Glass Transition Range Research Articles

A constitutive model for block-copolymers based on effective temperature

Phase segregated copolymers such as elastomeric copolymers find myriad applications especially in impact resistant structures. When domains with varying relaxation characteristics are present, these polymers exhibit thermorheologically complex behaviour. The multiple relaxation processes are herein captured using the effective temperature based thermodynamics, used extensively in modelling thermo-mechanical response of metals and polymers. Specifically, we use two slowly evolving configurational subsystems and a fast evolving kinetic-vibration (K-V) subsystem. The two configurational subsystems represent the inter-molecular and intra-molecular meso-scale configurational transformations occurring within the two domains. The K-V subsystem represents the faster atomic vibrations. The configurational subsystems are weakly coupled with the K-V through heat exchange which accounts for structural relaxations of the individual domains towards the equilibrium microstructure. Based on this, we are able to capture strain rate dependence and strain induced softening of these materials under cyclic loads. In comparison with the existing formulations for such copolymers, ours is perhaps a more transparent approach, as it uses quantities such as volume fraction, glass transition temperatures of individual domains as material parameters. Indeed, our formulation could be readily adapted for non-elastomeric copolymers. It should also be potentially useful as a design tool for copolymers with increased glass transition range.

Kinetic criteria of vitrification and pressure-induced glass transition: dependence on the rate of change of pressure

Kinetic criteria are formulated describing vitrification and devitrification of liquids in response to variations of the rate of change of external pressure. General analytical relations are derived allowing one to determine the pressure at the glass transition, pg, and the width of the glass transition interval, δpg, in dependence on the rate of change of pressure. In addition, a direct correlation between the pressure at the glass transition and the width of the glass transition interval is established. It is shown that the ratio δpg/pg is determined generally by an appropriately defined fragility index being a measure of the steepness of change of relaxation time at the glass transition, pg, relevant for the selected rate of change of pressure. Similar relations are derived also for dynamic glass transitions in response to oscillations of pressure. All these dependencies are widely determined by the Maxwellian relaxation time of the liquid under consideration. However, they are shown to hold independently of any particular assumptions concerning the particular type of dependence of viscosity and/or relaxation time on pressure and the set of structural order-parameters describing the effect of deviations from (metastable) thermodynamic equilibrium. The results are illustrated here utilizing a recently developed new relation for the pressure dependence of the Newtonian viscosity, respectively, the relation for the pressure dependence of the relaxation time corresponding to it. Similarly to vitrification caused by variations of temperature, the pressure at the glass transition and the width of the glass transition range are shown to be logarithmic functions of the rate of change of pressure. The analytical results are confirmed by numerical computations employing a simple statistical model of glass-forming liquids.

Correlation between glass transition temperature and the width of the glass transition interval

AbstractThe glass transition is a kinetic phenomenon. Its basic characteristics—the glass transition temperature, Tg, and the width, δTg, of the glass transition interval—depend significantly on cooling and heating rates as it is observed experimentally by standard DSC and fast scanning calorimetry. The knowledge of these and related correlations is of outstanding importance both for a theoretical understanding of vitrification and devitrification processes and their control in a variety of technological applications. By these reasons, general kinetic criteria of vitrification and, based on them, theoretical expressions for the glass transition temperature and the width of the glass transition range in dependence on rates of change of temperature have been derived in previous papers. These results are advanced here by establishing a direct correlation between these two quantities, Tg and δTg. The ratio δTg/Tg is shown, for arbitrary cooling and heating rates, to be a function of an appropriately defined index being a straightforward generalization of the definition introduced by Angell. The theoretical results are tested and confirmed by experiment. The methods employed here can be utilized generally for the description of vitrification caused also by a variation of other external control parameters like pressure.

