Williams Landel Ferry Research Articles

Viscoelastic properties of hollow glass particle filled vinyl ester matrix syntactic foams: effect of temperature and loading frequency

Viscoelastic properties of hollow particle-reinforced composites called syntactic foams are studied using a dynamic mechanical analyzer. Glass hollow particles of three different wall thicknesses are incorporated in the volume fraction range of 0.3–0.6 in vinyl ester resin matrix to fabricate twelve compositions of syntactic foams. Storage modulus, loss modulus, and glass transition temperature are measured and related to the microstructural parameters of syntactic foams. In the first step, a temperature sweep from −75 to 195 °C is applied at a fixed loading frequency of 1 Hz to obtain temperature dependent properties of syntactic foams. In the next step, selected four compositions of syntactic foams are studied for combined effect of temperature and loading frequency. A frequency sweep is applied in the range 1–100 Hz and the temperature is varied in the range 30–140 °C. Time–temperature superposition (TTS) principle is used to generate master curves for storage modulus over a wide frequency range. The room temperature loss modulus and maximum damping parameter, Tanδ, are found to have a linear relationship with the syntactic foam density. Increasing volume fraction of particles helps in improving the retention of storage modulus at high temperature in syntactic foams. Cole–Cole plot and William–Landel–Ferry equation are used to interpret the trends obtained from TTS. The correlations developed between the viscoelastic properties and material parameters help in tailoring the properties of syntactic foams as per requirements of an application.

Application of time–temperature–stress superposition on creep of wood–plastic composites

Time–temperature–stress superposition principle (TTSSP) was widely applied in studies of viscoelastic properties of materials. It involves shifting curves at various conditions to construct master curves. To extend the application of this principle, a temperature–stress hybrid shift factor and a modified Williams–Landel–Ferry (WLF) equation that incorporated variables of stress and temperature for the shift factor fitting were studied. A wood–plastic composite (WPC) was selected as the test subject to conduct a series of short-term creep tests. The results indicate that the WPC were rheologically simple materials and merely a horizontal shift was needed for the time–temperature superposition, whereas vertical shifting would be needed for time–stress superposition. The shift factor was independent of the stress for horizontal shifts in time–temperature superposition. In addition, the temperature- and stress-shift factors used to construct master curves were well fitted with the WLF equation. Furthermore, the parameters of the modified WLF equation were also successfully calibrated. The application of this method and equation can be extended to curve shifting that involves the effects of both temperature and stress simultaneously.

Investigation of the free volume and ionic conducting mechanism of poly(ethylene oxide)-LiClO4 polymeric electrolyte by positron annihilating lifetime spectroscopy

The positron annihilation lifetime and ionic conductivity are each measured as a function of organophilic rectorite (OREC) content and temperature in a range from 160 K to 300 K. According to the variation of ortho-positronium (o-Ps) lifetime with temperature, the glassy transition temperature is determined. The continuous maximum entropy lifetime (MELT) analysis clearly shows that the OREC and temperature have important effects on o-Ps lifetime and free volume distribution. The experimental results show that the temperature dependence of ionic conductivity obeys the Vogel—Tammann—Fulcher (VTF) and Williams—Landel—Ferry (WLF) equations, implying a free-volume transport mechanism. A linear least-squares procedure is used to evaluate the apparent activation energy related to the ionic transport in the VTF equation and several important parameters in the WLF equation. It is worthwhile to notice that a direct linear relationship between the ionic conductivity and free volume fraction is established using the WLF equation based on the free volume theory for nanocomposite electrolyte, which indicates that the segmental chain migration and ionic migration and diffusion could be explained by the free volume theory.

