arXiv subjects

Peter Virnau

Publications and source records attributed to Peter Virnau.

At least 55 records · Page 3Linked to original sources

arXiv2014

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.

cond-mat.soft↗

arXiv2014

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 $θ< π/2$ relative to the yz-plane is stabilized. In the y-direction, a generalization of the antiperiodic boundary condition is used that maintains the translational invariance in y-direction despite the inhomogeneity of the magnetization distribution in this system. This geometry allows a simultaneous study of the angle-dependent interface tension, the contact angle, and the line tension (which depends on the contact angle, and on temperature). All these quantities are extracted from suitable thermodynamic integration procedures. In order to keep finite size effects as well as statistical errors small enough, rather large lattice sizes (of the order of 46 million sites) are found necessary, availability of very efficient code implementation of graphics processing units (GPUs) was crucial for the feasibility of this study.

physics.comp-ph↗

arXiv2014

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.

physics.bio-ph↗

arXiv2014

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 fluctuations cause logarithmic finite-size effects of order $\ln (L) / L^{d-1}$ and order $\ln (L_z)/L ^{d-1}$, in addition to regular corrections (with leading order $\text{const}/L^{d-1}$). A phenomenological theory predicts that the prefactors of the logarithmic terms are universal (but depend on the applied boundary conditions and the considered statistical ensemble). The physical origin of these corrections are the translational entropy of the interface as a whole, "domain breathing" (coupling of interfacial fluctuations to the bulk order parameter fluctuations of the coexisting domains), and capillary waves. Using a new variant of the ensemble switch method, interfacial tensions are found from Monte Carlo simulations of $d=2$ and $d=3$ Ising models and a Lennard Jones fluid. The simulation results are fully consistent with the theoretical predictions.

cond-mat.stat-mech↗

arXiv2014

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".

cond-mat.stat-mech↗

arXiv2014

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.

cond-mat.stat-mech↗

arXiv2013

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 $ΔF^*$, 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. Using the definition of "physical" clusters based on the Fortuin-Kasteleyn mapping, the time-dependence of the cluster size distribution is studied for "quenching experiments" in the kinetic Ising model, and the cluster size $\ell ^*$ where the cluster growth rate changes sign is estimated. These studies of nucleation kinetics are compared to studies where the relation between cluster size and supersaturation is estimated from equilibrium simulations of phase coexistence between droplet and vapor in the canonical ensemble. The chemical potential is estimated from a lattice version of the Widom particle insertion method. For large droplets it is shown that the "physical clusters" have a volume consistent with the estimates from the lever rule. "Geometrical clusters" (defined such that each site belonging to the cluster is occupied and has at least one occupied neighbor site) yield valid results only for temperatures less than 60% of the critical temperature, where the cluster shape is non-spherical. We show how the chemical potential can be used to numerically estimate $ΔF^*$ also for non-spherical cluster shapes.

cond-mat.soft↗

arXiv2012

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 equilibrium. We find fair agreement with a prediction based on Young's equation, using estimates of interface and wall tension from the study of flat surfaces. It is shown that the pressure versus density curve of the finite system exhibits a loop, but the pressure maximum signifies the "droplet evaporation-condensation" transition and thus has nothing in common with a van der Waals-like loop. Preparing systems where the packing fraction is deep inside the two-phase coexistence region, the system spontaneously forms a "slab state", with two wall-attached crystalline domains separated by (flat) interfaces from liquid in full equilibrium with the crystal in between; analysis of such states allows a precise estimation of the bulk equilibrium properties at phase coexistence.

cond-mat.soft↗

arXiv2011

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 the effect of the polymers can be integrated out to yield an effective attractive potential between the colloids). Factors limiting the accuracy of the various methods are carefully discussed, and controlling these factors very good mutual agreement between the various methods is found.

cond-mat.soft↗

arXiv2011

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

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

cond-mat.stat-mech↗

arXiv2011

Anomalous Structure and Scaling of Ring Polymer Brushes

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

cond-mat.soft↗

arXiv2011

Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions

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

cond-mat.stat-mech↗

arXiv2010

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., J. Comp. Phys. 228, 4468 (2009)] 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 Parsing Interface (MPI) on the CPU level, a single Ising lattice can be updated by a cluster of GPUs in parallel. For large systems, the computation time scales nearly linearly with the number of GPUs used. As proof of concept we reproduce the critical temperature of the 2D Ising model using finite size scaling techniques.

physics.comp-ph↗

arXiv2010

Rounding of Phase Transitions in Cylindrical Pores

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

cond-mat.stat-mech↗

arXiv2010

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

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

cond-mat.stat-mech↗

arXiv2010

Monte Carlo Test of the Classical Theory for Heterogeneous Nucleation Barriers

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

cond-mat.stat-mech↗

arXiv2009

Implementation and performance analysis of bridging Monte Carlo moves for off-lattice single chain polymers in globular states

Bridging algorithms are global Monte Carlo moves which allow for an efficient sampling of single polymer chains. In this manuscript we discuss the adaptation of three bridging algorithms from lattice to continuum models, and give details on the corrections to the acceptance rules which are required to fulfill detailed balance. For the first time we are able to compare the efficiency of the moves by analyzing the occurrence of knots in globular states. For a flexible homopolymer chain of length N=1000, independent configurations can be generated up to two orders of magnitude faster than with slithering snake moves.

cond-mat.soft↗

arXiv2008

Statics and Dynamics of Colloid-Polymer Mixtures Near Their Critical Point of Phase Separation: A Computer Simulation Study of a Continuous AO 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 main advantage of the model is exploited - its suitability for Molecular Dynamics simulations - to study the dynamics of mean square displacements of the particles, transport coefficients such as the self-diffusion and interdiffusion coefficients, and dynamic structure factors. While the self-diffusion of polymers increases slightly when the critical point is approached, the self-diffusion of colloids decreases and at criticality the colloid self-diffusion coefficient is about a factor of 10 smaller than that of the polymers. Critical slowing down of interdiffusion is observed, which is qualitatively similar to symmetric binary Lennard-Jones mixtures, for which no dynamic asymmetry of self-diffusion coefficients occurs.

cond-mat.soft↗