Adsorption of binary mixtures on two-dimensional surfaces: theory and Monte Carlo simulations

The adsorption of binary mixtures on square lattices is studied by combining theoretical modeling and Monte Carlo (MC) simulations in grand canonical ensemble. The adsorption thermodynamics is analyzed through the total and partial isotherms. Two theoretical models have been used in the present study: (i) the first, which we called cluster approximation (CA), is based on exact calculations of configurations on finite cells. An efficient algorithm allows us to calculate the detailed structure of the configuration space for \(m = l \times l \) cells; and (ii) the second is a generalization of the classical quasi-chemical approximation (QCA) in which the adsorbate is a binary mixture of species \(a\) and \(b\) . Adsorbate–adsorbate lateral interactions are incorporated in the context of the two mentioned approximations. Results from CA and QCA are compared with MC simulations. Close agreement between simulated and theoretical data supports the validity of the theoretical models to describe the adsorption of mixed gases on two-dimensional surfaces.     

Monte Carlo simulations of the solution structure of simple alcohols in water-acetonitrile mixtures

Monte Carlo simulations have been performed to explore the solution structure of ethyl, isopropyl, isobutyl, and tertiary butyl alcohols in pure water, pure acetonitrile, and different mixtures of the two solvents. The explicit solvent studies in NpT ensembles at T = 298 K illustrate that the solute "discriminates" the solvent's components and that the composition of the first solvation shell differs from that of the bulk solution. Since the polarizable continuum dielectric method (PCM) does not presently model the solvation of molecules with both polar and apolar sites in mixed protic solvents, we suggest a direction for further program development wherein a continuum dielectric method would accept more than one solvent and the solute sites would be solvated by user-defined solvent components. The prevailing solvation model will be determined upon the lowest free energy calculated for a particular solvation pattern of the solute having a specific conformational/tautomeric state. Characterization of equilibrium hydrogen-bond formation becomes a complicated problem that depends on the chemical properties of the solute and its conformation, as well as upon the varying nature of the first solvation shell. For example, while the number of hydrogen bonds to secondary and tertiary alcohol solutes are nearly constant in pure water and in water-acetonitrile mixtures with at least 50% water content, the number of hydrogen bonds to primary alcohols gradually decreases for most of their conformations when acetonitrile content is increased. Nonetheless, the calculations indicate that O-H...O(water) hydrogen bonds are still possible in a small fraction of the arrangements for the solution models with water content of 30% or less. The isopentene solute does not form any observable hydrogen bonds, despite having an electron-rich, double-bond site.     

A metropolis Monte Carlo method for computing microcanonical statistical rate constants

A new method of computing microcanonical statistical rate constants is presented. The method utilizes the Metropolis Monte Carlo algorithm in a manner which circumvents some of the numerical inefficiency associated with other Metropolis and “shot-gun” Monte Carlo based schemes. It is therefore expected to be useful in studies of many degree of freedom systems where numerical efficiency is crucial. Optimization of the method efficiency with respect to its adjustable parameters is examined in detail, both theoretically and in a numerical study of the T-shaped Ar₃ “inversion” process. The energy dependence of the T-shaped Ar₃ inversion rate is studied in a sample application of the method. An application to full three dimensional Ar₃ will be presented in a future study.     

Structure of the liquid-vapor interface of water-methanol mixtures as seen from Monte Carlo simulations

Monte Carlo simulation of the vapor-liquid interface of water-methanol mixtures of different compositions, ranging from pure water to pure methanol, have been performed on the canonical (N, V, T) ensemble at 298 K. The analysis of the systems simulated has revealed that the interface is characterized by a double layer structure: methanol is strongly adsorbed at the vapor side of the interface, whereas this adsorption layer is followed at its liquid side by a depletion layer of methanol of lower concentration than in the bulk liquid phase of the system. The dominant feature of the interface has been found to be the adsorption layer in systems of methanol mole fractions below 0.2, and the depletion layer in systems of methanol mole fractions between 0.25 and 0.5. The orientation of the molecules located at the depletion layer is found to be already uncorrelated with the interface, whereas the methanol molecules of the adsorption layer prefer to align perpendicular to the interface, pointing straight toward the vapor phase by their methyl group. Although both the preference of the molecular plane for a perpendicular alignment with the interface and the preference of the methyl group for pointing straight to the vapor phase are found to be rather weak, the preference of the methyl group for pointing as straight toward the vapor phase as possible within the constraint imposed by the orientation of the molecular plane is found to be fairly strong. One of the two preferred orientations of the interfacial water molecules present in the neat system is found to disappear in the presence of methanol, because methanol molecules aligned in their preferred orientation can replace these water molecules in the hydrogen-bonding pattern of the interface.     

