Predictions Of Mode-coupling Theory Research Articles

Tests of mode-coupling theory in two dimensions

We analyze the glassy dynamics of binary mixtures of hard disks in two dimensions. Predictions of the mode-coupling theory (MCT) are tested with extensive Brownian dynamics simulations. Measuring the collective particle density correlation functions in the vicinity of the glass transition, we verify four predicted mixing effects. For instance, for large size disparities, adding a small amount of small particles at a fixed packing fraction leads to a speedup in the long-time dynamics, while for small size disparities it leads to a slowing-down. Qualitative features of the nonergodicity parameters and the β relaxation, which both depend in a nontrivial way on the mixing ratio, are found in the simulated correlators. Studying one system in detail, we are able to determine its ideal MCT glass transition point as φ(c)=0.7948 and test MCT predictions quantitatively.

Glass Transition of the Monodisperse Gaussian Core Model

We numerically investigate the dynamical properties of the one-component Gaussian core model in supercooled states. We find that nucleation is increasingly suppressed with increasing density. The system concomitantly exhibits glassy, slow dynamics characterized by the two-step stretched exponential relaxation of the density correlation and a drastic increase of the relaxation time. We also find a weaker violation of the Stokes-Einstein relation and a smaller non-Gaussian parameter than in typical model glass formers, implying weaker dynamic heterogeneities. Additionally, the agreement of the simulation data with the prediction of mode-coupling theory is exceptionally good, indicating that the nature of the slow dynamics of this ultrasoft particle fluid is mean-field-like. This fact may be understood as a consequence of the long-range nature of the interaction.

Dynamic Facilitation Picture of a Higher-Order Glass Singularity

We show that facilitated spin mixtures with a tunable facilitation reproduce, on a Bethe lattice, the simplest higher-order singularity scenario predicted by the mode-coupling theory (MCT) of liquid-glass transition. Depending on the facilitation strength, they yield either a discontinuous glass transition or a continuous one, with no underlying thermodynamic singularity. Similar results are obtained for facilitated spin models on a diluted Bethe lattice. The mechanism of dynamical arrest in these systems can be interpreted in terms of bootstrap and standard percolation and corresponds to a crossover from a compact to a fractal structure of the incipient spanning cluster of frozen spins. Theoretical and numerical simulation results are fully consistent with MCT predictions.

Slow Dynamics in Liquid Metals as Seen by QENS

Abstract The quasielastic dynamics in liquid metals has been investigated by neutron scattering extensively during the past years. Precise measurements of the self-particle dynamics and the coherent quasielastic response provided conclusive evidence that the relaxation dynamics is governed by at least two processes. These two time scales in the correlation functions appear as two dynamical processes in their associated memory functions. One process shows a fast decay and is related to stochastic binary collisions. The second slow process stems from a non-linear coupling of slow collective modes. These slow density fluctuations arise mainly from the dynamics around the structure factor maximum. A rigorous treatment of these effects can be accomplished by mode coupling theory. A few selective experiments from monatomic metals are presented to demonstrate the influence of slow effects on the dynamics. Experiments and MD-simulations show a surprising good agreement with predictions of mode coupling theory on a quantitative level. The slow decay process appears to be related to structural arrest in the supercooled state and might indicate a link to the solidification process, starting deep in the liquid state. Accurate quasielastic neutron scattering experiments are still and will remain a fundamental pillar for elucidating the complex dynamics in the liquid state of metals.

Mode-coupling behavior of a Lennard-Jones binary mixture upon increasing confinement

Molecular dynamics simulations are performed on a Lennard Jones binary mixture confined in off lattice matrices of soft spheres with increasing radius. We focus on dynamics upon supercooling and in particular on testing the mode coupling theory properties of the confined mixture. Parameters of mode coupling theory in going from bulk to weak confinement, and from weak to strong confinement are extracted from simulations and analyzed. We focus on the study of the behavior of the single particle density correlators. We find that the mode coupling theory retains its validity also in the case of strong confinement, with a reduction of range of validity. The role of hopping is discussed in relation with the differences between the results obtained from the diffusion coefficients and the mode coupling theory predictions.

Atomic motions in poly(vinyl methyl ether): A combined study by quasielastic neutron scattering and molecular dynamics simulations in the light of the mode coupling theory

Quasielastic neutron scattering experiments (time-of-flight, neutron spin echo, and backscattering) on protonated poly(vinyl methyl ether) (PVME) have revealed the hydrogen dynamics above the glass-transition temperature. Fully atomistic molecular dynamics simulations properly validated with the neutron scattering results have allowed further characterization of the atomic motions accessing the correlation functions directly in real space. Deviations from Gaussian behavior are found in the high-momentum transfer range, which are compatible with the predictions of mode coupling theory (MCT). We have applied the MCT phenomenological version to the self-correlation functions of PVME atoms calculated from our simulation data, obtaining consistent results. The unusually large value found for the lambda-exponent parameter is close to that recently reported for polybutadiene and simple polymer models with intramolecular barriers.

