Spinodal Decomposition Kinetics of Colloid-Polymer Mixtures Including Hydrodynamic Interactions

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?

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…

KnotGenome: a server to analyze entanglements of chromosomes.

Abstract The KnotGenome server enables the topological analysis of chromosome model data using three-dimensional coordinate files of chromosomes as input. In particular, it detects prime and composite knots in single chromosomes, and links between chromosomes. The knotting complexity of the chromosome is presented in the form of a matrix diagram that reveals the knot type of the entire polynucleotide chain and of each of its subchains. Links are determined by means of the Gaussian linking integral and the HOMFLY-PT polynomial. Entangled chromosomes are presented graphically in an intuitive way. It is also possible to relax structure with short molecular dynamics runs before the analysis. Kn…

Monte Carlo Simulation of Crystal-Liquid Phase Coexistence

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…

Coarse-grained models of double-stranded DNA based on experimentally determined knotting probabilities

Abstract To accurately model double-stranded DNA in a manner that is computationally efficient, coarse-grained models of DNA are introduced, where model parameters are selected by fitting the spectrum of observable DNA knots: We develop a general method to fit free parameters of coarse-grained chain models by comparing experimentally obtained knotting probabilities of short DNA chains to knotting probabilities that are computed in Monte Carlo simulations, resulting in coarse-grained DNA models which are tailored to reflect DNA topology in the best possible way. The method is exemplified by fitting ideal chain models as well as a bead-spring model with excluded volume interactions, to model …

Phase Separation of Colloid Polymer Mixtures Under Confinement

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.

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

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…

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

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…

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

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…

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

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…

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

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.

Monte Carlo Tests of Nucleation Concepts in the Lattice Gas Model

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…

Conformational Properties of Polymer Mushrooms Under Spherical and Cylindrical Confinement

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 breathing

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".

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

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 molecular dynamics

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…

Multi-GPU Accelerated Multi-Spin Monte Carlo Simulations of the 2D Ising Model

A Modern Graphics Processing unit (GPU) is able to perform massively parallel scientific computations at low cost. We extend our implementation of the checkerboard algorithm for the two-dimensional Ising model [T. Preis et al., Journal of Chemical Physics 228 (2009) 4468–4477] in order to overcome the memory limitations of a single GPU which enables us to simulate significantly larger systems. Using multi-spin coding techniques, we are able to accelerate simulations on a single GPU by factors up to 35 compared to an optimized single Central Processor Unit (CPU) core implementation which employs multi-spin coding. By combining the Compute Unified Device Architecture (CUDA) with the Message P…

Protein knot server: detection of knots in protein structures

KNOTS (http://knots.mit.edu) is a web server that detects knots in protein structures. Several protein structures have been reported to contain intricate knots. The physiological role of knots and their effect on folding and evolution is an area of active research. The user submits a PDB id or uploads a 3D protein structure in PDB or mmCIF format. The current implementation of the server uses the Alexander polynomial to detect knots. The results of the analysis that are presented to the user are the location of the knot in the structure, the type of the knot and an interactive visualization of the knot. The results can also be downloaded and viewed offline. The server also maintains a regul…

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

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…

Accelerated fluctuation analysis by graphic cards and complex pattern formation in financial markets

The compute unified device architecture is an almost conventional programming approach for managing computations on a graphics processing unit (GPU) as a data-parallel computing device. With a maximum number of 240 cores in combination with a high memory bandwidth, a recent GPU offers resources for computational physics. We apply this technology to methods of fluctuation analysis, which includes determination of the scaling behavior of a stochastic process and the equilibrium autocorrelation function. Additionally, the recently introduced pattern formation conformity (Preis T et al 2008 Europhys. Lett. 82 68005), which quantifies pattern-based complex short-time correlations of a time serie…

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

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…

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

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…

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

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…

Proteins' Knotty Problems

Abstract Knots in proteins are increasingly being recognized as an important structural concept, and the folding of these peculiar structures still poses considerable challenges. From a functional point of view, most protein knots discovered so far are either enzymes or DNA-binding proteins. Our comprehensive topological analysis of the Protein Data Bank reveals several novel structures including knotted mitochondrial proteins and the most deeply embedded protein knot discovered so far. For the latter, we propose a novel folding pathway based on the idea that a loose knot forms at a terminus and slides to its native position. For the mitochondrial proteins, we discuss the folding problem fr…

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

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}}…

Computer Simulation Studies of Chain Dynamics in Polymer Brushes

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…

Critical behavior of active Brownian particles

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}/\…

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

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

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…

A Stevedore's protein knot.

Protein knots, mostly regarded as intriguing oddities, are gradually being recognized as significant structural motifs. Seven distinctly knotted folds have already been identified. It is by and large unclear how these exceptional structures actually fold, and only recently, experiments and simulations have begun to shed some light on this issue. In checking the new protein structures submitted to the Protein Data Bank, we encountered the most complex and the smallest knots to date: A recently uncovered α-haloacid dehalogenase structure contains a knot with six crossings, a so-called Stevedore knot, in a projection onto a plane. The smallest protein knot is present in an as yet unclassified …

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

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...

