A simple model of entropy relaxation for explaining effective activation energy behavior below the glass transition temperature

Strong changes in relaxation rates observed at the glass transition region are frequently explained in terms of a physical singularity of the molecular motions. We show that the unexpected trends and values for activation energy and preexponential factor of the relaxation time tau, obtained at the glass transition from the analysis of the thermally stimulated current signal, result from the use of the Arrhenius law for treating the experimental data obtained in nonstationary experimental conditions. We then demonstrate that a simple model of structural relaxation based on a time dependent configurational entropy and Adam-Gibbs relaxation time is sufficient to explain the experimental behavior, without invoking a kinetic singularity at the glass transition region. The pronounced variation of the effective activation energy appears as a dynamic signature of entropy relaxation that governs the change of relaxation time in nonstationary conditions. A connection is demonstrated between the peak of apparent activation energy measured in nonequilibrium dielectric techniques, with the overshoot of the dynamic specific heat that is obtained in calorimetry techniques.     

Unveiling the impact of regioisomerism defects in the glass transition temperature of PVDF by the mean of the activation energy

Alternating two groups, CH₂ and CF₂, of very different polarities along the backbone chain of polyvinylidene fluoride (PVDF) leads to very interesting properties, such as ferroelectricity. However, these properties are affected by the presence of regioisomerism defects (monomer inversion) that appear during the synthesis. In this study, the influence of these defects on the glass transition temperature (T _g) is regarded. Using molecular simulation, we investigated their plasticizer effect. To highlight their role in modifying polymer chain relaxation, the activation energy (E _a) related with conformational transitions is computed. We show that a clear linear relationship can be established between E _a and T _g. E _a is then separated into different contributions associated with each type of bond. Mobility of individual segments can thus be accounted separately from the mobility of the whole chain. As a consequence, T _g of the alternate copolymer ethylene‐tetrafluoroethylene (E‐TFE), an isomeric polymer of PVDF, can be deduced. T _g of this copolymer is still source of discussion in the literature. The resulting value, ?97 °C, is found in good agreement with some experimental data, and also with T _g extracted from simulated dilatometry. Consequently, local mobility of a polymer chain can be retrieved from the whole mobility, and vice versa. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55 , 419–426     

Reorganization energy of electron transfer in viscous solvents above the glass transition

We present a molecular-dynamics study of the solvent reorganization energy of electron transfer in supercooled water. We observe a sharp decrease of the reorganization energy at a temperature identified as the temperature of structural arrest due to cage effect as discussed by the mode coupling theory. Both the heat capacity and dielectric susceptibility of the pure water show sharp drops at about the same temperature. This temperature also marks the onset of the enhancement of translational diffusion relative to rotational relaxation signaling the breakdown of the Stokes-Einstein relation. The change in the reorganization energy at the transition temperature reflects the dynamical arrest of the slow, collective relaxation of the solvent related to Debye relaxation of the solvent dipolar polarization.     

The glass transition

This work deals with a comparison of data obtained from differential scanning calorimetry (DSC) and thermally stimulated depolarization current (TSDC) investigations. Measurements were performed on various poly(ethylene terephthalate) films: a wholly amorphous, a thermally crystallized and drawn samples. For each specimen, the TSDC complex spectra, resolved into elementary ones, led to the determination of the classical compensation temperature (T _c ). The glass transition temperature (T _g) and the fictive equilibrium temperature (T _f) were determined by means of DSC. It appears thatT _c is different fromT _g and very close toT _f.     

A novel temperature‐step method to determine the glass transition temperature of ultrathin polymer films by liquid dewetting

A novel temperature‐step experimental method that extends the Bodiguel‐Fretigny liquid dewetting method of investigating polymer thin films is described and results presented from an investigation of thickness effects on the glass transition temperature (T_g) of ultrathin polystyrene (PS) films. Unlike most other methods of thin film investigation, this procedure promises a rapid screening tool to determine the overall profile of T_g versus film thickness for ultrathin polymer films using a limited number of samples. Similar to our prior observations and other literature data, with this new method obvious T_g depression was observed for PS thin films dewetting on both glycerol and an ionic liquid. The results for PS dewetting on the two different liquids are similar indicating only modest effects of the substrate on the T_g‐film thickness relationship. In both instances, the T_g depression is somewhat less than for similar PSs supported on silicon substrates reported in the literature. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013 , 51, 1343–1349     

Thermodynamics of the glass transition

A thermodynamic analysis of the glass transition in polymers is presented, which predicts, with a minimum of assumptions, three of the four inequalities which have consistently been observed experimentally: i.e., that specific heat and isothermal compressibility of the glass are lower than those of the rubber, and that the Prigogine-Defay ratio is larger than unity. The analysis cannot predict the fact that the thermal expansion coefficient of the glass is also lower than that of the rubber, and indeed the converse situation is not a thermodynamic impossibility.     

