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K. Binder

Publications and source records attributed to K. Binder.

At least 73 records · Page 4Linked to original sources
arXiv2000

Surface induced disorder in body-centered cubic alloys

We present Monte Carlo simulations of surface induced disordering in a model of a binary alloy on a bcc lattice which undergoes a first order bulk transition from the ordered DO3 phase to the disordered A2 phase. The data are analyzed in terms of an effective interface Hamiltonian for a system with several order parameters in the framework of the linear renormalization approach due to Brezin, Halperin and Leibler. We show that the model provides a good description of the system in the vicinity of the interface. In particular, we recover the logarithmic divergence of the thickness of the disordered layer as the bulk transition is approached, we calculate the critical behavior of the maxima of the layer susceptibilities, and demonstrate that it is in reasonable agreement with the simulation data. Directly at the (110) surface, the theory predicts that all order parameters vanish continuously at the surface with a nonuniversal, but common critical exponent. However, we find different exponents for the order parameter of the DO3 phase and the order parameter of the B2 phase. Using the effective interface model, we derive the finite size scaling function for the surface order parameter and show that the theory accounts well for the finite size behavior of the DO3 ordering but not for that of B2 ordering. The situation is even more complicated in the neighborhood of the (100) surface, due to the presence of an ordering field which couples to the B2 order.

cond-mat.stat-mech↗
arXiv2000

Elastic moduli, dislocation core energy and melting of hard disks in two dimensions

Elastic moduli and dislocation core energy of the triangular solid of hard disks of diameter $σ$ are obtained in the limit of vanishing dislocation- antidislocation pair density, from Monte Carlo simulations which incorporates a constraint, namely that all moves altering the local connectivity away from that of the ideal triangular lattice are rejected. In this limit, we show that the solid is stable against all other fluctuations at least upto densities as low as $ρσ^2 = 0.88$. Our system does not show any phase transition so diverging correlation lengths leading to finite size effects and slow relaxations do not exist. The dislocation pair formation probability is estimated from the fraction of moves rejected due to the constraint which yields, in turn, the core energy E_c and the (bare) dislocation fugacity y. Using these quantities, we check the relative validity of first order and Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) melting scenarios and obtain numerical estimates of the typical expected transition densities and pressures. We conclude that a KTHNY transition from the solid to a hexatic phase preempts the solid to liquid first order transition in this system albeit by a very small margin, easily masked by crossover effects in unconstrained ``brute-force'' simulations with small number of particles.

cond-mat.stat-mech↗
arXiv2000

Defect fugacity, Spinwave Stiffness and T_c of the 2-d Planar Rotor Model

We obtain precise values for the fugacities of vortices in the 2-d planar rotor model from Monte Carlo simulations in the sector with {\em no} vortices. The bare spinwave stiffness is also calculated and shown to have significant anharmonicity. Using these as inputs in the KT recursion relations, we predict the temperature T_c = 0.925, using linearised equations, and $T_c = 0.899 \pm >.005$ using next higher order corrections, at which vortex unbinding commences in the unconstrained system. The latter value, being in excellent agreement with all recent determinations of T_c, demonstrates that our method 1) constitutes a stringent measure of the relevance of higher order terms in KT theory and 2) can be used to obtain transition temperatures in similar systems with modest computational effort.

cond-mat.stat-mech↗
arXiv1999

Cooling Rate Dependence and Dynamic Heterogeneity Below the Glass Transition in a Lennard-Jones Glass

We investigate a binary Lennard-Jones mixture with molecular dynamics simulations. We consider first a system cooled linearly in time with the cooling rate gamma. By varying gamma over almost four decades we study the influence of the cooling rate on the glass transition and on the resulting glass. We find for all investigated quantities a cooling rate dependence; with decreasing cooling rate the system falls out of equilibrium at decreasing temperatures, reaches lower enthalpies and obtains increasing local order. Next we study the dynamics of the melting process by investigating the most immobile and most mobile particles in the glass. We find that their spatial distribution is heterogeneous and that the immobile/mobile particles are surrounded by denser/less dense cages than an average particle.

