Glass-forming Substances Research Articles

Can high pressure experiments shed light on the puzzles of glass transition? The problem ofextrapolation

The issues of the extrapolation to multi-GPa pressures of the experimental data obtainedat moderate pressures are considered for different classes of glass-forming substances. Forcovalent glass-forming substances, the phase transitions and structural changes are majorfactors that hamper extrapolation. Organic glass-forming liquids are not groundthermodynamic states of matter; under high pressures they transform to polymericsubstances and then to mixtures of simple inorganic compounds. Therefore, extrapolationof the data obtained at moderate pressures is hardly possible for this class either.Metallic melts and rare gas liquids are the only substances whose properties can beextrapolated into the megabar region. However, such an extrapolation is highlyuncertain due to the low viscosity and weak pressure dependences of the properties ofthese liquids. New experimental studies of rare gas and metallic liquids in thepressure region of tens of GPa are urgently needed for the extrapolation to bereliable.

The Protein “Glass” Transition and the Role of the Solvent

Hydrated proteins undergo a change in their dynamical properties in the neighborhood of a temperature. The change of dynamics has been likened to glass transition of glass-forming substances because similar properties were found. However, a complete understanding of the conformation fluctuations of hydrated proteins and their relation to the dynamics of the solvent is still not available, possibly due to the protein molecules being more complex than ordinary glass-formers. For this reason, we turn our attention to the experimental findings of the dynamics of mixtures of water with simpler glass-formers (small molecules and polymers). Two major relaxation processes have been observed in these aqueous mixtures. One is the structural alpha-relaxation of the hydrophilic glass-former hydrogen bonded to the water, which is responsible for glass transition. The other one is the local secondary beta-relaxation of water in the mixture. Remarkably, these two relaxation processes in aqueous mixtures have analogues in hydrated proteins with the same properties. The conformation fluctuations of the protein and the relaxation of the solvent in hydrated proteins behave like the alpha-relaxation of the hydrophilic glass-former hydrogen bonded to the water and the beta-relaxation of water in other aqueous mixtures, respectively. At low temperatures, the Arrhenius activation energy of the relaxation time of the solvent in a hydrated protein is almost the same as that of the beta-relaxation of water in the glassy states of aqueous mixtures. The Arrhenius T-dependence of the solvent relaxation times no longer holds at temperatures that exceed the "glass" transition temperature of the hydrated protein, defined as the temperature at which the conformation relaxation time is very long. This behavior of the solvent in hydrated proteins is similar to that found in the beta-relaxation of water in aqueous mixtures when crossing the glass transition temperature of the mixture (Capaccioli, S.; Ngai, K. L.; Shinyashiki, N. J. Phys. Chem. B 2007, 111, 8197). Furthermore, the same dynamics were found in mixtures of two van der Waals glass-formers, which are even simpler systems than aqueous mixtures because of the absence of hydrogen bonding. The experimental data of these ideal mixtures of van der Waals glass-formers have been given a satisfactory theoretical explanation. Since the properties of hydrated proteins, aqueous mixtures, and the mixtures of van der Waals liquids are similar, we transfer the theoretical understanding gained in the study of the last system sequentially to the two other increasingly more complex systems.

New sight into the structure of selenium: Four-valence Se in glass

A comparison of the known structural data, with our quantum-chemical results for a-Se, leads to the conclusion that a neutral four-valence state, Se40, represents the lowest-energy (0.4eV) defect, whose concentration is about 10% in the glass and greater in the melt. These results are expanded to other substances with the conclusion that the ability of a chemical bond system to generate low-energy network-linking alternative bonds (or ‘defects’) is a key property that distinguishes a group of glass-forming substances.

On the relevance of the coupling model to experiments

The research field of the glass transition is experimentally driven. There is an abundance ofexperimental data and facts accumulated in the past as well as the emergence of importantnew results every now and then. Therefore, when judging theories and models of the glasstransition, it is fair to ask the question of their relevance to experiments. Thisquestion was one of the themes of a round-table discussion session entitled Anassessment of current theories: interconnections and relevance to experiments,organized at the 4th Workshop on Non-equilibrium Phenomena in SupercooledFluids, Glasses and Amorphous Materials (4th WNEP). The coupling model has ahistory of making connections of its theoretical results with many experimentalfacts on dynamics of glass-forming substances. This characteristic of the couplingmodel is demonstrated herein by using it to explain or rationalize some of the newexperimental data reported at the 4th WNEP and published in this volume andelsewhere.

