0000000000291485
AUTHOR
Burkhard Dünweg
Multiple time step integrators and momentum conservation
Abstract By use of the standard Liouville operator formalism, we derive a new symplectic multiple time step integrator for Hamiltonian systems with disparate masses, which, in contrast to previous algorithms, conserves the total momentum exactly, and is only moderately slower. The new scheme is tested numerically by application to Molecular Dynamics simulations of a polymer melt whose monomers have different masses, and compared to earlier algorithms.
Electrophoresis of colloidal dispersions in the low-salt regime
We study the electrophoretic mobility of spherical charged colloids in a low-salt suspension as a function of the colloidal concentration. Using an effective particle charge and a reduced screening parameter, we map the data for systems with different particle charges and sizes, including numerical simulation data with full electrostatics and hydrodynamics and experimental data for latex dispersions, on a single master curve. We observe two different volume fraction-dependent regimes for the electrophoretic mobility that can be explained in terms of the static properties of the ionic double layer.
Phase Diagrams of Alloys and Adsorbed Monolayers: Some Recent Results
We discuss some recent work done on the calculation of phase diagrams of models of binary alloys and adsorbed monolayers. For the nearest-neighbor Ising antiferromagnet on the fcc lattice (model for the Cu-Au system) we study a rather large lattice of 4 x 643 spins. This is necessary since the inherent frustration of the lattice induces a very small interfacial tension between ordered domains. We find no indications for the suggested L′ phase, and locate the triple point at a nonzero temperature. There is some numerical evidence that it might in fact be a multicritical point. We then discuss the extension of lattice gas models to “elastic lattice gases” (ELGs) which include also translation…
Phase separation versus wetting: A mean field theory for symmetrical polymer mixtures confined between selectively attractive walls
Partially compatible symmetrical (N A # N B = N) binary mixtures of linear flexible polymers (A, B) are considered in the presence of two equivalent walls a distance D apart, assuming that both walls preferentially adsorb the same component. Using a Flory-Huggins type mean field approach analogous to previous work studying wetting phenomena in the semi-infinite version of this model, where D → ∞, it is shown that a single phase transition occurs in this thin film geometry, namely a phase separation between an A-rich and a B-rich phase (both phases include the bulk of the film). The coexistence curve is shifted to smaller values of the inverse Flory-Huggins parameter x -1 with decreasing D, …
A Monte Carlo Simulation of the Stillinger-Weber Model for Si-Ge Alloys
ABSTRACTThe bulk phase behavior of silicon-germanium alloys is investigated by means of a constant pressure Monte Carlo simulation of the Stillinger-Weber potential in the semi-grand-canonical ensemble. At low temperatures, Si and Ge phase separate into a Si-rich phase and a Ge-rich phase. The two-phase region is terminated by a critical point whose nature is investigated thoroughly by the multihistogram method combined with finite size scaling analysis. These results showed that the critical behavior of the alloy belongs to the mean field universality class, presumably due to the elastic degrees of freedom. We have also studied the structural properties of the mixture and found that the li…
Model calculations of phase diagrams of magnetic alloys on the body-centered-cubic lattice.
We treat a model for a binary (AB) alloy, where species A is magnetic (Ising spin σi = ± 1) while species B is not, and repulsive interactions are assumed between first and second neighbors of the same kind, in addition to a nearest-neighbor ferromagnetic exchange interaction. Both the mean-field approximation, the cluster variation (CV) method in the tetrahedron approximation and the Monte Carlo (MC) method are applied; comparing the phase diagrams obtained by the various approximations their accuracy is tested. It is shown that the CV method is in rather close agreement with the MC method for the present problem.
