Isothermal Frequency Sweeps Research Articles

Effect of moisture in flax fiber on viscoelastic properties of the manufactured flax fiber reinforced polymer by fractional-order viscoelastic model

Flax Fiber Reinforced Polymer (FFRP) composites, known for their eco-friendliness and mechanical strength, find extensive application in construction. This study investigates the influence of moisture content in flax fiber fabrics on FFRP's viscoelastic properties. Isothermal frequency sweep tests were conducted to assess dynamic mechanical properties under varying moisture levels. The Huet-Sayegh viscoelastic model, with fractional order integration, was employed for analysis. Results indicate optimal viscoelastic properties when fabric humidity matches manufacturing conditions. However, the correlation between the loss factor and the humidity is not straightforward. In summary, FFRP's capacity to store and dissipate energy diminishes with the increased moisture content, but the reduction does not follow a specific pattern with humidity levels.

Apparent Molecular Weight Distributions for Investigating Aging in Polymer-Modified Bitumen

The oxidative aging of bituminous binders affects the performance and durability of pavements. In the case of polymer-modified binders, aging involves both bitumen and polymers and has a strong impact on the whole architecture of the material. Rheology may help in understanding these structural changes, and interesting information may be obtained by analysing the evolution of apparent molecular weight distributions. This was demonstrated with a bituminous binder modified with a poly(styrene-butadiene) block copolymer and subjected to prolonged artificial aging. Isothermal frequency sweep tests were used to construct master curves of the phase angle and magnitude of the complex modulus. The master curves were then used to calculate relaxation spectra and apparent molecular weight distributions of the binders, as well as simulated temperature sweep tests. A comparison of the behaviour of the base and modified bitumen highlighted the role of the polymer in aging. Polymer degradation significantly damages the elastomeric network, yet the residual polymer chains still interact with the bitumen molecules and reduce their oxidative aging. The apparent molecular weight distributions were deconvoluted to create an aging index specifically developed for polymer-modified bitumen.

Temperature impact on the mechanical and fatigue behavior of a non-crystallizing rubber

Temperature is one of the main parameters affecting the mechanical behavior of rubbers. The impact of this parameter is particularly important in the case of cyclic loads. In this study the mechanical and fatigue behavior of a carbon filled acrylonitrile butadiene rubber (NBR) was investigated. Tensile tests revealed a general decrease of the ultimate properties with temperature. Moreover, the maximum chain extensibility, evaluated through Mooney-Rivlin plots, showed a similar trend and a minimum at intermediate temperature. The dynamic properties of the material were investigated through DMA measurements. Temperature sweep revealed an Arrhenius dependence of the dynamic moduli for temperatures above Tg + 30 °C. Master curves of the dynamic properties were generated through the application of the time-temperature superposition principle, by shifting horizontally the isothermal frequency sweeps. The fatigue behavior at different temperature was assessed through the crack growth approach and a lower crack growth resistance was found at higher temperatures. Finally, a new procedure for building fatigue master curves has been investigated by exploiting the temperature dependence of the loss modulus.

Synthesis and In Situ Gelation Behavior of Thermoresponsive Poly(N-isopropylacrylamide)/Chitosan Microgels

Thermoresponsive microgels composed of poly(N-isopropylacrylamide) (PNIPAM) and chitosan (CS) were synthesized by soap-free emulsion polymerization of N-isopropylacrylamide monomer in the presence of CS, using an anionic radical initiator and a chemical crosslinker. The resulting PNIPAM/CS microgels contracted in an aqueous phase at elevated temperature, exhibiting a negatively thermoresponsive nature with a volume phase transition temperature (VPTT) of about 34.6 °C. The microgel dispersions with a relatively high polymer content gelated when being heated across their VPTT due to their attractive hydrophobic interactions. We systematically investigated this thermo-induced in situ gelation behavior by small-deformation oscillatory rheological measurements within the linear viscoelastic region. The dynamic temperature ramp sweeps revealed that the gelation temperature was greatly influenced by the polymer content of the microgel dispersion, decreasing with increasing polymer content. The isothermal time sweeps showed that the gelation occurred more quickly at either higher polymer content or higher isothermal heating temperature. The relaxation dynamics for the as-formed gel were also studied by isothermal frequency sweeps. It was found that the gels exhibited a frequency-independent storage modulus in the lower frequency range, and the greater the polymer content of the microgel dispersions, the more elastic the gels that formed.