Why the glass transition problem remains unsolved?

Glass-forming substances are made of units having nontrivial mutual interactions. Therefore, structural relaxation of glass-formers is a many-body relaxation problem, which unfortunately is still an unsolved problem in statistical mechanics. Conventional theories and models of glass transition bypass solution of this problem, and hence glass transition also remains an unsolved problem. There are plenty of experimental evidences for the many-body relaxation dynamics, and some examples are given. The Coupling Model of the author is not a full solution of the many-body relaxation problem either. Nevertheless, its predictions can explain the properties of structural relaxation originating from many-body relaxation and their relations to its precursor, namely the Johari–Goldstein secondary relaxation. A demonstration of the utility of the Coupling Model is given here by solving two problems in glass transition that involve many-body relaxation. The problems are: (1) the breakdown of Stokes–Einstein and Debye–Stokes–Einstein relations in neat molecular glass-formers and colloidal suspension, and (2) the component dynamics of polymer blends and mixtures of non-polymeric glass-formers.

The vestige of many-body dynamics in relaxation of glass-forming substances and other interacting systems

Relaxation and diffusion in interacting systems including most glass-forming substances involve many-body dynamics. The stretch exponent, n, in the Kohlrasuch correlation function, , is a convenient measure of the many-body relaxation dynamics. Evidences of the importance of the many-body dynamics can be seen from the empirical facts that n either governs or correlates with several general relaxation properties. Two examples of this scenario are shown. The first is the ageing of colloidal glasses. The second is the breakdown of the Stokes–Einstein and the Debye–Stokes–Einstein relations in small molecular glass formers, colloidal particle suspensions and a Lennard-Jones system with rotational degree of freedom. The coupling model has a relation in which n plays a pivotal role in determining relaxation properties. The relation is used once more to explain the findings of the two examples given in this paper.

Molecular dynamics simulation of ion dynamics in glassy ionic conductors: Evidence of the primitive ion hopping process

Experiments have shown that the properties of the dynamics of ions in ionically conducting glasses are similar to the dynamics of molecules in glass-forming substances. The short time dynamics of ions when caged are manifested as the measured nearly constant loss at high frequencies seen also in glass-forming substances. The conductivity relaxation of ions at long times has properties similar to the terminal structural α-relaxation of glass-formers. However, while there is present the ubiquitous Johari–Goldstein β-relaxation playing the important role as the precursor of the α-relaxation, such corresponding relaxation has not been detected by experiment. We report molecular dynamics simulation of Li ion dynamics in lithium metasilicate glass performed specifically to look for this secondary relaxation. The data presented indicate its presence. Further support comes from conductivity relaxation data of ionic liquids. In ionic liquids, ions are molecules that have permanent dipole moments. Combined translational and rotational motion of the molecular ions should enable the primitive relaxation to be observed as a secondary relaxation in the dielectric loss spectra. From published data we calculate the primitive relaxation time, τ0, of the Coupling Model. It is nearly the same as the relaxation time, τβ, of the observed secondary relaxation.

Dielectric studies of molecular motions in glassy and liquid nicotine

The dielectric permittivity and loss spectra of glassy and liquidstates of nicotine have been measured over the frequency range10−2–109 Hz.The relaxation spectra are similar to common small molecular glass-forming substances, showing thestructural α-relaxation and its precursor, the Johari–Goldsteinβ-relaxation.The α-relaxation is well described by the Fourier transform of the Kohlrausch–Williams–Wattsstretched exponential function with an approximately constant stretch exponent that isequal to 0.70 as the glass transition temperature is approached. The dielectricα-relaxation time measured over 11 orders of magnitude cannot be described by a singleVogel–Fulcher–Tamman–Hesse equation. The most probable Johari–Goldsteinβ-relaxation time determined from the dielectric spectra is in good agreement with the primitiverelaxation time of the coupling model calculated from parameters of the structuralα-relaxation. The shape of the dielectric spectra of nicotine is compared with that of otherglass-formers having about the same stretch exponent, and they are shown to be nearlyisomorphic. The results indicate that the molecular dynamics of nicotine conform to thegeneral pattern found in other glass-formers, and the presence of the universalJohari–Goldstein secondary relaxation, which plays a role in the crystallization ofamorphous pharmaceuticals.