Structural properties ofSi1−xGexalloys: A Monte Carlo simulation with the Stillinger-Weber potential
The structural properties of binary silicon-germanium alloys are investigated by means of large-scale constant-pressure Monte Carlo simulations of the Stillinger-Weber model. At low temperatures, the binary-mixture phase separates into Si-rich and Ge-rich phases. The two-phase coexistence region is terminated by a critical point that belongs to the mean-field universality class. We also studied the structural properties of pure Si and Ge as well as the binary mixture. In particular, we found that the linear thermal expansions for both Si and Ge are in agreement with experiments, and that V\'egard's law is valid at temperatures above the critical point. Finally, we compare the bond-length an…
Systematic derivation of hydrodynamic equations for viscoelastic phase separation
(abridged) We present a detailed derivation of a simple hydrodynamic two-fluid model, which aims at the description of the phase separation of non-entangled polymer solutions, where viscoelastic effects play a role. It is directly based upon the coarse-graining of a well-defined molecular model, such that all degrees of freedom have a clear and unambiguous molecular interpretation. The considerations are based upon a free-energy functional, and the dynamics is split into a conservative and a dissipative part, where the latter satisfies the Onsager relations and the Second Law of thermodynamics. The model is therefore fully consistent with both equilibrium and non-equilibrium thermodynamics.…
Energy-Stable Numerical Schemes for Multiscale Simulations of Polymer–Solvent Mixtures
We present a new second-order energy dissipative numerical scheme to treat macroscopic equations aiming at the modeling of the dynamics of complex polymer–solvent mixtures. These partial differential equations are the Cahn-Hilliard equation for diffuse interface phase fields and the Oldroyd-B equations for the hydrodynamics of the polymeric mixture. A second-order combined finite volume/finite difference method is applied for the spatial discretization. A complementary approach to study the same physical system is realized by simulations of a microscopic model based on a hybrid Lattice Boltzmann/Molecular Dynamics scheme. These latter simulations provide initial conditions for the numerical…
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…
Surface-induced disordering at first-order transitions in body-centered cubic binary alloys: A Monte-Carlo simulation
Surface effects on the phase transition from theDO3 phase to the disordered phase are studied for a bcc Ising antiferromagnet with nearest and next-nearest neighbor exchange interactions in a magnetic field. This model can also be considered to represent binary alloys such as the FeAl-system; missing interactions near the surface translate then into surface magnetic fields. The change of the local magnetization near the surface then corresponds to “surface enrichment” of one component. For a plausible choice of parameters surface-induced disordering is found and the associated critical behavior is studied. Varying the bulk fieldH near the transition fieldHc, we find that the thickness of th…
A grand ensemble Monte Carlo study of metal adsorption on a (110) bcc substrate
Abstract The multilayer adsorption of a metal on a (110) bcc substrate has been studied by a grand-canonical Monte Carlo simulation in continuous, three-dimensional space. The obtained values of the critical parameters are compared with the results of a similar 2D Monte Carlo calculation and are interpreted in the spirit of the theory of Asada. A sharp transition from monolayer to multilayer adsorption is observed. The transition is accompanied by a substantial structural rearrangement in the adlayers immediately at the substrate. Generally it appears that the inclusion of the third dimension in the simulation reveals some important features of the phase transition and of the structure of t…
Nearest-neighbor Ising antiferromagnet on the fcc lattice: Evidence for multicritical behavior.
The phase behavior of the Ising model with nearest-neighbor antiferromagnetic interactions on the fcc lattice in a homogeneous magnetic field is studied by means of large-scale Monte Carlo simulations. In accordance with the most recent of the previous investigations, but with significantly higher accuracy, it is found that the ``triple'' point at which the disordered phase coexists with both the AB phase as well as with the ${\mathit{A}}_{3}$B phase (corresponding to the model's lattice gas interpretation as a binary alloy ${\mathit{A}}_{\mathit{xB}1\mathrm{\ensuremath{-}}\mathit{x}}$ such as ${\mathrm{Cu}}_{\mathit{x}}$${\mathrm{Au}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$) occurs at a nonz…
Microscopic verification of dynamic scaling in dilute polymer solutions: A molecular-dynamics simulation
The dynamics of a single polymer chain immersed in a large number of solvent particles is studied by molecular dynamics. This is the first simulation where chain length (30, 40, and 60 monomers) and statistical accuracy are sufficient to test the predictions of the Zimm model as a result of the particle-particle interactions: The short-time diffusion constant is in good agreement with the Kirkwood prediction, and the monomer motions exhibit the expected dynamic scaling. The long-range hydrodynamic interaction requires a data analysis that explicitly includes the periodic images via Ewald sums.