Effect of Recycled Asphalt Pavement Binder on Rheology of Crumb Rubber–Modified Binder—An Experimental, Analytical, and Analogical Study

Abstract The popularity of recycled asphalt pavement (RAP) is on the rise because of the benefits of sustainability. In an unavoidable scenario wherein crumb rubber–modified binder (CRMB) is adopted as a base binder in RAP mixes, the binder from RAP will blend with CRMB, thereby influencing its rheology and performance at high, intermediate, and low temperature. Hence, in this study, binder extracted from two RAP sources (RAP X and RAP Y) was blended with CRMB at varying proportions of 15, 25, and 40 % by weight. Isochronal temperature sweeps, isothermal frequency sweeps, and bending beam rheometer tests were conducted on the prepared blends. Thereafter, analytical and analogical studies were performed using master curve construction, 2S2P1D, and Huet modelling. The results indicated that RAP from different sources affects the high-, intermediate-, and low-temperature performance of CRMB. Different RAPs were observed to have contrasting effects on high-temperature performance grading. Intermediate-temperature performance based on cross-over temperature (TCROSS-OVER) indicated a compromise because of the inclusion of RAPs. An evaluation of the differences among critical temperatures at low temperature (ΔTc) indicated the degradation of low-temperature performance. Such changes in high-, intermediate-, and low-temperature performances were validated by complex modulus (G*), stiffness (S(t)), and stress relaxation (E(t)) master curves. Finally, the 2S2P1D and Huet model were observed to depict reasonably good fits for the prepared blends. This study concludes that RAPs from different sources have contrasting impact on CRMB and may adversely impact the intermediate- and low-temperature performance.

Polymer tethered graphene oxide influences miscibility and cooperative relaxation in LCST blends

The miscibility of a classical lower critical solution temperature (LCST) system; PMMA/SAN was probed by different rheological fingerprints such as isochronal temperature ramps, and isothermal frequency sweeps, in presence of graphene oxide (GO) and PMMA tethered GO. The chain length of the grafted polymer was varied to study its effect on miscibility, volume cooperativity, entanglement density and localization in the blends. The PMMA tethered GO alters the chain dynamics both at local and cooperative length scale through entropic and enthalpic interactions. It was perceived that the thermodynamic miscibility, cooperative relaxations and concentration fluctuation in PMMA/SAN blends are controlled by the spatial distribution of GO in the blend. By varying the chain length, we were able to understand that shorter tethered chains lead to early phase separation whereas the tethered chain length similar to that of the host matrix delays phase separation. Interestingly, irrespective of the length of the tethered polymer chain, the grafted GO sheets were not localized in the thermodynamically preferred phase (here PMMA). These findings are of great importance to further help us understand the theories and simulations which pertain to chain dynamics of PMMA/SAN blends containing polymer-tethered nanoparticles with large specific surface area like GO.

