arXiv subjects

Kurt Binder

Publications and source records attributed to Kurt Binder.

At least 109 records · Page 6Linked to original sources

arXiv2002

Statics and dynamics of the ten-state nearest-neighbor Potts glass on the simple-cubic lattice

We present the results of Monte Carlo simulations of two different Potts glass models with short range random interactions. In the first model a \pm J-distribution of the bonds is chosen, in the second model a Gaussian distribution. In both cases the first two moments of the distribution are chosen to be J_0=-1, Delta J=+1, so that no ferromagnetic ordering of the Potts spins can occur. We find that for all temperatures investigated the spin glass susceptibility remains finite, the spin glass order parameter remains zero, and that the specific heat has only a smooth Schottky-like peak. These results can be understood quantitatively by considering small but independent clusters of spins. Hence we have evidence that there is no static phase transition at any nonzero temperature. Consistent with these findings, only very minor size effects are observed, which implies that all correlation lengths of the models remain very short. We also compute for both models the time auto-correlation function C(t) of the Potts spins. While in the Gaussian model C(t) shows a smooth uniform decay, the correlator for the \pm J model has several distinct steps. These steps correspond to the breaking of bonds in small clusters of ferromagnetically coupled spins (dimers, trimers, etc.). The relaxation times follow simple Arrhenius laws, with activation energies that are readily interpreted within the cluster picture, giving evidence that the system does not have a dynamic transition at a finite temperature. Hence we find that for the present models all the transitions known for the mean-field version of the model are completely wiped out. Finally we also determine the time auto-correlation functions of individual spins, and show that the system is dynamically very heterogeneous.

cond-mat.stat-mech↗

arXiv2002

Amorphous silica between confining walls and under shear: a computer simulation study

Molecular dynamics computer simulations are used to investigate a silica melt confined between walls at equilibrium and in a steady-state Poisseuille flow. The walls consist of point particles forming a rigid face-centered cubic lattice and the interaction of the walls with the melt atoms is modelled such that the wall particles have only a weak bonding to those in the melt, i.e. much weaker than the covalent bonding of a Si-O unit. We observe a pronounced layering of the melt near the walls. This layering, as seen in the total density profile, has a very irregular character which can be attributed to a preferred orientational ordering of SiO4 tetrahedra near the wall. On intermediate length scales, the structure of the melt at the walls can be well distinguished from that of the bulk by means of the ring size distribution. Whereas essentially no structural changes occur in the bulk under the influence of the shear fields considered, strong structural rearrangements in the ring size distribution are present at the walls as far as there is a slip motion. For the sheared system, parabolic velocity profiles are found in the bulk region as expected from hydrodynamics and the values for the shear viscosity as extracted from those profiles are in good agreement with those obtained in pure bulk simulations from the appropriate Green-Kubo formula.

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arXiv2002

Cooperative motion and growing length scales in supercooled confined liquids

Using molecular dynamics simulations we investigate the relaxation dynamics of a supercooled liquid close to a rough as well as close to a smooth wall. For the former situation the relaxation times increase strongly with decreasing distance from the wall whereas in the second case they strongly decrease. We use this dependence to extract various dynamical length scales and show that they grow with decreasing temperature. By calculating the frequency dependent average susceptibility of such confined systems we show that the experimental interpretation of such data is very difficult.

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arXiv2002

Simulation of models for the glass transition: Is there progress?

The glass transition of supercooled fluids is a particular challenge for computer simulation, because the (longest) relaxation times increase by about 15 decades upon approaching the transition temperature T_g. Brute-force molecular dynamics simulations, as presented here for molten SiO_2 and coarse-grained bead-spring models of polymer chains, can yield very useful insight about the first few decades of this slowing down. Hence this allows to access the temperature range around T_c of the so-called mode coupling theory, whereas the dynamics around the experimental glass transition is completely out of reach. While methods such as ``parallel tempering'' improve the situation somewhat, a method that allows to span a significant part of the region T_g\leq T\leq T_c is still lacking. Only for abstract models such as the infinite range 10-state Potts glass with a few hundred spins this region can be explored. However this model suffers from very strong finite size effects thus making it difficult to extrapolate the results obtained for the finite system sizes to the thermodynamic limit. For the case of polymer melts, two different strategies to use lattice models instead of continuum models are discussed: In the first approach, a mapping of an atomistically realistic model of polyethylene to the bond fluctuation model with suitable effective potentials and a temperature-dependent time rescaling factor is attempted. In the second approach, devoted to a test of the entropy theory, moves that are artificial but which lead to a faster relaxation (``slithering snake'' algorithm) are used, to get at least static properties at somewhat lower temperatures than possible with a ``realistic'' dynamics. The merits and shortcomings of all these approaches are discussed.

