Monte Carlo simulation of many-arm star polymers in two-dimensional good solvents in the bulk and at a surface

1991

A Monte Carlo technique is proposed for the simulation of statistical properties of many-arm star polymers on lattices. In this vectorizing algorithm, the length of each arml is increased by one, step by step, from a starting configuration withl=1 orl=2 which is generated directly. This procedure is carried out for a large sample (e.g., 100,000 configurations). As an application, we have studied self-avoiding stars on the square lattice with arm lengths up tol max=125 and up tof=20 arms, both in the bulk and in the geometry where the center of the star is adsorbed on a repulsive surface. The total number of configurations, which behaves asN∼l γ G–1μ fl , whereμ=2.6386 is the usual effective…

Continuum Monte Carlo simulation of phase transitions in rod-like molecules at surfaces

1994

Stiff rod-like chain molecules with harmonic bond length potentials and trigonometric bond angle potentials are used to model Langmuir monolayers at high densities. One end of the rod-like molecules is strongly bound to a flat two-dimensional substrate which represents the air-water interface. A ground-state analysis is performed which suggests phase transitions between phases with and without collective uniform tilt. Large-scale off-lattice Monte Carlo simulations over a wide temperature range show in addition to the tilting transition the presence of a strongly constrained melting transition at high temperatures. The latter transition appears to be related to two-dimensional melting of th…

Elastic properties, structures and phase transitions in model colloids

2004

The nature of the melting transition for a system of hard discs with translational degrees of freedom in two spatial dimensions has been analysed by a combination of computer simulation methods and a finite size scaling technique. The behaviour of the system is consistent with the predictions of the Kosterlitz–Thouless–Halperin–Nelson–Young (KTHNY) theory. The structural and elastic properties of binary colloidal mixtures in two and three spatial dimensions are discussed as well as those of colloidal systems with quenched point impurities. Hard and soft discs in external periodic (light-) fields show rich phase diagrams including freezing and melting transitions when the density of the syst…

Conformations and orientational ordering of semiflexible polymers in spherical confinement.

2017

Semiflexible polymers in lyotropic solution confined inside spherical nanoscopic “containers” with repulsive walls are studied by molecular dynamics simulations and density functional theory, as a first step to model confinement effects on stiff polymers inside of miniemulsions, vesicles, and cells. It is shown that the depletion effects caused by the monomer-wall repulsion depend distinctly on the radius R of the sphere. Further, nontrivial orientational effects occur when R, the persistence length ℓp, and the contour length L of the polymers are of similar magnitude. At intermediate densities, a “shell” of wall-attached chains is forming, such that the monomers belonging to those chains a…

Scaling theory of star polymers and general polymer networks in bulk and semi-infinite good solvents

1988

Theorie d'echelle utilisant l'equivalence entre la fonction generatrice du nombre total de configuration et la fonction de correlation a plusieurs spins du modele de Heisenberg classique a n composantes dans la limite n→0

Pearl-necklace structures of molecular brushes with rigid backbone under poor solvent conditions: A simulation study

2010

Bottle-brush polymers, where flexible side chains containing N=20 to 50 effective monomers are grafted to a rigid backbone, are studied by molecular dynamics simulations, varying the grafting density σ and the solvent quality. Whereas for poor solvents and large enough σ the molecular brush is a cylindrical object, homogeneous in axial direction, for intermediate values of σ an axially inhomogeneous structure of "pearl-necklace" type is formed. The "pearls," however, have a strongly nonspherical ellipsoidal shape, due to the fact that several side chains cluster together in one pearl, qualitatively consistent with predictions of Sheiko et al. [Eur. Phys. J. E 13, 125 (2004)] We analyze the …

Bending or buckling: Compression-induced phase transition in a semi-flexible polymer brush

2013

Molecular-dynamics simulations are presented for systems of densely grafted semiflexible macromolecules grafted to a planar non-adsorbing substrate, studying the case where the persistence length of the polymers is of the same order as their contour length so that the polymer brush may exhibit nematic order. We focus our attention on the case where the first bond must orient perpendicularly to the substrate (so the structure resembles a "Fakir's bed" for short chains and a "polymer bristle" for longer chains). When such layers are exposed to uniform compression, the pressure vs. distance relationship exhibits two stages: i) for very small compression the chains exhibit "buckling" yet mainta…

Inter-Chain Structure Factors of Flexible Polymers in Solutions: A Monte Carlo Investigation

1997

Off-lattice Monte Carlo simulations of both the single chain structure factor h(q) and the inter-chain structure factor HD(q) of flexible polymers in solutions are presented over a wide range of both wavenumber q and concentration c from the dilute to the concentrated regime, for chain lengths up to N = 256. The single chain properties $\{$gyration radius 〈Rg2〉, $h(q)\}$ are in reasonable agreement with the expected theoretical behavior, showing a crossover from swollen chains $\{\langle R_{\rm g}^2\rangle \propto N^{2\nu} ,~ h(q) \propto q^{-1/\nu}\}$ to Gaussian chains, and the data comply with a scaling description, with a correlation length ξ∝c-ν/(3ν-1). However, the inter-chain structu…

Spinodal Decomposition Kinetics of Colloid-Polymer Mixtures Including Hydrodynamic Interactions

2012

The phase separation dynamics of a model colloid-polymer mixture is studied by taking explicitly the hydrodynamic interactions caused by the solvent into account. Based on the studies on equilibrium phase behavior we perform a volume quench from the homogeneous region of the phase diagram deep into the region where colloid-rich and polymer-rich phases coexist. We demonstrate that the Multiparticle Collision Dynamics (MPCD) algorithm is well suited to study spinodal decomposition and present first results on the domain growth behavior of colloid-polymer mixtures in quasi two-dimensional confinement. On the one hand side we find that the boundary condition of the solvent with respect to the r…

Do the contact angle and line tension of surface-attached droplets depend on the radius of curvature?

2018

Results from Monte Carlo simulations of wall-attached droplets in the three-dimensional Ising lattice gas model and in a symmetric binary Lennard-Jones fluid, confined by antisymmetric walls, are analyzed, with the aim to estimate the dependence of the contact angle $(\Theta)$ on the droplet radius $(R)$ of curvature. Sphere-cap shape of the wall-attached droplets is assumed throughout. An approach, based purely on "thermodynamic" observables, e.g., chemical potential, excess density due to the droplet, etc., is used, to avoid ambiguities in the decision which particles belong (or do not belong, respectively) to the droplet. It is found that the results are compatible with a variation $[\Th…

Monte Carlo Study of Critical Point Shifts in Thin Films

2000

We report preliminary results of Monte Carlo simulations of critical point shifts in thin slit-like capillaries. By making use of the isomorphism with an Ising model subject to bulk and surface fields and employing a multi-cluster update algorithm with ghost-spin term we obtain the coexistence curve and the behavior at the critical point for various film thicknesses D.

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

2001

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 ions in the sodium silicate systems with that in pure silica a…

Properties of the Ising magnet confined in a corner geometry

2007

Abstract The properties of Ising square lattices with nearest neighbor ferromagnetic exchange confined in a corner geometry, are studied by means of Monte Carlo simulations. Free boundary conditions at which boundary magnetic fields ± h are applied, i.e., at the two boundary rows ending at the lower left corner a field + h acts, while at the two boundary rows ending at the upper right corner a field − h acts. For temperatures T less than the critical temperature T c of the bulk, this boundary condition leads to the formation of two domains with opposite orientation of the magnetization direction, separated by an interface which for T larger than the filling transition temperature T f ( h ) …

Theory of first-order phase transitions

1987

An introductory review of various concepts about first-order phase transitions is given. Rules for classification of phase transitions as second or first order are discussed, as well as exceptions to these rules. Attention is drawn to the rounding of first-order transitions due to finite-size or quenched impurities. Computational methods to calculate phase diagrams for simple model Hamiltonians are also described. Particular emphasis is laid on metastable states near first-order phase transitions, on the 'stability limits' of such states (e.g. the 'spinodal curve' of the gas-liquid transition) and on the dynamic mechanisms by which metastable states decay (nucleation and growth of droplets …

Wetting and phase separation at surfaces

2005

We study the problem ofsurfacedirected spinodal decomposition, viz., the dynamical interplay of wetting and phase separation at surfaces. In particular, we focus on the kinetics of wetting-layer growth in a semi-infinite geometry for arbitrary surface potentials and mixture compositions. We also present representative results for phase separation in confined geometries, e.g., cylindrical pores, thin films, etc.

Critical Phenomena at the Surface of Systems Undergoing a Bulk First Order Transition: Are They Understood?

2002

Systems that exhibit a first-order phase transition in the bulk, such as binary alloys where the order parameter vanishes discontinuously at some critical value of a control parameter, may show a continuous vanishing of the local order parameter at the surface. This “surface-induced disordering” is described theoretically as a variant of critical wetting, where an interface between the locally disordered surface and the ordered bulk gradually moves towards the bulk. We test this description by Monte Carlo simulations for a body centered cubic model alloy, with interactions between nearest and next nearest neighbors, for which the phase diagram in the bulk has been calculated very accurately…

Understanding the properties of liquid-crystalline polymers by computational modeling

2020

Abstract A topical review of recent theoretical work on the properties of lyotropic solutions and melts containing semiflexible polymers in thermal equilibrium is given, with a focus on the liquid-crystalline and smectic order of these systems in the bulk and under confinement. Starting with a discussion of single chain properties in terms of the Kratky-Porod worm-like chain model and its limitations, extensions along the lines of Onsager’s theory for the isotropic-nematic transition of solutions of hard rods are briefly reviewed. This discussion is followed by a review of recent Molecular Dynamics simulations and classical Density Functional Theory calculations. It is argued that, even in …

1988

Monte Carlo simulations are presented for binary (AB) symmetric polymer mixtures (chain lengths NANBN) for the case that an attractive interaction ϵ exists between monomers of the same kind, and the limiting case that one species (B) is very diluted. It is shown that with increasing interaction strength ϵ/(kB · T), T being the absolute temperature, the minority chains collapse to a very dense configuration, while the majority chains stay nearly Gaussian. Both chain radii, structure factors and numbers of nearest neighbour contacts are discussed.

Orientational ordering transitions of semiflexible polymers in thin films: A Monte Carlo simulation

2011

Athermal solutions (from dilute to concentrated) of semiflexible macromolecules confined in a film of thickness D between two hard walls are studied by means of grand-canonical lattice Monte Carlo simulation using the bond fluctuation model. This system exhibits two phase transitions as a function of the thickness of the film and polymer volume fraction. One of them is the bulk isotropic-nematic first-order transition, which ends in a critical point on decreasing the film thickness. The chemical potential at this transition decreases with decreasing film thickness ("capillary nematization"). The other transition is a continuous (or very weakly first-order) transition in the layers adjacent …

Simulations of Glassforming Network Fluids: Classical Molecular Dynamics versus Car-Parrinello Molecular Dynamics

2010

Abstract Static and dynamic Properties of molten germanium dioxide are studied by two simulation methods, classical Molecular Dynamics (MD) using the Oeffner-Elliott (OE) potential, and “ab initio” Car-Parrinello Molecular Dynamics (CPMD). While CPMD provides a (presumably) more accurate description of the local structure and the forces, it severely suffers from finite size effects when the structure beyond the first neighbor shells is considered. For glassforming fluids, the demanding equilibrium needs are a further reason, why simply MD is still preferable, when a “good” effective potential is available.

Critical phenomena without “hyper scaling”: How is the finite-size scaling analysis of Monte Carlo data affected?

2010

Abstract The finite size scaling analysis of Monte Carlo data is discussed for two models for which hyperscaling is violated: (i) the random field Ising model (using a model for a colloid-polymer mixture in a random matrix as a representative) (ii) The Ising bi-pyramid in computing surface fields.

Diluted Heisenberg Ferromagnets with Competing Ferro- and Antiferromagnetic Interactions: Evidence for a New Universality Class?

1993

The site-diluted classical face-centered cubic (fee) Heisenberg model with exchange between nearest and (J nn > 0) next nearest (J nnn =-J nn /2) neighbors is studied by Monte Carlo simulations using the heatbath algorithm in conjunction with histogram reweighting techniques. Finite size scaling analysis suggests that the diluted system crosses over to a new type of critical behavior, different from that of the pure system, in contrast to the prediction of the Harris criterion. But this model possibly can explain related experimental findings in Eu x Sr 1-x S.

Study of the dynamical approach to the interface localization–delocalization transition of the confined Ising model

2004

Confined magnetic Ising films in a L ? D geometry (), with short-range competing magnetic fields?(h) acting at opposite walls along the D-direction, exhibit a slightly rounded localization?delocalization transition of the interface between domains of different orientations that runs parallel to the walls. This transition is the precursor of a wetting transition that occurs in the limit of infinite film thickness () at the critical curve Tw(h). For T Tw(h)) such an interface is bounded (unbounded) to the walls, while right at Tw(h) the interface is freely fluctuating around the centre of the film. Starting from disordered configurations, corresponding to , we quench to the wetting critical t…

Dynamics of confined polymer melts: Recent Monte Carlo simulation results

2000

The dynamic behavior of thin polymer films is studied by Monte Carlo simulations of a simplified lattice model. The film geometry is realized by two opposite hard walls whose distance is varied in the simulations. In the films the dynamics is accelerated with respect to the bulk, leading to a decrease of the extrapolated glass transition temperature with decreasing film thickness.

Rejection-Free Monte Carlo

2019

So far, we have been using the rejection Monte Carlo algorithms. To remind us, the algorithms proceed from state x to possible state \(x'\) as outlined in Algorithm 1.

Monte Carlo Simulation of Crystal-Liquid Phase Coexistence

2016

When a crystal nucleus is surrounded by coexisting fluid in a finite volume in thermal equilibrium, the thermodynamic properties of the fluid (density, pressure, chemical potential) are uniquely related to the surface excess free energy of the nucleus. Using a model for weakly attractive soft colloidal particles, it is shown that this surface excess free energy can be determined accurately from Monte Carlo simulations over a wide range of nucleus volumes, and the resulting nucleation barriers are completely independent from the size of the total volume of the system. A necessary ingredient of the analysis, the pressure at phase coexistence in the thermodynamic limit, is obtained from the in…

Brownian dynamics of grafted polymer chains: time dependent properties

1995

Results of computer simulations of polymer layers consisting of chains grafted by one end on an unpenetrable plane are presented. Characteristics of translational and rotational motion of different chain segments and correlation functions of chain radii were calculated both for single layers at different grafting densities s and for two interacting layers at different distances D between parallel grafting planes. Two values of grafting density were used in the latter case. The behavior of different correlation times as function of s and D and the interplay between the interpenetration of the brushes and rotational and translational motion are discussed. Both relaxation functions and mean sq…

Avoiding Boundary Effects in Wang-Landau Sampling

2003

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.

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

2008

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 a…

Finite-size scaling at the dynamical transition of the mean-field 10-state Potts glass

2001

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)^{-\Delta} 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 glas…

Path-integral Monte Carlo study of crystalline Lennard-Jones systems.

1995

The capability of the path-integral Monte Carlo (PIMC) method to describe thermodynamic and structural properties of solids at low temperatures is studied in detail, considering the noble-gas crystals as examples. In order to reduce the systematic limitations due to finite Trotter number and finite particle number we propose a combined Trotter and finite-size scaling. As a special application of the PIMC method we investigate $^{40}\mathrm{Ar}$ at constant volume and in the harmonic approximation. Furthermore, isotope effects in the lattice constant of $^{20}\mathrm{Ne}$ and $^{22}\mathrm{Ne}$ are computed at zero pressure. The obtained results are compared with classical Monte Carlo result…

Phase Separation in a Binary Mixture of Semiflexible Polymers Confined in a Repulsive Sphere

2021

A polymer chain trapped between two parallel repulsive walls: A Monte-Carlo test of scaling behavior

1998

An off-lattice bead-spring model of a polymer chain trapped between two parallel walls a distance D apart is studied by Monte-Carlo methods, using chain lengths N in the range $$32 \le N \le 512$$ and distances D from 4 to 32 (in units of the maximum spring extension). The scaling behavior of the coil linear dimensions parallel to the plates and of the force on the walls is studied and discussed with the help of current theoretical predictions. Also the density profiles of the monomers across the slit are obtained and it is shown that the predicted variation with the distance z from a wall, $$\rho (z) \propto {z^{1/\nu }}$$ , is obtained only when one introduces an extrapolation length λ in…

The liquid-solid transition of hard discs: first-order transition or Kosterlitz-Thouless-Halperin-Nelson-Young scenario?

2002

We consider the question of whether a two-dimensional hard-disc fluid has a first-order transition from the liquid state to the solid state as in the three-dimensional melting-crystallization transition or whether one has two subsequent continuous transitions, from the liquid to the hexatic phase and then to the solid phase, as proposed by Kosterlitz, Thouless, Halperin, Nelson and Young (KTHNY). Monte Carlo (MC) simulations of the fluid that study the growth of the bond orientational correlation length, and of the crystal are discussed. The emphasis is on a recent consistency test of the KTHNY renormalization group (RG) scenario, where MC simulations are used to estimate the bare elastic c…

Critical wetting in the square Ising model with a boundary field

1990

The Ising square lattice with nearest-neighbor exchangeJ>0 and a free surface at which a boundary magnetic fieldH1 acts has a second-order wetting transition. We study the surface excess magnetization and the susceptibility ofL×M lattices by Monte Carlo simulation and probe the critical behavior of this wetting transition, applying finite-size scaling methods. For the cases studied, the results are not consistent with the presumably exactly known values of the critical exponents, because the asymptotic critical region has not yet been reached. Implication of our results for critical wetting in three dimensions and for the application of the present model to adsorbed wetting layers at surfac…

Phase separation in thin films: Effect of temperature gradients

2013

We study the phase-separation kinetics of a binary (AB) mixture confined in a thin film of thickness D with a temperature gradient. Starting from a Kawasaki-exchange kinetic Ising model, we use a master-equation approach to systematically derive an extension of the Cahn-Hilliard model for this system. We study the effect of temperature gradients perpendicular to the film with "neutral" (no preference for either A or B) surfaces. We highlight the rich phenomenology and pattern dynamics which arises from the interplay of phase separation and the temperature gradient.

New Results on the Collapse Transition(s) of Flexible Homopolymers

2007

We analyze the collapse transition of flexible homopolymer chains in the bond-fluctuation model employing the Wang-Landau Monte Carlo algorithm. The coil-globule transition is followed by a first order transition into a solid state occurring in the collapsed globule. In the thermodynamic limit (chain length to infinity) the topology of the phase diagram depends on the range of the attractive interaction between the monomers. For sufficiently large interaction range a normal behaviour of a continuous coil-globule transition at the Θ-temperature followed by a crystallization transition at lower temperature is observed. For short interaction range the first-order transition asymptotically can …

Star polymers confined in a nanoslit: a simulation test of scaling and self-consistent field theories

2013

The free energy cost of confining a star polymer where f flexible polymer chains containing N monomeric units are tethered to a central unit in a slit with two parallel repulsive walls a distance D apart is considered, for good solvent conditions. Also the parallel and perpendicular components of the gyration radius of the star polymer, and the monomer density profile across the slit are obtained. Theoretical descriptions via Flory theory and scaling treatments are outlined, and compared to numerical self-consistent field calculations (applying the Scheutjens–Fleer lattice theory) and to Molecular Dynamics results for a bead-spring model. It is shown that Flory theory and self-consistent fi…

Phase transitions in adsorbed layers formed on crystals of square and rectangular surface lattice

2000

Abstract This article gives a survey of phase transitions in adsorbed films on well defined surfaces of square and rectangular symmetry of the lattice. The discussion concentrates on the effects of periodic changes of the adsorbate–substrate potential on the structure and thermodynamic properties of adsorbed films. Different theoretical approaches are briefly reviewed, with an emphasis on those which explicitly take into account final corrugation of the surface potential. Several aspects of statistical mechanical description of phase transitions in surface layers, such as order–disorder, melting, commensurate–incommensurate transitions in monolayer films as well as transitions connected wit…

Linear Dimensions of Adsorbed Semiflexible Polymers: What can be learned about their persistence length?

2019

Conformations of partially or fully adsorbed semiflexible polymer chains are studied varying both contour length $L$, chain stiffness, $\ensuremath{\kappa}$, and the strength of the adsorption potential over a wide range. Molecular dynamics simulations show that partially adsorbed chains (with ``tails,'' surface attached ``trains,'' and ``loops'') are not described by the Kratky-Porod wormlike chain model. The crossover of the persistence length from its three-dimensional value (${\ensuremath{\ell}}_{p}$) to the enhanced value in two dimensions ($2{\ensuremath{\ell}}_{p}$) is analyzed, and excluded volume effects are identified for $L\ensuremath{\gg}{\ensuremath{\ell}}_{p}$. Consequences fo…

What is the order of the two-dimensional polymer escape transition?

2007

An end-grafted flexible polymer chain in three-dimensional space between two pistons undergoes an abrupt transition from a confined coil to a flowerlike conformation when the number of monomers in the chain, $N$, reaches a critical value. In two-dimensional (2D) geometry, excluded-volume interactions between monomers of a chain confined inside a strip of finite length $2L$ transform the coil conformation into a linear string of blobs. However, the blob picture raises questions about the nature of this escape transition. To check theoretical predictions based on the blob picture we study 2D single-polymer chains with excluded-volume interactions and with one end grafted in the middle of a st…

Phase Separation of Colloid Polymer Mixtures Under Confinement

2013

Colloid polymer mixtures exhibit vapor-liquid like and liquid-solid like phase transitions in bulk suspensions, and are well-suited model systems to explore confinement effects on these phase transitions. Static aspects of these phenomena are studied by large-scale Monte Carlo simulations, including novel “ensemble switch” methods to estimate excess free energies due to confining walls. The kinetics of phase separation is investigated by a Molecular Dynamics method, where hydrodynamic effects due to the solvent are included via the multiparticle collision dynamics method.

Monte Carlo simulation of polymers at interfaces

1993

Abstract Polymers at interfaces pose challenging problems to statistical physics because their configurations often differ greatly from the bulk. Computer simulation of coarse-grained models then gives valuable insight and allows stringent tests of various theoretical predictions. Three examples are briefly treated: chain configurations of B-chains in the surface-enriched B-rich layer of an (AB) binary polymer mixture; “frustrated” lamellar ordering in ultra-thin block-copolymer films; and the collapse of polymer brushes in bad solvents.