Interrelation between Primary and Secondary Relaxations in Polymerizing Systems Based on Epoxy Resins

There is a wealth of experimental data published on the change of molecular dynamics of epoxy resins during polymerization reaction. Common aspects are an increase of the primary α-relaxation time τα and a broadening of the α-relaxation process during the polymerization reaction. In this paper we discuss systematic changes in the two secondary relaxations β and γ on the way from a neat molecular glass-former to the fully polymerized state based on literature data and new dielectric results for diglycidyl ether of bisphenol A (DGEBA) cured with ethylenediamine (EDA). The discussion is focused on common trends in the relaxation time τβ which were not reported previously. It is shown that the relative changes of τα andτβ during the polymerization process are in accord with the predictions of the coupling model and that it is the β-relaxation which is the initiator of the α-relaxation of the epoxy resins in its neat state as well as the initiator of the local segmental relaxation of polymerized or cross-linked epoxy resins. In the terminology of small molecular glass-forming substances, the β-relaxation of the epoxy resins would be called the Johari−Goldstein process.

Comparison of Dynamics of Ions in Ionically Conducting Materials and Dynamics of Glass-Forming Substances: Remarkable Similarities

Abstract We consider many of the fundamental dynamic properties of ionically conducting glasses, crystals and melts and show there are analogues in the dynamic properties of glass-forming substances. These similarities suggest the dynamics of these two classes of complex systems are governed by the same physics. We also show within each class, the evolution of dynamics from short time to long times are principally governed by the stretch exponent of the Kohlrasuch function, which determines either the primary relaxation of glass-formers or the conductivity relaxation of ionic conductors.

Relation between the activation energy of the Johari-Goldstein beta relaxation and T(g) of glass formers.

For glass-forming substances, we show that the ratio E(beta)/RT(g) can be predicted quantitatively from the coupling model. Here E(beta) is the glassy state activation enthalpy of the Johari-Goldstein beta relaxation, T(g) is the glass transition temperature of the alpha relaxation, and R is the gas constant. The calculated value is in good agreement with the experimental value in many glass formers. The results locate the origin of this cross correlation between E(beta) of the Johari-Goldstein beta relaxation and T(g) of the alpha relaxation, although there are some notable exceptions to this cross correlation.

Correlation of positron annihilation and other dynamic properties in small molecule glass-forming substances.

Positron annihilation spectroscopy is used to characterize the ortho-positronium lifetime, tau(3), in a broad range of small molecule organic glasses over a wide temperature range. The magnitude and thermal variations of tau(3) reflect changes in the dielectric alpha-relaxation time tau(alpha) and its non-Arrhenius or "fragile" characteristics. tau(3) also displays striking similarities with the fast relaxations reflected in the hydrogen-weighted mean square atomic displacements <u(2)>. The parallel temperature variations of <u(2)(T/T(g))>, tau(3)(T/T(g)), and tau(alpha)(T/T(g)), and their similar patterns of change between the different glasses, are discussed in terms of anharmonicity in the intermolecular caging potentials and the subnanometer density heterogeneities.

Structural dependence of fast relaxation in glass-forming substances and correlation with the stretch exponent of the slow structural α-relaxation

The fast relaxation in glass-forming substances is often identified with the β-relaxation of the idealized mode coupling theory (MCT), which involves a critical temperature, T c, higher than the glass transition temperature, T g. However, several recent experimental works indicate that the fast relaxation may not be so simply described. These findings include the breakdown of the predictions of the idealized MCT below T c in 0.4Ca(NO 3) 2–0.6KNO 3 (CKN) and ortho-terphenyl (OTP), the existence of the fast relaxation also in crystalline OTP, and the flat dielectric susceptibility minimum (i.e., nearly frequency independent or constant loss) observed in CKN and propylene carbonate at temperatures below T c. These experimental facts indicate that the fast relaxation observed below T c is outside the predictions of the idealized MCT and a recent two-component schematic model of MCT, which includes hopping. It is unlikely that this non-MCT fast relaxation existing below T c will abruptly vanish at temperatures above T c. The need for an alternative model of the fast relaxation not only below but also above T c is thus clear. We analyzed susceptibility spectra of many glass-formers with the assumption that the susceptibility minimum is caused by a temperature dependent near constant loss. Good fits to the susceptibility spectra were obtained and in the process the near constant loss was determined as a function of temperature. When compared in a plot against T g-scaled temperature, the near constant losses of different glass-formers exhibited a pattern that correlates with the stretch exponent, β α( T g), of the Kohlrausch–Williams–Watts (KWW) function which describes the time dependence of the structural α-relaxation at T g. The correlation suggests that the fast relaxation and the slow structural α-relaxation are both determined by the same factor, which we attribute to the anharmonic intermolecular potential of interactions between the molecules. The fast relaxation is suggested to be the relaxation of a vibration by anharmonicity. The vibration is likely the one that attempts to relax the structure of the glass-former.