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arXiv2002

Evidence against a glass transition in the 10-state short range Potts glass

We present the results of Monte Carlo simulations of two different 10-state Potts glasses with random nearest neighbor interactions on a simple cubic lattice. In the first model the interactions come from a \pm J distribution and in the second model from a Gaussian one, and in both cases the first two moments of the distribution are chosen to be equal to J_0=-1 and Delta J=1. At low temperatures the spin autocorrelation function for the \pm J model relaxes in several steps whereas the one for the Gaussian model shows only one. In both systems the relaxation time increases like an Arrhenius law. Unlike the infinite range model, there are only very weak finite size effects and there is no evidence that a dynamical or a static transition exists at a finite temperature.

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arXiv2001

The dynamics of sodium in sodium disilicate: Channel relaxation and sodium diffusion

We use molecular dynamics computer simulations to study the dynamics of amorphous (Na_2O)2(SiO_2). We find that the Na ions move in channels embedded in a SiO_2 matrix. The characteristic distance between these channels gives rise to a prepeak in the structure factor at around q=0.95 A^-1. The dynamics of sodium is given by a fast process which can be seen in the incoherent scattering function and a slow process which is seen in the coherent function. The relaxation time of the latter coincides with the alpha-relaxation time of the matrix. The Kohlrausch exponent of the fast process for q>1.6 A^1 is the same as the von Schweidler exponent for the slow one, demonstrating that the two processes are closely related.

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arXiv2001

Dynamical Heterogeneities Below the Glass Transition

We present molecular dynamics simulations of a binary Lennard-Jones mixture at temperatures below the kinetic glass transition. The ``mobility'' of a particle is characterized by the amplitude of its fluctuation around its average position. The 5% particles with the largest/smallest mean amplitude are thus defined as the relatively most mobile/immobile particles. We investigate for these 5% particles their spatial distribution and find them to be distributed very heterogeneously in that mobile as well as immobile particles form clusters. The reason for this dynamic heterogeneity is traced back to the fact that mobile/immobile particles are surrounded by fewer/more neighbors which form an effectively wider/narrower cage. The dependence of our results on the length of the simulation run indicates that individual particles have a characteristic mobility time scale, which can be approximated via the non-Gaussian parameter.

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arXiv2001

Recent MD Results on Supercooled Thin Polymer Films

The dynamic and static properties of a supercooled (non-entangled) polymer melt are investigated via molecular dynamics (MD) simulations. The system is confined between two completely smooth and purely repulsive walls. The wall-to-wall separation (film thickness), $D$, is varied from about 3 to about 14 times the bulk radius of gyration. Despite the geometric confinement, the supercooled films exhibit many qualitative features which were also observed in the bulk and could be analyzed in terms of mode-coupling theory (MCT). Examples are the two-step relaxation of the incoherent intermediate scattering function, the time-temperature superposition property of the late time $α$-process and the space-time factorization of the scattering function on the intermediate time scale of the MCT $β$-process. An analysis of the temperature dependence of the $α$-relaxation time suggests that the critical temperature, $\Tc$, of MCT decreases with $D$. If the confinement is not too strong ($D \ge 10 {monomer diameter}$) the static structure factor of the film coincides with that of the bulk when compared for the same distance, $T-\Tc(D)$, to the critical temperature. This suggests that $T-\Tc(D)$ is an important temperature scale of our model both in the bulk and in the films.

cond-mat.soft↗

arXiv2001

Classical and ab initio molecular dynamic simulation of an amorphous silica surface

We present the results of a classical molecular dynamic simulation as well as of an ab initio molecular dynamic simulation of an amorphous silica surface. In the case of the classical simulation we use the potential proposed by van Beest et al. (BKS) whereas the ab initio simulation is done with a Car-Parrinello method (CPMD). We find that the surfaces generated by BKS have a higher concentration of defects (e.g. concentration of two-membered rings) than those generated with CPMD. In addition also the distribution functions of the angles and of the distances are different for the short rings. Hence we conclude that whereas the BKS potential is able to reproduce correctly the surface on the length scale beyond approx 5 Angstroems, it is necessary to use an ab initio method to predict reliably the structure at small scales.