cond-mat.stat-mech↗
arXiv1999

Elastic constants from microscopic strain fluctuations

Fluctuations of the instantaneous local Lagrangian strain $ε_{ij}(\bf{r},t)$, measured with respect to a static ``reference'' lattice, are used to obtain accurate estimates of the elastic constants of model solids from atomistic computer simulations. The measured strains are systematically coarse- grained by averaging them within subsystems (of size $L_b$) of a system (of total size $L$) in the canonical ensemble. Using a simple finite size scaling theory we predict the behaviour of the fluctuations $<ε_{ij}ε_{kl}>$ as a function of $L_b/L$ and extract elastic constants of the system {\em in the thermodynamic limit} at nonzero temperature. Our method is simple to implement, efficient and general enough to be able to handle a wide class of model systems including those with singular potentials without any essential modification. We illustrate the technique by computing isothermal elastic constants of the ``soft'' and the hard disk triangular solids in two dimensions from molecular dynamics and Monte Carlo simulations. We compare our results with those from earlier simulations and density functional theory.

cond-mat↗
arXiv1999

Molecular-Dynamics Simulation of a Glassy Polymer Melt: Rouse Model and Cage Effect

We report results of molecular-dynamics simulations for a glassy polymer melt consisting of short, linear bead-spring chains. It was shown in previous work that this onset of the glassy slowing down is compatible with the predictions of the mode coupling theory. The physical process of `caging' of a monomer by its spatial neighbors leads to a distinct two step behavior in the particle mean square displacements. In this work we analyze the effects of this caging process on the Rouse description of the melt's dynamics. We show that the Rouse theory is applicable for length and time scales above the typical scales for the caging process. Futhermore, the monomer displacement is compared with simulation results for a binary Lennard-Jones mixture to point out the differences which are introduced by the connectivity of the particles.

cond-mat.soft↗
arXiv1998

Interfacial profiles between coexisting phases in thin films: Cahn Hilliard treatment versus capillary waves

We consider an interface between two demixed A and B phases, confined in a thin film between two antisymmetric walls, one of which prefers A and the other B. Above the wetting transition, the interface is stabilized in the center of the film. Based on a suitable extension of the Cahn-Hilliard gradient-square theory in combination with the capillary wave theory, we argue that the confinement influences the interfacial structure in two ways: It squeezes the intrinsic structure and cuts off the capillary wave spectrum. As a result, the interfacial width is proportional to the film thickness D in very thin films, and proportional to the square root of D in thicker films. These effects are then discussed in detail for the special case of an interface between demixed homopolymer phases. The width of the intrinsic profile is calculated analytically as a function of film thickness in the Cahn-Hilliard approximation (weak segregation limit) and in the Helfand theory (strong segregation limit), and numerically in the self-consistent field approximation. The results are confirmed by Monte Carlo simulations of a lattice model for a polymer mixture.

cond-mat.stat-mech↗
arXiv1998

Intrinsic profiles and capillary waves at homopolymer interfaces: a Monte Carlo study

A popular concept which describes the structure of polymer interfaces by ``intrinsic profiles'' centered around a two dimensional surface, the ``local interface position'', is tested by extensive Monte Carlo simulations of interfaces between demixed homopolymer phases in symmetric binary (AB) homopolymer blends, using the bond fluctuation model. The simulations are done in an LxLxD geometry. The interface is forced to run parallel to the LxL planes by imposing periodic boundary conditions in these directions and fixed boundary conditions in the D direction, with one side favoring A and the other side favoring B. Intrinsic profiles are calculated as a function of the ``coarse graining length'' B by splitting the system into columns of size BxBxD and averaging in each column over profiles relative to the local interface position. The results are compared to predictions of the self-consistent field theory. It is shown that the coarse graining length can be chosen such that the interfacial width matches that of the self-consistent field profiles, and that for this choice of B the ``intrinsic'' profiles compare well with the theoretical predictions.

cond-mat.soft↗
arXiv1998

Monte Carlo and Molecular Dynamics Simulation of the Glass Transition of Polymers