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

When a fluid that undergoes a vapor to liquid transition in the bulk is confined to a long cylindrical pore, the phase transition is shifted (mostly due to surface effects at the walls of the pore) and rounded (due to finite size effects). The nature of the phase coexistence at the transition depends on the length of the pore: For very long pores the system is axially homogeneous at low temperatures. At the chemical potential where the transition takes place fluctuations occur between vapor-like and liquid-like states of the cylinder as a whole. At somewhat higher temperatures (but still far below bulk criticality) the system at phase coexistence is in an axially inhomogeneous multi-domain …

Circuits and excitations to enable Brownian token-based computing with skyrmions

Brownian computing exploits thermal motion of discrete signal carriers (tokens) for computations. In this paper we address two major challenges that hinder competitive realizations of circuits and application of Brownian token-based computing in actual devices for instance based on magnetic skyrmions. To overcome the problem that crossings generate for the fabrication of circuits, we design a crossing-free layout for a composite half-adder module. This layout greatly simplifies experimental implementations as wire crossings are effectively avoided. Additionally, our design is shorter to speed up computations compared to conventional designs. To address the key issue of slow computation base…

A Successive Umbrella Sampling Algorithm to Sample and Overcome Free Energy Barriers

Free-energy barriers for crystal nucleation from fluid phases.

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…

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

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…

GPU Based Molecular Dynamics Simulations of Polymer Rings in Concentrated Solution: Structure and Scaling

We report on equilibrium properties of a concentrated solution of non-concatenated ring polymers by Molecular dynamics simulations using HooMD-blue, a fast implementation on graphics processor units (GPUs). We are able to identify the intermediate scaling regime for the radius of gyration Rg ∝ N as well as indication for a crossover to Rg ∝ N for rings with chain length N in our fully flexible off-lattice polymer model. This crossover takes place between a ring size of 2500 and 7500 monomers for monomer density ρ = 0.5. Our results are in agreement with recent studies for lattice and stiff off-lattice models and show once again that this scaling is not model dependent at all. Furthermore th…

A minimal Gō-model for rebuilding whole genome structures from haploid single-cell Hi-C data

Abstract We present a minimal computational model, which allows very fast, on-the-fly construction of three dimensional haploid interphase genomes from single-cell Hi-C contact maps using the HOOMD-blue molecular dynamics package on graphics processing units. Chromosomes are represented by a string of connected beads, each of which corresponds to 100,000 base pairs, and contacts are mediated via a structure-based harmonic potential. We suggest and test two minimization protocols which consistently fold into conformationally similar low energy states. The latter are similar to previously published structures but are calculated in a fraction of the time. We find evidence that mere fulfillment…

A Monte Carlo Study of Knots in Long Double-Stranded DNA Chains.

We determine knotting probabilities and typical sizes of knots in double-stranded DNA for chains of up to half a million base pairs with computer simulations of a coarse-grained bead-stick model: Single trefoil knots and composite knots which include at least one trefoil as a prime factor are shown to be common in DNA chains exceeding 250,000 base pairs, assuming physiologically relevant salt conditions. The analysis is motivated by the emergence of DNA nanopore sequencing technology, as knots are a potential cause of erroneous nucleotide reads in nanopore sequencing devices and may severely limit read lengths in the foreseeable future. Even though our coarse-grained model is only based on …

Comparing equilibration schemes of high-molecular-weight polymer melts with topological indicators.

Abstract Recent theoretical studies have demonstrated that the behaviour of molecular knots is a sensitive indicator of polymer structure. Here, we use knots to verify the ability of two state-of-the-art algorithms—configuration assembly and hierarchical backmapping—to equilibrate high-molecular-weight (MW) polymer melts. Specifically, we consider melts with MWs equivalent to several tens of entanglement lengths and various chain flexibilities, generated with both strategies. We compare their unknotting probability, unknotting length, knot spectra, and knot length distributions. The excellent agreement between the two independent methods with respect to knotting properties provides an addit…

Mapping onto ideal chains overestimates self-entanglements in polymer melts

In polymer physics it is typically assumed that excluded volume interactions are effectively screened in polymer melts. Hence, chains could be described by an effective random walk without excluded volume interactions. In this letter, we show that this mapping is problematic by analyzing the occurrence of knots, their spectrum and sizes in polymer melts, corresponding random walks and chains in dilute solution. The effective random walk severely overrates the occurrence of knots and their complexity, particularly when compared to melts of flexible chains, indicating that non-trivial effects due to remnants of self-avoidance still play a significant role for the chain lengths considered in t…

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

Influence of chain stiffness on knottedness in single polymers.

In the present article, we investigate and review the influence of chain stiffness on self-entanglements and knots in a single polymer chain with Monte Carlo simulations spanning good solvent, theta and globular phases. The last-named are of particular importance as a model system for DNA in viral capsids. Intriguingly, the dependence of knot occurrence and complexity with increasing stiffness is non-trivial, but can be understood with a few simple concepts outlined in the present article.

