Extension of the Angell Fragility Concept

Interplay of intermolecular interactions and flexibility to mediate glass forming ability and fragility: A study of chemical analogs

We have investigated the enthalpic and dielectric relaxations of four groups of quinoline analogs having similar structural properties (i.e., rigidity, stiffness, and bulkiness) but a different steric character and the nature of intermolecular interactions and flexibility. The dielectric fragility index (m_d) and the enthalpic one (m_H), determined by the Tool-Narayanaswamy-Moynihan-Hodge formalism, are comparable. Generally, for the four sets of molecules of similar structures, both the interactions and flexibility are found to be critical in making the large span of fragility (i.e., from 59 to 131) and glass forming ability. By contrast, individual impacts of the interaction and flexibility can only explain fragility partly among each group of isomers. We found that the molecules with high fragility are of relatively low liquid density, reflecting the joint impact of the interactions and flexibility. An interesting result is observed among the isomers that the molecules which are fragile have enhanced glass forming ability. The results are unveiling the joint impacts of molecular structure (flexibility) and intermolecular interaction on the molecular dynamics.

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.

Understanding fragility in supercooled Lennard-Jones mixtures. II. Potential energy surface

The connection between isobaric fragility and the properties of high-order stationary points of the potential energy surface in different supercooled Lennard-Jones mixtures was investigated. The increase of effective activation energies upon supercooling appears to be driven by the increase of average potential energy barriers measured by the energy dependence of the fraction of unstable modes. Such an increase is sharper, the more fragile the mixture. Correlations between fragility and other properties of high-order stationary points, including the vibrational density of states and the localization features of unstable modes, are also discussed.

Glass Transition Dynamics and Boiling Temperatures of Molecular Liquids and Their Isomers

The relation between a dynamic and a thermodynamic temperature, glass transition Tg and boiling point Tb, is investigated for various glass-forming liquids, with emphasis on monohydroxy alcohols. As is well known, Tb and Tg are positively correlated across a large variety of liquids. However, we found that the same quantities show a negative correlation within an isomeric series, i.e., Tb decreases with increasing Tg for different isomers of the same chemical formula. For the alcohol series, CnH2n+1OH with 3 < or = n < or = 10, a master curve of the negative Tg - Tb correlation is obtained if the temperatures are normalized to the respective values of the n-alkanols. This Tg - Tb dependence of isomeric liquids is linked to entropic effects and responsible for much of the scatter of the correlation observed for a large number of molecular organic glass-formers with 45 < Tg < 250 K. Dielectric relaxation is measured for three groups of isomers: (a) 3-methoxyl-1-butanol and 2-iso-propoxyethanol, (b) 1,4-, 1,2-, and 2,4-pentanediol, and (c) di-n- and di-iso-butyl phthalate. Two key parameters of the dynamics, fragility m and stretching exponent beta, are found to be indistinguishable within isomers of moderately different Tgs. Larger fragility differences are readily expected with pronounced structural change, but no systematic trend is observed within an isomer series. The results provide a useful tool for assessing Tg, m, and beta for marginal glass formers on the basis of their isomers.

On the mechanism of reorientational and structural relaxation in supercooled liquids: the role of border dynamics and cooperativity

Molecular dynamics simulation and analysis based upon the many-body potential energy landscape (PEL) are employed to characterize single molecule reorientation and structural relaxation, and their interrelation, in deeply supercooled liquid CS(2). The rotational mechanism changes from small-step Debye diffusion to sudden large angle reorientation (SLAR) as the temperature falls below the mode-coupling temperature T(c). The onset of SLAR is explained in terms of the PEL; it is an essential feature of low-T rotational dynamics, along with the related phenomena of dynamic heterogeneity and the bifurcation of slow and fast relaxation processes. A long trajectory in which the system is initially trapped in a low energy local minimum, and eventually escapes, is followed in detail, both on the PEL and in real space. During the trapped period, "return" dynamics occurs, always leading back to the trap. Structural relaxation is identified with irreversible escape to a new trap. These processes lead to weak and strong SLAR, respectively; strong SLAR is a clear signal of structural relaxation. Return dynamics involves small groups of two to four molecules, while a string-like structure composed of all the active groups participates in the escape. It is proposed that, rather than simple, nearly instantaneous, one-dimensional barrier crossings, relaxation involves activation of the system to the complex, multidimensional region on the borders of the basins of attraction of the minima for an extended period.

