Test Of Mode-coupling Theory Research Articles

Logarithmic Superdiffusion in Two Dimensional Driven Lattice Gases

The spreading of density fluctuations in two-dimensional driven diffusive systems is marginally anomalous. Mode coupling theory predicts that the diffusivity in the direction of the drive diverges with time as $(\ln t)^{2/3}$ with a prefactor depending on the macroscopic current-density relation and the diffusion tensor of the fluctuating hydrodynamic field equation. Here we present the first numerical verification of this behavior for a particular version of the two-dimensional asymmetric exclusion process. Particles jump strictly asymmetrically along one of the lattice directions and symmetrically along the other, and an anisotropy parameter $p$ governs the ratio between the two rates. Using a novel massively parallel coupling algorithm that strongly reduces the fluctuations in the numerical estimate of the two-point correlation function, we are able to accurately determine the exponent of the logarithmic correction. In addition, the variation of the prefactor with $p$ provides a stringent test of mode coupling theory.

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.

Tests of mode coupling theory in a simple model for two-component miscible polymerblends

We present molecular dynamics simulations of the structural relaxation of a simplebead–spring model for polymer blends. The introduction of a different monomer sizeinduces a large timescale separation for the dynamics of the two components. Simulationresults for a large set of observables probing density correlations, Rouse modes, andorientations of bond and chain end-to-end vectors are analysed within the framework of themode coupling theory (MCT). An unusually large value of the exponent parameter isobtained. This feature suggests the possibility of an underlying higher-order MCT scenariofor dynamic arrest.

Bond formation and slow heterogeneous dynamics in adhesive spheres with long-ranged repulsion: Quantitative test of mode coupling theory

A colloidal system of spheres interacting with both a deep and narrow attractive potential and a shallow long-ranged barrier exhibits a prepeak in the static structure factor. This peak can be related to an additional mesoscopic length scale of clusters and/or voids in the system. Simulation studies of this system have revealed that it vitrifies upon increasing the attraction into a gel-like solid at intermediate densities. The dynamics at the mesoscopic length scale corresponding to the prepeak represents the slowest mode in the system. Using mode coupling theory with all input directly taken from simulations, we reveal the mechanism for glassy arrest in the system at 40% packing fraction. The effects of the low-q peak and of polydispersity are considered in detail. We demonstrate that the local formation of physical bonds is the process whose slowing down causes arrest. It remains largely unaffected by the large-scale heterogeneities, and sets the clock for the slow cluster mode. Results from mode-coupling theory without adjustable parameters agree semiquantitatively with the local density correlators but overestimate the lifetime of the mesoscopic structure (voids).

Time-resolved optical Kerr effect experiments on supercooled benzene and test of mode-coupling theory

We have performed time-resolved optical Kerr effect experiments with heterodyne detection on benzene. We succeeded in supercooling benzene by 21 K below the melting point T m = 279 K, and we investigated the full range of existence from the supercooled phase up to the boiling point T b = 353 K. Our time-resolved data show clearly the complex relaxation pattern of benzene that is characterized by different time scales. These dynamic features, common to many other molecular liquids, to date have not been addressed and there is not a unique theoretical model able to explain them, even in a simple molecular liquid such as benzene. We compare our data with the predictions of a schematic mode-coupling model, fitting the experimental relaxations with a numerical solution of the time-dependent correlation functions. Although the temperature range investigated is clearly outside the asymptotic scaling regime, we found the mode-coupling model able to describe properly the measured dynamics in large time and temperature ranges.