When does Wenzel's extension of Young's equation for the contact angle of droplets apply? A density functional study.

2020

he contact angle of a liquid droplet on a surface under partial wetting conditions differs for a nanoscopically rough or periodically corrugated surface from its value for a perfectly flat surface. Wenzel's relation attributes this difference simply to the geometric magnification of the surface area (by a factor $r_{\rm w}$), but the validity of this idea is controversial. We elucidate this problem by model calculations for a sinusoidal corrugation of the form $z_{\rm wall}(y) = \Delta\cos(2\pi y/\lambda)$ , for a potential of short range $\sigma_{\rm w}$ acting from the wall on the fluid particles. When the vapor phase is an ideal gas, the change of the wall-vapor surface tension can be co…

Towards the Quantitative Prediction of the Phase Behavior of Polymer Solutions by Computer Simulation

2009

The phase diagram of polymer solutions (cf. e.g. alkanes dissolved in supercritical carbon dioxide) is complicated, since there are four control parameters (temperature, pressure, monomer volume fraction, chain length of the polymer) and due to the interplay of liquid-vapor transitions and fluid-fluid unmixing. As a result I very intricate phase diagram topologies can result. An attempt to develop coarse-1 grained models that can deal with this task will be described. As usual, the polymers I will be modelled as off-lattice bead-spring chains, where several chemical monomers I are integrated into one effective bond, torsional degrees of freedom being dis-I regarded. But also a coarse-graine…

Monte Carlo simulations of the polymer glass transition: From the test of theories to material modeling

1997

We present results on the glass transition in polymer melts using Monte Carlo simulations of the bond fluctuation lattice model. There are two questions we address in this work. What is the temperature dependence of the entropy density in such a model polymer melt and how well is it described by theories like the Gibbs-DiMarzio theory of the glass transition? And to what degree is one able to map the Hamiltonian of such an abstract lattice model onto a specific polymer material and use it to model the large scale and long time properties of a realistic polymer melt?

Monte Carlo simulation of a lyotropic first-order isotropic-nematic phase transition in a lattice polymer model

1999

We present a Monte Carlo simulation of the bond-fluctuation lattice model, using a Hamiltonian which introduces a change in the conformational statistics of the polymer chains from Gaussian behavior at high temperatures to rigid rod behavior at low temperatures. We do not introduce any attractive interaction between the chains. Upon cooling, the aspect ratio of the chains increases above the critical value for the density employed in the simulation, and we observe an entropically driven phase transition into a nematic phase. We examine this transition quantitatively by a careful finite size scaling study using an optimized cumulant intersection method, and show that the transition is of fir…

Growth of Domains and Scaling in the Late Stages of Phase Separation and Diffusion-Controlled Ordering Phenomena

1991

These lectures consider the kinetics of phase changes, induced by a sudden change of external thermodynamic parameters. E.g., we treat a system with a second-order transition at a critical temperature Tc (Fig. 1, left part). For T0 > Tc the system is disordered, while for T < Tc there is an order parameter ± ψ (implying one-component orderings, e.g., an Ising model; later we discuss generalizations). We consider a “quenching experiment”: The system is brought from an initially disordered state at T0 to a state at T where in equilibrium the system should be orderedl. Since no sign of ψ is preferred, the system starts forming locally ordered regions of either sign, separated by domain walls. …

Can one detach a fully adsorbed flexible polymer chain by an ultra-small external force?

2013

Full adsorption of flexible chains onto typical solid substrates occurs at a surface interaction energy of (5–10) kBT. The corresponding detachment force is in the range 10–50 pN. In contrast to “bare” solid substrates common to non-living materials, surfaces coated with brush-like polymer layers are very common in biological soft matter. We employ a simple mean-field approach to describe the effects of weak attraction between a floating long macromolecule and the brush. We show that even for a moderately thick brush a very small effective attraction is enough to produce complete binding of the long chain. The detachment force scales as , where W is the brush thickness. Hence the force coul…

Comparison of Dissipative Particle Dynamics and Langevin thermostats for out-of-equilibrium simulations of polymeric systems

2007

In this work we compare and characterize the behavior of Langevin and Dissipative Particle Dynamics (DPD) thermostats in a broad range of non-equilibrium simulations of polymeric systems. Polymer brushes in relative sliding motion, polymeric liquids in Poiseuille and Couette flows, and brush-melt interfaces are used as model systems to analyze the efficiency and limitations of different Langevin and DPD thermostat implementations. Widely used coarse-grained bead-spring models under good and poor solvent conditions are employed to assess the effects of the thermostats. We considered equilibrium, transient, and steady state examples for testing the ability of the thermostats to maintain const…

Reply to “Comment on ‘Elastic constants from microscopic strain fluctuations’ ”

2010

We agree with Coupier et al. [Phys. Rev. E 81, 013101 (2010)] that their technique for extracting elastic constants from microscopic strain fluctuations improves upon ours because of a more accurate computation of the integral of the elastic correlation function over sub-blocks. However, we believe that their interpretation of the physical relevance of the elastic correlation length extracted from the fits is misleading.

Stretching of Free Chains Confined in Concave Brush-Coated Nanocylinders

2012

The structure of a free flexible macromolecule confined in a cylindrical nanopore whose wall is coated by a polymer brush is studied by Monte Carlo simulation, varying the grafting density as well as the radius of the cylindrical pore. Because of this confinement, the free chain is stretched in axial direction; while for small grafting densities of the brush the end-to-end distance increases monotonously with decreasing pore radius, a nonmonotonic variation occurs for larger grafting densities. We show that this effect is due to strong interpenetration of the free chain and the brush chains; for very narrow pores a strong layering of cylindrical shells is found, and comparison with self-con…

Universal monomer dynamics of a two dimensional semi-flexible chain

2013

We present a unified scaling theory for the dynamics of monomers for dilute solutions of semiflexible polymers under good solvent conditions in the free draining limit. Our theory encompasses the well-known regimes of mean square displacements (MSDs) of stiff chains growing like t^{3/4} with time due to bending motions, and the Rouse-like regime t^{2 \nu / (1+ 2\nu)} where \nu is the Flory exponent describing the radius R of a swollen flexible coil. We identify how the prefactors of these laws scale with the persistence length l_p, and show that a crossover from stiff to flexible behavior occurs at a MSD of order l^2_p (at a time proportional to l^3_p). A second crossover (to diffusive moti…

Interfaces between coexisting phases of polymer mixtures: Comparison between Monte Carlo simulations and theoretical predictions

1997

Large scale Monte Carlo investigations of the interface between A-rich and B-rich phases of symmetric binary (AB) polymer mixtures are presented, using the bond fluctuation model of flexible chains with NA=NB=N=32 effective monomers. The temperature range studied, 0.144<T/Tc0.759, includes both the strong and the weak segregation limit. Interfacial free energy and interfacial structure are studied, and compared to predictions based on the selfconsistent field theory. Also the broadening of the interfacial width due to capillary waves is considered, and finite size effects due to the confinement of interfaces in thin films of polymer blends are discussed.

Osmotic pressure, atomic pressure and the virial equation of state of polymer solutions: Monte Carlo simulations of a bead-spring model

1994

A recently introduced coarse-grained model of polymer chains is studied analyzing various contributions to the pressure as obtained from the virial theorem as a function of chain length N, temperature T and density ϕ. The off-lattice model of the polymer chains has anharmonic springs between the beads, but of finite extensibility, and the Morse-type interaction between beads is repulsive at very short distances and attractive at intermediate distances. Solvent molecules are not explicitly included. It is found that the covalent forces along the chain (modelled by the spring potentials) contribute a negative term to the pressure, irrespective of temperature, which vanishes linearly in ϕ as ϕ…

Investigation of Finite-Size Effects in the Determination of Interfacial Tensions

2014

The interfacial tension between coexisting phases of a material is an important parameter in the description of many phenomena such as crystallization, and even today its accurate measurement remains difficult. We have studied logarithmic finite-size corrections in the determination of the interfacial tension with large scale Monte Carlo simulations, and have identified several novel contributions which not only depend on the ensemble, but also on the type of the applied boundary conditions. We present results for the Lennard-Jones system and the Ising model, as well as for hard spheres, which are particularly challenging. In the future, these findings will contribute to the understanding a…

Polymer Brushes on Flat and Curved Substrates: What Can be Learned from Molecular Dynamics Simulations

2017

Ising systems with pairwise competing surface fields

2005

The magnetization distribution and phase behaviour of large but finite Ising simple cubic L × L × L lattices in d = 3 dimensions and square L × L lattices in d = 2 dimensions are studied for the case where four free boundaries are present, at which surface fields +Hs act on one pair of opposite boundaries while surface fields −Hs act on the other pair (in d = 3, periodic boundary conditions are used for the remaining pair). Both the distribution PL(m) of the global magnetization and also the distribution of the local magnetization m(x,z) are obtained by Monte Carlo simulations, where x and z denote the coordinates when the boundaries are oriented along the x-axis and z-axis (in d = 2); or a…

Efficient prediction of thermodynamic properties of quadrupolar fluids from simulation of a coarse-grained model: the case of carbon dioxide.

2008

Monte Carlo simulations are presented for a coarse-grained model of real quadrupolar fluids. Molecules are represented by particles interacting with Lennard-Jones forces plus the thermally averaged quadrupole-quadrupole interaction. The properties discussed include the vapor-liquid coexistence curve, the vapor pressure along coexistence, and the surface tension. The full isotherms are also accessible over a wide range of temperatures and densities. It is shown that the critical parameters (critical temperature, density, and pressure) depend almost linearly on a quadrupolar parameter q=Q(*4)T*, where Q* is the reduced quadrupole moment of the molecule and T* the reduced temperature. The mode…

The mean field to Ising crossover in the critical behavior of polymer mixtures : a finite size scaling analysis of Monte Carlo simulations

1993

Monte Carlo simulations of the bond fluctuation model of symmetrical polymer mixtures (chain lengths N A =N B =N) are analyzed near the critical temperature T c (N) of their unmixing transition. Two choices of interaction range are studied, using a square-well potential with effective coordination number z eff ≃ 14 or z eff ≃ 5, respectively, at a volume fraction O= 0.5 of occupied lattice sites, and chain lengths in the range 8≤ N≤ 512. A linear relation between N and T c (N) is established, T c (N)= AN+B, where the correction term B is positive for z eff = 14 but negative for z eff = 5. The critical behavior of the models is analyzed via finite size scaling techniques, paying attention to…

Finite size effects at thermally-driven first order phase transitions: A phenomenological theory of the order parameter distribution

1993

We consider the rounding and shifting of a firstorder transition in a finited-dimensional hypercubicL d geometry,L being the linear dimension of the system, and surface effects are avoided by periodic boundary conditions. We assume that upon lowering the temperature the system discontinuously goes to one ofq ordered states, such as it e.g. happens for the Potts model ind=3 forq≧3, with the correlation length ξ of order parameter fluctuation staying finite at the transition. We then describe each of theseq ordered phases and the disordered phase forL≫ξ by a properly weighted Gaussian. From this phenomenological ansatz for the total distribution of the order parameter, all moments of interest…

LARGE-SCALE SIMULATIONS IN CONDENSED MATTER PHYSICS —THE NEED FOR A TERAFLOP COMPUTER

1992

The introduction of vector processors {“supercomputers” with a performance in the range of 109 floating point operations (1 GFLOP) per second} has had an enormous impact on computational condensed matter physics. The possibility of a substantially enhanced performance by massively parallel processors (“teraflop” machines with 1012 floating point operations per second) will allow satisfactory treatment of a large range of important scientific problems which have to a great extent thus far escaped numerical resolution. The present paper describes only a few examples (out of a long list of interesting research problems!) for which the availability of “teraflops” will allow spectacular progres…

Theoretical Foundations of the Monte Carlo Method and Its Applications in Statistical Physics

2002

In this chapter we first introduce the basic concepts of Monte Carlo sampling, give some details on how Monte Carlo programs need to be organized, and then proceed to the interpretation and analysis of Monte Carlo results.

Semiflexible Polymers in the Bulk and Confined by Planar Walls

2016

Semiflexible polymers in solution under good solvent conditions can undergo an isotropic-nematic transition. This transition is reminiscent of the well-known entropically-driven transition of hard rods described by Onsager’s theory, but the flexibility of the macromolecules causes specific differences in behavior, such as anomalous long wavelength fluctuations in the ordered phase, which can be understood by the concept of the deflection length. A brief review of the recent progress in the understanding of these problems is given, summarizing results obtained by large-scale molecular dynamics simulations and density functional theory. These results include also the interaction of semiflexib…

On the polymer physics origins of protein folding thermodynamics

2016

A remarkable feature of the spontaneous folding of many small proteins is the striking similarity in the thermodynamics of the folding process. This process is characterized by simple two-state thermodynamics with large and compensating changes in entropy and enthalpy and a funnel-like free energy landscape with a free-energy barrier that varies linearly with temperature. One might attribute the commonality of this two-state folding behavior to features particular to these proteins (e.g., chain length, hydrophobic/hydrophilic balance, attributes of the native state) or one might suspect that this similarity in behavior has a more general polymer-physics origin. Here we show that this behavi…

Kinetics of the Formation of Ordered Domains on Surfaces: Theoretical Considerations and Monte-Carlo Simulation

1986

When an adsorbed monolayer which initially is in a disordered state is suddenly brought to a temperature in the regime of the ordered phase, domains of the ordered phase are predicted to form and grow with time t after the quench according to a power law, i.e. linear dimension L(t) ∞ tx. At the same time, the structure function S(k,t) is predicted to satisfy a scaling law, S(k,t) = S(k,tx), k being the difference between the wave vector observed in the scattering and the Bragg wave vector describing the long range order. The theoretical ideas which lead to this behaviour are briefly reviewed, and evidence from simulations of simple lattice gas models and Potts models is presented. Particula…

Monte Carlo renormalization group methods

2014

Theory of glass transition in spin glasses, orientational glasses and structural glasses

2008

Theoretical concepts about the glass transition are briefly reviewed, and the test of these ideas by Monte Carlo simulations of simple lattice models is described, with an emphasis on isotropic and anisotropic orientational glasses, and the bond fluctuation model of polymer melts. It is suggested that orientational glasses do have an equilibrium phase transition at zero temperature (in d = 3 dimensions!) only, in contrast to the Ising spin glass which orders at nonzero temperature. A diverging glass correlation length is identified that is responsible for the anomalous slowing down. For the Potts glass, the divergence seems to be exponential, implying that the model is at its lower critical…

Monte Carlo Simulations of Surfaces and Interfaces in Materials

1996

Many applications of materials are controlled by their surface and interface properties. In particular, metallic alloys (but also mixed dielectric materials and amorphous polymer blends) are not homogeneously mixed on a microscopic length scale, although they are macroscopically homogeneous. Depending on the preparation of the sample, there exists a heterophase microstructure, with typical domain sizes, e.g. in the 1 to 102 µm range, separated by interfaces between them. The physical properties of such intrinsic interfaces (grain boundaries between small crystallites, antiphase domain boundaries in ordered alloys, Bloch walls in magnetic materials, etc.) are not only an important controllin…

Finite-size effects on liquid-solid phase coexistence and the estimation of crystal nucleation barriers.

2015

A fluid in equilibrium in a finite volume $V$ with particle number $N$ at a density $\rho = N/V$ exceeding the onset density $\rho_f $ of freezing may exhibit phase coexistence between a crystalline nucleus and surrounding fluid. Using a method suitable for the estimation of the chemical potential of dense fluids we obtain the excess free energy due to the surface of the crystalline nucleus. There is neither a need to precisely locate the interface nor to compute the (anisotropic) interfacial tension. As a test case, a soft version of the Asakura-Oosawa model for colloid polymer-mixtures is treated. While our analysis is appropriate for crystal nuclei of arbitrary shape, we find the nucleat…

The smectic phase in semiflexible polymer materials: A large scale Molecular Dynamics study

2019

Abstract Semiflexible polymers in concentrated lyotropic solution are studied within a bead-spring model by molecular dynamics simulations, focusing on the emergence of a smectic A phase and its properties. We systematically vary the density of the monomeric units for several contour lengths that are taken smaller than the chain persistence length. The difficulties concerning the equilibration of such systems and the choice of appropriate ensemble (constant volume versus constant pressure, where all three linear dimensions of the simulation box can fluctuate independently) are carefully discussed. Using HOOMD-blue on graphics processing units, systems containing more than a million monomeri…

Unmixing of Polymer Blends Confined in Ultrathin Films:  Crossover between Two-Dimensional and Three-Dimensional Behavior

2006

The interplay between chain conformations and phase separation in binary symmetric polymer mixtures confined into thin films by "neutral" hard walls (i.e., walls that do not preferentially attract or repel one of the two components of the mixture) is studied by Monte Carlo simulations. Using the bond fluctuation model on a simple cubic lattice in the semi grand canonical ensemble, we locate the critical temperature of demixing via finite size scaling methods for a wide range of chain lengths (16/= N/= 256 effective monomers per chain) and film thicknesses (2/= D/= 19 lattice spacings). Simultaneously, we investigate the geometrical structure of the chains, showing that despite using melt de…

Spinodal decomposition in a binary polymer mixture: Dynamic self-consistent-field theory and Monte Carlo simulations

2001

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…

Slowing down in the three-dimensional three-state Potts glass with nearest neighbor exchange : A Monte Carlo study

1998

,Static and dynamic properties of the Potts model on the simple cubic lattice with nearest neighbor ±Ĵ-interaction are obtained from Monte Carlo simulations in a temperature range where full thermal equilibrium still can be achieved (T/Ĵ ≥ 0.6). For a lattice size L = 16, in this range finite size effects are still negligible, but the data for the spin glass susceptibility agree with previous extrapolations based on finite size scaling of very small lattices. While the static properties are compatible with a zero temperature transition, they certainly do not prove it. Unlike the Ising spin glass, the decay of the time-dependent order parameter is compatible with a simple Kohlrausch function…

What can be learned from the rotational motion of single molecules in a polymer melt near the glass transition?

2007

We develop a framework for the interpretation of single-molecule (SM) spectroscopy experiments of probe dynamics in a complex glass-forming system. Specifically, from molecular dynamics simulations of a single probe molecule in a coarse-grained model of a polymer melt, we show the emergence of sudden large angular reorientations (SLARs) of the SM as the mode coupling critical temperature is closely approached. The large angular jumps are intimately related to meta-basin transitions in the potential energy landscape of the investigated system and cause the appearance of stretched exponential relaxations of various rotational observables, reported in the SM literature as dynamic heterogeneity…

Phase Behavior of Active Swimmers in Depletants: Molecular Dynamics and Integral Equation Theory

2013

We study the structure and phase behavior of a binary mixture where one of the components is self-propelling in nature. The inter-particle interactions in the system were taken from the Asakura-Oosawa model, for colloid-polymer mixtures, for which the phase diagram is known. In the current model version the colloid particles were made active using the Vicsek model for self-propelling particles. The resultant active system was studied by molecular dynamics methods and integral equation theory. Both methods produce results consistent with each other and demonstrate that the Vicsek model based activity facilitates phase separation, thus broadening the coexistence region.

Growing length scales in a supercooled liquid close to an interface

2002

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 differe…

Hydrokinetic simulations of nanoscopic precursor films in rough channels

2009

We report on simulations of capillary filling of high-wetting fluids in nano-channels with and without obstacles. We use atomistic (molecular dynamics) and hydrokinetic (lattice-Boltzmann) approaches which point out clear evidence of the formation of thin precursor films, moving ahead of the main capillary front. The dynamics of the precursor films is found to obey a square-root law as the main capillary front, z^2(t) ~ t, although with a larger prefactor, which we find to take the same value for the different geometries (2D-3D) under inspection. The two methods show a quantitative agreement which indicates that the formation and propagation of thin precursors can be handled at a mesoscopic…

Surface effects on spinodal decomposition in binary mixtures: The case with long-ranged surface fields

1997

We present detailed numerical results for phase-separation kinetics of critical binary mixtures in the vicinity of a surface that exerts a long-ranged attractive force on one of the components of the mixture. We consider surface potentials of the form $V(Z)\ensuremath{\sim}{Z}^{\ensuremath{-}n}$, where $Z$ is the distance from the surface and $n=1,2,3$. In particular, we investigate the interplay of the surface wetting layer with the dynamics of domain growth. We find that the wetting layer at the surface exhibits power-law growth with an exponent that depends on $n$, in contrast to the case with a short-ranged surface potential, where the growth is presumably logarithmic. From correlation …

Depletion induced isotropic-isotropic phase separation in suspensions of rod-like colloids

2007

When non-adsorbing polymers are added to an isotropic suspension of rod-like colloids, the colloids effectively attract each other via depletion forces. We performed Monte Carlo simulations to study the phase diagram of such rod-polymer mixture. The colloidal rods were modeled as hard spherocylinders; the polymers were described as spheres of the same diameter as the rods. The polymers may overlap with no energy cost, while the overlap of polymers and rods is forbidden. Large amounts of depletant cause phase separation of the mixture. We estimated the phase boundaries of isotropic-isotropic coexistence both in the bulk and in confinement. To determine the phase boundaries we applied the gra…

How does stiffness of polymer chains affect their adsorption transition?

2020

The adsorption transition and the structure of semiflexible adsorbed macromolecules are studied by a molecular dynamics simulation of a coarse-grained, bead-spring type model. Varying chain length N and stiffness κ (which is proportional to the persistence length lp in d = 3 dimensions) as well as the strength ϵwall of the adsorption potential, the adsorbed monomer fraction, orientational bond order parameter, and chain linear dimensions are studied. In the simulations, excluded volume interactions normally are included but can be “switched off,” and thus, the influence of excluded volume (leading to deviations from predictions of the wormlike chain model) can be identified. It is shown tha…

Coil-bridge transition in a single polymer chain as an unconventional phase transition: theory and simulation.