Single-Particle and Collective Slow Dynamics of Colloids in Porous Confinement

Using molecular dynamics simulations, we study the slow dynamics of a hard sphere fluid confined in a disordered porous matrix. The presence of both discontinuous and continuous glass transitions as well as the complex interplay between single-particle and collective dynamics are well captured by a recent extension of mode-coupling theory for fluids in porous media. The degree of universality of the mode-coupling theory predictions for related models of colloids is studied by introducing size disparity between fluid and matrix particles, as well as softness in the interactions.

Dynamics in Cu46Zr42Al7Y5 melts: Interplay between packing density and viscosity

We have investigated microscopic dynamics in the bulk glass-forming Cu46Zr42Al7Y5 melts using quasielastic neutron scattering (QENS). Self-correlation functions show a fast β and a slow α-relaxation process. α relaxation exhibits stretching and is independent of momentum transfer and temperature. The melt is characterized by low packing density and high viscosity. The dynamics observed and the critical packing density derived from the QENS data are in good agreement with mode-coupling theory predictions for hard-sphere liquids. However, we can show that viscosity dominates over packing density in determining the atomic dynamics and glass-forming ability of the metallic melt.

Ergodicity breaking in strong and network-forming glassy systems

The temperature dependence of the nonergodicity factor of vitreous ${\text{GeO}}_{2}$, ${f}_{q}(T)$, as deduced from elastic and quasielastic neutron scattering experiments, is analyzed. The data are collected in a wide range of temperatures from the glassy phase, up to the glass-transition temperature, and well into the undercooled liquid state. Notwithstanding the investigated system is classified as prototype of strong glass, it is found that the temperature and the $q$ behavior of ${f}_{q}(T)$ follow some of the predictions of mode coupling theory. The experimental data support the hypothesis of the existence of an ergodic to nonergodic transition also in network-forming glassy systems.

Rheology of liquid fcc metals: Equilibrium and transient-time correlation-function nonequilibrium molecular dynamics simulations

Using classical molecular dynamics simulation together with the quantum-corrected Sutton-Chen many-body embedded-atom model, we study the rheology of several liquid fcc metals (Pb, Pt, Ir, Ag, and Rh) at ambient pressure and at four temperatures ranging from 5% below the melting temperature to 75% above the melting temperature. We first carry out equilibrium molecular dynamics simulations and determine, using Green-Kubo's formalism, the shear viscosity ${\ensuremath{\eta}}_{\text{GK}}$, the shear modulus ${G}_{\ensuremath{\infty}}$, and the Maxwell relaxation time ${\ensuremath{\tau}}_{M}$. By scaling the shear stress autocorrelation function or, equivalently, the time-dependent viscosity $\ensuremath{\eta}(t)$ by ${\ensuremath{\eta}}_{\text{GK}}$ and the time $t$ by ${\ensuremath{\tau}}_{M}$, we show that the scaled time-dependent viscosity for all metals collapses onto the same curve. This demonstrates that the relaxation behavior is the same for all metals studied here. We then apply transient-time correlation-function nonequilibrium molecular dynamics simulations to determine the response of liquid metals subjected to shear rates ranging from $10\text{ }{\text{s}}^{\ensuremath{-}1}$ to $5\ifmmode\times\else\texttimes\fi{}{10}^{12}\text{ }{\text{s}}^{\ensuremath{-}1}$. We show that for all metals, the shear rate-dependent viscosity $\ensuremath{\eta}(\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}})$ (scaled by ${\ensuremath{\eta}}_{\text{GK}}$) as a function of the applied shear rate $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}$ (scaled by the inverse of ${\ensuremath{\tau}}_{M}$) collapses onto the same curve. We obtain the same result for the shear rate-dependent pressure $P(\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}})$ (scaled by ${G}_{\ensuremath{\infty}}$) and for the potential energy (scaled by its equilibrium value). Fits to power-law expressions show that $\ensuremath{\eta}(\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}})$ follows the prediction of mode-coupling theory and that nonanalytic exponents are found for the shear rate dependence of pressure and potential energy.

