Relaxation Master Curves Research Articles

Time–Temperature Superposition and the Controlling Role of Solvation in the Viscoelastic Properties of Polyaniline Thin Films

Comprehensive exploration of the viscoelastic properties of polyaniline films exposed to aqueous perchloric acid has been made as a function of applied potential (E), temperature (T), and mechanical oscillation frequency (f = ω/2π) using high-frequency acoustic wave resonators. The outcomes are expressed in terms of storage and loss shear modulus signatures, G'(E, T, ω) and G″(E, T, ω). Surprisingly, these are barely sensitive to potential, through which both polymer charge and solvation are manipulated, and only modestly sensitive to temperature. In contrast, the response to timescale is dramatic. Using the principle of time-temperature superposition, G' and G″ at different temperatures and frequencies (time scales) can each be placed on master relaxation curves. Models developed for mechanical properties of bulk polymers at low frequency were applied to these thin film responses at high frequency. These include the Williams-Landel-Ferry model, the activation model, and the Rouse-Zimm model based, respectively, on concepts of free volume, thermal activation, and relaxation. Each of the models could be applied with physically reasonable outcomes in terms of the relevant parameters (thermal expansion coefficient, glass transition temperature, and activation enthalpy). G' and G″ values are correlated with solvent content. The enthalpy change for solvent entry is small, positive and relatively independent of polymer charge state, all of which contrast sharply with the behavior of thiophene-based conducting polymers in organic solvents.

Combined use of the free volume and coupling theories in the glass transition of polysaccharide/co-solute systems

The structural properties of the glass dispersion in agarose, κ-carrageenan and deacylated gellan with co-solute (glucose syrup) at 80.0% (w/w) solids were studied. Investigative techniques were small-deformation stress relaxation and dynamic oscillation on shear. Vitrification was monitored between −2 and −50 °C with continuous thermal runs and isothermal frequency or time sweeps obtained at constant temperature intervals. The time–temperature superposition principle was utilized to compose master curves. The Williams, Landel and Ferry equation was able to pinpoint the network T g for these systems as the turning point from the predictions of the free volume theory in the transition region to those of the reaction rate theory at the glassy state. Further insights into the physics of intermolecular interactions at the vicinity of T g were obtained using the coupling model of molecular dynamics in the form of the Kohlrausch, Williams and Watts function. The model described well the spectral shape of the local segmental motions in polysaccharide/co-solute samples at the short-time region of the stress–relaxation master curve. Analysis provided the intermolecular interaction constant and apparent relaxation time, which are valuable parameters for the elucidation of structural morphology at T g.

Characterization of the Compressive Behavior of Glass Fiber Reinforced Polyurethane Foam at Different Strain Rates

A glass fiber reinforced polyurethane foam (R-PUF), used for thermal insulation of liquefied natural gas tanks, was characterized to determine its compressive strength, modulus, and relaxation behavior. Compressive tests were conducted at different strain rates, ranging from 10−3 s−1 to 10 s−1 using a servohydraulic material testing system, and from 40 s−1 to 103 s−1 using a long split Hopkinson pressure bar (SHPB) designed for materials with low mechanical impedance such as R-PUF. Results indicate that in general both Young’s modulus and collapse strength increase with the strain rate at both room and cryogenic (−170°C) temperatures. The R-PUF shows a linearly viscoelastic behavior prior to collapse. Based on time-temperature superposition principle, relaxation curves at several temperatures were shifted horizontally to determine Young’s relaxation master curve. The results show that Young’s relaxation modulus decreases with time. The relaxation master curve obtained can be used to convert to Young’s modulus at strain rates up to 103 s−1 following linearly viscoelastic analysis after the specimen size effect has been considered.

Nonlinear rheology of model comb polymers

We measure the stress relaxation of linear comb polymer solutions, after a large amplitude step shear strain. We apply the time-temperature superposition principle in order to construct stress relaxation master curves that span many orders of magnitude in time and cover the entire comb relaxation from early branch retraction to backbone reptation. We find evidence of distinct relaxation processes and dynamic tube dilation that can be attributed to the architectural features of the polymer.

Evaluation of Time Dependent Behavior of a Wood Flour/High Density Polyethylene Composite

Short-term flexural creep and stress relaxation tests were conducted on a wood plastic composite containing 30% high density polyethylene (HDPE), 67% fir wood flour, 2% compatibilizer (MAPE), and 1% lubricant. In creep tests, applied stress levels ranged from 30 to 60% of measured flexural strength. The principle of time—stress superposition was applied to form a master curve extending for a maximum of 4 years. The horizontal shift factors conformed to an Arrhenius type equation. Stress relaxation tests were also carried out at strain levels ranging from 30 to 60% of the ultimate strain. The principle of time—strain superposition was applied to form a stress relaxation master curve that extended for 67 days. The horizontal shift factors also conformed to an Arrhenius type equation. The resulting master curves were compared with extrapolated creep and stress relaxation models. To determine whether time—stress superposition is valid for the studied composite material, creep shift factors were applied to stress relaxation data and vice versa. In both creep and stress relaxation tests, it was found that the application of superposition was verified. The results indicated that the studied composite material was rheologically simple, and a single horizontal shifting on time axis was adequate to predict the long term performance of the material.

