a series of unentangled ethylhexyl acrylate-based polymers for which the concentration of randomly distributed supramolecular side groups is systematically varied. We perform a detailed investigation of the applicability of time temperature superposition (TTS) for our polymers; small amplitude oscillatory shear rheology is combined with stress relaxation experiments to identify the dynamic range over which TTS is a reasonable approximation. Moreover, we find that the “sticky-Rouse” model normally used to interpret the rheological response of supramolecular polymers fits our experimental data well in the terminal regime, but is less successful in the rubbery plateau regime. We propose some modifications to the “sticky-Rouse” model, which includes more realistic assumptions with regard to (i) the random placement of the stickers along the backbone, (ii) the contributions from dangling chain ends, and (iii) the chain motion upon dissociation of a sticker and reassociation with a new co-ordination which involves a finite sized “hop” of the chain. Our model provides an improved description of the plateau region. Finally, we measure the extensional rheological response of one of our supramolecular polymers. For the probed extensional flow rates, which are small compared to the characteristic rates of sticker dynamics, we expect a Rouse-type description to work well. We test this by modeling the observed strain hardening using the upper convected Maxwell model and demonstrate that this simple model can describe the data well, confirming the prediction and supporting our determination of sticker dynamics based on linear shear rheology.

Molecular simulations of asphalt rheology: Application of time–temperature superposition principle

We show that the several decades gap between the time scales of experiments and atomistic simulations can be significantly reduced by applying time-temperature superposition (TTS) to the simulation results for various rheological properties of asphalt. Molecular dynamics simulations with atomistically detailed models were performed to characterize the temperature dependence of shear viscosity, dynamic modulus, and tensile creep compliance of AAM–1 asphalt. The TTS principle was successfully applied to the data to construct master curves of these rheological properties, and a comparison of simulation data with experiments showed good agreement. Application of TTS resulted in a six decade increase in the frequency range available for moduli determination and a two decade increase in both the shear rate range available for viscosity determination and the time scale available for characterization of creep compliance. The horizontal shift factors (aT) used in the construction of the master curves for the different rheological properties were quantitatively consistent with each other. The corresponding temperature dependence of the scaled relaxation times was compared with the expectations from three literature models, namely, the Vogel–Fulcher–Tammann, double exponential, and parabolic–Arrhenius models. A distinct change from super-Arrhenius to Arrhenius behavior was observed for the scaled relaxation times below the glass transition temperature (Tg). Only the parabolic-Arrhenius model was able to capture the temperature dependence of the data over the entire temperature range that covers both the glassy and the rubbery states.We show that the several decades gap between the time scales of experiments and atomistic simulations can be significantly reduced by applying time-temperature superposition (TTS) to the simulation results for various rheological properties of asphalt. Molecular dynamics simulations with atomistically detailed models were performed to characterize the temperature dependence of shear viscosity, dynamic modulus, and tensile creep compliance of AAM–1 asphalt. The TTS principle was successfully applied to the data to construct master curves of these rheological properties, and a comparison of simulation data with experiments showed good agreement. Application of TTS resulted in a six decade increase in the frequency range available for moduli determination and a two decade increase in both the shear rate range available for viscosity determination and the time scale available for characterization of creep compliance. The horizontal shift factors (aT) used in the construction of the master curves for the diffe...

Shape‐memory behavior of high‐strength amorphous thermoplastic poly(para‐phenylene)

ABSTRACTThe purpose of this study was to investigate the shape‐memory behavior of poly(para‐phenylene) (PPP) under varying programming temperatures, relaxation times, and recovery conditions. PPP is an inherently stiff and strong aromatic thermoplastic, not previously investigated for use as a shape‐memory material. Initial characterization of PPP focused on the storage and relaxation moduli for PPP at various frequencies and temperatures, which were used to develop continuous master curves for PPP using time–temperature superposition (TTS). Shape‐memory testing involved programming PPP samples to 50% tensile strain at temperatures ranging from 155°C to 205°C, with varying relaxation holds times before cooling and storage. Shape‐recovery behavior ranged from nearly complete deformation recovery to poor recovery, depending heavily on the thermal and temporal conditions during programming. Straining for extended relaxation times and elevated temperatures significantly decreased the recoverable deformation in PPP during shape‐memory recovery. However, PPP was shown to have nearly identical full recovery profiles when programmed with decreased and equivalent relaxation times, illustrating the application of TTS in programming of the shape‐memory effect in PPP. The decreased shape recovery at extended relaxation times was attributed to time‐dependent visco‐plastic effects in the polymer becoming significant at longer time‐scales associated with the melt/flow regime of the master curve. Under constrained‐recovery, recoverable deformation in PPP was observed to have an exponentially decreasing relationship to the bias stress. This study demonstrated the effective use of PPP as a shape‐memory polymer (SMP) both in mechanical behavior as well as in application. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016, 133, 42903.