Evaluation of the relevance of the glassy state as stability criterion for freeze-dried bacteria by application of the Arrhenius and WLF model

The aim of this work was to describe the temperature dependence of microbial inactivation for several storage conditions and protective systems (lactose, trehalose and dextran) in relation to the physical state of the sample, i.e. the glassy or non-glassy state. The resulting inactivation rates k were described by applying two models, Arrhenius and Williams–Landel–Ferry (WLF), in order to evaluate the relevance of diffusional limitation as a protective mechanism. The application of the Arrhenius model revealed a significant decrease in activation energy Ea for storage conditions close to Tg. This finding is an indication that the protective effect of a surrounding glassy matrix can, at least, partly be ascribed to its inherent restricted diffusion and mobility. The application of the WLF model revealed that the temperature dependence of microbial inactivation above Tg is significantly weaker than predicted by the universal coefficients. Thus, it can be concluded that microbial inactivation is not directly linked with the mechanical relaxation behavior of the surrounding matrix as it was reported for viscosity and crystallization phenomena in case of disaccharide systems.

Prediction of Storage Life of Propellants having Different Burning Rates using Dynamic Mechanical Analysis

Propellants, visco-elastic in nature, show time and temperature dependent behaviour on deformation. Hence, the time–temperature superposition principle may be applied to the visco-elastic properties of propellants. In the present study, dynamic mechanical analyser (DMA) was used to evaluate the dynamic mechanical properties and quantify the storage life of four different propellants based on hydroxyl terminated polybutadiene, aluminium and ammonium perchlorate having different burning rates ranging from 5 mm/s to 25 mm/s. Each sample was given a multi-frequency strain of 0.01 per cent at three discrete frequencies (3.5 Hz, 11 Hz, 35 Hz) in the temperature range - 80 °C to + 80 °C. The storage modulus, loss modulus, tan delta and glass transition temperature (Tg) for each propellant samples have been evaluated and it is observed that all the propellants have shown time (frequency) and temperature dependent behaviour on deformation. A comparison of the log aT versus temperature curves (where aT is horizontal (or time) shift factor) for all four propellants indicate conformance to the Williams–Landel–Ferry (WLF) equation. The master curves of storage modulus (log E versus log ω plots) were generated for each propellant. A plot of E versus time for all propellants was generated up to 3 years, 6 years, and 10 years of time, respectively. The drop in the storage modulus below the acceptable limit with time may be used to predict the shelf life of the propellant. Defence Science Journal, 2012, 62(5), pp.290-294 , DOI:http://dx.doi.org/10.14429/dsj.62.2480

Development of a methodology for numerical simulation of non-isothermal viscoelastic fluid flows with application to axisymmetric 4:1 contraction flows

In this work we focus on developing a methodology for the free-to-use software OpenFOAM® to simulate non-isothermal viscoelastic flows, which is generally applicable to any mesh type and geometry. The methodology is validated by simulating non-isothermal viscoelastic flows in 4:1 axisymmetric contractions, in which the viscoelastic fluid is governed by the Oldroyd-B constitutive equation. The thermorheological modeling may vary between pure energy elasticity and entropy elasticity depending on a pre-determined split coefficient. The temperature-dependent viscosity and relaxation time are modeled using the WLF (Williams–Landel–Ferry) relation. The governing equations are discretized in OpenFOAM® using a collocated finite volume method. The DEVSS technique is employed for stabilization of the numerical algorithm at high Deborah numbers. An extrapolation method is proposed for the viscoelastic stress on solid walls, which is subsequently being evaluated regarding accuracy and stability. Next, flows in axisymmetric 4:1 contractions with a temperature jump at the contraction are simulated, similar to the studies of Wachs and Clermont (2000) [24]. The influence of the Deborah number and the temperature jump on the flow behavior, such as the vortex length, is examined. Furthermore, the asymptotic behavior at the singularity is examined for different Deborah numbers.

