arXiv subjects

Kurt Binder

Publications and source records attributed to Kurt Binder.

At least 55 records · Page 3Linked to original sources

arXiv2011

Hard sphere fluids confined between soft repulsive walls: A comparative study using Monte Carlo and density functional methods

Hard-sphere fluids confined between parallel plates a distance $D$ apart are studied for a wide range of packing fractions, including also the onset of crystallization, applying Monte Carlo simulation techniques and density functional theory. The walls repel the hard spheres (of diameter $σ$) with a Weeks-Chandler-Andersen (WCA) potential $V_{WCA}(z) = 4 ε[(σ_w/z)^{12}-(σ_w/z)^6 + 1/4]$, with range $σ_w = σ/2$. We vary the strength $ε$ over a wide range and the case of simple hard walls is also treated for comparison. By the variation of $ε$ one can change both the surface excess packing fraction and the wall-fluid $(γ_{wf})$ and wall-crystal $(γ_{wc})$ surface free energies. Several different methods to extract $γ_{wf}$ and $γ_{wc}$ from Monte Carlo (MC) simulations are implemented, and their accuracy and efficiency is comparatively discussed. The density functional theory (DFT) using Fundamental Measure functionals is found to be quantitatively accurate over a wide range of packing fractions; small deviations between DFT and MC near the fluid to crystal transition need to be studied further. Our results on density profiles near soft walls could be useful to interpret corresponding experiments with suitable colloidal dispersions.

cond-mat.stat-mech↗

arXiv2011

Anomalous Structure and Scaling of Ring Polymer Brushes

A comparative simulation study of polymer brushes formed by grafting at a planar surface either flexible linear polymers (chain length $N_L$) or (non-catenated) ring polymers (chain length $N_R=2 N_L$) is presented. Two distinct off-lattice models are studied, one by Monte Carlo methods, the other by Molecular Dynamics, using a fast implementation on graphics processing units (GPUs). It is shown that the monomer density profiles $ρ(z)$ in the $z$-direction perpendicular to the surface for rings and linear chains are practically identical, $ρ_R(2 N_L, z)=ρ_L(N_L, z)$. The same applies to the pressure, exerted on a piston at hight z, as well. While the gyration radii components of rings and chains in $z$-direction coincide, too, and increase linearly with $N_L$, the transverse components differ, even with respect to their scaling properties: $R_{gxy}^{(L)} \propto N_L^{1/2}$, $R_{gxy}^{(R)} \propto N_L^{0.4}$. These properties are interpreted in terms of the statistical properties known for ring polymers in dense melts.

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arXiv2011

Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions

Excess contributions to the free energy due to interfaces occur for many problems encountered in the statistical physics of condensed matter when coexistence between different phases is possible (e.g. wetting phenomena, nucleation, crystal growth, etc.). This article reviews two methods to estimate both interfacial free energies and line tensions by Monte Carlo simulations of simple models, (e.g. the Ising model, a symmetrical binary Lennard-Jones fluid exhibiting a miscibility gap, and a simple Lennard-Jones fluid). One method is based on thermodynamic integration. This method is useful to study flat and inclined interfaces for Ising lattices, allowing also the estimation of line tensions of three-phase contact lines, when the interfaces meet walls (where "surface fields" may act). A generalization to off-lattice systems is described as well. The second method is based on the sampling of the order parameter distribution of the system throughout the two-phase coexistence region of the model. Both the interface free energies of flat interfaces and of (spherical or cylindrical) droplets (or bubbles) can be estimated, including also systems with walls, where sphere-cap shaped wall-attached droplets occur. The curvature-dependence of the interfacial free energy is discussed, and estimates for the line tensions are compared to results from the thermodynamic integration method. Basic limitations of all these methods are critically discussed, and an outlook on other approaches is given.

cond-mat.stat-mech↗

arXiv2010

Polymer chain stiffness versus excluded volume: A Monte Carlo study of the crossover towards the wormlike chain model

When the local intrinsic stiffness of a polymer chain varies over a wide range, one can observe both a crossover from rigid-rod-like behavior to (almost) Gaussian random coils and a further crossover towards self-avoiding walks in good solvents. Using the pruned-enriched Rosenbluth method (PERM) to study self-avoiding walks of up to $N_b=50000$ steps and variable flexibility, the applicability of the Kratky-Porod model is tested. Evidence for non-exponential decay of the bond-orientational correlations $<\cos θ(s) >$ for large distances $s$ along the chain contour is presented, irrespective of chain stiffness. For bottle-brush polymers on the other hand, where experimentally stiffness is varied via the length of side-chains, it is shown that these cylindrical brushes (with flexible backbones) are not described by the Kratky-Porod wormlike chain model, since their persistence length is (roughly) proportional to their cross-sectional radius, for all conditions of practical interest.