Glass–liquid–glass reentrance in mono-component colloidal dispersions

The self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics isemployed to describe the ergodic–non-ergodic transition in model mono-disperse colloidaldispersions whose particles interact through hard-sphere plus short-ranged attractive forces.The ergodic–non-ergodic phase diagram in the temperature–concentration state space isdetermined for the hard-sphere plus attractive Yukawa model within the meanspherical approximation for the static structure factor by solving a remarkably simpleequation for the localization length of the colloidal particles. Finite real values ofthis property signals non-ergodicity and determines the non-ergodic parametersf(k) and fs(k). The resulting phase diagram for this system, which involves the existence of reentrant(repulsive and attractive) glass states, is compared with the corresponding prediction ofmode coupling theory. Although both theories coincide in the general features of this phasediagram, there are also clear qualitative differences. One of the most relevant is the SCGLEprediction that the ergodic–attractive glass transition does not preempt the gas–liquidphase transition, but always intersects the corresponding spinodal curve on itshigh-concentration side. We also calculate the ergodic–non-ergodic phase diagram for thesticky hard-sphere model to illustrate the dependence of the predicted SCGLE dynamicphase diagram on the choice of one important constituent element of the SCGLE theory.

Liquid-to-glass transition in bulk glass-formingCu60Ti20Zr20alloy by molecular dynamics simulations

We report results from molecular dynamics studies concerning the microscopic structure and dynamics of the ternary, bulk metallic glass-forming Cu60Ti20Zr20 alloy. In detail we consider the partial radial distribution functions, nearest-neighbor numbers, specific heat, simulated glass temperature, diffusion coefficients, and incoherent intermediate scattering function (ISF). The applied atomic model reproduces well experimental x-ray data of the total radial distribution function. It provides for Cu60Ti20Zr20 a structure with marked intermediate-range order. The ISF is analyzed within an extension of mode-coupling theory, where the effective memory kernel is evaluated from the Laplace transform of the ISF. The dynamics of the system fulfills in most respects the predictions of mode-coupling theory (MCT), up to an absence of the algebraic t{-a} decay in the early beta range. Comparison with the calculated memory kernel shows that this absence can be traced back to deviations of the kernel from its approximate form analyzed in MCT. As by-product, our investigation provides a method to reconstruct around the critical temperature major parts of the memory kernel from lambda and the plateau value f{c} of the ISF, and it indicates why the critical dynamics predicted by mode-coupling theory can be observed in a temperature interval of more than 500 K.

Spontaneous and induced dynamic correlations in glass formers. II. Model calculations and comparison to numerical simulations

We study in detail the predictions of various theoretical approaches, in particular, mode-coupling theory (MCT) and kinetically constrained models (KCMs), concerning the time, temperature, and wave vector dependence of multipoint correlation functions that quantify the strength of both induced and spontaneous dynamical fluctuations. We also discuss the precise predictions of MCT concerning the statistical ensemble and microscopic dynamics dependence of these multipoint correlation functions. These predictions are compared to simulations of model fragile and strong glass-forming liquids. Overall, MCT fares quite well in the fragile case, in particular, explaining the observed crucial role of the statistical ensemble and microscopic dynamics, while MCT predictions do not seem to hold in the strong case. KCMs provide a simplified framework for understanding how these multipoint correlation functions may encode dynamic correlations in glassy materials. However, our analysis highlights important unresolved questions concerning the application of KCMs to supercooled liquids.

Viscoelasticity and shear melting of colloidal star polymer glasses

Dispersions of multiarm star polymers in an athermal solvent are studied as a model system to explore the effects of soft colloidal interactions on the dynamics of colloidal glasses. Linear viscoelastic measurements in the glassy state are congruent with Mode Coupling Theory predictions for hard sphere glasses at moderate frequencies, indicating similarities in the relaxation processes of hard and soft colloidal glasses near equilibrium. On the other hand, distinct features of the star relaxation (related to arm disengagement) are observed to affect the nonlinear behavior associated with shear melting of the glass, which exhibits transitions previously unreported for hard sphere systems. Whereas a single maximum in G″(γ) is evident under large amplitude oscillatory shear at frequencies near the beta relaxation, secondary transitions between yielding and the onset of macroscopic flow are observed at higher and lower frequencies. The latter are annealed out upon complete fluidization of the star polymer suspension. The overall nonlinear behavior of the soft glassy suspension is interpreted in terms of two primary mechanisms: (i) deformation and yielding of the cage-like glassy microstructure, as in the hard sphere case, and (ii) local stretching and disengagement of interpenetrating arms of the colloidal star polymers.

Collective excitations in an early molten transition metal

We report inelastic x-ray scattering measurements of the atomic collective excitations of an early transition metal, namely liquid titanium at T=2020 K. The data show well-defined sound excitations with a low damping constant comparable to the damping observed in liquid alkali metals. Calculations of the spectrum of density fluctuations as a function of the excitation wave number based on a self-consistent mode-coupling approach were carried out. The calculations use only the number density and measured structure factors for the titanium and have no adjustable parameters. A remarkable agreement between the prediction of mode-coupling theory and experimental results was observed.