A robotic multiple-shape-memory ionic polymer–metal composite (IPMC) actuator: modeling approach

The multiple-shape-memory ionic polymer–metal composite (MSM-IPMC) actuator can demonstrate complex 3D deformation. The MSM-IPMC has two distinct characteristics, which are the electromechanical actuation effect and the thermal-mechanical shape memory effect. The bending, twisting, and oscillating motions of the actuator could be controlled simultaneously or separately by means of thermal-mechanical and electromechanical transduction. In this study, a theoretical model for the MSM-IPMC was developed and experimentally investigated. Based on previous studies on the electromechanical actuation effect of ionic polymer–metal composite (IPMC), a comprehensive physics-based model of MSM-IPMC which couples the actuation effect and the multiple shape memory effect was developed. To verify the model, an MSM-IPMC sample was prepared and used in experimental testing. The simulation results were shown to be in good agreement with the experimental results obtained. The multiple shape memory and recovery rate of three different polymers, namely the Nafion, Aquivion and GEFC of different ions, which are the hydrogen, lithium and sodium, were also tested. Based on the results, it is shown that all the polymers demonstrate the multiple shape memory effect with varying amounts of programmable shapes. The ion type was shown to have an influence on the broad glass transition range of the polymers, which in turn dictated the number of possible programmable shapes for each membrane. The current study is beneficial for the better understanding of the multiple shape memory effect of MSM-IPMC.

Thermomechanical behavior of amorphous alloys based on titanium at the temperature range of the glass transition and crystallization

Knowledge and systematic research on the mechanical properties of amorphous materials in the transition temperature range from amorphous to crystalline is a fundamental scientific interest. Planning the use of these materials must be based on thermomechanical properties information. TiZrCuPd amorphous alloys belong to the potentially lead-free solders of relatively large glass forming ability. The paper presents results of the differential scanning calorimetry, thermomechanical, microstructural and phase analysis of the TiZrCuPd amorphous alloys containing 14 at% Pd and 2 and 3 at% Sn additions at the expenses of Cu content. The samples were investigated in the tensile-load modulated and dilatometric modes in the temperature range of the glass transition and crystallization. The relation between two steps of crystallization process, plastic flow and resulting ability for the deformation was analyzed and related to the microstructure and phase analysis. The determined temperature range of glass transition and primary crystallization show enhanced ductility in the dependence on the Sn additions and homogeneous deformation in this range. The engineering strain of alloys reveals its dependence on the temperature, especially visible in the sample for the 2 at% Sn additive.

Amorphous Fluoropolymer Membrane for Gas Separation Applications.

Amorphous fluoropolymers have been studied in the past few decades and received extensive attention due to their unique and useful properties. One of the remarkable properties of amorphous fluoropolymers is high fractional free volume (FFV), and they tend to retain large amounts of solvent inside their polymer chains. In this study, amorphous flouoropolymer membranes were employed to examine the influences of the residual solvent and drying condition on the thermal properties, gas permeation behavior, and structure change by the polymer chains. Thermal properties of the produced membranes were characterized by differential scanning calorimetry (DSC) and a thermogravimetric analysis (TGA) to verify the effects of residual solvent. The residual solvent content and the glass transition temperature (Tg) of amorphous fluoropolymer membranes prepared with both solvents decrease with increasing drying temperature. The effect of the thermal treatment method on the d-spacing between the polymer chains of the prepared membranes was investigated using X-ray diffraction (XRD). The d-spacing decreased with drying below the Tg whereas it drastically increased near the Tg because of chain relaxation. From these phenomena, the helium permeability of the membranes treated at 120 °C radically increased. However, the oxygen and nitrogen permeability decreased with decreasing residual solvent content. The glass transition range shifted to higher temperature, from 75 °C to 133 °C, depending on the reduced amount of residual solvent.

Investigating relaxation of glassy materials based on natural vibration of beam: A comparative study of borosilicate and chalcogenide glasses

The present work investigates the validity of using the frequency and decay rate of free-free beam vibration, which are measured by the impulse excitation technique (IET), to characterize the viscoelastic properties of glass in the temperature range of glass transition. Based first on the classical Burgers model, we show that the temperature-dependent flow viscosity of borosilicate glass, calculated from the measured frequency and amplitude decay rate of the flexural vibration, agrees very well with the existing data. While for chalcogenide glass, the same calculation approach does not render the similar agreement, and the reason probably lies in non-exponential effects. To comprehend the IET data in the temperature range of glass transition, we propose a simplified theoretical framework for describing the transition from the solid-like to liquid-like viscoelastic behavior and discuss the cause of difference of the rheology behaviors of these two types of glass based on the formulation of non-exponential relaxation.