Frequency-dependent material properties of copper and aluminum alloys

In this paper, the dynamic behavior of copper and aluminum alloys as used in electric drive units is investigated. Isothermal frequency sweeps are performed from 0.1 up to 50 Hz at temperatures of up to 400 °C. An evaluation of the test results at a constant frequency of 1 Hz shows a decrease in the storage modulus and an increase in the material damping. Considering all frequencies, a supplementary frequency dependency related to the material composition is detected. The lower the volume fraction of the alloying elements, the higher the impact of temperature and frequency on the material properties. The variations of the material parameters allow applying the time temperature superposition principle to estimate the dynamic behavior beyond the limited tested frequency range and temperatures by fitting the Williams–Landel–Ferry equation. Additional thermal aging of CU-ETP specimens does not affect the storage modulus, but diminishes the material damping. The findings show that each material has to be tested with regard to its respective application, material composition and manufacturing process. Furthermore, they demonstrate the relevance of considering the frequency-dependent material properties of low-alloyed copper and aluminum, especially in case of temperatures above 100 °C.

Rheological study on the thermoinduced gelation behavior of poly(N‐isopropylacrylamide‐co‐acrylic acid) microgel suspensions

ABSTRACTSubmicron‐sized thermoresponsive poly(N‐isopropylacrylamide‐co‐acrylic acid) microgels were synthesized by soap‐free emulsion polymerization. The physical state of the microgel suspensions, in a wide range of polymer concentrations (1.1–7.1 wt %), transformed from fluid to gel when the temperature was elevated across their volume phase transition temperature at pH = 3.0. Such thermoinduced gelation behavior was studied in detail by small‐deformation oscillatory rheological measurements within the linear viscoelastic region. It was found that the gelation temperature was strongly affected by the polymer concentration, decreasing as the polymer concentration increased. The gelation kinetics showed that the suspension gelled more quickly at either larger polymer concentration or higher isothermal heating temperature. In an isothermal frequency sweep for the as‐formed gels, both storage and loss moduli, G′ and G″, exhibited a power‐law behavior, that is, G′(ω) ∼ ω0.2–0.4 and G″(ω) ∼ ω0.46−0.50 within the frequency range where G′ dominates G″. In addition, the elasticity of the gels, which results from the attractive particle bonds, increased markedly with increasing polymer concentration. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017, 134, 45259.

A method for the determination and correction of the effect of thermal degradation on the viscoelastic properties of degradable polymers

Small amplitude oscillatory shear is carried out during isothermal degradation of poly(lactic acid) (PLA) in order to determine the evolution of the characteristic relaxation time with degradation time and temperature. After reducing the relaxation time data to a single mastercurve, a 4-parameter function is fitted to the data to allow prediction of the change in relaxation time following an arbitrary thermal history. The method enables separation of the effects of temperature and of degradation on the relaxation time, both of which lead to a horizontal shift of dynamic data along the frequency axis, and hence enable a correction for thermal degradation during rheometry to be carried out. To validate the method, two isothermal frequency sweeps were measured with different temperature histories, producing different mastercurves due to dissimilar in-test thermal degradation. After correcting for thermal degradation using the function and the thermal histories, the two frequency sweeps reduce to the same viscoelastic mastercurve in the undegraded pre-test state.

Viscoelastic melt rheology and time–temperature superposition of polycarbonate–multi-walled carbon nanotube nanocomposites

Abstract This work investigates the linear and non-linear viscoelastic melt rheology of four grades of polycarbonate melt compounded with 3 wt% Nanocyl NC7000 multi-walled carbon nanotubes and of the matching matrix polymers. Amplitude sweeps reveal an earlier onset of non-linearity and a strain overshoot in the nanocomposites. Mastercurves are constructed from isothermal frequency sweeps using vertical and horizontal shifting. Although all nanocomposites exhibit a second plateau at ∼105 Pa, the relaxation times estimated from the peak in loss tangent are not statistically different from those of pure melts estimated from cross-over frequencies: all relaxation timescales scale with molar mass in the same way, evidence that the relaxation of the polymer network is the dominant mechanism in both filled and unfilled materials. Non-linear rheology is also measured in large amplitude oscillatory shear. A comparison of the responses from frequency and amplitude sweep experiments reveals the importance of strain and temperature history on the response of such nanocomposites.