Two coarse-grained models for polymer chains in dense glass-forming polymer melts are studied by computer simulation: the bond-fluctuation model on a simple cubic lattice, where a bond-length potential favors long bonds, is treated by dynamic Monte Carlo methods, and a bead-spring model in the continuum with a Lennard-Jones potential between the beads is treated by Molecular Dynamics. While the dynamics of both models differ for short length scales and associated time scales, on mesoscopic spatial and temporal scales both models behave similarly. In particular, the mode coupling theory of the glass transition can be used to interpret the slowing down of the undercooled polymer melt. For the off-lattice model, the approach to the critical point of mode coupling is both studied for constant pressure and for constant volume. The lattice model allows a test of the Gibbs-Di Marzio entropy theory of the glass transition, and our finding is that although the entropy does decrease significantly, there is no ``entropy catastrophe'', where the fluid entropy would turn negative. Finally, an outlook on confinement effects on the glass transition in thin film geometry is given.

cond-mat.soft↗
arXiv1998

Wetting and Capillary Condensation in Symmetric Polymer Blends: A comparison between Monte Carlo Simulations and Self-Consistent Field Calculations

We present a quantitative comparison between extensive Monte Carlo simulations and self-consistent field calculations on the phase diagram and wetting behavior of a symmetric, binary (AB) polymer blend confined into a film. The flat walls attract one component via a short range interaction. The critical point of the confined blend is shifted to lower temperatures and higher concentrations of the component with the lower surface free energy. The binodals close the the critical point are flattened compared to the bulk and exhibit a convex curvature at intermediate temperatures -- a signature of the wetting transition in the semi-infinite system. Investigating the spectrum of capillary fluctuation of the interface bound to the wall, we find evidence for a position dependence of the interfacial tension. This goes along with a distortion of the interfacial profile from its bulk shape. Using an extended ensemble in which the monomer-wall interaction is a stochastic variable, we accurately measure the difference between the surface energies of the components, and determine the location of the wetting transition via the Young equation. The Flory-Huggins parameter at which the strong first order wetting transition occurs is independent of chain length and grows quadratically with the integrated wall-monomer interaction strength. We estimate the location of the prewetting line. The prewetting manifests itself in a triple point in the phase diagram of very thick films and causes spinodal dewetting of ultrathin layers slightly above the wetting transition. We investigate the early stage of dewetting via dynamic Monte Carlo simulations.

cond-mat.stat-mech↗
arXiv1997

Molecular Dynamics Simulations of the Thermal Glass Transition in Polymer Melts: Alpha-Relaxation Behaviour

We present Molecular Dynamics simulations of the thermal glass transition in a dense model polymer liquid. We performed a comparative study of both constant volume and constant pressure cooling of the polymer melt. Great emphasis was laid on a careful equilibration of the dense polymer melt at all studied temperatures. Our model introduces competing length scales in the interaction to prevent any cristallisation tendency. In this first manuscript we we analyse the structural properties as a function of temperature and the long alpha-relaxation behaviour as observed in the dynamic structure factor and the self-diffusion of the polymer chains. The relaxation can be consistently analysed in terms of the mode coupling theory (MCT) of the glass transition. The mode coupling critical temperature and the exponent gamma, defining the power law divergence of the alpha-relaxation timescale both depend on the thermodynamic ensemble employed in the simulation.

cond-mat.stat-mech↗
arXiv1997

Orthorhombic Phase of Crystalline Polyethylene: A Constant Pressure Path Integral Monte Carlo Study

In this paper we present a Path Integral Monte Carlo (PIMC) simulation of the orthorhombic phase of crystalline polyethylene, using an explicit atom force field with unconstrained bond lengths and angles. This work represents a quantum extension of our recent classical simulation (J. Chem. Phys. 106, 8918 (1997)). It is aimed both at exploring the applicability of the PIMC method on such polymer crystal systems, as well as on a detailed assessment of the importance of quantum effects on different quantities. We used the $NpT$ ensemble and simulated the system at zero pressure in the temperature range 25 - 300 K, using Trotter numbers between 12 and 144. In order to investigate finite-size effects, we used chains of two different lengths, C_12 and C_24, corresponding to the total number of atoms in the super-cell being 432 and 864, respectively. We show here the results for structural parameters, like the orthorhombic lattice constants a,b,c, and also fluctuations of internal parameters of the chains, such as bond lengths and bond and torsional angles. We have also determined the internal energy and diagonal elastic constants c_11, c_22 and c_33. We discuss the temperature dependence of the measured quantities and compare to that obtained from the classical simulation. For some quantities, we discuss the way they are related to the torsional angle fluctuation. In case of the lattice parameters we compare our results to those obtained from other theoretical approaches as well as to some available experimental data. In order to study isotope effects, we simulated also a deuterated polyethylene crystal at a low temperature. We also suggest possible ways of extending this study and present some general considerations concerning modeling of polymer crystals.