Cooling history of a wet-granulated blast furnace slag (GBS)

Granulated blast furnace slag (GBS) is a glassy by-product of the steel industry that is formed during quenching of the molten slag after the blast furnace in a water-jet. To elucidate the cooling history of GBS, calorimetric scanning in the glass transition range and viscometric experiments at temperatures above the liquidus were performed. The GBS studied was of industrial origin with a d50 = 700 μm and > 99% glassy. It is found that GBS glass is of high potential energy, showing a fictive temperature that is approx. 160 K higher than the glass transition temperature under standard cooling conditions. Using different viscosity models and the relationship between quench rate and shear viscosity at the fictive temperature it is calculated that GBS was formed at a cooling rate of approx. 2.6 × 105 K s−1 corresponding to a shear viscosity of 105.9 Pa s. Due to the high Tf and high amount of heat that is released during structural relaxation, GBS is assigned to the class of hyperquenched glasses.

Understanding the Thermal Properties of Precursor-Ionomers to Optimize Fabrication Processes for Ionic Polymer-Metal Composites (IPMCs)

Ionic polymer-metal composites (IPMCs) are one of many smart materials and have ionomer bases with a noble metal plated on the surface. The ionomer is usually Nafion, but recently Aquivion has been shown to be a promising alternative. Ionomers are available in the form of precursor pellets. This is an un-activated form that is able to melt, unlike the activated form. However, there is little study on the thermal characteristics of these precursor ionomers. This lack of knowledge causes issues when trying to fabricate ionomer shapes using methods such as extrusion, hot-pressing, and more recently, injection molding and 3D printing. To understand the two precursor-ionomers, a set of tests were conducted to measure the thermal degradation temperature, viscosity, melting temperature, and glass transition. The results have shown that the precursor Aquivion has a higher melting temperature (240 °C) than precursor Nafion (200 °C) and a larger glass transition range (32–65 °C compared with 21–45 °C). The two have the same thermal degradation temperature (~400 °C). Precursor Aquivion is more viscous than precursor Nafion as temperature increases. Based on the results gathered, it seems that the precursor Aquivion is more stable as temperature increases, facilitating the manufacturing processes. This paper presents the data collected to assist researchers in thermal-based fabrication processes.

New Approach to Justification of the Williams–Landel–Ferry Equation

A derivation of the Williams–Landel–Ferry equation for the temperature dependence of relaxation time τ(T) in the glass transition range is proposed. This derivation is of a general character and is not related to any particular form of the functional dependence τ(T), in contrast to the known approaches. The modification of the Williams–Landel–Ferry equation and examples of its practical applications are considered.

Glass Transition, Crystallization of Glass-Forming Melts, and Entropy

A critical analysis of possible (including some newly proposed) definitions of the vitreous state and the glass transition is performed and an overview of kinetic criteria of vitrification is presented. On the basis of these results, recent controversial discussions on the possible values of the residual entropy of glasses are reviewed. Our conclusion is that the treatment of vitrification as a process of continuously breaking ergodicity with entropy loss and a residual entropy tending to zero in the limit of zero absolute temperature is in disagreement with the absolute majority of experimental and theoretical investigations of this process and the nature of the vitreous state. This conclusion is illustrated by model computations. In addition to the main conclusion derived from these computations, they are employed as a test for several suggestions concerning the behavior of thermodynamic coefficients in the glass transition range. Further, a brief review is given on possible ways of resolving the Kauzmann paradox and its implications with respect to the validity of the third law of thermodynamics. It is shown that neither in its primary formulations nor in its consequences does the Kauzmann paradox result in contradictions with any basic laws of nature. Such contradictions are excluded by either crystallization (not associated with a pseudospinodal as suggested by Kauzmann) or a conventional (and not an ideal) glass transition. Some further so far widely unexplored directions of research on the interplay between crystallization and glass transition are anticipated, in which entropy may play—beyond the topics widely discussed and reviewed here—a major role.

The influence of temperature on wave scattering of damaged segments within composite structures

The increased use of composite materials in modern aerospace and automotive structures, and the broad range of launch vehicles’ operating temperature imply a great temperature range for which the structures has to be frequently and thoroughly inspected. A thermal mechanical analysis is used to experimentally measure the temperature-dependent mechanical properties of a composite layered panel in the range of -100°C to 150°C. A hybrid wave finite element/finite element computational scheme is developed to calculate the temperature-dependent wave propagation and interaction properties of a system of two structural waveguides connected through a coupling joint. Calculations are made using the measured thermomechanical properties. Temperaturedependent wave propagation constants of each structural waveguide are obtained by the wave finite element approach and then coupled to the fully finite element described coupling joint, on which damage is modelled, in order to calculate the scattering magnitudes of the waves interaction with damage across the coupling joint. The significance of the panel’s glass transition range on the measured and calculated properties is emphasised. Numerical results are presented as illustration of the work.

