Application of time–temperature superposition principle to polymer transition kinetics

The time–temperature equivalence equation is deduced simply in view of the transition kinetics of a polymer. The independent variables time and temperature are separated in the two sides of the resulting equation. Thus, a physical property of the polymer, which is temperature dependent, can be matched with the theoretical calculated curve from a supposed model of transition kinetics in which only time is involved as the independent variable. By comparing different models, one may judge which model is probably more correct. The procedure of data fitting is described. As an application example, the measured viscosity data at different temperatures for the coil–globule transition of poly(N‐isopropylacrylamide) in aqueous solution is tested to judge its transition mechanism. A transition mechanism involving a two‐stage reversible reaction fits the experimental data in a satisfactory way. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 99: 1767–1772, 2006     

The viscoelastic properties of polymer‐modified asphalts

The linear viscoelastic properties of one family of base asphalts, unmodified or modified by the simple addition of an elastomer or by further in‐situ crosslinking, have been investigated. The time‐temperature superposition principle was shown to be valid for the base as well as for the modified asphalts. The addition of the elastomer styrene‐butadiene (SB) copolymer increased drastically the storage modulus and the elastic character of the asphalts. The thermal susceptibility of the polymer modified asphalts was considerably reduced and this combined with an increased resistance to deformation (larger complex modulus) suggests much better performances for road applications. The chemically modified asphalt containing 3% SB showed similar viscoelastic properties as the physical blend containing 6% SB.     

Step‐strain stress relaxation of carbon black‐loaded natural rubber vulcanizates

Step‐strain stress relaxation experiments were performed on natural rubber vulcanizates of various carbon black (HAF) concentrations by subjecting the samples to a very rapid strain and fixing its length at the deformed state. Time–temperature superposition in the viscoelastic region was evaluated to investigate the effect of temperature on the relaxation times of the rubbery composites. Remarkably, it was observed that, at higher HAF concentrations, increasing the temperature had a lesser effect on decreasing the overall stress values. That was attributed to the lower number of elastomeric chains per unit volume due to the agglomeration of the carbon black particles. The energy barrier resulting from the adsorption of the rubbery chains on the filler particles was insufficient to drastically reduce the diffusion and rearrangement of the polymer chains. The activation energy of the rubber‐like deformation calculated from the time–temperature superposition was shown to be independent of temperature. Interestingly, the viscosity coefficients showed a large increase with a modest addition of the carbon black. This is due to the long‐range nature of the temporary bonds formed between the polymer molecules and the surface‐active carbon black. The stress–strain of the rubbery composites was shown to behave in a Gaussian manner in accordance with the Mooney–Rivlin relationship. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 3387–3393, 2004     

Mechanical properties developing at the interface of amorphous miscible polymers,below the glass transition temperature: Time–temperature superposition

The bonding of amorphous polystyrene (PS) and poly(2,6‐dimethyl‐1,4‐phenylene oxide) (PPO) was conducted over a broad range of time and temperatures, but always below the (bulk) glass transition temperature (T_g). Stress–strain properties developing at the symmetric (PS/PS and PPO/PPO) and asymmetric interfaces (PS/PPO), in a lap–shear joint geometry, were measured at room temperature as a function of contact time and bonding temperature. Master curves of shear strength and modulus, obtained by time–temperature superposition, were constructed over several decades of time. Arrhenius apparent activation energies calculated for shear strength are 99, 81, and 144 kcal/mol for, respectively, PS/PS, PPO/PPO, and PS/PPO interfaces. A higher value of 191 kcal/mol was calculated for the shear modulus at the PS/PS interface, suggesting that the development of the strength and modulus is controlled by different molecular factors, that is, the modulus is controlled by the number of chains across the interface and the strength by the depth of penetration. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 825–830, 1999     

Time–temperature superposition principle applied to a kenaf‐fiber/high‐density polyethylene composite