2014

The coil-bridge transition in a self-avoiding lattice chain with one end fixed at height H above the attractive planar surface is investigated by theory and Monte Carlo simulation. We focus on the details of the first-order phase transition between the coil state at large height H ⩾ Htr and a bridge state at H ⩽ Htr, where Htr corresponds to the coil-bridge transition point. The equilibrium properties of the chain were calculated using the Monte Carlo pruned-enriched Rosenbluth method in the moderate adsorption regime at (H/Na)tr ⩽ 0.27 where N is the number of monomer units of linear size a. An analytical theory of the coil-bridge transition for lattice chains with excluded volume interact…

Anomalous Fluctuations of Nematic Order in Solutions of Semiflexible Polymers

2016

The nematic ordering in semiflexible polymers with contour length $L$ exceeding their persistence length $\ell_p$ is described by a confinement of the polymers in a cylinder of radius $r_{eff}$ much larger than the radius $r_\rho$, expected from the respective concentration of the solution. Large scale Molecular Dynamics simulations combined with Density Functional Theory are used to locate the Isotropic-Nematic ($I-N$)-transition and to validate this cylindrical confinement. Anomalous fluctuations, due to chain deflections from neighboring chains in the nematic phase are proposed. Considering deflections as collective excitations in the nematically ordered phase of semiflexible polymers el…

On melting of two-dimensional monolayer films

1996

The melting of two-dimensional films formed on the (100) fcc crystal is studied by Monte Carlo simulation. The results obtained suggest that in systems with only weakly corrugated surface potential, exhibiting the hexagonal close packed solid structure, the melting transition is followed by the lsing-like transition as predicted by the theory of Nelson and Halperin. In the case of highly corrugated surface potential, the film forms registered structure which disorders gradually as the temperature is raised.

Adsorption of Oligomers and Polymers into a Polymer Brush Formed from Grafted Ring Polymers

2013

The interaction of a ring polymer brush with a solution containing oligomers or free linear flexible macromolecules is studied by Monte Carlo simulation, varying the chain length of the free chains, and in selected cases also the lengths of the rings. Two grafting densities are studied, corresponding to semidilute and very concentrated conditions, and a comparison with the corresponding case of brushes formed from grafted linear chains is made. Although the ring polymer linear dimensions in the brushes show an anomalous scaling with ring length, similar to (noncatenated) ring polymer melts, the concentration profiles of oligomers and long macromolecules in ring polymer brushes differ only v…

Classical Heisenberg antiferromagnets with nearest and next-nearest neighbor interactions on the face-centered cubic lattice: a model for EuTe?

1989

Magnetic properties of the Heisenberg antiferromagnet with spin quantum numberS→∞ on the face-centered cubic lattice are studied as function of temperature and magnetic field, using molecular field approximation and Monte Carlo methods. In order to model Europiumtelluride, we use isotropic exchange interactions between nearest- and nextnearest neighbors; the values of these exchange constants are taken from experiments. In addition, a pseudo-dipolar anisotropy (truncated after the next-nearest neighbor distance) is included; the molecular field calculations also are performed with the full dipolar of real EuTe in two respects: the structure in zero magnetic field involves 8 sublattices in t…

Monte Carlo investigations of phase transitions: status and perspectives

2000

Using the concept of finite-size scaling, Monte Carlo calculations of various models have become a very useful tool for the study of critical phenomena, with the system linear dimension as a variable. As an example, several recent studies of Ising models are discussed, as well as the extension to models of polymer mixtures and solutions. It is shown that using appropriate cluster algorithms, even the scaling functions describing the crossover from the Ising universality class to the mean-field behavior with increasing interaction range can be described. Additionally, the issue of finite-size scaling in Ising models above the marginal dimension (d*=4) is discussed.

Monte Carlo and molecular dynamics simulation of the glass transition of polymers

1998

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…

Stochastic dynamics of polymer brushes under shear deformation

1998

The dynamical properties of polymer brushes under shear deformation have been studied by computer simulation. Both the local and the global dynamic properties at various shear rates have been calculated. The distribution of orientational and translational mobilities of the different monomers along the chain have been obtained. It was shown that the local mobility of the brushes changes very slowly with increasing of shear rates up to the largest rates. Increase in grafting density leads to an increasingly step like dependence of the correlation times as a function of shear rate.

Monte Carlo calculation of free energy for a fcc lattice-gas model

1990

A face-centered-cubic Ising lattice-gas model with nearest- and next-nearest-neighbor interactions is studied, and an accurate determination of the transition temperature for the discontinuous order-disorder transition is obtained. This model is of interest in the studies of phase diagrams for metallic alloys. The location of the transition was previously not known accurately, and its estimation has a number of applications. Very accurate absolute free-energy densities for the two coexisting phases have been obtained from a combination of the standard thermodynamic integration method and the method of sampling finite-size dependence. The latent-heat also is calculated with good precision.

Crossover scaling in semidilute polymer solutions: a Monte Carlo test

1991

Formation of metastable structures by phase separation triggered by initial composition gradients in thin films.

2012

Phase separation kinetics of a binary (A,B) mixture contained in a thin film of thickness D induced by a quench from the one-phase region into the miscibility gap is studied by simulations using a Cahn-Hilliard-Cook model. The initial randomly mixed state (50% A, 50% B) contains a concentration gradient perpendicular to the film, while the surfaces of the film are "neutral" (no preference for either A or B). In thermal equilibrium, a pattern of large A-rich and B-rich domains must result, separated by domain walls oriented perpendicularly to the external surfaces of the thin film. However, it is shown that for many choices of D and the strength of the initial gradient Ψ(g), instead a very l…

Unconventional ordering behavior of semi-flexible polymers in dense brushes under compression

2014

Using a coarse-grained bead-spring model for semi-flexible macromolecules which form a polymer brush, the structure and dynamics of the polymers were investigated, varying the chain stiffness and the grafting density. The anchoring conditions for the grafted chains were chosen such that their first bonds were oriented along the normal to the substrate plane. The compression of such a semi-flexible brush by a planar piston was observed to be a two-stage process: for a small compression the chains were shown to contract by "buckling" deformation whereas for a larger compression the chains exhibited a collective (almost uniform) bending deformation. Thus, the stiff polymer brush underwent a 2n…

Dynamics of a supercooled polymer melt above the mode-coupling critical temperature: cage versus polymer-specific effects

2000

This paper reports results of molecular dynamics simulations for a glassy polymer melt consisting of short, non-entangled chains. The temperature region studied covers the supercooled state of the melt above the mode-coupling critical temperature. The analysis focuses on the interplay of simple-liquid and polymer-specific effects. One can clearly distinguish two regimes: a regime of small and one of large monomer displacements. The first regime corresponds to motion of a monomer in its local environment. It is dominated by the cage effect and well described by the idealized mode-coupling theory. The second regime is governed by the late-β/early-α process. In this regime the connectivity of …

Simulations of critical phenomena: from Ising models to fluids

2015

A brief retrospective is given, how simulations of critical phenomena started about 45 years ago, and how finite size scaling concepts helped to make such studies quantitative.

Structure of bottle-brush polymers in solution: A Monte Carlo test of models for the scattering function

2008

Extensive Monte Carlo results are presented for a lattice model of a bottle-brush polymer under good solvent or Theta solvent conditions. Varying the side chain length, backbone length, and the grafting density for a rigid straight backbone, both radial density profiles of monomers and side chain ends are obtained, as well as structure factors describing the scattering from a single side chain and from the total bottle-brush polymer. To describe the structure in the interior of a very long bottle-brush, a periodic boundary condition in the direction along the backbone is used, and to describe effects due to the finiteness of the backbone length, a second set of simulations with free ends of…

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

2010

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 $\sigma=1$, i.e., parameters that correspond well to the experimentally accessible range. When the adsorption energy strength $\epsilon$ is varied, we find that the adsorption tra…

Surface Effects on Block Copolymer Melts Above the Order-Disorder Transition: Linear Theory of Equilibrium Properties and the Kinetics of Surface-Ind…

1997

A phenomenological theory is developed for static and dynamic aspects ofsurface- induced ordering of symmetrical block copolymers taking fluctuation corrections into account, but, considering conditions where the bulk block copolymer melt is still disordered, and a lin- earized version of the resulting Ginzburg-Landau type equation suffices. Both the semi-infinite geometry and symmetrical films of thickness 2L are treated, applying the same boundary con- ditions as used previously for a treatment of wetting in polymer blends, assuming short range surface forces and a long Wavelength approximation. For the static order parameter profile in thin film geometry, We derive an oscillatory converg…

Evidence for the time-temperature superposition principle from Monte-Carlo simulations of the glass transition in two-dimensional polymer melts

1992

The bond fluctuation model on a square lattice with a bond-length dependent potential exhibits in simulations of slow cooling a kinetic glass transition where the system falls out of equilibrium. Extending previous work, the relaxation functions of gyration radius and end-to-end distance, and the bond autocorrelation function of the polymers are presented and related to the time-dependent displacements of inner monomeric units and center of gravity of the whole chains, respectively. Over a wide temperature range the data can be collapsed on master curves satisfying the time-temperature superposition principle for Rouse dynamics.

Structure and dynamics of thin polymer films: a case study with the bond-fluctuation model

2002

Abstract This paper reports Monte Carlo simulation results of a polymer melt of short, non-entangled chains which are embedded between two impenetrable walls. The melt is simulated by the bond-fluctuation lattice model under athermal conditions, i.e. only excluded volume interactions between the monomers and between the monomers and the walls are taken into account. In the simulations, the wall separation is varied from about one to about 15 times the bulk radius of gyration R g . The confinement influences both static and dynamic properties of the films: Chains close to the walls preferentially orient parallel to it. This parallel orientation decays with increasing distances from the wall …

Entropic Unmixing in Nematic Blends of Semiflexible Polymers

2020

Binary mixtures of semiflexible polymers with the same chain length but different persistence lengths separate into two coexisting different nematic phases when the osmotic pressure of the lyotropic solution is varied. Molecular Dynamics simulations and Density Functional Theory predict phase diagrams either with a triple point, where the isotropic phase coexists with two nematic phases, or a critical point of unmixing within the nematic mixture. The difference in locally preferred bond angles between the constituents drives this unmixing without any attractive interactions between monomers.

Interfaces in immiscible polymer blends: A Monte Carlo simulation approach on the CRAY T3E

1999

Polymeric materials pose a challenge for Monte Carlo simulations because of the widely spread length and time scales involved. Using large scale computer simulations we investigate the interfacial structure in a partially compatible polymer mixture. The problem is studied in the framework of a coarse grained lattice model - the bond fluctuation model on the simple cubic lattice, choosing N = 32 and lattice linear dimensions L × L × D up to 512 × 512 × 64. We employ a two dimensional geometric decomposition scheme to implement this algorithm on the CRAY T3E. The algorithm scales very well with the number of processors. The structure of polymer coils near interfaces between coexisting phases …

Computer simulation of models for orientational glasses

1991

Abstract Monte Carlo studies of two- and three-dimensional lattice models where quadrupoles interact with a nearest-neighbor Gaussian coupling are reviewed. None of these models has a thermodynamic glass phase transition at non-zero temperature like the Ising spin glass: rather, phase transitions at zero temperature occur that exhibit a dynamical freeze-in spread out over a wide temperature range and are characterized by a strongly non-exponential relaxation. The time-dependent glass order parameter, q(t), decays with time, t, compatible with a stretched exponential decay q(t) ∼ exp [− (t/τ)y] with a strongly temperature-dependent exponent. While the static glass ‘susceptibility’ for isotro…

Unmixing of binary alloys by a vacancy mechanism of diffusion: a computer simulation

1991

The initial stages of phase separation are studied for a model binary alloy (AB) with pairwise interactions e AA , e AB , e BB between nearest neighbors, assuming that there is no direct interchange of neighboring atoms possible, but only an indirect one mediated by vacancies (V) occurring in the system at a concentrationc v and which are strictly conserved, as are the concentrationsc A andc B of the two species.A-atoms may jump to vacant sites with jump rateГ A , B-atoms with jump rateГ B (in the absence of interactions). Particular attention is paid to the question to what extent nonuniform distribution of vacancies affects the unmixing kinetics. Our study focuses on the special caseГ A =…

The relaxation dynamics of a supercooled liquid confined by rough walls

2004

We present the results of molecular dynamics computer simulations of a binary Lennard-Jones liquid confined between two parallel rough walls. These walls are realized by frozen amorphous configurations of the same liquid and therefore the structural properties of the confined fluid are identical to the ones of the bulk system. Hence this setup allows us to study how the relaxation dynamics is affected by the pure effect of confinement, i.e. if structural changes are completely avoided. We find that the local relaxation dynamics is a strong function of z, the distance of the particles from the wall, and that close to the surface the typical relaxation times are orders of magnitude larger tha…

Interfaces in the confined Ising system with competing surface fields

2005

Abstract When a magnetic Ising film is confined in a L × M geometry ( L ⪡ M ) short-range competing magnetic fields ( h 1 ) are applied at opposite walls along the M -direction, a (weakly rounded) localization–delocalization transition of the interface between domains of different orientation that runs parallel to walls can be observed. This transition is the precursor of a wetting phase transition that occurs in the limit of infinite film thickness ( L → ∞ ) at the critical curve T w ( h 1 ) . For T T w ( h 1 ) ( T > T w ( h 1 ) ) such an interface is bound to (unbound from) the walls, while right at T w ( h 1 ) the interface is freely fluctuating around the center of the film. We present …

Understanding the Multiple Length Scales Describing the Structure of Bottle-brush Polymers by Monte Carlo Simulation Methods

2011

Bottle-brush polymers contain a long flexible macromolecule as a backbone to which flexible side chains are grafted. Through the choice of the grafting density and the length of the side chains the local stiffness of this cylindrical molecular brush can be controlled, but a quantitative understanding of these phenomena is lacking. Monte Carlo simulation results are presented and discussed which address this issue, extractingmesoscopic length scales (such as the cross-sectional radius, persistence length, and contour length of these objects). Large-scale simulations of the bond fluctuation model are combined with simulations of the simple selfavoiding walk (SAW) model with flexibility contro…

Dynamics of Glassy Polymer Melts in Confined Geometry: A Monte Carlo Simulation

1996

Dynamic properties of a dense polymer melt confined between two hard walls are investigated over a wide range of temperatures by dynamic Monte Carlo simulation. The temperature interval ranges from the ordinary liquid to the strongly supercooled melt. The influence of temperature, density and confinement on the polymer dynamics is studied by various mean-square displacements, structural relaxation functions and quantities derived from them (relaxation times, apparent diffusion coefficients, monomer relaxation rates), yielding the following results: The motion of the monomers and polymers close to the walls is enhanced in parallel, but reduced in perpendicular direction. This dynamic anisotr…

Finite-size scaling in a microcanonical ensemble

1988

The finite-size scaling technique is extended to a microcanonical ensemble. As an application, equilibrium magnetic properties of anL×L square lattice Ising model are computed using the microcanonical ensemble simulation technique of Creutz, and the results are analyzed using the microcanonical ensemble finite-size scaling. The computations were done on the multitransputer system of the Condensed Matter Theory Group at the University of Mainz.

Monte Carlo Tests of Nucleation Concepts in the Lattice Gas Model

2013

The conventional theory of homogeneous and heterogeneous nucleation in a supersaturated vapor is tested by Monte Carlo simulations of the lattice gas (Ising) model with nearest-neighbor attractive interactions on the simple cubic lattice. The theory considers the nucleation process as a slow (quasi-static) cluster (droplet) growth over a free energy barrier $\Delta F^*$, constructed in terms of a balance of surface and bulk term of a "critical droplet" of radius $R^*$, implying that the rates of droplet growth and shrinking essentially balance each other for droplet radius $R=R^*$. For heterogeneous nucleation at surfaces, the barrier is reduced by a factor depending on the contact angle. U…

A new boundary-controlled phase transition: Phase separation in an Ising bi-pyramid with competing surface fields

2005

We study phase coexistence of an Ising ferromagnet in a bi-pyramid geometry with a square basal plane of linear extension 2L + 1. Antisymmetric surface fields act on the pyramid surfaces above and below the basal plane. In the limit L → ∞, the magnetisation stays zero at the bulk critical temperature, but becomes discontinuously non-zero at the cone filling critical temperature associated with a single pyramid. Monte Carlo simulations and scaling considerations show that this transition is described by a Landau theory with size-dependent coefficients that give rise to singular critical amplitudes.

Characteristic Length Scales and Radial Monomer Density Profiles of Molecular Bottle-Brushes: Simulation and Experiment

2010

Extensive Monte Carlo simulations are presented for bottle-brush polymers under good solvent conditions, using the bond fluctuation model on the simple cubic lattice. Varying the backbone length (from Nb = 67 to Nb = 259 effective monomers) as well as the side chain length (from N = 6 to N = 48), for a physically reasonable grafting density of one chain per backbone monomer, we find that the structure factor describing the total scattering from the bottle-brush provides an almost perfect match for some combinations of (Nb, N) to experimental data of Rathgeber et al. [J. Chem. Phys. 2005, 122, 124904], when we adjust the length scale of the simulation to reproduce the experimental gyration r…

Neutrons detect order in glasses

2005

The first glassy material was probably made in ancient Egypt some 4500 years ago, so the fact that the structure of glass is still one of the biggest puzzles in physics may come as a surprise. When a liquid is cooled very quickly, the atoms do not have time to arrange themselves into an ordered crystalline solid. Instead, the super cooled liquid falls out of equilibrium and into a disordered amorphous network, more commonly known as a glass.

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

2001

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 …

Surface-directed spinodal decomposition in a thin-film geometry: A computer simulation

1994

The phase separation kinetics of a two-dimensional binary mixture at critical composition confined between (one-dimensional) straight walls which preferentially attract one component of the mixture is studied for a wide range of distancesD between the walls. Following earlier related work on semiinfinite systems, two choices of surface forces at the walls are considered, one corresponding to an incompletely wet state of the walls, the other to a completely wet state (forD→∞). The nonlinear Cahn-Hilliard-type equation, supplemented with appropriate boundary conditions which account for the presence of surfaces, is replaced by a discrete equivalent and integrated numerically. Starting from a …

Conformational Properties of Polymer Mushrooms Under Spherical and Cylindrical Confinement

2010

A coarse grained model of a flexible macromolecule end-grafted on the inside of a sphere or a cylinder under good solvent conditions is studied by Monte Carlo simulations. For cylindrical confinement, two regimes are found: when the cylinder radius R exceeds the gyration radius R 90 of the polymer mushroom grafted to a planar surface, a simple scaling description holds. In the opposite case, a non-monotonic crossover to a cigar-like quasi-one-dimensional structure occurs, and the distribution P e (x) of the free chain end in the x-direction along the cylinder axis becomes bimodal. Spherical confinement, on the other hand, causes a crossover from dilute to semidilute behavior of the structur…

Determination of the origin and magnitude of logarithmic finite-size effects on interfacial tension: Role of interfacial fluctuations and domain brea…

2014

The ensemble-switch method for computing wall excess free energies of condensed matter is extended to estimate the interface free energies between coexisting phases very accurately. By this method, system geometries with linear dimensions $L$ parallel and $L_z$ perpendicular to the interface with various boundary conditions in the canonical or grandcanonical ensemble can be studied. Using two- and three-dimensional Ising models, the nature of the occurring logarithmic finite size corrections is studied. It is found crucial to include interfacial fluctuations due to "domain breathing".

An Ising ferromagnet with an antiferromagnetic surface layer: A simple model for magnetic surface reconstruction

1985

Simple cubic Ising lattices are studied by Monte Carlo simulation, using a thin film geometry (usually 40 atomic layers thick), with nearest neighbour ferromagnetic exchange J in the bulk and nearest neighbour antiferromagnetic interaction Js between surface spins. Applying a technique of preferential sampling in the surface layers, we investigate the ordering for a variety of values of JsJ and for various temperatures. For JsAF < Js < − 0.25J (where JsAF ≈ − 2.01J) ferromagnetic ordering occurs at a higher temperature than the antiferromagnetic surface ordering, while for − 0.25J < Js no antiferromagnetic long range order is possible. For Js < JsAF the surface transition occurs at a higher…

Monte Carlo simulation of the glass transition in polymeric systems: Recent developments

1995

Abstract The bond fluctuation model on square and s.c. lattices is used as a coarse-grained model for flexible polymers in dense melts. Using an energy that favours long bonds, a conflict is created between the tendency of the bonds to stretch at low temperatures and packing constraints. This simple concept of ‘geometric frustration’ leads to glass transition. Both static and dynamic properties of this model are investigated by Monte Carlo simulations, paying attention to effects found by varying the cooling rate and the chain length N of the polymers. In two and three spatial dimensions an effective (cooling-rate dependent) glass transition temperature T g can be defined, where the system …

Finite-size scaling analysis of the ?4 field theory on the square lattice

1986

Monte-Carlo calculations are performed for the model Hamiltonian ℋ = ∑i[(r/2)Φ 2(i)+(u/4)/gF4(i)]+∑ (C/2)[Φ (i)−Φ(j)]2 for various values of the parametersr, u, C in the crossover region from the Ising limit (r→-∞,u+∞) to the displacive limit (r=0). The variableφ(i) is a scalar continuous spin variable which can lie in the range-∞<φ(i)<+∞, for each lattice site (i).φ(i) is a priori selected proportional to the single-site probability in our Monte Carlo algorithm. The critical line is obtained in very good agreement with other previous approaches. A decrease of apparent critical exponents, deduced from a finite-size scaling analysis, is attributed to a crossover toward mean-field values at t…

Low-temperature anharmonic lattice deformations near rotator impurities: A quantum Monte Carlo approach.

