arXiv subjects

K. Binder

Publications and source records attributed to K. Binder.

At least 55 records · Page 3Linked to original sources

arXiv2003

The droplet evaporation/condensation transition in a finite volume

A fluid in the NVT ensemble at T less than the critical temperature T_c and rho = N/V somewhat in excess of rho_coex (density of the saturated gas in the gas-liquid transition) is considered. For V->infinity, a macroscopic liquid droplet coexists with surrounding saturated gas according to the lever rule. For finite V, droplets can only exist if they exceed a minimum size. A (rounded) first order transition of the system occurs when the droplet evaporates into the supersaturated gas.Simulation evidence for this transition is given for a Lennard-Jones model and interpreted by a phenomenological theory. At the transition, the chemical potential difference mu_t-mu_coex scales like L^(-d/(d+1)) for a cubic volume V=L^d in d dimensions, as L->infinity.

cond-mat.soft↗

arXiv2003

Reply to the Comment by M. Biskup, L. Chayes and R. Kotecky

In their comment to the paper ``Theory of the evaporation/condensation transition of equilibrium droplets in finite volumes'' [Physica A, 319, 99 (2003)], Biskup et al. claim that in finite systems at fixed density ``the physical significance of the conjugate thermodynamic variable is of dubious value''. This claim is critically discussed.

cond-mat.stat-mech↗

arXiv2003

Avoiding Boundary Effects in Wang-Landau Sampling

A simple modification of the ``Wang-Landau sampling'' algorithm removes the systematic error that occurs at the boundary of the range of energy over which the random walk takes place in the original algorithm.

cond-mat.stat-mech↗

arXiv2002

The importance of intermediate range order in silicates: molecular dynamics simulation studies

We present the results of large scale computer simulations in which we investigate the structural and dynamic properties of silicate melts with the compositions (Na_2O)2(SiO_2) and (Al_2O_3)2(SiO_2). In order to treat such systems on a time scale of several nanoseconds and for system sizes of several thousand atoms it is necessary to use parallel supercomputers like the CRAY T3E. We show that the silicates under consideration exhibit additional intermediate range order as compared to silica (SiO_2) where the characteristic intermediate length scales stem from the tetrahedral network structure. For the sodium silicate system it is demonstrated that the latter structural features are intimately connected with a surprising dynamics in which the one--particle motion of the sodium ions appears on a much smaller time scale than the correlations between different sodium ions.

cond-mat.stat-mech↗

arXiv2001

Flat Histogram Method of Wang-Landau and N-fold Way

We present a method for estimating the density of states of a classical statistical model. The algorithm successfully combines the Wang-Landau flat histogram method with the N-fold way in order to improve efficiency of the original single spin flip version. We test our implementation of the Wang-Landau method with the two-dimensional nearest neighbor Ising model for which we determine the tunneling time and the density of states. Furthermore, we show that our new algorithm performs correctly at right edges of an energy interval over which the density of states is computed. This removes a disadvantage of the original single spin flip Wang-Landau method where results showed systematically higher errors in the density of states at right boundaries. We compare our data with the detailed numerical tests presented in a study by Wang and Swendsen where the original Wang-Landau method was tested against various other methods. Finally, we apply our method to a thin Ising film of size $32\times 32\times 6$ with antisymmetric surface fields. With the density of states obtained from the simulations we calculate canonical averages related to the energy such as internal energy, Gibbs free energy and entropy, but we also sample microcanonical averages during simulations in order to determine canonical averages of the susceptibility, the order parameter and its fourth order cumulant. We compare our results with simulational data obtained from a conventional MC algorithm.

cond-mat.stat-mech↗

arXiv2001

Spinodal Decomposition in a Binary Polymer Mixture: Dynamic Self Consistent Field Theory and Monte Carlo Simulations

We investigate how the dynamics of a single chain influences the kinetics of early stage phase separation in a symmetric binary polymer mixture. We consider quenches from the disordered phase into the region of spinodal instability. On a mean field level we approach this problem with two methods: a dynamical extension of the self consistent field theory for Gaussian chains, with the density variables evolving in time, and the method of the external potential dynamics where the effective external fields are propagated in time. Different wave vector dependencies of the kinetic coefficient are taken into account. These early stages of spinodal decomposition are also studied through Monte Carlo simulations employing the bond fluctuation model that maps the chains -- in our case with 64 effective segments -- on a coarse grained lattice. The results obtained through self consistent field calculations and Monte Carlo simulations can be compared because the time, length, and temperature scales are mapped onto each other through the diffusion constant, the chain extension, and the energy of mixing. The quantitative comparison of the relaxation rate of the global structure factor shows that a kinetic coefficient according to the Rouse model gives a much better agreement than a local, i.e. wave vector independent, kinetic factor. Including fluctuations in the self consistent field calculations leads to a shorter time span of spinodal behaviour and a reduction of the relaxation rate for smaller wave vectors and prevents the relaxation rate from becoming negative for larger values of the wave vector. This is also in agreement with the simulation results.