Long time dynamics of Met-enkephalin: Tests of mode-coupling theory and implicit solvent models

We test a theory for the long time conformational dynamics of the penta-peptide Met-enkephalin by comparison with the explicit solvent molecular dynamics and implicit solvent Langevin dynamics simulations described earlier. Using the requisite equilibrium averages computed from these simulations and friction coefficients evaluated from shorter simulations obtained with the Pastor–Karplus scheme, the generalized Rouse and mode-coupling theory (MCT) generate a variety of time-correlation functions that probe both local and global dynamics. The comparison between different levels of MCT calculations demonstrates that the smallest eigenvalues (corresponding to the relaxation rates of the slowest modes) are insensitive to the choice of the high frequency coupled modes. Compared with the direct simulations, the MCT time correlation functions for the dynamics involving the motion of certain rigid groups, such as end-to-end, interphenyl vector or certain vectors between bonded backbone atoms, often exhibit a too rapid short time decay but an excellent representation of the long time relaxation rate. Thus, the MCT demonstrates its ability to predict the long time dynamics of solvated peptides using only atom friction coefficients and equilibrium averages, which are easier to simulate than the long time trajectories that are usually employed for probing dynamics with either explicit or implicit solvent descriptions.

Test of molecular mode coupling theory for general rigid molecules

We report recent progress on the test of mode coupling theory for molecular liquids (MMCT) for molecules of arbitrary shape. The MMCT equations in the long time limit are solved for supercooled water including all molecular degrees of freedom. In contrast to our earlier treatment of water as a linear molecule, we find that the glass-transition temperature T(c) is overestimated by the theory as was found in the case of simple liquids. The nonergodicity parameters are calculated from the "full" set of MMCT equations truncated at l(co)=2. These results are compared (i) with the nonergodicity parameters from MMCT with l(co)=2 in the "dipole" approximation n=n(')=0 and the diagonalization approximation n=n(')=0, l=l(') and (ii) with the corresponding results from a MD simulation. This work supports the possibility that a reduction to the most prominent correlators may constitute a valid approximation for solving the MMCT equations for rigid molecules.

Test of mode coupling theory for a supercooled liquid of diatomic molecules. I. Translational degrees of freedom

A molecular dynamics simulation is performed for a supercooled liquid of rigid diatomic molecules. The time-dependent self and collective density correlators of the molecular centers of mass are determined and compared with the predictions of the ideal mode coupling theory (MCT) for simple liquids. This is done in real as well as in momentum space. One of the main results is the existence of a unique transition temperature T_c, where the dynamics crosses over from an ergodic to a quasi-nonergodic behavior. The value for T_c agrees with that found earlier for the orientational dynamics within the error bars. In the beta- regime of MCT the factorization of space- and time dependence is satisfactorily fulfilled for both types of correlations. The first scaling law of ideal MCT holds in the von Schweidler regime, only, since the validity of the critical law can not be confirmed, due to a strong interference with the microscopic dynamics. In this first scaling regime a consistent description within ideal MCT emerges only, if the next order correction to the asymptotic law is taken into account. This correction is almost negligible for q=q_max, the position of the main peak in the static structure factor S(q), but becomes important for q=q_min, the position of its first minimum. The second scaling law, i.e. the time-temperature superposition principle, holds reasonably well for the self and collective density correlators and different values for q. The alpha-relaxation times tau_q^(s) and tau_q follow a power law in T-T_c over 2 -- 3 decades. The corresponding exponent gamma is weakly q-dependent and is around 2.55. This value is in agreement with the one predicted by MCT from the value of the von Schweidler exponent but at variance with the corresponding exponent gamma

Dynamics of a Supercooled Lennard-Jones System: Qualitative and Quantitative Tests of Mode-Coupling Theory

Using molecular dynamics computer simulations, we investigate the dynamics of a binary Lennard-Jones system at low temperatures. We show that this dynamics can be described well by mode-coupling theory. By solving numerically the mode-coupling equations for this system, we demonstrate that the theory is not only able to correctly predict the universal properties of this dynamics but also the nonuniversal properties.