Computer Simulations for Polymer Dynamics
In this paper we review recent work on the dynamics of polymeric systems using computer simulation methods. For a two-dimensional polymer melt, we show that the chains segregate and the dynamics can be described very well by the Rouse model. This simulation was carried out using the bond fluctuation Monte Carlo method. For three-dimensional (3d) melts and for the study of hydrodynamic effects, we use a molecular dynamics simulation. For 3d melts our results strongly support the concept of reptation. A detailed comparison to experiment shows that we can predict the time and length scales for the onset of reptation for a variety of polymeric liquids. For a single chain, we find the expected h…
Monte Carlo studies of adsorbed monolayers: Lattice-gas models with translational degrees of freedom
Standard lattice-gas models for the description of the phase behavior of adsorbed monolayers are generalized to ``elastic lattice gases'' which allow for translational degrees of freedom of the adsorbate atoms but have the substrate lattice structure built into the adsorbate-adsorbate interaction. For such models, we derive a simple and efficient grand-canonical Monte Carlo algorithm, which treats the occupied and empty sites in precisely the same way. Using this method, we calculate the phase diagram of a simple model for the adsorption of hydrogen on palladium (100); this model includes only pairwise interactions and exhibits an ordered $c(2\ifmmode\times\else\texttimes\fi{}2)$ structure.…
Analysis of a viscoelastic phase separation model
A new model for viscoelastic phase separation is proposed, based on a systematically derived conservative two-fluid model. Dissipative effects are included by phenomenological viscoelastic terms. By construction, the model is consistent with the second law of thermodynamics, and we study well-posedness of the model, i.e., existence of weak solutions, a weak-strong uniqueness principle, and stability with respect to perturbations, which are proven by means of relative energy estimates. A good qualitative agreement with mesoscopic simulations is observed in numerical tests.
Considerations on correlations in shift-register pseudorandom number generators and their removal
Abstract We present a simple calculation quantitatively explaining the triplet correlations in the popular shift-register random number generator “R250”, which were recently observed numerically by Schmid and Wilding, and are known from general analysis of this type of generator. Starting from these considerations, we discuss various methods to remove these correlations by combining different shift-register generators. We implement and test a particularly simple and fast version, based on an XOR combination of two independent shift-register generators with different time lags. The results indicate that this generator has much better statistical properties than R250, while being only a facto…
BROWNIAN DYNAMICS SIMULATIONS WITHOUT GAUSSIAN RANDOM NUMBERS
We point out that in a Brownian dynamics simulation it is justified to use arbitrary distribution functions of random numbers if the moments exhibit the correct limiting behavior prescribed by the Fokker-Planck equation. Our argument is supported by a simple analytical consideration and some numerical examples: We simulate the Wiener process, the Ornstein-Uhlenbeck process and the diffusion in a Φ4 potential, using both Gaussian and uniform random numbers. In these examples, the rate of convergence of the mean first exit time is found to be nearly identical for both types of random numbers.
Energy-stable linear schemes for polymer-solvent phase field models
We present new linear energy-stable numerical schemes for numerical simulation of complex polymer-solvent mixtures. The mathematical model proposed by Zhou, Zhang and E (Physical Review E 73, 2006) consists of the Cahn-Hilliard equation which describes dynamics of the interface that separates polymer and solvent and the Oldroyd-B equations for the hydrodynamics of polymeric mixtures. The model is thermodynamically consistent and dissipates free energy. Our main goal in this paper is to derive numerical schemes for the polymer-solvent mixture model that are energy dissipative and efficient in time. To this end we will propose several problem-suited time discretizations yielding linear scheme…
Suppression of capillary wave broadening of interfaces in binary alloys due to elastic interactions.
By Monte Carlo simulations in the constant-temperature--constant-pressure ensemble a planar interface between unmixed A-rich and B-rich phases of a binary (A, B) alloy on a compressible diamond lattice is studied. No significant capillary wave broadening of the concentration profile across the interface is observed, unlike lattice models of incompressible mixtures and fluids. The distortion of the lattice structure across the interface is studied.
Fourier-Accelerated Polymer Dynamics
Fourier acceleration methods are applied to simulations of two-dimensional isolated ring polymers of up to N = 64 monomers. Three simulation schemes are compared: (i) a simple Langevin simulation with local updating, (ii) a Langevin algorithm with Fourier acceleration, and (iii) a Fourier accelerated Langevin algorithm combined with Metropolis acceptance of the moves (Force Biased Monte Carlo). In contrast to (i) and (ii), method (iii) is not hampered by systematic discretization errors, which, in case (ii), seem to grow systematically with chain length N. The results on the correlation time 4 are not very accurate, however, the data are in rough agreement with τ s N z with z= 2.5 (Rouse mo…