The Time-temperature Superposition Principle Research Articles

Compositional dependence of electrochemical properties in biopolymer blend-based solid electrolytes doped with sodium perchlorate for EDLC applications

Biopolymer-based blends of solid electrolytes capable of conducting sodium ions were prepared via solution casting by incorporating sodium carboxymethyl cellulose (NaCMC) and polyvinyl alcohol (PVA) with varying concentrations of sodium perchlorate monohydrate (NaClO4.H2O), which was used as the dopant. The prepared electrolytes were characterized to reveal their structural, vibrational, electrical, and electrochemical properties that make them promising as solid polymer electrolytes (SPEs). X-ray diffraction (XRD) analysis showed that the amorphous nature of the sample increased with the addition of NaClO4.H2O salt concentrations of up to 30 wt.%. The complexation between the polymers and salt was confirmed by Fourier-Transform Infrared (FTIR) analysis. The SPE exhibited an optimal ionic conductivity of (1.90 ± 0.05) ×10−5 S cm−1, which is three orders higher than that of the pristine polymer blend with (5.31 ± 0.61) ×10−8 S cm−1, as determined by electrochemical impedance spectroscopy (EIS) analysis. Scaling studies conducted based on AC conductivity and tangent loss revealed that these measurements could be represented by a single master curve, which suggests that the optimal sample adheres to the time-temperature superposition principle (TTSP). The temperature dependence of Jonscher's exponent indicates that the conduction mechanism can be effectively represented by the Quantum Mechanical Tunneling model (QMT). Both transference number measurement (TNM) and linear sweep voltammetry (LSV) analyses validated the electrolyte's suitability for energy device applications by demonstrating its high ion transference number and electrochemical potential window of 3.93 V. The optimized SPE film was subsequently utilized in an electrochemical double-layer capacitor (EDLC) device to evaluate its performance as both an electrolyte and separator. The supercapacitor exhibited an impressive energy density of 15.18 Wh kg−1 and a power density of 4512.5 W kg−1, along with remarkable stability in terms of cycle life.

Investigation of Dynamic Viscoelastic Asymmetric Response of PA6 Film Based on Fractional Rheological Model.

Polyamide 6 (PA6) film as a typical viscoelastic material, satisfies the time-temperature superposition (TTS), and demonstrates obvious dynamic strain amplitude and frequency correlation under dynamic load. The investigation of the dynamic mechanical behavior of PA6 film is essential to ensure the safety of these materials in practical applications. In addition, dynamic mechanical property testing under conventional experimental conditions generally focuses on the short-term mechanical performance of materials. Therefore, the dynamic viscoelasticity of PA6 film was tested using a dynamic thermo-mechanical analyzer (DMA) in this study, and the complex modulus master curve was constructed based on time-temperature superposition (TTS) to realize the accelerated characterization of long-term mechanical properties. Furthermore, according to experimentally obtained asymmetric characteristics of the Cole-Cole diagram and the loss modulus master curve of the PA6 film, the parameter distribution of the fractional Zener model and the modified fractional Zener model were compared, and the asymmetric dynamic viscoelastic response of PA6 film under different conditions was systematically investigated using these models. The results indicate that the modified fractional Zener model can truly describe the dynamic asymmetric characteristics of PA6 film, verify the feasibility and advantages of the modified fractional rheological model, and provide some theoretical guidance for exploring the tensile rheological mechanism of PA6 film.

Application of time-temperature superposition principle for cracking characterization of asphalt mixtures using semi-circular bend test

In recent decades, numerous laboratory tests have been developed to characterize the cracking performance of asphalt mixtures. Among these, the semi-circular bend (SCB)-based Illinois flexibility index test (I-FIT) (AASHTO T 393) has emerged as a favored method due to its straightforward specimen preparation and better sensitivity to mixture variables. However, the cracking susceptibility of asphalt mixtures is significantly influenced by temperature and loading rate, leading to a discrepancy in performance between standard test conditions and real-world scenarios. To address this challenge, this study explores the applicability of the time-temperature superposition principle (TTSP) for the SCB test. The study evaluates four mixtures incorporating reclaimed asphalt pavement (RAP) and/or reclaimed asphalt shingles (RAS) across various loading rates and temperature combinations. Findings suggest that TTSP can be applied to the SCB test without significantly impacting cracking performance indices such as flexibility index and post-peak slope. Furthermore, the study also demonstrates that TTSP can be applied in the crack propagation phase during the post-peak domain of the mixtures. The findings of the study will allow laboratories to develop more flexible testing plans without compromising the accuracy and reliability of performance parameters by adjusting the loading rate corresponding to the test temperature and vice versa. Consequently, this approach can potentially make a balanced mix design (BMD) practice more implementable.