Effects of annealing time and temperature on the crystallinity and heat resistance behavior of injection‐molded poly(lactic acid)

AbstractThe effects of annealing time and temperature on the crystallinity of injection‐molded poly(lactic acid) (PLA) were investigated using differential scanning calorimetry and wide‐angle x‐ray diffraction. Differential scanning calorimetry, tensile test, and dynamic mechanical analysis showed that an increase in crystallinity in the PLA parts from the annealing treatment offers several benefits such as a higher glass transition temperature, better heat resistance, and greater storage modulus and tensile strength. Based on the experimental data, the degree of crystallinity, annealing time, and annealing temperature were found to closely follow the time–temperature superposition relationship. Namely, a master curve could be constructed based on either the Williams–Landel–Ferry equation or the Arrhenius relationship by shifting the crystallinity isotherms in the logarithmic scale horizontally along the log‐time axis. This relationship provides a quantitative guideline for annealing postinjection‐molded PLA parts to improve the heat resistance and mechanical properties. An increase of over 17% and 26% in tensile strength was achieved at an annealing temperature of 80°C for 30 min and 65°C for 31 h, respectively. POLYM. ENG. SCI. 2013. © 2012 Society of Plastics Engineers

Mechanical spectra and calorimetric evaluation of gelatin–xanthan gum systems with high levels of co-solutes in the glassy state

Mechanical properties of gelatin–xanthan gum (XG) mixtures with high levels of co-solutes were examined by dynamic mechanical analysis (DMA). The mechanical spectra of the samples were modeled according to the Williams–Landel–Ferry (WLF) equation/free-volume theory, which requires an entropic lightly cross-linked network. For the α dispersion, E′ and E′′ superposed with the horizontal shift factor aT, which was temperature-dependent according to the WLF equation; no other secondary dispersion mechanism was detected. The addition of XG to gelatin networks with high levels of co-solutes changed the glass transition temperature (Tg) and kinetics of glass transition and glassy states. In the glassy state, the WLF equation was unable to follow progress in the mechanical properties, which were better described by the Andrade equation. The calorimetric measurements of the gelatin–XG systems were made using a modulated temperature differential scanning calorimetry (MTDSC) to improve the determination of Tg. The samples were exposed to two cooling and heating cycles to provide a controlled recent thermal history in the temperature range of 40 °C to −70 °C. The Tg values of the samples were determined from the second heating cycle in the reversing heat signal. The calorimetric Tg values increased with increasing glucose syrup:sucrose ratio due to increased crosslinking, whereas mechanical Tg decreased with increased XG content due to network formation.

Prediction of compressive creep behaviour in flexible polyurethane foam over long time scales and at elevated temperatures

Compressive creep gradually affects the structural performance of flexible polymeric foam material over extended time periods. When designing components, it is often difficult to account for long-term creep, as accurate creep data over long time periods or at high temperatures is often unavailable. This is mainly due to the lengthy testing times and/or inadequate high temperature testing facilities. This issue can be resolved by conducting a range of short-term creep tests and applying accurate prediction methods to the results. Short-term creep testing was conducted on viscoelastic polyurethane foam, a material commonly used in seating and bedding systems. Tests were conducted over a range of temperatures, providing the necessary results to allow for the generation of predictions of long-term creep behaviour using time-temperature superposition. Additional predictions were generated, using the William Landel Ferry time-temperature empirical relations, for material performance at temperatures above and below the reference temperature range. Further tests validated the results generated from these theoretical predictions.

Measuring physico-chemical interaction in mastics using glass transition

The current design standard for asphalt mixtures provides guidance on selection of aggregates, asphalt binder and includes requirements for the amount of mineral filler to be included. The amount of filler that can be included is limited to a ratio in the range of 0.6–1.2 by mass of the binder. However, this range is based on experience rather than on scientific evaluation of the interaction between filler and binder. Although many researchers acknowledge the physico-chemical interaction between asphalt binder and the mineral filler, currently a procedure to quantify this interaction, and consider it in selecting favorable filler to binder ratio, is not available. In this paper, the effect of fillers on the glass transition temperature (T g) of the base binder was used to evaluate the physico-chemical interaction in mastics. The total reinforcement of the filler, which is measured in terms of relative viscosity of the filled binder to the unfilled binder, consists of two parts: mechanical and physico-chemical. The mechanical reinforcement part is calculated based on micromechanical models commonly used in the literature that take into account volume filling effects and particle-to-particle interactions. Physico-chemical reinforcement is estimated based on the change in the T g in both Williams-Landel-Ferry (WLF) and Arrhenius time-temperature shift models. The concept introduced in this study is evaluated by viscosity and dilatometric T g testing of three binders mixed with three different fillers, at different concentrations. Results show that the physico-chemical interaction between the mineral filler and the binder can be accurately estimated from the difference in the glass transition temperature of the mastics and the binder.

