K. L. Ngai

Nonexponential relaxations in strong and fragile glass formers

Deviations from thermally activated and from exponential response are typical features of the vitrification phenomenon and previously have been studied using viscoelastic, dielectric, calorimetric, optical, and other techniques. Linear response data from literature on about 70 covalent glass formers, ionic melts, supercooled liquids, amorphous polymers, and glassy crystals are surveyed. Except for orientational glasses and monohydric aliphatic alcohols a distinct but broad correlation of non‐Debye behavior with non‐Arrhenius relaxations is found. Within the broad trend several groups of materials, distinguished by their respective molecular complexity, can be identified and are shown to exhibit narrow correlations. At a given degree of deviation from Arrhenius behavior externally imposed stresses are relaxed with a departure from exponential behavior which is stronger the more the molecular or atomic subunits of the glassforming material are interconnected with each other.

Relaxation in glassforming liquids and amorphous solids

The field of viscous liquid and glassy solid dynamics is reviewed by a process of posing the key questions that need to be answered, and then providing the best answers available to the authors and their advisors at this time. The subject is divided into four parts, three of them dealing with behavior in different domains of temperature with respect to the glass transition temperature, Tg , and a fourth dealing with ‘‘short time processes.’’ The first part tackles the high temperature regime T.Tg ,i n which the system is ergodic and the evolution of the viscous liquid toward the condition at Tg is in focus. The second part deals with the regime T;Tg , where the system is nonergodic except for very long annealing times, hence has time-dependent properties ~aging and annealing!. The third part discusses behavior when the system is completely frozen with respect to the primary relaxation process but in which secondary processes, particularly those responsible for ‘‘superionic’’ conductivity, and dopart mobility in amorphous silicon, remain active. In the fourth part we focus on the behavior of the system at the crossover between the low frequency vibrational components of the molecular motion and its high frequency relaxational components, paying particular attention to very recent developments in the short time dielectric response and the high Q mechanical response.

Relaxation and diffusion in complex systems

Introduction.- Universal Relaxation and Diffusion Properties in Complex Systems.- Experimental Evidences.- Computer Simulations.- Theoretical Modeling and Interpretations.- Many-Body Relaxation Dynamic and Relation to Chaos.- Glass Transition and the Glassy State.- Role of Thermodynamics, Volume, Entropy and Temperature.- Polymer Viscoelasticity.- Ionic Conductivity Relaxation in Ionically Conducting Materials.- Relaxation and Diffusion at Nanometer Scales.- Relaxation in Biomolecules.

Dynamic and thermodynamic properties of glass-forming substances

Abstract We review the important general dynamic and thermodynamic properties of structural glass-forming substances and classify them into 12 different categories. Our understanding of glass-forming substances is incomplete until all these properties have been explained. The dynamic properties considered include those relating to the high frequency fast relaxation, the Johari–Goldstein β-relaxation, and the slow structural α-relaxation. Practically all the important relaxation and diffusion processes in the time region extending from 10−13 to 106 s have been discussed. We show from experimental data that the properties in different categories bear some relations to each other. Some issues that impede progress of our understanding of the behavior of glass-forming substances are accentuated by formulating them as questions. Answers to these questions by future experimental and theoretical investigations will improve our understanding. Specific suggestions for future research efforts that can provide some answers to these questions are also made. 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−β), where β is the fractional exponent in the Kohlrausch expression, exp[−(t/τ)β]. These patterns, as well as their correlations with (1−β), suggest that the salient dynamic properties (or phenomenology) of glass-forming substances are all governed by the non-exponential nature of the structural relaxation, i.e., the quantity (1−β). Therefore, a theory or model capable of relating the structural relaxation time τ to (1−β) has the potential of explaining many of the salient dynamic properties of glass-forming substances.

Relation between some secondary relaxations and the α relaxations in glass-forming materials according to the coupling model

Some secondary or β relaxations in glass-forming materials involve molecular motions that bear strong resemblance to the primitive α relaxations of the coupling model, although the two are not identical. For these β relaxations, at the glass transition temperature Tg the relaxation time τβ(Tg) is expected to be shorter than but not too different in order of magnitude from τ0(Tg), the primitive α-relaxation time at Tg. The latter can be calculated by the coupling model from the relaxation time τα(Tg), the exponent (1−n) of the Kohlrausch–Williams–Watts (KWW) correlation function exp[−(t/τα)1−n], and the experimental crossover time, tc≈2 ps, of the α relaxation. From experimental data of β and α relaxations in a variety of glass-forming materials, it is found that τβ(Tg) and τ0(Tg) are close to each other in order of magnitude as anticipated. The results indicate these β relaxations indeed bear some close relation to the corresponding primitive α relaxation, although they are not the same process. Since the...