The Kauzmann Paradox Revisited

Many glass-forming substances display heat capacities for their supercooled liquids that substantially exceed those of the corresponding crystals. Reasonable extrapolation below the kinetic glass transition temperature indicates that the molar entropies of the supercooled liquid and crystal phases would become equal at a “Kauzmann temperature” TK > 0. Furthermore, continuing such extrapolation below TK to absolute zero suggests that the disordered liquid attains lower entropy than the crystal, in conflict with the third law of thermodynamics (hence the “Kauzmann paradox”). The present study cites data for real substances and results from numerical simulation and theoretical modeling in the temperature−pressure plane to demonstrate that a Kauzmann locus TK(p) can indeed occur, though not necessarily for all materials. No third-law conflict arises. Also, the analysis provides no support for the concept of an “ideal glass transition” at positive temperature, often mentioned in connection with glass formers. In the event that classical statistical mechanics is applicable to a substance of interest, the low-temperature endpoint of the Kauzmann locus involves the maximum isotropic tension sustainable by spatially uniform amorphous deposits, a state which coincides in pressure and density with the minimum of the T = 0 liquid spinodal.

Coupling model explanation of salient dynamic properties of glass-forming substances

Most of the important and general dynamic properties of structural glass-forming substances have been classified into twelve different categories in a recent review. Within the same property in each category, by examining a large number of glass-formers, a pattern of variation is found which correlates with the departure of the structural relaxation of the glass-former from exponential decay or the quantity 1-/spl beta/, where /spl beta/ is the fractional exponent in the Kohlrausch expression exp[-(t//spl tau/)/sup /spl beta//], that well describes the time dependence of the structural at relaxation. The correlation of the patterns or trends with 1-/spl beta/ suggests that the salient dynamic properties, or phenomenology, of glass-forming substances, all are governed by the non-exponential nature of the structural relaxation, i.e. the quantity 1-/spl beta/. Therefore, a theory or model capable of relating the structural relaxation time /spl tau/ to 1-/spl beta/ has the potential of explaining most, if not all, of the salient dynamic properties of glass-forming substances. The coupling model of the author has this relation. In this accompanying paper we show the coupling model can either explain or interpret all these properties.

Short-time and long-time relaxation dynamics of glass-forming substances: acoupling model perspective

The coupling model, based on fundamental properties of nonintegrableHamiltonian systems (chaos), captures one important aspect of the many-bodyrelaxation dynamics, namely the existence of a temperature insensitivecrossover time, tc, when in its neighbourhood the fast independentrelaxation of an individual unit at earlier times is slowed down to become thecooperative and dynamically heterogeneous relaxation at longer times. Formolecular systems, tc is of the order of a picosecond and thus the couplingmodel bridges relaxation dynamics at microscopic times to that at macroscopictimes. One result, which relates the slowed-down cooperative relaxation timeto the independent relaxation time of an individual unit, has spawned manyapplications. A nonlinearly coupled arrays of oscillators model, which has allthe features of the coupling model, is further exploited to show that thestrength of intermolecular interaction determines the nonexponentiality andfragility of the long-time dynamics of glass-formers. A related model isinvoked to consider the relaxation of the (precursor) vibration attempting thestructural relaxation. The fast relaxation that originates from suchvibrational relaxation is shown to be a plausible cause of the susceptibilityminimum seen in dielectric relaxation, light and neutron scatteringexperiments. The model predicts that the degree of nonexponentiality of thestructural relaxation is correlated with the strength of the fast precursorvibrational relaxation, in agreement with experimental observation.