Applicability of the time–temperature superposition principle in modeling dynamic response of a polyurea

This paper addresses the applicability of the Time–Temperature Superposition Principle in the dynamic response of a polyurea polymer at high strain rates and different temperatures. Careful and extensive measurements in the time domain of the relaxation behavior and subsequent deduction of a master-relaxation curve establish the mechanical behavior for quasistatic deformations over a time range of 16 decades. To examine its validity in a highly dynamic environment, experiments with the aid of a split Hopkinson (Kolsky) pressure bar are carried out. The use of a two-material pulse shaper allows for stress equilibrium across the specimen during the compression process, to concentrate on the initial, small deformation part that characterizes linearly viscoelastic behavior. This behavior of polyurea at high strain rates and different temperatures is then investigated by comparing results from a physically fully three-dimensional (axisymmetric) numerical model, employing the quasistatically obtained properties, with corresponding Hopkinson bar measurements. The experimentally determined wave history entering the specimen is used as input to the model. Experimental and simulation results are compared with each other to demonstrate that the Time–Temperature Superposition Principle can indeed provide the requisite data for high strain rate loading of viscoelastic solids, at least to the extent that linear viscoelasticity applies with respect to the polyurea material.

Pressure relaxation of polystyrene and its comparison to the shear response

AbstractIsothermal pressure relaxation as a function of temperature in two pressure ranges has been measured for polystyrene using a self‐built pressurizable dilatometer. A master curve for pressure relaxation in each pressure regime is obtained based on the time–temperature superposition principle, and time–pressure superposition of the two master curves is found to be applicable when the master curves are referenced to their pressure‐dependent Tg. The pressure relaxation master curves, the shift factors, and retardation spectra obtained from these curves are compared with those obtained from shear creep compliance measurements for the same material. The shift factors for the bulk and shear responses have the same temperature dependence, and the retardation spectra overlap at short times. Our results suggest that the bulk and shear response have similar molecular origin, but that long‐time chain mechanisms available to shear are lost in the bulk response. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3375–3385, 2007

Correlation of Viscoelastic Properties with Solvation of Regioregular Poly(3-decylthiophene) Films

Viscoelastic properties of regioregular poly(3-decylthiophene) films cast on gold electrodes and exposed to acetonitrile/LiClO4 solution were studied using high-frequency acoustic impedance. Values of shear moduli, G = G' + jG'', were determined under conditions of potentiodynamic and potentiostatic electrochemical control, as functions of potential (0.0 < E/V < 0.8), temperature (5 < T/ degrees C < 70), and angular frequency (omega = 2pi f; 10 < f/MHz < 110). The effect of potential was small, of temperature was significant, and of frequency was dominant. The principle of time-temperature equivalence was used to construct master relaxation curves. Application of activation, Williams-Landel-Ferry, and Rouse-Zimm models shows the material to be quite different from other thiophene-based conducting polymers, namely, poly(3,4-ethylenedioxythiophene) and regioregular poly(3-hexylthiophene). Detailed exploration of the data reveals novel insights into the compositional origins--notably with regard to solvation--of the shear modulus behavior.

DMTA analysis for long-term mechanical behaviour prediction of PMMA-based bone cements

Poly(methyl methacrylate) (PMMA) is commonly used as acrylic bone cement to fix bone implants. In vivo degradation of bone cement may lead to a decrease in mechanical properties and result in aseptic loosening. Creeping can promote failure of the implant. This study used dynamic mechanical thermal analysis (DMTA) equipment, in the 0.01 to 50 Hz frequency range, to investigate the dynamic viscoelastic relaxation characteristics of CMW™, PROFIT QUIRÚRGICO and PALACOS PMMA-based bone cements. Their initial moduli were measured as 2450, 1850 and 1710 MPa, respectively. Relaxation master curves displayed similar features. The DMTA temperature range was between 20 and 75°C. Predictions for long-term relaxation moduli were analyzed and compared against published experimental data. The comparison revealed that master curves obtain using the time-temperature-superposition principle (TTSP) present a much slower relaxation modulus compared to long-term experimental data above 1000 s. However, extrapolations based on a time-power law applied to isothermal experimental data allow better long-term predictions.