Oscillatory Rheology of Lentil Starch/Nanoclay Blend Suspension: Applicability of Time-Temperature Superposition

The effect of incorporating montmorillonite nanoclay into lentil starch dispersion was studied by oscillatory rheological measurement. Rheological measurements were carried out at non-isothermal (40–95°C) and isothermal (70–90°C) condition. The elastic modulus (G′) of starch/clay blend showed a significant improvement in the magnitude in the melt when clay concentration was at 5% wt or higher. The peak complex viscosity modulus (Tη*max) decreased from 81.6 to 80.4°C with increasing clay concentration during non-isothermal heating. The empirical principle of time-temperature superposition was tested to bring experimental dynamic rheological data at selected temperatures together into single master curves at a reference temperature of 80°C. The complex viscosity (η*) master curve was found to follow the rule with slight deviation. The elastic modulus superposition (G′-ω) was found to fail in the temperature regime considered in this study. The failure of time-temperature superposition was believed to have happened due to complex starch-nanoclay-water matrix formation, temperature response of individual components, and phase change during gelatinization of starch.

The Peculiar Temperature Response of Dynamic Rheological Behaviors of Poly (Vinyl Chloride)/trioctyl Trimellitate (100/70) System

The dynamic rheological behavior, application of time-temperature superposition (TTS) and the failure mechanism of TTS are studied for the poly(vinyl chloride) (PVC)/trioctyl trimellitate (TOTM) (100/70) system. The Arrhenius equation, Williams–Landel—Ferry (WLF) equation, mathematical non-linear fitting and manual shift are applied to TTS fitting. For the PVC/TOTM (100/70) system, none of those methods can give well-superimposed master curves with either single horizontal shift or two-dimensional (horizontal and vertical) shift. The failure reason is attributed to the thermorheological complexity of the PVC/TOTM (100/70) system. Curves of the storage modulus versus the frequency can be well fitted with an empirical equation (G′=G′0+Kω n ) usually used to describe filled polymer systems, indicating the multilevel flowing unit characteristic in this system. With the increase of test temperature, the structure of the PVC/TOTM (100/70) system changes and an apparent transition appears in the rheological behavior. Differential scanning calorimetry (DSC) results reveal that for the PVC/TOTM (100/70) system there are microcrystallites present below 220°C, but above the rheological transition temperature (190°C) the bulk of the microcrystallites melted, which corresponds to the appearance of viscous flow participating in the rheological behavior. It verifies the fact that the gel networks crosslinked by microcrystallites dominate the rheological behavior below the transition temperature in the PVC/TOTM (100/70) system. The quantity of microcrystallites remaining in the melt determines the perfection of the physical gel networks. With the increase of test temperature, the microcrystallites melted gradually and the gel networks are broken up.

Modelling and analysis of creep data for plastics at elevated temperatures

Absract Procedures are considered for determining the long-term creep behaviour of plastics at ambient temperature from experimental data obtained from short-term tests over a range of elevated temperature. Errors in long-term properties derived from the application of time-temperature superposition can arise unless proper account is taken of changes to creep behaviour caused by physical ageing. Short-term changes in age state and, hence, creep behaviour occur when the temperature of a specimen is raised. These changes are caused by the erasing of physical ageing that has occurred at ambient temperature prior to the temperature increase. Subsequent reactivation of physical ageing leads to further changes in creep behaviour with time at the elevated temperature. The results of creep tests at different temperatures have been analysed by theoretical expressions that separate the contributions to creep behaviour from structure and temperature changes.

On Interconversion of Various Material Functions of PMMA

The interconversion between various linear viscoelastic functions forPoly (methyl) methacrylate (PMMA) is explored. With the availability offour time or frequency-dependent material functions (shear, bulk,uniaxial and Poisson) on the same material, various material functionsare computed using the correspondence principle of the linearized theoryof viscoelasticity through the use of standard relations. Computedmaterial functions are evaluated against the directly measuredproperties and the limitations imposed on successful interconversion dueto the experimental errors in the underlying physical data are explored.It is observed that the differences between the computed and measuredfunctions were larger than suggested by experimental error. The resultsintimates the need to thoroughly re-examine the applicability oftime-temperature superposition principle often employed to develop`master curves' for viscoelastic functions, especially with respect tothe glassy domain.

