Microscopic theory of network glasses

A theory of the glass transition of network liquids is developed using self-consistent phonon and liquid state approaches. The dynamical transition and entropy crisis characteristic of random first-order transitions are mapped as a function of the degree of bonding and density. Using a scaling relation for a soft-core model to crudely translate the densities into temperatures, theory predicts that the ratio of the dynamical transition temperature to the laboratory transition temperature rises as the degree of bonding increases, while the Kauzmann temperature falls explaining why highly coordinated liquids are "strong" while van der Waals liquids without coordination are "fragile."     

Generalized hydrodynamic equations and correlation functions for thermoviscoelastic fluids

For very viscous liquids a phenomenological theory of thermoviscoelasticity is formulated, in which the retarded reaction of thermal variables, which arises from structural relaxation, is taken into account. The theory describes the effect of the slowing down of the structural relaxation near a glass transition on the fluctuation spectra of density and entropy; in particular, the intensity of the slow relaxational component of the fluctuation spectra, which is frozen in the glass below the glass transition, is derived. Conditions for positive energy dissipation and symmetry relations are obtained in the framework of thermodynamic relaxation theory, and the memory functions occurring in the Mori-Zwanzig projection operator formalism are calculated.Dedicated to K. Dransfeld on the occasion of his 60th birthday     

Theoretical approaches to the glass transition in simple liquids

Theoretical approaches to the development of an understanding of the behaviour of simple supercooled liquids near the structural glass transition are reviewed and our work on this problem, based on the density functional theory of freezing and replicated liquid state theory, are summarized in this context. A few directions for further work on this problem are suggested.     

Macroscopic excitations in superconductors

The dynamical density functional theory (DDFT) as an alternative approach to the mode coupling theory (MCT) for supercooled liquids and glass transitions was recast in the path integral form, which can then be analyzed by the methods of equilibrium statistical mechanics. The hope is to avoid drastic approximations entering the original MCT such as factorization of the multiparticle correlation function. The renormalized perturbation theory is developed and the freezing is interpreted as a result of the life-time renormalization. The multicomponent extension of the theory is proposed, which could be treated exactly in the limit of infinite number of the components.     

Atomic mechanism of glass formation in supercooled monatomic liquids

Atomic mechanism of glass formation in supercooled monatomic liquids is monitored via analyzing the spatial arrangement of solid-like atoms. The supercooled states are obtained by cooling from the melt using molecular dynamics (MD) simulation. Solid-like atoms, detected via Lindemann-like freezing criterion, are found throughout the liquid. Their number increases with decreasing temperature and they form clusters. In the deeply supercooled region, all solid-like atoms form a single percolation cluster which spans throughout the system. The number of atoms in this cluster increases steeply with further cooling. Glass formation in supercooled liquids occurs when a single percolation cluster of solid-like atoms involves the majority of atoms in the system to form a relatively rigid glassy solid. By analyzing the temperature dependence of static and dynamic properties, we identify three characteristic temperatures of glass formation in supercooled liquids including the Vogel–Fulcher temperature.     

Statistical mechanics of the glass transition in one-component liquids with an anisotropic potential

We study a recently introduced model of one-component glass-forming liquids whose constituents interact with an anisotropic potential. This system is interesting per se and as a model of liquids such as glycerol (interacting via hydrogen bonds) which are excellent glass formers. We work out the statistical mechanics of this system, encoding the liquid and glass disorder using appropriate quasiparticles (36 of them). The theory provides a full explanation of the glass transition phenomenology, including the identification of a diverging length scale and a relation between the structural changes and the diverging relaxation times.     

Evolution of vibrational excitations in glassy systems

The equations of the mode-coupling theory (MCT) for ideal liquid-glass transitions are used for a discussion of the evolution of the density-fluctuation spectra of glass-forming systems for frequencies within the dynamical window between the band of high-frequency motion and the band of low-frequency-structural-relaxation processes. It is shown that the strong interaction between density fluctuations with microscopic wavelength and the arrested glass structure causes an anomalous-oscillation peak, which exhibits the properties of the so-called boson peak. It produces an elastic modulus which governs the hybridization of density fluctuations of mesoscopic wavelength with the boson-peak oscillations. This leads to the existence of high-frequency sound with properties as found by x-ray-scattering spectroscopy of glasses and glassy liquids. The results of the theory are demonstrated for a model of the hard-sphere system. It is also derived that certain schematic MCT models, whose spectra for the stiff-glass states can be expressed by elementary formulas, provide reasonable approximations for the solutions of the general MCT equations.     

