An upper limit to kinetic fragility in glass-forming liquids

The kinetic fragility of a liquid is correlated to the magnitude of enthalpy hysteresis in various glass-forming materials during thermal cycling across the glass transition. While the lower bound of liquid fragility is well known, there has been little research into the possibility of an inherent upper limit to fragility. In this paper, we present a theoretical argument for the existence of a maximum fragility and show that the correlation between fragility and enthalpy hysteresis allows for an empirical evaluation of the upper limit of fragility. This upper limit occurs as the enthalpy hysteresis involved in thermal cycling about the glass transition approaches zero, leading to m(max)≈175. This result agrees remarkably well with our previous estimate. The dynamics of maximum fragility liquids are discussed, and a critical temperature of ～1.5 T(g) (where T(g) is the glass transition temperature) is revealed where a transition from nonexponential to exponential structural relaxation occurs.     

Gaussian excitations model for glass-former dynamics and thermodynamics

We describe a model for the thermodynamics and dynamics of glass-forming liquids in terms of excitations from an ideal glass state to a Gaussian manifold of configurationally excited states. The quantitative fit of this three parameter model to the experimental data on excess entropy and heat capacity shows that "fragile" behavior, indicated by a sharply rising excess heat capacity as the glass transition is approached from above, occurs in anticipation of a first-order transition--usually hidden below the glass transition--to a "strong" liquid state of low excess entropy. The distinction between fragile and strong behavior of glass formers is traced back to an order of magnitude difference in the Gaussian width of their excitation energies. Simple relations connect the excess heat capacity to the Gaussian width parameter, and the liquid-liquid transition temperature, and strong, testable, predictions concerning the distinct properties of energy landscape for fragile liquids are made. The dynamic model relates relaxation to a hierarchical sequence of excitation events each involving the probability of accumulating sufficient kinetic energy on a separate excitable unit. Super-Arrhenius behavior of the relaxation rates, and the known correlation of kinetic with thermodynamic fragility, both follow from the way the rugged landscape induces fluctuations in the partitioning of energy between vibrational and configurational manifolds. A relation is derived in which the configurational heat capacity, rather than the configurational entropy of the Adam-Gibbs equation, controls the temperature dependence of the relaxation times, and this gives a comparable account of the experimental observations without postulating a divergent length scale. The familiar coincidence of zero mobility and Kauzmann temperatures is obtained as an approximate extrapolation of the theoretical equations. The comparison of the fits to excess thermodynamic properties of laboratory glass formers, and to configurational thermodynamics from simulations, reveals that the major portion of the excitation entropy responsible for fragile behavior resides in the low-frequency vibrational density of states. The thermodynamic transition predicted for fragile liquids emerges from beneath the glass transition in case of laboratory water and the unusual heat capacity behavior observed for this much studied liquid can be closely reproduced by the model.     

Hiking down the energy landscape: progress toward the Kauzmann temperature via vapor deposition

Physical vapor deposition was employed to prepare amorphous samples of indomethacin and 1,3,5-(tris)naphthylbenzene. By depositing onto substrates held somewhat below the glass transition temperature and varying the deposition rate from 15 to 0.2 nm/s, glasses with low enthalpies and exceptional kinetic stability were prepared. Glasses with fictive temperatures that are as much as 40 K lower than those prepared by cooling the liquid can be made by vapor deposition. As compared to an ordinary glass, the most stable vapor-deposited samples moved about 40% toward the bottom of the potential energy landscape for amorphous materials. These results support the hypothesis that enhanced surface mobility allows stable glass formation by vapor deposition. A comparison of the enthalpy content of vapor-deposited glasses with aged glasses was used to evaluate the difference between bulk and surface dynamics for indomethacin; the dynamics in the top few nanometers of the glass are about 7 orders of magnitude faster than those in the bulk at Tg - 20 K.     

Split-step eigenvector-following technique for exploring enthalpy landscapes at absolute zero

The mapping of enthalpy landscapes is complicated by the coupling of particle position and volume coordinates. To address this issue, we have developed a new split-step eigenvector-following technique for locating minima and transition points in an enthalpy landscape at absolute zero. Each iteration is split into two steps in order to independently vary system volume and relative atomic coordinates. A separate Lagrange multiplier is used for each eigendirection in order to provide maximum flexibility in determining step sizes. This technique will be useful for mapping the enthalpy landscapes of bulk systems such as supercooled liquids and glasses.     