Skyrmion pinning energetics in thin film systems

AbstractA key issue for skyrmion dynamics and devices are pinning effects present in real systems. While posing a challenge for the realization of conventional skyrmionics devices, exploiting pinning effects can enable non-conventional computing approaches if the details of the pinning in real samples are quantified and understood. We demonstrate that using thermal skyrmion dynamics, we can characterize the pinning of a sample and we ascertain the spatially resolved energy landscape. To understand the mechanism of the pinning, we probe the strong skyrmion size and shape dependence of the pinning. Magnetic microscopy imaging demonstrates that in contrast to findings in previous investigation…

The droplet evaporation/condensation transition in a finite volume

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

Molecular dynamics simulations in hybrid particle-continuum schemes: Pitfalls and caveats

Heterogeneous multiscale methods (HMM) combine molecular accuracy of particle-based simulations with the computational efficiency of continuum descriptions to model flow in soft matter liquids. In these schemes, molecular simulations typically pose a computational bottleneck, which we investigate in detail in this study. We find that it is preferable to simulate many small systems as opposed to a few large systems, and that a choice of a simple isokinetic thermostat is typically sufficient while thermostats such as Lowe-Andersen allow for simulations at elevated viscosity. We discuss suitable choices for time steps and finite-size effects which arise in the limit of very small simulation bo…

Spherically averaged versus angle-dependent interactions in quadrupolar fluids

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…

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

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…

Skyrmion Lattice Phases in Thin Film Multilayer

Phases of matter are ubiquitous with everyday examples including solids and liquids. In reduced dimensions, particular phases, such as the two-dimensional (2D) hexatic phase and corresponding phase transitions occur. A particularly exciting example of 2D ordered systems are skyrmion lattices, where in contrast to previously studied 2D colloid systems, the skyrmion size and density can be tuned by temperature and magnetic field. This allows us to drive the system from a liquid phase to a hexatic phase as deduced from the analysis of the hexagonal order. Using coarse-grained molecular dynamics simulations of soft disks, we determine the skyrmion interaction potentials and we find that the sim…

Heterogeneous nucleation at a wall near a wetting transition: a Monte Carlo test of the classical theory

While for a slightly supersaturated vapor the free energy barrier ΔF(hom)(*), which needs to be overcome in a homogeneous nucleation event, may be extremely large, nucleation is typically much easier at the walls of the container in which the vapor is located. While no nucleation barrier exists if the walls are wet, for incomplete wetting of the walls, described via a nonzero contact angle Θ, classical theory predicts that nucleation happens through sphere-cap-shaped droplets attracted to the wall, and their formation energy is ΔF(het)(*) = ΔF(hom)(*)f(Θ), with f(Θ) = (1-cosΘ)(2)(2+cosΘ)/4. This prediction is tested through simulations for the simple cubic lattice gas model with nearest-nei…

A combined molecular dynamics and Monte Carlo study of the approach towards phase separation in colloid-polymer mixtures.

A coarse-grained model for colloid-polymer mixtures is investigated where both colloids and polymer coils are represented as point-like particles interacting with spherically symmetric effective potentials. Colloid-colloid and colloid-polymer interactions are described by Weeks-Chandler-Andersen potentials, while the polymer-polymer interaction is very soft, of strength k(B)T/2 for maximum polymer-polymer overlap. This model can be efficiently simulated both by Monte Carlo and molecular dynamics methods, and its phase diagram closely resembles that of the well-known Asakura-Oosawa model. The static and dynamic properties of the model are presented for systems at critical colloid density, va…

The ensemble switch method and related approaches to obtain interfacial free energies between coexisting phases from simulations: a brief review

The accurate estimation of the excess free energy due to an interface between coexisting phases of a model system by computer simulation often is a challenging task. We review here two methods, whi...

Knots in finite memory walks

We investigate the occurrence and size of knots in a continuum polymer model with finite memory via Monte Carlo simulations. Excluded volume interactions are local and extend only to a fixed number of successive beads along the chain, ensuring that at short length scales the excluded volume effect dominates, while at longer length scales the polymer behaves like a random walk. As such, this model may be useful for understanding the behavior of polymers in a melt or semi-dilute solution, where exactly the same crossover is believed to occur. In particular, finite memory walks allow us to investigate the role of local interactions in the transition from highly knotted ideal polymers to almost…

Monte Carlo simulations of the 2d-Ising model in the geometry of a long stripe

Abstract The two-dimensional Ising model in the geometry of a long stripe can be regarded as a model system for the study of nanopores. As a quasi-one-dimensional system, it also exhibits a rather interesting “phase behavior”: At low temperatures the stripe is either filled with “liquid” or “gas” and “densities” are similar to those in the bulk. When we approach a “pseudo-critical point” (below the critical point of the bulk) at which the correlation length becomes comparable to the length of the stripe, several interfaces emerge and the systems contains multiple “liquid” and “gas” domains. The transition depends on the size of the stripe and occurs at lower temperatures for larger stripes.…

Scaling behavior of topologically constrained polymer rings in a melt

Large scale molecular dynamics simulations on graphic processing units (GPUs) are employed to study the scaling behavior of ring polymers with various topological constraints in melts. Typical sizes of rings containing $3_1$, $5_1$ knots and catenanes made up of two unknotted rings scale like $N^{1/3}$ in the limit of large ring sizes $N$. This is consistent with the crumpled globule model and similar findings for unknotted rings. For small ring lengths knots occupy a significant fraction of the ring. The scaling of typical ring sizes for small $N$ thus depends on the particular knot type and the exponent is generally larger than 0.4.