Effect of planar defects on the stability of the Bragg glass phase of type-II superconductors

It is shown that the Bragg glass phase can become unstable with respect to planar crystal defects as twin or grain boundaries. A single defect plane that is oriented parallel to the magnetic field as well as to one of the main axis of the Abrikosov flux line lattice is always relevant, whereas we argue that a plane with higher Miller index is irrelevant, even at large defect potentials. A finite density of parallel defects with random separations can be relevant even for larger Miller indices. Defects that are aligned with the applied field restore locally the flux density oscillations which decay algebraically with distance from the defect. The current-voltage relation is changed to lnV(J) approximately -J(-1). The theory exhibits striking similarities to the physics of Luttinger liquids with impurities.     

Nearly logarithmic decay of correlations in glass-forming liquids

Nearly logarithmic decay of correlations, which was observed for several supercooled liquids in optical-Kerr-effect experiments [Phys. Rev. Lett. 84, 2437 (2000)]; Phys. Rev. Lett. 90, 197401 (2003)]], is explained within the mode-coupling theory for ideal glass transitions as a manifestation of the beta-peak phenomenon. A schematic model, which describes the dynamics by only two correlators, one referring to density fluctuations and the other to the reorientational fluctuations of the molecules, yields for strong rotation-translation coupling response functions in agreement with those measured for benzophenone and Salol for the time interval extending from 2 ps to about 20 and 200 ns, respectively.     

The relationship between kinetic and thermodynamic fragilities in metallic glass-forming liquids

The correlation between the temperature dependence of the kinetic and thermodynamic properties of a series of metallic glass-forming liquids is investigated using the concept of fragility. The results indicate a correlation between the kinetic fragility and thermodynamic fragility in these liquids. The correlation depends critically on the approach used to evaluate the thermodynamic fragility. Two distinct correlation lines are found for the metal–metalloid and for the all-metallic-constituents glass-forming liquids. For the same thermodynamic fragility the metal–metalloid liquids exhibit a distinctively larger kinetic fragility than the pure-metallic liquids. From the evaluation of the Gibbs free-energy difference between the undercooled liquid and the crystalline phase mixture, a correlation between the kinetic fragility and the driving force for nucleation is found, showing that for glass formation in metallic alloys the thermodynamic and kinetic contributions act together.     

Thermodynamic Properties of Inhomogeneous Structures in Supercooled Liquids

The weighted density-functional theory is applied to investigate the free-energy landscape of dense supercooled liquids. Metastable states intermediate to the liquid and crystal phases are found, which can be identified with the supercooled states seen in computer simulations. These states are marked by a lower degree of mass localization as compared to the highly localized state termed as "hard-sphere glass" found in earlier studies. We evaluate the free energy using the modified weighted density approximation (MWDA), as formulated by Denton and Ashcroft (1989) Phys. Rev. A , 39 , 4701. The inhomogeneous density is parametrized in terms of Gaussian profiles centered around random lattice sites. The effects of heterogeneity coming from a fluctuation of the width of these Gaussian profiles show that the free energy of the system increases with increase in the fluctuations and, finally, the metastable minima disappear with growing fluctuations.     

Idealized glass transitions under pressure: dynamics versus thermodynamics

The interplay of slow dynamics and thermodynamic features of dense liquids is studied by examining how the glass transition changes depending on the presence or absence of Lennard-Jones-like attractions. Quite different thermodynamic behavior leaves the dynamics unchanged, with important consequences for high-pressure experiments on glassy liquids. Numerical results are obtained within mode-coupling theory (MCT), but the qualitative features are argued to hold more generally. A simple square-well model can be used to explain generic features found in experiment.     

Theory of long wavelength collective motion in liquids

The theory of collective motion of liquids, recently suggested by the authors, has been found to explain successfully the three-peak structure for small momentum transfers, observed experimentally and confirmed by molecular dynamical calculations, in liquid rubidium. The theory happens to be the first microscopic theory of liquids which joins smoothly the zero-sound and hydrodynamical regions of density fluctuations in liquids.     