Glass transition in an isostatically compressed calcium metaphosphate glass

The authors report an ambient-pressure differential scanning calorimetric study of a calcium metaphosphate glass that has been isostatically compressed slightly above its glass transition temperature and was frozen-in under pressure. It is shown that the enthalpy overshoot of the calorimetric glass transition is enhanced by this treatment. This enhancement is associated with a decrease in the apparent fictive temperature TfA that is determined using the enthalpy-matching approach. The origin of this correlation is discussed.     

A study of enthalpic relaxation of a liquid crystal

A liquid crystal, BL038, which was observed not to crystallize, has a glass transition at 215 K and a nematic to isotropic transition at 380 K. Samples aged below the glass transition at various temperatures T _a, exhibited an endotherm at the transition which developed with extent of ageing time, t _a. We attribute this endotherm to the relaxation of the glass towards the equilibrium liquid. The progress of the relaxation process was measured using differential scanning calorimetry. On subsequent reheating, the aged glass showed an apparent shift in the glass transition to higher temperatures. The endotherm was used to define the extent of enthalpic relaxation and the maximum value observed was found to increase initially then decrease, with the extent of undercooling from the glass transition temperature, Δ T, passing through a maximum for a Δ T = 15 K. From the temperature dependence of the relaxation times, an apparent activation enthalpy for the relaxation process of 85 ± 10 kJ mol^-1 was determined. The small value of the activation enthalpy compared with that found in the ageing of polymers reflects differences in the molecular species involved in relaxation processes.     

The rigid amorphous fraction in semicrystalline macromolecules

The first experimental evidence of the existence of the rigid amorphous fraction (RAF) was reported by Menczel and Wunderlich for several semicrystalline polymers. It was observed that the hysteresis peak at the glass transition was absent when these polymers were heated much faster than they had previously been cooled. In the glass transition behavior of poly(ethylene terephthalate) (PET), the hysteresis peak gradually disappeared as the crystallinity increased. At the same time, it was noted that the ΔC _p of higher crystallinity PET samples was much smaller than could be expected on the basis of the crystallinity calculated from the heat of fusion. It was also observed that this behavior was not unique to PET only, but is characteristic of most semicrystalline polymers: the sum of the crystallinity calculated from the heat of fusion and the amorphous content calculated from the ΔC _p at the glass transition is much less than 100% (a typical difference is ~20–30%). This 20–30% difference was attributed to the existence of the “RAF”. The presence of the RAF also affected the unfreezing behavior of the “mobile (or traditional) amorphous fraction.” As a consequence, the phenomenon of the enthalpy relaxation diminished with increasing rigid amorphous content. It was suggested that the disappearance of the enthalpy relaxation was caused by the disappearance or drastic decrease of the time dependence of the glass transition. To check the validity of this suggestion, the glass transition had to be also measured on cooling in order to overlay it on the DSC curves measured on heating. However, before this overlaying work could be accomplished, the exact temperatures on cooling had to be determined since the temperature of the DSC instruments that time could not be calibrated on cooling using the usual low molecular weight standards due to the common phenomenon of supercooling. Therefore, a temperature calibration method needed to be developed for cooling DSC experiments utilizing high purity liquid crystals using the isotropic → nematic, the isotropic → cholesteric, and other liquid crystal → liquid crystal transitions. After the cooling calibration was accomplished, the cooling glass transition experiments indicated that the glass transition in semicrystalline polymers is not completely time independent, because its width depends on the ramp rate. However, it was shown that the time dependence is drastically reduced, and the midpoint of the glass transition seems to be constant which can explain the absence of the enthalpy relaxation. The work presented here has led to a number of studies showing the universality of the rigid amorphous phase for semicrystalline polymers as well as an ASTM standard for DSC cooling calibration.     