The ensemble switch method for computing interfacial tensions

We present a systematic thermodynamic integration approach to compute interfacial tensions for solid-liquid interfaces, which is based on the ensemble switch method. Applying Monte Carlo simulations and finite-size scaling techniques, we obtain results for hard spheres, which are in agreement with previous computations. The case of solid-liquid interfaces in a variant of the effective Asakura-Oosawa model and of liquid-vapor interfaces in the Lennard-Jones model are discussed as well. We demonstrate that a thorough finite-size analysis of the simulation data is required to obtain precise results for the interfacial tension.

Overview: Understanding nucleation phenomena from simulations of lattice gas models

Monte Carlo simulations of homogeneous and heterogeneous nucleation in Ising/lattice gas models are reviewed with an emphasis on the general insight gained on the mechanisms by which metastable states decay. Attention is paid to the proper distinction of particles that belong to a cluster (droplet), that may trigger a nucleation event, from particles in its environment, a problem crucial near the critical point. Well below the critical point, the lattice structure causes an anisotropy of the interface tension, and hence nonspherical droplet shapes result, making the treatment nontrivial even within the conventional classical theory of homogeneous nucleation. For temperatures below the rough…

Statics and dynamics of colloid-polymer mixtures near their critical point of phase separation: A computer simulation study of a continuous Asakura–Oosawa model

We propose a new coarse-grained model for the description of liquid-vapor phase separation of colloid-polymer mixtures. The hard-sphere repulsion between colloids and between colloids and polymers, which is used in the well-known Asakura-Oosawa (AO) model, is replaced by Weeks-Chandler-Anderson potentials. Similarly, a soft potential of height comparable to thermal energy is used for the polymer-polymer interaction, rather than treating polymers as ideal gas particles. It is shown by grand-canonical Monte Carlo simulations that this model leads to a coexistence curve that almost coincides with that of the AO model and the Ising critical behavior of static quantities is reproduced. Then the …

How Do Droplets Depend on the System Size? Droplet Condensation and Nucleation in Small Simulation Cells

Using large scale grandcanonical Monte Carlo simulations in junction with a multicanonical reweighting scheme we investigate the liquid-vapor transition of a Lennard—Jones fluid. Particular attention is focused on the free energy of droplets and the transition between different system configurations as the system tunnels between the vapor and the liquid state as a function of system size. The results highlight the finite size dependence of droplet properties in the canonical ensemble and free energy barriers along the path from the vapor to the liquid in the grandcanonical ensemble.

Coarse-graining dipolar interactions in simple fluids and polymer solutions: Monte Carlo studies of the phase behavior

In this paper we investigate the phase diagram of pure dipolar substances and their mixtures with short alkanes, using grand canonical Monte Carlo simulations of simplified coarse-grained models. Recently, an efficient coarse-grained model for simple quadrupolar molecules, based on a Lennard-Jones (LJ) interaction plus a spherically averaged quadrupolar potential, has been shown to be successful in predicting single-component and mixture phase diagrams. Motivated by these results, we investigate the phase diagrams of simple dipolar molecules (and their mixtures with alkanes) using a spherically averaged potential. First, we test the model on pure components. A generalized (state-dependent) …

Anisotropic interfacial tension, contact angles, and line tensions: A graphics-processing-unit-based Monte Carlo study of the Ising model

As a generic example for crystals where the crystal-fluid interface tension depends on the orientation of the interface relative to the crystal lattice axes, the nearest neighbor Ising model on the simple cubic lattice is studied over a wide temperature range, both above and below the roughening transition temperature. Using a thin film geometry $L_x \times L_y \times L_z$ with periodic boundary conditions along the z-axis and two free $L_x \times L_y$ surfaces at which opposing surface fields $\pm H_{1}$ act, under conditions of partial wetting, a single planar interface inclined under a contact angle $\theta < \pi/2$ relative to the yz-plane is stabilized. In the y-direction, a generaliza…

Structures and folding pathways of topologically knotted proteins

In the last decade, a new class of proteins has emerged that contain a topological knot in their backbone. Although these structures are rare, they nevertheless challenge our understanding of protein folding. In this review, we provide a short overview of topologically knotted proteins with an emphasis on newly discovered structures. We discuss the current knowledge in the field, including recent developments in both experimental and computational studies that have shed light on how these intricate structures fold.

Spinodal decomposition of polymer solutions: A parallelized molecular dynamics simulation

In simulations of phase separation kinetics, large length and time scales are involved due to the mesoscopic size of the polymer coils, and the structure formation on still larger scales of length and time. We apply a coarse-grained model of hexadecane dissolved in supercritical carbon dioxide, for which in previous work the equilibrium phase behavior has been established by Monte Carlo methods. Using parallelized simulations on a multiprocessor supercomputer, large scale molecular dynamics simulations of phase separation following pressure jumps are presented for systems containing $N=435\phantom{\rule{0.2em}{0ex}}136$ coarse-grained particles, which correspond to several millions of atoms…

Equilibrium between a Droplet and Surrounding Vapor: A Discussion of Finite Size Effects

In a theoretical description of homogeneous nucleation one frequently assumes an "equilibrium" coexistence of a liquid droplet with surrounding vapor of a density exceeding that of a saturated vapor at bulk vapor-liquid two-phase coexistence. Thereby one ignores the caveat that in the thermodynamic limit, for which the vapor would be called supersaturated, such states will at best be metastable with finite lifetime, and thus not be well-defined within equilibrium statistical mechanics. In contrast, in a system of finite volume stable equilibrium coexistence of droplet and supersaturated vapor at constant total density is perfectly possible, and numerical analysis of equilibrium free energie…

Detection and visualization of physical knots in macromolecules

Abstract This manuscript provides a pedagogical introduction on how to determine and visualize simple physical knots occurring in polymers, proteins and DNA. We explain how the Alexander polynomial is computed and implemented in a simulation code, and how the structure can be simplified beforehand to save computer time. The concept of knottedness can also be extended in a statistical framework to chains which are not closed. The latter is exemplified by comparing statistics of knots in open random walks and closed random loops.

