Relationship between kinetics and thermodynamics of supercooled liquids

Effect of intermolecular hydrogen bonding strength on the dynamic fragility of amorphous polyamides

Small-molecular-induced intermolecular hydrogen bonding (inter-HB) interactions were reported to increase the glass transition temperature (Tg) while decrease the dynamic fragility (m) of polymers. Herein, enthalpy relaxation parameters heat capacity jump (ΔCp) at Tg and enthalpy hysteresis (ΔHR) were investigated to help clarify the effect of macromolecular-induced inter-HB on Tg and m using amorphous polyamides as model polymers. The inter-HB strength was weakened by random copolymerization with varied chain rigidity, but was enhanced by decreasing steric hindrance. It was found that Tg and m increased after copolymerization due to the increased chain rigidity. Nevertheless, increasing steric hindrance leads to an increased Tg while anomalously reduced m. Further results found that m can be well correlated to Tg·ΔCp/ΔHR. ΔCp increases more significantly than ΔHR in co-polyamides, and thus the entropy change dominates the activation free energy of cooperative rearrangement. By contrast, ΔHR increases more significantly than ΔCp with increasing steric hindrance, and thus it is reasonable that Tg increases while m decreases. Most importantly, ΔCp and ΔHR decrease with increasing inter-HB strength regardless of the variation of Tg. These results indicate that the inter-HB strength may be very strong and insensitive to temperature in polyamides, thus behaving like physical cross-linking.

Temperature Dependence of Structural Relaxation in Glass-Forming Liquids and Polymers

Understanding the microscopic mechanism of the transition of glass remains one of the most challenging topics in Condensed Matter Physics. What controls the sharp slowing down of molecular motion upon approaching the glass transition temperature T_g, whether there is an underlying thermodynamic transition at some finite temperature below T_g, what the role of cooperativity and heterogeneity are, and many other questions continue to be topics of active discussions. This review focuses on the mechanisms that control the steepness of the temperature dependence of structural relaxation (fragility) in glass-forming liquids. We present a brief overview of the basic theoretical models and their experimental tests, analyzing their predictions for fragility and emphasizing the successes and failures of the models. Special attention is focused on the connection of fast dynamics on picosecond time scales to the behavior of structural relaxation on much longer time scales. A separate section discusses the specific case of polymeric glass-forming liquids, which usually have extremely high fragility. We emphasize the apparent difference between the glass transitions in polymers and small molecules. We also discuss the possible role of quantum effects in the glass transition of light molecules and highlight the recent discovery of the unusually low fragility of water. At the end, we formulate the major challenges and questions remaining in this field.

Fluctuation Effects in the Adam-Gibbs Model of Cooperative Relaxation

A generalization of the Adam-Gibbs model of relaxation in glass-forming liquids is formulated that takes into account fluctuation in the number of molecules inside the cooperative region. The configurational fraction links the excess entropy with kinetic properties described in the Adam-Gibbs model. We express the configurational fraction at the glass-transition temperature in terms of the width of the distribution of relaxation times, the nonlinearity parameter that demarcates the variations of the relaxation time with structure and temperature, the steepness index that is proportional to the slope of the logarithm of the relaxation time with respect to temperature, the excess heat capacity under constant pressure, and the number of correlated molecules or structural units. The configurational fraction in the absence of fluctuation effects is also determined for several glass-forming liquids at the glass-transition temperature.