Study on the Application of Kramers-Kronig Relation for Polyurethane Mixture.

Polyurethane (PU) mixture, which is a new pavement mixture, exhibits different dynamic properties compared to a hot-mixed asphalt mixture (HMA). This paper analyzed whether the Kramers-Kronig (K-K) relation and thermorheologically simple properties applied to the PU mixture. Based on the results, the PU mixture exhibited thermorheologically simple properties within the test conditions. The time-temperature superposition principle (TTSP) was applicable for the PU mixture to construct a dynamic modulus master curve using the standard logistic sigmoidal (SLS) model, the generalized logistic sigmoidal (GLS) model, and the Havriliak-Negami (HN) model. The Hilbert integral transformed SLS and GLS models for the phase angle can accurately fit the measured phase angle data with newly fitted shift factors and predict the phase angle within the viscoelastic range. The core-core and black space diagrams both displayed single continuous smooth curves, which can be utilized to characterize the viscoelastic property of the PU mixture. The K-K relation is applicable for the PU mixture to obtain the phase angle master curve model, storage modulus, and loss modulus from the complex modulus test results with the test temperatures and loading frequencies. The phase angle of the PU mixture at extremely high or low test temperatures cannot be derived from the dynamic modulus data.

Stress relaxation experimental research and prediction of GFRP pipes under ring deflection condition

Abstract Glass fiber-reinforced plastic (GFRP) pipes are widely used as buried pipes in petrochemical and other industries. At present, in-depth studies have been conducted on GFRP pipes in terms of internal hydrostatic pressure, axial compression, and cyclic internal pressure, especially limited research has been carried out on transverse load, especially stress relaxation behavior. In this study, GFRP pipes with three different component contents were subjected to different initial deflections at different temperatures and subjected to stress relaxation tests for 1000 h. The findings demonstrate that the stress relaxation behavior of GFRP pipes is not affected by the initial deflection. Rather, it is primarily influenced by temperature and sand entrapment content, which are identified as the key factors determining the stress relaxation behavior of GFRP pipes. In addition, the time-temperature superposition principle (TTSP) was used to pass the test results to obtain a smooth master curve and verify the applicability of TTSP on GFRP pipes. Subsequently, the relaxation performance of GFRP pipes was predicted after 50 years. This research result contributes to a more comprehensive understanding of the stress relaxation behavior of GFRP through accelerated testing and offers crucial insights into the application of GFRP pipes.

94‐2: Improved Simulation Accuracy for a Front‐Firing Panel Speaker (FFPS) with Thin‐Actuator by Adopting Frequency‐Dependent Viscoelastic Properties

In this study, we examine methods to enhance the simulation accuracy of Front‐Firing Panel Speakers (FFPS) based on thin actuators. Specifically, we investigate the frequency‐dependent behavior of adhesives’ viscoelastic properties. By leveraging the time‐temperature superposition (TTS) principle, we can accurately determine the material properties at audio frequencies and integrate them into the simulation process. We anticipate that our finding will enhance the efficiency of the design process for FFPS and its display components by simulating more accurate results.

Role of charge-compensation process on the structural, microstructure and electrical properties of pure and Nb-doped Sr2SnO4

