Thermodynamics and partitioning of homopolymers into a slit-A grand canonical Monte Carlo simulation study

Grand canonical ensemble Monte Carlo simulation (GCMC) combined with the histogram reweighting technique was used to study the thermodynamic equilibrium of a homopolymer solution between a bulk and a slit pore. GCMC gives the partition coefficients that agree with those from canonical ensemble Monte Carlo simulations in a twin box, and it also gives results that are not accessible through the regular canonical ensemble simulation such as the osmotic pressure of the solution. In a bulk polymer solution, the calculated osmotic pressure agrees very well with the scaling theory predictions both for the athermal polymer solution and the theta solution. However, one cannot obtain the osmotic pressure of the confined solution in the same way since the osmotic pressure of the confined solution is anisotropic. The chemical potentials in GCMC simulations were found to differ by a translational term from the chemical potentials obtained from canonical ensemble Monte Carlo simulations with the chain insertion method. This confirms the equilibrium condition of a polymer solution partition between the bulk and a slit pore: the chemical potentials of the polymer chain including the translational term are equal at equilibrium. The histogram reweighting method enables us to obtain the partition coefficients in the whole range of concentrations based on a limited set of simulations. Those predicted bulk-pore partition coefficient data enable us to perform further theoretical analysis. Scaling predictions of the partition coefficient at different regimes were given and were confirmed by the simulation data.     

Combining reactive and configurational-bias Monte Carlo: confinement influence on the propene metathesis reaction system in various zeolites

In order to efficiently calculate chemical equilibria of large molecules in a confined environment the reactive Monte Carlo technique is combined with the configurational-bias Monte Carlo approach. To prove that detailed balance is fulfilled the acceptance rule for this combination of particular Monte Carlo techniques is derived in detail. Notably, by using this derivation all other acceptance rules of any Monte Carlo trial moves usually carried out in combination with the configurational-bias Monte Carlo approach can be deduced from it. As an application of the combination of reactive and configurational-bias Monte Carlo the influence of different zeolitic confinements (MFI, TON, LTL, and FER) on the reaction equilibrium and the selectivity of the propene metathesis reaction system was investigated. Compared to the bulk phase the conversion is increased significantly. The authors study this reaction system in the temperature range between 300 and 600 K, and the pressure range from 1 to 7 bars. In contrast to the bulk phase, pressure and temperature have a strong influence on the composition of the reaction mixture in confinement. At low pressures and temperatures both conversion and selectivity are highest. Furthermore, the equilibrium composition is strongly dependent on the type of zeolite. This demonstrates the important role of the host structure in catalytic systems.     

Monte Carlo simulation of equilibrium reactions at vapor-liquid interfaces

Chemical reactions are known to behave differently, depending upon their local environment. While the interactions with neighboring molecules may alter both the kinetics of chemical reactions and the overall equilibrium conversion, we have performed simulations of the latter. The particular environment that we address is the vapor-liquid interface, since only a few, limited studies have explored the influence of an interface on equilibrium reaction behavior. Simple dimerization reactions are modeled, as well as more complex multicomponent reactions, using the reactive Monte Carlo (RxMC) simulation technique. We find that the conversion of a reaction can be markedly different at an interface as compared to the bulk vapor and liquid phases, and these trends are analyzed with respect to specific intermolecular interactions. In conjunction, we calculate the surface tension of the reacting fluids at the interface, which is found to have unusual scaling behavior, with respect to the system temperature.     

Mesoscale simulation of polymer reaction equilibrium: combining dissipative particle dynamics with reaction ensemble Monte Carlo. I. Polydispersed polymer systems