The time–temperature superposition principle was applied to the viscoelastic properties of a kenaf‐fiber/high‐density polyethylene (HDPE) composite, and its validity was tested. With a composite of 50% kenaf fibers, 48% HDPE, and 2% compatibilizer, frequency scans from a dynamic mechanical analyzer were performed in the range of 0.1–10 Hz at five different temperatures. Twelve‐minute creep tests were also performed at the same temperatures. Creep data were modeled with a simple two‐parameter power‐law model. Frequency isotherms were shifted horizontally and vertically along the frequency axis, and master curves were constructed. The resulting master curves were compared with an extrapolated creep model and a 24‐h creep test. The results indicated that the composite material was thermorheologically complex, and a single horizontal shift was not adequate to predict the long‐term performance of the material. This information will be useful for the eventual development of an engineering methodology for creep necessary for the design of structural building products from these composites. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 1995–2004, 2005     

Linear viscoelastic properties of HFPE‐II‐52 polyimide

The polyimide HFPE‐II‐52 was developed at NASA Glenn Research Center for use as a matrix in high temperature composite materials. The unique properties of such composites stem largely from the performance of the matrix at high temperature. Thus, as part of a larger effort to study high temperature composite materials, the linear viscoelastic properties of HFPE are measured and a mathematical model of the properties is developed. In particular, storage, loss, and stress relaxation moduli were obtained from cyclic and transient loading experiments. A Prony series was fit to the relaxation modulus data. As a cross check, the fit to the relaxation modulus was converted to storage and loss moduli and compared with those measured directly. Effects of postcuring and of moisture on the properties are investigated as well. These results provide researchers with a constitutive model for HFPE‐II‐52 and provide some insight into the performance of HFPE matrix composites at high temperatures. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 3255–3263, 2006     

A method for determination of time‐ and temperature‐dependences of stress threshold of linear–nonlinear viscoelastic transition: Energy‐Based Approach

A methodology for determination of time‐ and temperature‐dependences of stress threshold of linear–nonlinear viscoelastic transition is proposed and validated by example of uniaxial creep of epoxy resin. Energy approach is applied for characterization of the region of linear viscoelasticity (LVE) and the threshold of LVE is given in the stress–strain representation as the master curve independent of time and temperature. Time‐ and temperature‐dependences of the stress threshold are calculated by extending LVE theory and time–temperature superposition principles (TTSP) to the energy relations. Reasonable agreement between experimental data and calculations is obtained. It is shown that number of tests required for characterization of LVE region in a wide range of test time and temperatures can be considerably reduced by applying the proposed methodology. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Thermal polymerization of thiol–ene network‐forming systems

The thermal polymerization of a tetrafunctional thiol (PETMP) and divinyl ether (TEGDVE) was monitored by temperature‐ramping differential scanning calorimetry (DSC) and the effects of inhibitor type and concentration, oxygen inhibition and initiator type were studied. The incorporation of inhibitors was required to produce a stable system at room temperature. Butylated hydroxytoluene (BHT) inhibited polymerization at low temperatures, but was inefficient at high temperatures and polymerization rates, and hence BHT is an ideal stabilizer. In contrast, a nitroxide inhibitor (NO‐67) was a very effective inhibitor and no polymerization occurred until all of the nitroxide was depleted. The presence of oxygen retarded the onset of polymerization but did not change the final conversion significantly. Polymerization with initiators having higher half‐life temperatures shifted the DSC peak to higher temperature because the rate of initiator decomposition and thus initiation was slower. Rheological investigations of the cure at different temperatures revealed that the gel time decreased significantly with increasing cure temperature, and the calculated apparent activation energy for PETMP/TEGDVE was 54 kJ mol^?1. Dynamical mechanical thermal analysis of the cured material was undertaken and frequency‐superposed results revealed that the glass transition region of PETMP/TEGDVE/azobisisobutyronitrile was much narrower than that of free‐radically cured dimethacrylate, but was similar to that of an epoxy resin cured with an aromatic diamine. This behaviour could be attributed to PETMP/TEGDVE network homogeneity, or to the less constrained crosslinks in the PETMP/TEGDVE network. Copyright © 2007 Society of Chemical Industry     