Molecular Dynamics Simulations of Diffusion of O2 and N2 Penetrants in Polydimethylsiloxane-Based Nanocomposites

Recently, metal particle polymer composites have been proposed as sensing materials for micro corrosion sensors. To design the sensors, a detailed understanding of diffusion through metal particle polymer composites is necessary. Accordingly, in this work molecular dynamics (MD) simulations are used to study the diffusion of O2 and N2 penetrants in metal particle polymer nanocomposites composed of an uncross-linked polydimethylsiloxane (PDMS) matrix with Cu nanoparticle inclusions. PDMS is modeled using a hybrid interatomic potential with explicit treatment of Si and O atoms along the chain backbone and coarse-grained methyl side groups. In most models examined in this work, MD simulations show that diffusion coefficients of O2 and N2 molecules in PDMS-based nanocomposites are lower than that in pure PDMS. Nanoparticle inclusions act primarily as geometric obstacles for the diffusion of atmospheric penetrants, reducing the available porosity necessary for diffusion, with instances of O2 and N2 molecule trapping also observed at or near the PDMS/Cu nanoparticle interfaces. In models with the smallest gap between Cu nanoparticles, MD simulations show that O2 and N2 diffusion coefficients are higher than that in pure PDMS at the lowest temperatures studied. This is due to PDMS chain confinement at low temperatures in the presence of the Cu nanoparticles, which induces low-density regions within the PDMS matrix. MD simulations show that the role of temperature on diffusion can be modeled using the Williams–Landel–Ferry equation, with parameters influenced by nanoparticle content and spacing.

Influence of magic angle spinning on T1H of SBR studied by solid state 1H NMR

We have investigated the influence of the high centrifugal pressure caused by fast magic-angle spinning (MAS) on the molecular motion of styrene–butadiene rubbers (SBR) filled with SiO2 (SBR/Si composite) though solid-state magic-angle spinning nuclear magnetic Resonance (1H MAS NMR) measurements. Because the 1H–1H dipolar interaction of elastomers is weak compared with that of glassy polymers, a narrower 1H linewidth is observed under fast MAS. The temperature dependence of the 1H spin-lattice relaxation time (T1H) revealed that the T1H minimum increases with the MAS rate. Furthermore, we observed a difference in the temperature dependence of T1H between end-chain-modified SBR and normal (unmodified) SBR in the SBR/Si composites. The temperature dependence of T1H is described by the Bloembergen–Purcell–Pound theory, with the assumption that the correlation time obeys the Williams–Landel–Ferry empirical theory. The fitting showed that the molecular motion does not change significantly until a MAS rate of 20 kHz, with the motional mode changing considerably at a MAS rate of 25 kHz. The motion of SBR in the unmodified SBR/Si composite was greatly affected by the fast MAS rates. Furthermore, the plot of the estimated centrifugal pressure versus the T1H minimum resembled the stress–strain curve. This result enables the detection of macroscopic physical deformation by the microscopic parameter T1H. Temperature-dependent curves of T1H for the SBR with and without end-chain modification in the SBR/Si composites showed the increment of the T1H values as the MAS rate increases and the considerable change at the fast MAS rate of 25 kHz. The increase of T1H values is represented by the factor f that decides the observed T1H minimum value. The plot of centrifugal pressure caused by MAS as a function of 1/f exhibited the similar trend to that of the stress–strain curve. The differences in the T1H between the end-chain-modified and normal SBR under fast MAS was attributed to the Payne effect.