Controlling the wetting properties of the Asakura-Oosawa model and applications to spherical confinement.

We demonstrate for the Asakura-Oosawa model and an extension of this model that uses continuous rather than hard potentials, how wetting properties at walls can be easily controlled. By increasing the interaction range of the repulsive wall potential acting on the colloids (while keeping the polymer-wall interactions constant) polymers begin to substitute colloids at walls and the system can be driven from complete wetting of colloids via partial wetting to complete wetting of polymers. As an application, we discuss the morphology and wetting behavior of colloid-polymer mixtures in spherical confinement. We apply the recently developed 'ensemble switch method' where the Hamiltonian is exten…

Structure Formation of Polymeric Building Blocks: Complex Polymer Architectures

This chapter describes macromolecules with a complex structure, their defined aggregation in solution, their adsorption to surfaces, and their possible aggregation on surfaces. The term “complex structure” implies that the macromolecules show different, distinct structural elements or building blocks on a supra-atomic length scale. Key to understanding the complex structure of macromolecules, their aggregation, and adsorption to surfaces are intra- and intermolecular interactions such as van der Waals, electrostatic, π–π interactions, and hydrogen bonds.

Finite-size scaling analysis of the anisotropic critical behavior of the two-dimensional Ising model under shear

The critical behavior of the two-dimensional Ising Model with non-conserved order parameter in steady-state shear is studied by large-scale Monte Carlo simulations. Studying the structure factor S(qx,qy) in the disordered phase, the ratio of correlation length exponents νx/νy in the two lattice directions (x,y) is estimated, and the critical temperature is determined as a function of the shear rate as Tc() − Tc(0) ∝ with ≈0.45. Critical exponents β≈0.37, γ≈1.1, ; ν⊥≈0.46, ν∥≈1.38 are roughly compatible with anisotropic hyperscaling.

Are There Knots in Chromosomes?

Recent developments have for the first time allowed the determination of three-dimensional structures of individual chromosomes and genomes in nuclei of single haploid mouse embryonic stem (ES) cells based on Hi⁻C chromosome conformation contact data. Although these first structures have a relatively low resolution, they provide the first experimental data that can be used to study chromosome and intact genome folding. Here we further analyze these structures and provide the first evidence that G1 phase chromosomes are knotted, consistent with the fact that plots of contact probability vs sequence separation show a power law dependence that is intermediate between that of a fractal globule …

Motion, relaxation dynamics, and diffusion processes in two-dimensional colloidal crystals confined between walls

The dynamical behavior of single-component two-dimensional colloidal crystals confined in a slit geometry is studied by Langevin dynamics simulation of a simple model. The colloids are modeled as pointlike particles, interacting with the repulsive part of the Lennard-Jones potential, and the fluid molecules in the colloidal suspension are not explicitly considered. Considering a crystalline strip of triangular lattice structure with n=30 rows, the (one-dimensional) walls confining the strip are chosen as two rigidly fixed crystalline rows at each side, commensurate with the lattice structure and, thus, stabilizing long-range order. The case when the spacing between the walls is incommensura…

Computer Simulations and Coarse-Grained Molecular Models Predicting the Equation of State of Polymer Solutions

Monte Carlo and molecular dynamics simulations are, in principle, powerful tools for carrying out the basic task of statistical thermodynamics, namely the prediction of macroscopic properties of matter from suitable models of effective interactions between atoms and molecules. The state of the art of this approach is reviewed, with an emphasis on solutions of rather short polymer chains (such as alkanes) in various solvents. Several methods of constructing coarse-grained models of the simple bead–spring type will be mentioned, using input either from atomistic models (considering polybutadiene as an example) or from experiment. Also, the need to have corresponding coarse-grained models of t…

Commensurability between Element Symmetry and the Number of Skyrmions Governing Skyrmion Diffusion in Confined Geometries

Magnetic skyrmions are topological magnetic structures, which exhibit quasi-particle properties and can show enhanced stability against perturbation from thermal noise. Recently, thermal Brownian diffusion of these quasi-particles has been found in continuous films and applications in unconventional computing have received significant attention, which however require structured elements. Thus, as the next necessary step, we here study skyrmion diffusion in confined geometries and find it to be qualitatively different: The diffusion is governed by the interplay between the total number of skyrmions and the structure geometry. In particular, we ascertain the effect of circular and triangular …

Logarithmic finite-size effects on interfacial free energies: Phenomenological theory and Monte Carlo studies

The computation of interfacial free energies between coexisting phases (e.g.~saturated vapor and liquid) by computer simulation methods is still a challenging problem due to the difficulty of an atomistic identification of an interface, and due to interfacial fluctuations on all length scales. The approach to estimate the interfacial tension from the free energy excess of a system with interfaces relative to corresponding single-phase systems does not suffer from the first problem but still suffers from the latter. Considering $d$-dimensional systems with interfacial area $L^{d-1}$ and linear dimension $L_z$ in the direction perpendicular to the interface, it is argued that the interfacial …