cond-mat.soft↗

arXiv2010

Conformational Studies of bottle-brush polymers absorbed on a flat solid surface

The adsorption of a bottle-brush polymer end-grafted with one chain end of its backbone to a flat substrate surface is studied by Monte Carlo simulation of a coarse-grained model, that previously has been characterized in the bulk, assuming a dilute solution under good solvent conditions. Applying the bond fluctuation model on the simple cubic lattice, we vary the backbone chain length $N_b$ from $N_b=67$ to $N_b = 259$ effective monomeric units, the side chain length $N$ from N=6 to N=48, and the grafting density $σ=1$, i.e., parameters that correspond well to the experimentally accessible range. When the adsorption energy strength $ε$ is varied, we find that the adsorption transition (which becomes well-defined in the limit $N_b \rightarrow \infty$, for arbitrary finite $N$) roughly occurs at the same value $ε_c$ as for ordinary linear chains (N=0), at least within our statistical errors. Mean square end-to-end distances and gyration radii of the side chains are obtained, as well as the monomer density profile in the direction perpendicular to the adsorbing surface. We show that for longer side chains the adsorption of bottle-brushes is a two step process, the decrease of the perpendicular linear dimension of side chains with adsorption energy strength can even be non-monotonic. Also the behavior of the static structure factor $S(q)$ is analyzed, evidence for a quasi-two-dimensional scaling is presented, and consequences for the interpretation of experiments are discussed.

cond-mat.soft↗

arXiv2010

Does Young's equation hold on the nanoscale? A Monte Carlo test for the binary Lennard-Jones fluid

When a phase-separated binary ($A+B$) mixture is exposed to a wall, that preferentially attracts one of the components, interfaces between A-rich and B-rich domains in general meet the wall making a contact angle $θ$. Young's equation describes this angle in terms of a balance between the $A-B$ interfacial tension $γ_{AB}$ and the surface tensions $γ_{wA}$, $γ_{wB}$ between, respectively, the $A$- and $B$-rich phases and the wall, $γ_{AB} \cos θ=γ_{wA}-γ_{wB}$. By Monte Carlo simulations of bridges, formed by one of the components in a binary Lennard-Jones liquid, connecting the two walls of a nanoscopic slit pore, $θ$ is estimated from the inclination of the interfaces, as a function of the wall-fluid interaction strength. The information on the surface tensions $γ_{wA}$, $γ_{wB}$ are obtained independently from a new thermodynamic integration method, while $γ_{AB}$ is found from the finite-size scaling analysis of the concentration distribution function. We show that Young's equation describes the contact angles of the actual nanoscale interfaces for this model rather accurately and location of the (first order) wetting transition is estimated.

cond-mat.stat-mech↗

arXiv2010

Rounding of Phase Transitions in Cylindrical Pores

Phase transitions of systems confined in long cylindrical pores (capillary condensation, wetting, crystallization, etc.) are intrinsically not sharply defined but rounded. The finite size of the cross section causes destruction of long range order along the pore axis by spontaneous nucleation of domain walls. This rounding is analyzed for two models (Ising/lattice gas and Asakura-Oosawa model for colloid-polymer mixtures) by Monte Carlo simulations and interpreted by a phenomenological theory. We show that characteristic differences between the behavior of pores of finite length and infinitely long pores occur. In pores of finite length a rounded transition occurs first, from phase coexistence between two states towards a multi-domain configuration. A second transition to the axially homogeneous phase follows near pore criticality.

cond-mat.stat-mech↗

arXiv2010

Capillary Condensation in Cylindrical Pores: Monte Carlo Study of the Interplay of Surface and Finite Size Effects

When a fluid that undergoes a vapor to liquid transition in the bulk is confined to a long cylindrical pore, the phase transition is shifted (mostly due to surface effects at the walls of the pore) and rounded (due to finite size effects). The nature of the phase coexistence at the transition depends on the length of the pore: For very long pores the system is axially homogeneous at low temperatures. At the chemical potential where the transition takes place fluctuations occur between vapor-like and liquid-like states of the cylinder as a whole. At somewhat higher temperatures (but still far below bulk criticality) the system at phase coexistence is in an axially inhomogeneous multi-domain state, where long cylindrical liquid-like and vapor-like domains alternate. Using Monte Carlo simulations for the Ising/lattice gas model and the Asakura-Oosawa model of colloid-polymer mixtures the transition between these two different scenarios is characterized. It is shown that the density distribution changes gradually from a double-peak structure to a triple-peak shape, and the correlation length in axial direction (measuring the equilibrium domain length) becomes much smaller than the cylinder length. The (rounded) transition to the disordered phase of the fluid occurs when the axial correlation length has decreased to a value comparable to the cylinder diameter. It is also suggested that adsorption hysteresis vanishes when the transition from the simple domain state to the multi-domain state of the cylindrical pore occurs. We predict that the difference between the pore critical temperature and the hysteresis critical emperature should increase logarithmically with the length of the pore.