Heat capacity and glass transition of ethylene oxide clathrate hydrate

The heat capacity of structure I ethylene oxide clathrate hydrate EO-6.86 H₂O was measured in the temperature range 6–300 K with an adiabatic calorimeter. The temperature and enthalpy of congruent melting were determined to be (284.11 ± 0.02) K and 48.26 kJ mol^–1, respectively. A glass transition related to the proton configurational mode in the hydrogen-bonded host was observed around 90 K. This glass transition was similar to the one observed previously for the structure II tetrahydrofuran hydrate but showed a wider distribution of relaxation times. The anomalous heat capacity and activation enthalpy associated with the glass transition were almost the same as those for THF-hydrate.Dedicated to Dr D. W. Davidson in honor of his great contributions to the sciences of inclusion phenomena.Author for correspondence.     

不同结晶度的乙二醇及其水溶液玻璃化转变与焓松弛

为了考察晶体成分对无定形成分玻璃化转变和结构松弛行为的影响,利用差示扫描量热法(DSC),结合低温显微技术,研究了乙二醇(EG)及其50％水溶液在不同结晶度时的玻璃化转变和焓松弛行为.采用等温结晶方法控制骤冷的部分结晶玻璃体中的晶体份额.DSC结果表明,对于部分结晶的EG,只有单一的玻璃化转变过程,而对于50％EG,当结晶度不同时,不同程度地表现出两次玻璃化转变（无定形相Ⅰ和无定形相Ⅱ）.相Ⅰ的玻璃化转变温度和完全无定形态的含水EG的玻璃化转变温度相一致;相Ⅱ的玻璃化转变温度要比此温度约高6 ℃.低温显微观察结果印证了DSC实验结果.DSC等温退火的实验和KWW(Kohlrausch-Williams-Watts)衰变函数分析结果表明,EG无定形和50％EG中的两种无定形有不同的焓松弛行为.     

Glass transition and enthalpy relaxation of ethylene glycol and its aqueous solution

Differential scanning calorimetry (DSC) and cryomicroscopy were employed to investigate the glass transition and enthalpy relaxation behaviors of ethylene glycol (EG) and its aqueous solution (50% EG) with different crystallization percent. Isothermal crystallization method was used in devitrification region to get different crystallinity after samples quenched below glass transition temperature. The DSC thermograms upon warming showed that the pure EG has a single glass transition, while the 50% EG solution has two if the solution crystallized partially. It is believed that the lower temperature transition represents the glass transition of bulk amorphous phase of EG aqueous solution glass state, while the higher one is related to ice inclusions, whose mobility is restricted by ice crystal. Cryomicroscopic observation indicated that the EG crystal has regular shape while the ice crystal in 50% EG aqueous solution glass matrix has no regular surface. Isothermal annealing experiments at temperatures lower than T_g were also conducted on these amorphous samples in DSC, and the results showed that both the two amorphous phases presented in 50% EG experience enthalpy relaxation. The relaxation process of restricted amorphous phase is more sensitive to annealing temperature.     

Freezing-in and production of entropy in vitrification

Following the classical concepts developed by Simon [Z. Anorg. Allg. Chem. 203, 219 (1931)], vitrification in the cooling of glass-forming melts is commonly interpreted as the transformation of a thermodynamically (meta)stable equilibrium system into a frozen-in, thermodynamically nonequilibrium system, the glass. Hereby it is assumed that the transformation takes place at some well-defined sharp temperature, the glass transition temperature Tg. However, a more detailed experimental and theoretical analysis shows that the transition to a glass proceeds in a broader temperature range, where the characteristic times of change of temperature, tauT=-(TT), and relaxation times, tau, of the system to the respective equilibrium states are of similar order of magnitude. In this transition interval, the interplay of relaxation and change of external control parameters determines the value of the structural order parameters. In addition, irreversible processes take place in the transition interval, resulting both in an entropy freezing-in as well as in an irreversible increase of entropy and, as a result, in significant changes of all other thermodynamic parameters of the vitrifying systems. The effect of entropy production on glass transition and on the properties of glasses is analyzed here for the first time. In this analysis, the structural order-parameter concept as developed by de Donder and van Rysselberghe [Thermodynamic Theory of Affinity (Stanford University Press, Stanford, 1936)] and Prigogine and Defay [Chemical Thermodynamics (Longmans, London, 1954)] is employed. In the framework of this approach we obtain general expressions for the thermodynamic properties of vitrifying systems such as heat capacity, enthalpy, entropy, and Gibbs' free energy, and for the entropy production. As one of the general conclusions we show that entropy production has a single maximum upon cooling and two maxima upon heating in the glass transition interval. The theoretical concepts developed allow us to explain in addition to the thermodynamic parameters also specific features of the kinetic parameters of glass-forming melts such as the viscosity. Experimental results are presented which confirm the theoretical conclusions. Further experiments are suggested, allowing one to test several additional predictions of the theory.     