The linear viscoelastic properties of copolypropylene–clay nanocomposites

The linear viscoelastic properties of copolypropylene (cPP)–clay nanocomposites (cPPCNs) prepared by melt intercalating with different amounts of clay were extensively examined by rheological measurements. Meanwhile, the clay effects on the cPP confinements were first estimated by calculating the activation energy of different cPP moving units, including the whole molecular chain, the chain segment, and smaller unit such as chain link. The results showed that the stability of cPPCNs melts wrecked when the clay loading was above 5 wt %. An increase in clay loading of cPPCNs gave rise to a strong low frequency solid‐like response (G′ > G″). Unlike the matrix polymer, cPPCN5 (with 5 wt % clay) exhibited a relaxation plateau as relaxation time prolonged above 100 s, and displayed a maximal linear modulus. The variations of the activation energy of different cPP moving units revealed that the mobility of cPP molecular chains was restricted by clay layers, while these restrictions were not only related to the clay loadings but also largely depended on the clay dispersion status in the matrix. The motions of cPP chain segments were greatly limited at 3–5 wt % loading of clay, but drastically activated with the addition of 7 wt % clay due to the increasing stacks of clay layers within the matrix. However, it was found that the presence of clay had little effect on the mobility of small cPP moving units such as chain links. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 99: 1523–1529, 2006     

Experimental analysis and prediction of viscoelastic creep properties of PP/EVA/LDH nanocomposites using master curves based on time–temperature superposition

Prediction of viscoelastic behavior of polymers over a long‐term period is of vital importance for engineering applications. An attempt was made to uncover the interplay between the morphology and viscoelastic behavior of compatibilized polypropylene/ethylene vinyl acetate (EVA) copolymer blends in the presence of layered double hydroxide (LDH) nanoplatelets. The time–temperature superposition (TTS) principle and WLF equations were merged to obtain master curves of storage modulus at defined reference temperatures enabling prediction of storage modulus at high frequency ranges which are not experimentally measureable. Moreover, the creep compliance master curves were acquired for different reference temperatures to predict the creep compliance of nanocomposites over long period of times. It was found that the presence of LDH decreases the creep compliance at long period of times while it decreases the unrecoverable deformation of EVA domains. A simple mechanism was proposed to explain the creep and recovery behavior of samples blend at different temperatures. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 46725.     

Failure mechanism of time‐temperature superposition for poly(vinyl chloride)/dioctylphthalate (100/70) system

The failure behavior and its mechanism of time‐temperature superposition (TTS) poly(vinyl chloride) (PVC)/dioctylphthalate (DOP) (100/70) system were studied from low to high temperatures with a step of 10°C. Arrhenius equation, WLF equation, mathematical nonlinear fitting, and manual shift were applied for TTS fitting. None of these methods could obtain the well‐superposed master curves with either single horizontal shift or two‐dimensional (horizontal and vertical) shift. The rheological data and differential scanning calorimeter (DSC) results were used to explain the failure mechanism of the TTS fitting. The curves of storage modulus versus frequency were well fitted to an empirical equation G^′ = G + Kωⁿ. The yield behavior was used to analyze the influence of test temperature on the dynamic rheological behavior for the PVC/DOP (100/70) system. A transition of rheological behavior from the solid‐like to the linear viscoelastic could be observed at 190°C because of the gradual melting of microcrystallites and the destruction of gel networks, which were confirmed by DSC analysis. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Experimental investigation of the linear viscoelastic response of EVA‐based nanocomposites

Linear viscoelastic behaviors of ethylene‐vinyl acetate (EVA)‐layered silicate nanocomposites were investigated. EVA with vinyl acetate (VA) content of 18 and 28% by weight and commercially modified montmorillonite clay (Cloisite® 30B) were melt blended in a twin‐screw extruder. Nanocomposites of 2.5, 5 and 7.5% by weight were produced. Wide angle X‐ray scattering was used to ascertain the degree of layer swelling that could be attributed to the intercalation of polymer chains into the interlayer of the silicates. Transmission electron microscopy was used to analyze the dispersion and extent of exfoliation of the layered silicates in the polymer matrix. All nanocomposites were found to have mixed intercalated/exfoliated morphologies. Both storage and loss moduli and complex viscosity showed improvement at all frequencies tested with increase in silicate loading. Terminal zone behavior was also shown to disappear gradually with silicate content. Increase in silicate loading had caused the divergence of viscosity profile from low‐frequency Newtonian plateau to non‐Newtonian slope corresponding to a possible finite yield stress. The gradual disappearances of terminal zone and Newtonian homopolymer‐like characteristics with silicate loading were attributed to the formation of lattice spanning three‐dimensional network structures. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 2127–2135, 2006     