Low-Temperature Oxidation Kinetics of Asphalt Binders

A simple dual-mechanism model successfully fits the oxidation of 12 unmodified asphalt binders originating from a wide variety of sources. The kinetic formulation includes fast and slow reaction paths in parallel with free radical interactions between the two reaction pathways. The same Arrhenius parameters are used for all 12 binders studied. The differences in asphalt binder oxidation rates can be explained with the use of only one adjustable parameter, the amount of reactive material available for the fast reaction. This result suggests that unmodified asphalt binders oxidize with essentially the same chemical mechanisms. Because the Arrhenius parameters apply universally, a simple test may be performed to characterize the oxidation kinetics for unmodified binders without expensive, long-term oxidation experiments at multiple temperatures. A rheological study of the materials generated in the aging of the 12 binders using dynamic shear rheometry was also performed to investigate the relationship of rheological changes with chemical changes as binders oxidize. The rheometry consisted of the generation of a series of isothermal frequency sweeps, followed by fitting the resulting master curve with the Christensen–Anderson model. Simple shifting cannot account for the master curve changes, but changes in the model parameters follow a log-linear relationship for oxidation chemical changes. These fits appear to be source dependent, suggesting that a method with two aging time conditions would be required to characterize the rheological property changes in an unmodified asphalt binder as it ages. Such a method would produce a complete master curve–shift function set at any extent of aging, suitable for input into rational performance models.

Use of Dielectric Spectroscopy To Monitor Molecular Mobility in Glassy and Supercooled Trehalose

Dielectric spectroscopy was used to comprehensively characterize the molecular mobility in amorphous trehalose, an extensively used bioprotective agent. Isothermal frequency sweeps were carried out at different temperatures in the glassy and supercooled liquid states of freeze-dried trehalose. Two previously reported secondary relaxations were observed at temperatures far below its glass transition temperature (T(g)). At temperatures close to T(g), removal of dc conductivity contribution revealed a relaxation peak. The origin of this peak was evaluated using several diagnostic tests and determined to be the α-relaxation. There was also an excess wing in the high-frequency tail of α-relaxation. Sub-T(g) annealing caused the primary relaxation to shift to lower frequencies, enabling resolution of the excess wing, which was characterized to be the true Johari-Goldstein (JG) relaxation. A qualitatively similar effect of annealing on JG relaxation was also observed. The average relaxation times of the two previously reported secondary relaxations were unaffected by annealing.

Enhancing the viscoelastic properties of bituminous binders via thiourea-modification

Although added in a very low concentration, bitumen controls the final properties and performance of the resulting asphalt mixture. As an alternative to classic bitumen modification with polymers, we herein propose the use of thiourea, which has proved to efficiently enhance the binder thermo-rheological properties in a broad temperature interval. As revealed by thermogravimetric and chemical analysis, benefits above may derive from new structures, probably formed by the interaction between ammonium thiocyanate and bitumen most polar fraction. Thus, flexural DMTA and dynamic shear tests demonstrated an improvement in the binder flexibility and an increase in its elasticity, at low and medium/high in-service temperatures, respectively. In addition, this research emphasizes the use of isothermal frequency sweep tests (and frequency/temperature-dependence conversion) as a means of achieving glass transition temperature values which, in contrast to isochronal temperature sweep tests, do not depend on the selected heating rate.

Hydration of Gelatin Molecules in Glycerol–Water Solvent and Phase Diagram of Gelatin Organogels