1994

At zero temperature the equilibrium structures of a system consisting of a quantum rotator (${\mathrm{N}}_{2}$) embedded in a relaxing lattice (Ar) surrounding are studied with a variational approach. With symmetric wave functions (para-${\mathrm{N}}_{2}$), we obtain a cubic lattice deformation near the rotator, while with antisymmetric wave functions (ortho-${\mathrm{N}}_{2}$), we obtain a tetragonal lattice deformation forming a stable oriented ground state. At low temperatures, we investigate the properties of this system with a quantum Monte Carlo simulation. On top of the tetragonal deformation the width of the nearest-neighbor oscillations follows classical ``scaling'' laws according …

Perspective: The Asakura Oosawa model: A colloid prototype for bulk and interfacial phase behavior

2014

In many colloidal suspensions, the micrometer-sized particles behave like hard spheres, but when non-adsorbing polymers are added to the solution a depletion attraction (of entropic origin) is created. Since 60 years the Asakura-Oosawa model, which simply describes the polymers as ideal soft spheres, is an archetypical description for the statistical thermodynamics of such systems, accounting for many features of real colloid-polymer mixtures very well. While the fugacity of the polymers (which controls their concentration in the solution) plays a role like inverse temperature, the size ratio of polymer versus colloid radii acts as a control parameter to modify the phase diagram: when this …

A new insight into the isotropic–nematic phase transition in lyotropic solutions of semiflexible polymers: density-functional theory tested by molecu…

2016

Semiflexible polymers in solution are studied for a wide range of both contour length L and persistence length lp as a function of monomer concentration under good solvent conditions. Both density-functional theory (DFT) and molecular dynamics (MD) simulation methods are used, and a very good agreement between both techniques is observed for rather stiff polymers. Evidence for a new mechanism of order parameter fluctuations in the nematic phase is presented, namely collective deformations of bundles of wormlike chains twisted around each other, and the typical wavelengths and amplitudes of these modes are estimated. These long wavelength fluctuations cause a reduction of the order parameter…

Finite-Size Scaling Study of the Simple Cubic Three-State Potts Glass

1991

During the last few years the Potts glass model has attracted more and more attention. It is considered as a first step towards modelling the phase transition of structural and orientational glasses. A mean-field approach /1/ predicts a low temperature behavior completely different from what is known from Ising spin glasses /2/. But short range models differ markedly from mean-field-predictions. So it is natural to ask, how the short range Potts glass behaves. Especially the question of the lower critical dimension d l is important, below which a finite temperature transition ceases to occur. We tried to answer this by combining Monte-Carlo simulations with a finite-size scaling analysis. T…

Phase transitions of single polymer chains and of polymer solutions: insights from Monte Carlo simulations

2008

The statistical mechanics of flexible and semiflexible macromolecules is distinct from that of small molecule systems, since the thermodynamic limit can also be approached when the number of (effective) monomers of a single chain (realizable by a polymer solution in the dilute limit) is approaching infinity. One can introduce effective attractive interactions into a simulation model for a single chain such that a swollen coil contracts when the temperature is reduced, until excluded volume interactions are effectively canceled by attractive forces, and the chain conformation becomes almost Gaussian at the theta point. This state corresponds to a tricritical point, as the renormalization gro…

Pulling Single Adsorbed Bottle-Brush Polymers off a Flat Surface: A Monte Carlo Simulation

2013

Force versus extension behavior of flexible chains and semiflexible bottle-brush polymers adsorbed from a good solvent on a planar substrate is studied by Monte Carlo simulation of the bond fluctua...

Scattering function of semiflexible polymer chains under good solvent conditions

2012

Using the pruned-enriched Rosenbluth Monte Carlo algorithm, the scattering functions of semiflexible macromolecules in dilute solution under good solvent conditions are estimated both in $d=2$ and $d=3$ dimensions, considering also the effect of stretching forces. Using self-avoiding walks of up to $N = 25600$ steps on the square and simple cubic lattices, variable chain stiffness is modeled by introducing an energy penalty $\epsilon_b$ for chain bending; varying $q_b=\exp (- \epsilon_b/k_BT)$ from $q_b=1$ (completely flexible chains) to $q_b = 0.005$, the persistence length can be varied over two orders of magnitude. For unstretched semiflexible chains we test the applicability of the Krat…

Molecular Dynamics Simulations

2003

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 (NVE) ensemble (N= particle number, V = volume, E = energy) is discussed, as well as the realization of other ensembles (e.g. the NVT ensemble). For a typical application example, molten SiO2, the estimation of various transport coefficients (self-diffusion constants, viscosity, thermal conductivity) is d…

Structure and dynamics of grafted polymer layers: A Monte Carlo simulation

1991

The bond fluctuation model of polymer chains on lattices is used to study layers of polymers anchored with one end at a hard wall, assuming good solvent conditions and repulsive interactions between the monomers and the wall. Chain lengths from N=10 to N=80 and grafting densities σ from 0.025 to 0.20 are considered, both for the ‘‘quenched’’ case, where the anchor points are kept fixed at randomly chosen surface sites, and the ‘‘annealed’’ case, where lateral diffusion of the anchored ends at the wall is considered. Profiles of monomer density and free end density, chain linear dimensions parallel and perpendicular to the wall, as well as corresponding mean square displacements of inner and…

Shape of cross-over between mean-field and asymptotic critical behavior three-dimensional Ising lattice

1999

Abstract Recent numerical studies of the susceptibility of the three-dimensional Ising model with various interaction ranges have been analyzed with a cross-over model based on renormalization-group matching theory. It is shown that the model yields an accurate description of the cross-over function for the susceptibility.

Static and dynamical properties of a supercooled liquid confined in a pore

2000

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 p…

Phase separation versus wetting: A mean field theory for symmetrical polymer mixtures confined between selectively attractive walls

1996

Partially compatible symmetrical (N A # N B = N) binary mixtures of linear flexible polymers (A, B) are considered in the presence of two equivalent walls a distance D apart, assuming that both walls preferentially adsorb the same component. Using a Flory-Huggins type mean field approach analogous to previous work studying wetting phenomena in the semi-infinite version of this model, where D → ∞, it is shown that a single phase transition occurs in this thin film geometry, namely a phase separation between an A-rich and a B-rich phase (both phases include the bulk of the film). The coexistence curve is shifted to smaller values of the inverse Flory-Huggins parameter x -1 with decreasing D, …

Chain linear dimensions in the surface-enriched layer of polymer mixtures

1992

We calculate the mean-square end-to-end distances and mean-square gyration radii using the bond fluctuation model for a binary polymer blend in the presence of a wall by Monte Carlo simulation. In the bulk, the size of the minority, low-concentration polymer species is compressed compared to the majority one. In the vicinity of the wall, where the minority polymer concentration is enriched due to attraction from the wall, the dimensions of the two types of polymers are approximately equal and are essentially the same as in an athermal polymer melt. Thus, the geometric constraint is more important to the structure of the polymers than the polymer-polymer and polymer-wall interactions.

Nucleation phenomena in polymeric systems

1995

Materials formed from long flexible macromolecules differ from their small-molecule analogs, because corresponding collective length scales are distinctly larger and many dynamical phenomena are very much slower; in addition, the variation of chain length N yields a control parameter that leaves intermolecular forces invariant, but allows a stringent test of theories. These concepts are exemplified in a discussion of nucleation barriers for symmetrical polymer (A, B)-mixtures (chain lengths NA = NB = N) near the critical temperature Tc, and for symmetrical block copolymers near the (fluctuation-induced) first order transition between the disordered melt and the lamellar mesophase. While in …

Second inflection point of water surface tension in the deeply supercooled regime revealed by entropy anomaly and surface structure using molecular d…

2019

The surface tension of supercooled water is of fundamental importance in physical chemistry and materials and atmospheric sciences. Controversy, however, exists over its temperature dependence in the supercooled regime, especially on the existence of the second inflection point (SIP). Here, we use molecular dynamics simulations of the SPC/E water model to study the surface tension of water (sigma(w)) as a function of temperature down to 198.15 K, and find a minimum point of surface excess entropy per unit area around approximate to 240-250 K. Additional simulations with the TIP4P/2005 water model also show consistent results. Hence, we predict an SIP of sigma(w) roughly in this region, at t…

Capillary Waves in a Colloid-Polymer Interface

2004

The structure and the statistical fluctuations of interfaces between coexisting phases in the Asakura-Oosawa (AO) model for a colloid--polymer mixture are analyzed by extensive Monte Carlo simulations. We make use of a recently developed grand canonical cluster move with an additional constraint stabilizing the existence of two interfaces in the (rectangular) box that is simulated. Choosing very large systems, of size LxLxD with L=60 and D=120, measured in units of the colloid radius, the spectrum of capillary wave-type interfacial excitations is analyzed in detail. The local position of the interface is defined in terms of a (local) Gibbs surface concept. For small wavevectors capillary wa…

Monte Carlo Simulations in Polymer Science

2012

Monte Carlo methods are useful for computing the statistical properties of both single macromolecules of various chemical architectures and systems containing many polymers (solutions, melts, blends, etc.). Starting with simple models (lattice models such as the self-avoiding walk or the bond fluctuation model, as well as coarse-grained or chemically realistic models in the continuum) various algorithms exist to generate conformations typical for thermal equilibrium, but dynamic Monte Carlo methods can also model diffusion and relaxation processes (as described by the Rouse and the reptation models for polymer melt dynamics). Limitations of the method are explained, and also the measures to…

Specific Heat of Amorphous Silica within the Harmonic Approximation

1999

We investigate to what extent the specific heat of amorphous silica can be calculated within the harmonic approximation. For this we use molecular dynamics computer simulations to calculate, for a simple silica model (the BKS potential), the velocity autocorrelation function and hence an effective density of states g(ν). We find that the harmonic approximation is valid for temperatures below 300 K but starts to break down at higher temperatures. We show that, to obtain a reliable description of the low-frequency part of g(ν), i.e., where the boson peak is observed, it is essential to use large systems for the simulations and small cooling rates to quench the samples. We find that the calcul…

On the commensurate–incommensurate transition in adsorbed monolayers

1999

Abstract A Monte Carlo simulation method is used to study the commensurate–incommensurate phase transition in monolayers and the formation of bilayer films on the (100) face of an fcc crystal. The phase diagram for the system which forms the registered (1×1) and high density incommensurate phases in the monolayer has been determined. It is shown that the registered phase undergoes the transition to a denser incommensurate solid phase when the film density increases. The mechanism of melting of the monolayer film is found to depend on the film density. In particular, the melting of dense incommensurate solid monolayer film is found to be accompanied by the transfer of adsorbed molecules into…

Computer Simulations of the Dynamics of Amorphous Silica

1999

We present the results of a large scale computer simulation we performed to investigate the dynamical properties of supercooled silica. We show that parallel supercomputers such as the CRAY-T3E are very well suited to solve these type of problems. We find that at low temperatures the transport properties such as the diffusion constants and the viscosity agree well with the experimental data. At high temperatures this simulation predicts that in the transport quantities significant deviations from the Arrhenius law should be observed. Finally we show that such types of simulations can be used to investigate also complex dynamical quantities, such as the dynamical structure factor, and that t…

Phase separation of symmetrical polymer mixtures in thin-film geometry

1995

Monte Carlo simulations of the bond fluctuation model of symmetrical polymer blends confined between two “neutral” repulsive walls are presented for chain lengthNA=NB=32 and a wide range of film thicknessD (fromD=8 toD=48 in units of the lattice spacing). The critical temperaturesTc(D) of unmixing are located by finite-size scaling methods, and it is shown that\(T_c (\infty ) - T_c (D) \propto D^{ - {1 \mathord{\left/ {\vphantom {1 {v_3 }}} \right. \kern-\nulldelimiterspace} {v_3 }}} \), wherev3≈0.63 is the correlation length exponent of the three-dimensional Ising model universality class. Contrary to this result, it is argued that the critical behavior of the films is ruled by two-dimensi…

Phase Separation and Nematic Order in Lyotropic Solutions: Two Types of Polymers with Different Stiffnesses in a Common Solvent

2021

The interplay of the isotropic-nematic transition and phase separation in lyotropic solutions of two types of semiflexible macromolecules with pronounced difference in chain stiffness is studied by Density Functional Theory and Molecular Dynamics simulations. While the width of the isotropic-nematic two-phase coexistence region is narrow for solutions with a single type of semiflexible chain, the two-phase coexistence region widens for solutions containing two types of chains with rather disparate stiffness. In the nematic phase, both types of chains contribute to the nematic order, with intermediate values of the order parameter compared to the corresponding single component solutions. As …

Water adsorption on amorphous silica surfaces: A Car-Parrinello simulation study

2005

A combination of classical molecular dynamics (MD) and ab initio Car-Parrinello molecular dynamics (CPMD) simulations is used to investigate the adsorption of water on a free amorphous silica surface. From the classical MD SiO_2 configurations with a free surface are generated which are then used as starting configurations for the CPMD.We study the reaction of a water molecule with a two-membered ring at the temperature T=300K. We show that the result of this reaction is the formation of two silanol groups on the surface. The activation energy of the reaction is estimated and it is shown that the reaction is exothermic.

Monte Carlo simulation of crystalline polyethylene

1996

Abstract We consider here the problem of constructing an efficient algorithm for a classical Monte Carlo simulation of crystalline polyethylene with unconstrained bond lengths and angles. This macromolecular crystal presents a particular example of a system with many different energy scales, ranging from soft ones represented by nonbonded van der Waals interactions, to stiff ones, represented in particular by bond stretching. A proper sampling of all the energy scales poses a problem and it is shown that a standard Metropolis algorithm employing just local moves is not very efficient at low temperatures. As a solution it is proposed to employ also global moves consisting of displacements of…

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

1996

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.

Two-state protein-like folding of a homopolymer chain

2010

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 …

Statics and Dynamics of Bidisperse Polymer Melts:  A Monte Carlo Study of the Bond-Fluctuation Model

1998

As a first step toward the computer simulation of polydisperse polymeric melts, a lattice model containing two types of chains with lengths N1 = 20 − x and N2 = 20 + 4x (0 ≤ x ≤ 10 ) is studied. This variation of x, together with the fixed composition of 80% of short and 20% of long chains, leads to a polydispersity of 1 ≤ Nw/Nn ≤ 2 (Nw, Nn:  weight-, number-average chain lengths). To represent dense melts, the bond-fluctuation model at a volume fraction, φ = 1/2, of occupied lattice sites is used. The simulation treats both the athermal case (chain connectivity and excluded volume interaction only) and a thermal case, where additionally a choice for the bond length and bond angle potential…

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

2000

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 temper…

ChemInform Abstract: Specific Heat of Amorphous Silica within the Harmonic Approximation.

2010

We investigate to what extent the specific heat of amorphous silica can be calculated within the harmonic approximation. For this we use molecular dynamics computer simulations to calculate, for a simple silica model (the BKS potential), the velocity autocorrelation function and hence an effective density of states g(ν). We find that the harmonic approximation is valid for temperatures below 300 K but starts to break down at higher temperatures. We show that, to obtain a reliable description of the low-frequency part of g(ν), i.e., where the boson peak is observed, it is essential to use large systems for the simulations and small cooling rates to quench the samples. We find that the calcul…

Simulation of Dense Polymer Systems in Two and Three Dimensions

1991

Dense polymer systems are modeled by self- and mutually avoiding walks on lattices. Both simple models where the step length is one lattice spacing and more complicated models where the step length is distinctly longer and may fluctuate (“bond fluctuation model”) are discussed, and it is shown that the computer simulation of such models gives useful insight to understand the thermodynamic phase behavior and the relaxational dynamics of dense polymer solutions and polymer melts. The huge demands in computing power needed for a successful simulation of such systems can be covered by parallel computers such as the multitransputer facility of the University of Mainz.

3D Conformations of Thick Synthetic Polymer Chains Observed by Cryogenic Electron Microscopy.

2019

The backbone conformations of individual, unperturbed synthetic macromolecules have so far not been observed directly in spite of their fundamental importance to polymer physics. Here we report the dilute solution conformations of two types of linear dendronized polymers, obtained by cryogenic transmission electron stereography and tomography. The three-dimensional trajectories show that the wormlike chain model fails to adequately describe the scaling of these thick macromolecules already beyond a few nanometers in chain length, in spite of large apparent persistence lengths and long before a signature of self-avoidance appears. This insight is essential for understanding the limitations o…

Interfaces in polymer blends

2000

We investigate the structure and thermodynamics of interfaces in dense polymer blends using Monte Carlo (MC) simulations and self-consistent field (SCF) calculations. For structurally symmetric blends we find quantitative agreement between the MC simulations and the SCF calculations for excess quantities of the interface (e.g., interfacial tension or enrichment of copolymers at the interface). However, a quantitative comparison between profiles across the interface in the MC simulations and the SCF calculations has to take due account of capillary waves. While the profiles in the SCF calculations correspond to intrinsic profiles of a perfectly flat interface the local interfacial position f…

Three-step decay of time correlations at polymer-solid interfaces

2012

Two-step decay of relaxation functions, i.e., time scale separation between microscopic dynamics and structural relaxation, is the defining signature of the structural glass transition. We show that for glass-forming polymer melts at an attractive surface slow desorption kinetics introduces an additional time scale separation among the relaxational degrees of freedom leading to a three-step decay. The inherent length scale of this process is the radius of gyration in contrast to the segmental scale governing the glass transition. We show how the three-step decay can be observed in incoherent scattering experiments and discuss its relevance for the glass transition of confined polymers by an…

Phase transitions in a single polymer chain: A micro-canonical analysis of Wang–Landau simulations

2008

Abstract We present simulation results for the phase behavior of a single chain for a flexible lattice polymer model using the Wang–Landau sampling idea. Using the micro-canonical density of states obtained with this method we will discuss the ability of an analysis in the micro-canonical ensemble to locate the coil-globule (continuous) and liquid–solid (first-order) transitions found for this problem using a canonical analysis.

Continuous Phase Transitions at Surfaces of CuAu Alloy Models — A Monte Carlo Study of Surface Induced Order and Disorder

1996

The influence of surface on phase transitions has found significant attention in recent years, and a number of excellent reviews exists. [1, 2, 3] A variety of complex phenomena occur which are also related to the physics of adsorption and wetting. The scenario of wetting requires three distinct phases, for instance the vacuum, the bulk phase and a third phase intervening in between at equilibrium. In case of surface induced disorder (SID, a film of disordered layers at the surface “wets” the bulk phase as the temperature approaches the bulk transition temperature T c,b. The transition at the surface may be continuous (standard critical wetting phenomena), and, as theoretically investigated…

Smectic C and Nematic Phases in Strongly Adsorbed Layers of Semiflexible Polymers

2017

Molecular dynamics simulations of semiflexible polymers in a good solvent reveal a dense adsorbed layer when the solution is exposed to an attractive planar wall. This layer exhibits both a nematic and a smectic phase (smA for short and smC for longer chains) with bond vectors aligned strictly parallel to the wall. The tilt angle of the smC phase increases strongly with the contour length of the polymers. The isotropic-nematic transition is a Kosterlitz-Thouless transition and also the nematic-smectic transition is continuous. Our finding demonstrates thus a two-dimensional realization of different liquid crystalline phases, ubiquitous in three dimensions, that occurs in a single monomolecu…

How do droplets on a surface depend on the system size?

2002

Abstract We investigate the thermodynamics of inhomogeneous polymer melts in the framework of a coarse grained off-lattice model. Properties of the liquid–vapour interface and the packing of the melt in contact with an attractive wall are considered. We employ Monte Carlo simulations in the grand canonical ensemble to determine excess free energies, the wetting temperature and the pre-wetting line, as well as the pre-wetting critical point. Having determined the wetting properties and the phase diagram of the model polymer, we perform canonical Monte Carlo simulations of small droplets on a surface. This allows us to study the dependence of droplet size on the wetting properties. It is foun…

Surface-induced ordering and disordering in face-centered-cubic alloys: A Monte Carlo study

1996

Using extensive Monte Carlo simulations we have studied phase transitions in a fcc model with antiferromagnetic nearest-neighbor couplings $J$ in the presence of different free surfaces which lead either to surface-induced order or to surface-induced disorder. Our model is a prototype for CuAu-type ordering alloys and shows a strong first-order bulk transition at a temperature $\frac{k{T}_{\mathrm{cb}}}{|J|}=1.738005(50)$. For free (100) surfaces, we find a continuous surface transition at a temperature ${T}_{\mathrm{cs}}g{T}_{\mathrm{cb}}$ exhibiting critical exponents of the two-dimensional Ising model. Surface-induced ordering occurs as the temperature approaches ${T}_{\mathrm{cb}}$ and …

Gas transport through polymer membranes and free volume percolation

1998

We consider the influence of structural and dynamical properties of a polymer membrane on the gas transport through this matrix. The diffusant and the polymer only interact through repulsive interactions. In the case of a glassy polymer, when one can consider the matrix as frozen, the gas particle diffusion is determined by the free volume structure of the system. We show how the percolation properties of the free volume show up in a subdiffusive behavior of the diffusant. When one takes matrix mobility into account the ideal percolation transition vanishes but its trace can still be found in a subdiffusive regime in the gas particle mean square displacement. In the statically non-percolati…

Dynamics of a Spreading Nanodroplet: A Molecular Dynamic Simulation

2003

The spreading of polymer nanodroplets upon a sudden change from partial to complete wetting on an ideally flat and structureless solid substrate has been studied by molecular dynamic simulations using a coarse-grained bead-spring model of flexible macromolecules. Tanner's law for the growth of the lateral droplet radius {R(f) t 0.1 } is found to hold as long as the droplet does not disintegrate into individually moving chains. The data for the contact angle θ following from Tanner's law correspond to a dependence on time {θ(t) t -0.3 }. Our analysis of the mean square displacements of the polymer centers of mass reveals several dynamic regimes during the process of spreading. PACS numbers: …

Confinement-induced screening of hydrodynamic interactions and spinodal decomposition: Multiscale simulations of colloid-polymer mixtures

2012

Phase separation kinetics of a colloid-polymer mixture confined between two planar repulsive walls is studied by a multiscale simulation approach. Colloids and polymers are described by particles interacting with continuous potentials suitable for molecular-dynamics simulation, while hydrodynamic interactions mediated by solvent particles are accounted for by the multiparticle collision dynamics method. Varying the distance D between the walls and the character of the boundary conditions, the interplay of structure formation parallel and perpendicular to the walls is studied, and the effect of hydrodynamics on the growth of domain size ld(t) with time t is elucidated. Only for slip boundary…

From capillary condensation to interface localization transitions in colloid-polymer mixtures confined in thin-film geometry.

2008

Monte Carlo simulations of the Asakura-Oosawa (AO) model for colloid-polymer mixtures confined between two parallel repulsive structureless walls are presented and analyzed in the light of current theories on capillary condensation and interface localization transitions. Choosing a polymer to colloid size ratio of q=0.8 and studying ultrathin films in the range of D=3 to D=10 colloid diameters thickness, grand canonical Monte Carlo methods are used; phase transitions are analyzed via finite size scaling, as in previous work on bulk systems and under confinement between identical types of walls. Unlike the latter work, inequivalent walls are used here: while the left wall has a hard-core rep…

Finite-size tests of hyperscaling.

1985

The possible form of hyperscaling violations in finite-size scaling theory is discussed. The implications for recent tests in Monte Carlo simulations of the d = 3 Ising model are examined, and new results for the d = 5 Ising model are presented.