A comparative study of the viscosity of ion conducting polymers based on the bond strength-coordination number fluctuation model and other models

According to the bond strength-coordination number fluctuation (BSCNF) model of viscosity proposed some years ago by one of the authors, viscosity is controlled by the relaxation of structural units that form the melt, and is described in terms of the average bond strength, coordination number, and their fluctuations of the structural units. In the present paper, a comparative study of the viscosity of ion conducting polymeric system is presented. The analysis has been done though the BSCNF model and other models widely used in the literature such as Vogel–Fulcher–Tamman and Williams–Landel–Ferry equations. The result reveals that the three models describe well the temperature dependence of the viscosity reported experimentally. As a gross trend, the fragility of the polymeric system in consideration increases with the increase in the concentration of salts. Based on the analysis with the BSCNF model, such a behavior has been interpreted to arise from the disruption of the network that results by the addition of salts. The comparative study also reveals that the BSCNF model could provide a physical interpretation to the empirical parameters used in other models.

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

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

Dielectric and mechanical relaxations in the vicinity of glass transitions in confined polar copolymers VDF/Te and VDF/Tr

The low-frequency elastic and dielectric properties of composite materials prepared by embedding of vinylidene fluoride–tetrafluoroethylene (V DF88/Te12) and vinylidene fluoride–trifluoroethylene (V DF60/Tr40) polar copolymers in porous glass matrices with a mean pore diameter of around 320 nm were investigated in the temperature range 150–330 K. Maxima of internal friction have been found near the glass transition temperatures Tg1 and Tg2 of the polymer amorphous fraction. Strong dielectric relaxation with characteristic time corresponding to the Williams–Landel–Ferry law was observed in the vicinity of temperature Tg1. An increase (≈10 K) of Tg1 temperature of the amorphous fraction of incorporated polymeric materials was detected. It was found that the low-frequency dielectric and mechanical losses in the vicinity of Tg1 are due to the same mechanism.

Viscoelastic effects in thermoplastic poly(styrene-acrylonitrile)-modified epoxy–DDM system during reaction induced phase separation

The viscoelastic phase separation of a poly(styrene-co-acrylonitrile) (SAN) modified epoxy system based on the diglycidyl ether of bisphenol A (DGEBA) cured with 4,4′-diaminodiphenylmethane (DDM) has been monitored in situ using rheometry, optical microscopy (OM) and small angle laser light scattering (SALLS). The amount of SAN in the epoxy blends were 3.6, 6.9, 10, and 12.9 wt%. The relationship between rheological properties and phase separation was carefully explored. The evolution of storage modulus, loss modulus, and tan δ were found to be closely related to the evolution of complex phase separation. From the rheological profile, two gel points are identified, corresponding to physical gelation and chemical gelation, the first one because of viscoelastic phase separation and the second one related to crosslinking of the epoxy resin, these depend on the cure temperature and amount of thermoplastic. Further SALLS investigations investigated the mechanism of phase separation. The time-dependent peak scattering vector was simulated with a Maxwell-type viscoelastic relaxation equation. Relaxation times obtained at different temperatures for the blends could be described by the Williams–Landel–Ferry equation. Moreover, the development of light scattering profile follows the Tanaka model of viscoelastic phase separation.