Parallel Markov chain Monte Carlo simulations

With strict detailed balance, parallel Monte Carlo simulation through domain decomposition cannot be validated with conventional Markov chain theory, which describes an intrinsically serial stochastic process. In this work, the parallel version of Markov chain theory and its role in accelerating Monte Carlo simulations via cluster computing is explored. It is shown that sequential updating is the key to improving efficiency in parallel simulations through domain decomposition. A parallel scheme is proposed to reduce interprocessor communication or synchronization, which slows down parallel simulation with increasing number of processors. Parallel simulation results for the two-dimensional lattice gas model show substantial reduction of simulation time for systems of moderate and large size.     

Reactive Monte Carlo and grand-canonical Monte Carlo simulations of the propene metathesis reaction system

The influence of silicalite-1 pores on the reaction equilibria and the selectivity of the propene metathesis reaction system in the temperature range between 300 and 600 K and the pressure range from 0.5 to 7 bars has been investigated with molecular simulations. The reactive Monte Carlo (RxMC) technique was applied for bulk-phase simulations in the isobaric-isothermal ensemble and for two phase systems in the Gibbs ensemble. Additionally, Monte Carlo simulations in the grand-canonical ensemble (GCMC) have been carried out with and without using the RxMC technique. The various simulation procedures were combined with the configurational-bias Monte Carlo approach. It was found that the GCMC simulations are superior to the Gibbs ensemble simulations for reactions where the bulk-phase equilibrium can be calculated in advance and does not have to be simulated simultaneously with the molecules inside the pore. The confined environment can increase the conversion significantly. A large change in selectivity between the bulk phase and the pore phase is observed. Pressure and temperature have strong influences on both conversion and selectivity. At low pressure and temperature both conversion and selectivity have the highest values. The effect of confinement decreases as the temperature increases.     

Monte Carlo simulations of vapor–liquid–liquid equilibrium of some ternary petrochemical mixtures

The aim of this study was to determine the capability and accuracy of Monte Carlo simulations to predict ternary vapor–liquid–liquid equilibrium (VLLE) for some industrial systems. Hence, Gibbs ensemble Monte Carlo simulations in the isobaric–isothermal (NpT) and isochoric–isothermal (NVT) ensembles were performed to determine vapor–liquid–liquid equilibrium state points for three ternary petrochemical mixtures: methane/n-heptane/water (1), n-butane/1-butene/water (2) and n-hexane/ethanol/water (3). Since mixture (1) exhibits a high degree of mutual insolubility amongst its components, and hence has a large three-phase composition region, simulations in the NpT ensemble were successful in yielding three distinct and stable phases at equilibrium. The results were in very good agreement with experimental data at 120 kPa, but minor deviations were observed at 2000 kPa. Obtaining three phases for mixture (2) with the NpT ensemble is very difficult since it has an extremely narrow three-phase region at equilibrium, and hence the NVT ensemble was used to simulate this mixture. The simulated results were, once again, in excellent agreement with experimental data. We succeeded in obtaining three-phase equilibrium in the NpT ensemble only after knowing, a priori, the correct three-phase pressure (corresponding to the force fields that were implemented) from NVT simulations. The success of the NVT simulation, compared to NpT, is due to the fact that the total volume can spontaneously partition itself favorably amongst the three boxes and only one intensive variable (T) is fixed, whereas the pressure and the temperature are fixed in an NpT simulation. NpT simulations yielded three distinct phases for mixture (3), but quantitative agreement with experimental data was obtained at very low ethanol concentrations only.     