Simulation studies of gas-liquid transitions in two dimensions via a subsystem-block-density distribution analysis

1993

The finite-size scaling analysis of the density distribution function of subsystems of a system studied at constant total density is studied by a comparative investigation of two models: (i) the nearest-neighbor lattice gas model on the square lattice, choosing a total lattice size of 64×64 sites. (ii) The two-dimensional off-lattice Lennard-Jones system (truncated at a distance of 2.5 σ, σ being the range parameter of the interaction) withN=4096 particles, applying the NVT ensemble. In both models, the density distribution functionPL(ρ) is obtained forL×L subsystems for a wide range of temperaturesT, subblock linear dimensionsL and average densities . Particular attention is paid to the qu…

Monte Carlo Simulations of Body Centered Cubic Alloys

1994

We illustrate the use of Monte Carlo simulations in the study of order-disorder phenomena in metallic alloys by presenting detailed work on a fairly realistic lattice model for iron aluminum. The model has been constructed based on recent measurements of effective interaction parameters and includes a description of the magnetism of iron within a Heisenberg Hamiltonian. We show that it reproduces the bulk phase diagram in a qualitatively correct way. Then internal antiphase boundaries and free surfaces in the (100)-direction are studied. An interfacial roughening transition is predicted as well as critical broadening of the profiles as the bulk approaches a second order transition. Nonstoec…

Monte Carlo Study of a Lattice Gas Model with Nonadditive Lateral Interactions

1986

Interactions between polymer brush-coated spherical nanoparticles: the good solvent case.

2011

The interaction between two spherical polymer brushes is studied by molecular dynamics simulation varying both the radius of the spherical particles and their distance, as well as the grafting density and the chain length of the end-grafted flexible polymer chains. A coarse-grained bead-spring model is used to describe the macromolecules, and purely repulsive monomer-monomer interactions are taken throughout, restricting the study to the good solvent limit. Both the potential of mean force between the particles as a function of their distance is computed, for various choices of the parameters mentioned above, and the structural characteristics are discussed (density profiles, average end-to…

Model calculations of phase diagrams of magnetic alloys on the body-centered-cubic lattice.

1987

We treat a model for a binary (AB) alloy, where species A is magnetic (Ising spin σi = ± 1) while species B is not, and repulsive interactions are assumed between first and second neighbors of the same kind, in addition to a nearest-neighbor ferromagnetic exchange interaction. Both the mean-field approximation, the cluster variation (CV) method in the tetrahedron approximation and the Monte Carlo (MC) method are applied; comparing the phase diagrams obtained by the various approximations their accuracy is tested. It is shown that the CV method is in rather close agreement with the MC method for the present problem.

Curvature dependence of surface free energy of liquid drops and bubbles: A simulation study.

2010

We study the excess free energy due to phase coexistence of fluids by Monte Carlo simulations using successive umbrella sampling in finite LxLxL boxes with periodic boundary conditions. Both the vapor-liquid phase coexistence of a simple Lennard-Jones fluid and the coexistence between A-rich and B-rich phases of a symmetric binary (AB) Lennard-Jones mixture are studied, varying the density rho in the simple fluid or the relative concentration x_A of A in the binary mixture, respectively. The character of phase coexistence changes from a spherical droplet (or bubble) of the minority phase (near the coexistence curve) to a cylindrical droplet (or bubble) and finally (in the center of the misc…

The phase diagram of a single polymer chain: New insights from a new simulation method

2006

We present simulation results for the phase behavior of a single chain for a flexible lattice polymer model using the Wang-Landau sampling idea. Applying this new algorithm to the problem of the homopolymer collapse allows us to investigate not only the high temperature coil–globule transition but also an ensuing crystallization at lower temperature. Performing a finite size scaling analysis on the two transitions, we show that they coincide for our model in the thermodynamic limit corresponding to a direct collapse of the random coil into the crystal without intermediate coil–globule transition. As a consequence, also the many chain phase diagram of this model can be predicted to consist o…

Semiflexible Polymers in Spherical Confinement: Bipolar Orientational Order Versus Tennis Ball States

2017

Densely packed semiflexible polymers with contour length L confined in spheres with radius R of the same order as L cannot exhibit uniform nematic order. Depending on the chain stiffness (which we vary over a wide range), highly distorted structures form with topological defects on the sphere surface. These structures are completely different from previously observed ones of very long chains winding around the inner surface of spheres and from nematic droplets. At high densities, a thin shell of polymers close to the sphere surface exhibits a tennis ball texture due to the confinement-induced gradual bending of polymer bonds. In contrast, when the contour length of the chains is significant…

Polymer droplets on substrates with striped surface domains: molecular dynamics simulations of equilibrium structure and liquid bridge rupture

2005

The structure of a polymer nanodroplet adsorbed on a flat lyophobic substrate chemically decorated with a lyophilic stripe of width 2RD is studied by molecular dynamics simulation of a coarse-grained bead–spring model of short macromolecules (containing N = 20 effective monomers). Varying the stripe width, the strength of the monomer–wall attraction and the temperature, the equilibrium morphology of the resulting droplets is studied and discussed in terms of current phenomenological theories. In the second part, the behaviour of a liquid bridge connecting two such lyophilic stripes a distance L apart is analysed. It is shown that for large enough L such free-standing films are unstable and …

Estimation of Nucleation Barriers from Simulations of Crystal Nuclei Surrounded by Fluid in Equilibrium

2016

Nucleation rates for homogeneous nucleation are commonly estimated in terms of an Arrhenius law involving the nucleation barrier, written in terms of a competition of the contribution in surface free energy of the nucleus and the free energy gain proportional to the nucleus volume. For crystal nuclei this “classical nucleation theory” is hampered by the problem that the nucleus in general is non spherical, since the interfacial excess free energy depends on the orientation of the interface relative to the crystal axes. This problem can be avoided by analyzing the equilibrium of a crystal nucleus surrounded by fluid in a small simulation box in thermal equilibrium. Estimating the fluid press…

Phase Behavior and Microscopic Transport Processes in Binary Metallic Alloys: Computer Simulation Studies

2009

In a binary liquid mixture, different kinds of phase transitions can occur that are associated with various mass transport phenomena in the liquid. First, there is the possibility that the liquid undergoes a liquid-liquid demixing transition [1]. Near the critical point of this transition, a slowing down of dynamic properties is observed which is characterized, e.g., by a vanishing interdiffusion coefficient at the critical point [2, 3]. Another possible phase transition is a first-order transition of the liquid into a crystalline structure. In this case, crystal nucleation and growth are limited by the diffusive transport in the liquid [1, 4]. In a binary liquid, crystal nucleation process…

Monte Carlo Simulations of Semi-Flexible Polymers

2005

We present Monte Carlo simulations on the phase behavior of semiflexible macromolecules. For a single chain this question is of biophysical interest given the fact that long and stiff DNA chains are typically folded up into very tight compartments. So one can ask the question how the state diagram of a semiflexible chain differs from the coilglobule behavior of a flexible macromolecule. Another effect connected with rigidity of the chains is their tendency to aggregate and form nematically ordered structures. As a consequence one has two competing phase transitions: a gas-liquid and an isotropic-nematic transition potentially giving rise to a complicated phase diagram.

Surface-induced disorder in body-centered-cubic alloys

2000

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 o…

Structure of Polymer Brushes in Cylindrical Tubes: A Molecular Dynamics Simulation

2006

Molecular Dynamics simulations of a coarse-grained bead-spring model of flexible macromolecules tethered with one end to the surface of a cylindrical pore are presented. Chain length $N$ and grafting density $\sigma$ are varied over a wide range and the crossover from ``mushroom'' to ``brush'' behavior is studied for three pore diameters. The monomer density profile and the distribution of the free chain ends are computed and compared to the corresponding model of polymer brushes at flat substrates. It is found that there exists a regime of $N$ and $\sigma$ for large enough pore diameter where the brush height in the pore exceeds the brush height on the flat substrate, while for large enoug…

Glass physics: still not transparent

1999

Glass is a commonplace word. One immediately thinks of windows or bottles and of properties like brittleness or transparency. However, for a glass blower another feature is more important: glass does not melt abruptly, as a crystal does, but gradually over a range of temperatures. This means that he or she can alter the temperature at which glass solidifies or becomes a liquid by changing the rate at which it is cooled or heated. This is in stark contrast to the behaviour observed when the crystalline form of a material is heated: it will always melt at the same temperature.

Surface critical behaviour near the uniaxial Lifshitz point of the axial next-nearest-neighbour Ising model

1999

The semi-infinite axial next-nearest-neighbour Ising (ANNNI) model in the disordered phase is treated within a molecular-field approximation, and the singularities of various response functions characterizing the critical behaviour at the surface are obtained. In previous work (Binder K and Frisch H L 1999 Eur. Phys. J. B 10 71) the axis where a nearest-neighbour ferromagnetic (J 1 ) and next-nearest-neighbour antiferromagnetic (J 2 ) exchange compete was chosen perpendicular to the surface plane. In the present work we consider an orientation of this axis parallel to the surface, allowing also for different values of these exchange interactions (j 1 ,j 2 ) in the surface plane. We derive t…

The dielectric α -relaxation in polymer films: A comparison between experiments and atomistic simulations

2013

The question of whether the glass transition temperature in thin polymer films depends on the film thickness or not has given rise to heated debate for almost two decades now. One of the most puzzling findings is the seemingly universal thickness independence of the dielectric α-relaxation observed for supported films. It is puzzling not only in view of the fact that other techniques or other geometries sometimes showed a significant shift of as a function of film thickness, but more so, because computer simulations for all types of polymer film models revealed changes in the structure and dynamics close to a hard surface or a free surface. Our results suggest to explain this apparent contr…

Confined Crystals on Substrates: Order and Fluctuations in Between One and Two Dimensions

2010

The effect of lateral confinement on a crystal of point particles in d = 2 dimensions in a strip geometry is studied by Monte Carlo simulations and using phe- nomenological theoretical concepts. Physically, such systems confined in long strips of width D can be realized via colloidal particles at the air-water interface, or by adsorbed monolayers at suitably nanopatterned substrates, etc. As a generic model, we choose a repulsive interparticle potential decaying with the twelfth inverse power of distance. This system has been well studied in the bulk as a model for two- dimensional melting. The state of the system is found to depend very sensitively on the boundary conditions providing the …

Unexpectedly normal phase behavior of single homopolymer chains

2006

Employing Monte Carlo simulations, we show that the topology of the phase diagram of a single flexible homopolymer chain changes in dependence on the range of an attractive square well interaction between the monomers. For a range of attraction larger than a critical value, the equilibrium phase diagram of the single polymer chain and the corresponding polymer solution phase diagram exhibit vapor (swollen coil, dilute solution), liquid (collapsed globule, dense solution), and solid phases. Otherwise, the liquid-vapor transition vanishes from the equilibrium phase diagram for both the single chain and the polymer solution. This change in topology of the phase diagram resembles the behavior k…

Finite-size scaling in Ising-like systems with quenched random fields: Evidence of hyperscaling violation

2010

In systems belonging to the universality class of the random field Ising model, the standard hyperscaling relation between critical exponents does not hold, but is replaced by a modified hyperscaling relation. As a result, standard formulations of finite size scaling near critical points break down. In this work, the consequences of modified hyperscaling are analyzed in detail. The most striking outcome is that the free energy cost \Delta F of interface formation at the critical point is no longer a universal constant, but instead increases as a power law with system size, \Delta F proportional to $L^\theta$, with $\theta$ the violation of hyperscaling critical exponent, and L the linear ex…

Monte Carlo simulation of phase separation and clustering in the ABV model

1991

As a model for a binary alloy undergoing an unmixing phase transition, we consider a square lattice where each site can be either taken by an A atom, a B atom, or a vacancy (V), and there exists a repulsive interaction between AB nearest neighbor pairs. Starting from a random initial configuration, unmixing proceeds via random jumps of A atoms or B atoms to nearest neighbor vacant sites. In the absence of any interaction, these jumps occur at jump ratesΓ A andΓ B, respectively. For a small concentration of vacancies (c v=0.04) the dynamics of the structure factorS(k,t) and its first two momentsk 1(t),k 2 2 (t) is studied during the early stages of phase separation, for several choices of co…

Heterogeneous nucleation of a droplet pinned at a chemically inhomogeneous substrate: A simulation study of the two-dimensional Ising case

2018

Heterogeneous nucleation is studied by Monte Carlo simulations and phenomenological theory, using the two-dimensional lattice gas model with suitable boundary fields. A chemical inhomogeneity of length b at one boundary favors the liquid phase, while elsewhere the vapor is favored. Switching on the bulk field Hb favoring the liquid, nucleation and growth of the liquid phase starting from the region of the chemical inhomogeneity are analyzed. Three regimes occur: for small fields, Hb bcrit, the critical droplet radius is so large that a critical droplet having the contact angle θc required by Young's equation in the region of the chemical inhomogeneity does not yet "fit" there since the base…

Monte Carlo studies ofd= 2 Ising strips with long-range boundary fields

2000

A two-dimensional Ising model with nearest-neighbour ferromagnetic exchange confined in a strip of width L between two parallel boundaries is studied by Monte Carlo simulations. `Free' boundaries are considered with unchanged exchange interactions at the boundary but long-range boundary fields of the form H (n ) = ? h [n -3 - (L - n + 1) -3 ], where n = 1, 2, ... ,L labels the rows across the strip. In the case of competing fields and L , the system exhibits a critical wetting transition of a similar type as in the well studied case of short-range boundary fields. At finite L , this wetting transition is replaced by a (rounded) interface localization-delocalization transition at Tc (h , L )…

Monte carlo studies of phase transitions in polymer blends and block copolymer melts

1994

The unmixing transition of both symmetrical polymer blends AB (i.e. chain lengthsNA=NB=N) and asymmetrical ones (NB/NA=2,3) is studied by large-scale Monte Carlo simulations of the bond fluctuation model. Combination of semi-grand-canonical simulation techniques, «histogram reweighting» and finitesize scaling allows an accurate location of the coexistence curve in the critical region. The variation of the critical temperature with chain length (N) is studied and compared to theoretical predictions. For the symmetrical case, use of chain lengths up toN=512 allows a rough estimation of crossover scaling functions for the crossover from Ising to mean-field exponents. The order-disorder transit…

On the Ground State Structure of Adsorbed Monolayers: Can One Find them by Monte Carlo Simulation?

2002

While the classical ground state structure of an atomic monolayer adsorbed at a noncorrugated perfectly flat substrate trivially is a triangular lattice, the spacing being the minimum of the interatomic potential, nontrivial structures occur on corrugated substrates. This problem is exemplified for the (100) face of a face-centered cubic crystal, varying both the density of the adsorbed monolayer and the strength of the potential due to the surface. Increasing the density beyond that of the commensurate c(2 x 2) structure, incommensurate patterns become stable with “heavy” walls (HW) oriented along the face diagonals [including the “crossing heavy walls” (CRHW) phase]. It is shown that slow…

Simulation of vapor-liquid coexistence in finite volumes: a method to compute the surface free energy of droplets.

2009

When a fluid at a constant density $\ensuremath{\rho}$ in between the densities of coexisting vapor $({\ensuremath{\rho}}_{\text{v}})$ and liquid $({\ensuremath{\rho}}_{\ensuremath{\ell}})$ at temperatures below criticality is studied in a (cubic) box of finite linear dimension $L$, phase separation occurs in this finite volume, provided $L$ is large enough. For a range of densities, one can observe a liquid droplet (at density ${\ensuremath{\rho}}_{\ensuremath{\ell}}^{\ensuremath{'}}$ slightly exceeding ${\ensuremath{\rho}}_{\ensuremath{\ell}}$) coexisting in stable thermal equilibrium with surrounding vapor (with density ${\ensuremath{\rho}}_{\text{v}}^{\ensuremath{'}}g{\ensuremath{\rho}}…

Interface Localization-Delocalization in a Double Wedge: A New Universality Class with Strong Fluctuations and Anisotropic Scaling

2002

Using Monte Carlo simulations and finite-size scaling methods we study ``wetting'' in Ising systems in a $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}{L}_{y}$ pore with quadratic cross section. Antisymmetric surface fields ${H}_{s}$ act on the free $L\ifmmode\times\else\texttimes\fi{}{L}_{y}$ surfaces of the opposing wedges, and periodic boundary conditions are applied along the $y$ direction. In the limit $L\ensuremath{\rightarrow}\ensuremath{\infty}$, ${L}_{y}/{L}^{3}=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$, the system exhibits a new type of phase transition, which is the analog of the ``filling transition'' that occurs in a single wedge. It is charac…

Structure and dynamics of polymer brushes near the Θ point: A Monte Carlo simulation

1992

Grafted polymer layers under variable solvent conditions are studied by Monte Carlo simulations using the bond fluctuation model. Structural information such as monomer density profiles, brush thickness, mean‐square displacement of monomers, and positions of the monomers along the chain are obtained for temperatures above, at, and below the Θ point. In particular, the scaling of the brush thickness is formulated and verified by the simulation data. At the Θ point, more extensive simulations are performed to investigate the structural and dynamical properties. While the brush thickness at the Θ point agrees very well with the scaling and self‐consistent field predictions, the latter deviate …

Numerical investigations of complex nano-systems

2005

The nature of the melting transition for a system of hard disks with translational degrees of freedom in two spatial dimensions has been analysed by a combination of computer simulation methods and a finite size scaling technique. The behaviour of the system is consistent with the predictions of the Kosterlitz–Thouless–Halperin–Nelson–Young (KTHNY) theory. The structural and elastic properties of binary colloidal mixtures in two and three spatial dimensions are discussed as well as those of colloidal systems with quenched point impurities. Hard and soft disks in external periodic (light) fields show rich phase diagrams, including freezing and melting transitions when the density of the syst…

Conformational Changes of a Single Semiflexible Macromolecule Near an Adsorbing Surface: A Monte Carlo Simulation

2009

The properties of a single semiflexible chain tethered to a planar surface with a long-ranged attractive potential are studied by means of Monte Carlo simulations. We employ the bond fluctuation lattice model and the Wang-Landau sampling technique. We present the diagram of states for semiflexible chains consisting of N = 64 and 128 monomer units as a function of temperature T and strength of the adsorption potential, epsilon(w), and also compare this with the diagram of states for flexible chains of these two lengths. The diagram of states consists of the regions of a coil, liquid globule, solid isotropic globule, adsorbed coil, and quasi-two-dimensional solid globule with nematic bond ord…

Critical properties and finite-size effects of the five-dimensional Ising model

1985

Monte Carlo calculations of the thermodynamic properties (energy, specific heat, magnetization suceptibility, renormalized coupling) of the nearest-neighbour Ising ferromagnet on a five-dimensional hypercubic lattice are presented and analyzed. Lattices of linear dimensionsL=3, 4, 5, 6, 7 with periodic boundary conditions are studied, and a finite size scaling analysis is performed, further confirming the recent suggestion thatL does not scale with the correlation length ξ (the temperature variation of which near the critical temperatureT c is ξ∝|1-T/T c |−1/2), but rather with a “thermodynamic length”l (withl∝|1-T/T c |−2/d ,d=5 here). The susceptibility (extrapolated to the thermodynamic …

Interfaces between coexisting phases in polymer mixtures: What can we learn from Monte Carlo simulations?

1999

Symmetric binary polymer mixtures are studied by Monte Carlo simulation of the bond fluctuation model, considering both interfaces between coexisting bulk phases and interfaces confined in thin films. It is found that the critical behavior of interfacial tension and width is compatible with that of the Ising model, as expected from the universality principle. In the strong segregation limit, only qualitative but not quantitative agreement with the self-consistent field (SCF) theory is found. It is argued that the SCF theory requires √ 6 X √D for short-range forces, in agreement with experiment.

Monte Carlo simulation in polymer physics: Some recent developments

1991

The computer simulation of macromolecular materials has to deal with phenomena on length scales from 1A to 100A, as well as with time scales ranging over many orders of magnitude, and thus still presents a challenge. With suitably coarse-grained models which disregard detailed information on chemical structure nevertheless collective phenomena can be described, such as unmixing of polymer blends, mesophase ordering of block-copolymer melts, “blob formation” in semidilute solutions, etc. Simulations of such models provide a sensitive test of approximate theories and give valuable hints for experiments.

Competition between liquid-crystalline ordering and glassy freezing in melts of semiflexible polymers: A monte carlo simulation

1999

We present results of a Monte Carlo simulation of dense melts of semiflexible polymers using the bond-fluctuation model. The chosen Hamiltonian increases the chain stiffness upon cooling which in turn leads to glass-transition like freezing of the polymer mobility. Employing an efficient simulation algorithm, which is able to equilibrate the simulated systems to lower temperature than the Rouse-type algorithm showing the glassy freezing, we are able to observe an isotropic-nematic phase transition. This transition lies above the glass transition temperature one would extrapolate from the observed freezing behavior.