Modeling Thermal Stress in Asphalt Mixtures Undergoing Glass Transition and Physical Hardening

Asphalt binders have been shown to undergo significant time-dependent stiffening when stored at low temperatures. This physical hardening has a significant effect on the laboratory performance of asphalt binders. However, the importance of isothermal conditioning for asphalt mixtures and its effect on thermal cracking performance have been a subject of significant debate. A theoretical approach accounting for the glass transition and physical hardening in the thermal stress buildup in mixtures was derived from relaxation modulus master curves, the William–Landel–Ferry equation, Boltzmann's superposition principle, and a model describing the isothermal contraction of asphalt as a continuous function of conditioning time and temperature. With the model predictions, it is shown that thermal stress relaxation and stress buildup induced by physical hardening can continuously affect thermal stress throughout the cooling process. The cooling rate also affected the amount of delayed stress buildup that occurred after the temperature had stabilized at isothermal conditions as a result of physical hardening. A relatively simple device was developed and used for verification and support of the thermal stress model. Mixture measurements performed at different cooling rates and isothermal conditions supported the theoretical predictions. The findings clearly show that the effect of physical hardening on stress buildup in mixtures is measurable and important. Therefore, the glass transition of asphalts and their behavior under isothermal conditioning needs to be measured to better predict thermal cracking.

Rheological evaluation of gelatin–xanthan gum system with high levels of co-solutes in the rubber-to-glass transition region

Effects of moisture content, xanthan gum (XG) addition, and glucose syrup (GS):sucrose ratio on the gelation of gelatin-XG systems with high levels of co-solutes were investigated in the rubbery and the glass transition regions. Frequency sweep tests were performed between 0.1 and 100 rad and the storage (G′) and loss (G″) moduli of the system were measured in the temperature range of 60 to −15 °C. The onset of glass transition region increased with decreasing moisture content. The time–temperature superposition yielded master curves of G′ and G″ as a function of timescale of measurement. G″ and G″ were superimposed with the horizontal shift factor aT, which was temperature dependent according to the Williams–Landel–Ferry (WLF) equation. Glass transition temperature (Tg) of the samples were determined by dynamic mechanical analysis (DMA) from the peak of tan δ. Tg decreased with XG addition. The energy of vitrification of samples with XG increased compared to samples containing only gelatin. Relaxation spectra of the samples were calculated from rheological measurements using the first and second approximations. The Rouse theory was more closely followed with the second approximation.

Viscoelastic properties and determination of free volume fraction of multi-walled carbon nanotube/epoxy composite using dynamic mechanical thermal analysis

Various weight fractions of multi-walled carbon nanotubes (MWNTs) were added to the epoxy as reinforcement to fabricate MWNT/epoxy nanocomposites by using ultrasonication and cast molding method. Dilatometeric measurements and Dynamic mechanical thermal analysis (DMTA) were used to determine the William–Landel–Ferry (WLF) constants and the effect of MWNT on viscoelastic behavior of nanocomposites in the glass transition region respectively. The results showed that addition of nanotubes to epoxy had significant effect on the viscoelastic properties. However, use of 0.5wt.% increased the viscoelastic properties more significantly. The WLF constants C1 and C2 were affected by MWNT amount. They seem to be interrelated as C2/C1=3.21–6.27K. It explains a relationship between the free volume fraction (fg) at glass transition temperature (Tg) and the thermal expansion coefficient (CTE). The relationship found between the experimental values of C1, C2 and Δα, clearly disagrees with the classical free volume interpretation of the WLF relationship.

Investigation of the Effects of Temperature and Strain on the Damping Properties of Polycarbonate/Multiwalled Carbon Nanotube Composites

The effects of temperature and strain on the free volume and damping properties of polycarbonate/multiwalled carbon nanotube (PC/MWCNT) composites were investigated by positron annihilation lifetime spectroscopy and dynamic mechanical thermal analysis. The damping dependence on temperature indicated that the damping factors remain at a low constant value in the polymer glassy state and increase rapidly in the glass-transition area. During the glass-transition area, a direct linear relationship between the fractional free volume and the damping has been obtained using the Williams–Landel–Ferry equation based on the free volume theory, which indicates that the free volume plays an important role in determining the damping property. The strain–damping experiments reveal that a high damping factor is still obtained. A “stick–slip” model has been used to analyze the damping dependence on strain for PC/MWCNT composites, which reveals a damping mechanism of interfacial slip between the MWCNTs and the matrix.