arXiv subjects

Kurt Binder

Publications and source records attributed to Kurt Binder.

At least 91 records · Page 5Linked to original sources

arXiv2006

Phase diagram and structure of colloid-polymer mixtures confined between walls

The influence of confinement, due to flat parallel structureless walls, on phase separation in colloid-polymer mixtures, is investigated by means of grand-canonical Monte Carlo simulations. Ultra-thin films, with thicknesses between $D=3-10$ colloid diameters, are studied. The Asakura-Oosawa model [J. Chem. Phys. 22, 1255 (1954)] is used to describe the particle interactions. To simulate efficiently, a ``cluster move'' [J. Chem. Phys. 121, 3253 (2004)] is used in conjunction with successive umbrella sampling [J. Chem. Phys. 120, 10925 (2004)]. These techniques, when combined with finite size scaling, enable an accurate determination of the unmixing binodal. Our results show that the critical behavior of the confined mixture is described by ``effective'' critical exponents, which gradually develop from values near those of the two-dimensional Ising model, to those of the three-dimensional Ising model, as $D$ increases. The scaling predictions of Fisher and Nakanishi [J. Chem. Phys. 75, 5875 (1981)] for the shift of the critical point are compatible with our simulation results. Surprisingly, however, the colloid packing fraction at criticality approaches its bulk ($D \to \infty$) value non-monotonically, as $D$ is increased. Far from the critical point, our results are compatible with the simple Kelvin equation, implying a shift of order 1/D in the coexistence colloid chemical potential. We also present density profiles and pair distribution functions for a number of state points on the binodal, and the influence of the colloid-wall interaction is studied.

cond-mat.soft↗

arXiv2006

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

Molecular Dynamics simulations of a coarse-grained bead-spring model of flexible macromolecules tethered with one end to the surface of a cylindrical pore are presented. Chain length $N$ and grafting density $σ$ are varied over a wide range and the crossover from ``mushroom'' to ``brush'' behavior is studied for three pore diameters. The monomer density profile and the distribution of the free chain ends are computed and compared to the corresponding model of polymer brushes at flat substrates. It is found that there exists a regime of $N$ and $σ$ for large enough pore diameter where the brush height in the pore exceeds the brush height on the flat substrate, while for large enough $N$ and $σ$ (and small enough pore diameters) the opposite behavior occurs, i.e. the brush is compressed by confinement. These findings are used to discuss the corresponding theories on polymer brushes at concave substrates.

cond-mat.soft↗

arXiv2006

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

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

cond-mat.stat-mech↗

arXiv2006

Static and Dynamic Critical Behavior of a Symmetrical Binary Fluid: A Computer Simulation

A symmetrical binary, A+B Lennard-Jones mixture is studied by a combination of semi-grandcanonical Monte Carlo (SGMC) and Molecular Dynamics (MD) methods near a liquid-liquid critical temperature $T_c$. Choosing equal chemical potentials for the two species, the SGMC switches identities (${\rm A} \to {\rm B} \to {\rm A}$) to generate well-equilibrated configurations of the system on the coexistence curve for $T T_c$. A finite-size scaling analysis of the concentration susceptibility above $T_c$ and of the order parameter below $T_c$ is performed, varying the number of particles from N=400 to 12800. The data are fully compatible with the expected critical exponents of the three-dimensional Ising universality class. The equilibrium configurations from the SGMC runs are used as initial states for microcanonical MD runs, from which transport coefficients are extracted. Self-diffusion coefficients are obtained from the Einstein relation, while the interdiffusion coefficient and the shear viscosity are estimated from Green-Kubo expressions. As expected, the self-diffusion constant does not display a detectable critical anomaly. With appropriate finite-size scaling analysis, we show that the simulation data for the shear viscosity and the mutual diffusion constant are quite consistent both with the theoretically predicted behavior, including the critical exponents and amplitudes, and with the most accurate experimental evidence.

