Glasses are disordered materials that lack the periodicity of crystals but behave mechanically like solids. The most common way of making a glass is by cooling a viscous liquid fast enough to avoid crystallization. Although this route to the vitreous state-supercooling-has been known for millennia, the molecular processes by which liquids acquire amorphous rigidity upon cooling are not fully understood. Here we discuss current theoretical knowledge of the manner in which intermolecular forces give rise to complex behaviour in supercooled liquids and glasses. An intriguing aspect of this behaviour is the apparent connection between dynamics and thermodynamics. The multidimensional potential energy surface as a function of particle coordinates (the energy landscape) offers a convenient viewpoint for the analysis and interpretation of supercooling and glass-formation phenomena. That much of this analysis is at present largely qualitative reflects the fact that precise computations of how viscous liquids sample their landscape have become possible only recently.

Supercooled liquids and the glass transition

The electronic properties and stereochemistry of mono-nuclear complexes of the copper(II) ion

The general expression for the exact forces on the nuclei (negative derivatives of the total energy with respect to the nuclear coordinates) is applied for Hartree-Fock wavefunctions. It is suggested that force constants should be calculated by differentiating the forces numerically. This method, called the force method, is numerically more accurate and requires less computation than the customary one of differentiating the energy numerically twice. It permits the quick determination of the equilibrium geometry by relaxing the nuclear coordinates until the forces vanish. The unreliability of the methods using the Hellmann-Feynman forces is re-emphasized. The question of which force constants can be best calculated ab initio is discussed.

Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules

Although it has long been recognized that dynamics in supercooled liquids might be spatially heterogeneous, only in the past few years has clear evidence emerged to support this view. As a liquid is cooled far below its melting point, dynamics in some regions of the sample can be orders of magnitude faster than dynamics in other regions only a few nanometers away. In this review, the experimental work that characterizes this heterogeneity is described. In particular, the following questions are addressed: How large are the heterogeneities? How long do they last? How much do dynamics vary between the fastest and slowest regions? Why do these heterogeneities arise? The answers to these questions influence practical applications of glass-forming materials, including polymers, metallic glasses, and pharmaceuticals.

Spatially Heterogeneous Dynamics in Supercooled Liquids

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. © 2000 American Institute of Physics.@S0021-8979~00!02213-1#

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1065&context=mse_pubs

Relaxation in glassforming liquids and amorphous solids

ESR spectra of copper complexes have been interpreted by means of molecular orbital theory, and the ``covalent'' character of both σ and π bonds have been discussed for a variety of compounds. Overlap integrals have been considered in a consistent manner in treating σ bonds. Particular attention has been given to Cu phthalocyanine and several of its derivatives. The in‐plane π bonding may be as important in determining the properties of a Cu complex as is the in‐plane σ bonding.

ESR Studies on the Bonding in Copper Complexes

A theory of ESR linewidths for substances in which the magnetic anisotropy is small and for which the orbital magnetism has been essentially quenched is developed. Nuclear quadrupole moments, zero field splittings, anisotropic Zeeman terms, and intramolecular electron‐nuclear dipolar interactions, as well as motional and exchange effects are considered in the strong field case. The theory is developed in a manner that is particularly adaptable to the study of liquids but it is also applied to crystals since the resulting equations, though only applicable for small anisotropies, are particularly simple. The theory provides an extension of previous theories on ESR spectra in liquids. Several applications of the theory are discussed with particular emphasis on V4+ chelates. The theory of exchange in liquids, a phenomenon which is complicated by the noncommutivity of the motional and exchange Hamiltonians is considered in special detail. It is shown that this theory can be used to explain Hausser's results—th...

Theory of ESR Linewidths of Free Radicals

The ESR spectra of vanadyl acetylacetonate and tetraphenylporphyrin have been studied in various liquid solvents and frozen glasses. The spectra have been analyzed and the components of the g tensor and of the vanadium hyperfine interaction tensors have been determined, and for the porphyrin the nitrogen extrahyperfine interaction tensor has been obtained. The unpaired electron is in the b2g* orbital. The extrahyperfine splitting is very isotropic which indicates that the b2g* orbital is localized on the vanadium in the porphyrin complex and the ``in‐plane π bonding'' is slight. An explanation of the origin of this extrahyperfine splitting is discussed in terms of configuration interaction. An analysis of the vanadium hyperfine interaction indicates that the b2g* orbital is localized on the vanadium in the acetylacetonate also, and that the Fermi contact interaction depends upon a number of excited configurations and varies from complex to complex and with change of solvent. The g‐tensor analysis suggests...

ESR Studies and the Electronic Structure of Vanadyl Ion Complexes

A novel thermodynamic theory of the properties of supercooled liquids as they get glassy is presented. It is based on the postulated existence of a narrowly avoided thermodynamic phase transition at a temperature T ∗ ⩾ T m , where Tm is the melting point, and the “avoidance” is due to geometric frustration. We show that as a consequence two large emergent length scales develop at temperatures less than T ∗ , and we also show that this picture is consistent with appropriate statistical mechanical models. A theoretical expression is obtained which permits collapse of the viscosity versus temperature of all known glass-formers onto a single master-curve.

A thermodynamic theory of supercooled liquids

A first‐order treatment yields the relation W=W0+A1W02+A2W0J(J+1)+A3J2(J+1)2+A4J(J+1)〈Pz2〉+A5〈Pz4〉+A6W0〈Pz2〉 for the rotational energy W of a nonrigid asymmetric rotor. The A's are constants independent of the rotational quantum numbers (J, K−1, K+1) while W0 is the rigid‐rotor energy. Pz is the operator for the component of angular momentum along the axis of quantization. Formulas are given for 〈Pz2〉 and 〈Pz4〉, based on continued fractions, as well as expansions useful for nearly symmetric cases. As a special case, the corrections are derived for transitions between the components of asymmetry doublets.

Daniel Kivelson

Papers

ESR Studies on the Bonding in Copper Complexes

Theory of ESR Linewidths of Free Radicals

ESR Studies and the Electronic Structure of Vanadyl Ion Complexes

A thermodynamic theory of supercooled liquids

Approximate Treatment of the Effect of Centrifugal Distortion on the Rotational Energy Levels of Asymmetric‐Rotor Molecules