Glass Transition In Amorphous Polymers Research Articles

Traversing with quantitative fidelity through the glass transition of amorphous polymers: Modeling the thermodynamic dilatational flow of polycarbonate

We follow the assumption that the dilatational response of glassy polymers can be characterized by a back-stress type analog that includes a thermal expansion for each elastic component and with a viscosity that is dependent on the expansion of the elastic back-stress component. To this, we add the assumption of an unloaded equilibrium temperature that correlates to the past processing through the viscous flow. After setting this in a thermodynamically consistent structure, elastic, elastic back-stress, thermal expansion, back-stress thermal expansion, heat capacity, and viscous damping are evaluated using existing experiments for the response of polycarbonate over the glassy and rubbery ranges. For the demonstration, this is done entirely using a WLF shift factor that is augmented to include, in addition, back strain superposition. We then examine the resulting model under different thermal and mechanical loadings that have the material passing through the glass transition.

Influence of Carbon Dioxide on the Glass Transition of Styrenic and Vinyl Pyridine Polymers: Comparison of Calorimetric, Creep, and Rheological Experiments

The glass transition of amorphous polymers determines the mobility of polymer chains and the time scale of relaxation processes. The glass transition temperature is reduced by the presence of low molecular weight molecules, e.g., dissolved gases or organic solvents. The quantitative knowledge of reduction of the glass transition temperature caused by the addition of carbon dioxide in a polymer melt is highly relevant for foam extrusion. However, measurement of the reduction of glass transition temperature caused by gas loading has to be performed under elevated pressure which implies high experimental efforts. In this work, we discuss and compare three methods for determination of the influence of carbon dioxide on thermal properties of amorphous polymers, i.e., calorimetric measurements, creep tests, and rheological experiments. The advantages and disadvantages of these methods are elucidated. Furthermore, the influence of molecular structure of the styrenic and vinylpyridine polymers on the glass transition temperature is discussed. Polystyrene generally shows the highest reduction of glass transition temperature. Poly(2-vinylpyridine) and poly(4-vinylpyridine) show a slightly less pronounced behaviour in comparison to polystyrene because of the lower polarity of polystyrene. Poly(α-methyl styrene) is associated with a different dependence of glass transition temperature on gas loading in calorimetric and rheological experiments.

All-atomistic molecular dynamics study of the glass transition of amorphous polymers

Glass transition is an intensively studied topic but many questions in this regard remain unaddressed. This is an important phenomenon related to the physical and mechanical properties of amorphous polymer materials. In this study, existing and newly performed all-atomistic molecular dynamics (MD) simulations of polycarbonate (PC) and poly-(methyl methacrylate) (PMMA) cooling processes were analyzed to address their glass transitions from a molecular perspective. Additionally, potential energy, radius of gyration, dihedral transition, and end effects were characterized. Further analyses were performed to characterize the individual degrees of freedom (DoFs) by the variance, correlation between two DoFs by the correlation coefficient, and collective motions by instantaneous normal mode (INM) analysis. Various DoFs experienced glass transition at temperatures slightly different from the glass transition temperature T g , presumably owing to their different spatial scales and chemical environments. This suggests that the experimentally observed broad T g may be attributed to a similar hierarchy of motions. Collective motions characterized by INM revealed slightly different behaviors for PC and PMMA. • T g of million-atom atomistic models of PC and PMMA were investigated by MD. • Potential energy, Rg, dihedral transition, end effect across T g were characterized. • Abrupt variance uprises and peaks in correlation showed local DoFs' responses to T g . • Hierarchy of local DoFs' characteristic temperatures possibly widened T g range. • INM showed responses to T g at low mode and differences between PC and PMMA.

The glass transition of amorphous polymers: About a continuous equation of state and its derivatives

AbstractDescribing the pressure‐volume‐temperature (PVT) behavior of polymers is often hindered due to limitations of models and theories. In this work, we propose the logistic function to derive a phenomenological equation of state (EOS) that overcomes these limitations. Without dividing the temperature domain into several intervals, this continuous EOS describes the PVT behavior of amorphous polymers in the equilibrium state, the vitreous state and at glass transition. Discontinuities at glass transition are inherently eliminated. The EOS is continuously differentiable with respect to temperature and pressure. The thermal expansion coefficient and compression modulus thus can be determined at any valid reference state. The EOS linearly depends on temperature both in the equilibrium state and vitreous state. Furthermore, a parameter of the EOS is interpreted as the pressure‐dependent glass transition temperature. Using PVT data of polyethersulfone (PES), measured in the temperature range of 20 − 360 °C and pressure range of 10 − 200 MPa in both the isobaric and standard isothermal mode, the validity of the EOS is discussed. Polymer processing simulation and solid mechanics benefit from the EOS and its derivatives, respectively. In addition, the EOS can be used to determine the glass transition temperature from PVT data.

