arXiv subjects

Walter Kob

Publications and source records attributed to Walter Kob.

At least 145 records · Page 8Linked to original sources

arXiv2000

Structure and Dynamics of amorphous Silica Surfaces

We use molecular dynamics computer simulations to study the equilibrium properties of the surface of amorphous silica. Two types of geometries are investigated: i) clusters with different diameters (13.5Å, 19Å, and 26.5Å) and ii) a thin film with thickness 29Å. We find that the shape of the clusters is independent of temperature and that it becomes more spherical with increasing size. The surface energy is in qualitative agreement with the experimental value for the surface tension. The density distribution function shows a small peak just below the surface, the origin of which is traced back to a local chemical ordering at the surface. Close to the surface the partial radial distribution functions as well as the distributions of the bond-bond angles show features which are not observed in the interior of the systems. By calculating the distribution of the length of the Si-O rings we can show that these additional features are related to the presence of two-membered rings at the surface. The surface density of these structures is around 0.6/nm^2 in good agreement with experimental estimates. From the behavior of the mean-squared displacement at low temperatures we conclude that at the surface the cage of the particles is larger than the one in the bulk. Close to the surface the diffusion constant is somewhat larger than the one in the bulk and with decreasing temperature the relative difference grows. The total vibrational density of states at the surface is similar to the one in the bulk. However, if only the one for the silicon atoms is considered, significant differences are found.

cond-mat.stat-mech↗

arXiv2000

Finite-size scaling at the dynamical transition of the mean-field 10-state Potts glass

We use Monte Carlo simulations to study the static and dynamical properties of a Potts glass with infinite range Gaussian distributed exchange interactions for a broad range of temperature and system size up to N=2560 spins. The results are compatible with a critical divergence of the relaxation time tau at the theoretically predicted dynamical transition temperature T_D, tau \propto (T-T_D)^{-Δ} with Delta \approx 2. For finite N a further power law at T=T_D is found, tau(T=T_D) \propto N^{z^\star} with z^\star \approx 1.5 and for T>T_D dynamical finite-size scaling seems to hold. The order parameter distribution P(q) is qualitatively compatible with the scenario of a first order glass transition as predicted from one-step replica symmetry breaking schemes.

cond-mat.stat-mech↗

arXiv2000

The Debye-Waller factor of liquid silica: Theory and simulation

We show that the prediction of mode-coupling theory for a model of a network-forming strong glass-former correctly describes the wave-vector dependence of the Debye-Waller factor. To obtain a good description it is important to take into account the triplet correlation function c_3, which we evaluate from a computer simulation. Our results support the possibility that this theory is able to accurately describe the non-ergodicity parameters of simple as well as of network-forming liquids.

cond-mat.stat-mech↗

arXiv2000

Frequency dependent specific heat of viscous silica

We apply the Mori-Zwanzig projection operator formalism to obtain an expression for the frequency dependent specific heat c(z) of a liquid. By using an exact transformation formula due to Lebowitz et al., we derive a relation between c(z) and K(t), the autocorrelation function of temperature fluctuations in the microcanonical ensemble. This connection thus allows to determine c(z) from computer simulations in equilibrium, i.e. without an external perturbation. By considering the generalization of K(t) to finite wave-vectors, we derive an expression to determine the thermal conductivity λfrom such simulations. We present the results of extensive computer simulations in which we use the derived relations to determine c(z) over eight decades in frequency, as well as λ. The system investigated is a simple but realistic model for amorphous silica. We find that at high frequencies the real part of c(z) has the value of an ideal gas. c'(ω) increases quickly at those frequencies which correspond to the vibrational excitations of the system. At low temperatures c'(ω) shows a second step. The frequency at which this step is observed is comparable to the one at which the α-relaxation peak is observed in the intermediate scattering function. Also the temperature dependence of the location of this second step is the same as the one of the $α-$peak, thus showing that these quantities are intimately connected to each other. From c'(ω) we estimate the temperature dependence of the vibrational and configurational part of the specific heat. We find that the static value of c(z) as well as λare in good agreement with experimental data.

cond-mat.stat-mech↗

arXiv2000

The entrance dynamics of polymers into a gel

We use computer simulations to study the (driven) dynamics of a charged polymer in a disordered medium, thus mimicking the setting used in gel electrophoresis. In agreement with experiments, we find that inside the gel the mobility of the polymer is only a weak function of its length N. In contrast to this, the mean entrance time into the gel, is a very strong function of N, \propto N^1.3, and does not show any sign of saturation with increasing N. We rationalize this effect by means of a simple model and propose an experimental setup that should allow to increase the separation ability of gel electrophoresis significantly.