cond-mat.stat-mech↗

arXiv2001

Statics and Dynamics of the 10-state mean-field Potts glass model: A Monte Carlo study

We investigate by means of Monte Carlo simulations the fully connected p-state Potts model for different system sizes in order to see how the static and dynamic properties of a finite model compare with the, exactly known, behavior of the system in the thermodynamic limit. Using p=10 we are able to study the equilibrium dynamics for system sizes as large as N=2560. We find that the static quantities, such as the energy, the entropy, the spin glass susceptibility as well as the distribution of the order parameter P(q) show very strong finite size effects. From P(q) we calculate the forth order cumulant g_4(N,T) and the Guerra parameter G(N,T) and show that these quantities cannot be used to locate the static transition temperature for the system sizes investigated. Also the spin-autocorrelation function C(t) shows strong finite size effects in that it does not show a plateau even for temperatures around the dynamical critical temperature T_D. We show that the N-and T-dependence of the α-relaxation time can be understood by means of a dynamical finite size scaling Ansatz. C(t) does not obey the time-temperature superposition principle for temperatures around T_D, but does so for significantly lower T. Finally we study the relaxation dynamics of the individual spins and show that their dependence on time depends strongly on the chosen spin, i.e. that the system is dynamically very heterogeneous, which explains the non-exponentiality of C(t).

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arXiv2001

Growing length scales in a supercooled liquid close to an interface

We present the results of molecular dynamics computer simulations of a simple glass former close to an interface between the liquid and the frozen amorphous phase of the same material. By investigating F_s(q,z,t), the incoherent intermediate scattering function for particles that have a distance z from the wall, we show that the relaxation dynamics of the particles close to the wall is much slower than the one for particles far away from the wall. For small z the typical relaxation time for F_s(q,z,t) increases like exp(Delta/(z-z_p)), where Delta and z_p are constants. We use the location of the crossover from this law to the bulk behavior to define a first length scale tilde{z}. A different length scale is defined by considering the Ansatz F_s(q,z,t) = F_s^{bulk}(q,t) +a(t) exp[-(z/xi(t))^{beta(t)}], where a(t), xi(t), and beta(t) are fit parameters. We show that this Ansatz gives a very good description of the data for all times and all values of z. The length xi(t) increases for short and intermediate times and decreases again on the time scale of the alpha-relaxation of the system. The maximum value of xi(t) can thus be defined as a new length scale xi_max. We find that tilde{z} as well as xi_max increase with decreasing temperature. The temperature dependence of this increase is compatible with a divergence of the length scale at the Kauzmann temperature of the bulk system.

cond-mat.stat-mech↗

arXiv2001

The High Temperature Dynamics of a mean field Potts glass

We use Monte Carlo simulations to investigate the dynamical properties of the infinite range 10 states Potts glass. By analyzing the spin autocorrelation function for system sizes up to N=2560, we show that strong finite size effects are present around the predicted dynamical transition temperature. The autocorrelation function shows strong self-averaging at high temperatures, whereas close to the dynamical transition they show the lack of self-averaging.

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arXiv2001

A Monte Carlo Test of the Fisher-Nakanishi-Scaling Theory for the Capillary Condensation Critical Point

Extending the Swendsen-Wang cluster algorithm to include both bulk (H) and surface fields (H_1) in L x L x D Ising films of thickness D and two free L x L surfaces, a Monte Carlo study of the capillary condensation critical point of the model is presented. Applying a finite-size scaling analysis where the lateral linear dimension L is varied over a wide range, the critical temperature T_c(D) and the associated critical field H_c(D) are estimated for 4 <= D <= 32 lattice spacings, for a choice of the surface field H_1 small enough that the dependence of H_c(D) on H_1 is still linear. It is shown that the results are consistent with the power laws predicted by Fisher and Nakanishi [M.E. Fisher and H. Nakanishi, J. Chem. Phys. 75, 5857 (1981)], namely T_c(\infty)-T_c(D) \propto D^{-1/ν}, H_c(D) \propto D^{-(Δ-Δ_1)/ν}, where νis the bulk correlation length exponent of the three-dimensional Ising model, and Δ, Δ_1 are the corresponding ``gap exponents'' associated with bulk and surface fields, respectively. As expected, the order parameter of the thin film near its critical point exhibits critical behavior compatible with the universality class of the two-dimensional Ising model.

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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

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.

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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.

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