G. P. Johari

Localized molecular motions of β-relaxation and its energy landscape

Abstract The β-relaxation process in a highly viscous liquid and mechanically rigid glass may be attributed to reorientational motions of (i) essentially all molecules with a nearly temperature-independent small angle, or (ii) a small number of molecules or molecular groups confined to certain sites of loose packing resulting from frozen-in density fluctuations. Relative merits of these mechanisms are examined by considering the changes in the orientation polarization and entropy observed on changing the temperature, and observed on spontaneous structural relaxation at a fixed temperature. The effects of isothermal densification by pressure and by structural relaxation are also considered. It is found that when several properties are examined, the first mechanism for the β-relaxation is not supported. The β-relaxation process also involves translational diffusion, which has been overlooked. Implications of these finding for the β-relaxation landscape in the currently used potential energy surface are discussed. Experiments have been suggested for resolving the mechanism of this important process.

Two Calorimetrically Distinct States of Liquid Water Below 150 Kelvin

Vapor-deposited amorphous solid and hyperquenched glassy water were found to irreversibly transform, on compression at 77 kelvin, to a high-density amorphous solid. On heating at atmospheric pressure, this solid became viscous water (water B), with a reversible glass-liquid transition onset at 129 ± 2 kelvin. A different form of viscous water (water A) was formed by heating the uncompressed vapor-deposited amorphous solid and hyperquenched liquid water. On thermal cycling up to 148 kelvin, water B remained kinetically and thermodynamically distinct from water A. The occurrence of these two states, which do not interconvert, helps explain both the configurational relaxation of water and stress-induced amorphization.

A resolution for the enigma of a liquid’s configurational entropy-molecular kinetics relation

The literature data on the entropy and heat capacity of 33 glass-forming liquids have been used to examine the validity of the Adam–Gibbs relation between a liquid’s configurational entropy, Sconf, and its molecular kinetics. The critical entropy, sc*, of kB ln 2 (=0.956×10−23 J molecule−1 K−1) in the equation is less than even the residual entropy per molecule in a glass at 0 K, and this creates difficulties in determining the size of the cooperatively rearranging region, z*, in the liquid. It is argued that, z*=[1−(T0/T)]−1, and the temperature-invariant energy term, Δμ, is equal to RB, which has been determined from the knowledge of the Vogel–Fulcher–Tamman parameters B and T0, with R being the gas constant, and on the basis of the argument that the preexponential term of this equation is identical to that of the Adam–Gibbs relation. As the lattice modes in a glass are lower in frequency and more anharmonic than in its crystal, its vibrational entropy, Svib, would be higher than that of the crystal pha...

Calorimetric studies of the kinetic unfreezing of molecular motions in hydrated lysozyme, hemoglobin, and myoglobin.

Differential scanning calorimetric (DSC) studies of the glassy states of as-received and hydrated lysozyme, hemoglobin, and myoglobin powders, with water contents of < or = 0.25, < or = 0.30, and < or = 0.29 g/g of protein, show that their heat capacity slowly increases with increasing temperature, without showing an abrupt increase characteristic of glass-->liquid transition. Annealing (also referred to as physical aging) of the hydrated proteins causes their DSC scans to show an endothermic region, similar to an overshoot, immediately above the annealing temperature. This annealing effect appears at all temperatures between approximately 150 and 300 K. The area under these peaks increases with increasing annealing time at a fixed temperature. The effects are attributed to the presence of a large number of local structures in which macromolecular segments diffuse at different time scales over a broad range. The lowest time scale corresponds to the > N-H and -O-H group motions which become kinetically unfrozen at approximately 150-170 K on heating at a rate of 30 K min-1 and which have a relaxation time of 5-10 s in this temperature range. The annealing effects confirm that the individual glass transition of the relaxing local regions is spread over a temperature range up to the denaturation temperature region of the proteins. The interpretation is supported by simulation of DSC scans in which the distribution of relaxation times is assumed to be exceptionally broad and in which annealing done at several temperatures over a wide range produces endothermic effects (or regions of DSC scans) qualitatively similar to those observed for the hydrated proteins.

Dielectric relaxations in the liquid and glassy states of poly(propylene oxide) 4000

Abstract The dielectric permittivity and loss of poly(propylene oxide) of molecular weight 4000, PPO(4000), have been measured in the temperature range 77K–305K and frequency range 10−2 −2 × 105 Hz. Two relaxation regions are observed above the glass transition temperature, Tg(=200K), and two below Tg. The rate of the highest temperature, or lowest frequency, α′ relaxation processes has a temperature dependence which indicates its approach below Tg towards that of the lower-temperature higher frequency, α, process. The rates of both processes can be described by the Vogel-Fulcher-Tamman equation with nearly the same value of To. The rate of β-relaxation shows an Arrhenius dependence on temperature with an activation energy of 19.4kJ mol−1, and may merge with the α-relaxation at T>250K. The relaxations in PPO(4000) are remarkably similar to those observed in molecular liquids and glasses.