We present a mesoscale simulation technique, called the reaction ensemble dissipative particle dynamics (RxDPD) method, for studying reaction equilibrium of polymer systems. The RxDPD method combines elements of dissipative particle dynamics (DPD) and reaction ensemble Monte Carlo (RxMC), allowing for the determination of both static and dynamical properties of a polymer system. The RxDPD method is demonstrated by considering several simple polydispersed homopolymer systems. RxDPD can be used to predict the polydispersity due to various effects, including solvents, additives, temperature, pressure, shear, and confinement. Extensions of the method to other polymer systems are straightforward, including grafted, cross-linked polymers, and block copolymers. To simulate polydispersity, the system contains full polymer chains and a single fractional polymer chain, i.e., a polymer chain with a single fractional DPD particle. The fractional particle is coupled to the system via a coupling parameter that varies between zero (no interaction between the fractional particle and the other particles in the system) and one (full interaction between the fractional particle and the other particles in the system). The time evolution of the system is governed by the DPD equations of motion, accompanied by changes in the coupling parameter. The coupling-parameter changes are either accepted with a probability derived from the grand canonical partition function or governed by an equation of motion derived from the extended Lagrangian. The coupling-parameter changes mimic forward and reverse reaction steps, as in RxMC simulations.     

Polymorphism in simple liquids: a Gibbs ensemble Monte Carlo study

We perform Gibbs ensemble Monte Carlo (GEMC) simulations of a one-component system of hard spheres with a repulsive shoulder and an attractive well. We show the existence of two distinct liquid-gas and liquid-liquid phase equilibria. The GEMC estimate of the critical parameters, as following from an interpolation of the binodal points, is only slightly influenced by finite size effects. The liquid-gas critical temperature and pressure are lower than those of the liquid-liquid phase separation. A discussion of our findings in comparison with those of previous numerical studies is also presented.     

Phase coexistence in heterogeneous porous media: a new extension to Gibbs ensemble Monte Carlo simulation method

The effect of confinement on phase behavior of simple fluids is still an area of intensive research. In between experiment and theory, molecular simulation is a powerful tool to study the effect of confinement in realistic porous materials, containing some disorder. Previous simulation works aiming at establishing the phase diagram of a confined Lennard-Jones-type fluid, concentrated on simple pore geometries (slits or cylinders). The development of the Gibbs ensemble Monte Carlo technique by Panagiotopoulos [Mol. Phys. 61, 813 (1987)], greatly favored the study of such simple geometries for two reasons. First, the technique is very efficient to calculate the phase diagram, since each run (at a given temperature) converges directly to an equilibrium between a gaslike and a liquidlike phase. Second, due to volume exchange procedure between the two phases, at least one invariant direction of space is required for applicability of this method, which is the case for slits or cylinders. Generally, the introduction of some disorder in such simple pores breaks the initial invariance in one of the space directions and prevents to work in the Gibbs ensemble. The simulation techniques for such disordered systems are numerous (grand canonical Monte Carlo, molecular dynamics, histogram reweighting, N-P-T+test method, Gibbs-Duhem integration procedure, etc.). However, the Gibbs ensemble technique, which gives directly the coexistence between phases, was never generalized to such systems. In this work, we focus on two weakly disordered pores for which a modified Gibbs ensemble Monte Carlo technique can be applied. One of the pores is geometrically undulated, whereas the second is cylindrical but presents a chemical variation which gives rise to a modulation of the wall potential. In the first case almost no change in the phase diagram is observed, whereas in the second strong modifications are reported.     

Chemical reaction equilibrium in nanoporous materials: NO dimerization reaction in carbon slit nanopores

We present a molecular-level simulation study of the effects of confinement on chemical reaction equilibrium in nanoporous materials. We use the reaction ensemble Monte Carlo (RxMC) method to investigate the effects of temperature, nanopore size, bulk pressure, and capillary condensation on the nitric oxide dimerization reaction in a model carbon slit nanopore in equilibrium with a bulk reservoir. In addition to the RxMC simulations, we also utilize the molecular-dynamics method to determine self-diffusion coefficients for confined nonreactive mixtures of nitric oxide monomers and dimers at compositions obtained from the RxMC simulations. We analyze the effects of the temperature, nanopore width, bulk pressure, and capillary condensation on the reaction equilibrium with respect to the reaction conversion, fluid structure, and self-diffusion coefficients. We show that the influence of the temperature, nanopore size, and capillary condensation on the confined reaction equilibrium is quite dramatic while the effect of the bulk pressure on the reaction equilibrium in the carbon slit nanopore is only moderate. This work is an extension of previous work by Turner et al. [J. Chem. Phys. 114, 1851 (2001)] on the confined reactive nitric oxide system.     