Effects of prior aging at 288°C in argon environment on time‐dependent deformation behavior of a thermoset polymer at elevated temperature,part 1: Experiments

The inelastic deformation behavior of PMR‐15 neat resin, a high‐temperature thermoset polymer, aged at 288°C in argon environment for up to 2000 h was investigated. The experimental program was designed to explore the in?uence of prior isothermal aging on monotonic loading and unloading at various strain rates. In addition, the relaxation response and the creep behavior of specimens subjected to prior aging of various durations were evaluated. All tests were performed at 288°C. The time‐dependent mechanical behavior of the PMR‐15 polymer is strongly influenced by prior isothermal aging. The elastic modulus increased and the departure from quasi‐linear behavior was delayed with prior aging time. Stress levels in the region of inelastic flow increased with prior aging time. Furthermore, prior aging significantly decreased the polymer's capacity for inelastic straining, including the material's capacity to accumulate creep strain. Conversely, the relaxation response was not affected by the prior aging. © 2009 Wiley Periodicals, Inc.? J Appl Polym Sci, 2009     

Determination of dynamic mechanical properties of engineering thermoplastics at wide frequency range using Havriliak–Negami model

Using Havriliak–Negami (HN) model of time–temperature superposition, dynamic mechanical properties for two thermorheologically simple engineering thermoplastics, viz., polyether ether ketone (PEEK) and polycarbonate (PC) were determined. Calculations have been made with respect to (i) temperature‐independent HN parameters from dynamic mechanical analysis (DMA) and (ii) activation energies of the deformation processes involved. Viscoelastic properties, over a wide frequency range, were predicted from the HN model, which were further correlated with the experimentally determined quantities and chemical structure of the polymers. The mathematical calculations were done using Matlab® software. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 677–683, 2006     

Effects of prior aging at 288°C in argon environment on time‐dependent deformation behavior of a thermoset polymer at elevated temperature,Part 2: Modeling with viscoplasticity theory based on overstress

The viscoplasticity based on overstress (VBO) is augmented to model the effects of prior isothermal aging in an argon environment on the inelastic deformation behavior of PMR‐15 neat resin, a high‐temperature thermoset polymer. VBO is a unified state variable theory with growth laws for three state variables: the equilibrium stress, the kinematic stress and the isotropic stress. A systematic model characterization procedure based on a limited number of well defined experiments is employed to determine the VBO parameters. Experimental findings presented in Part I reveal the equilibrium stress and the kinematic stress to be affected by prior aging. Based on the experimental results, the isotropic stress is developed as a function of prior aging time. In addition, several VBO model parameters are made dependent on prior aging time. Comparison with experimental data demonstrates that the modified VBO successfully predicts the inelastic deformation behavior of the PMR‐15 polymer subjected to prior isothermal aging for up to 2000 h. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Modification of a two‐component system by introducing an epoxy‐reactive diluent: Construction of a time–temperature–transformation (TTT) diagram

Curing reactions of a three‐component system consisting of an epoxy resin diglycidyl ether of bisphenol A (DGEBA n = 0), 1,2‐diaminecyclohexane as curing agent, and vinylcyclohexene dioxide as a reactive diluent were studied to calculate a time–temperature–transformation isothermal cure diagram for this system. Differential scanning calorimetry (DSC) was used to calculate the vitrification times. DSC data show a one‐to‐one relationship between T_g and fractional conversion α, independent of cure temperature. As a consequence, T_g can be used as a measure of conversion. The activation energy for the polymerization overall reaction was calculated from the gel times obtained using the solubility test (58.5 ± 1.3 kJ/mol). This value was similar to the results obtained for other similar epoxy systems. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 1190–1198, 2004     