Interfacial tension, morphology and linear viscoelasticity behavior of PP/PS blends

Blends of polypropylene and polystyrene compatibilized with styrene-butadiene-styrene (SBS) or styrene-ethylene/butylene-styrene (SEBS) copolymers were studied. The morphology of these blends was studied by Scanning Electron Microscopy. Emulsion curves relating the average radius of the dispersed phase to the concentration of compatibilizer added to the blend were obtained. The rheological behavior of the blends was studied by small amplitude oscillatory shear, and correlated to the morphological observations. The interfacial tension between the components of the blends was evaluated from the rheological data. In addition, the applicability of time-temperature superposition (TTS) method for PP/PS blend was studied.

Ordering and structure formation in triblock copolymer solutions. Part I. Rheological observations

The linear viscoelastic properties of a poly(styrene)-poly(ethylene, butylene) triblock copolymer in the presence of a hydrocarbon oil have been investigated. The samples were followed rheologically, during annealing at different temperatures. In a relatively small temperature interval, tan δ-curves, recorded at different frequencies, evolved in a pattern which is typical for a physical gelation. It allowed determination of the gel time. The kinetics of gel formation were found to be affected by the annealing temperature, and the rate was maximum at an intermediate temperature that depended on the polymer content of the sample. Increasing the polymer content shifted this maximum to higher temperatures. At lower temperatures, a glass transition of the polystyrene end-blocks was detected. The microphase separation temperature however, could not be determined. In addition, the influence of strain and the applicability of time-temperature superposition was analysed.

Assessment of time-temperature superposition of linear viscoelastic behaviour of strongly interacting polymer blends: N-methylated nylon-2,10 and lightly sulfonated polystyrene ionomers

The applicability of time-temperature superposition of dynamic mechanical data for miscible polymer blends that exhibit strong intermolecular interactions was investigated. Blends of the lithium salt of lightly sulfonated polystyrene ionomers (Li-SPS), 9–12 mol% sulfonation, and N-methylated nylon-2, 10 (mPA) were miscible over the composition range studied, 30–70 wt% ionomer. Time—temperature superposition (TTS) of the storage and loss shear moduli measured at frequencies of 0.01–500 rad s −1 was applicable over the temperature range from 95 to 185°C. The molecular-weight distribution of the ionomer had no effect on the applicability of TTS. The success of TTS was attributed to the complexation of the metal sulfonate and amide groups, which couple the relaxation times of the two polymers in the blend. Na-SPS (9.5 mol%) and mPA were immiscible and TTS failed for these blends. TTS was obeyed for blends of Zn-SPS and mPA, though these blends appeared to be immiscible or partially miscible.

The application of time-temperature superposition to printing inks

A simple model ink consisting of 80% polybutene and 20% pigment was tested for time-temperature superposition. The principle appeared to work but when the polybutene without pigment was tested, time-temperature superposition did not work completely. Further details of this work may be found inBayford (8).

Time-temperature superposition applied to crosslinked polymers in creep with superimposed hydrostatic pressure

The creep of an epoxy composition under combined tension and hydrostatic pressure (up to 800 kgf/cm2) has been investigated. The applicability of time-temperature superposition to a complex state of stress is demonstrated. Hydrostatic pressure is shown to affect the deformability of crosslinked polymers in tension.

Time-Temperature Superposition of Time-Dependent Birefringence for High Density Polyethylene

The strain-optical coefficient and relaxation modulus were simultaneously measured of high density polyethylene at various temperatures ranging from 12 to 100°C. Not only the horizontal but also the vertical shifts Were necessary to obtain smooth master curves by application of time-tem perature superposition. However, the relaxation modulus decreases with rising temperature, While the strain-optical coefficient increases, indicating that the variation of the relaxation modulus and the strain-optical coefficient with time can not be explained by decrease in crystallinity With rising temperature, since decrease in crystallinity usually causes decrease in the strain-optical coefficient. It is required that some other explanation will be sought for the vertical shift in the time-temperature superposition of the time-dependence curves of the relaxation modulus and the strain-optical coefficient at various temperatures. The master curve of the strain-optical coefficient or the optical distribution function of relaxation times determined from it serves to distinguish the type and thermal history of the polyethylene.