Time−Temperature Superposition for Viscoelastic Properties of Regioregular Poly(3-hexylthiophene) Films

Shear moduli were determined for chemically polymerized and solvent cast regioregular poly(3-hexylthiophene) films, using thickness shear mode acoustic wave resonators. The results are strikingly different to those for electropolymerized regiorandom poly(3-hexylthiophene) films. The time scale of the measurement was varied directly by use of higher harmonics of the acoustic wave resonator and indirectly via temperature. The significant variations in shear modulus with effective time scale can be "normalized"onto a stress master relaxation curve by using the concept of time-temperature superposition; this is the first time this has been demonstrated for electroactive films. The shift factors required to effect this normalization do not follow the classical Williams-Landel-Ferry (WLF) equation developed for long-range backbone motions of bulk polymers. Instead, they follow an Arrhenius-like behavior, commonly used to describe secondary motions of polymer side-chains. The activation enthalpy associated with this is independent of applied potential, is the same as for as cast (undoped) films, and is similar to that for rotation about a carbon-carbon single bond. These all point to the hexyl side-chains as the origins of the observed phenomena, consistent with the "melting point" separating two temperature-dependent phases and with the different molecular packing arrangements that would necessarily apply to regioregular and regiorandom materials.

Magnetic relaxation in a model of interacting nanoparticles in terms of microscopic energy barriers

Monte Carlo simulations are used to study the magnetic relaxation of a system of single domain particles with dipolar interactions modeled by a chain of Heisenberg classical spins. We show that the so-called T ln (t/τ0) method can be extended to interacting systems and how, from the computed master relaxation curves, the effective energy barrier distributions responsible for the relaxation can be obtained. A transition from a quasi-logarithmic to power-law behavior of the relaxation as the interaction strength is increased is found. By direct computation of the effective energy barriers of the system, we show that this is due to the appearance of an increasing number of small energy barriers caused by the reduction of the anisotropy energy barriers as the local dipolar fields increase. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Linear Stress Relaxation Behavior of Amorphous Ethylene−Styrene Interpolymers

Amorphous ethylene−styrene interpolymers (ESIs) provide an excellent model system for testing contemporary concepts of molecular dynamics. Moreover, the results can be extrapolated to the chain reptation dynamics of amorphous polyethylene at ambient temperature which cannot be assessed by direct experimental techniques. Previous studies of creep and nonlinear stress relaxation were extended to test theoretical relaxation functions for monodisperse polymers and proposed combining rules against the linear stress relaxation behavior of ESIs in the plateau and terminal regions. Master curves were constructed by time−temperature superposition of data at temperatures from Tg to Tg + 30. The temperature dependence of the shift factor was independent of molecular weight and styrene content and was well described by the WLF equation. The master curves were satisfactorily fit by the empirical KWW equation. Relaxation master curves were modeled with theoretical relaxation functions for monodisperse polymers, appropriate combining rules, and known molecular weight distributions. The Doi−Edwards single reptation model did not give satisfactory results. However, the des Cloizeaux double reptation approach successfully described the relaxation master curves. Excellent agreement was found between the resulting plateau moduli and those from a previous study of creep in the glass transition region. The calculated entanglement molecular weight (1250−2290 g mol-1) was much closer to that of polyethylene (480−860 g mol-1) than to that of polystyrene (13 500 g mol-1) due to the unique chain microstructure of these ESIs with no head-to-tail styrene chain insertions.

Thermal and mechanical characterization of amine-epoxy/Kevlar fibre composites

Experimental results of dynamic-mechanical measurements and differential scanning calorimetry are compared for a pure diglycidyl-type epoxy/tetrafunctional aliphatic amine system and for a composite containing Kevlar fibres as reinforcement. The presence of fibres had marked effects on the curing reaction, depending on the curing temperature. At low curing temperatures, the extent of the reaction was lower for reinforced than for neat formulations. For higher curing temperatures, the thermograms shifted to shorter times as the fibre content increased. In dynamic curing, an increase in the fibre content affected the curing kinetics by slightly shifting the heat flow curves to higher temperatures, and resulted also in a reduction of the glass transition temperature of the matrix if postcuring was not applied. The dependence of the dynamic-mechanical spectra of the samples on fibre content was satisfactorily modelled with the aid of Takayanagi's block model. An analysis of the main relaxation master curve shows that relaxation broadens as fibre content increases. © 1999 Society of Chemical Industry

Behavior of waves in high density polyethylene geomembranes: a laboratory study

In this laboratory study, the behavior of waves of the type seen in field deployed high density polyethylene (HDPE) geomembranes was studied. Four experimental variables were evaluated: normal stress, original wave height, thickness of geomembrane and temperature. Twenty-five separate tests were conducted, each for 1000 hours duration. Each of the tests utilized HDPE geomembranes with strain gages attached in a number of critical locations. The results of the 1000-hour strain measurements were modeled and extrapolated to 10,000 hours using the Kelvin-chain model. The measured and extrapolated strains were then converted to stresses via the Maxwell–Weichert model and stress relaxation master curves. With the completion of the experiments and their extrapolation into a near steady state condition, it was found that tensile strains up to 4.9% remained in the geomembranes. The equivalent residual stresses were as high as 22% of the yield stress. Full contacts between the geomembrane and the underlying subgrade soil was not achieved in any of the tests performed.