Examination of the time–water content superposition on the dynamic viscoelasticity of moistened polyamide 6 and epoxy

We have investigated the behavior of moisture absorption by the polyamide 6 and epoxy samples in various humid environments at constant temperature and also examined the effect of absorbed moisture on their dynamic viscoelastic properties. The moisture absorption was revealed to show the Fickian type of diffusion and to shift the dynamic viscoelastic properties of the specimen to those at lower temperature, as an effect of plasticization. Anti‐plasticization taken with an increase in the storage modulus was also observed in a low‐temperature range below ?50°C. The time–water content superposition was confirmed to hold at various equilibrium water contents at constant temperature for both polyamide 6 and epoxy. The relation of the shift factor, log a_H, to the equilibrium water content for polyamide 6 has a form similar to WLF equation of time–temperature superposition, whereas the log a_H for epoxy does not have such a form. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 560–567, 2004     

Effects of microstructures on the viscoelastic and rheological properties of metallocene‐catalyzed cyclo‐olefin copolymers: A preliminary study

We characterized metallocene‐catalyzed cyclo‐olefin copolymers (mCOCs) with similar heat distortion temperatures but dramatic differences in melt‐flow indices to understand how the molecular conformation affected their rheological and viscoelastic properties. The mCOC conformations were identified with ¹³C‐NMR, whereas the viscoelastic and rheological properties were measured with cone‐and‐plate and high‐pressure capillary rheometers. Our preliminary results showed that the mCOC rheological and viscoelastic properties might depend strongly on the conformation rather than the norbornene content, molecular weight, and molecular weight distribution. mCOCs containing ‐NNN‐ locks (where N represents norbornene) exhibited stronger molecular entanglements than those having no ‐NNN‐ blocks, as reflected in lower crossover frequencies and higher crossover torque. Furthermore, the existence of larger rigid ‐NNN‐ blocks resulted in higher molten viscosities and flow activation energies. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 3695–3701, 2002     

Internal lipid content and viscoelastic behavior of wool fibers

Wool is a natural keratin fiber made up of cuticle and cortical cells held together by the cell membrane complex (CMC), which contains few internal lipids (IWLs) (1.5% by mass). IWL arouse considerable cosmetic and dermatological interest because of its high proportion of ceramides. In this work, IWLs were extracted with acetone, methanol, and dichloromethane/acetone solvents, and the possible alteration of the extracted fibers with respect to their textile feasibility was analyzed. Parameters of yield, fibril, and matrix viscoelastic behavior, deformation work, and breaking elongation were useful in highlighting the effect of internal wool lipids on the mechanical properties of the fibers. The extraction with acetone and methanol solvents supplied good yields of IWL. Although extraction with methanol achieved the richest extracts, the fibers were chemically modified. By contrast, although acetone‐extracted fibers had similar properties after treatment, alkaline solubility was lower and fiber length and barb were superior. In the mechanical analysis, a prior extraction of IWL increased yield tenacity and decreased the elongation at break of the fibers, maintaining the feasibility of extracted wool for textile purposes. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 3252–3259, 2004     

Convenience of immobilized Bacillus licheniformis α-amylase as time—temperature-integrator (TTI)

For the immobilization of Bacillus licheniformis α-amylase to porous glass beads, the performances of three possible linking agents, glutaric dialdehyde, benzoquinone and S-trichlorotriazine were assessed in respect of the protein yield, the enzymic activity and the thermostability of the immobilized enzyme. These three properties are to be evaluated in view of the possible use of the enzyme preparations as time–temperature-integrators (TTIs) for assessing the severity of heat pasteurization or sterilization processes of food or pharmaceuticals. All three linkers improved the enzymes's resistance to irreversible heat inactivation to a similar extent and in each case biphasic inactivation kinetics were observed, whereas the dissolved B. licheniformis α-amylase showed a simple first order decay. The immobilization yield, measured as protein per carrier weight, did not differ markedly for the three linkers, although the enzymic activity of the glutaric dialdehyde-linked enzyme was lower than that of the benzoquinone- and S-trichlorotriazine-linked preparations.