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

Large scale Monte Carlo investigations of the interface between A-rich and B-rich phases of symmetric binary (AB) polymer mixtures are presented, using the bond fluctuation model of flexible chains with N_A=N_B=N=32 effective monomers. The temperature range studied, 0.144<T/T_c0.759, includes both the strong and the weak segregation limit. Interfacial free energy and interfacial structure are studied, and compared to predictions based on the selfconsistent field theory. Also the broadening of the interfacial width due to capillary waves is considered, and finite size effects due to the confinement of interfaces in thin films of polymer blends are discussed.     

Three-dimensional modeling of EXAFS spectral mixtures by combining Monte Carlo simulations and target transformation factor analysis

We have developed a new method for the three-dimensional modeling of extended X-ray absorption fine structure (EXAFS) spectra which enables the extraction of the local structure of aqueous metal complexes from spectral mixtures of several components. The new method combines two techniques: Monte Carlo simulation and target transformation factor analysis (TFA). Monte Carlo simulation is used to create random arrangements between the X-ray absorbing metal ion and the ligand atoms, and to calculate the theoretical EXAFS spectrum of each arrangement. The theoretical EXAFS spectrum is then introduced as test spectrum in the TFA procedure, to test whether or not the test spectrum is likely to be a component of the spectral mixtures. This coupled procedure is repeated until the error in the test spectrum is minimized. The new method can thus be used to isolate and refine the structure of complexes from spectral mixtures and to determine their relative concentrations, solely on the basis of an estimate of a ligand structure. The performance of the proposed method is validated using uranium Liii-edge EXAFS spectra of binary mixtures of two uranium(VI) 3,4-dihydroxybenzoic acid complexes.     

Monte Carlo simulations of low background detectors

An implementation of the Electron Gamma Shower 4 code (EGS4) has been developed to allow convenient simulation of typical gamma ray measurement systems. Coincidence gamma rays, beta spectra, and angular correlations have been added to adequately simulate a complete nuclear decay and provide corrections to experimentally determined detector efficiencies. This code has been used to strip certain low-background spectra for the purpose of extremely low-level assay. Monte Carlo calculations of this sort can be extremely successful since low background detectors are usually free of significant contributions from poorly localized radiation sources, such as cosmic muons, secondary cosmic neutrons, and radioactive construction or shielding materials. Previously, validation of this code has been obtained from a series of comparisons between measurements and blind calculations. An example of the application of this code to an exceedingly low background spectrum stripping will be presented.Pacific Northwest Laboratory is operated by Battelle Memorial Institute for the US Department of Energy under Contract DE-AC06-76RLO 1830.     

Dynamic Monte Carlo simulations of anisotropic colloids

We put forward a simple procedure for extracting dynamical information from Monte Carlo simulations, by appropriate matching of the short-time diffusion tensor with its infinite-dilution limit counterpart, which is supposed to be known. This approach - discarding hydrodynamics interactions - first allows us to improve the efficiency of previous dynamic Monte Carlo algorithms for spherical Brownian particles. In the second step, we address the case of anisotropic colloids with orientational degrees of freedom. As an illustration, we present a detailed study of the dynamics of thin platelets, with emphasis on long-time diffusion and orientational correlations.     

Thermodynamic properties of van der Waals fluids from Monte Carlo simulations and perturbative Monte Carlo theory

Computer simulations have been performed for fluids with van der Waals potential, that is, hard spheres with attractive inverse power tails, to determine the equation of state and the excess energy. On the other hand, the first- and second-order perturbative contributions to the energy and the zero- and first-order perturbative contributions to the compressibility factor have been determined too from Monte Carlo simulations performed on the reference hard-sphere system. The aim was to test the reliability of this "exact" perturbation theory. It has been found that the results obtained from the Monte Carlo perturbation theory for these two thermodynamic properties agree well with the direct Monte Carlo simulations. Moreover, it has been found that results from the Barker-Henderson [J. Chem. Phys. 47, 2856 (1967)] perturbation theory are in good agreement with those from the exact perturbation theory.     