Monte Carlo adiabatic simulation of equilibrium reacting systems: The ammonia synthesis reaction

We present an application of the recently developed Monte Carlo method for simulations at fixed total enthalpy [W. R. Smith, M. Lísal, Phys. Rev. E 66 (2002) 01114-1–01114-3], combined with the reaction ensemble Monte Carlo method, for the direct prediction of equilibrium reactive adiabatic processes. For the industrially important ammonia synthesis reaction in an adiabatic plug-flow reactor, we perform direct simulations of the equilibrium reaction temperature and the composition of the exit stream as a function of the temperature and pressure of the inlet stream. The chemical species of the system are represented by all-atom potentials with interaction parameters taken from the literature. The accuracy of the molecular model is validated by comparing simulation results with experimental data. We also compare the simulation results with a macroscopic thermodynamic model based on the Soave–Redlich–Kwong equation of state. The simulation results for the reaction conversion show very good agreement with available experimental data over a wide range of temperatures and pressures, whereas the corresponding results from the macroscopic thermodynamic model slightly deteriorate with increasing pressure. Based on these comparisons, the predicted values of the reaction temperature and composition of the exit stream from the simulations are more accurate than the corresponding predicted values from the macroscopic thermodynamic model.     

Molecular simulations of confined liquids: an alternative to the grand canonical Monte Carlo simulations

Commonly, the confinement effects are studied from the grand canonical Monte Carlo (GCMC) simulations from the computation of the density of liquid in the confined phase. The GCMC modeling and chemical potential (μ) calculations are based on the insertion/deletion of the real and ghost particle, respectively. At high density, i.e., at high pressure or low temperature, the insertions fail from the Widom insertions while the performing methods as expanded method or perturbation approach are not efficient to treat the large and complex molecules. To overcome this problem we use a simple and efficient method to compute the liquid's density in the confined medium. This method does not require the precalculation of μ and is an alternative to the GCMC simulations. From the isothermal-isosurface-isobaric statistical ensemble we consider the explicit framework/liquid external interface to model an explicit liquid's reservoir. In this procedure only the liquid molecules undergo the volume changes while the volume of the framework is kept constant. Therefore, this method is described in the Np(n)AV(f)T statistical ensemble, where N is the number of particles, p(n) is the normal pressure, V(f) is the volume of framework, A is the surface of the solid/fluid interface, and T is the temperature. This approach is applied and validated from the computation of the density of the methanol and water confined in the mesoporous cylindrical silica nanopores and the MIL-53(Cr) metal organic framework type, respectively.     

Monte Carlo simulations of thermodynamic and structural properties of Mie(14,7) fluids

The vapor-liquid phase envelope of Mie(14,7) fluids is determined by the Gibbs ensemble Monte Carlo (MC) simulation technique. The NVT-MC simulation method is then utilized to compute the equation of state and the pair correlation function over a wide range of densities and temperatures. The effective diameters are calculated via the virial minimization method and the results are applied as the repulsion-attraction splitting distance within the generic van der Waals (GvdW) theory to compute the mean free volume. The density and temperature dependence of these parameters are studied and discussed. The results for the effective diameter, and the GvdW parameters are fitted to analytical functions of density and temperature. An examination of the results for the fluid phase equilibria of argon shows excellent agreement with empirical data for the densities of the coexisting phases, the vapor pressure, and the critical point. The computed free volumes are used to compute the diffusion coefficient of argon and the results are compared with experimental data.     

Effect of surface active sites on adsorption of associating chain molecules in pores: A Monte Carlo study

This work describes the adsorption behavior of associating and non-associating chains and their mixtures in pores with activated surfaces. The systems are studied using Gibbs ensemble Monte Carlo molecular simulations. Fluid molecules are modeled as freely jointed Lennard-Jones chains. Associating chains have, additionally, an associating square-well site placed in an end sphere. The pores are modeled as regular slit pores via an integrated Lennard-Jones potential (10-4-3); activation is achieved by placing specific association sites protruding from the surface. Two different solid-fluid interaction parameters are used, one of which corresponds roughly to alkanes on graphite, the other being a much weaker interaction. Adsorption isotherms are presented for several different cases: associating and non-associating chains confined within both neutral and activated walls. Mixtures of associating and non-associating chains are also considered. The effects of pore size, temperature and chain length are quantified. Selectivities obtained are in the range of those seen in adsorption experiments of alkane-alkanol mixtures.     