cond-mat.stat-mech↗

arXiv2010

Two-state protein-like folding of a homopolymer chain

Many small proteins fold via a first-order "all-or-none" transition directly from an expanded coil to a compact native state. Here we study an analogous direct freezing transition from an expanded coil to a compact crystallite for a simple flexible homopolymer. Wang-Landau sampling is used to construct the 1D density of states for square-well chains of length 128. Analysis within both the micro-canonical and canonical ensembles shows that, for a chain with sufficiently short-range interactions, the usual polymer collapse transition is preempted by a direct freezing or "folding" transition. A 2D free-energy landscape, built via subsequent multi-canonical sampling, reveals a dominant folding pathway over a single free-energy barrier. This barrier separates a high entropy ensemble of unfolded states from a low entropy set of crystallite states and the transition proceeds via the formation of a transition-state folding nucleus. Despite the non-unique homopolymer ground state, the thermodynamics of this direct freezing transition are identical to the thermodynamics of two-state protein folding. The model chain satisfies the van't Hoff calorimetric criterion for two-state folding and an Arrhenius analysis of the folding/unfolding free energy barrier yields a Chevron plot characteristic of small proteins.

cond-mat.soft↗

arXiv2010

Spherical Polymer Brushes Under Good Solvent Conditions: Molecular Dynamics Results Compared to Density Functional Theory

A coarse grained model for flexible polymers end-grafted to repulsive spherical nanoparticles is studied for various chain lengths and grafting densities under good solvent conditions, by Molecular Dynamics methods and density functional theory. With increasing chain length the monomer density profile exhibits a crossover to the star polymer limit. The distribution of polymer ends and the linear dimensions of individual polymer chains are obtained, while the inhomogeneous stretching of the chains is characterized by the local persistence lengths. The results on the structure factor of both single chain and full spherical brush as well as the range of applicability of the different theoretical tools are presented. Eventually an outlook on experiments is given.

cond-mat.soft↗

arXiv2010

Out of Equilibrium Characteristics of a Forced Translocating Chain through a Nanopore

Polymer translocation through a nano-pore in a thin membrane is studied using a coarse-grained bead-spring model and Langevin dynamics simulation with a particular emphasis to explore out of equilibrium characteristics of the translocating chain. We analyze the out of equilibrium chain conformations both at the $cis$ and the $trans$ side separately either as a function of the time during the translocation process or as as function of the monomer index $m$ inside the pore. A detailed picture of translocation emerges by monitoring the center of mass of the translocating chain, longitudinal and transverse components of the gyration radii and the end to end vector. We observe that polymer configurations at the $cis$ side are distinctly different from those at the $trans$ side. During the translocation, and immediately afterwards, the chain is clearly out of equilibrium, as different parts of the chain are characterized by a series of effective Flory exponents. We further notice that immediately after the translocation the last set of beads that have just translocated take a relatively compact structure compared to the first set of beads that translocated earlier, and the chain immediately after translocation is described by an effective Flory exponent $0.45 \pm 0.01$. The analysis of these results is further strengthened by looking at the conformations of chain segments of equal length as they cross from the $cis$ to the $trans$ side, We discuss implications of these results to the theoretical estimates and numerical simulation studies of the translocation exponent reported by various groups.

cond-mat.soft↗

arXiv2010

Monte Carlo Test of the Classical Theory for Heterogeneous Nucleation Barriers

Flat walls facilitate the condensation of a supersaturated vapor: Classical theory of heterogeneous nucleation predicts that the free energy barrier $ΔF_{\rm het}^*$ which needs to be overcome for the formation of sphere-cap shaped nucleation seeds is smaller than the barrier $ΔF^*_{\rm hom}$ for spherical droplets in the bulk by a factor $0<f(θ)<1$, which only depends on the contact angle $θ$. In this letter we compute both $ΔF^*_{\rm hom}$ and $ΔF^*_{\rm het}$ from Monte Carlo simulations and test the theory for the lattice gas model (for which $θ$ can be readily controlled). Even though the theory is only based on macroscopic arguments, it is shown to hold for experimentally relevant nanoscopic nucleation seeds ($20\leqΔF^*_{\rm hom}/k_BT\leq 200)$ if (independently estimated) line tension effects are considered.

cond-mat.stat-mech↗

arXiv2009

Soliton Staircases and Standing Strain Waves in Confined Colloidal Crystals

We show by computer simulation of a two-dimensional crystal confined by corrugated walls that confinement can be used to impose a controllable mesoscopic superstructure of predominantly mechanical elastic character. Due to an interplay of the particle density of the system and the width D of the confining channel, "soliton staircases" can be created along both parallel confining boundaries, that give rise to standing strain waves in the entire crystal. The periodicity of these waves is of the same order as D. This mechanism should be useful for structure formation in the self-assembly of various nanoscopic materials.