Thermo-Responsive Shape-Memory Effect and Surface Features in Polycarbonate (PC)

The influence of programming strain and temperature on the shape memory effect and surface morphology in programmed polycarbonate (PC) samples via uni-axial stretching is investigated. It is found that the samples programmed at around the glass transition start temperature not only have micro-cracks on their surface, but also show a necking phenomenon. Furthermore, the surface of the necked area is concave, but the surface of the non-necked area is convex. On the other hand, despite the samples programmed at high temperatures being able to deform in a uniform manner at macroscopic scale, their surfaces are still uneven, either concave or convex. While the samples programmed at low temperatures are able to achieve full shape recovery, stretching at higher temperatures over the glass transition range to a higher strain may result in non-recoverable deformation.

The impact of temperature on wave interaction with damage in composite structures

The increased use of composite materials in modern aerospace and automotive structures, and the broad range of launch vehicles’ operating temperature imply a great temperature range for which the structures has to be frequently and thoroughly inspected. A thermal mechanical analysis is used to experimentally measure the temperature-dependent mechanical properties of a composite layered panel in the range of −100 ℃ to 150 ℃. A hybrid wave finite element/finite element computational scheme is developed to calculate the temperature-dependent wave propagation and interaction properties of a system of two structural waveguides connected through a coupling joint. Calculations are made using the measured thermomechanical properties. Temperature-dependent wave propagation constants of each structural waveguide are obtained by the wave finite element approach and then coupled to the fully finite element described coupling joint, on which damage is modelled, in order to calculate the scattering magnitudes of the waves interaction with damage across the coupling joint. The significance of the panel’s glass transition range on the measured and calculated properties is emphasised. Numerical results are presented as illustration of the work.

Elimination of porosity in bulk metallic glass castings using hot isostatic pressing

This study presents design and implementation of a systematic method to remove the pores in as-cast bulk metallic glass using hot isostatic pressing, without changing the amorphous structure of the samples. The supercooled liquid region of Zr44Cu40Al8Ag8 was characterized using differential scanning calorimetry and dynamic mechanical analysis. This enabled informed choice of the range of hot isostatic pressing process variables likely to result in successful reduction of the porosity in the glassy alloy. The operating pressure in hot isostatic press processing was relatively less influential than either the temperature or the dwell time in controlling the porosity. It was shown that the dwell time should be longer than the average relaxation time in the glass transition range. With the specific bulk amorphous alloy under study, the optimized temperature, pressure and dwell time are 475°C, 50MPa and 3min, respectively. Excess dwell times will result in crystallization.

Thermodynamic Properties of Iron Melts with Titanium, Zirconium, and Hafnium

The literature data on the enthalpies of mixing and thermodynamic activities of Fe–Ti, Fe–Zr, and Fe–Hf liquid alloys are summarized. It is shown that the thermodynamic properties of these systems are characterized by significant negative deviations from the ideal behavior. In the framework of the associated solution model, the composition and temperature dependences of the thermodynamic functions of mixing for the Fe–Ti, Fe–Zr, and Fe–Hf systems are described. The temperature dependence of the thermodynamic properties of the considered systems is characterized by increase in negative deviations from the ideality with decreasing temperature and increasing thermodynamic stability of supercooled melts. Analysis of the degree of short-range order in the system melts, estimated as the total mole fraction of associates Σxass at the glass transition temperature, allows us to successfully interpret the known composition ranges of glass transition for the Fe–Zr and Fe–Hf melts and predict the composition range of glass transition for the Fe–Ti melts.