Effects of confinement and external fields on structure and transport in colloidal dispersions in reduced dimensionality

In this work, we focus on low-dimensional colloidal model systems, via simulation studies and also some complementary experiments, in order to elucidate the interplay between phase behavior, geometric structures and transport properties. In particular, we try to investigate the (nonlinear!) response of these very soft colloidal systems to various perturbations: uniform and uniaxial pressure, laser fields, shear due to moving boundaries and randomly quenched disorder.We study ordering phenomena on surfaces or in monolayers by Monte Carlo computer simulations of binary hard-disk mixtures, the influence of a substrate being modeled by an external potential. Weak external fields allow a control…

Sequence Determines Degree of Knottedness in a Coarse-Grained Protein Model

Knots are abundant in globular homopolymers but rare in globular proteins. To shed new light on this long-standing conundrum, we study the influence of sequence on the formation of knots in proteins under native conditions within the framework of the hydrophobic-polar (HP) lattice protein model. By employing large scale Wang-Landau simulations combined with suitable Monte Carlo trial moves we show that, even though knots are still abundant on average, sequence introduces large variability in the degree of self-entanglements. Moreover, we are able to design sequences which are either almost always or almost never knotted. Our findings serve as proof of concept that the introduction of just o…

Semiflexible polymers under good solvent conditions interacting with repulsive walls.

Solutions of semiflexible polymers confined by repulsive planar walls are studied by density functional theory and Molecular Dynamics simulations, to clarify the competition between the chain alignment favored by the wall and the depletion caused by the monomer-wall repulsion. A coarse-grained bead-spring model with bond bending potential is studied, varying both the contour length and the persistence length of the polymers, as well as the monomer concentration in the solution (good solvent conditions are assumed throughout, and solvent molecules are not included explicitly). The profiles of monomer density and pressure tensor components near the wall are studied, and the surface tension of…

Anomalous Structure and Scaling of Ring Polymer Brushes

A comparative simulation study of polymer brushes formed by grafting at a planar surface either flexible linear polymers (chain length $N_L$) or (non-catenated) ring polymers (chain length $N_R=2 N_L$) is presented. Two distinct off-lattice models are studied, one by Monte Carlo methods, the other by Molecular Dynamics, using a fast implementation on graphics processing units (GPUs). It is shown that the monomer density profiles $\rho(z)$ in the $z$-direction perpendicular to the surface for rings and linear chains are practically identical, $\rho_R(2 N_L, z)=\rho_L(N_L, z)$. The same applies to the pressure, exerted on a piston at hight z, as well. While the gyration radii components of ri…

Polymer Dynamics in a Polymer-Solid Interphase: Molecular Dynamics Simulations of 1,4-Polybutadiene At a Graphite Surface

A chemically realistic model of 1,4-polybutadiene confined by graphite walls in a thin film geometry was studied by molecular dynamics simulations. The chemically realistic approach allows for a quantitative determination of a variety of experimentally accessible relaxation functions (e.g., dielectric, NMR, or neutron scattering responses). The simulations yield these experimental observables. Additionally, the simulations can be resolved as a function of distance to the solid interface on a much finer scale than experimentally possible, providing a detailed mechanistic picture of the segmental and large scale motions of polymers in the interfacial region between bulk polymer melts and soli…

Structure and pair correlations of a simple coarse grained model for supercritical carbon dioxide

A recently introduced coarse-grained pair potential for carbon dioxide molecules is used to compute structural properties in the supercritical region near the critical point, applying Monte Carlo simulations. In this model, molecules are described as point particles, interacting with Lennard-Jones (LJ) forces and a (isotropically averaged) quadrupole–quadrupole potential, the LJ parameters being chosen such that gratifying agreement with the experimental phase diagram near the critical point is obtained. It is shown that the model gives also a reasonable account of the pair correlation function, although in the nearest neighbour shell some systematic discrepancies between the model predicti…

Hydrodynamic mechanisms of spinodal decomposition in confined colloid-polymer mixtures: A multiparticle collision dynamics study

A multiscale model for a colloid-polymer mixture is developed. The colloids are described as point particles interacting with each other and with the polymers with strongly repulsive potentials, while polymers interact with each other with a softer potential. The fluid in the suspension is taken into account by the multiparticle collision dynamics method (MPC). Considering a slit geometry where the suspension is confined between parallel repulsive walls, different possibilities for the hydrodynamic boundary conditions (b.c.) at the walls (slip versus stick) are treated. Quenching experiments are considered, where the system volume is suddenly reduced (keeping the density of the solvent flui…

Simulation of fluid-solid coexistence in finite volumes: A method to study the properties of wall-attached crystalline nuclei

The Asakura-Oosawa model for colloid-polymer mixtures is studied by Monte Carlo simulations at densities inside the two-phase coexistence region of fluid and solid. Choosing a geometry where the system is confined between two flat walls, and a wall-colloid potential that leads to incomplete wetting of the crystal at the wall, conditions can be created where a single nanoscopic wall-attached crystalline cluster coexists with fluid in the remainder of the simulation box. Following related ideas that have been useful to study heterogeneous nucleation of liquid droplets at the vapor-liquid coexistence, we estimate the contact angles from observations of the crystalline clusters in thermal equil…

