Jürgen Horbach

Static and dynamic properties of a viscous silica melt

We present the results of a large scale molecular dynamics computer simulation in which we investigated the static and dynamic properties of a silica melt in the temperature range in which the viscosity of the system changes from O(10 −2 ) Poise to O(10 2 ) Poise. We show that even at temperatures as high as 4000 K the structure of this system is very similar to the random tetrahedral network found in silica at lower temperatures. The temperature dependence of the concentration of the defects in this network shows an Arrhenius law. From the partial structure factors we calculate the neutron scattering function and find that it agrees very well with experimental neutron scattering data. At low temperatures the temperature dependence of the diffusion constants D shows an Arrhenius law with activation energies which are in very good agreement with the experimental values. With increasing temperature we find that this dependence shows a cross-over to one which can be described well by a power-law, D ∝ (T − Tc). The critical temperature Tc is 3330 K and the exponent is close to 2.1. Since we find a similar cross-over in the viscosity we have evidence that the relaxation dynamics of the system changes from a flow-like motion of the particles, as described by the ideal version of mode-coupling theory, to a hopping like motion. We show that such a change of the transport mechanism is also observed in the product of the diffusion constant and the life time of a Si-O bond, or the space and time dependence of the van Hove correlation functions.

FINITE SIZE EFFECTS IN SIMULATIONS OF GLASS DYNAMICS

We present the results of a molecular dynamics computer simulation in which we investigate the dynamics of silica. By considering different system sizes, we show that in simulations of the dynamics of this strong glass former surprisingly large finite size effects are present. In particular, we demonstrate that the relaxation times of the incoherent intermediate scattering function and the time dependence of the mean squared displacement are affected by such finite size effects. By compressing the system to high densities, we transform it to a fragile glass former and find that for that system these types of finite size effects are much weaker.

Molecular Dynamics Simulations

A tutorial introduction to the technique of molecular dynamics (MD) is given, and some characteristic examples of applications are described. The purpose and scope of these simulations and the relation to other simulation methods is discussed, and the basic MD algorithms are described. The sampling of intensive variables (temperature T, pressure p) in runs carried out in the microcanonical (NV E) ensemble (N = particle number, V = volume, E = energy) is discussed, as well as the realization of other ensembles (e.g. the NV T ensemble). For a typical application example, molten SiO2, the estimation of various transport coefficients (self-diffusion constants, viscosity, thermal conductivity) is discussed. As an example of non-equilibrium molecular dynamics, a study of a glass-forming polymer melt under shear is mentioned.

Influence of chemical short-range order on atomic diffusion in Al–Ni melts

We use inelastic neutron scattering and molecular dynamics simulation to investigate the chemical short-range order (CSRO), visible through prepeaks in the structure factors, and its relation to self-diffusion in Al–Ni melts. As a function of composition at 1795K, Ni self-diffusion coefficients from experiment and simulation exhibit a nonlinear dependence with a pronounced increase on the Al-rich side. This comes along with a change in CSRO with increasing Al content that is related to a more dense packing of the atoms in Ni-rich Al–Ni systems.

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

Abstract 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 atoms 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.

From equilibrium to steady state: the transient dynamics of colloidal liquids under shear

We investigate stresses and particle motion during the start-up of flow in a colloidal dispersion close to arrest into a glassy state. A combination of molecular dynamics simulation, mode-coupling theory and confocal microscopy experiments is used to investigate the origins of the widely observed stress overshoot and (previously not reported) super-diffusive motion in the transient dynamics. A link between the macro-rheological stress versus strain curves and the microscopic particle motion is established. Negative correlations in the transient auto-correlation function of the potential stresses are found responsible for both phenomena, and arise even for homogeneous flows and almost Gaussian particle displacements.

High frequency sound and the boson peak in amorphous silica

We present the results of extensive molecular dynamics computer simulations in which the high frequency dynamics of silica, ν > 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, ν) and J t (q, ν), the longitudinal and transverse current correlation function, respectively. For wave–vectors q > 0.4 ˚ A −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 ν < 20 THz, the intensity of J l (q, ν) and J t (q, ν) 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 ν > 20 THz. The dynamic structure factor S(q, ν) exhibits for q > 0.23Å −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 ˚ A −1 , the location of the first sharp diffraction peak in the static structure factor. By studying S(q, ν) 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.

Channel formation and intermediate range order in sodium silicate melts and glasses

We use inelastic neutron scattering and molecular dynamics simulation to investigate the interplay between the structure and the fast sodium ion diffusion in various sodium silicates. With increasing temperature and decreasing density the structure factors exhibit an emerging prepeak around 0.9 A(-1). We show that this prepeak has its origin in the formation of sodium rich channels in the static structure. The channels serve as preferential ion conducting pathways in the relative immobile Si-O matrix. On cooling below the glass transition this intermediate range order is frozen in.

Grand canonical Monte Carlo simulation of a model colloid-polymer mixture: coexistence line, critical behavior, and interfacial tension.

Grand canonical Monte Carlo simulations are used to study phase separation in a simple colloid-polymer model, the so-called Asakura-Oosawa model. To overcome the problem of small acceptance rates of the grand-canonical moves, cluster moves are introduced. Successive umbrella sampling, recently introduced by Virnau and Muller [J. Chem. Phys. 120, 10925 (2004)], is used to access the phase-separated regime. The unmixing binodal and the interfacial tension are measured and compared to theoretical predictions. By means of finite-size scaling, the behavior close to the critical point is also investigated. Close to criticality, we observe substantial deviations from mean-field behavior.We present a Monte Carlo method to simulate asymmetric binary mixtures in the grand canonical ensemble. The method is used to study the colloid-polymer model of Asakura and Oosawa. We determine the phase diagram of the fluid-fluid unmixing transition and the interfacial tension, both at high polymer density and close to the critical point. We also present density profiles in the two-phase region. The results are compared to predictions of a recent density functional theory.

Monte Carlo simulations of the solid-liquid transition in hard spheres and colloid-polymer mixtures

Monte Carlo simulations at constant pressure are performed to study coexistence and interfacial properties of the liquid-solid transition in hard spheres and in colloid-polymer mixtures. The latter system is described as a one-component Asakura-Oosawa (AO) model where the polymers degrees of freedom are incorporated via an attractive part in the effective potential for the colloid-colloid interactions. For the considered AO model, the polymer reservoir packing fraction is eta(p) (r)=0.1 and the colloid-polymer size ratio is q[triple bond]sigma(p)/sigma=0.15 (with sigma(p) and sigma as the diameter of polymers and colloids, respectively). Inhomogeneous solid-liquid systems are prepared by placing the solid fcc phase in the middle of a rectangular simulation box, creating two interfaces with the adjoined bulk liquid. By analyzing the growth of the crystalline region at various pressures and for different system sizes, the coexistence pressure p(co) is obtained, yielding p(co)=11.576 k(B)T/sigma(3) for the hard-sphere system and p(co)=8.00 k(B)T/sigma(3) for the AO model (with k(B) as the Boltzmann constant and T as the temperature). Several order parameters are introduced to distinguish between solid and liquid phases and to describe the interfacial properties. From the capillary-wave broadening of the solid-liquid interface, the interfacial stiffness is obtained for the (100) crystalline plane, giving the values gamma approximately 0.49 k(B)T/sigma(2) for the hard-sphere system and gamma approximately 0.95 k(B)T/sigma(2) for the AO model.