Nature and properties of the Johari–Goldstein β-relaxation in the equilibrium liquid state of a class of glass-formers

Previous dielectric relaxation measurements of glycerol and propylene carbonate and new results on propylene glycol performed below the conventional glass transition temperatures Tg after long periods of aging all show that the excess wing (a second power law at higher frequencies) in the isothermal dielectric loss spectrum, develops into a shoulder. These results suggest that the excess wing, a characteristic feature of a variety of glass-formers, is the high frequency flank of a Johari–Goldstein β-relaxation loss peak submerged under the α-relaxation loss peak. With this interpretation of the excess wing assured, the dielectric spectra of all three glass-formers measured at temperatures above Tg are analyzed as a sum of a α-relaxation modeled by the Fourier transform of a Kohlrausch–Williams–Watts function and a β-relaxation modeled by a Cole–Cole function. Good fits to the experimental data have been achieved. In addition to the newly resolved β-relaxation on propylene glycol, the important results of ...

Slowing down of relaxation in a complex system by constraint dynamics

In this paper we view a relaxing complex system such as entangled polymer melt to consist of three parts: (1) an individual primary species PS of interest; (2) a heat bath (HB) whose interaction with the PS provides the primary mechanism of relaxation; (3) other relaxing species whose interactions with the PS, the PS‐C coupling, are for us the principal characteristic of complexity. The PS‐C coupling is represented by time dependent constraints whose effect begins only after the primary relaxation process due to the PS‐HB interaction is already underway. The overall process is described both physically and theoretically. The latter is described classically by means of time dependent Dirac constraint theory applied to a Liouville operator formalism. The physical and theoretical discussion leads to a time dependent relaxation rate W(t). The specific form of W(t) is adduced based on the requirement of time‐temperature equivalence or thermorheological simplicity. The result is a time independent relaxation ra...

Flow, diffusion and crystallization of supercooled liquids: Revisited

Within the last five years, investigators using NMR and forced Raleigh scattering techniques have found that the Stokes–Einstein (S–E) relation breaks down in supercooled liquids. It has been pointed out that the shear viscosity has a significantly stronger temperature dependence than either the self-diffusion coefficient, D(T), or the translational diffusion coefficient of tracer molecules of comparable size (not shape) to the host liquid. These observations confirm our results on trinaphthylbenzene (TNB) and 1,2 diphenylbenzene (OTP), published in a series of papers more than 30 years ago. An analysis of crystal growth rate measurements on these materials demonstrated that the transport-dominated crystal growth rate, G′(T), exhibited a weaker temperature dependence than the shear viscosity, η(T). Where the expression G(T)=f(T)/η(T) is often substituted for the more basic growth rate relationship G(T)=D(T)f(T). We showed that this practice (often used) is invalid. Here, f(T) is a nucleation/growth free e...

RELATIONSHIP BETWEEN THE PRIMARY AND SECONDARY DIELECTRIC RELAXATION PROCESSES IN PROPYLENE GLYCOL AND ITS OLIGOMERS

Dielectric relaxation measurements were performed on propylene glycol (PG) and oligomers having different number of repeat units (N=2, 3, and 69). The primary α-relaxation had the Kohlrausch–Williams–Watts (KWW) form, with a stretch exponent (1−n) which decreased with increasing N. The temperature dependence of the α-relaxation time, as reflected in the fragility index, increased with N. A broad, rather symmetric secondary β-relaxation was observed at higher frequencies in the dielectric loss spectrum for all samples with N>1. This is the first observation of the β-relaxation peak in dipropylene glycol (N=2) and tripropylene glycol (N=3). The separation between the α- and β-relaxations increased with increasing N. This trend indicates that the separation is minimal in PG, which makes it difficult to resolve the β-relaxation from the more intense α-relaxation. This, together with the fact that the strength of the β-relaxation decreases with the molecular weight of PPG, as found by Johari and coworkers, exp...

PROPERTIES OF THE CONSTANT LOSS IN IONICALLY CONDUCTING GLASSES, MELTS, AND CRYSTALS

A frequency independent or nearly frequency independent contribution to the dielectric loss is present in all ionic conductors independent of the chemical and physical structures. An exhaustive collection of dielectric relaxation data of glassy, crystalline, and molten ionic conductors are analyzed to obtain the magnitudes of their constant losses and the dependencies on temperature, ion density, ion mass, dc conductivity activation energy, dc conductivity level, the nonexponential conductivity relaxation parameter β, the mixed alkali effect, and the decoupling index Rτ. Trends of changes in the constant loss when modifying the structure of the glassy matrix or mixing two different alkali ions are also found. In a glass-forming molten salt, 0.4Ca(NO3)2⋅0.6KNO3, the constant loss turns out to have approximately the same temperature dependence as the mean square displacement of the ions obtained by elastic neutron scattering measurement. All dependencies and properties found indicate that the physical origi...