Shear-Thinning in Oligomer Melts—Molecular Origins and Applications

We investigate the molecular origin of shear-thinning in melts of flexible, semiflexible and rigid oligomers with coarse-grained simulations of a sheared melt. Entanglements, alignment, stretching and tumbling modes or suppression of the latter all contribute to understanding how macroscopic flow properties emerge from the molecular level. In particular, we identify the rise and decline of entanglements with increasing chain stiffness as the major cause for the non-monotonic behaviour of the viscosity in equilibrium and at low shear rates, even for rather small oligomeric systems. At higher shear rates, chains align and disentangle, contributing to shear-thinning. By performing simulations …

Magnetic Direct-Write Skyrmion Nanolithography

Magnetic skyrmions are stable spin textures with quasi-particle behavior and attract significant interest in fundamental and applied physics. The metastability of magnetic skyrmions at zero magnetic field is particularly important to enable, for instance, a skyrmion racetrack memory. Here, the results of the nucleation of stable skyrmions and formation of ordered skyrmion lattices by magnetic force microscopy in (Pt/CoFeSiB/W)n multilayers, exploiting the additive effect of the interfacial Dzyaloshinskii-Moriya interaction, are presented. The appropriate conditions under which skyrmion lattices are confined with a dense two-dimensional liquid phase are identified. A crucial parameter to con…

A slow process in confined polymer melts: layer exchange dynamics at a polymer solid interface

Employing Molecular Dynamics simulations of a chemically realistic model of 1,4-polybutadiene between graphite walls we show that the mass exchange between layers close to the walls is a slow process already in the melt state. For the glass transition of confined polymers this process competes with the slowing down due to packing effects and intramolecular rotation barriers.

Stick-slip motion and plastic flow of a two-dimensional colloidal crystal confined to moving corrugated rigid boundaries

Computer simulations are presented where a model for a two-dimensional colloidal crystal confined to corrugated walls is exposed to a steady-state shear deformation. Following up on an earlier study, where average velocity profiles of the particles in the crystal across the slit have been obtained, we now analyse the time dependence of the particle motions and of the resulting shear forces. We discuss the extent to which the resulting irregular and damped oscillatory motions can be associated with stick-slip motions familiar from friction phenomena.

How molecular knots can pass through each other

We propose a mechanism in which two molecular knots pass through each other and swap positions along a polymer strand. Associated free energy barriers in our simulations only amount to a few $k_{B}T$, which may enable the interchange of knots on a single DNA strand.

Effective stiffening of DNA due to nematic ordering causes DNA molecules packed in phage capsids to preferentially form torus knots.

Observation that DNA molecules in bacteriophage capsids preferentially form torus type of knots provided a sensitive gauge to evaluate various models of DNA arrangement in phage heads. Only models resulting in a preponderance of torus knots could be considered as close to reality. Recent studies revealed that experimentally observed enrichment of torus knots can be qualitatively reproduced in numerical simulations that include a potential inducing nematic arrangement of tightly packed DNA molecules within phage capsids. Here, we investigate what aspects of the nematic arrangement are crucial for inducing formation of torus knots. Our results indicate that the effective stiffening of DNA by …

Rounding of Phase Transitions in Cylindrical Pores

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

Phase transitions and phase equilibria in spherical confinement

Phase transitions in finite systems are rounded and shifted and affected by boundary effects due to the surface of the system. This interplay of finite size and surface effects for fluids confined inside of a sphere of radius $R$ is studied by a phenomenological theory and Monte Carlo simulations of a model for colloid-polymer mixtures. For this system the phase separation in a colloid-rich phase and a polymer-rich phase has been previously studied extensively in the bulk. It is shown that spherical confinement can strongly enhance the miscibility of the mixture. Depending on the wall potentials at the confining surface, the wetting properties of the wall can be controlled, and this interpl…

Confined binary two-dimensional colloidal crystals: Monte Carlo simulation of crack formation.

Binary mixtures (A, B) of colloidal particles of different sizes in two dimensions may form crystals with square lattice structure (the A-particles occupying the white sites and the B-particles the black sites of a checkerboard). Confining such a system by two parallel 'walls' a distance D apart, long-range order in the direction parallel to the walls is stabilized by 'corrugated walls' that are commensurate with the lattice structure but destabilized by structureless 'hard walls', even if there is no misfit between the strip width D and the crystal lattice spacing. The crossover to quasi-one-dimensional behavior is studied by Monte Carlo simulations, analyzing Lindemann parameters and disp…

Phase transitions and phase coexistence: equilibrium systems versus externally driven or active systems - Some perspectives

A tutorial introduction to the statistical mechanics of phase transitions and phase coexistence is presented, starting out from equilibrium systems and nonequilibrium steady-state situations in ext...

Active nonlinear microrheology in a glass-forming Yukawa fluid.

A molecular dynamics computer simulation of a glass-forming Yukawa mixture is used to study the anisotropic dynamics of a single particle pulled by a constant force. Beyond linear response, a scaling regime is found where a force-temperature superposition principle of a Peclet number holds. In the latter regime, the diffusion dynamics perpendicular to the force can be mapped on the equilibrium dynamics in terms of an effective temperature, whereas parallel to the force a superdiffusive behavior is seen in the long-time limit. This behavior is associated with a hopping motion from cage to cage and can be qualitatively understood by a simple trap model.