Polymer translocation through a nanopore induced by adsorption: Monte Carlo simulation of a coarse-grained model

2004

Dynamic Monte Carlo simulation of a bead-spring model of flexible macromolecules threading through a very narrow pore in a very thin rigid membrane are presented, assuming at the cis side of the membrane a purely repulsive monomer-wall interaction, while the trans side is attractive. Two choices of monomer-wall attraction epsilon are considered, one choice is slightly below and the other slightly above the "mushroom to pancake" adsorption threshold epsilon(c) for an infinitely long chain. Studying chain lengths N=32, 64, 128, and 256 and varying the number of monomers N(trans) (time t=0) that have already passed the pore when the simulation started, over a wide range, we find for epsiloneps…

Monte Carlo Methods: a powerful tool of statistical physics

1998

Statistical mechanics of condensed matter systems (solids, fluids) tries to express macroscopic equilibrium properties of matter as averages computed from a Hamiltonian that expresses interactions of an atomistic many body system. While analytic methods for most problems involve crude and uncontrolled approximations, the Monte Carlo computer simulation method allows a numerically exact treatment of this problem, apart from “statistical errors” which can be made as small as desired, and the systematic problem that a system of finite size is treated rather than the thermodynamic limit. However, the simulations of phase transitions then elucidate how a symmetry breaking arises via breaking of …

Computer Simulation Studies of Chain Dynamics in Polymer Brushes

2012

Center-of-mass and single monomer motion in grafted chains comprising a strongly stretched polymer brush in thermal equilibrium are studied by large scale molecular dynamics and Monte Carlo simulations of a coarse-grained model. Good solvent conditions are assumed. Our findings seriously question earlier theoretical predictions about the relaxation described by Rouse dynamics of brush coatings. Thus, the correlation functions of parallel and perpendicular components of the mean distance of the center-of-mass from the grafting site, the squared gyration radius and end-to-end distance, are found to deviate strongly from a simple exponential decay. While the relaxation times extracted from the…

Kinetics of domain growth in finite Ising strips

1992

Abstract Monte Carlo simulations are presented for the kinetics of ordering of the two-dimensional nearest-neighbor Ising models in an L x M geometry with two free boundaries of length M ⪢ L . This geometry models a “terrace” of width L on regularly stepped surfaces, adatoms adsorbed on neighboring terraces being assumed to be noninteracting. Starting out with an initially random configuration of the atoms in the lattice gas at coverage θ = 1 2 in the square lattice, quenching experiments to temperatures in the range 0.85⩽ T / T c ⩽1 are considered, assuming a dynamics of the Glauber model type (no conservation laws being operative). At T c the ordering behavior can be described in terms of…

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

2001

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 w…

Nanodroplets on a solid plane: wetting and spreading in a Monte Carlo simulation

2002

Abstract The wetting behavior and spreading dynamics of small polymer melt droplets in the course of transition from partial to complete wetting conditions on a flat structureless solid substrate have been studied by dynamic Monte Carlo simulation. From the density profiles of the drops we determine the contact angles at varying strength of the van der Waals surface forces in the whole interval of partial wetting. The validity of Young's equation is then tested whereby the surface tension of the melt/vapor interface is derived independently from interfacial fluctuation analysis, and the surface free energy of the melt at the substrate—from the anisotropy of the local pressure at the wall. T…

The Ising model as a playground for the study of wetting and interface behavior

2000

Computer simulations have played an important role in the elucidation of wetting and interface unbinding phenomena. In particular, use of the Ising-lattice-gas model in a film geometry and subject to diverse surface and bulk magnetic fields has permitted extensive Monte Carlo simulations to reveal new features of the phase diagrams associated with these phenomena and to provoke new theoretical studies. The status of our knowledge about the nature of wetting and interface-delocalization transitions which has resulted from these Ising model simulations will be summarized.

Molecular dynamics simulations of capillary rise experiments in nanotubes coated with polymer brushes.

2007

The capillary filling of a nanotube coated with a polymer brush is studied by molecular dynamics simulations of a coarse-grained model, assuming various conditions for the fluid-wall and fluid-brush interactions. Whereas the fluid is modeled by simple point particles interacting with Lennard-Jones forces, the (end-grafted, fully flexible) polymers that form the brush coating are described by a standard bead-spring model. Our experiments reveal that capillary filling is observed even for walls that would not be wetted by the fluid, provided the polymer brush coating itself wets. Generally, it is found that the capillary rise always proceeds through a t1/2 law with time t while the underlying…

Scaling concepts for polymer brushes and their test with computer simulation

2004

After a brief review of the scaling concepts for static and dynamic properties of polymer brushes in good solvents and Theta solvents, the Monte Carlo evidence is discussed. It is shown that under typical conditions the diameter of the last blob is of the order of 10-20% of the brush height, and therefore pronounced deviations from the self-consistent field predictions occur. In bad solvents, lateral microphase separation occurs leading to an irregular pattern of "dimples". Particularly interesting is the response of brushes to shear deformation, and the interaction between two interpenetrating brushes. Recent attempts to understand the resulting shear forces via molecular-dynamics simulati…

Critical behavior of active Brownian particles

2017

We study active Brownian particles as a paradigm for a genuine nonequilibrium phase transition requiring steady driving. Access to the critical point in computer simulations is obstructed by the fact that the density is conserved. We propose a method based on arguments from finite-size scaling to determine critical points and successfully test it for the two-dimensional (2D) Ising model. Using this method allows us to accurately determine the critical point of two-dimensional active Brownian particles at ${\mathrm{Pe}}_{\text{cr}}=40(2), {\ensuremath{\phi}}_{\text{cr}}=0.597(3)$. Based on this estimate, we study the corresponding critical exponents $\ensuremath{\beta}, \ensuremath{\gamma}/\…

Monte Carlo tests of theoretical predictions for critical phenomena: still a problem?

2000

Two Monte Carlo studies of critical behavior in ferromagnetic Ising models are described: the first one deals with the crossover from the Ising class to the mean field class, when the interaction range increases. The second study deals with the finite size behavior at dimensionalities above the marginal dimension where Landau theory applies. The numerical results are compared to pertinent theoretical predictions, and unsolved problems are briefly described.

Surface-directed spinodal decomposition: Phenomenology and numerical results.

1992

We present a phenomenological theory for surface effects on spinodal decomposition in mixtures and related phenomena such as the dynamics of surface segregation. Numerical solutions of our equations show striking similarity to recent results from experiments on polymer mixtures with one component preferentially attracted to a wall.

Anomalous diffusion: Summary

2007

Monte Carlo studies of finite-size effects at first-order transitions

1990

Abstract First-order phase transitions are ubiquitous in nature but their presence is often uncertain because of the effects which finite size has on all transitions. In this article we consider a general treatment of size effects on lattice systems with discrete degrees of freedom and which undergo a first-order transition in the thermodynamic limit. We review recent work involving studies of the distribution functions of the magnetization and energy at a first-order transition in a finite sample of size N connected to a bath of size N′. Two cases: N′ = ∞ and N′ = finite are considered. In the former (canonical ensemble) case, the distributions are approximated by a superposition of Gaussi…

On the first-order collapse transition of a three-dimensional, flexible homopolymer chain model

2005

We present simulation results for the phase behavior of flexible lattice polymer chains using the Wang-Landau sampling idea. These chains display a two-stage collapse through a coil-globule transition followed by a crystallization at lower temperatures. Performing a finite-size scaling analysis on the two transitions, we show that they coincide in the thermodynamic limit corresponding to a direct collapse of the random coil into the crystal without intermediate coil-globule transition.

Ordering of two-dimensional crystals confined in strips of finite width.

2007

Monte Carlo simulations are used to study the effect of confinement on a crystal of point particles interacting with an inverse power law potential $\ensuremath{\propto}{r}^{\ensuremath{-}12}$ in $d=2$ dimensions. This system can describe colloidal particles at the air-water interface, a model system for experimental study of two-dimensional melting. It is shown that the state of the system (a strip of width $D$) depends very sensitively on the precise boundary conditions at the two ``walls'' providing the confinement. If one uses a corrugated boundary commensurate with the order of the bulk triangular crystalline structure, both orientational order and positional order is enhanced, and suc…

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

2000

Elastic moduli and dislocation core energy of the triangular solid of hard disks of diameter $\sigma$ 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 $\rho \sigma^2 = 0.88$. 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 …

Spherical polymer brushes under good solvent conditions: molecular dynamics results compared to density functional theory.

2010

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 theoretic…

Structure and transport properties of amorphous aluminium silicates: computer simulation studies

2005

The structure and transport properties of SiO2-Al2O3 melts containing 13 mol% and 47 mol% Al2O3 are investigated by means of large scale molecular dynamics computer simulations. The interactions between the atoms are modelled by a pair potential which is a modified version of the one proposed by Kramer et al. [J. Am. Chem. Soc. 64, 6435 (1991)]. Fully equilibrated melts in the temperature range 6000 K &gt;= T &gt; 2000 K are considered as well as glass configurations, that were obtained by a rapid quench from the lowest melt temperatures. Each system is simulated at two different densities in order to study the effect of pressure on structural and dynamic properties. We find that the Al ato…

The relaxation dynamics of a simple glass former confined in a pore

2000

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 …

Finite-size scaling above the upper critical dimension revisited: The case of the five-dimensional Ising model

1999

Monte Carlo results for the moments of the magnetization distribution of the nearest-neighbor Ising ferromagnet in a L^d geometry, where L (4 \leq L \leq 22) is the linear dimension of a hypercubic lattice with periodic boundary conditions in d=5 dimensions, are analyzed in the critical region and compared to a recent theory of Chen and Dohm (CD) [X.S. Chen and V. Dohm, Int. J. Mod. Phys. C (1998)]. We show that this finite-size scaling theory (formulated in terms of two scaling variables) can account for the longstanding discrepancies between Monte Carlo results and the so-called ``lowest-mode'' theory, which uses a single scaling variable tL^{d/2} where t=T/T_c-1 is the temperature distan…

Estimation of the critical behavior in an active colloidal system with Vicsek-like interactions

2016

We study numerically the critical behavior of a modified, active Asakura-Oosawa model for colloid-polymer mixtures. The colloids are modeled as self-propelled particles with Vicsek-like interactions. This system undergoes phase separation between a colloid-rich and a polymer-rich phase, whereby the phase diagram depends on the strength of the Vicsek-like interactions. Employing a subsystem-block-density distribution analysis, we determine the critical point and make an attempt to estimate the critical exponents. In contrast to the passive model, we find that the critical point is not located on the rectilinear diameter. A first estimate of the critical exponents $\beta$ and $\nu$ is consist…

Simulation of Transport in Partially Miscible Binary Fluids: Combination of Semigrandcanonical Monte Carlo and Molecular Dynamics Methods

2004

Binary Fluids that exhibit a miscibility gap are ubiquitous in nature (glass melts, polymer solutions and blends, mixtures of molten metals, etc.) and exhibit a delicate interplay between static and dynamic properties. This is exemplified for a simple model system, the symmetrical AB Lennard-Jones mixture. It is shown how semigrandcanonical Monte Carlo methods, that include A→B (B→A) identity switches as Monte Carlo moves, can yield the phase diagram, the interfacial tension between coexisting phases, and various pair correlation functions and structure factors. In addition to the build-up of long-ranged concentration correlations near the critical point, unmixing is also accompanied by the…

Recent Developments in Monte Carlo Simulations of Lattice Models for Polymer Systems

2008

A brief review is given of methodological advances made during the past decade with the Monte Carlo sampling of equilibrium properties of simple lattice models of polymer systems, and representative applications of these new algorithms are summarized. These algorithms include Wang−Landau (WL) sampling, the pruned-enriched Rosenbluth method (PERM), and topology violating dynamic Monte Carlo algorithms such as combinations of local moves, slithering snake moves, and “double bridging” moves for the bond fluctuation model. The applications mentioned concern phase-transition-like phenomena of single chains (collapse and crystallization in bad solvents; interplay of collapse and adsorption; escap…

Stability of thin polymer films: influence of solvents.

2004

The interface and surface properties and the wetting behavior of polymer-solvent mixtures are investigated using Monte Carlo simulations and self-consistent field calculations. We carry out Monte Carlo simulations in the framework of a coarse-grained bead-spring model using short chains (oligomers) of N(P)=5 beads and a monomeric solvent, N(S)=1. The self-consistent field calculations are based on a simple phenomenological equation of state for compressible binary mixtures and we employ Gaussian chain model. The bulk behavior of the polymer-solvent mixture belongs to type III in the classification of van Konynenburg and Scott [Phil. Trans. R. Soc. London, Ser. A 298, 495 (1980)]. It is char…

Simulation of Order-Disorder Phenomena and Diffusion in Metallic Alloys

1991

The application of the Monte Carlo method to lattice-statistics problems in metallurgy is reviewed. Examples are given for the prediction of phase diagrams from simple model assumptions for effective interatomic potentials and for the calculation of parameters describing long- and short-range order, ordering energy, etc., both for face-centered cubic (fcc) and body-centered cubic (bcc) lattices. Applications to real systems such as Cu—Au and Fe—Al alloys are discussed.

Polymeric alloys: Model materials for the understanding of the statistical thermodynamics of mixtures

1997

Polymeric materials find industrial applications that are comparable to those of metals and ceramics.1 In addition to the great variability via the synthesis of various monomers and the choice of the degree of polymerization (N), alloying of polymers finds increasing attention for combining favorable materials properties.1,2 But polymeric (binary) alloys (A,B) of flexible polymers with chain lengths NA, NB are also most interesting for testing theoretical concepts: changing NA, NB one controls the entropy of mixing, keeping intermolecular forces invariant. Variation of these control parameters thus allows stringent tests of the theories on miscibility, unmixing etc. Furthermore, the large s…

Friction between Polymer Brushes in Good Solvent Conditions:  Steady-State Sliding versus Transient Behavior

2003

Previous molecular dynamics simulations of friction between polymer brushes in relative sliding motion [Kreer, T.; Muser, M. H.; Binder, K.; Klein, J. Langmuir 2001, 17, 7804] are extended beyond steady-state conditions. We study two different protocols:  (i) stop and return and (ii) stop and go. In protocol (i), the relative, lateral motion between the two surfaces is stopped abruptly and reimposed opposite to the initial direction after the system could relax for some time. Protocol (ii) is similar except that the sliding direction is maintained. In the constant-velocity steady state, the average lateral extension lc of the polymers is found to be a power law of the sliding velocity v, na…

Phase behaviour of heteronuclear dimers in three-dimensional systems—a Monte Carlo study

2008

Monte Carlo simulation in the grand canonical ensemble, the histogram reweighting technique and finite size scaling are used to study the phase behaviour of dimers in three-dimensional systems. A single molecule is composed of two segments A and B, and the bond between them cannot be broken. The phase diagrams have been estimated for a set of model systems. Different structures formed by heteronuclear dimers have been found. The results show a great variety of vapour–liquid coexistence behaviour depending on the strength of the interactions between segments.

Two-dimensional isotropic orientational glasses: a computer-simulation study

1989

The analogue of the Edwards-Anderson model for isotropic vector spin glasses, but taking three-component quadrupoles instead of spins at each lattice site, is studied on the square lattice with extensive Monte Carlo calculations, using a nearest-neighbor symmetric gaussian interaction. It is shown that at low temperaturesT the model develops a short range order both with respect to glass like correlations and with respect to “ferromagnetic” correlations among the quadrupoles. The associated correlation lengths and susceptibilities diverge asT→0, and the critical exponents for this zero-temperature phase transition are estimated. Dynamic correlation functions are analyzed as well and it is s…

Blends of Semiflexible Polymers: Interplay of Nematic Order and Phase Separation

2021

Mixtures of semiflexible polymers with a mismatch in either their persistence lengths or their contour lengths are studied by Density Functional Theory and Molecular Dynamics simulation. Considering lyotropic solutions under good solvent conditions, the mole fraction and pressure is systematically varied for several cases of bending stiffness κ (the normalized persistence length) and chain length N. For binary mixtures with different chain length (i.e., NA=16, NB=32 or 64) but the same stiffness, isotropic-nematic phase coexistence is studied. For mixtures with the same chain length (N=32) and large stiffness disparity (κB/κA=4.9 to 8), both isotropic-nematic and nematic-nematic unmixing oc…

Breakdown of the Kratky-Porod Wormlike Chain Model for Semiflexible Polymers in Two Dimensions

2011

By large-scale Monte Carlo simulations of semiflexible polymers in $d=2$ dimensions the applicability of the Kratky-Porod model is tested. This model is widely used as "standard model" for describing conformations and force versus extension curves of stiff polymers. It is shown that semiflexible polymers in $d=2$ show a crossover from hard rods to self-avoiding walks, the intermediate Gaussian regime (implied by the Kratky-Porod model) is completely absent. Hence the latter can also describe force versus extension curves only if the contour length is only a few times larger than the persistence length. Consequences for experiments on biopolymers at interfaces are briefly discussed.

The phase coexistence method to obtain surface free energies and nucleation barriers: a brief review

2018

A recently developed method where one analyses the finite size effects associated with liquid–solid phase equilibria including vapour–crystal coexistence is briefly reviewed. It is shown that the e...

Finite-size scaling for a first-order transition where a continuous symmetry is broken: The spin-flop transition in the three-dimensional XXZ Heisenb…

2019

Finite-size scaling for a first-order phase transition where a continuous symmetry is broken is developed using an approximation of Gaussian probability distributions with a phenomenological ``degeneracy'' factor included. Predictions are compared with data from Monte Carlo simulations of the three-dimensional, $XXZ$ Heisenberg antiferromagnet in a field in order to study the finite-size behavior on a $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L$ simple cubic lattice for the first-order ``spin-flop'' transition between the Ising-like antiferromagnetic state and the canted, $XY$-like state. Our theory predicts that for large linear dimension $L$ the field dependen…

A finite size scaling study of the five-dimensional Ising model

1994

For systems above the marginal dimension d*, where mean field theory starts to become valid, such as Ising models in d = 5 for which d* = 4, hyperscaling is invalid and hence it was suggested that finite size scaling is not ruled by the correlation length ξ (∝ |t| −1/2 in Landau theory, t being the distance from the critical point) but by a “thermodynamic length” l (∝ |t| −2/d). Early simulation work by Binder et al. using nearest neighbor hypercubic L5 lattices with L ⩽ 7 yielded some evidence for this prediction, but the renormalized coupling constant gL = −3 + 〈M4〉/〈M2〉2 at Tc was gL ≈ −1.0 instead of the prediction of Brezin and Zinn-Justin, gL(Tc) = −3 + Γ4(1/4)/(8 π2) ≈ −0.812. In the…

Capillary condensation in cylindrical pores: Monte Carlo study of the interplay of surface and finite size effects.

2010

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 …

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

2010

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 polymer's 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=sigma_p/\sigma=0.15 (with sigma_p and sigma the diameter of polymers and colloids, respectively). Inhomogeneous solid-liquid systems are prepared by placing the solid fc…

Capillary Rise in Nanopores: Molecular Dynamics Evidence for the Lucas-Washburn Equation

2007

When a capillary is inserted into a liquid, the liquid will rapidly flow into it. This phenomenon, well studied and understood on the macroscale, is investigated by Molecular Dynamics simulations for coarse-grained models of nanotubes. Both a simple Lennard-Jones fluid and a model for a polymer melt are considered. In both cases after a transient period (of a few nanoseconds) the meniscus rises according to a $\sqrt{\textrm{time}}$-law. For the polymer melt, however, we find that the capillary flow exhibits a slip length $\delta$, comparable in size with the nanotube radius $R$. We show that a consistent description of the imbibition process in nanotubes is only possible upon modification o…

Multiscale Computer Simulations in Physics, Chemistry, and Biology: The Example Of Silica

2002

We show to what extent molecular dynamics simulations (MD) can explore struc-tural and dynamic properties of atomic systems whereby the system under consideration is amorphous silica (SiO2). Two studies are presented: (i) a large scale simulation of the dynam-ics of a SiO2 melt and (ii) the investigation of free silica surfaces where a mixture of a classical MD and a Car-Parrinello molecular dynamics is used.

Universal critical behavior of curvature-dependent interfacial tension.

2011

From the analysis of Monte Carlo simulations of a binary Lennard-Jones mixture in the coexistence region, we provide evidence that the curvature dependence of the interfacial tension can be described by a simple theoretical function σ(R)ξ(2)=C(1)/[1+C(2)(ξ/R)(2)], where ξ is the correlation length and R is the droplet radius. The universal constants C(1) and C(2) are estimated. In the model, a Tolman length is strictly absent, but, since its critical behavior is believed to be much weaker than ξ, we argue that it only provides a correction to scaling and does not affect the leading critical behavior, which should be described by the above function for any system in the Ising universality cl…

Surface-directed phase separation with off-critical composition: Analytical and numerical results

2002

We study the interplay of wetting and phase separation in an unstable binary mixture $(\mathrm{AB})$ with off-critical composition, placed in contact with a surface which prefers the component $A.$ We consider surface potentials $V(z)\ensuremath{\sim}{z}^{\ensuremath{-}n},$ where z is the distance from the surface, and present analytical arguments and detailed numerical results to elucidate wetting-layer kinetics for arbitrary mixture compositions. If the preferred component is the minority phase, the wetting-layer thickness exhibits a potential-specific behavior at early times $\ensuremath{\tau},$ ${R}_{1}\ensuremath{\sim}{\ensuremath{\tau}}^{1/(n+2)},$ before crossing over to the universa…

Computer simulations of SiO2 and GeO2

2004

Classical Molecular Dynamics (MD) simulations are used to study structural and dynamic properties of amorphous germania (GeO2) in comparison to those of silica (SiO2). The total structure factor, as obtained from these simulations, is in very good agreement with that of neutron scattering experiments, both for germania and silica. The tetrahedral network structure in silica and germania leads to a prepeak in the structure factor that appears at slightly smaller wavenumbers in GeO2 than in SiO2. At high temperatures the diffusion constants are very similar in both systems whereas at low temperatures diffusion is significantly faster in germania than in silica. We also outline the strategy fo…

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

2002

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 evi…

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

2009

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 $\sigma$. 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 challen…

Brownian dynamics simulation of grafted polymer brushes

1995

We present results of computer simulations by the method of Brownian dynamics of polymeric brushes attached to impenetrable planes. For testing both model and method we have used one polymer brush attached to a repulsive plane and compare some results with Monte Carlo results of Lai and Binder on the bond fluctuation model. We have also studied two polymeric brushes attached to two parallel planes at different distances between planes, and investigate the interplay between the interpenetration of the brushes and the configurational properties of the grafted chains.

Phase Transitions of Polymer Blends and Block Copolymer Melts in Thin Films

1999

Static and dynamic glass transitions in the 10-state Potts glass: What can Monte Carlo simulations contribute?

2002

The p-state Potts glass with infinite range Gaussian interactions can be solved exactly in the thermodynamic limit and exhibits an unconventional phase behavior if p >4: A dynamical transition from ergodic to non-ergodic behavior at a temperature T D is followed by a first order transition at T 0 < T D, where a glass order parameter appears discontinuously, although the latent heat is zero. If one assumes that a similar scenario occurs for the structural glass transition as well (though with the singular behavior at T D rounded off), the p-state Potts glass should be a good test case to develop methods to deal with finite size effects for the static as well as the dynamic transition, and to…

Free-energy barriers for crystal nucleation from fluid phases.

2017

Monte Carlo simulations of crystal nuclei coexisting with the fluid phase in thermal equilibrium in finite volumes are presented and analyzed, for fluid densities from dense melts to the vapor. Generalizing the lever-rule for two-phase coexistence in the canonical ensemble to finite volume, "measurements" of the nucleus volume together with the pressure and chemical potential of the surrounding fluid allows to extract the surface free energy of the nucleus. Neither the knowledge of the (in general non-spherical) nucleus shape nor of the angle-dependent interface tension is required for this task. The feasibility of the approach is demonstrated for a variant of the Asakura-Oosawa model for c…

Cooperative motion and growing length scales in supercooled confined liquids

2002

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.