cond-mat.stat-mech↗

arXiv2006

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

Local pressures are important in the calculation of interface tensions and in analyzing micromechanical behavior. The calculation of local pressures in computer simulations has been limited to systems with pairwise interactions between the particles, which is not sufficient for chemically detailed systems with many-body potentials such as angles and torsions. We introduce a method to calculate local pressures in systems with n-body interactions (n=2,3,4, . . .) based on a micromechanical definition of the pressure tensor. The local pressure consists of a kinetic contribution from the linear momentum of the particles and an internal contribution from dissected many-body interactions by infinitesimal areas. To define dissection by a small area, respective n-body interactions are divided into two geometric centers, effectively reducing them to two-body interactions. Consistency with hydrodynamics-derived formulas for systems with two-body interactions (J. H. Irving and J. G. Kirkwood, J. Chem. Phys. 18, 817 (1950)), for average cross-sectional pressures (B. D. Todd, D. J. Evans, and P. J. Daivis, Phys. Rev. E 52, 1627 (1995)), and for volume averaged pressures (virial formula) is shown. As a simple numerical example, we discuss liquid propane in a cubic box. Local, crosssectional,and volume-averaged pressures as well as relative contributions from two-body and three-body forces are analyzed with the proposed method, showing full numerical equivalence with the existing approaches. The method allows computing local pressures in the presence of many-body interactions in atomistic simulations of complex materials and biological systems.

cond-mat.stat-mech↗

arXiv2006

Spinodal Decomposition in Thin Films: Molecular Dynamics Simulations of a Binary Lennard-Jones Fluid Mixture

We use molecular dynamics (MD) to simulate an unstable homogeneous mixture of binary fluids (AB), confined in a slit pore of width $D$. The pore walls are assumed to be flat and structureless, and attract one component of the mixture (A) with the same strength. The pair-wise interactions between the particles is modeled by the Lennard-Jones potential, with symmetric parameters that lead to a miscibility gap in the bulk. In the thin-film geometry, an interesting interplay occurs between surface enrichment and phase separation. We study the evolution of a mixture with equal amounts of A and B, which is rendered unstable by a temperature quench. We find that A-rich surface enrichment layers form quickly during the early stages of the evolution, causing a depletion of A in the inner regions of the film. These surface-directed concentration profiles propagate from the walls towards the center of the film, resulting in a transient layered structure. This layered state breaks up into a columnar state, which is characterized by the lateral coarsening of cylindrical domains. The qualitative features of this process resemble results from previous studies of diffusive Ginzburg-Landau-type models [S.~K. Das, S. Puri, J. Horbach, and K. Binder, Phys. Rev. E {\bf 72}, 061603 (2005)], but quantitative aspects differ markedly. The relation to spinodal decomposition in a strictly 2-$d$ geometry is also discussed.

cond-mat.dis-nn↗

arXiv2005

Static and dynamic properties of the interface between a polymer brush and a melt of identical chains

Molecular dynamics simulations of a short-chain polymer melt between two brush-covered surfaces under shear have been performed. The end-grafted polymers which constitute the brush have the same chemical properties as the free chains in the melt and provide a soft deformable substrate. Polymer chains are described by a coarse-grained bead-spring model with Lennard-Jones interactions between the beads and a FENE potential between nearest neighbors along the backbone of the chains. The grafting density of the brush layer offers a way of controlling the behavior of the surface without altering the molecular interactions. We perform equilibrium and non-equilibrium Molecular Dynamics simulations at constant temperature and volume using the Dissipative Particle Dynamics thermostat. The equilibrium density profiles and the behavior under shear are studied as well as the interdigitation of the melt into the brush, the orientation on different length scales (bond vectors, radius of gyration, and end-to-end vector) of free and grafted chains, and velocity profiles. The viscosity and slippage at the interface are calculated as functions of grafting density and shear velocity.