Distinct Difference in Ionic Transport Behavior in Polymer Electrolytes Depending on the Matrix Polymers and Incorporated Salts

Two different electrolyte salts, lithium bis(trifluoromethanesulfonyl)imide (LiTFSI), and a room temperature ionic liquid, 1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide (EMITFSI), were incorporated into network polymers to obtain ion-conductive polymer electrolytes. Network polymers of poly(ethylene oxide-co-propylene oxide) (P(EO/PO)) and poly(methyl methacrylate) (PMMA) were chosen as matrixes for LiTFSI and EMITFSI, respectively. Both of the polymer electrolytes were single-phase materials and were completely amorphous. Ionic conductivity of the polymer electrolytes was measured over a wide temperature range, with the lowest temperatures close to or below the glass transition temperatures (Tg). The Arrhenius plots of the conductivity for both of the systems exhibited positively curved profiles and could be well fit to the Vogel-Tamman-Fulcher (VTF) equation. The conductivity of the PMMA/EMITFSI electrolytes was higher at most by 3 orders of magnitude than that of the LiTFSI/P(EO/ PO) electrolytes at ambient temperature. When the ideal glass transition temperature, T0 (one of the VTF fitting parameters), was compared with the Tg, a difference in the ionic conduction was apparent in these systems. In the P(EO/PO)/LiTFSI electrolytes, the T0 and Tg increased in parallel with salt concentration and the T0 was lower than the Tg by ca. 50 degrees C. On the contrary, the difference between the T0 and the Tg increased with increasing content of PMMA in the PMMA/EMITFSI electrolytes, with the observed difference in the concentration range studied reaching up to ca. 100 degrees C. The conductivity at the Tg, sigma(Tg), for the LiTFSI/P(EO/PO) electrolytes was on the order of 10(-14-)10(-13) S cm(-1) and increased with increasing salt concentration, whereas that for the PMMA/EMITFSI polymer electrolytes reached 10(-7) S cm(-1) when the concentration of PMMA was high. The ion transport mechanism was discussed in terms of the concepts of coupling/decoupling and strong/fragile for the two different polymer electrolytes.

Landscapes and fragilities

The concept of fragility provides a possibility to rank different supercooled liquids on the basis of the temperature dependence of dynamic and/or thermodynamic quantities. We recall here the definitions of kinetic and thermodynamic fragility proposed in the last years and discuss their interrelations. At the same time we analyze some recently introduced models for the statistical properties of the potential energy landscape. Building on the Adam-Gibbs relation, which connects structural relaxation times to configurational entropy, we analyze the relation between statistical properties of the landscape and fragility. We call attention to the fact that the knowledge of number, energy depth, and shape of the basins of the potential energy landscape may not be sufficient for predicting fragility. Finally, we discuss two different possibilities for generating strong behavior.

Disentangling density and temperature effects in the viscous slowing down of glassforming liquids

We present a consistent picture of the respective role of density (rho) and temperature (T) in the viscous slowing down of glassforming liquids and polymers. Specifically, based in part upon a new analysis of simulation and experimental data on liquid ortho-terphenyl, we conclude that a zeroth-order description of the approach to the glass transition (in the range of experimentally accessible pressures) should be formulated in terms of a temperature-driven super-Arrhenius activated behavior rather than a density-driven congestion or jamming phenomenon. The density plays a role at a quantitative level, but its effect on the viscosity and the alpha-relaxation time can be simply described via a single parameter, an effective interaction energy that is characteristic of the high-T liquid regime; as a result, rho does not affect the "fragility" of the glassforming system.