Contributions to the entropy of a glass and liquid, and the dielectric relaxation time

An analysis of the heat capacity data of 21 materials shows that a glass loses 17%–80% of its entropy on cooling from its Tg to 0 K, and that the entropy difference between a glass and crystal phase at Tg, ΔS(Tg), is 1.2 to 4.9 times the entropy difference at 0 K. This is contrary to the premise that the vibrational entropy of a glass is the same as the entropy of its crystal phase, or that ΔS(Tg) is equal to Sconf(Tg), the configurational entropy at Tg. The excess entropy of a glass over the crystal phase is attributed to (i) the relatively lower frequency and greater anharmonicity of lattice vibrations which contribute to their vibrational entropy, (ii) the kinetically unfrozen modes corresponding to the tail of the distribution of the α-relaxation times, which contribute to the configurational entropy, and (iii) localized relaxations of molecular groups which also contribute to the configurational entropy. These contributions vanish or become negligible at 0 K. Therefore, ΔS(Tg) cannot be used in place...

Crystallization kinetics of water below 150 K

Metastable liquid water, obtained by heating its hyperquenched glassy state above its glass→liquid transition temperature, crystallizes to cubic ice. Kinetics of this crystallization has been studied by Fourier transform infrared spectroscopy by determining the change in the spectra of stretching vibrations of the decoupled OD oscillator in 3.6 mole % HOD in H2O. The crystallization kinetics follows the equation x=[1−exp(−ktn)] and is diffusion controlled. Annealing at a temperature below its glass→liquid transition temperature alters this kinetics as the grain–growth process begins to control the early stages of crystallization.

Structural relaxation of acetaminophen glass.

PurposeThe aim is to determine the structural stability of acetaminophen glass with time and temperature change, and to examine the merits of adapting the structural relaxation models of the glassy state for pharmaceuticals.MethodsDifferential scanning calorimetry technique has been used to study the acetaminophen glass after keeping the samples for various periods at fixed temperatures and after keeping at various temperatures for fixed periods.ResultsA general formalism for thermodynamic changes during storage in a temperature fluctuating environment is given and the kinetics of the enthalpy and entropy decrease determined. At a fixed temperature, the decrease occurs according to a non-exponential kinetics. For the same storage time, but at different temperatures, the enthalpy and entropy decrease rises to a maximum value at a certain temperature and then declines. The peak appears at the temperature at which the internally equilibrated state of the sample is reached for a fixed storage time. The change in the normalized heat capacity during the heating of acetaminophen has been analysed in terms of a non-exponential, non-linear enthalpy relaxation model.ConclusionA single set of parameters that fit the data for unannealed acetaminophen glass does not fit the calorimetric data for annealed glass. Since acetaminophen molecules form intermolecular hydrogen-bonds in the crystal state and likely to form such bonds more easily in the disordered state, effect of such bonds on structural relaxation is likely to be significant.

Water’s size-dependent freezing to cubic ice

Water has been occasionally found to freeze to cubic ice. To investigate this occurrence thermodynamically, we use the known enthalpy and interfacial energy of hexagonal and cubic ices and calculate a critical radius r(c) of appromximately 15 nm for a water droplet and a critical thickness delta(c) of approximately 10 nm for waters flat film. Accordingly, water droplets smaller than 15 nm radius and films thinner than 10 nm would freeze to cubic ice in the 160-220 K range and bigger droplets and thicker films would freeze to hexagonal ice. This provides a thermodynamic basis for the occasionally found presence of cubic ice in the atmosphere, and explains why waters nanometer-sized clusters and water confined to nanometer-sized pores freeze to cubic ice. Conditions for cubic ice-hexagonal ice phase inversion have been discussed. Impurities in water and different extents of proton ordering in the crystallites of cubic and hexagonal ices would have a significant effect on r(c) and delta(c).

An equilibrium supercooled liquid’s entropy and enthalpy in the Kauzmann and the third law extrapolations, and a proposed experimental resolution

In our current discussion of the thermodynamics and molecular kinetics of glass-forming liquids, the entropy is extrapolated below a liquid’s vitrification temperature Tg along a curve of progressively increasing slope until a temperature Tk is reached. Here the entropy and heat capacity, Cp, of the equilibrium liquid become equal to those of its crystal. Several observations have indicated fundamental difficulties with this extrapolation, thus suggesting the need for an alternative. We propose one alternative, in which Cp of an equilibrium liquid decreases along a sigmoid-shape path stretched over a broad temperature range from above Tg to 0 K. Its entropy and Cp become equal to those of its crystal at 0 K, as required by the third law of thermodynamics, and the enthalpy and volume remain higher. To elaborate, the available Cp data of 12 supercooled liquids have been interpolated between T>Tg and 0 K, and the enthalpy of their equilibrium state at 0 K, as well as the Gibbs free energy and enthalpy at T