cond-mat.soft↗

arXiv2005

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

The structure and transport properties of SiO2-Al2O3 melts containing 13 mol% and 47 mol% Al2O3 are investigated by means of large scale molecular dynamics computer simulations. The interactions between the atoms are modelled by a pair potential which is a modified version of the one proposed by Kramer et al. [J. Am. Chem. Soc. 64, 6435 (1991)]. Fully equilibrated melts in the temperature range 6000 K >= T > 2000 K are considered as well as glass configurations, that were obtained by a rapid quench from the lowest melt temperatures. Each system is simulated at two different densities in order to study the effect of pressure on structural and dynamic properties. We find that the Al atoms are, like the Si atoms, mainly four-fold coordinated by oxygen. However, the packing of the AlO4 tetrahedra is very different from that of the SiO4 tetrahedra, which is reflected by the presence of triclusters (O atoms surrounded by three cations) and edge--sharing AlO4 tetrahedra. On larger length scales, a micro-segregation occurs, resulting in an Al-rich network percolating through the Si-O network. This is reflected in a prepeak of concentration-concentration structure factors around 0.5 A^-1 (both in the system with 47 mol% and 13 mol% Al2O3!). We also address the interplay between structure and mass transport. To this end, the behavior of the selfdiffusion constants for the different compositions and densities is studied.

cond-mat.dis-nn↗

arXiv2005

Kinetics of Phase Separation in Thin Films: Simulations for the Diffusive Case

We study the diffusion-driven kinetics of phase separation of a symmetric binary mixture (AB), confined in a thin-film geometry between two parallel walls. We consider cases where (a) both walls preferentially attract the same component (A), and (b) one wall attracts A and the other wall attracts B (with the same strength). We focus on the interplay of phase separation and wetting at the walls, which is referred to as {\it surface-directed spinodal decomposition} (SDSD). The formation of SDSD waves at the two surfaces, with wave-vectors oriented perpendicular to them, often results in a metastable layered state (also referred to as ``stratified morphology''). This state is reminiscent of the situation where the thin film is still in the one-phase region but the surfaces are completely wet, and hence coated with thick wetting layers. This metastable state decays by spinodal fluctuations and crosses over to an asymptotic growth regime characterized by the lateral coarsening of pancake-like domains. These pancakes may or may not be coated by precursors of wetting layers. We use Langevin simulations to study this crossover and the growth kinetics in the asymptotic coarsening regime.

cond-mat.soft↗

arXiv2005

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

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

cond-mat.dis-nn↗

arXiv2004

The bulk viscosity of a symmetrical Lennard--Jones mixture above and at liquid--liquid coexistence: A computer simulation study

A Lennard--Jones model of a binary dense liquid (A,B) with a symmetrical miscibility gap is investigated by means of computer simulation methods. Semigrand--canonical Monte Carlo simulations yield the phase diagram in the $T$--$x$ plane ($T$: temperature, $x$: concentration of A or B particles) as well as equilibrated configurations at coexistence. Then Molecular Dynamics simulations use these configurations to determine static properties (isothermal compressibility $κ_T$ and concentration susceptibility $χ$) as well as the shear and the bulk viscosity $η_{\rm s}$ and $η_{\rm B}$, respectively. The latter quantities are calculated along a path approaching the coexistence line from high temperatures in the one--phase region and ending at a state at the coexistence line about 15% below the critical point. We find that $κ_T$ and $χ$ increase significantly near the coexistence line reflecting the vicinity of the critical point. Whereas $η_{\rm s}$ exhibits a weak temperature dependence, $η_{\rm B}$ increases significantly near the coexistence curve.

cond-mat.stat-mech↗

arXiv2003

Analysis of the Phase Transitions in Alkyl- Mica by Density and Pressure Profiles