cond-mat.soft↗

arXiv2009

The Observation of Formation and Annihilation of Solitons and Standing Strain Wave Superstructures in a Two-Dimensional Colloidal Crystal

Confining a colloidal crystal within a long narrow channel produced by two parallel walls can be used to impose a meso-scale superstructure of a predominantly mechanical elastic character [Chui et al., EPL 2008, 83, 58004]. When the crystal is compressed in the direction perpendicular to the walls, we obtain a structural transition when the number of rows of particles parallel to the walls decreases by one. All the particles of this vanishing row are distributed throughout the crystal. If the confining walls are structured (say with a corrugation along the length of the walls), then these extra particles are distributed neither uniformly nor randomly; rather, defect structures are created along the boundaries resembling "soliton staircases", inducing a non-uniform strain pattern within the crystal. Here we study the conditions of stability, formation and annihilation of these solitons using a coarse grained description of the dynamics. The processes are shown by comparing superimposed configurations as well as molecular animations obtained from our simulations. Also the corresponding normal and shear stresses during the transformation are calculated. A study of these dynamical processes should be useful for controlling strain wave superstructures in the self-assembly of various nano- and meso scaled particles.

cond-mat.soft↗

arXiv2009

Effective interactions and melting of a one dimensional defect lattice within a two-dimensional confined colloidal solid

We report Monte Carlo studies of a two-dimensional soft colloidal crystal confined in a strip geometry by parallel walls. The wall-particle interaction has corrugations along the length of the strip. Compressing the crystal by decreasing the distance between the walls induces a structural transition characterized by the sudden appearance of a one-dimensional array of extended defects each of which span several lattice parameters, a "soliton staircase". We obtain the effective interaction between these defects. A Lindemann criterion shows that the reduction of dimensionality causes a finite periodic chain of these defects to readily melt as the temperature is raised. We discuss possible experimental realizations and speculate on potential applications.

cond-mat.soft↗

arXiv2009

How to Define Variation of Physical Properties Normal to an Undulating One-Dimensional Object

One-dimensional flexible objects are abundant in physics, from polymers to vortex lines to defect lines and many more. These objects structure their environment and it is natural to assume that the influence these objects exert on their environment depends on the distance from the line-object. But how should this be defined? We argue here that there is an intrinsic length scale along the undulating line that is a measure of its "stiffness" (i.e., orientational persistence), which yields a natural way of defining the variation of physical properties normal to the undulating line. We exemplify how this normal variation can be determined from a computer simulation for the case of a so-called bottle-brush polymer, where side chains are grafted onto a flexible backbone.

cond-mat.soft↗

arXiv2009

Phase Transitions and Relaxation Processes in Macromolecular Systems: The Case of Bottle-brush Polymers

As an example for the interplay of structure, dynamics, and phase behavior of macromolecular systems, this article focuses on the problem of bottle-brush polymers with either rigid or flexible backbones. On a polymer with chain length $N_b$, side-chains with chain length $N$ are endgrafted with grafting density $σ$. Due to the multitude of characteristic length scales and the size of these polymers (typically these cylindrical macromolecules contain of the order of 10000 effective monomeric units) understanding of the structure is a challenge for experiment. But due to excessively large relaxation times (particularly under poor solvent conditions) such macromolecules also are a challenge for simulation studies. Simulation strategies to deal with this challenge, both using Monte Carlo and Molecular Dynamics Methods, will be briefly discussed, and typical results will be used to illustrate the insight that can be gained.

cond-mat.soft↗

arXiv2009

Multiscale modeling of polymers at interfaces

A brief review of modeling and simulation methods for a study of polymers at interfaces is provided. When studying truly multiscale problems as provided by realistic polymer systems, coarse graining is practically unavoidable. In this process, degrees of freedom on smaller scales are eliminated to the favor of a model suitable for efficient study of the system behavior on larger length and time scales. We emphasize the need to distinguish between dynamic and static properties regarding the model validation. A model which accurately reproduces static properties may fail completely, when it comes to the dynamic behavior of the system. Furthermore, we comment on the use of Monte Carlo method in polymer science as compared to molecular dynamics simulations. Using the latter approach, we also discuss results of recent computer simulations on the properties of polymers close to solid substrates. This includes both generic features (as also observed in the case of simpler molecular models) as well as polymer specific properties. Predictive power of computer simulations is highlighted by providing experimental evidence for these observations. Some important implications of these results for an understanding of mechanical properties of thin polymer films and coatings are also worked out.

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