cond-mat.stat-mech↗

arXiv2000

Equilibrating Glassy Systems with Parallel Tempering

We discuss the efficiency of the so-called parallel tempering method to equilibrate glassy systems also at low temperatures. The main focus is on two structural glass models, SiO_2 and a Lennard-Jones system, but we also investigate a fully connected 10 state Potts-glass. By calculating the mean squared displacement of a tagged particle and the spin-autocorrelation function, we find that for these three glass-formers the parallel tempering method is indeed able to generate, at low temperatures, new independent configurations at a rate which is O(100) times faster than more traditional algorithms, such as molecular dynamics and single spin flip Monte Carlo dynamics. In addition we find that this speedup increases with decreasing temperature. The reliability of the results is checked by calculating the distribution of the energy at various temperatures and by showing that these can be mapped onto each other by the reweighting technique.

cond-mat.stat-mech↗

arXiv2000

The relaxation dynamics of a simple glass former confined in a pore

We use molecular dynamics computer simulations to investigate the relaxation dynamics of a binary Lennard-Jones liquid confined in a narrow pore. We find that the average dynamics is strongly influenced by the confinement in that time correlation functions are much more stretched than in the bulk. By investigating the dynamics of the particles as a function of their distance from the wall, we can show that this stretching is due to a strong dependence of the relaxation time on this distance, i.e. that the dynamics is spatially very heterogeneous. In particular we find that the typical relaxation time of the particles close to the wall is orders of magnitude larger than the one of particles in the center of the pore.

cond-mat.stat-mech↗

arXiv2000

Static and dynamical properties of a supercooled liquid confined in a pore

We present the results of a Molecular Dynamics computer simulation of a binary Lennard-Jones liquid confined in a narrow pore. The surface of the pore has an amorphous structure similar to that of the confined liquid. We find that the static properties of the liquid are not affected by the confinement, while the dynamics changes dramatically. By investigating the time and temperature dependence of the intermediate scattering function we show that the dynamics of the particles close to the center of the tube is similar to the one in the bulk, whereas the characteristic relaxation time tau_q(T,rho) of the intermediate scattering function at wavevector q and distance rho from the axis of the pore increases continuously when approaching the wall, leading to an apparent divergence in the vicinity of the wall. This effect is seen for intermediate temperatures down to temperatures close to the glass transition. The rho-dependence of tau_q(T,rho) can be described by an empirical law of the form tau_q(T,ρ)=f_q(T) exp [Delta_q/(rho_p-rho)], where Delta_q and ρ_q are constants, and f_q(T) is the only parameter which shows a significant temperature dependence.

cond-mat.stat-mech↗

arXiv2000

Replica-exchange molecular dynamics simulation for supercooled liquids

We investigate to what extend the replica-exchange Monte Carlo method is able to equilibrate a simple liquid in its supercooled state. We find that this method does indeed allow to generate accurately the canonical distribution function even at low temperatures and that its efficiency is about 10-100 times higher than the usual canonical molecular dynamics simulation.

cond-mat.soft↗

arXiv1999

Supercooled Liquids and Glasses

In these lectures, which were presented at "Soft and Fragile Matter, Nonequilibrium Dynamics, Metastability and Flow" University of St. Andrews, 8 July - 22 July, 1999, I give an introduction to the physics of supercooled liquids and glasses and discuss some computer simulations done to investigate these systems.

cond-mat.stat-mech↗

arXiv1999

Structural and dynamical properties of sodium silicate melts: An investigation by molecular dynamics computer simulation

We present the results of large scale computer simulations in which we investigate the static and dynamic properties of sodium disilicate and sodium trisilicate melts. We study in detail the static properties of these systems, namely the coordination numbers, the temperature dependence of the Q^(n) species and the static structure factor, and compare them with experiments. We show that the structure is described by a partially destroyed tetrahedral SiO_4 network and the homogeneously distributed sodium atoms which are surrounded on average by 16 silicon and other sodium atoms as nearest neighbors. We compare the diffusion of the ions in the sodium silicate systems with that in pure silica and show that it is much slower in the latter. The sodium diffusion is characterized by an activated hopping through the Si-O matrix which is frozen with respect to the movement of the sodium atoms. We identify the elementary diffusion steps for the sodium and the oxygen diffusion and find that in the case of sodium they are related to the breaking of a Na-Na bond and in the case of oxygen to that of a Si-O bond. From the self part of the van Hove correlation function we recognize that at least two successive diffusion steps of a sodium atom are spatially highly correlated with each other. With the same quantity we show that at low temperatures also the oxygen diffusion is characterized by activated hopping events.

cond-mat.stat-mech↗

arXiv1999

Aging in a simple glassformer

Using molecular dynamics computer simulations we investigate the out-of-equilibrium dynamics of a Lennard-Jones system after a quench from a high temperature to one below the glass transition temperature. By studying the radial distribution function we give evidence that during the aging the system is very close to the critical surface of mode-coupling theory. Furthermore we show that two-time correlation functions show a strong dependence on the waiting time since the quench and that their shape is very different from the one in equilibrium. By investigating the temperature and time dependence of the frequency distribution of the normal modes we show that the energy of the inherent structures can be used to define an effective (time dependent) temperature of the aging system.