cond-mat.mtrl-sci↗
arXiv1997

Interfaces in partly compatible polymer mixtures: A Monte Carlo simulation approach

The structure of polymer coils near interfaces between coexisting phases of symmetrical polymer mixtures (AB) is discussed, as well as the structure of symmetric diblock copolymers of the same chain length N adsorbed at the interface. The problem is studied by Monte Carlo simulations of the bond fluctuation model on the simple cubic lattice, using massively parallel computers (CRAY T3D). While homopolymer coils in the strong segregation limit are oriented parallel to the interface, the diblocks form ``dumbbells'' oriented perpendicular to the interface. However, in the dilute case (``mushroom regime'' rather than ``brush regime''), the diblocks are only weakly stretched. Distribution functions for monomers at the chain ends and in the center of the polymer are obtained, and a comparison to the self consistent field theory is made.

cond-mat.soft↗
arXiv1997

Diblock copolymers at a homopolymer-homopolymer-interface: a Monte Carlo simulation

The properties of diluted symmetric A-B diblock copolymers at the interface between A and B homopolymer phases are studied by means of Monte Carlo (MC) simulations of the bond fluctuation model. We calculate segment density profiles as well as orientational properties of segments, of A and B blocks, and of the whole chain. Our data support the picture of oriented ``dumbbells'', which consist of mildly perturbed A and B Gaussian coils. The results are compared to a self consistent field theory (SCFT) for single copolymer chains at a homopolymer interface. We also discuss the number of interaction contacts between monomers, which provide a measure for the ``active surface'' of copolymers or homopolymers close to the interface.

physics.chem-ph↗
arXiv1996

Small-Angle Excess Scattering: Glassy Freezing or Local Orientational Ordering?

We present Monte Carlo simulations of a dense polymer melt which shows glass-transition-like slowing-down upon cooling, as well as a build up of nematic order. At small wave vectors q this model system shows excess scattering similar to that recently reported for light-scattering experiments on some polymeric and molecular glass-forming liquids. For our model system we can provide clear evidence that this excess scattering is due to the onset of short-range nematic order and not directly related to the glass transition.

cond-mat.stat-mech↗
arXiv1996

Orthorhombic Phase of Crystalline Polyethylene: A Monte Carlo Study

In this paper we present a classical Monte Carlo simulation of the orthorhombic phase of crystalline polyethylene, using an explicit atom force field with unconstrained bond lengths and angles and periodic boundary conditions. We used a recently developed algorithm which apart from standard Metropolis local moves employs also global moves consisting of displacements of the center of mass of the whole chains in all three spatial directions as well as rotations of the chains around an axis parallel to the crystallographic c-direction. Our simulations are performed in the NpT ensemble, at zero pressure, and extend over the whole range of temperatures in which the orthorhombic phase is experimentally known to be stable (10 - 450 K). In order to investigate the finite-size effects in this extremely anisotropic crystal, we used different system sizes and different chain lengths, ranging from C_12 to C_96 chains, the total number of atoms in the super-cell being between 432 and 3456. We show here the results for structural parameters, such as the orthorhombic cell parameters a,b,c, and the setting angle of the chains, as well as internal parameters of the chains, such as the bond lengths and angles. Among thermodynamic quantities, we present results for thermal expansion coefficients, elastic constants and specific heat. We discuss the temperature dependence of the measured quantities as well as the related finite-size effects. In case of lattice parameters and thermal expansion coefficients, we compare our results to those obtained from other theoretical approaches as well as to some available experimental data. We also suggest some possible ways of extending this study.

cond-mat.mtrl-sci↗
arXiv1996

Some 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.

cond-mat.stat-mech↗