Relaxation scenarios in a mixture of large and small spheres: Dependence on the size disparity

We present a computational investigation on the slow dynamics of a mixture of large and small soft spheres. By varying the size disparity at a moderate fixed composition different relaxation scenarios are observed for the small particles. For small disparity density-density correlators exhibit moderate stretching. Only small quantitative differences are observed between dynamic features for large and small particles. On the contrary, large disparity induces a clear time scale separation between the large and small particles. Density-density correlators for the small particles become extremely stretched and display logarithmic relaxation by properly tuning the temperature or the wave vector. Self-correlators decay much faster than density-density correlators. For very large size disparity, a complete separation between self- and collective dynamics is observed for the small particles. Self-correlators decay to zero at temperatures where density-density correlations are frozen. The dynamic picture obtained by varying the size disparity resembles features associated with mode coupling transition lines of the types B and A at, respectively, small and very large size disparities. Both lines might merge, at some intermediate disparity, at a higher-order point, to which logarithmic relaxation would be associated. This picture resembles predictions of a recent mode coupling theory for fluids confined in matrices with interconnected voids [V. Krakoviack, Phys. Rev. Lett. 94, 065703 (2005)].

Mode-coupling theory predictions for a limited valency attractive square wellmodel

Recently we have studied, using numerical simulations, a limited valencymodel, i.e. an attractive square well model with a constraint on the maximumnumber of bonded neighbours. Studying a large region of temperaturesT and packingfractions ϕ, we have estimated the location of the liquid–gas phase separation spinodaland the loci of dynamic arrest, where the system is trapped in a disorderednon-ergodic state. Two distinct arrest lines for the system are present in thesystem: a (repulsive) glass line at high packing fraction, and a gel line at lowϕ andT. The former isessentially vertical (ϕ controlled), while the latter is rather horizontal(T controlled)in the (ϕ–T) plane. We here complement the molecular dynamics results with mode coupling theorycalculations, using the numerical structure factors as input. We find that the theorypredicts a repulsive glass line—in satisfactory agreement with the simulationresults—and an attractive glass line, which appears to be unrelated to the gel line.

Glass transition in 1,4-polybutadiene: Mode-coupling theory analysis of molecular dynamics simulations using a chemically realistic model

We present molecular dynamics simulations of the glass transition in a chemically realistic model of 1,4-polybutadiene (PBD). Around 40 K above the calorimetric glass transition of this polymer the simulations reveal a well-developed two-stage relaxation of all correlation functions. We have analyzed the time-scale separation between vibrational degrees of freedom (subpicosecond dynamics) and the alpha relaxation behavior (nanosecond to microsecond dynamics) using the predictions of mode-coupling theory (MCT). Our value for the mode-coupling critical temperature Tc agrees perfectly with prior experimental estimates for PBD. The predictions of MCT for the scaling behavior of the so-called beta relaxation, the plateau regime separating vibrational dynamics and the alpha relaxation, are well fulfilled. Furthermore, we are able to derive a consistent set of MCT exponents, completely characterizing the scaling behavior of relaxation processes in the vicinity of Tc. For the temperature dependence of the alpha relaxation we find deviations from MCT predictions which we trace to the influence of torsional barriers on the atomic motions.

Is there a higher-order mode coupling transition in polymer blends?

We present simulations on a binary blend of bead-spring polymer chains. The introduction of monomer size disparity yields very different relaxation times for each component of the blend. Competition between two different arrest mechanisms, namely, bulklike dynamics and confinement, leads to an anomalous relaxation scenario for the fast component, characterized by sublinear time dependence for mean squared displacements, or logarithmic decay and convex-to-concave crossover for density-density correlators. These anomalous dynamic features, which are observed over time intervals extending up to 4 decades, strongly resemble predictions of mode coupling theory for nearby higher-order transitions. Chain connectivity extends anomalous relaxation over a wide range of blend compositions.

Dynamics of fluids near the consolute critical point: A molecular-dynamics study of the Widom–Rowlinson mixture

Molecular-dynamics simulations are presented for the dynamic behavior of the Widom-Rowlinson mixture [B. Widom, and J. S. Rowlinson, J. Chem. Phys. 52, 1670 (1970)] at its critical point. This model consists of two components where like species do not interact and unlike species interact via a hard-core potential. Critical exponents are obtained from a finite-size scaling analysis. The self-diffusion coefficient shows no anomalous behavior near the critical point. The shear viscosity and thermal conductivity show no divergent behavior for the system sizes considered, although there is a significant critical enhancement. The mutual diffusion coefficient, D(AB), vanishes as D(AB) approximately xi(-1.26 +/- 0.08), where xi is the correlation length. This is different from the renormalization-group (D(AB) approximately xi(-1.065)) mode coupling theory (D(AB) approximately xi(-1)) predictions. The theories and simulations can be reconciled if we assume that logarithmic corrections to scaling are important.