In a previous work [H. Heinz, H. J. Castelijns, U. W. Suter, J. Am. Chem. Soc. 115, 9500 (2003)], we developed an accurate force field and simulated the phase transitions in C18-mica (octadecyltrimethylammonium-mica) as well as the absence of such transitions in 2C18-mica (dioctadecyldimethylammonium-mica) between room temperature and 100 deg C. Here we analyze (i) average z coordinates of the carbon atoms and interdigitation of the hydrocarbon bilayers, (ii) density profiles and (iii) pressure profiles of the structures along all Cartesian axes. In C18-mica, the standard deviation in the z coordinate for the chain atoms is high and more than doubles in the disordered phase. The order-disorder transition is accompanied by a change in the orientation of the ammonium headgroup, as well as decreasing tensile and shear stress in the disordered phase. In 2C18-mica, the standard deviation in the z coordinate for the chain atoms is low and does not increase remarkably on heating. The backbones display a highly regular structure, which is slightly obscured by rotations in the C18 backbones and minor headgroup displacements at 100 deg C. Close contacts between the bulky headgroups with sidearms cause significant local pressure which is in part not relieved at 100 deg C. An increase of the basal-plane spacing at higher temperature is found in both systems due to larger separation between the two hydrocarbon layers and an increased z spacing between adjacent chain atoms (=decreased tilt of the chains relative to the surface normal), and, in C18-mica only, a stronger upward orientation of the C18 chain at the ammonium headgroup. The likelihood for chain interdigitation between the two hydrocarbon layers is 0.24 to 0.30 for C18-mica,and 0.65 to 0.26 for 2C18-mica (for 20 deg C to 100 deg C).

cond-mat.soft↗

arXiv2003

The relaxation dynamics of a supercooled liquid confined by rough walls

We present the results of molecular dynamics computer simulations of a binary Lennard-Jones liquid confined between two parallel rough walls. These walls are realized by frozen amorphous configurations of the same liquid and therefore the structural properties of the confined fluid are identical to the ones of the bulk system. Hence this setup allows us to study how the relaxation dynamics is affected by the pure effect of confinement, i.e. if structural changes are completely avoided. We find that the local relaxation dynamics is a strong function of z, the distance of the particles from the wall, and that close to the surface the typical relaxation times are orders of magnitude larger than the ones in the bulk. Because of the cooperative nature of the particle dynamics, the slow dynamics also affects the dynamics of the particles for large values of z. Using various empirical laws, we are able to parameterize accurately the z-dependence of the generalized incoherent intermediate scattering function F_s(q,z,t) and also the spatial dependence of structural relaxation times. These laws allow us to determine various dynamical length scales and we find that their temperature dependence is compatible with an Arrhenius law. Furthermore, we find that at low temperatures time and space dependent correlation function fulfill a generalized factorization property similar to the one predicted by mode-coupling theory for bulk systems. For thin films and/or at sufficiently low temperatures, we find that the relaxation dynamics is influenced by the two walls in a strongly non-linear way in that the slowing down is much stronger than the one expected from the presence of only one confining wall. ....

cond-mat↗

arXiv2003

Amorphous silica at surfaces and interfaces: simulation studies

The structure of surfaces and interfaces of silica (SiO2) is investigated by large scale molecular dynamics computer simulations. In the case of a free silica surface, the results of a classical molecular dynamics simulation are compared to those of an ab initio method, the Car-Parrinello molecular dynamics. This comparative study allows to check the accuracy of the model potential that underlies the classical simulation. By means of a pure classical MD, the interface between amorphous and crystalline SiO2 is investigated, and as a third example the structure of a silica melt between walls is studied in equilibrium and under shear. We show that in the latter three examples important structural information such as ring size distributions can be gained from the computer simulation that is not accessible in experiments.

cond-mat.dis-nn↗

arXiv2003

Molecular Dynamics Simulations

A tutorial introduction to the technique of Molecular Dynamics (MD) is given, and some characteristic examples of applications are described. The purpose and scope of these simulations and the relation to other simulation methods is discussed, and the basic MD algorithms are described. The sampling of intensive variables (temperature T, pressure p) in runs carried out in the microcanonical (NVE) ensemble (N= particle number, V = volume, E = energy) is discussed, as well as the realization of other ensembles (e.g. the NVT ensemble). For a typical application example, molten SiO2, the estimation of various transport coefficients (self-diffusion constants, viscosity, thermal conductivity) is discussed. As an example of Non-Equilibrium Molecular Dynamics (NEMD), a study of a glass-forming polymer melt under shear is mentioned.

cond-mat.dis-nn↗

arXiv2003

Structure and diffusion in amorphous aluminium silicate: A molecular dynamics computer simulation