Dynamics of a Supercooled Lennard-Jones System: Qualitative and Quantitative Tests of Mode-Coupling Theory

We present the results of a molecular dynamics computer simulation of a supercooled binary Lennard-Jones mixture. By investigating the temperature dependence of the diffusion constant and of the intermediate scattering function, we show that the ideal version of the mode-coupling theory of the glass transition is able to give a good qualitative description of the dynamics of this system. Using the partial structure factors, as determined from the simulation, as input, we solve the mode-coupling equations in the long time limit. From the comparison of the prediction of the theory for the critical temperature, the exponent parameter, the wave-vector dependence of the nonergodicity parameters and the critical amplitudes with the results of the simulation, we conclude that the theory is also able to predict correctly the non-universal properties of the dynamics of a supercooled simple liquid.

Testing of mode-coupling theory through impulsive stimulated thermal scattering

Abstract Impulsive stimulated thermal scattering, a time-domain light scattering technique spanning ps-ms time scales, allows a number of experimental tests of mode-coupling theory (MCT) predictions. Time-dependent acoustic responses and also slower relaxational responses to sudden heating are observed. From the acoustic responses, mechanical modulus spectra are deduced which permit testing of MCT predictions for α and β relaxation dynamics. From the relative intensities of acoustic and relaxational signals, the prediction of a cusp in the temperature-dependence of the nonergodicity parameter (Debye-Waller factor) can be tested. ISTS results from a concentrated (13 m%) aqueous LiCl solution, the molten salt [Ca(NO3)2]0.4[KNO3]0.6, and salol are reviewed.

Light scattering spectroscopy of the liquid-glass transition

Supercooled liquids approaching the liquid-glass transition exhibit unusual properties associated with structural relaxation. The mode-coupling theory (MCT) of supercooled liquid dynamics shows that non-linear interactions among density fluctuation modes can produce effects resembling these observations. MCT produces detailed predictions for the dynamics of density fluctuations in supercooled liquids, including a crossover from liquid to glassy dynamics at a critical temperature Tc. Recent light scattering studies of supercooled CaKNO3 are described that have provided detailed tests of MCT both above and below Tc, including a cusp in the scaling time at Tc=105+or-5 degrees C. These experiments are reviewed, and comparisons with both the idealized and extended versions of MCT are described.

Relaxation dynamics in a lattice gas: A test of the mode-coupling theory of the ideal glass transition.

By means of computer simulations we investigate the dynamical behavior of a binary lattice-gas mixture with short-range interactions in order to provide a stringent test of mode-coupling theory (MCT). The dynamics of the particles is given by Monte Carlo-like moves that change the positions of the particles and binary collisions that change the velocities. By monitoring the self part of the van Hove correlation function we find the low-temperature dynamics to be glasslike. In accordance with MCT, the imaginary part of the dynamic susceptibility χ'' shows a well-defined α peak whose high frequency wing follows a von Schweidler law with an exponent that is independent of temperature

Long-time tails of the velocity autocorrelation function in two- and three-dimensional lattice-gas cellular automata: A test of mode-coupling theory.

We report simulations of the velocity autocorrelation function (VACF) of a tagged particle in two- and three-dimensional lattice-gas cellular automata, using a new technique that is about a million times more efficient than the conventional techniques. The simulations clearly show the algebraic ${\mathit{t}}^{\mathrm{\ensuremath{-}}\mathit{D}/2}$ tail of the VACF. We compare the observed long-time tail with the predictions of mode-coupling theory. In three dimensions, the amplitude of this tail is found to agree within the (small) statistical error with these predictions. In two dimensions small but significant deviations from mode-coupling theory of up to 5% are observed.

Simulation of diffusion in a two-dimensional lattice-gas cellular automaton: A test of mode-coupling theory.

We compute the velocity autocorrelation function of a tagged particle in a two-dimensional lattice-gas cellular automaton using a method that is about a million times more efficient than existing techniques. A ${\mathrm{t}}^{\mathrm{\ensuremath{-}}1}$ algebraic tail in the tagged-particle velocity autocorrelation function is clearly observed. The amplitude of this tail is predicted to within a few percent by a lattice-gas version of mode-coupling theory. The magnitude of logarithmic corrections to the ${\mathrm{t}}^{\mathrm{\ensuremath{-}}1}$ tail is much smaller than expected for continuous fluids.