Evaluation of glassy-state dynamics from the width of the glass transition: Results from theoretical simulation of differential scanning calorimetry and comparisons with experiment

The purpose of this study is to investigate the quantitative relationship between the width of the glass transition, DeltaTg, and glass fragility or activation energy for structural relaxation. The ultimate objective is the estimation of structural relaxation time as a function of temperature from the width of the glass transition region, allowing characterization of glass dynamics by a single simple measurement. The Moynihan correlation indicates that activation energy for structural relaxation should be inversely proportional to the width of the glass transition, but recent experimental studies suggest this relationship is a poor approximation for glasses of pharmaceutical interest. The present study is an effort to better understand the validity of the Moynihan correlation by selected experimental studies and a theoretical analysis of those factors that impact the glass transition width. Experimental data for glass transition widths for (poly)vinylpyrrolidone, sucrose, and trehalose are obtained using a variety of procedures, and relaxation time data are obtained using the thermal activity monitor. The theoretical analysis begins by simulating the temperature dependence of the heat capacity by breaking the cooling and heating scans into a large number of temperature steps followed by isothermal holds, during which relaxation of the material is calculated. Here, the modified VTF equation is used for relaxation time and the generalized Kohlraush-Williams-Watts stretched exponential function is used to describe the relaxation kinetics. Simulations are performed for materials of varying fragility and varying "stretched exponential" constants, beta, and the width of the glass transition region, DeltaTg, is evaluated from the simulated heat capacity versus temperature curves as one would do with experimental data. Agreement between the theoretical simulations and experimental DeltaTg data is excellent. The simulations demonstrate that although the Moynihan correlation is not valid for variable beta, a modification of the Moynihan correlation which includes variation in beta is a good approximation. Thus, an estimate of fragility may be obtained from glass transition width data provided an estimate of beta is available. Furthermore, it is shown that a first approximation for beta may be obtained from the magnitude (i.e., height) of the differential scanning calorimetry thermal overshoot. We also find that using the modified VTF equation to evaluate the temperature dependence of the structural relaxation time at the glass transition, and integrating this expression to lower temperatures, it is possible to obtain an evaluation of the relaxation time constant, tau(beta), in the glass at any temperature, using only the DeltaTg and beta values obtained from a single differential scanning calorimetry scan. These estimated time constants correlate very well with the values directly measured with the thermal activity monitor.

Random energy model for dynamics in supercooled liquids: N dependence

The random energy model (REM) for the critical points (saddles and minima) of the potential energy landscape of liquids is further developed. While thermodynamic properties may be calculated from the unconditional distribution of states G(E), dynamics requires the distribution G(c)(E';E) of energies E' of neighbors connected to a state with energy E. Previously it was shown [T. Keyes, Phys. Rev. E 62, 7905 (2000)] that an uncorrelated REM, G(c)(E';E)=G(E'), is badly behaved in the thermodynamic limit N--> infinity. In the following, a simple expression is obtained for G(c)(E';E), which leads to reasonable N dependences. Results are obtained for the fraction f(u) of imaginary-frequency instantaneous normal modes, the configuration entropy S(c), the distributions of the different-order critical points, and the rate R of escape from a state. Simulation data on f(u)(T) and the density of minima rho(0)(E) in Lennard-Jones and CS2 are fit with the theory, allowing a determination of some model parameters. A universal scaling form for f(u), and a consequent scheme for calculating the mode-coupling temperature T(c) consistently among different materials, is demonstrated. The dependence of the self-diffusion constant D upon R and f(u) is discussed, with the conclusion that D proportional, variant f(u) in deeply supercooled states. The phenomenology of fragile supercooled liquids is interpreted. It is shown that the REM need not have a Kauzmann transition in the relevant temperature range, i.e., above the glass transition.