Predicting glass transition of amorphous polymers by application of cheminformatics and molecular dynamics simulations

Predicting the glass-transition temperatures (Tg) of glass-forming polymers is of critical importance as it governs the thermophysical properties of polymeric materials. The cheminformatics approaches based on machine learning algorithms are becoming very useful in predicting the quantitative relationships between key molecular descriptors and various physical properties of materials. In this work, we developed a modeling framework by integrating the cheminformatics approach and coarse-grained molecular dynamics (CG-MD) simulations to predict Tg of a diverse set of polymers. The developed machine learning-based QSPR model identified the most prominent molecular descriptors influencing the Tg of a hundred of polymers. Informed by the QSPR model, CG-MD simulations are performed to further delineate mechanistic interpretation and systematic dependence of these influential molecular features on Tg by investigating three major CG model parameters, namely the cohesive interaction, chain stiffness, and grafting density. The CG-MD simulations reveal that the higher intermolecular interaction and chain stiffness increase the Tg of CG polymers, where their relative influences are coupled with the existence of side chains grafted on the backbone. This synergistic modeling framework provides valuable insights into the roles of key molecular features influencing the Tg of polymers, paving the way to establishing a materials-by-design framework for polymeric materials via molecular engineering.

A thermodynamic modeling approach for dynamic softening in glassy amorphous polymers

Strain softening is highly dependent on the thermo-mechanical history. The degree of post-yield strain softening increases with the aging time, which is dependent on the aging temperature, and decreases with plastic strain. In this paper, we present two approaches to describe the strain softening. The first approach is an extension of the widely applied dynamic softening method that evolves the yield strength with the effective plastic strain rate. Though this approach can quantitatively capture the main experimental observations, it is empirical and does not capture the physical mechanism behind aging and strain softening. The second approach couples inelastic deformation with an evolution of the nonequilibrium state. The approach is based on the effective temperature nonequilibrium thermodynamic framework that introduces a thermodynamic state variable, the effective temperature to characterize the nonequilibrium state. The temperature-dependent evolution of the effective temperature describes the glass transition of amorphous polymers. We show that the physical aging and dynamic softening arise from the evolution of the effective temperature towards equilibrium and with plastic deformation towards a steady-state value away from equilibrium.

On the relaxation nature of the glass transition of amorphous polymers and low-molecular amorphous materials

The relative temperature range (δTg/Tg) characterizing the liquid-to-glass transition is a single-valued function of the fluctuation volume fraction fg frozen at the glass transition temperature Tg. The fluctuation volume ΔVe of the amorphous material is determined by delocalization of active (excited)) atoms, i.e., their thermal displacements from equilibrium positions. The fluctuation volume fraction f = ΔVe/V controls the molecular mobility that is characteristic of delocalized atoms in the liquid-glass transition region. It is shown that δTg for the majority of amorphous materials is only 0.7% of the glass transition temperature Tg. The narrow temperature range δTg is consistent with the classical Simon concept on the insignificant temperature range in which the structure is frozen.

Glass Transition and Phase Stability in Asphalt Binders

ABSTRACT Major aspects of the glass transition of asphalt binders are described and an extensive literature review of the phenomenon and its relation to chemical composition is presented. The glass transition of asphalt binders was studied by modulated differential scanning calorimetry and also via dynamic mechanical analysis. A certain analogy between the glass transition of amorphous polymers and asphalts is suggested. The overall transition was found to be very broad on the temperature scale. The effects of evaporation of light-end components and oxidation on asphalt phase stability and glass transition were studied. It was suggested that phase incompatibility may exist in asphalts; however, the phase separation is observable after long-term isothermal conditioning at a temperature within the glass transition range. Based on the presented results, it is suggested that phase incompatibility develops if there is a discontinuity in the molecular distribution. Such discontinuity may be present in some neat binders as well as in severely oxidized or aged asphalt binders.