We present a systematic investigation of hydration and gelation of the polypeptide gelatin in water-glycerol mixed solvent (glycerol solutions). Raman spectroscopy results indicated enhancement in water structure in glycerol solutions and the depletion of glycerol density close to hydration sheath of the protein molecule. Gelation concentration (c(g)) was observed to decrease from 1.92 to 1.15% (w/v) while the gelation temperature (T(g)) was observed to increase from 31.4 to 40.7 °C with increase in glycerol concentration. Data on hand established the formation of organogels having interconnected networks, and the universal gelation mechanism could be described through an anomalous percolation model. The viscosity of sol diverged as η ∼ (1 - c(g)/c)(-k) as c(g) was approached from below (c < c(g)), while the elastic storage modulus grew as G' ∼ (c/c(g) - 1)(t) (for c > c(g)). It is important to note that values determined for critical exponents k and t were universal; that is, they did not depend on the microscopic details. The measured values were k = 0.38 ± 0.10 and t = 0.92 ± 0.17 whereas the percolation model predicts k = 0.7-1.3 and t = 1.9. Isothermal frequency sweep studies showed power-law dependence of gel storage modulus (G') and loss modulus (G'') on oscillation frequency ω given as G'(ω) ∼ ω(n') and G''(ω) ∼ ω(n''), and consistent with percolation model prediction it was found that n' ≈ n'' ≈ δ ≈ 0.73 close to gelation concentration. We propose a unique 3D phase diagram for the gelatin organogels. Circular dichroism data revealed that the gelatin molecules retained their biological activity in these solvents. Thus, it is shown that the thermomechanical properties of these organogels could be systematically tuned and customized as per application requirement.

Rheological properties of binary and ternary protein–polysaccharide co-hydrogels and comparative release kinetics of salbutamol sulphate from their matrices

Rheological properties of binary (AgarGelA and AgarGelB) and ternary (AgarGelAB and GelABAgar) co-hydrogels of agar (polysaccharide) with gelatin A and gelatin B (proteins) were studied to investigate their differential viscoelastic behavior. Two sets of rheological experiments, isochronal temperature and isothermal frequency sweep, were performed and the storage modulii, G′ was measured which could be correlated to the gel strengths. Two separate peaks at 70 °C and 35 °C, corresponding to melting temperatures of agar and gelatin gels respectively, were obtained when derivative of G′ with respect to temperature, d G′/d T was plotted against temperature which clearly showed the presence of two separate networks of gelatin and agar interconnected to each other. The results revealed that AgarGelAB was the strongest and AgarGelA was the weakest gel among all the gels studied. In order to see the effect of gel microstructure on drug encapsulation and release behavior, a model drug salbutamol was encapsulated in various gel matrices and the release of the same was seen in phosphate buffer pH 7.4, in simulated gastric fluid pH 1.2 (SGF) and in simulated intestinal fluid pH 6.8 (SIF) media. The drug release behavior universally followed sigmoidal kinetics invariant of gel composition. It is concluded that the hydrogel microstructure influenced the release behavior and best release, in all the three media, could be found with binary gel, AgarGelB, and ternary gel, AgarGelAB. Finally, microstructure of these gels is proposed.

Electromechanical properties of high- coupling (1-ξ)Pb(Zn1/3Nb2/3)O3-(ξ)PbTiO3 single crystals for sound projectors

Isothermal weak field frequency sweeps were conducted over the temperature range 30 to 140 degrees C on multidomain, oriented, and poled (1-x)Pb(Zn(1/3)Nb(2/3))O(3)-xPbTiO(3) (PZN-PT) single crystals with x = 0.045, 0.06, 0.07, and 0.08 near the ferroelectric rhombohedral (FR)-ferroelectric tetragonal (F(T)) morphotropic phase boundary (MPB). The temperature dependencies of the small-signal 33-mode electromechanical properties were derived from the isothermal frequency sweeps. Morphotropic compositions with x = 0.06 and 0.07 PT were found to exhibit the largest electromechanical coupling and piezoelectric coefficient, with k(33) > 0.90 and d(33) approximately 2300 pC/N, and the lowest short-circuit Young's modulus of approximately 9 GPa. Reversible zero-field elastic instability attributable to a F(R)- F(O) transition was observed under isothermal compression-decompression of a 0.94PZN-0.06PT single crystal. The application of a dc bias field enhanced the F(R) stability under compression. The large-signal, dc biased, 33-mode electromechanical response was measured under mechanical compressions similar to those used in sound projectors. The remarkable small-signal electromechanical properties are in a good agreement with the large-signal response. The crystal response to thermal, electrical, and mechanical variable is discussed in terms of high-coupling single crystal models.