Heterogeneous dynamics at the glass transition in van der Waals liquids, in the bulk and in thin films

It has been shown over the last few years that the dynamics close to the glass transition is strongly heterogeneous, both by measuring the diffusion coefficient of tagged particles or by NMR studies. Recent experiments have also demonstrated that the glass transition temperature of thin polymer films can be shifted as compared to the same polymer in the bulk. We propose here first a thermodynamical model for van der Waals liquids, which accounts for experimental results regarding the bulk modulus of polymer melts and the evolution of the density with temperature. This model allows us to describe the density fluctuations in such van der Waals liquids. Then, by considering the thermally induced density fluctuations in the bulk, we propose that the 3D glass transition is controlled by the percolation of small domains of slow dynamics, which allows to explain the heterogeneous dynamics close to T _g. We show then that these domains percolate at a lower temperature in the quasi-2D case of thin suspended polymer films and we calculate the corresponding glass transition temperature reduction, in quantitative agreement with experimental results of Jones and co-workers. In the case of strongly adsorbed films, we show that the strong adsorption amounts to enhance the slow domains percolation. This effect leads to 1) a broadening of the glass transition and 2) an increase of T _g in quantitative agreement with experimental results. For both strongly and weakly adsorbed films, the shift in T _g is given by a power law, the exponent being the inverse of that of the correlation length of 3D percolation. Received 21 March 2000 and Received in final form 4 December 2000     

Out of Equilibrium Dynamics of the Toy Model with Mode Coupling and Trivial Hamiltonian

We extend our previous analysis of the toy model that mimics the mode coupling theory of supercooled liquids and glass transitions to the out of equilibrium dynamics. We derive a self-consistent set of equations for correlation and response functions.     

Can dynamic neutron scattering help to understand a thermodynamic variant of an internal quantum-mechanical experiment in the angstrom range?

A chain of ideas is described connecting the theory of quantum-mechanical experiments with practical research in the relaxation of liquids, biological materials, and materials science. The chain culminates at the proposal of an experimentum crucis comparing dynamic neutron scattering, dynamic calorimetry, and computer simulation of the same substances at the crossover region of the dynamic glass transition. The conclusiveness of the experimentum crucis backwards the chain is discussed. The role of relaxation of liquids in confining geometries is also discussed, especially with respect to the confirmation of the von Laue variant for the characteristic length of glass transition as alternative to their Gibbs treatment that results in too large lengths.Received: 1 January 2003, Published online: 14 October 2003PACS: 03.65.Ta Foundations of quantum mechanics; measurement theory - 64.70.Pf Glass transitions - 61.12.-q Neutron diffraction and scattering     

Laser-induced plasmas in liquids for nanoparticle synthesis

Spatially and temporally resolved emission spectroscopy is used to study the major features of the onset and evolution of plasmas created by pulsed laser irradiation of targets immersed in liquids. It is shown that double pulse operation provides an enhanced rate of nanoparticle formation and increases the emission signal from the plasma atoms and ions owing to more efficient ablation of the target material. The main parameters (density of atoms, electron temperature and density) of laser-induced plasmas in liquids are estimated. The prospects of laser ablation in liquids as a method for producing nanoparticles are analyzed.     

Glass-forming liquids,anomalous liquids,and polyamorphism in liquids and biopolymers

Summary Glass formation in nature and materials science is reviewed and the recent recognition of polymorphism within the glassy state, polyamorphism, is discussed. The process by which the glassy state originates during the continuous cooling or viscous slowdown process, is examined and the three canonical characteristics of relaxing liquids are correlated through the fragility. The conversion of strong liquids to fragile liquids by pressure-induced coordination number increases is discussed, and then it is shown that for the same type of system it is possible to have the same conversion accomplished via a first-order transition within the liquid state. The systems in which this can happen are of the same type which exhibit polyamorphism, and the whole phenomenology can be accounted for by a recent simple modification of the van der Waals model for tetrahedrally bonded liquids. The concept of complex amorphous systems which can lose a significant number of degrees of freedom through weak first-order transitions is then used to discuss the relation between native and denatured hydrated proteins, since the latter have much in common with plasticized chain polymer systems. Finally, we close the circle by taking a short-time-scale phenomenon given much attention by protein physicists,viz., the onset of an anomaly in the Debye-Waller factor with increasing temperature, and showing that for a wide variety of liquids, including computer-simulated strong and fragile ionic liquids, this phenomenon is closely correlated with the experimental glass transition temperature. This implies that the latter owes its origin to the onset of strong anharmonicity in certain components of the vibrational density of states (evidently related to the boson peak) which then permits the system to gain access to its configurational degrees of freedom. The more anharmonic these vibrational components, the closer to the Kauzmann temperature will commence the exploration of configuration space and, for a given configurational microstate degeneracy, the more fragile the liquid will be. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.