This article explores the charge compensation method by synthesising Sr2SnO4, Sr2Sn0.99Nb0.01O4, and Sr1.995Sn0.99Nb0.01O4. The synthesis of a monophasic, tetragonal sample was achieved using a typical ceramic approach and high-temperature heat treatment. The XRD followed by Rietveld refinement, confirmed the crystallization of material under the space group I4/mmm. The crystallite sizes for all samples determined to be less than 50 nm, while the micro-strain falls within the range of (1.78–2.93) × 10–3. The microstructure exhibits a cuboidal shape for all samples, and the grain size is observed to decrease with the addition of Nb. The dielectric characteristics of the samples indicate the existence of Maxwell-Wagner and Orientational polarization in the sample. The sample Sr2Sn0.99Nb0.01O4 demonstrates a greater conductivity value compared to Sr1.995Sn0.99Nb0.01O4. This is attributed to the presence of excess electrons that compensate for the overall charge, as opposed to Sr1.995Sn0.99Nb0.01O4 where the extra charge is compensated by a cationic vacancy VSr″. The time-temperature-superposition principle (TTSP) is applicable to all compositions and indicates that similar sources are responsible for both conduction and relaxation processes. The dielectric permittivity and dissipation factor are found to be in the range of 150 to 175 and 0.2 to 0.5, respectively. This suggests that they have potential for future use in millimeter-wave communication with dielectric resonator antennas (DRAs). Due to the presence of oxygen ions and the ability to conduct both ions and electrons, at temperatures above 400 °C, it is a suitable choice for electrode materials in the application of intermediate temperature solid oxide fuel cell (IT-SOFCs). Exploring the manipulation of defects using electrical and ionic charge compensation methods shows potential for enhancing materials in semiconductor technology.

The Time-Temperature Superposition of Polymeric Rubber Gels Treated by Means of the Mode-Coupling Theory.

Viscoelastic relaxation measurements on styrene-butadiene rubbers (SBRs) doped with carbon nanotube (CNT) at different concentrations around the sol-gel transition show the time-temperature superposition (TTS). This process is described in terms of the mode coupling theory (MCT) approach to viscoelasticity by considering the frequency behavior of the loss modulus E″(ω) and showing that the corresponding TTS is linked to ω1/2 decay. From the analysis of the obtained data, we observe that the interaction between SBRs and CNT determines different levels of decay according to their concentration. Systems with the lowest CNT concentration are only characterized in the studied T-range by their fragile glass-forming behavior. However, at a specific temperature TL, those with the highest CNT concentration show a crossover towards pure Arrhenius that, according to the MCT, indicates the presence of kinetic glass transition (KGT), where system response functions are characterized by scaling behaviors.

Elaboration of La (Sr/Na) Mn (Ti) O3 ceramic, structural, and morphological investigations, and contribution of direct and indirect interactions on transport properties

The charge carrier's dynamics of La0.7(Sr5/6Na1/6)0.3Mn0.7Ti0.3O3 (LSNMTO) ceramic is conducted using the temperature and frequency dependences of the electrical conductivity and their scaling formalisms. The structural study indicates that LSNMTO crystallizes in a rhombohedral R3‾c perovskite structure with no detectible secondary phases. A phase transition from the high-temperature metallic behavior to the low-temperature semiconductor nature is observed from the electrical conductivity curve at TS-M = 415 K. Further, it is observed that the cation-anion-cation and the cation-cation interactions are present in the material, and play important role in governing the electrical behaviors of LSNMTO. From 200 K to 415 K, the Non-adiabatic Small Polaron Hopping is the predominant conduction process, although the Mott-Variable Range Hopping mechanism governs the conductivity at low temperatures. In the intermediate temperature range, the dynamic of the charge carriers is explained using the Shklovskii Efros model. The frequency-activated conductivity obeyed the universal laws (double-Jonscher and Jonscher laws). At high frequencies, the dispersion of the conductivity spectra is attributed to the presence of hopping and tunneling conduction processes. The Time-Temperature Superposition Principle (TTSP) is obeyed over a large temperature range from 160 K to 350 K. Below 160 K, the deviation from the TTSP is attributed to the coexistence of hopping and tunneling conduction mechanisms. Deviations from the Summerfield scaling and shifts of the isotherms to higher values on decreasing the temperature are due to the local structural disorder in LSNMTO. Therefore, the structural particularities of LSNMTO can result in diverse conduction pathways giving an increase to the deviations from the Summerfield scaling. The studied ceramic exhibits a very motivating maximum negative temperature coefficient of resistance NTCR = −13.36% which is significantly elevated as compared to previously investigated compounds.