Universal Growth of Microdomains and Gelation Transition in Agar Hydrogels

Investigations were carried out on aqueous sols and gels of agar (extracted from red seaweed Gelidiella acerosa) to explore the growth of microdomains en route to gelation. Isothermal frequency sweep studies on gel samples revealed master plots showing power-law dependence of gel elastic modulus, |G*|, on oscillation frequency, omega as |G*| approximately omegan, independent of temperature, with 0.5<or=n<or=1.4. Dynamic structure factor data from sol samples comprised of a double-exponential relaxation function, S(q,t)=A exp(-DSq2t)+B exp(-DLq2t) where DS and DL are the two translational diffusion coefficients and q is the scattering wave vector. This yielded hydrodynamic radii (from DS), with RS varying from approximately 20 nm (for sol) to 250 nm (at gelation point). The second hydrodynamic radius (from DL) obtained was RL in the range of approximately 200-500 nm (for sol) to approximately 1000 nm (at 38 degrees C, gelation point). These data could be universally fitted to RS approximately epsilon(-3/5) and RL approximately epsilon-1/3 (epsilon=(T/Tg-1), T>Tg). The S(q,t) behavior close to the gel transition point (Tg approximately (38+/-3 degrees C determined from rheology) followed a stretched exponential function: S(t)=A exp(-t/ts)beta. The beta factor increased from 0.25 to 1 as the gel temperature approached 25 degrees C from Tg, and relaxation time, ts, showed a peak at T approximately 30 degrees C. The SLS data (in the sol state) suggested the scaling of scattered intensity, Is(q) approximately epsilon(-gamma) (epsilon=(T/Tg-1), T>Tg) with gamma=0.13+/-0.03, and the presence of two distinct domains characterized by a Guinier regime (low q) and a power-law regime (high q). Close to and above Tg (+2 degrees C), IS(q) scaled with q as Is(q) approximately q(-alpha) with alpha=2.2+/-0.2, which decreased to 1.4+/-1 just below Tg (-2 degrees C), implying a coil-helix transition for 0.2% (w/v) and 0.3% (w/v) samples. For a 0.01% sample, alpha=3.5+/-0.5 which indicated the presence of spherical microgels.

Transient Solidlike Behavior near the Cylinder/Disorder Transition in Block Copolymer Solutions

A nearly symmetric polystyrene-block-polyisoprene diblock copolymer dissolved at a concentration of 40% in styrene-selective solvents exhibited a cylinder-to-disorder transition upon heating. The solvents used were diethyl phthalate (DEP) and 75:25 and 50:50 mixtures of DEP with di-n-butyl phthalate (DBP). In DEP, the most styrene-selective of the three solvents, rheological measurements indicated a distinct plateau in the temperature-dependent elastic modulus across the 8 degrees C interval above the order-disorder transition temperature, T(ODT) = 116 degrees C. Previous small-angle neutron scattering measurements in this regime indicated the equilibrium phase to be a liquidlike solution of approximately spherical micelles. An isothermal frequency sweep in this regime indicated a very long relaxation time. Annealing eventually led to the recovery of liquidlike rheological response, over a time scale of hours. Qualitatively similar phenomena were also observed in 75:25 DEP/DBP and 50:50 DEP/DBP solutions, except the fact that the temperature window of the transient response is narrow and the time scale for the recovery diminishes significantly. Neither small-angle X-ray scattering nor static birefringence gave any clear signature of the transient structure. The structure that leads to the transient rheological response is attributed to micellar congestion due to the slow relaxation of anisotropic micelles into an equilibrium distribution of micelles. Possible origins of the remarkable solvent selectivity dependence are also discussed.