The amorphous aluminium silicate (Al2O3)2(SiO2) [AS2] is investigated by means of large scale molecular dynamics computer simulations. We consider fully equilibrated melts in the temperature range 6100K >= T >= 2300K as well as glass configurations that were obtained from cooling runs from T=2300K to 300K with a cooling rate of about 10^12K/s. Already at temperatures as high as 4000K, most of the Al and Si atoms are four-fold coordinated by oxygen atoms. Thus, the structure of AS2 is that of a disordered tetrahedral network. The packing of AlO4 tetrahedra is very different from that of SiO4 tetrahedra in that Al is involved with a relatively high probability in small-membered rings and in triclusters in which an O atom is surrounded by four cations. We find as typical configurations two-membered rings with two Al atoms in which the shared O atoms form a tricluster. On larger length scales, the system shows a microphase separation in which the Al-rich network structure percolates through the SiO2 network. The latter structure gives rise to a prepeak in the static structure factor at a wavenumber q=0.5Å^{-1}. The comparison of experimental X-ray data with the results from the simulation shows a good agreement for the structure function. The diffusion dynamics in AS2 is found to be much faster than in SiO2. We show that the self-diffusion constants for O and Al are very similar and that they are by a factor of 2-3 larger than the one for Si.

cond-mat.stat-mech↗

arXiv2003

Interplay between wetting and phase behavior in binary polymer films and wedges: Monte Carlo simulations and mean field calculations

We study the interplay between wetting and miscibility of a symmetric polymer mixture via MC simulations and SCF calculations. The film surfaces interact with the monomers via short ranged potentials and the wetting transition is of first order. If both surfaces in a film attract the same component, capillary condensation occurs and the critical point is close to the critical point of the bulk. If surfaces attract different components, an interface localization occurs which gives rise to phase diagrams with two critical points in the vicinity of the pre-wetting critical point. The crossover between these two types of phase diagrams as a function of the surface field asymmetry is studied. We investigate the dependence of the phase diagram on the film thickness D for antisymmetric surface fields. Upon decreasing the film thickness the two critical points approach the symmetry axis of the phase diagram, and below a certain thickness D_tri there remains only a single critical point at symmetric composition. This corresponds to a second order interface localisation transition even though the wetting transition is of first order. At a specific film thickness, D_tri, tricritical behavior is found. The behavior of antisymmetric films is compared with the phase behavior in an antisymmetric double wedge. While the former is the analogon of the wetting transition of a planar surface, the latter is the analogon of the filling behavior of a single wedge. We present evidence for a second order interface localization transition in an antisymmetric double wedge and relate its unconventional critical behavior to the predictions of Parry et al. PRL 83 5535 (1999) for wedge filling. The critical behavior differs from the Ising universality class and is characterized by strong anisotropic fluctuations.

cond-mat.soft↗

arXiv2003

Transport phenomena and microscopic structure in partially miscible binary fluids: A simulation study of the symmetrical Lennard-Jones mixture

Static and dynamic structure factors and various transport coefficients are computed for a Lennard-Jones model of a binary fluid (A,B) with a symmetrical miscibility gap, varying both temperature and relative concentration of the mixture. The model is first equilibrated by a semi-grandcanonical Monte Carlo method, choosing the temperature and chemical potential difference $Δμ$ between the two species as the given independent variables. Varying for $Δμ=0$ the temperature and particle number $N$ over a wide range, the location of the coexistence curve in the thermodynamic limit is estimated. Well-equilibrated configurations from these Monte Carlo runs are used as initial states for microcanonical Molecular Dynamics runs, in order to study the microscopic structure and the behavior of transport coefficients as well as dynamic correlation functions along the coexistence curve. Dynamic structure factors $S_{αβ} (q,t)$ (and the corresponding static functions $S_{αβ} (q)$) are recorded ($α, β, \in$ A,B), $q$ being the wavenumber and $t$ the time, as well as the mean square displacements of the particles (to obtain the self-diffusion constants $D_{\rm A}$, $D_{\rm B}$) and transport coefficients describing collective transport, such as the interdiffusion constant and the shear viscosity. The minority species is found to diffuse a bit faster than the majority species. Despite the presence of strong concentration fluctuations in the system the Stokes-Einstein relation is a reasonable approximation.

cond-mat.stat-mech↗