Dynamics and thermodynamics of polymer glasses

The fate of matter when decreasing the temperature at constant pressure is that of passing from gas to liquid and, subsequently, from liquid to crystal. However, a class of materials can exist in an amorphous phase below the melting temperature. On cooling such materials, a glass is formed; that is, a material with the rigidity of a solid but exhibiting no long-range order. The study of the thermodynamics and dynamics of glass-forming systems is the subject of continuous research. Within the wide variety of glass formers, an important sub-class is represented by glass forming polymers. The presence of chain connectivity and, in some cases, conformational disorder are unfavourable factors from the point of view of crystallization. Furthermore, many of them, such as amorphous thermoplastics, thermosets and rubbers, are widely employed in many applications. In this review, the peculiarities of the thermodynamics and dynamics of glass-forming polymers are discussed, with particular emphasis on those topics currently the subject of debate. In particular, the following aspects will be reviewed in the present work: (i) the connection between the pronounced slowing down of glassy dynamics on cooling towards the glass transition temperature (Tg) and the thermodynamics; and, (ii) the fate of the dynamics and thermodynamics below Tg. Both aspects are reviewed in light of the possible presence of a singularity at a finite temperature with diverging relaxation time and zero configurational entropy. In this context, the specificity of glass-forming polymers is emphasized.

Two factors governing fragility: stretching exponent and configurational entropy

We derive an analytical expression showing that the fragility of a supercooled liquid is a result of (i) a thermodynamic term depending on change in configurational entropy and (ii) a kinetic term depending on change in the nonexponentiality or "stretching" of the relaxation function, as quantified by the exponent beta of the Kohlrausch-Williams-Watts (KWW) relaxation function. Our expression indicates that there is not a direct correlation between the non-Arrhenius scaling of liquid viscosity and the nonexponential nature of glassy relaxation. Rather, the temperature dependence of the stretching exponent beta provides a lower limit for fragility, which can be increased through changes in the configurational entropy. Our result explains the apparent contradiction between those researchers showing a correlation between beta and fragility and those who question such a correlation due to the spread of the data.

What Can We Learn by Squeezing a Liquid?

Relaxation times tau(T,upsilon) for different temperatures, T, and specific volumes, upsilon, collapse to a master curve vs Tupsilon(gamma), with gamma a material constant. The isochoric fragility, mV, is also a material constant, inversely correlated with gamma. From these experimental facts, we obtain a three-parameter function that accurately fits tau(T,upsilon) data for several glass-formers over the supercooled regime, without any divergence of tau below Tg. Although the values of the three parameters depend on the material, only gamma significantly varies; thus, by normalizing material-specific quantities related to gamma, a universal power law for the dynamics is obtained.

A thermodynamic approach to the fragility of glass-forming polymers

We have connected the dynamic fragility, namely, the steepness of the relaxation-time variation upon temperature reduction, to the excess entropy and heat capacity of a large number of glass-forming polymers. The connection was obtained in a natural way from the Adam-Gibbs equation, relating the structural relaxation time to the configurational entropy. We find a clear correlation for a group of polymers. For another group of polymers, for which this correlation does not work, we emphasize the role of relaxation processes unrelated to the alpha process in affecting macroscopic thermodynamic properties. Once the residual excess entropy at the Vogel temperature is removed from the total excess entropy, the correlation between dynamic fragility and thermodynamic properties is reestablished.

Dielectric Studies of Molecular Motions in Amorphous Solid and Ultraviscous Acetaminophen

The dielectric permittivity and loss spectra of glassy and ultraviscous states of acetaminophen have been measured over the frequency range 10 Hz-0.4 MHz. The relaxation spectra show an asymmetric distribution of times expressed in terms of the Kohlrausch exponent, beta, which remains constant at 0.79+/-0.02 over the 305-341 K range. The dielectric relaxation time increases on cooling according to the Vogel-Fulcher-Tammann equation. However, the values of the parameters are considerably different from the values deduced from earlier work by other researchers using the heat capacity of ultraviscous acetaminophen and relating it to its molecular mobility. The calorimetric glass softening temperature of 296 K obtained from differential scanning calorimetry is close to the value measured from dielectric relaxation. The equilibrium permittivity of ultraviscous acetaminophen decreases on heating like that of a normal dipolar liquid, as anticipated from the Curie law. But, its value decreases rapidly with time when it begins to crystallize. The equilibrium permittivity of this crystal phase is approximately 3.1 at 300 K and increases with temperature, which indicates a partial, orientational-disordering of its structure. The results show limitations of the procedures used in the modeling of the kinetics of molecular motions, that is, estimating physical stability, using thermodynamic considerations based on thermal analyses of the amorphous solid phase of acetaminophen.