Mechanics of ABS Polymer under Low & Intermediate Strain Rates

Thermoplastics polymers like Acrylonitrile Butadiene Styrene (ABS) are often reinforced with nano/micro reinforcements to enhance their mechanical, thermal and electrical properties. However, the viscoelastic nature of these polymers results in their strong dependence on the applied strain rate and temperature sensitivity, leading to their characterization complexity. Hence it is paramount to study the strain rate-dependent mechanics of neat ABS. In this study, the effect of strain rate and temperature on Young’s modulus of ABS polymer was characterized using a dynamic mechanical analyzer (DMA). Storage modulus curves at various temperatures and frequencies were transformed into a representative master curve at a specific temperature using the time-temperature superposition (TTS) principle. Based on this curve‘s storage modulus and frequency relation, an empirical fit function was developed and the strain rate values were extrapolated. Using integral relations of viscoelasticity, the results were further transformed to a time domain relaxation function to extract the strain rate-sensitive Young’s modulus at different loading rates. This method was validated by comparing the data with tensile tests conducted on ABS coupons as per ASTM D638-14. The results were acceptable over a wide range of strain rates and indicated a clear sensitivity of ABS to strain rate and temperature. The strategy used in this work can be employed to study the effect of reinforcement morphology in ABS thermoplastics using DMA.

Creep behaviors of HTPE propellants

AbstractIn this paper, creep tests were carried out on HTPE/AP/Al/RDX propellant specimens to investigate the effects of stress level and temperature on their creep behavior and to investigate the creep mechanism. Higher stresses and temperature can cause greater creep strain in the propellant, ultimately leading to its destruction. On this basis, the creep master curve was further obtained based on the Time‐Temperature Superposition Principle (TTSP), extending the creep investigation time range to 1010 s. Based on previous experience, some explorations have been made on constitutive equations. The burgers model fits the creep behavior under different conditions more closely, while the Norton model has higher stress sensitivity.

The application of the accelerated test methods on the creep analysis of flax fiber reinforced polymer composites

Flax fiber-reinforced polymer (FFRP) composites are getting more and more popular in the construction industry as an emerging environmental-friendly material. However, their obvious creep behavior makes it a design concern for the creep development of structures made from FFRP. Though the creep behavior of the FFRP is critical for the structural design, the creep tests before structure design is not common due to the tests can take a very long time. The Time-temperature superposition principle provides a good theoretical basis for the accelerated creep tests to shorten the testing time, but the specific application of the FFRP is not clear and needs to be further developed. This study is to investigate the application methods of the Time-Temperature Superposition Principle (TTSP) theory on the FFRP material with unidirectional fibers. The three most related methods are used for constructing the creep master curves during the TTSP application to determine the most efficient application process of TTSP. The results indicate that the creep of FFRP can be effectively analyzed by the TTSP accelerated creep testing method with the proper application process.

Summerfield scaling model and electrical conductivity study for understanding transport mechanisms of a Cr3+ substituted ZnAl2O4 ceramic.

Solid-state and sol-gel procedures were used to prepare ZnAl1.95Cr0.05O4 nanocrystal spinels. From the results obtained by X-ray diffraction (XRD) and transmission electron microscopy (TEM), it can be concluded that the samples prepared by sol-gel synthesis are better crystallized than the ones resulting from the solid-state method. Studies by spectroscopy of impedance were done in function of frequency (40-107 Hz) and temperature (540-680 K) in the sample prepared by sol-gel synthesis. The electrical conductivity spectra obey Jonscher's law and two models were observed studying the variation of the exponent 's' as a function of temperature, Correlated Barrier Hopping (CBH) and Non-overlapping Small Polaron Tunnelling (NSPT). The predominant conduction mechanism is bipolaron hopping. The scaling behavior of conductivity spectra was checked by Summerfield scaling laws. The time-temperature superposition principle (TTSP) points to a common transport mechanism working for the low and middle frequency ranges. The scaling mechanism fails in the high-frequency ranges suggesting that conduction dynamics, and the usual hopping distance of mobile species, have changed. The values obtained for the activation energy from the hopping frequency, conductivity σ dc, bulk resistance R gb, and relaxation (f max), in the temperature range of 540-680 K, are very close. A higher and negative temperature coefficient of resistivity (TCR coefficient) equal to -2.7% K-1 is found at 560 K. This result shows that our compound is suitable for uncooled infrared bolometric applications and infrared detectors.