Methods to Compute Pressure and Wall Tension in Fluids containing Hard Particles

Colloidal systems are often modelled as fluids of hard particles (possibly with an additional soft attraction, e.g. caused by polymers also contained in the suspension). in simulations of such systems, the virial theorem cannot be straightforwardly applied to obtain the components of the pressure tensor. In systems confined by walls, it is hence also not straightforward to extract the excess energy due to the wall (the "wall tension") from the pressure tensor anisotropy. A comparative evaluation of several methods to circumvent this problem is presented, using as examples fluids of hard spheres and the Asakura-Oosawa model of colloid-polymer mixtures with a size ratio $q=0.15$ (for which th…

GPU accelerated Monte Carlo simulation of the 2D and 3D Ising model

The compute unified device architecture (CUDA) is a programming approach for performing scientific calculations on a graphics processing unit (GPU) as a data-parallel computing device. The programming interface allows to implement algorithms using extensions to standard C language. With continuously increased number of cores in combination with a high memory bandwidth, a recent GPU offers incredible resources for general purpose computing. First, we apply this new technology to Monte Carlo simulations of the two dimensional ferromagnetic square lattice Ising model. By implementing a variant of the checkerboard algorithm, results are obtained up to 60 times faster on the GPU than on a curren…

Crystal nuclei in melts: A Monte Carlo simulation of a model for attractive colloids

As a model for a suspension of hard-sphere like colloidal particles where small nonadsorbing dissolved polymers create a depletion attraction, we introduce an effective colloid-colloid potential closely related to the Asakura-Oosawa model but that does not have any discontinuities. In simulations, this model straightforwardly allows the calculation of the pressure from the Virial formula, and the phase transition in the bulk from the liquid to crystalline solid can be accurately located from a study where a stable coexistence of a crystalline slab with a surrounding liquid phase occurs. For this model, crystalline nuclei surrounded by fluid are studied both by identifying the crystal-fluid …

Entropic Interactions between Two Knots on a Semiflexible Polymer.

Two knots on a string can either be separated or intertwined, and may even pass through each other. At the microscopic scale, such transitions may occur spontaneously, driven by thermal fluctuations, and can be associated with a topological free energy barrier. In this manuscript, we study the respective location of a trefoil ( 3 1 ) and a figure-eight ( 4 1 ) knot on a semiflexible polymer, which is parameterized to model dsDNA in physiological conditions. Two cases are considered: first, end monomers are grafted to two confining walls of varying distance. Free energy profiles and transition barriers are then compared to a subset of free chains, which contain exactly one 3 1 and one 4 1 kn…

Spinodal decomposition of polymer solutions: molecular dynamics simulations of the two-dimensional case.

As a generic model system for phase separation in polymer solutions, a coarse-grained model for hexadecane/carbon dioxide mixtures has been studied in two-dimensional geometry. Both the phase diagram in equilibrium (obtained from a finite size scaling analysis of Monte Carlo data) and the kinetics of state changes caused by pressure jumps (studied by large scale molecular dynamics simulations) are presented. The results are compared to previous work where the same model was studied in three-dimensional geometry and under confinement in slit geometry. For deep quenches the characteristic length scale ℓ(t) of the formed domains grows with time t according to a power law close to [Formula: see…

Monte Carlo Test of the Classical Theory for Heterogeneous Nucleation Barriers

Flat walls facilitate the condensation of a supersaturated vapor: Classical theory of heterogeneous nucleation predicts that the free energy barrier $\Delta F_{\rm het}^*$ which needs to be overcome for the formation of sphere-cap shaped nucleation seeds is smaller than the barrier $\Delta F^*_{\rm hom}$ for spherical droplets in the bulk by a factor $0<f(\theta)<1$, which only depends on the contact angle $\theta$. In this letter we compute both $\Delta F^*_{\rm hom}$ and $\Delta F^*_{\rm het}$ from Monte Carlo simulations and test the theory for the lattice gas model (for which $\theta$ can be readily controlled). Even though the theory is only based on macroscopic arguments, it is shown …

Langevin dynamics simulations of a two-dimensional colloidal crystal under confinement and shear

Langevin dynamics simulations are used to study the effect of shear on a two-dimensional colloidal crystal (with implicit solvent) confined by structured parallel walls. When walls are sheared very slowly, only two or three crystalline layers next to the walls move along with them, while the inner layers of the crystal are only slightly tilted. At higher shear velocities, this inner part of the crystal breaks into several pieces with different orientations. The velocity profile across the slit is reminiscent of shear banding in flowing soft materials, where liquid and solid regions coexist; the difference, however, is that in the latter case the solid regions are glassy while here they are …

Can Soft Models Describe Polymer Knots?

Similar to macroscopic ropes and cables, long polymers create knots. We address the fundamental question whether and under which conditions it is possible to describe these intriguing objects with crude models that capture only mesoscale polymer properties. We focus on melts of long polymers which we describe by a model typical for mesoscopic simulations. A worm-like chain model defines the polymer architecture. To describe nonbonded interactions, we deliberately choose a generic "soft" repulsive potential that leads to strongly overlapping monomers and coarse local liquid structure. The soft model is parametrized to accurately reproduce mesoscopic structure and conformations of reference p…