Physical ageing in poly(vinyl acetate) 1. Enthalpy relaxation

The enthalpy changes ΔH_∞ between a poly(vinyl acetate) glass formed by rapid cooling and the corresponding fully relaxed glass have been estimated at four temperatures below the glass transition. The values obtained were different to those expected by extrapolating liquid behavior below the glass transition and were found to agree well with the predictions of a simple expression for the combined main chain conformational and free volume contributions to enthalpy. Conformational contributions from the side chain alone were also considered but were not required to obtain agreement with experiment. It can be concluded that the side chains remained mobile below the glass transition and do not contribute to the heat capacity discontinuity at T_g. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1107–1116, 1997     

A lattice model of vitrification and gelation

In this work we introduce a simple lattice model with T-shaped molecules in two dimensions that exhibits a rich range of morphological behaviors. Depending on the volume fraction and quench path, this system can adopt uniform liquid, solution, and phase-separated states, as well as inhomogeneous glass or gel-like states, as revealed by dynamic mean-field simulations. An important characteristic of this system is the existence of a large number of degenerate low-energy states with small barriers that leads to a broad, kinetically explored landscape. The mean-field stability and phase diagram of this model is constructed and provides a useful guide for understanding the complex behaviors of the system. One striking feature is that there is a cascade of instabilities that converge to mark the onset of what we identify as the glass transition. Both dynamic mean-field and Monte Carlo simulations reveal glass-like relaxation dynamics. Our results lead to a picture of gelation as a continuation of the glass transition into the two-phase region, or equivalently, as an incomplete phase separation arrested by the onset of the glass transition.     

Enthalpy relaxation of an epoxy–anhydride resin by temperature‐modulated differential scanning calorimetry

The enthalpy relaxation of an epoxy–anhydride resin was studied by physical aging and frequency‐dependence experiments with alternating differential scanning calorimetry (ADSC), which is a temperature‐modulated differential scanning calorimetry technique. The samples were aged at 80 °C, about 26 K below the glass‐transition temperature, for periods up to 3800 h and then scanned under the following modulation conditions: underlying heating rate of 1 K min⁻¹, amplitude of 0.5 K, and period of 1 min. The enthalpy loss was calculated by the total heat‐flow signal, and its variation with the log (aging time) gives a relaxation rate (per decade), this value being in good agreement with that calculated by conventional DSC. The enthalpy loss was also analyzed in terms of the nonreversing heat flow, revealing that this property is not suitable for calculating enthalpy loss. The effect of aging on the modulus of the complex heat capacity, |Cp*|, is shown by a sharper variation on the low side of the glass transition and an increase in the inflexional slope of |Cp*|. Likewise, the phase angle also becomes sharper in the low‐temperature side of the relaxation. The area under the corrected out‐phase heat capacity remains fairly constant with aging. The dependence of the dynamic glass transition, measured at the midpoint of the variation of |Cp*|, on ln(frequency) allows one to determine an apparent activation energy, Δh*, which gives information about the temperature dependence of the relaxation times in equilibrium over a range close to the glass transition. The values of Δh*, determined from ADSC experiments in a range of frequencies between 4.2 and 33 mHz and at an amplitude of 0.5 K, and an underlying heating rate of 1 K min⁻¹, were analyzed and compared with that obtained by conventional DSC from the dependence of the fictive temperature on the cooling rate. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2272–2284, 2000     

Thermal behaviour of some sugar alcohols

The glass transition of isomalt and its components, the enthalpy of solution (crystalline state, glassy state) and the enthalpy of melting are reported. From the measured data (solution enthalpy, enthalpy of fusion and heat capacities) a cycle like the BORN-HABER cycle can be constructed. It is possible to calculate the amounts of amorphous isomalt from measured solution enthalpies; however, the values obtained do not agree with those provided by X-ray powder diffraction studies.This study was supported by Südzucker AG, Mannheim/Ochsenfurt. We thank Dr. M. Kunz and G. Witte of Südzucker AG for discussions.