Heat capacities and volumetric changes in the glass transition range: a constitutive approach based on the standard linear solid

A novel approach to represent the glass transition is proposed. It is based on a physically motivated extension of the linear viscoelastic Poynting–Thomson model. In addition to a temperature-dependent damping element and two linear springs, two thermal strain elements are introduced. In order to take the process dependence of the specific heat into account and to model its characteristic behaviour below and above the glass transition, the Helmholtz free energy contains an additional contribution which depends on the temperature history and on the current temperature. The model describes the process-dependent volumetric and caloric behaviour of glass-forming materials, and defines a functional relationship between pressure, volumetric strain, and temperature. If a model for the isochoric part of the material behaviour is already available, for example a model of finite viscoelasticity, the caloric and volumetric behaviour can be represented with the current approach. The proposed model allows computing the isobaric and isochoric heat capacities in closed form. The difference \(c_\mathrm{p} -c_\mathrm{v} \) is process-dependent and tends towards the classical expression in the glassy and equilibrium ranges. Simulations and theoretical studies demonstrate the physical significance of the model.

Light scattering by boron oxide in the temperature range of 225–330°C

It is found that the process of variation in the intensity of the polarized component of the light scattered by boron oxide in the temperature range of 250–290°C after cooling from temperatures of 330 and 450°C possesses the peculiarities similar to those found earlier for the step-by-step mode of cooling for temperatures higher than 295°C and is characterized by the formation of a minimum. It is also detected that at lower temperatures the minimum possesses an asymmetric shape. It is shown that the process of increasing the intensity in time is satisfactorily approximated by an empirical equation of an exponential form. It is found that the change in the relaxation times with the temperature corresponds to an exponential law for the entire set of the data that we have obtained. It is found that the change in the depolarized component intensity in the region of low temperatures is relatively small, which makes it possible to associate the behavior of the polarized component with the change in the value of isotropic scattering. It is shown that in agreement with the results obtained earlier the time dependence of the intensity of the polarized component at a higher temperature for a sample preliminarily annealed at a low temperature is characterized by the formation of a maximum. The experimental results that we have obtained indicate the universal character of the manifestation of a peculiarity in the behavior of the scattered light intensity in the process of cooling and heating of boron oxide in the glass transition range.

Leakage behaviour of elastomer seals under dynamic unloading conditions at low temperatures

In technical applications, static seals are sometimes also subjected to dynamic loadings. Therefore, the leakage behaviour under dynamic conditions has to be evaluated as well. For this purpose, FKM elastomer seals have been tested by using newly designed equipment that allows for rapid partial release of the seal and simultaneous leakage rate measurement at a wide range of test temperatures. Furthermore, material characterisation was done by using Dynamic Mechanical Analysis, Differential Scanning Calorimetry and Compression Set. It was shown that, under static conditions, the leakage rate increased significantly during cooling at temperatures around 18 K lower than the glass transition range. On reheating, the seal's functionality was restored in the high temperature region of the glass rubber transition. In the subsequent dynamic release tests, that comprised a reduction of the seal compression within 1 s from 25% to 23%, increased leakage rates were observed in the high temperature region of the glass transition range. It was shown that the temperature that is critical for increased leakage is significantly lower under static conditions compared to dynamic conditions. The obtained leakage rates for static tests and dynamic release tests at different temperatures were analysed with reference to results of the material characterisation.

Reconciling calorimetric and kinetic fragilities of glass-forming liquids

The liquid fragility index (mvis) describes the rate of viscosity change of a glass-forming liquid with temperature at the glass transition temperature (Tg), which is very important for understanding liquid dynamics and the glass transition itself. Fragility can be directly determined using viscosity measurements. However, due to various technical complications with determining viscosity, alternative methods to obtain fragility are needed. One simple method is based on measurement of the calorimetric fragility index (mDSC), i.e., the changing rate of fictive temperature (Tf) with heating (cooling) rate in a small Tf range around Tg. The crucial question is how mDSC is quantitatively related to mvis. Here, we establish this relation by performing both dynamic and calorimetric measurements on some selected glass compositions covering a wide range of liquid fragilities. The results show that mDSC deviates systematically from mvis. The deviation is attributed to the Arrhenian approximation of the log(1/qc)~Tg/Tf relationship in the glass transition range. We have developed an empirical model to quantify the deviation, by which mvis can be well predicted from mDSC across a large range of fragilities. Combined with the high-T viscosity limit (10–2.93Pa·s), we are able to obtain the entire viscosity curve of a glass-forming liquid by only performing DSC measurements.