Creep or Relaxation Master Curves Calculated from Experimental Dynamic Viscoelastic Function

Creep or Relaxation Master Curves Calculated from Experimental Dynamic Viscoelastic Function

Energy barrier distributions in magnetic systems from the Tln(t/τ0) scaling

A method based in the Tln(t/τ0) scaling is proposed to obtain the energy barrier distribution of a randomly oriented assembly of magnetic entities. It essentially consists on performing the logarithmic time derivative of the master relaxation curve. The method has been applied to two small particle systems and the obtained distributions are in good agreement with the ones used to fit the master curves to the magnetization decay of a system following the Arrhenius law. The effect of the specific shape of the distribution functions on the low temperature behaviour of the relaxation rate and the possibility to erroneously attribute this behaviour to non-thermal processes is also discussed.

Strain and Age Effects on Behavior of a Concrete Pavement Joint Sealant Material

A one-part self-leveling silicone joint sealant material was experimentally investigated in the laboratory. It was found that strain and age had apparent effects on the relaxation modulus of the material. Relaxation tests were conducted under different strain levels. The test samples were exposed to ultraviolet radiation and moisture for artificial aging before testing. For this largely deformable material, finite strain formulas were used in analysis of experimental data. Strain and age effects were successfully normalized in the relaxation master curve by using the superposition principle. On the basis of the master curve, a material model of the generalized Maxwell model in parallel type was constructed. The real time was scaled to the reduced time by time-strain shift and time-age shift factors so as to characterize the strain and age effects. This model is mathematically simple and can be easily applied in finite element programs for concrete pavement joint analysis.

Strain and Age Effects on Behavior of a Concrete Pavement Joint Sealant Material

A one-part self-leveling silicone joint sealant material was experimentally investigated in the laboratory. It was found that strain and age had apparent effects on the relaxation modulus of the material. Relaxation tests were conducted under different strain levels. The test samples were exposed to ultraviolet radiation and moisture for artificial aging before testing. For this largely deformable material, finite strain formulas were used in analysis of experimental data. Strain and age effects were successfully normalized in the relaxation master curve by using the superposition principle. On the basis of the master curve, a material model of the generalized Maxwell model in parallel type was constructed. The real time was scaled to the reduced time by time-strain shift and time-age shift factors so as to characterize the strain and age effects. This model is mathematically simple and can be easily applied in finite element programs for concrete pavement joint analysis.

Build-up of structure and viscoelastic properties in epoxy and acrylate resins cured below their ultimate glass transition temperature

The build-up of structure and viscoelastic properties with conversion during cure below the ultimate glass transition temperature of epoxy and acrylate resins has been investigated. Using a torsional dynamic mechanical analyser, dynamic shear modulus and change in sample thickness was monitored simultaneously, thus giving information on both the physical properties (stiffness) and the progress of the reaction (shrinbdkage) in one experiment. Two step-wise curing epoxy systems and two chain-wise curing acrylate systems with different crosslink densities were studied and compared. The results showed that in the epoxies vitrification was a distinct event, occurring separately from gelation and ending with the end of the cure reaction. In the acrylates vitrification began immediately after gelation, the two events being indistinguishable, and lasted until the end of the reaction, leaving the sample in its transition zone. Scaling of modulus—cure time data obtained at different frequencies showed that the data for each system followed one single curve, independent of frequency over five decades. This made it possible to estimate the modulus development at low frequencies early in the reaction, which is difficult to measure directly. From the shrinkage and storage moduli approximate values of the relaxation modulus as a function of chemical conversion were calculated. The relaxation modulus curves at different conversions were then shifted along the time axis to provide a relaxation master curve. The data and understanding gained in this work provide the basis for analysing the time-dependent mechanical behaviour during cure, e.g. build-up and relaxation of residual stresses.

Characterization of the shielding current decay in superconductors: A unified picture

By utilizing an analytical implicit solution we are able to discuss in a unified picture the characterization of the shielding current decay in superconductors with an arbitrary concave current dependence of the effective activation energy U( J). The time scales in the transient and long-time stages of the relaxation are found. The inflexion time t F which experimentalists have paid attention to is worked out. It is shown for the first time that in the case of nonlinear U( J) dependence t F could be significantly smaller than the true transient time τ ∗, the time scale that governs the nonlogarithmic decay on the short-time side in relaxation measurements, which is itself sample and initial-condition dependent. Furthermore, the master relaxation curve is discussed. The relatation between this master curve and the underlying U( J) dependence is elaborated.