Moderately and strongly supercooled liquids: A temperature-derivative study of the primary relaxation time scale

The primary relaxation time scale tau(T) derived from the glass forming supercooled liquids (SCLs) is discussed within ergodic-cluster Gaussian statistics, theoretically justified near and above the glass-transformation temperature T(g). An analysis is given for the temperature-derivative data by Stickel et al. on the steepness and the curvature of tau(T). Near the mode-coupling-theory (MCT) crossover T(c), these derivatives separate by a kink and a jump, respectively, the moderately and strongly SCL states. After accounting for the kink and the jump, the steepness remains a piecewise conitnuous function, a material-independent equation for the three fundamental characteristic temperatures, T(g), T(c), and the Vogel-Fulcher-Tamman (VFT) T(0), is found. Both states are described within the heterostructured model of solidlike clusters parametrized in a self-consistent manner by a minimum set of observable parameters: the fragility index, the MCT slowing-down exponent, and the chemical excess potential of Adam and Gibbs model (AGM). Below the Arrhenius temperature, the dynamically and thermodynamically stabilized clusters emerge with a size of around of seven to nine and two to three molecules above and close to T(g) and T(c), respectively. On cooling, the main transformation of the moderately into the strongly supercooled state is due to rebuilding of the cluster structure, and is attributed to its rigidity, introduced through the cluster compressibility. It is shown that the validity of the dynamic AGM (dynamically equivalent to the standard VFT form) is limited by the strongly supercooled state (T(g) < T < T(c)) where the superrigid cooperative rearranging regions are shown to be well-chosen parametrized solidlike clusters. Extension of the basic parameter set by the observable kinetic and diffusive exponents results in prediction of a subdiffusion relaxation regime in SCLs that is distinct from that established for amorphous polymers.

Thermodynamics and the glass transition in model energy landscapes

We determine the liquid-state thermodynamics for a model energy landscape corresponding to soft spheres with a mean-field attraction. We consider two approximations, in which the distribution of potential energy minima is either Gaussian or binomial, and for each we calculate the liquid spinodal, binodal, and "effective" glass transition locus. The resulting models provide a unified description of the liquid state across the complete range from low-temperature glassiness to high-temperature instability with respect to the vapor phase.

Relation between thermodynamics and kinetics of glass-forming liquids

Vitrification of a supercooled liquid is often characterized by the hypothetical kinetic instability point, the Vogel-Fulcher temperature T0, and the thermodynamic one, the Kauzmann temperature T(K). The widely believed relation T0 congruent with T(K) is regarded as the supporting evidence of a direct connection between the thermodynamics and kinetics of glass-forming liquids. Here we demonstrate that T(K)/T(0) systematically increases from unity with a decrease in the fragility, contrary to the common belief. This systematic deviation may be explained by a synergistic effect between the weaker cooperativity and the stronger tendency of short-range ordering in stronger glass formers.

On the nature of a glassy state of matter in a hydrated protein: Relation to protein function

Diverse biochemical and biophysical experiments indicate that all proteins, regardless of size or origin, undergo a dynamic transition near 200 K. The cause of this shift in dynamic behavior, termed a "glass transition," and its relation to protein function are important open questions. One explanation postulated for the transition is solidification of correlated motions in proteins below the transition. We verified this conjecture by showing that crambin's radius of gyration (Rg) remains constant below approximately 180 K. We show that both atom position and dynamics of protein and solvent are physically coupled, leading to a novel cooperative state. This glassy state is identified by negative slopes of the Debye-Waller (B) factor vs. temperature. It is composed of multisubstate side chains and solvent. Based on generalization of Adam-Gibbs' notion of a cooperatively rearranging region and decrease of the total entropy with temperature, we calculate the slope of the Debye-Waller factor. The results are in accord with experiment.