Molecular-dynamics simulation study of the glass transition in amorphous polymers with controlled chain stiffness

We report computation results obtained from extensive coarse-grained molecular-dynamics simulations of amorphous ensembles of polymer chains at constant density. In our polymer model, we use bending and torsion potentials acting along the polymer backbone to control the chain stiffness. The static and dynamic properties of the polymer bulk have been analyzed over a large temperature interval in search for the onset of the glass transition. The glass transition temperatures Tg, for different types of chain stiffness, have been determined from the dependence of the self-diffusion coefficient D on the temperature T as the limiting value where the diffusion vanishes. Increasing the chain stiffness induces an increase of the glass transition temperature. The Tg values estimated from diffusion are confirmed by analyzing the relaxation times of the autocorrelation functions for the torsion angle and for the end-to-end vector. The dependence of the diffusion coefficient D on the chain length N is strongly affected by temperature for chains with bending and torsion stiffness. For systems with relatively short chains (N<or=50), the exponent nu from D proportional to N(-nu) increases from the value nu approximately 1 expected in the Rouse regime to nu approximately 2 as the temperature is lowered towards Tg.

Measurements of the viscoelastic moduli of an acrylate polymer in bulk and film form using a contact method

This paper describes a new method for the measurement of the viscoelastic properties of polymers using a contact mechanics approach. The latter is based on the determination of the tangential response of a macroscopic contact between a polymer specimen and a rigid sphere under small amplitude cyclic micro-motions. Using an acrylate polymer, it was found possible to achieve contact conditions where the tangential behaviour of the contact is strictly linear. Under such conditions, the measurement of the contact stiffness allowed to determine the viscoelastic moduli of the bulk polymer through the glass transition zone. In addition, it was also found to be possible to measure the damping properties of thin films (30 μm) using the same method. The results indicated a shift of the glass transition temperature of the films as compared to bulk specimens. This result was interpreted as an indication of the sensitivity of the glass transition of amorphous polymers to the hydrostatic pressure.

Thermodynamic description of geometrical confinement. Application to the glassy state and the glass transition of amorphous polymers

Based on the analysis of the geometrical confinements and the interactions between neighbor segments in polymeric systems, besides the quasi-lattice model used in Gibbs–DiMarzio entropy theory, an alternative theoretical method was developed here to investigate the thermodynamic aspect of the glassy state and the glass transition of amorphous polymers. A glass forming process through solvent evaporation from amorphous polymer-good solvent system was investigated, and the functional relationship between the glass transition temperature ( T g ) and Kauzmann temperature ( T K ) at which configurational entropy equals zero was derived. The ratio T g / T K =e 1/4 was also deduced as a good approximation for a large amount of glassy polymers. The ratio is consistent with the empirical result T g / T K =1.30±8.4%, which was proposed by Adam and Gibbs. The theoretical method presented here was also applied to investigate the compositional variation of glass transition temperatures; equations, which are consistent with experiments, were also derived.

Characterisation of Glass Transition of Durum Wheat Semolina using Modulated Differential Scanning Calorimetry

The glass transition of wheat durum semolina was characterised at different moisture contents using modulated differential scanning calorimetry. The total, reversing and non-reversing heat flows were quantified during heating, cooling and re-heating. An endothermic peak was observed on the non-reversing heat flow during first heating and was not greatly affected by changes in moisture content (below 20 g water/100 g dry matter). This peak was associated with endothermic relaxation of the protein fraction in wheat semolina. An endothermic baseline shift was observed on the reversing heat flow during first heating, cooling and re-heating. The temperature at baseline shift decreased (from 110 °C to 27 °C) when moisture content increased (from 6% to 27% db). The measured heat capacity change (0·10–0·25 J/g/°C) was not significantly affected by moisture content. This endothermic baseline shift was presumed to be the glass transition of amorphous polymers in wheat durum semolina. The plasticising effect of water on the glass transition temperature (Tg) was described using Gordon Taylor and Kwei models and compared with Tg of the main wheat components.

Fine Structure of the Glass Transition in Amorphous Polymers: Slight Shoulder in the Shear H Spectrum at the L Peak

A slight shoulder in the shear relaxation spectrum (H) at the relaxation time for the main maximum of the retardation spectrum (L) was detected for three amorphous polymers : polystyrene, poly(vinyl acetate), and a slightly vulcanized natural rubber. This finding is discussed in terms of a distinctive manifestation of different molecular modes across the glass (main) transition.