cond-mat.stat-mech↗

arXiv1999

High Frequency Dynamics of Amorphous Silica

We present the results of extensive molecular dynamics computer simulations in which the high frequency dynamics of silica, nu>0.5 THz, is investigated in the viscous liquid state as well as in the glass state. We characterize the properties of high frequency sound modes by analyzing J_l(q,nu) and J_t(q,nu), the longitudinal and transverse current correlation function, respectively. For wave-vectors q>0.4 Angstrom^{-1} the spectra are sitting on top of a flat background which is due to multiphonon excitations. In the acoustic frequency band, i.e. for nu<20 THz, the intensity of J_l(q,nu) and J_t(q,nu) in the liquid and the glass approximately proportional to temperature, in agreement with the harmonic approximation. In contrast to this, strong deviations from a linear scaling are found for nu>20 THz. The dynamic structure factor S(q,nu) exhibits for q>0.23 Angstrom^{-1} a boson peak which is located nearly independent of q around 1.7 THz. We show that the low frequency part of the boson peak is mainly due to the elastic scattering of transverse acoustic modes with frequencies around 1 THz. The strength of this scattering depends on q and is largest around q=1.7 Angstrom^{-1}, the location of the first sharp diffraction peak in the static structure factor. By studying S(q,nu) for different system sizes we show that strong finite size effects are present in the low frequency part of the boson peak in that for small systems part of its intensity is missing. We discuss the consequences of these finite size effects for the structural relaxation.

cond-mat.stat-mech↗

arXiv1999

Fluctuations, response and aging dynamics in a simple glass-forming liquid out of equilibrium

By means of molecular dynamics computer simulations we investigate the out of equilibrium relaxation dynamics of a simple glass former, a binary Lennard-Jones system, after a quench to low temperatures. We study both one time quantities and two-times correlation functions. Two-times correlation functions show a strong time and waiting time $t_w$ dependence. For large $t_w$ and times corresponding to the early $β$-relaxation regime the correlators approach the Edwards-Anderson value by means of a power-law in time. at long times $τ$ the correlation functions can be expressed as $C_{\rm AG}(h(t_w+τ)/h(t_w))$ and compute the function $h(t)$. This function is found to show a $t$-dependence which is a bit stronger than a logarithm and to depend on the observable considered. Finally we discuss our measurements of the time dependent response function. We find that at long times the correlation functions and the response are not related by the usual fluctuation dissipation theorem but that this relation is similar to the one found for spin glasses with one step replica symmetry breaking.

cond-mat.dis-nn↗

arXiv1999

Aging as dynamics in configuration space

The relaxation dynamics of many disordered systems, such as structural glasses, proteins, granular materials or spin glasses, is not completely frozen even at very low temperatures. This residual motion leads to a change of the properties of the material, a process commonly called aging. Despite recent advances in the theoretical description of such aging processes, the microscopic mechanisms leading to the aging dynamics are still a matter of dispute. In this Letter we investigate the aging dynamics of a simple glass former by means of molecular dynamics computer simulation. Using the concept of the inherent structure we give evidence that aging dynamics can be understood as a decrease of the effective configurational temperature T of the system. From our results we conclude that the equilibration process is faster when the system is quenched to T_c, the critical T of mode-coupling theory, and that thermodynamic concepts are useful to describe the out-of-equilibrium aging process.

cond-mat.soft↗

arXiv1999

The Structure and Dynamics of Sodium Disilicate

We investigate the structure and dynamics of sodium disilicate by means of molecular dynamics computer simulation. We show that the structure is described by a partially destroyed tetrahedral SiO_4 network and a spherical super structure formed by the silicon and sodium atoms. The static structure factor of our simulation is in very good agreement with one from a neutron scattering experiment. For 1008 particles we find strong finite size effects in the dynamics which are due to the missing of modes contributing to the boson peak.

cond-mat.stat-mech↗

arXiv1999

The beta-relaxation dynamics of a simple liquid

We present a detailed analysis of the beta-relaxation dynamics of a simple glass former, a Lennard-Jones system with a stochastic dynamics. By testing the various predictions of mode-coupling theory, including the recently proposed corrections to the asymptotic scaling laws, we come to the conclusion that in this time regime the dynamics is described very well by this theory.

cond-mat.stat-mech↗

arXiv1999

The Boson Peak in Amorphous Silica: Results from Molecular Dynamics Computer Simulations

We investigate a prominent vibrational feature in amorphous silica, the so-called boson peak, by means of molecular dynamics computer simulations. The dynamic structure factor S(q,nu) in the liquid, as well as in the glass state, scales roughly with temperature, in agreement with the harmonic approximation. By varying the size of the system and the masses of silicon and oxygen we show that the excitations giving rise to the boson peak are due to the coupling to transverse acoustic modes.

cond-mat.stat-mech↗