Simulation of Phase Transitions of Single Polymer Chains: Recent Advances

2006

The behaviour of a flexible polymer chain in solvents of variable quality in dilute solution is discussed both in the bulk and in the presence of an adsorbing wall. Monte Carlo simulations of coarse-grained bead-spring models and of the bond fluctuation model are presented and interpreted in terms of phenomenological theories and scaling concepts. Particular attention is paid to the behaviour of the polymer chain when the temperature of the polymer solution gets lower than the Theta temperature. It is argued that the adsorption transition line at the Theta temperature splits into lines of wetting and drying transitions of polymer globules attached to the wall. In addition, it is shown that …

Quantum effects on the herringbone ordering ofN2on graphite

1993

The effects of quantum fluctuations on the ``2-in'' herringbone ordering in a realistic model of 900 ${\mathrm{N}}_{2}$ molecules adsorbed in the (\ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 )R30\ifmmode^\circ\else\textdegree\fi{} structure on graphite are studied via path-integral Monte Carlo (PIMC) simulations. Quasiclassical and quasiharmonic calculations agree for high and low temperatures, respectively, but only PIMC gives satisfactory results over the entire temperature range. We can quantify the lowering of the transition temperature and the depression of the ground state order to 10% as compared to classical modeling.

Molecular-dynamics simulation of a glassy polymer melt: Incoherent scattering function

1999

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 si…

Structure of bottle brush polymers on surfaces: weak versus strong adsorption.

2011

Large-scale Monte Carlo simulations are presented for a coarse-grained model of cylindrical molecular brushes adsorbed on a flat structureless substrate, varying both the chain length N of the side chains and the backbone chain length N(b). For the case of good solvent conditions, both the cases of weak adsorption (only 10 to 15% of the monomers being bound to the surface) and strong adsorption (~40% of the monomers being bound to the surface, forcing the bottle brush into an almost 2D conformation) are studied. We focus on the scaling of the total linear dimensions of the cylindrical brush with both chain lengths N and N(b), demonstrating a crossover from rod-like behavior (for not very la…

Nonmonotonical crossover of the effective susceptibility exponent

1997

We have numerically determined the behavior of the magnetic susceptibility upon approach of the critical point in two-dimensional spin systems with an interaction range that was varied over nearly two orders of magnitude. The full crossover from classical to Ising-like critical behavior, spanning several decades in the reduced temperature, could be observed. Our results convincingly show that the effective susceptibility exponent gamma_eff changes nonmonotonically from its classical to its Ising value when approaching the critical point in the ordered phase. In the disordered phase the behavior is monotonic. Furthermore the hypothesis that the crossover function is universal is supported.

The high-temperature dynamics of a mean-field Potts glass

2002

Abstract We use Monte Carlo simulations to investigate the dynamic properties of the ten-state infinite-range 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 dynamic transition temperature. The autocorrelation function shows strong self-averaging at high temperatures, whereas close to the dynamic transition shows lack of self-averaging.

Computer Simulation of Molten and Glassy Silica and its Mixtures with Sodium Oxide and Aluminium Oxide

2007

Dynamics of wetting transitions: A time-dependent Ginzburg-Landau treatment

1987

The dynamic behavior at wetting transitions is studied for systems with short-range forces and nonconserved order parameter. From a continuum limit of a purely relaxational lattice model in mean-field approximation, a time-dependent Ginzburg-Landau equation with a time-dependent boundary condition at the surface is derived in the long wavelength approximation. The dynamics of relaxation close to stable and metastable states is treated in linear response. A divergence of the relaxation time occurs both for critical wetting and along the surface spinodal lines (in the case of first-order wetting), although the static surface layer susceptibilities χ1, χ11 stay finite at the surface spinodal i…

Capillary Rise in Nanotubes Coated with Polymer Brushes

2009

The spontaneous rise of a fluid in a brush-coated nanocapillary is studied by molecular dynamics simulation of a coarse-grained model. The cases of changing wettability of both the capillary walls and the brush were examined. We also investigated the impact of polymer chain length on the transport of fluid along the nanotube. We found that capillary filling takes place in both lyophilic and lyophobic tubes, provided that the polymer brush coating is wetted by the fluid. In all the cases studied, capillary rise proceeds by a time-square law, but the mechanisms behind them (Lucas-Washburn or diffusive propagation) differ, depending on the chain length N. For a wettable wall, the speed of flui…

Anomalous diffusion of polymers in supercooled melts near the glass transition

2007

Two coarse-grained models for polymer chains in dense melts near the glass transition are investigated: the bond fluctuation lattice model, where long bonds are energetically favored, is studied by dynamic Monte Carlo simulation, and an off-lattice bead-spring model with Lennard-Jones forces between the beads is treated by Molecular Dynamics. We compare the time-dependence of the mean square displacements of both models, and show that they become very similar on mesoscopic scales (i.e., displacements larger than a bond length). The slowing down of motions near the glass transition is discussed in terms of the mode coupling theory and other concepts.

Dynamics of Polymer Melts above the Glass Transition:  Monte Carlo Studies of the Bond Fluctuation Model

1997

The bond fluctuation model on the simple cubic lattice with a bond-length dependent potential energy favoring long bonds exhibits a glassy freezing in as the temperature is lowered, many properties being qualitatively similar to experiment. The present paper studies the dynamical properties of the model (as they result from the random hopping algorithm), using configurations of undercooled polymer melts that have been carefully equilibrated by the slithering snake algorithm. In this way quantitatively reliable data can be obtained for distinctly lower temperatures than in the previous work on the dynamics of this model that used the random hopping algorithm for equilibration as well. If var…

Temperature dependence of single chain properties in a binary polymer blend

1996

The temperature dependence of the correlation length of composition fluctuations and single chain statics and dynamics is studied in a symmetric, binary polymer blend. Our Monte Carlo simulation reveals a pronounced shrinking of the chain in the minority phase at low temperatures. However, only a weak temperature dependence of the single chain properties is found above criticality. Especially there is only a weak coupling between the correlation length of composition fluctuations and the relaxation of the internal chain structure. The coherent dynamic structure factor does not show any signs of a spatial restricted motion for our chain length N = 16, which is far below the entanglement leng…

Competition between submonolayer ordering and multilayer adsorption: Studies of simple lattice gas models

1986

Abstract We model condensation of adatoms at a substrate surface by a semi-infinite simple cubic lattice gas system. While in the bulk there is just a nearest-neighbour attractive interaction, in the first layer adjacent to the surface we allow for a periodic potential due to the substrate with a period of two lattice spacings, or for a next-nearest-neighbour repulsive interaction mediated by the substrate. Hence order-disorder phenomena may occur in the first layer, while only gas-liquid condensation transitions can occur in layers further away from the substrate surface. The ground-state phase diagrams of this model are obtained exactly, while the behaviour at nonzero temperatures is obta…

Macromol. Theory Simul. 7/2007

2007

Calculation of phase diagrams for models of metallic alloys

2007

We briefly review a longstanding problem of metallurgy and statistical physics, namely, the prediction of phase diagrams of binary alloys from simple model assumptions on the atomic interactions, such as Ising-type models. Various methods of statistical mechanics which have been applied to this problem are introduced and compared to each other, such as the cluster-variation method and Monte-Carlo simulation. The merits as well as the limitations of these methods are discussed, emphasizing examples of fcc and bcc lattices which are potentially relevant for the problem of short-range order and long-range order in metallic alloys such as Cu−Au, Ni−Cr, and Fe−Al.A brief comparison with correspo…

Computer simulations of a Lennard-Jones model for Ar1—x(N2)x: A prototype system for quadrupolar glasses

1998

Abstract Recent theoretical studies of orientational ordering in pure and diluted nitrogen crystals are summarized. While pure N2 has a first order phase transition from a plastic crystal to a phase with long-range orientational order, dilution with argon atoms leads to a quadrupolar glass phase. Monte Carlo simulations are used to study these phases, considering also the behavior of isolated N2 impurities in Ar crystals. It is shown that a simple model that neglects electrostatic interactions and takes only Lennard-Jones interactions into account can describe already many properties in qualitative agreement with experiment. Even the slow dynamics of the quadrupole moments can be modeled by…

Hard sphere fluids at a soft repulsive wall: A comparative study using Monte Carlo and density functional methods

2011

Hard-sphere fluids confined between parallel plates at 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) = 4ε[(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 t…

How Well Can Coarse-Grained Models of Real Polymers Describe Their Structure? The Case of Polybutadiene

2015

Coarse-graining of chemical structure of macromolecules in the melt is investigated using extensive molecular dynamics simulation data which are based on a united atom force-field model of polybutadiene. Systematically increasing the number, n, of the united atoms approximated by an effective coarse-grained monomer, we study the influence of degree of coarse-graining on the structure functions such as the segment-segment intermolecular and intramolecular correlation functions. These results are compared to Monte Carlo simulations of the corresponding coarse-grained bead-spring model and Chen-Kreglewski potential for chain molecules. In contrast to the atomistic chemically realistic model of…

Capillary Nematization of Semiflexible Polymers

2016

emiflexible polymers under good solvent conditions confined by two planar parallel repulsive walls are investigated for a wide range of monomer concentrations and distances between the walls, for a case where persistence length and contour length of the macromolecules are almost equal. Chain conformations and local nematic ordering near the walls are studied by both molecular dynamics methods and density functional theory, putting it in perspective with the recent work where the isotropic phase of semiflexible polymer solutions in the vicinity of a single repulsive wall in semi-infinite geometry is considered. Profiles of the total density of monomers as well as densities of end- and middle…

Understanding the glass transition and the amorphous state of matter: can computer simulation solve the challenge?

1999

The glass transition of supercooled fluids is one of the big puzzles of condensed matter physics, because there occurs a dramatic slowing down (the viscosity η can increase from about η = 1 Poise at the melting transition to η 10 13 Poise at the glass transition temperature T g ), but one hardly sees any accompanying change in the static structure. Theoretical concepts are very controversial - e.g., the Gibbs-di Marzio theory attributes glassy freezing to an underlying entropy catastrophe (the entropy of the supercooled fluid would fall below the crystal entropy at the Kauzmann temperature T 0 T g . Computer simulations offer the advantage that atomistically detailed information on structur…

Equation of State for Macromolecules of Variable Flexibility in Good Solvents: A Comparison of Techniques for Monte Carlo Simulations of Lattice Mode…

2007

The osmotic equation of state for the athermal bond fluctuation model on the simple cubic lattice is obtained from extensive Monte Carlo simulations. For short macromolecules (chain length N=20) we study the influence of various choices for the chain stiffness on the equation of state. Three techniques are applied and compared in order to critically assess their efficiency and accuracy: the repulsive wall method, the thermodynamic integration method (which rests on the feasibility of simulations in the grand canonical ensemble), and the recently advocated sedimentation equilibrium method, which records the density profile in an external (e.g. gravitation-like) field and infers, via a local …

Guide to Practical Work with the Monte Carlo Method

2002

The guide is structured such that we proceed from the “easy” simulation methods and algorithms to the more sophisticated. For each method the algorithms are presented by the technique of stepwise refinement. We first present the idea and the basic outline. From then on we proceed by breaking up the larger logical and algorithmic structures into smaller ones, until we have reached the level of single basic statements. Sometimes we may elect not to go to such a depth and the reader is asked to fill in the gaps.

Quantum Monte Carlo methods

2005

Introduction In most of the discussion presented so far in this book, the quantum character of atoms and electrons has been ignored. The Ising spin models have been an exception, but since the Ising Hamiltonian is diagonal (in the absence of a transverse magnetic field), all energy eigenvalues are known and the Monte Carlo sampling can be carried out just as in the case of classical statistical mechanics. Furthermore, the physical properties are in accord with the third law of thermodynamics for Ising-type Hamiltonians (e.g. entropy S and specific heat vanish for temperature T → 0, etc.) in contrast to the other truly classical models dealt with in previous chapters (e.g. classical Heisenbe…

Monte Carlo Calculations on Phase Transitions in Adsorbed Layers

2007

How to define variation of physical properties normal to an undulating one-dimensional object.

2009

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 b…

Spinodal decomposition in thin films: Molecular-dynamics simulations of a binary Lennard-Jones fluid mixture

2005

We use molecular dynamics (MD) to simulate an unstable homogeneous mixture of binary fluids (AB), confined in a slit pore of width $D$. The pore walls are assumed to be flat and structureless, and attract one component of the mixture (A) with the same strength. The pair-wise interactions between the particles is modeled by the Lennard-Jones potential, with symmetric parameters that lead to a miscibility gap in the bulk. In the thin-film geometry, an interesting interplay occurs between surface enrichment and phase separation. We study the evolution of a mixture with equal amounts of A and B, which is rendered unstable by a temperature quench. We find that A-rich surface enrichment layers fo…

How does the pattern of grafting points influence the structure of one-component and mixed polymer brushes?

2005

Using Monte Carlo simulations of a coarse-grained bead-spring model we study the lateral structure formation of one-component polymer brushes in a bad solvent and of a mixed polymer brush upon increasing the incompatibility of the two species. We compare the morphology of the brush with a regular distribution of grafting points and with a random arrangement. Density or composition fluctuations of the grafting points enhance the formation of irregular structures but randomness prevents the formation of long-range order. Even small fluctuations of the grafting points are sufficient to pin the lateral structures of the brush.

Corner wetting in the two-dimensional Ising model: Monte Carlo results

2003

Square L ? L (L = 24?128) Ising lattices with nearest neighbour ferromagnetic exchange are considered using free boundary conditions at which boundary magnetic fields ? h are applied, i.e., at the two boundary rows ending at the lower left corner a field +h acts, while at the two boundary rows ending at the upper right corner a field ?h acts. For temperatures T less than the critical temperature Tc of the bulk, this boundary condition leads to the formation of two domains with opposite orientations of the magnetization direction, separated by an interface which for T larger than the filling transition temperature Tf (h) runs from the upper left corner to the lower right corner, while for T …

Finite-size-scaling study of the simple cubic three-state Potts glass: Possible lower critical dimension d=3.

1990

For small lattices with linear dimension L ranging from L=3 to L=8 we obtain the distribution function P(q) of the overlap q between two real replicas of the three-state Potts-glass model with symmetric nearest-neighbor interaction with a Gaussian distribution. A finite-size-scaling analysis suggests a zero-temperature transition to occur with an exponentially diverging correlation length ${\ensuremath{\xi}}_{\mathrm{SG}}$\ensuremath{\sim}exp(C/${\mathit{T}}^{\mathrm{\ensuremath{\sigma}}}$). This implies that d=3 is the lower critical dimension.

Elastic constants from microscopic strain fluctuations

1999

Fluctuations of the instantaneous local Lagrangian strain $\epsilon_{ij}(\bf{r},t)$, 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 $$ 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 e…

Atomistic Simulation of Transport Phenomena in Simple and Complex Fluids and Fluid Mixtures

2003

Computer simulations of fluids in thermal equilibrium can yield information on transport coefficients such as self—diffusion and interdiffusion coefficients, viscosity, and thermal conductivity. While the estimation of self—diffusion coefficients from the mean square displacements of the respective particles is rather straightforward, the estimation of other transport coefficients is less straightforward, and can be based on either an analysis of time correlation functions of the appropriate collective variables, or on nonequilibrium techniques where the linear response to appropriate perturbations is measured.

Finite-size scaling approach for critical wetting: rationalization in terms of a bulk transition with an order parameter exponent equal to zero.

2012

Clarification of critical wetting with short-range forces by simulations has been hampered by the lack of accurate methods to locate where the transition occurs. We solve this problem by developing an anisotropic finite-size scaling approach and show that then the wetting transition is a ``bulk'' critical phenomenon with order parameter exponent equal to zero. For the Ising model in two dimensions, known exact results are straightforwardly reproduced. In three dimensions, it is shown that previous estimates for the location of the transition need revision, but the conclusions about a slow crossover away from mean-field behavior remain unaltered.

MONTE CARLO METHODS FOR FIRST ORDER PHASE TRANSITIONS: SOME RECENT PROGRESS

1992

This brief review discusses methods to locate and characterize first order phase transitions, paying particular attention to finite size effects. In the first part, the order parameter probability distribution and its fourth-order cumulant is discussed for thermally driven first-order transitions (the 3-state Potts model in d=3 dimensions is treated as an example). First-order transitions are characterized by a minimum of the cumulant, which gets very deep for large enough systems. In the second part, we discuss how to locate first order phase boundaries ending in a critical point in a large parameter space. As an example, the study of the unmixing transition of asymmetric polymer mixtures…

Double-well thermodynamic potentials and spinodal curves: how real are they?

2007

The concept of double-well thermodynamic potentials, ubiquitous since the van der Waals description of the vapour-to-liquid transition and the Landau theory of phase transitions, is critically re-examined. Particular emphasis is put on the extent to which spinodal curves (separating ‘metastable’ from ‘unstable’ states) are meaningful. It is argued that in full thermodynamic equilibrium spinodals are well-defined when one either considers finite subsystems of an infinitely large system, or systems with all linear dimensions finite. Evidence is given that in a finite (cubic) d-dimensional box the spinodals correspond (in a fluid) to the rounded ‘droplet evaporation’ or ‘bubble condensation’ t…

Critical phenomena in colloid-polymer mixtures: interfacial tension, order parameter, susceptibility, and coexistence diameter.

2004

The critical behavior of a model colloid-polymer mixture, the so-called AO model, is studied using computer simulations and finite size scaling techniques. Investigated are the interfacial tension, the order parameter, the susceptibility and the coexistence diameter. Our results clearly show that the interfacial tension vanishes at the critical point with exponent 2\nu ~ 1.26. This is in good agreement with the 3D Ising exponent. Also calculated are critical amplitude ratios, which are shown to be compatible with the corresponding 3D Ising values. We additionally identify a number of subtleties that are encountered when finite size scaling is applied to the AO model. In particular, we find …

Phase Transitions in Polymeric Systems

1995

The study of collective phenomena in polymeric systems is a particular challenge,because there occurs structure simultaneously on many length scales. Restricting attention to neutral flexible linear macromolecules, we disregard here interesting problems like polyelectrolytes, stiff chains or chains with stiff parts, branched chains and polymer networks, and all combinations thereof including e.g. liquid crystalline polymers, and treat only the simplest case. But already then there occurs structure from the scale of a covalent bond along the backbone of a chain (~ 1 A) over the scale of the persistence length (~ 10 A) to the coil gyration radius R g (~ 102 A), in the description of a single …

Statistical Mechanics of Polymers: New Developments - International Workshop

2007

Cylindrical confinement of solutions containing semiflexible macromolecules: surface-induced nematic order versus phase separation

2021

Solutions of semiflexible polymers confined in cylindrical pores with repulsive walls are studied by Molecular Dynamics simulations for a wide range of polymer concentrations. Both the case where both lengths are of the same order and the case when the persistence length by far exceeds the contour length are considered, and the enhancement of nematic order along the cylinder axis is characterized. With increasing density the character of the surface effect changes from depletion to the formation of a layered structure. For binary 50 : 50 mixtures of the two types of polymers an interplay between surface enrichment of the stiffer component and the isotropic-nematic transition is found, and a…

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

1998

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 e…

Enrichment of the chain ends in polymer melts at interfaces

1991

How Does the Relaxation of a Supercooled Liquid Depend on Its Microscopic Dynamics?

1998

Using molecular dynamics computer simulations we investigate how the relaxation dynamics of a simple supercooled liquid with Newtonian dynamics differs from the one with a stochastic dynamics. We find that, apart from the early beta-relaxation regime, the two dynamics give rise to the same relaxation behavior. The increase of the relaxation times of the system upon cooling, the details of the alpha-relaxation, as well as the wave vector dependence of the Edwards-Anderson-parameters are independent of the microscopic dynamics.

Theory of the evaporation/condensation transition of equilibrium droplets in finite volumes

2003

Abstract A phenomenological theory of phase coexistence of finite systems near the coexistence curve that occurs in the thermodynamic limit is formulated for the generic case of d-dimensional ferromagnetic Ising lattices of linear dimension L with magnetization m slightly less than mcoex. It is argued that in the limit L→∞ an unconventional first-order transition occurs at a characteristic value mt

Phase diagram of a model anticlustering binary mixture in two dimensions: A semi-grand-canonical Monte Carlo study

1994

The temperature-density phase diagram of a model binary mixture in two dimensions is investigated using a semi-grand-canonical Monte Carlo simulation scheme which allows for exchange between the two species while keeping the total number of atoms fixed. The gas-liquid and the gas-solid regions of the phase diagram are mapped out using the efficient block analysis method incorporating finite-size scaling of the various coexisting densities. An ordered square lattice structure is seen to be stable at low temperatures. Interesting short-range ordering phenomena resulting in a ``disorder line'' in the fluid phase are also analyzed and compared with results from liquid-state integral equation th…

Dynamics of multilayer adsorption: a Monte Carlo simulation

1992

Abstract The growth of an adsorbed film at an initially empty surface which is exposed at time t = 0 to a gas is studied within the framework of a kinetic lattice gas model by Monte Carlo simulation. The model includes an attractive potential V ( z ) between adsorbed particles at distance z from the surface, V(z) = −A z 3 and a nearest-neighbor attractive interaction between the gas atoms. Several choices of the surface potential depth A , corresponding to different sequence of layering transitions, are considered. The Monte Carlo process assumes random evaporation/condensation events of gas atoms in adsorbed layers close to the surface, while surface diffusion is disregarded. For temperatu…

Critical Dynamics in a Binary Fluid: Simulations and Finite-Size Scaling

2006

We report comprehensive simulations of the critical dynamics of a symmetric binary Lennard-Jones mixture near its consolute point. The self-diffusion coefficient exhibits no detectable anomaly. The data for the shear viscosity and the mutual-diffusion coefficient are fully consistent with the asymptotic power laws and amplitudes predicted by renormalization-group and mode-coupling theories {\it provided} finite-size effects and the background contribution to the relevant Onsager coefficient are suitably accounted for. This resolves a controversy raised by recent molecular simulations.