cond-mat.stat-mech↗

arXiv2001

Reduction of the Glass Transition Temperature in Polymer Films: A Molecular-Dynamics Study

We present results of molecular dynamics (MD) simulations for a non-entangled polymer melt confined between two completely smooth and repulsive walls, interacting with inner particles via the potential $U_{\rm wall}\myeq (σ/z)^9$, where $z \myeq |z_{\rm particle}-z_{\rm wall}|$ and $σ$ is (roughly) the monomer diameter. The influence of this confinement on the dynamic behavior of the melt is studied for various film thicknesses (wall-to-wall separations) $D$, ranging from about 3 to about 14 times the bulk radius of gyration. A comparison of the mean-square displacements in the film and in the bulk shows an acceleration of the dynamics due to the presence of the walls. %Consistent with this result is the observation that, within %the film, regions closer to the walls have higher mobility than those further %away towards the film center. This leads to a reduction of the critical temperature, $T_{\rm{c}}$, of mode-coupling theory with decreasing film thickness. Analyzing the same data by the Vogel-Fulcher-Tammann equation, we also estimate the VFT-temperature $T_{\rm{0}}(D)$. The ratio $T_{\mr{0}}(D)/T^{\mr{bulk}}_{\mr{0}}$ decreases for smaller $D$ similarly to $T_{\mr{c}}(D)/T^{\mr{bulk}}_{\mr{c}}$. These results are in qualitative agreement with that of the glass transition temperature observed in some experiments on supported polymer films.

cond-mat.soft↗

arXiv2000

Polymer Films in the Normal-Liquid and Supercooled State: A Review of Recent Monte Carlo Simulation Results

This paper reviews recent Monte Carlo simulation studies of the glassy behavior in thin polymer films. The simulations employ a version of the bond-fluctuation lattice model, in which the glass transition is driven by the competition between a stiffening of the polymers and their dense packing in the melt. The melt is geometrically confined between two impenetrable walls separated by distances ranging from once to about fifteen times the bulk radius of gyration. The confinement influences static and dynamic properties of the films: Chains close to the wall preferentially orient parallel to it. This orientation tendency propagates through the film and leads to a layer structure at low temperatures and small thicknesses. The layer structure strongly suppresses out-of-plane reorientations of the chains. In-plane reorientations have to take place in a high density environment which gives rise to an increase of the corresponding relaxation times. However, local density fluctuations are enhanced if film thickness and temperature decrease. This implies a reduction of the glass transition temperature with decreasing film thickness.

cond-mat.soft↗

arXiv2000

Molecular Dynamics Results on the Pressure Tensor of Polymer Films

Polymeric thin films of various thicknesses, confined between two repulsive walls, have been studied by molecular dynamics simulations. Using the anisotropy of the perpendicular and parallel components of the pressure tensor the surface tension of the system is calculated for a wide range of temperature and for various film thicknesses. Three methods of determining the pressure tensor are compared: the method of Irving and Kirkwood (IK), an approximation thereof (IK1), and the method of Harasima (H). The IK- and the H-methods differ in the expression for the parallel component, but not for the normal component of the pressure tensor. Both methods yield a constant normal component throughout the film, as required by mechanical stability, whereas the IK1-method leads to strong oscillations. However, all methods give the same expression for the surface tension.

cond-mat.soft↗

arXiv2000

Path integral Monte Carlo simulations of silicates

We investigate the thermal expansion of crystalline SiO$_2$ in the $β$-- cristobalite and the $β$-quartz structure with path integral Monte Carlo (PIMC) techniques. This simulation method allows to treat low-temperature quantum effects properly. At temperatures below the Debye temperature, thermal properties obtained with PIMC agree better with experimental results than those obtained with classical Monte Carlo methods.

cond-mat.stat-mech↗

arXiv2000

Interface localisation-delocalisation transition in a symmetric polymer blend: a finite-size scaling Monte Carlo study

