Application Of Mode-coupling Theory Research Articles

Mode-Coupling Theory of the Glass Transition: A Primer

Understanding the physics of glass formation remains one of the major unsolved challenges of condensed matter science. As a material solidifies into a glass, it exhibits a spectacular slowdown of the dynamics upon cooling or compression, but at the same time undergoes only minute structural changes. Among the numerous theories put forward to rationalize this complex behavior, Mode-Coupling Theory (MCT) stands out as the only framework that provides a fully first-principles-based description of glass phenomenology. This review outlines the key physical ingredients of MCT, its predictions, successes, and failures, as well as recent improvements of the theory. We also discuss the extension and application of MCT to the emerging field of non-equilibrium active soft matter

Glass physics: from fundamentals to applications

A new focus on glass physics has arisen with the emergence, on the one hand, of soft glassy materials in technologically significant and biological contexts, and, on the other hand, of metallic glasses that present intriguing opportunities for the efficient manufacture of valuable high strength components. The slow dynamics that develops in liquids cooled toward the glass transition temperature and the nature of the glass transition that follows remain at the core of the glass puzzle, and endure as grand theoretical challenges in understanding condensed matter. However, a focus on the applications of these new materials has resulted in a flowering of investigations on the origin of aging, dynamical heterogeneity and slow relaxation with a focus on relating glass structure to the prediction of important properties such as fragility, glass formability, rheology and elastic and plastic responses to mechanical stress. Simultaneously the scope of research has expanded in new directions owing to advances in research tools ranging from more powerful computational capabilities to improved scattering facilities and advanced imaging techniques. Sustained engagement between physical scientists and the materials science communities working to unlock the technological capabilities of specific glasses has generated a renewed interest in previously underappreciated gaps in our understanding, expanding the productive interface between fundamental and applied investigations in glass physics. This special issue in European Physical Journal E brings together a cross-section of research advances, highlighting the diversity of basic and applied interest in glassy behavior in a wide range of systems (colloidal, polymer, chalcogenide, metallic, granular, biomolecular, organic and oxide glasses). Several papers discuss theoretical and computational investigations of model glass formers such as a critique of structure-based microscopic theories of dynamics and a field-theoretic description of dynamical heterogeneity. The papers in this issue showcase examples of cross-fertilization, such as the application of mode-coupling theory, extensively employed in analyzing slow dynamics in glass-forming liquids, to analyzing motion under shear, but also energy-landscape analysis of mechanical deformation, the study of heterogeneity effects in polymer thin films and the jamming behavior in polymer solutions, to name but a few examples. We hope that this compilation will serve the purpose of furthering the interaction across the boundaries between fundamental and applied research, and among practitioners in different sub-areas, leading to the emergence of new thrust directions, concepts, and exciting developments.

Dynamics of hydrogen bonds: how to probe their role in the unusual properties of liquidwater

The dynamics of hydrogen bonds between water molecules is probed by means of coherentquasielastic neutron scattering. The choice of appropriate values of the momentum transfergives information about the time dependence of the DD partial of the scattering function ofD2O. Experimental results demonstrate that the temperature dependence of the dynamics ofhydrogen bonds is weak, in contrast with that of the transport properties of liquid water.We discuss our results in view of a recent application of mode coupling theory to describethe dynamics in polymer melts (Richter et al 1998 Physica B 241–243 1005). In particular,we give arguments in favour of a normal (Arrhenius) temperature dependence ofhydrogen bond dynamics at extremely low temperatures. We relate this dynamics toβ relaxation. This is in contrast to what happens with polymer gels, where theα processes, related to backbone movement, block the molecular motions. The anomalous(non-Arrhenius) temperature dependence of the transport properties of water is thereforedue to the increased number of hydrogen bonds, rather then to their intrinsic dynamics,which remains fast.

Shear viscosity of molten alkali halides from equilibrium and nonequilibrium molecular-dynamics simulations

The shear viscosity of molten NaCl and KCl was calculated through equilibrium (EMD) and nonequilibrium molecular-dynamics (NEMD) simulations in the canonical (N,V,T) ensemble. Two rigid-ion potentials were investigated, namely, the Born-Mayer-Huggins-Tosi-Fumi potential and the Michielsen-Woerlee-Graaf-Ketelaar potential with the parameters proposed by Ladd. The NEMD simulations were performed using the SLLOD equations of motion [D. J. Evans and G. P. Morriss, Phys. Rev. A 30, 1528 (1984)] with a Gaussian isokinetic thermostat and the results are compared with those obtained from Green-Kubo EMD (N,V,T) simulations and experimental shear viscosity data. The NEMD zero strain rate shear viscosity, eta(0), was obtained by fitting a simplified Carreau-type equation and by application of mode-coupling theory, i.e., a eta-gamma(1/2) linear relationship. The values obtained from the first method are found to be significantly lower than those predicted by the second. The agreement between the EMD and NEMD results with experimental data is satisfactory for the two potentials investigated. The ion-ion radial distribution functions obtained with the two rigid-ion potentials for both molten salts are discussed in terms of the differences between the two models.

