arXiv subjects

Walter Kob

Publications and source records attributed to Walter Kob.

171 records · Page 10Linked to original sources

arXiv1997

Molecular Dynamics Computer Simulation of the Dynamics of Supercooled Silica

We present the results of a large scale computer simulation of supercooled silica. We find that at high temperatures the diffusion constants show a non-Arrhenius temperature dependence whereas at low temperature this dependence is also compatible with an Arrhenius law. We demonstrate that at low temperatures the intermediate scattering function shows a two-step relaxation behavior and that it obeys the time temperature superposition principle. We also discuss the wave-vector dependence of the nonergodicity parameter and the time and temperature dependence of the non-Gaussian parameter.

cond-mat.dis-nn↗

arXiv1997

The electronic structure of amorphous silica: A numerical study

We present a computational study of the electronic properties of amorphous SiO2. The ionic configurations used are the ones generated by an earlier molecular dynamics simulations in which the system was cooled with different cooling rates from the liquid state to a glass, thus giving access to glass-like configurations with different degrees of disorder [Phys. Rev. B 54, 15808 (1996)]. The electronic structure is described by a tight-binding Hamiltonian. We study the influence of the degree of disorder on the density of states, the localization properties, the optical absorption, the nature of defects within the mobility gap, and on the fluctuations of the Madelung potential, where the disorder manifests itself most prominently. The experimentally observed mismatch between a photoconductivity threshold of 9 eV and the onset of the optical absorption around 7 eV is interpreted by the picture of eigenstates localized by potential energy fluctuations in a mobility gap of approximately 9 eV and a density of states that exhibits valence and conduction band tails which are, even in the absence of defects, deeply located within the former band gap.

cond-mat.dis-nn↗

arXiv1996

A quantitative test of the mode-coupling theory of the ideal glass transition for a binary Lennard-Jones system

Using a molecular dynamics computer simulation we determine the temperature dependence of the partial structure factors for a binary Lennard-Jones system. These structure factors are used as input data to solve numerically the wave-vector dependent mode-coupling equations in the long time limit. Using the so determined solutions, we compare the predictions of mode-coupling theory (MCT) with the results of a previously done molecular dynamics computer simulation [Phys. Rev. E 51, 4626 (1995), ibid. 52, 4134 (1995)]. From this comparison we conclude that MCT gives a fair estimate of the critical coupling constant, a good estimate of the exponent parameter, predicts the wave-vector dependence of the various nonergodicity parameters very well, except for very large wave-vectors, and gives also a very good description of the space dependence of the various critical amplitudes. In an attempt to correct for some of the remaining discrepancies between the theory and the results of the simulation, we investigate two small (ad hoc) modifications of the theory. We find that one modification gives a worse agreement between theory and simulation, whereas the second one leads to an improved agreement.

cond-mat↗

arXiv1996

Cooling rate effects in amorphous Silica: A Computer Simulation Study

Using molecular dynamics computer simulations we investigate how in silica the glass transition and the properties of the resulting glass depend on the cooling rate with which the sample is cooled. By coupling the system to a heat bath with temperature $T_b(t)$, we cool the system linearly in time, $T(t)=T_i-γt$, where $γ$ is the cooling rate. We find that the glass transition temperature $T_g$ is in accordance with a logarithmic dependence on the cooling rate. In qualitative accordance with experiments, the density shows a local maximum, which becomes more pronounced with decreasing cooling rate. The enthalpy, density and the thermal expansion coefficient for the glass at zero temperature decrease with decreasing $γ$. We show that also microscopic quantities, such as the radial distribution function, the bond-bond angle distribution function, the coordination numbers and the distribution function for the size of the rings depend significantly on $γ$. We demonstrate that the cooling rate dependence of these microscopic quantities is significantly more pronounced than the one of macroscopic properties. Furthermore we show that these microscopic quantities, as determined from our simulation, are in good agreement with the ones measured in real experiments, thus demonstrating that the used potential is a good model for silica glass. The vibrational spectrum of the system also shows a significant dependence on the cooling rate and is in qualitative accordance with the one found in experiments. Finally we investigate the properties of the system at finite temperatures in order to understand the microscopic mechanism for the density anomaly. We show that the anomaly is related to a densification and subsequent opening of the tetrahedral network when the temperature is decreased, whereas

cond-mat↗

arXiv1996

How do the properties of a glass depend on the cooling rate? A computer simulation study of a Lennard-Jones system

Using molecular dynamics computer simulations we investigate how the glass transition and the properties of the resulting glass depend on the cooling rate with which the sample has been quenched. This is done by studying a two component Lennard-Jones system which is coupled to a heat bath whose temperature is decreased from a high temperature, where the system is a liquid, to zero temperature, where the system is a glass. The temperature $T_b$ of the heat bath is decreased linearly in time, i.e. $T_b=T_0-γt$, where $γ$ is the cooling rate. In accordance with simple theoretical arguments and with experimental observations we find that the glass transition, as observed in the specific heat and the thermal expansion coefficient, becomes sharper when $γ$ is decreased. A decrease of the cooling rate also leads to a decrease of the glass transition temperature $T_g$ and we show that the dependence of $T_g$ on $γ$ can be rationalized by assuming that the temperature dependence of the relaxation times of the system is given by either a Vogel-Fulcher law or a power-law. By investigating the structural properties of the glass, such as the radial distribution functions, the coordination numbers and the angles between three neighbor-sharing particles, we show how the local order of the glass increases with decreasing cooling rate. The enthalpy and the density of the glass decrease and increase, respectively, with decreasing $γ$. By investigating the $γ$ dependence of clusters of nearest neighbors, we show how these observations can be understood from a microscopic point of view. We also show that the spectrum of the glass, as computed from the dynamical matrix, shows a shift towards higher frequencies when $γ$ is decreased. All these effects show that there is a significant

cond-mat↗

arXiv1995

Testing Mode-Coupling Theory for a Supercooled Binary Lennard-Jones Mixture II: Intermediate Scattering Function and Dynamic Susceptibility