The fast relaxation process near the glass transition in amorphous polymers with different microstructure

Inelastic neutron scattering results on polymers with different microstructure and fragility (polybutadiene, polyisoprene, poly(ethylene-propylene) and polyisobutylene) are presented. The experimental results from polybutadiene are briefly reviewed and new data for the fast relaxation process which appears near the glass transition temperature in polyisoprene and poly(ethylene-propylene) are presented. The recent observation that the fast relaxation process is of inelastic nature in polyisobutylene, a weakly fragile glass former, is discussed, and also a correlation between the Boson peak position in the glass and the monomeric friction coefficient in the melt is pointed out. Finally the results in connection with the mode coupling theory and the soft potential model are discussed.

Molecular motion in a blend of poly(vinylphenol) and poly(ethylene oxide) as studied by high-resolution solid-state carbon-13 NMR spectroscopy

Molecular motion in a poly(vinylphenol) (PVPh)/poly(ethylene oxide) (PEO) blend (PVPh/pEO) is studied by examining the temperature dependence of the line width of high-resolution solid-state 13 C NMR spectra. PEO molecules in the crystalline phase undergo motion in the vicinity of room temperature. The motion is governed by an activation energy and correlation time similar to those related to the glass transition of amorphous polymers. For PVPh/PEO, the onset of backbone chain motion of amorphous PEO and PVPh in the blend reflects on the temperature dependence of 13 C line width. The molecular motions of the two polymers in the miscible amorphous phase affect each other strongly although the chain dynamics of the two polymers still have a different characteristic temperature dependence

Determination of the parameters of the relaxation spectrum of polymers from the results of calorimetric measurements

AbstractA method is suggested which allows the determination of a complex of relaxation characteristics describing the process of glass transition of amorphous polymers from the results of calorimetric measurements in one single experiment.

Ultrasonic examination of the dynamic glass transition in amorphous polymers

Ultrasonic measurements were performed at 1 MHz for two amorphous polymers, polybutadiene ( M w = 13 000) and polyphenylmethylsiloxane ( M w = 4100), in order to derive the temperature dependence of the longitudinal moduli components, M′ ( T) and M″ ( T). The results were analyzed in the framework of linear viscoelasticity using the Kohlrausch-Williams-Watts (KWW) relaxation function incorporating the Vogel-Fulcher-Tammann-Hesse equation which describes the temperature dependence of the main relaxation time. The only adjustable parameter was the KWW parameter β. The possibility of a temperature-dependent β-parameter to describe the data was also considered.

Thermal Analysis of Polymers

Thermal analysis embraces a group of analytical methods in which a physical property - e.g. enthalpy, mass, volume or birefringence - is measured as a function of temperature. This paper briefly presents differential scanning calorimetry (DSC), differential thermal analysis (DTA), thermogravimetry (TG), thermal mechanical analysis (TMA) and thermal optical analysis (TOA) as methods and describes in more detail their application on polymers. Examples are presented to demonstrate that the use of these methods and the interpretation of the results obtained requires special attention. The non-equilibrium nature of different polymers is illustrated by the melting and crystallization behaviour of flexible-chain polymers, the glass transition of amorphous polymers and phase transitions in liquid crystalline polymers. The information provided by thermal analysis about the morphology of crystalline polymers, the morphology of polymer blends and the chemical stability of polymers is also discussed.

Physical ageing and glass transition in amorphous polymers as revealed by microhardness

Microhardness (MH) data as a function of temperature for two amorphous polymers [poly(methylmethacrylate) and poly(vinylacetate)] and two semicrystalline polymers [poly(ethyleneterephthalate) and poly(arylether ether ketone)] quenched into the amorphous state are presented. It is shown that MH can conveniently detect the glass transition temperature (T g) for the above mentioned polymers. Molecular rearrangements taking place above and belowT g, such as physical ageing leading to a more compact molecular packing, and thermal expansion can also be followed by means of MH measurements. Finally, the presence of a crystalline phase in these materials has been shown to shift theT g value towards higher temperatures.

Fine structure of the glass transition in amorphous polymers. Part 2. Interpretation of the G″ peak and J″ peak by different molecular motion

AbstractA survey of transition phenomenology in amorphous entangled polymers is presented. Using a general scaling hypothesis characteristic lengths are systematically attached to the different zones of the multiple glass transition. New experimental results show the location of caloric spectra between the peaks of G″ and J″ on the common frequency scale. A fine structure of the main transition is suggested. There are two components: (i) The proper glass transition zone with mode lengths up to 2 nm. This length scale is determined from the caloric spectra. (ii) The hindering zone of cooperative motion of polymer chain segments between entanglement points with mode lengths up to 10 nm.