Characteristic Length of Dynamic Glass Transition near Tg for a Wide Assortment of Glass-Forming Substances

Dynamic heterogeneity is an active field of glass-transition research. The length scale of this heterogeneity is called the characteristic length. It can be calculated from complex heat capacity curves in the equilibrium liquid or from dynamic calorimetry curves corrected with regard to nonequilibrium. No molecular parameters or microscopic models are necessary for obtaining the length. We report the characteristic length near glass temperature for about 30 glass formers including small-molecule liquids, polymers, silicate glasses, a metallic glass, a liquid crystal, and a plastic crystal. The lengths are between 1.0 and 3.5 nm with certain cumulations between 1.0 and 2.0 nm and between 2.5 and 3.5 nm. To try a correlation to other properties, we find that at least two should be included, e.g., Angell's fragility and the distance of Tg from the crossover temperature, Tc.

The Dynamics of Interacting Systems: Glassy Ionic Conductors and Glass-Forming Materials

ABSTRACTThe dynamics of densely packed interacting systems including glass-forming materials and glassy ionic conductors of various chemical and micro structures have been investigated experimentally by many workers, covering an immense time range from microscopic times shorter than 10−12 s to macroscopic times as long as 104 s. The short time dynamics is fundamental because it can directly reveal the microscopic mechanism of the relaxation. Several experimental investigations of structural relaxation in glass-forming substances have found that the short time dynamics shows exponential relaxation with a correlation function well described by exp(−t/τo) for t&lt;tc where tc is temperature insensitive and has the order of magnitude of a picosecond. The correlation function then crosses over at tc to assumes the stretched exponential form, exp[−(t/τ)β], for t&gt;tc. The relaxation times τ and τo are related by the expression τ = [tc−(1−β)τo]1/β. In this work, we focus on glassy ionic conductors and ionic glass-forming materials and experiments that employ dielectric spectroscopic and conductivity relaxation techniques, the theme of this Symposium. We show that these experimental data exhibit the same feature as described above for structural relaxation and are in accord with the predictions of the coupling model proposed by one of the authors.

Activated dynamics, loss of ergodicity, and transport in supercooled liquids.

The dynamics of the transition from supercooled liquid to glass is examined in terms of several probes: ergodic measures, self-diffusion coefficients, the Van Hove self-correlation functions, and the shear viscosity. Constant-pressure molecular-dynamics calculations at several temperatures are performed for a Lennard-Jones mixture and binary mixtures of soft spheres. The temperature dependence of the ergodicity diffusion parameters for both systems follow the Vogel-Fulcher law. On the other hand, the self-diffusion coefficients exhibit Arrhenius behavior for the soft-sphere system, but Vogel-Fulcher behavior for the Lennard-Jones system. These observations suggest that loss of effective ergodicity may be the universal feature of glass-forming substances. Various probes of the dynamics of the mixtures studied here suggest that the mechanism for mass transport dramatically changes from a simple diffusive process to one that involves activated transitions. The temperature at which this occurs is higher than the glass transition temperature ${\mathit{T}}_{\mathit{g}}$ and lies in the range 1.1T/${\mathit{T}}_{\mathit{g}}$1.3. In this temperature range the effective ergodic times also increase very rapidly and suggest that the relaxation process is dominated by the presence of barriers in configuration space. We also show that the Stokes-Einstein relation between the shear viscosity and the self-diffusion coefficients starts to break down in the temperature range where the ergodic convergence times increase dramatically.

Rawson's criterion and intermolecular interactions in glass-forming melts

The modification of Rawson's criterion B M−O/ T m ( B M−O is a single bond strength, T M is a melting temperature) into the form E a /RT m or E a /RT b ( E a is the averaged atomization energy, T m and T b are melting and boiling points) gives an opportunity to analyze all kinds of substances which are divided into three groups: glass-forming, molecular and normal substances. Such an analysis leads to the conclusion that in glass formers there exist special bonds (at least in molten and glassy states) in addition to covalent bonds. Besides that, the self-organization of these bonds into a sub-system is necessary for glass formation. In some respects this sub-system plays a role analogous to that of intermolecular bond sub-systems in molecular substances. The similarity and difference of the two groups of substances and the nature of ‘intermolecular’ bonds in the case of glass-forming melt are discussed.