How to determine high growth speeds in polymer crystallization

With the fast crystallizing polymers HDPE and i-PP it is extremely difficult to extend the range of measurements of the growth speed of spherulites to temperatures as low as 80 °C. So far the lower limit for these measurements has been about 120 °C for both polymers. Several possibilities for this kind of measurements are explored in the present paper. It appears that none of these measurements is without uncertainties. So, only the comparison of results, as obtained with several independent measurements and with theory furnishes a sufficient credibility. Optical measurements, from light scattering to visual inspection, all under very special conditions of heat transfer, are described.Dedicated to Prof. Dr. D.W. van Krevelen, Arnhem     

Thermal jump measurement of the activation energy of trapped electrons in 3-methylpentane glass

When the temperature of a photoionized TMPD-3MP glassy solution is suddenly raised from 77 K to 77 K + ΔT (ΔT ～ 1 K), the recombination luminescence is enhanced, goes through a broad maximum and starts decaying. This is interpreted in terms of glass relaxation on warming. By means of a formally described model, the activation energy for electron detrapping is found to be 0.65 eV. In our opinion this large value indicates that electron detrapping is due to slow molecular rearrangements in the matrix.     

Analysis of carbon in archaeological glass and pottery by low energy deuteron activation technique

Journal of Radioanalytical and Nuclear Chemistry - Carbon in archaeological glass and pottery is determined in a simple and elegant way by deuteron activation based on C-12(d,n)N-13 nuclear...     

A contribution to the theory of the structural glass transition

The equations characterizing the temperature dependence of the mobility of molecules in the glass transition region are compared and analysed. A relationship between the parameters of the relaxation theory of the glass transition and the concept of free volume is established. The Williams-Landel-Ferry equation is treated in terms of the relaxation theory of glass transition.     

Local dynamics and glass transition

The dynamics of polymer chains in the bulk state are discussed at three different temperature scales: (i) Well above the glass transition temperature where the basic step of motion is the rotameric transition of bonds. In this regime, the dynamics may conveniently be analyzed by the rotational isomeric state model, (ii) In the vicinity of glass transition where friction forces from the environment dominate. In this regime, the dynamics may be modeled according to the cooperative kinematics model, (iii) Well below glass transition. Here, an analogy with a native protein is made, and the mean-squared fluctuations are analyzed by adopting the Gaussian Network Model, which recently proved successful in describing fluctuations in native proteins.     

Characteristic length of the glass transition

The definition of molecular cooperativity is discussed. The characteristic length of the glass transition describes the size of this cooperativity. Differential scanning calorimetry (DSC) and heat capacity spectroscopy (HCS) results of a series of poly(n-alkyl methacrylates) (alkyl = methyl, ethyl, propyl, butyl, pentyl, hexyl, and octyl) and a series of statistical copolymers poly(n-butylmethacrylate-stat-styrene) are discussed in terms of molecular cooperativity in the αβ splitting region, where a high-frequency dispersion zone a splits off into the main transition zone α and a Goldstein Johari process β at lower frequencies. The characteristic length tends to small values of order one monomer diameter in the splitting region for scenarios with an α relaxation onset. The statements about the size scale of cooperativity are conditional upon certain assumptions leading to the equation used for calculation of this size from HCS and DSC data. The step height of heat capacity (Δc_p) and, with less certainty, the square root of the cooperativity volume or number (V^1/2_α or ^1/2_α) are proportional to the temperature distance from the cooperativity onset, T = T_ons. © 1996 John Wiley & Sons, Inc.     

Determination of the glass transition temperature

The definition of the glass transition temperature, T _g, is recalled and its experimental determination by various techniques is reviewed. The diversity of values of T _g obtained by the different methods is discussed, with particular attention being paid to Differential Scanning Calorimetry (DSC) and to dynamic techniques such as Dynamic Mechanical Thermal Analysis (DMTA) and Temperature Modulated DSC (TMDSC). This last technique, TMDSC, in particular, is considered in respect of ways in which the heterogeneity of the glass transformation process can be quantified.     

The glass transition temperature of polystyrene

A round robin test was performed to determine the reliability of values for the glass transition temperatureT _g as determined by DTA on polymers. Ten different instruments were involved. The test material was high molecular weight polystyrene. Values forT _g (midpoint) were reported in the range 107°C±2 K. The respective heat flow curves differed considerably in shape. In the literature aT _g of 100°C is often given for polystyrene. The discrepancy between this value and the value of 107°C found in the round robin test is due to three differences: the thermal history of the sample, the evaluation of the heat flow curves, and the effect of finite sample size.     

Study of the effective phase transition activation energy in K2SeO4 crystals

The high-temperature phase transition of K₂SeO₄ was studied by using differential thermal analysis. The Kissinger equation and the Mahadevan approximation were applied to evaluate the effective phase transition activation energy (E). The average value ofE was 12.85 ±0.04 eV.

---

Zusammenfassung Mittels DTA wurde die Hochtemperatur-Phasenumwandlung von K₂SeO₄ untersucht. Für die Ermittlung der effektiven Aktivierungsenergie der Phasenumwandlung (E) wurde die Kissinger-Gleichung und die Mahadevan-NÄherung angewendet. Der mittlere Wert fürE betrug 12.85±0.04 eV.

---

---

This work was partly supported by a Grant-in-Aid for Scientific Research from the Deutsche Gesellschaft für Technische Zusammenarbeit (GTZ) and DAAD, Germany.