Effect of the solvent quality on the structural rearrangement of spherical brushes: coarse-grained models

2012

A coarse-grained model for flexible polymers end-grafted to repulsive spherical nanoparticles is studied for various polymer lengths, grafting densities, and nanoparticle sizes by molecular dynamics simulations, considering variable solvent quality in the framework of an implicit solvent treatment. Below the theta point, the tuning of the temperature strongly influences the coverage of the nanoparticle surface by collapsed single chains or clusters of several chains. The shape and size of the aggregates depend on the number of monomers and surface density of the polymers. Specifically we analyzed the effect of the solvent quality on the density profiles and radius of gyration of the single …

Computer simulations of undercooled fluids and the glass transition

2000

Abstract Two model studies are presented that attempt to describe the static and dynamic properties of glass-forming fluids via molecular dynamics simulations: The first model is an atomistically realistic model of SiO 2 , the second model provides a coarse-grained description of polymer liquids, i.e., typical `fragile' glassformers, while SiO 2 is the prototype of a `strong glassformer'. For both models, attention is given to the questions as to which range of temperatures are properties in equilibrium, and whether such simulations can help to interpret experiments and/or check theoretical predictions. While in the simulation of SiO 2 using the potential of van Beest, Kramer and van Santen…

Molecular Simulation of Polymer Melts and Blends: Methods, Phase Behavior, Interfaces, and Surfaces

2016

Kinetics of phase separation in thin films: simulations for the diffusive case.

2005

We study the diffusion-driven kinetics of phase separation of a symmetric binary mixture (AB), confined in a thin-film geometry between two parallel walls. We consider cases where (a) both walls preferentially attract the same component (A), and (b) one wall attracts A and the other wall attracts B (with the same strength). We focus on the interplay of phase separation and wetting at the walls, which is referred to as {\it surface-directed spinodal decomposition} (SDSD). The formation of SDSD waves at the two surfaces, with wave-vectors oriented perpendicular to them, often results in a metastable layered state (also referred to as ``stratified morphology''). This state is reminiscent of th…

Computer Simulations of Undercooled Fluids and Glasses

2007

An introduction to the Molecular Dynamics (MD) simulation of chemically realistic models for undercooled fluids and glasses is given, emphasizing silicatic materials such as molten silicon dioxide and its mixtures with sodium oxide and aluminium oxide, and comparing the simulation results to experimental data whenever possible.

Polymer solutions confined in slit-like pores with attractive walls: An off-lattice Monte Carlo study of static properties and chain dynamics

1996

Using a bead spring model of flexible polymer chains, the density profiles and chain configurational properties of polymer solutions confined between parallel plates were studied. A wide range of density ϕ, chain length N, and strength e of a short-range attractive wall potential was investigated. Both a temperature T in the good solvent regime (T > θ, θ being the Theta temperature where a chain in unconfined bulk three-dimensional solution would behave ideally) and a temperature in the bad solvent regime (T θ) show a crossover from two-dimensional excluded volume behavior (Rg ∝ N2ν with ν = 3/4) to ideal random walk behavior (ν = 1/2), the relaxation times show effective exponents Zeff (τ …

Calculation of local pressure tensors in systems with many-body interactions

2005

Local pressures are important in the calculation of interface tensions and in analyzing micromechanical behavior. The calculation of local pressures in computer simulations has been limited to systems with pairwise interactions between the particles, which is not sufficient for chemically detailed systems with many-body potentials such as angles and torsions. We introduce a method to calculate local pressures in systems with n-body interactions (n=2,3,4,) based on a micromechanical definition of the pressure tensor. The local pressure consists of a kinetic contribution from the linear momentum of the particles and an internal contribution from dissected many-body interactions by infinitesim…

Reduction of the glass transition temperature in polymer films: A molecular-dynamics study

2001

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 $U_{\rm wall}\myeq (\sigma/z)^9$, where $z \myeq |z_{\rm particle}-z_{\rm wall}|$ and $\sigma$ 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…

Effects of inhomogeneities of cross-links on a microphase separation of polymer mixtures

1994

We generalize de Gennes' theory of the microphase separation of cross-linked polymer mixtures to take into account the spatial fluctuations of the elasticity constant c, preventing the mixture from complete segregation. Within a mean-field analysis we found that the spatial fluctuations of c(r), which are assumed to obey the Poisson distribution, enlarge the size of the domains. The latter is obtained to be temperature dependent.


Computer simulation of bottle-brush polymers with flexible backbone: good solvent versus theta solvent conditions.

2011

By Molecular Dynamics simulation of a coarse-grained bead-spring type model for a cylindrical molecular brush with a backbone chain of $N_b$ effective monomers to which with grafting density $\sigma$ side chains with $N$ effective monomers are tethered, several characteristic length scales are studied for variable solvent quality. Side chain lengths are in the range $5 \le N \le 40$, backbone chain lengths are in the range $50 \le N_b \le 200$, and we perform a comparison to results for the bond fluctuation model on the simple cubic lattice (for which much longer chains are accessible, $N_b \le 1027$, and which corresponds to an athermal, very good, solvent). We obtain linear dimensions of …

Monte Carlo simulations of phase transitions of systems in nanoscopic confinement

2007

Abstract When simple or complex fluids are confined to ultrathin films or channels or other cavities of nanoscopic linear dimensions, the interplay of finite size and surface controls the phase behavior, and may lead to phase transitions rather different from the corresponding phenomena in the bulk. Monte Carlo simulation is a very suitable tool to clarify the complex behavior of such systems, since the boundary conditions providing the confinement can be controlled and arbitrarily varied, and detailed structural information on the inhomogeneous states of the considered systems is available. Examples used to illustrate these concepts include simple Ising models in pores and double-pyramid-s…

Monte Carlo methods for polymer chains in two - dimensional geometries (polymers at surfaces and interfaces)

1993

Coarse-grained models of polymers at interfaces can be defined such that their treatment by Monte Carlo simulation is most convenient and efficient for the problem at hand. This simulation strategy is briefly illustrated with three examples: (1) The orientational ordering of rigid rod-like polymers grafted to a surface, where “table methods” can be used, applying a fine discretization of the angles describing rod orientation. (2) Surface enrichment of one species in a polymer blend is treated by a semi-grand-canonical technique. (3) The number of configurations and structure of a star polymer attached with its center to a wall is studied by a “growth technique” generalizing simple sampling …

High-temperature series analysis of the p-state Potts glass model on d-dimensional hypercubic lattices

1999

We analyze recently extended high-temperature series expansions for the “Edwards-Anderson” spin-glass susceptibility of the p-state Potts glass model on d-dimensional hypercubic lattices for the case of a symmetric bimodal distribution of ferro- and antiferromagnetic nearest-neighbor couplings \(\). In these star-graph expansions up to order 22 in the inverse temperature \(\), the number of Potts states p and the dimension d are kept as free parameters which can take any value. By applying several series analysis techniques to the new series expansions, this enabled us to determine the critical coupling Kc and the critical exponent \(\) of the spin-glass susceptibility in a large region of …

Monte Carlo simulation studies of the interfaces between polymeric and other solids as models for fiber-matrix interactions in advanced composite mat…

1996

As a coarse-grained model for dense amorphous polymer systems interacting with solid walls (i.e., the fiber surface in a composite), the bond fluctuation model of flexible polymer chains confined between two repulsive surfaces is studied by extensive Monte Carlo simulations. Choosing a potential for the length of an effective bond that favors rather long bonds, the full temperature region from ordinary polymer melts down to the glass transition is accessible. It is shown that in the supercooled state near the glass transition an “interphase” forms near the walls, where the structure of the melt is influenced by the surface. This “interphase” already shows up in static properties, but also h…

Calculation of local pressure tensors in systems with many-body interactions

2003

Local pressures are important in the calculation of interface tensions and in analyzing micromechanical behavior. The calculation of local pressures in computer simulations has been limited to systems with pairwise interactions between the particles, which is not sufficient for chemically detailed systems with many-body potentials such as angles and torsions. We introduce a method to calculate local pressures in systems with n-body interactions (n=2,3,4, . . .) based on a micromechanical definition of the pressure tensor. The local pressure consists of a kinetic contribution from the linear momentum of the particles and an internal contribution from dissected many-body interactions by infin…

Scattering function and the dynamics of phase separation in polymer mixtures under shear flow

1988

The phenomenological mean-field theory describing concentration fluctuations and spinodal decomposition of binary mixtures of long flexible macromolecules is generalized to mixtures under steady shear flow. This shear flow leads to a partial orientation and stretching of the coils, as well as to an anisotropic deformation of concentration fluctuations. Generalizing the approach of Onuki and Kawasaki, we obtain the collective scattering function describing these concentration fluctuations in the mixture under shear flow. Both the steady-state situation in the one-phase region and the initial stages of spinodal decomposition for concentrations inside of the spinodal curve are considered.

Intra- and Interchain Correlations in Semidilute Polymer Solutions:  Monte Carlo Simulations and Renormalization Group Results

2000

We investigate the intra- and intermolecular correlations in semidilute polymer solutions by large-scale computer simulations and renormalization group calculations. In the framework of the bond fluctuation model we study polymers with chain lengths up to N = 2048 monomers and determine the intermolecular pair correlation function, the coherent scattering intensity, and its distinct part at all length scales. The simulations are compared quantitatively to renormalization group calculations of the universal crossover scaling function. Special attention is paid to length scales smaller than the density screening length ξ, where the distinct part of the scattering function in the simulations i…

One- and two-component bottle-brush polymers: simulations compared to theoretical predictions

2007

Scaling predictions and results from self-consistent field calculations for bottle-brush polymers with a rigid backbone and flexible side chains under good solvent conditions are summarized and their validity and applicability is assessed by a comparison with Monte Carlo simulations of a simple lattice model. It is shown that under typical conditions, as they are also present in experiments, only a rather weak stretching of the side chains is realized, and then the scaling predictions based on the extension of the Daoud-Cotton blob picture are not applicable. Also two-component bottle brush polymers are considered, where two types (A,B) of side chains are grafted, assuming that monomers of …

GLASS TRANSITION IN THIN POLYMER FILMS: A MOLECULAR DYNAMICS STUDY

2002

A melt of nonentangled polymer chains confined between two smooth and purely repulsive walls is studied for various film thicknesses D and temperatures. The dynamics of the supercooled films is qualitatively identical to that of the bulk, but the walls lead to faster relaxation. To quantify this observation we analyze the data by the mode-coupling theory (MCT) of the glass transition. We find that the critical temperature of MCT, Tc(D), decreases with D and that T - Tc(D) is a relevant temperature scale. The static structure factor and dynamic correlation functions at intermediate times coincide with bulk behavior when compared to the same T - Tc(D).

Selfdiffusion of polymer chains in solutions and melts

2005

Anomalous diffusion of monomers of polymer chains, as well as motion of these chains as a whole, is discussed with an emphasis on Monte Carlo simulations and simple scaling concepts. While the behavior of isolated chains in good solvents or Theta-solvents without excluded volume interactions is fully accounted for by the Rouse model, the behavior is less clear both for isolated chains in bad solvents and for chains in dense melts. Collapsed chains are shown to diffuse as g3(t) = <([rCM (t) -rCM(0)]2〉 ∝ tξ3 where the (effective?) exponent ξ3 simply seems to be linearly temperature-dependent for temperatures T lower than the Σ-temperature, ξ3 T/Θ. A relaxation time τ oc N3 is found, and scali…

Anomalous Diffusion and Relaxation of Collapsed Polymer Chains

1994

Time-dependent displacement of monomers and the centre-of-gravity motion of a polymer chain at various temperatures below the theta-temperature are studied by Monte Carlo simulation of an off-lattice model. While inner monomers diffuse Rouse-like, [ri(t) − ri(0)]2  t1/2, the centre of mass exhibits pronounced anomalous diffusion, [rc.m.(t) − rc.m.(0)]2  ta, where the exponent a seems to depend on temperature. The resulting anomalous dependence of the relaxation times on chain length is discussed in terms of scaling ideas. A possible relation to a glasslike freezing in of the collapsed globules is pointed out.

The droplet evaporation/condensation transition in a finite volume

2003

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-&gt;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+…

Phase diagram of polymer blends in confined geometry

2001

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 smei-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 surfaces 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 exh…

Mechanical desorption of a single chain: unusual aspects of phase coexistence at a first-order transition.

2012

The phase transition occurring when a single polymer chain adsorbed at a planar solid surface is mechanically desorbed is analyzed in two statistical ensembles. In the force ensemble, a constant force applied to the nongrafted end of the chain (that is grafted at its other end) is used as a given external control variable. In the $z$-ensemble, the displacement $z$ of this nongrafted end from the surface is taken as the externally controlled variable. Basic thermodynamic parameters, such as the adsorption energy, exhibit a very different behavior as a function of these control parameters. In the thermodynamic limit of infinite chain length the desorption transition with the force as a contro…

Monte Carlo Simulation of a Homopolymer−Copolymer Mixture Interacting with a Surface: Bulk versus Surface Micelles and Brush Formation

2008

Using Monte Carlo simulations of the bond fluctuation model, we study the formation of micelles in a confined mixture of asymmetric AB-diblock copolymers and homopolymers. The composition of the sphere-forming AB-diblock copolymers is fA = 1/8. The mixture is confined into a thin film. The film surfaces attract the minority component of the diblock with strength, eW. To efficiently sample the micelle size distribution and establish equilibrium between the surface and the bulk, we work in the semigrandcanonical ensemble, i.e. at fixed density and fixed chemical potential difference between the two types of chains, choosing a large incompatibility χN ≃ 100 (strong segregation regime). The com…

Spherically averaged versus angle-dependent interactions in quadrupolar fluids

2008

Employing simplified models in computer simulation is on the one hand often enforced by computer time limitations but on the other hand it offers insights into the molecular properties determining a given physical phenomenon. We employ this strategy to the determination of the phase behaviour of quadrupolar fluids, where we study the influence of omitting angular degrees of freedom of molecules via an effective spherically symmetric potential obtained from a perturbative expansion. Comparing the liquid-vapor coexistence curve, vapor pressure at coexistence, interfacial tension between the coexisting phases, etc., as obtained from both the models with the full quadrupolar interactions and th…

Polymer brushes on flat and curved surfaces: How computer simulations can help to test theories and to interpret experiments

2012

Theoretical descriptions of static properties of polymer brushes are reviewed, with an emphasis on monodisperse macromolecules grafted to planar, cylindrical, or spherical substrates. Blob concepts and resulting scaling relations are outlined, and various versions of the self-consistent field theory are summarized: the classical approximation and the strong stretching limit, as well as the lattice formulation. The physical justification of various inherent assumptions is discussed, and computer simulation results addressing the test of the validity of these approximations are reviewed. Also, alternative theories, such as the single chain mean field theory and the density functional theory, …

Interplay of order-disorder phenomena and diffusion in rigid binary alloys in the presence of vacancies: Monte Carlo simulations

2006

Transport phenomena are studied for a binary $(AB)$ alloy on a rigid square lattice with nearest-neighbor attraction between unlike particles, assuming a small concentration ${c}_{v}$ of vacancies $V$ being present, to which $A$ $(B)$ particles can jump with rates ${\ensuremath{\Gamma}}_{A}$ $({\ensuremath{\Gamma}}_{B})$ in the case where the nearest-neighbor attractive energy ${ϵ}_{AB}$ is negligible in comparison with the thermal energy ${k}_{B}T$ in the system. This model exhibits a continuous order-disorder transition for concentrations ${c}_{A},{c}_{B}=1\ensuremath{-}{c}_{A}\ensuremath{-}{c}_{V}$ in the range ${c}_{A,1}^{\mathit{crit}}\ensuremath{\leqslant}{c}_{A}\ensuremath{\leqslant}…

Activity mediated phase separation: Can we understand phase behavior of the nonequilibrium problem from an equilibrium approach?

2016

We present results for structure and dynamics of mixtures of active and passive particles, from molecular dynamics (MD) simulations and integral equation theory (IET) calculations, for a physically motivated model. The perfectly passive limit of the model corresponds to the phase-separating Asakura-Oosawa model for colloid-polymer mixtures in which, for the present study, the colloids are made self-propelling by introducing activity in accordance with the well known Vicsek model. Such activity facilitates phase separation further, as confirmed by our MD simulations and IET calculations. Depending upon the composition of active and passive particles, the diffusive motion of the active specie…

Monte Carlo study of surface phase transitions in the three-dimensional Ising model.

1990

We present the results of extensive Monte Carlo simulations of phase transitions and critical behavior at the surface of a simple cubic Ising model. Profiles of the magnetization and internal energy are determined as a function of the distance from the surface, and we extract surface and bulk properties as a function of temperature and surface coupling ${\mathit{J}}_{\mathit{s}}$. The surface-bulk multicritical point is located with improved precision, ${\mathit{J}}_{\mathit{s}}$/J=1.52\ifmmode\pm\else\textpm\fi{}0.02, and crossover behavior is studied. New estimates for critical exponents are extracted, ${\ensuremath{\gamma}}_{1}$=0.78\ifmmode\pm\else\textpm\fi{}0.06, ${\ensuremath{\gamma}…

Intramolecular phase separation of copolymer "bottle brushes": No sharp phase transition but a tunable length scale

2006

A lattice model for a symmetrical copolymer "bottle brush" molecule, where two types (A,B) of flexible side chains are grafted with one chain end to a rigid backbone, is studied by a variant of the pruned-enriched Rosenbluth method (PERM), allowing for simultaneous growth of all side chains in the Monte Carlo sampling. Choosing repulsive binary interactions between unlike monomers and varying the solvent quality, it is found that phase separation into an $A$-rich part of the cylindrical molecule and a $B$-rich part can occur only locally. Long range order (in the direction of the backbone) does not occur, and hence the transition from the randomly mixed state of the bottle brush to the phas…

Modelling of Orientational Ordering in Lipid Monolayers

1993

Lipid monolayers at high densities are modelled as rigid rods grafted to an interface at the sites of a regular lattice. The transition between the state where the rods are uniformly tilted to a disordered state with no (average) tilt is studied by computer simulation methods. For the one-dimensional model, the molecular dynamics approach is found much less suitable to equilibrate the system rather than Monte Carlo methods. Both in d=2 discretized versions of Monte Carlo codes are much more efficient than continuum Monte Carlo methods, in spite of huge storage requirements. While in d=l the transition occurs at temperature T=0 via the spontaneous creation of solitons, at d=2 a finite temper…

Structural properties of concave cylindrical brushes interacting with free chains

2011

We present a self-consistent field theoretical study of the microstructure of concave cylindrical brushes as a function of the cylinder radius, grafting density, grafted chain length, and the solvent quality. We show that the results for the radial monomer density profile and the distribution of the free ends are in good agreement with the corresponding molecular dynamics results. Part of the investigation is focused on the conformational behavior of a free macromolecule in a cylindrical brush. A central result is the observed non-monotonous variation of the size of a free chain in a brush-coated tube when the tube radius is systematically changed. An interpretation of this behavior which d…

Simple sampling Monte Carlo methods

2005

Monte Carlo Methods for the Sampling of Free Energy Landscapes

2019

In this chapter, we return to classical statistical mechanics, wherein the canonical ensemble averages of an observable \(A(\overrightarrow{x})\), where \(\overrightarrow{x} \) stands symbolically for the “microstate” coordinate in the configurational part of the phase space of the system, are given by (cf. Sect. 2.1.1)

Wetting in fluid systems. Wetting and capillary condensation of lattice gases in thin film geometry

1994

Monte Carlo studies of lattice gas models with attractive interactions between nearest neighbors on a simple cubic lattice are carried out for a L×L×D geometry with two hard walls of size L×L and periodic boundary conditions parallel to the wall. Two types of short-range forces at the walls are considered: (i) Both walls are of the same type and exert an attractive force of the same strength (in Ising model terminology, surface fields HD = H1 occur). (ii) The walls differ, one attracts and the other repels particles, again with the same strength (HD = −H1). In the first case, capillary condensation occurs at a chemical potential differing from its value for phase coexistence in the bulk, an…

The Ising square lattice in aL�M geometry: A model for the effect of surface steps on phase transitions in adsorbed monolayers

1989

Critical phenomena in adsorbed monolayers on surfaces are influenced by limited substrate homogeneity, such as surface steps. We consider the resulting finite-size and boundary effects in the framework of a lattice gas system with nearest neighbor attraction in aL×M geometry, with two free boundaries of lengthM≫L, and periodic boundary conditions in the other direction (along the direction of the steps). This geometry thus models a “terrace” of the stepped surface, and adatoms adsorbed on neighboring terraces are assumed to be non-interacting. Also the effect of boundary “fields” is considered (describing the effects of missing neighbors and changed binding energy to the substrate near the …

Phase transition shifts in films

1991

Abstract We present a Monte Carlo computer simulation study of phase transitions in a three-dimensional Ising/lattice gas model with nearest neighbor attractive coupling and confined to a slit-like capillary with absorbing walls. Data are generated for thicknesses D ⩽ 40 and are used to study the shift of the phase boundaries due to finite wall separation.

On the order of the herringbone transition of N2 on graphite: a Monte Carlo study

1993

Using the anisotropic planar-rotor model we investigate the herringbone phase transition of N2 in the (√3 × √3)R30° commensurate phase on graphite by large scale Monte Carlo simulations. The effective correlation length ξ is measured near the transition temperature T0. The data, extrapolated to T0, yield a large but finite ξ at T0 demonstrating that the herringb ordering is a weak first order transition.

First Versus Second Order Phase Transitions in the Three-Dimensional Three-State Potts Model in Random Fields

1995

The ordering of three-states Potts ferromagnets on the simple cubic lattice exposed to random fields is investigated by extensive Monte Carlo simulations. Evidence is presented that the transition is second order for intermediate strength of the fields, while it presumably is first order for large field strength. The implications for various theoretical predictions are briefly discussed.

Comparison of model potentials for molecular-dynamics simulations of silica.

2005

Structural, thermomechanical, and dynamic properties of pure silica SiO2 are calculated with three different model potentials, namely, the potential suggested by van Beest, Kramer, and van Santen (BKS) [Phys. Rev. Lett. 64, 1955 (1990)], the fluctuating-charge potential with a Morse stretch term for the short-range interactions proposed by Demiralp, Cagin, and Goddard (DCG)[Phys. Rev. Lett. 82, 1708 (1999)], and a polarizable force field proposed by Tangney and Scandolo (TS) [J. Chem. Phys. 117, 8898 (2002)]. The DCG potential had to be modified due to flaws in the original treatment. While BKS reproduces many thermomechanical properties of different polymorphs rather accurately, it also sh…