An Orthotropic Nonlinear Thermoviscoelastic Model for Polymeric Battery Separators

Structural responses of separators are critical to battery safety. Commonly used separators are dry-processed polymers with anisotropic microstructures. Due to the material anisotropy, rate dependence, and temperature dependence, developing a model for predicting the thermomechanical response of polymeric battery separators has been challenging. This paper presents an orthotropic nonlinear thermoviscoelastic model for predicting the response of polymeric battery separators in thermal ramp scenarios. The model was based on the Schapery nonlinear viscoelastic model and the temperature dependence was introduced through the time-temperature superposition principle (TTSP). The model was implemented in LS-DYNA® finite element (FE) package as a user-defined material model. The model parameters were determined for a polypropylene (PP) separator. The predicted material responses under large deformations in isothermal and non-isothermal temperature conditions for stress relaxation, creep and tensile loadings at different rates agree well with the experimental data.

Residual Life Prediction of XLPE Distribution Cables Based on Time-Temperature Superposition Principle by Non-Destructive BIS Measuring on Site.

Crosslinked polyethylene (XLPE) distribution cables are prone to segmented thermal aging after long-term operation owing to the large spatial spans and complex operating environments, and accurate residual life prediction of each aging cable segment could provide a theoretical basis and reference for performance monitoring, maintenance and the replacement of cables. Existing studies mainly focus on the residual life prediction methods for uniform aging cables, which are not suitable for segmented-aging cables. In this paper, a residual life prediction method for segmented-aging XLPE distribution cables based on the time-temperature superposition principle (TTSP) by non-destructive BIS measuring on site was proposed. Firstly, the applicability of the TTSP in the transformation of the changing process of elongation at break (EAB) of XLPE at different thermal aging temperatures was verified based on the Arrhenius equation. Secondly, to better simulate the thermal aging process under working conditions, XLPE cables were subjected to accelerated external stress aging at 140 °C for different aging times, and the corresponding changing process of EAB along with aging time was further measured. The relationship between the EAB of XLPE cables and aging time was well fitted by an equation, which could be used as a reference curve to predict the thermal aging trends and residual life of service-aged XLPE cables. After that, a calculation method for the transformation of the changing process of EAB of XLPE at different thermal aging temperatures was proposed, in which the corresponding multiplicative shift factor could be obtained based on the TTSP instead of the Arrhenius equation extrapolation. Moreover, the availability of the above calculation method was further proved by accelerated thermal aging experiments at 154 °C; the results show that the prediction error for the cable's EAB is no more than 3.15% and the prediction error for residual life is within 10% in this case. Finally, the realization of non-destructive residual life prediction combined with BIS measuring on site was explained briefly.

An investigation of the effect of relative humidity on viscoelastic properties of flax fiber reinforced polymer by fractional-order viscoelastic model

As an environmental-friendly material with eligible mechanical properties, FFRP (Flax Fiber Reinforced Polymer) composites are being widely studied and used in the construction industry. This paper presents an investigation of the effect of environmental humidity on the viscoelastic properties of FFRP. Frequency sweep tests are conducted, and results are re-organized by the Time-Temperature Superposition Principle (TTSP). The Huet-Sayegh viscoelastic model is introduced to describe the relationship between viscoelastic properties and loading frequency. The fractional derivative is applied to the model for more accurate results. It is found both storage modulus and loss modulus decrease with the increase of relative humidity. However, the loss factor does not have a monotonical correlation with the relative humidity of the environment. In general, it can be concluded both the capacity of FFRP to store and dissipate the energy decreases over the hygroscopicity absorption in the air, but there is no specific relationship between the amount of their reduction.

Instantaneous and long-term mechanical properties of Polyethylene Terephthalate Glycol (PETG) additively manufactured by pellet-based material extrusion

Polyethylene Terephthalate Glycol (PETG) is a highly popular feedstock for extrusion-based additive manufacturing. While data are available on the instantaneous properties of additively manufactured PETG, few research have been done on forecasting the creep behaviour of additively manufactured PETG while accounting for the material altering effects of ageing. This research article aims to enhance the understanding of both the instantaneous and time-dependent mechanical properties of additively manufactured PETG through a series of tensile, FEA simulations, Dynamic Mechanical Analysis (DMA), and two types of creep experiments. The details of experimental and mathematical calculations of the instantaneous and time-dependent properties of additively manufactured PETG are provided. Nine independent material parameters have been determined including three Young’s moduli, three shear moduli and three Poisson’s ratios, to fully quantify an orthotropic material model of additively manufactured PETG. The printed material exhibited a Young’s modulus that is 86.5% of the theoretically possible value in direction 1, a Young’s modulus in direction 2 is 66.0% of the theoretical optimum, and a Young’s modulus in direction 3 is within 1% of its theoretical maximum. In addition to reporting the creep behaviour of PETG, the novel application of the Time-Temperature Superposition Principle (TTSP) to additively manufactured PETG has been shown to produce an age-affected creep prediction for up to 3.88 years based on samples aged for 221 h and at 23 °C. The methodology and data models have been found to enable predictions for other ages and temperatures. It was concluded that the application of the TTSP creep methodology was limited by the creep test temperature, 60 °C, after which the material began to behave in a non rheologically-simple manner.