Post-seismic relaxation theory on a laterally heterogeneous viscoelastic model

Investigation was carried out into the problem of relaxation of a laterally heterogeneous viscoelastic Earth following an impulsive moment release event. The formal solution utilizes a semi-analytic solution for post-seismic deformation on a laterally homogeneous Earth constructed from viscoelastic normal modes, followed by application of mode coupling theory to derive the response on the aspherical Earth. The solution is constructed in the Laplace transform domain using the correspondence principle and is valid for any linear constitutive relationship between stress and strain. The specific implementation described in this paper is a semi-analytic discretization method which assumes isotropic elastic structure and a Maxwell constitutive relation. It accounts for viscoelastic–gravitational coupling under lateral variations in elastic parameters and viscosity. For a given viscoelastic structure and minimum wavelength scale, the computational effort involved with the numerical algorithm is proportional to the volume of the laterally heterogeneous region. Examples are presented of the calculation of post-seismic relaxation with a shallow, laterally heterogeneous volume following synthetic impulsive seismic events, and they illustrate the potentially large effect of regional 3-D heterogeneities on regional deformation patterns.

On the applicability of mode coupling theory to a ϕ 4-model with first order phase transition

A ϕ 4-model with symmetric double-well-like on-site potential and anharmonic, infinite range interactions is investigated. This model exhibits a first order phase transition at a temperature T c. The time-dependent displacement correlation function is studied in the framework of the mode coupling theory (MCT). Depending on the choice of slow modes, MCT makes qualitatively different predictions which are compared with MD-results. These numerical results suggest that only the order parameter mode {ie1-1} should be considered as slow. In that case it is shown that MCT yields a dynamical transition in the supercooled high-temperature phase {ie1-2} at a temperature T* which coincides with the spinodal temperature T s (T s = 0 for our model) where the metastable supercooled phase becomes instable.

Ergodicity of a system with second-order phase transition: applicability of mode coupling theory

The authors investigate the applicability of mode coupling theory (MCT) to a system with a second-order phase transition. They have calculated numerically the time autocorrelation function of pseudo-spin variables for a phi 4-model with infinite range interactions. In contrast to some Lennard-Jones liquids they do not find any evidence for an ergodic to non-ergodic instability as predicted by Aksenov et al. using MCT. They argue that this instability, at least for the phi 4-model (with short- or long-range interactions), is a consequence of the approximations performed within the MCT. However, they stress that the results do not imply the same conclusion for supercooled liquids. The relaxation is non-Debye with a mean relaxation time tau (T, N) (N is the number of atoms) exhibiting a rather unusual temperature dependence. In contrast to Arrhenius behaviour the relaxation becomes accelerated with decreasing temperature as long as T is sufficiently above the critical temperature Tc. For finite N the results indicate a scaling law tau (T, N)=N tau 0(T) for large N.

The application of mode coupling theory to the transmission of sound in the sidebranch of a rectangular duct system

Mode coupling is applied to rectangular ducts of the size encountered in modern ventilation systems. Theory is developed to describe the transmission of sound along a straight duct, and along a sidebranch. Acoustic impedance boundary conditions at the duct walls are included. Experimental and predicted results are presented for the frequency spectra, cross-sectional variation and longitudinal variation in the entry and sidebranch ducts caused by a pure tone source. Good agreement is shown between the two sets of results.

Application of Mode-Coupling Theory to Nonlinear Stress Tensor in Fluids

In a steady state of fluid the nonlinear dependence of stress tensor on a thermal driving force is investigated by a direct extension of the mode-coupling theory to far-from-equilibrium situation. The steady state is generated from a local equilibrium state having the same average values of gross variables as in the steady state. In the lowest approximation for the mode-coupling term ·the explicit expression of the stress tensor is obtained and evaluated. The effects of the higher mode-coupling approximations on the stress tensor are also briefly examined.