Effect of Moisture Content on Viscoelastic Properties of Hydrated Gliadin

ABSTRACTThe effect of moisture content on the linear viscoelastic properties of gliadin hydrated to 30 and 40% moisture content [gliadin(30%) and gliadin(40%), respectively] was determined. These two moisture contents bracketed the equilibrium moisture content of gliadin, which was 37.6%. Time‐temperature‐superposition was used to develop master curves of the elastic modulus (G′), viscous modulus (G″), dynamic viscosity (η′), and tan δ (G″/G′) from isothermal frequency sweep data obtained at 25–80°C. Smooth master curves were obtained for all of the viscoelastic functions for both gliadins. G′ and G″ showed a power law dependency on frequency (with G″ &gt; G′) for frequencies &lt;0.1 rad/sec for gliadin(30%) and &lt;1 rad/sec for gliadin(40%). The low‐frequency‐limiting slopes on log‐log coordinates for G′ and G″ were 0.700 and 0.646 for gliadin(30%), respectively. Corresponding values were 0.658 and 0.614 for gliadin(40%). G′ crossed over G″ at a frequency of ≈0.3 rad/sec for gliadin(30%), while G′ and G″ for gliadin(40%) only became congruent at higher frequencies. Both gliadin samples showed appreciable frequency dependence of η′ over the entire frequency range, while η′ was greater for gliadin(30%) than for gliadin(40%) at all frequencies, but especially at the lowest frequencies. Tan δ increased gradually from a value of ≈1 at 0.1 rad/sec to ≈2 at the lowest frequency of 0.0002 rad/sec for both gliadins, but tan δ decreased rapidly for gliadin(30%) for frequencies &gt;0.1 rad/sec. Thus, the main difference between gliadin(30%) and gliadin(40%) was that elastic effects (G′ &gt; G″ and decreased tan δ were more prominent for gliadin(30%) at the higher frequencies. In addition, the frequency dependence of G′, G″, η′, and tan δ for the two gliadin samples was compared directly with two samples of poly(dimethylsiloxane) (PDMS) a linear silicone‐based entangled polymer with molecular weights (MW) of 140,000 and 385,000. The substantial differences in the magnitude and overall patterns of the frequency dependence of the viscoelastic functions between the gliadin and PDMS samples was attributed to the dominant effect that noncovalent secondary associations apparently have on the linear viscoelasticity of the gliadins. The energy of activation for flow (determined from the temperature dependence of the shift factors) for the gliadin samples for the range 25–45°C was higher than is typical for entangled linear polymer melts. The activation energy decreased for temperatures greater than ≈60°C for gliadin(30%) and ≈50°C for gliadin(40%). Thus, hydrated gliadin cannot be considered to be a simple viscoelastic liquid.

Constitutive equations for polymer viscoelasticity derived from hierarchical models in cases of failure of time–temperature superposition

Hierarchical viscoelastic elements whose behaviour is intermediate between linear elasticity and Newtonian viscosity (springpots) have been introduced previously into classical analog models describing linear viscoelastic behaviour. This approach allows a concise description of typical polymer behaviour, including non-exponential relaxation, memory effects and hierarchy of viscoelastic transitions. This approach is extended in the present work to describe complex behaviour, including failure of time–temperature superposition in a semi-crystalline polymer, and the terminal transition from self-similar viscoelasticity to pure flow in a thermoplastic elastomer. Tschoegl's formulation of a finite Gross Marvin ladder model is generalized and applied to other models, and this approach is compared with Friedrich's method based on application of an exponential cutoff to the relaxation function. The method is illustrated using dynamic mechanical measurements on a triblock adhesive in isothermal frequency sweeps. This material displays thermorheological complexity precluding application of time–temperature superposition. Tschoegl's formulation affords a better description of this material than Friedrich's approach. The method described here is a useful alternative to time–temperature superposition requiring a limited number of adjustable parameters.