Influence of PVB Interlayer Mechanical Properties on Laminated Glass Elements Design in Dependence of Real Time-Temperature Changes.

Most used laminated glass is composed of float glass plies bonded together with a viscoelastic Polyvinyl Butyral (PVB) interlayer. The shear stiffness of the polymeric interlayer is the key factor in the behavior of laminated glass. Structural engineers in the past were designing laminated glass regardless of the shear coupling of the plies. This approach with a high level of reliability led to expensive laminated glass structures due to insufficient knowledge of foil properties. Most of the current standards suggest methods that consider the shear coupling of the plies. This paper presents the experimental data from a static loading test performed on a laminated glass panel exposed to changing temperatures. The deformations were observed for 48 h. The measured results were compared with the known analytical design approaches and in addition with the finite element modeling (FEM) analysis in the available software for laminated glass design. A simplified design approach that simulates foil behavior in dependence on load duration and temperature change was adopted in this study. Design approaches that use effective thickness calculations are used with the Young and shear relaxation modulus provided by the foil producer. The imprecision of the Eurocode standards for glass design, and the propensity to change the approach to the calculation by introducing more precise parameters were expounded. The results when combining the time-temperature superposition (TTS) and the Wölfel–Bennison approach were found to be in very good agreement with the FEM analysis of 3D solid elements in Abaqus and measured data.

Time-temperature superposition principle for the shear fracture behaviour of soft adhesive layers: From bulk to interface

Soft adhesive layers have attracted great attention as a commonly used adhesive technique, particularly because of their shear fracture behaviour at extreme loading rates and temperatures. Therefore, the present study examined the shear fracture properties of a soft adhesive layer through systematic rheological experiments, loading-unloading shear tests and shear fracture tests. Due to a similar viscoelastic characteristic in rheological properties and fracture properties, the time-temperature superposition principle (TTSP) was extended from the bulk to the interface to investigate its shear cohesive failure. A shear fracture toughness master curve was defined using the time-temperature equivalence shift factors derived from the rheological properties. The shear fracture behaviour of the soft adhesive layer could be predicted using data from a narrow range of loading rates/temperatures. The results demonstrated the potential of extending the TTSP approach from the bulk to a soft adhesive layer having viscoelastic character, which might be utilised to predict the shear fracture toughness of soft adhesive materials under extreme conditions.

Lifetime prediction of non-woven face masks in ocean and contributions to microplastics and dissolved organic carbon

This study explored the degradation behavior of three types of disposable face masks in simulated seawater via the accelerated aging experiments. Microplastics (MPs) and dissolved organic carbon (DOC) were monitored in UV- and thermal-treated mask suspensions and their concentrations increased slowly in the early stage at 50 ℃ and 58 ℃. Owing to the high energy supply, the release rates of MPs and DOC at 76 ℃ were much faster than the above two temperatures. The time-temperature superposition principle (TTSP) was used to superpose the MPs/DOC release kinetics from other tested temperatures to the reference temperature and its applicability was verified by the similar activation energy. Then, a release kinetics model was established and fitted well with the superposed MP data (R2 ≥ 0.96). Since less than 0.1 % of carbon was leached, the superposed DOC data was roughly modelled by the exponential function (R2 ≥ 0.90). According to the TTSP and the established kinetics models, about 15 years were estimated to decompose half of a certain marine mask waste, together with leaching 0.21 ± 0.02 mg∙g-mask−1 of DOC. If mask consumption remains the same before 2025, they would contribute 40000–230000 tonnes of MPs and 13–97 tonnes of DOC to the ocean by 2040.