Using extensive Monte Carlo simulations we study the phase diagram of a symmetric binary (AB) polymer blend confined into a thin film as a function of the film thickness D. The monomer-wall interactions are short ranged and antisymmetric, i.e, the left wall attracts the A-component of the mixture with the same strength as the right wall the B-component, and give rise to a first order wetting transition in a semi-infinite geometry. The phase diagram and the crossover between different critical behaviors is explored. For large film thicknesses we find a first order interface localisation/delocalisation transition and the phase diagram comprises two critical points, which are the finite film width analogies of the prewetting critical point. Using finite size scaling techniques we locate these critical points and present evidence of 2D Ising critical behavior. When we reduce the film width the two critical points approach the symmetry axis $ϕ=1/2$ of the phase diagram and for $D \approx 2 R_g$ we encounter a tricritical point. For even smaller film thickness the interface localisation/delocalisation transition is second order and we find a single critical point at $ϕ=1/2$. Measuring the probability distribution of the interface position we determine the effective interaction between the wall and the interface. This effective interface potential depends on the lateral system size even away from the critical points. Its system size dependence stems from the large but finite correlation length of capillary waves. This finding gives direct evidence for a renormalization of the interface potential by capillary waves in the framework of a microscopic model.

cond-mat.stat-mech↗

arXiv2000

Monte Carlo Simulation of Long Chain Polymer Melts: Crossover from Rouse to Reptation Dynamics

We present data of Monte Carlo simulations for monodisperse linear polymer chains in dense melts with degrees of polymerization between N=16 and N=512. The aim of this study is to investigate the crossover from Rouse-like dynamics for short chains to reptation-like dynamics for long chains. To address this problem we calculate a variety of different quantities: standard mean-square displacements of inner monomers and of the chain's center of mass, the recently proposed cubic invariant, persistence of bond-vector orientation with time, and the auto-correlation functions of the bond vector, the end-to-end vector and the Rouse modes. This analysis reveals that the crossover from non- to entangled dynamics is very protracted. Only the largest chain length N=512, which is about 13 times larger than the entanglement length, shows evidence for reptation.

cond-mat.soft↗

arXiv2000

Phase diagram of polymer blends in confined geometry

Within self-consistent field theory we study the phase behavior of a symmetrical binary AB polymer blend confined into a thin film. The film surfaces interact with the monomers via short range potentials. One surface attracts the A component and the corresponding semi-infinite system exhibits a first order wetting transition. The surface interaction of the opposite surface is varied as to study the crossover from capillary condensation for symmetric surface fields to the interface localization/delocalization transition for antisymmetric surface fields. In the former case the phase diagram has a single critical point close to the bulk critical point. In the latter case the phase diagram exhibits two critical points which correspond to the prewetting critical points of the semi-infinite system. Only below a triple point there is a single two phase coexistence region. The crossover between these qualitatively different limiting behaviors occurs gradually, however, the critical temperature and the critical composition exhibit a non-monotonic dependence on the surface field. The dependence of the phase behavior for antisymmetric boundaries is studied as a function of the film thickness and the strength of the surface interactions. Upon reducing the film thickness or decreasing the strength of the surface interactions we can change the order of the interface localization/delocalization transition from first to second. The role of fluctuations is explored via Monte Carlo simulations of a coarse grained lattice model. Close to the (prewetting) critical points we observe 2D Ising critical behavior. At lower temperatures capillary waves of the AB interface lead to a pronounced dependence of the effective interface potential on the lateral system size.

cond-mat.stat-mech↗

arXiv2000

A symmetric polymer blend confined into a film with antisymmetric surfaces: interplay between wetting behavior and phase diagram

We study the phase behavior of a symmetric binary polymer blend which is confined into a thin film. The film surfaces interact with the monomers via short range potentials. We calculate the phase behavior within the self-consistent field theory of Gaussian chains. Over a wide range of parameters we find strong first order wetting transitions for the semi-infinite system, and the interplay between the wetting/prewetting behavior and the phase diagram in confined geometry is investigated. Antisymmetric boundaries, where one surface attracts the A component with the same strength than the opposite surface attracts the B component, are applied. The phase transition does not occur close to the bulk critical temperature but in the vicinity of the wetting transition. For very thin films or weak surface fields one finds a single critical point at $ϕ_c=1/2$. For thicker films or stronger surface fields the phase diagram exhibits two critical points and two concomitant coexistence regions. Only below a triple point there is a single two phase coexistence region. When we increase the film thickness the two coexistence regions become the prewetting lines of the semi-infinite system, while the triple temperature converges towards the wetting transition temperature from above. The behavior close to the tricritical point, which separates phase diagrams with one and two critical points, is studied in the framework of a Ginzburg-Landau ansatz. Two-dimensional profiles of the interface between the laterally coexisting phases are calculated, and the interfacial and line tensions analyzed. The effect of fluctuations and corrections to the self-consistent field theory are discussed.