We have performed a molecular dynamics computer simulation of a supercooled binary Lennard-Jones system in order to compare the dynamical behavior of this system with the predictions of the idealized version of mode-coupling theory (MCT). By scaling the time $t$ by the temperature dependent $α$-relaxation time $τ(T)$, we find that in the $α$-relaxation regime $F(q,t)$ and $F_s(q,t)$, the coherent and incoherent intermediate scattering functions, for different temperatures each follows a $q$-dependent master curve as a function of scaled time. We show that during the early part of the $α$-relaxation, which is equivalent to the late part of the $β$-relaxation, these master curves are well approximated by the master curve predicted by MCT for the $β$-relaxation. This part is also fitted well by a power-law, the so-called von Schweidler law. We show that the effective exponent $b'$ of this power-law depends on the wave vector $q$ if $q$ is varied over a large range. The early part of the $β$-relaxation regime does not show the critical decay predicted by MCT. The $q$-dependence of the nonergodicity parameter for $F_{s}(q,t)$ and $F(q,t)$ are in qualitative agreement with MCT. On the time scale of the late $α$-relaxation the correlation functions show a Kohlrausch-Williams-Watt behavior (KWW). The KWW exponent $β$ is significantly different from the effective von Schweidler exponent $b'$. At low temperatures the $α$-relaxation time $τ(T)$ shows a power-law behavior with a critical temperature that is the same as the one found previously for the diffusion constant [Phys. Rev. Lett. {\bf 73}, 1376 (1994)]. The critical exponent of this power-law and the von Schweidler exponent $b'$ fulfill the connection proposed by MCT between these two quantities. We also show that the

cond-mat↗

arXiv1995

Testing Mode-Coupling Theory for a Supercooled Binary Lennard-Jones Mixture I: The van Hove Correlation Function

We report the results of a large scale computer simulation of a binary supercooled Lennard-Jones liquid. We find that at low temperatures the curves for the mean squared displacement of a tagged particle for different temperatures fall onto a master curve when they are plotted versus rescaled time $tD(T)$, where $D(T)$ is the diffusion constant. The time range for which these curves follow the master curve is identified with the $α$-relaxation regime of mode-coupling theory (MCT). This master curve is fitted well by a functional form suggested by MCT. In accordance with idealized MCT, $D(T)$ shows a power-law behavior at low temperatures. The critical temperature of this power-law is the same for both types of particle and also the critical exponents are very similar. However, contrary to a prediction of MCT, these exponents are not equal to the ones determined previously for the divergence of the relaxation times of the intermediate scattering function [Phys. Rev. Lett. {\bf 73}, 1376 (1994)]. At low temperatures the van Hove correlation function (self as well as distinct part) shows hardly any sign of relaxation in a time interval that extends over about three decades in time. This time interval can be interpreted as the $β$-relaxation regime of MCT. From the investigation of these correlation functions we conclude that hopping processes are not important on the time scale of the $β$-relaxation for this system and for the temperature range investigated. We test whether the factorization property predicted by MCT holds and find that this is indeed the case for all correlation functions investigated. The distance dependence of the critical amplitudes are in qualitative accordance with the ones predicted by MCT for some other mixtures. The non-gaussian parameter for the self part of the van

cond-mat↗

arXiv1994

Scaling behavior in the dynamics of a supercooled Lennard-Jones mixture

We present the results of a large scale molecular dynamics computer simulation of a binary, supercooled Lennard-Jones fluid. At low temperatures and intermediate times the time dependence of the intermediate scattering function is well described by a von Schweidler law. The von Schweidler exponent is independent of temperature and depends only weakly on the type of correlator. For long times the correlation functions show a Kohlrausch behavior with an exponent $β$ that is independent of temperature. This dynamical behavior is in accordance with the mode-coupling theory of supercooled liquids.

cond-mat↗

arXiv1994

Scaling behavior in the $β$-relaxation regime of a supercooled Lennard-Jones mixture

We report the results of a molecular dynamics simulation of a supercooled binary Lennard-Jones mixture. By plotting the self intermediate scattering functions vs. rescaled time, we find a master curve in the $β$-relaxation regime. This master curve can be fitted well by a power-law for almost three decades in rescaled time and the scaling time, or relaxation time, has a power-law dependence on temperature. Thus the predictions of mode-coupling-theory on the existence of a von Schweidler law are found to hold for this system; moreover, the exponents in these two power-laws are very close to satisfying the exponent relationship predicted by the mode-coupling-theory. At low temperatures, the diffusion constants also show a power-law behavior with the same critical temperature. However, the exponent for diffusion differs from that of the relaxation time, a result that is in disagreement with the theory.

cond-mat↗