Titration of hydrophobic polyelectrolytes using Monte Carlo simulations

The conformation and titration curves of weak (or annealed) hydrophobic polyelectrolytes have been examined using Monte Carlo simulations with screened Coulomb potentials in the grand canonical ensemble. The influence of the ionic concentration pH and presence of hydrophobic interactions has been systematically investigated. A large number of conformations such as extended, pearl-necklace, cigar-shape, and collapsed structures resulting from the subtle balance of short-range hydrophobic attractive interactions and long-range electrostatic repulsive interactions between the monomers have been observed. Titration curves were calculated by adjusting the pH-pK(0) values (pK(0) represents the intrinsic dissociation constant of an isolated monomer) and then calculating the ionization degree alpha of the polyelectrolyte. Important transitions related to cascades of conformational changes were observed in the titration curves, mainly at low ionic concentration and with the presence of strong hydrophobic interactions. We demonstrated that the presence of hydrophobic interactions plays an important role in the acid-base properties of a polyelectrolyte in promoting the formation of compact conformations and hence decreasing the polyelectrolyte degree of ionization for a given pH-pK(0) value.     

Efficient Monte Carlo trial moves for polypeptide simulations

A new move set for the Monte Carlo simulations of polypeptide chains is introduced. It consists of a rigid rotation along the (C(alpha)) ends of an arbitrary long segment of the backbone in such a way that the atoms outside this segment remain fixed. This fixed end move, or FEM, alters only the backbone dihedral angles phi and psi and the C(alpha) bond angles of the segment ends. Rotations are restricted to those who keep the alpha bond angles within their maximum natural range of approximately +/-10 degrees. The equations for the angular intervals (tau) of the allowed rigid rotations and the equations required for satisfying the detailed balance condition are presented in detail. One appealing property of the FEM is that the required number of calculations is minimal, as it is evident from the simplicity of the equations. In addition, the moving backbone atoms undergo considerable but limited displacements of up to 3 A. These properties, combined with the small number of backbone angles changed, lead to high acceptance rates for the new conformations and make the algorithm very efficient for sampling the conformational space. The FEMs, combined with pivot moves, are used in a test to fold a group of coarse-grained proteins with lengths of up to 200 residues.     

Kinetic Monte Carlo simulations of nucleation and growth in electrodeposition

Nucleation and growth during bulk electrodeposition is studied using kinetic Monte Carlo (KMC) simulations. Ion transport in solution is modeled using Brownian dynamics, and the kinetics of nucleation and growth are dependent on the probabilities of metal-on-substrate and metal-on-metal deposition. Using this approach, we make no assumptions about the nucleation rate, island density, or island distribution. The influence of the attachment probabilities and concentration on the time-dependent island density and current transients is reported. Various models have been assessed by recovering the nucleation rate and island density from the current-time transients.     

Equilibrium states of self-assembly systems: Monte Carlo simulations

We investigated the equilibrium states of the self-assembly of amphiphilic molecules in water. The amphiphiles are represented by chains of the type H1T4, where H is the hydrophilic part of the molecule and T is its hydrophobic portion formed by four monomers. We have performed Monte Carlo simulations on a two-dimensional lattice, in which each water molecule occupies a single site, and the amphiphiles occupy five sites of the lattice. We have determined the aggregate distribution curves for the system at low concentration and fixed temperature. We have shown that the criterion to determine the equilibrium states of the system, based on the stabilization of energy curves as a function of the simulation time, is not reliable. The best way to ensure that the equilibrium state was reached was to follow the route to equilibrium of all aggregate sizes of the system.     

Monte Carlo simulations of polymer dynamics: Recent advances

A brief review is given of applications of Monte Carlo simulations to study the dynamical properties of coarse-grained models of polymer melts, emphasizing the crossover from the Rouse model toward reptation, and the glass transition. The extent to which Monte Carlo algorithms can mimic the actual chain dynamics is critically examined, and the need for the use of coarse-grained rather than fully atomistic models for such simulations is explained. It is shown that various lattice and continuum models yield qualitatively similar results, and the behavior agrees with the findings of corresponding molecular dynamics simulations and experiments, where available. It is argued that these simulations significantly enhance our understanding of the theoretical concepts on the dynamics of dense macromolecular systems. © 1997 John Wiley & Sons, Inc.