cond-mat.stat-mech↗

arXiv2000

Equation of state and critical behavior of polymer models: A quantitative comparison between Wertheim's thermodynamic perturbation theory and computer simulations

We present an application of Wertheim's Thermodynamic Perturbation Theory (TPT1) to a simple coarse grained model made of flexibly bonded Lennard-Jones monomers. We use both the Reference Hyper-Netted-Chain (RHNC) and Mean Spherical approximation (MSA) integral equation theories to describe the properties of the reference fluid. The equation of state, the density dependence of the excess chemical potential, and the critical points of the liquid--vapor transition are compared with simulation results and good agreement is found. The RHNC version is somewhat more accurate, while the MSA version has the advantage of being almost analytic. We analyze the scaling behavior of the critical point of chain fluids according to TPT1 and find it to reproduce the mean field exponents: The critical monomer density is predicted to vanish as $n^{-1/2}$ upon increasing the chain length $n$ while the critical temperature is predicted to reach an asymptotic finite temperature that is attained as $n^{-1/2}$. The predicted asymptotic finite critical temperature obtained from the RHNC and MSA versions of TPT1 is found to be in good agreement with the $Θ$ point of our polymer model as obtained from the temperature dependence of the single chain conformations.

cond-mat.stat-mech↗

arXiv2000

Finite size effects on the phase diagram of a binary mixture confined between competing walls

A symmetrical binary mixture AB that exhibits a critical temperature T_{cb} of phase separation into an A-rich and a B-rich phase in the bulk is considered in a geometry confined between two parallel plates a distance D apart. It is assumed that one wall preferentially attracts A while the other wall preferentially attracts B with the same strength (''competing walls''). In the limit $D\to \infty$, one then may have a wetting transition of first order at a temperature T_{w}, from which prewetting lines extend into the one phase region both of the A-rich and the B-rich phase. It is discussed how this phase diagram gets distorted due to the finiteness of D% : the phase transition at T_{cb} immediately disappears for D<\infty due to finite size rounding, and the phase diagram instead exhibit two two-phase coexistence regions in a temperature range T_{trip}<T<T_{c1}=T_{c2}. In the limit D\to \infty T_{c1},T_{c2} become the prewetting critical points and T_{trip}\to T_{w}. For small enough D it may occur that at a tricritical value D_{t} the temperatures T_{c1}=T_{c2} and T_{trip} merge, and then for D<D_{t} there is a single unmixing critical point as in the bulk but with T_{c}(D) near T_{w}. As an example, for the experimentally relevant case of a polymer mixture a phase diagram with two unmixing critical points is calculated explicitly from self-consistent field methods.

cond-mat.stat-mech↗

arXiv2000

Non-monotonous crossover between capillary condensation and interface localisation/delocalisation transition in binary polymer blends

Within self-consistent field theory we study the phase behaviour of a symmetric binary AB polymer blend confined into a thin film. The film surfaces interact with the monomers via short range potentials. One surface attracts the A component and the corresponding semi-infinite system exhibits a first order wetting transition. The surface interaction of the opposite surface is varied as to study the crossover from capillary condensation for symmetric surface fields to the interface localisation/delocalisation transition for antisymmetric surface fields. In the former case the phase diagram has a single critical point close to the bulk critical point. In the latter case the phase diagram exhibits two critical points which correspond to the prewetting critical points of the semi-infinite system. The crossover between these qualitatively different limiting behaviours occurs gradually, however, the critical temperature and the critical composition exhibit a non-monotonic dependence on the surface field.

cond-mat.stat-mech↗

arXiv2000

Order and Disorder Phenomena at Surfaces of Binary Alloys

We present recent Monte Carlo results on surfaces of bcc-structured binary alloys which undergo an order-disorder phase transformation in the bulk. In particular, we discuss surface order and surface induced disorder at the bulk transition between the ordered (DO3) phase and the disordered (A2) phase. An intricate interplay between different ordering and segregation phenomena leads to a complex surface behavior, which depends on the orientation of the surface under consideration. abstract

cond-mat.mtrl-sci↗