Structure and adsorption of a hard-core multi-Yukawa fluid confined in a slitlike pore: grand canonical Monte Carlo simulation and density functional study

Because of the increasing interest in studying the phenomenon exhibited by charge-stabilized colloidal suspensions in confining geometry, we present a density functional theory (DFT) for a hard-core multi-Yukawa fluid. The excess Helmholtz free-energy functional is constructed by using the modified fundamental measure theory and Rosenfeld's perturbative method, in which the bulk direct correlation function is obtained from the first-order mean spherical approximation. To validate the established theory, grand canonical ensemble Monte Carlo (GCMC) simulations are carried out to determine the density profiles and surface excesses of multi-Yukawa fluid in a slitlike pore. Comparisons of the theoretical results with the GCMC data suggest that the present DFT gives very accurate density profiles and surface excesses of multi-Yukawa fluid in the slitlike pore as well as the radial distribution functions of the bulk fluid. Both the DFT and the GCMC simulations predict the depletion of the multi-Yukawa fluid near a nonattractive wall, while the mean-field theory fails to describe this depletion in some cases. Because the simple form of the direct correlation function is used, the present DFT is computationally as efficient as the mean-field theory, but reproduces the simulation data much better than the mean-field theory.     

Monte Carlo simulation of polarizable systems: Early rejection scheme for improving the performance of adiabatic nuclear and electronic sampling Monte Carlo simulations

An early rejection scheme for trial moves in adiabatic nuclear and electronic sampling Monte Carlo simulation (ANES-MC) of polarizable intermolecular potential models is presented. The proposed algorithm is based on Swendsen–Wang filter functions for prediction of success or failure of trial moves in Monte Carlo simulations. The goal was to reduce the amount of calculations involved in ANES-MC electronic moves, by foreseeing the success of an attempt before making those moves. The new method was employed in Gibbs ensemble Monte Carlo (GEMC) simulations of the polarizable simple point charge-fluctuating charge (SPC-FQ) model of water. The overall improvement in GEMC depends on the number of swap attempts (transfer molecules between phases) in one Monte Carlo cycle. The proposed method allows this number to increase, enhancing the chemical potential equalization. For a system with 300 SPC-FQ water molecules, for example, the fractions of early rejected transfers were about 0.9998 and 0.9994 at 373 and 423 K, respectively. This means that the transfer moves consume only a very small part of the overall computing effort, making GEMC almost equivalent to a simulation in the canonical ensemble.     

芳香类化合物在ITQ-1分子筛中吸附特性的蒙特卡罗模拟

用巨正则统计系综蒙特卡罗模拟研究了苯、甲苯以及间二甲苯分子在ITQ-1分子筛中的吸附特性.从这3种分子的粒子分布云图上,可发现分子的扩散和吸附主要在十二元环超笼内发生,在十元环通道内的吸附和扩散则相对较难.从一系列不同压力下的蒙特卡罗模拟还预测了3种分子的吸附等温线,预测结果与实验结果相符.这3种分子在一定压力下,都可通过十元环通道或连接十二元环超笼的十元环窗口到达分子筛孔道内部,达到较好的吸附平衡状态.     

Monte Carlo simulation of equilibrium reactions at modified vapor-liquid interfaces

The equilibrium conversion of a chemical reaction is known to be affected by its local environment. Various factors may alter reaction equilibria, including shifts in pressure or temperature, solvation, adsorption within porous materials, or the presence of an interface. Previously, reactive Monte Carlo simulations have been used to predict the equilibrium behavior of chemical reactions at vapor-liquid interfaces. Here, a route is tested for tuning the interfacial conversion of a Lennard-Jones dimerization reaction by adding surfactants to the vapor-liquid interface. Several temperatures are explored as well as several different surfactant models. Even with the addition of a small concentration of surfactants, the simulations predict significant shifts in the conversion at the interface. In general, the shifts in the conversion tend to be related to the values of the interfacial tension.     

Partial molar volume and solvation structure of naphthalene in supercritical carbon dioxide: a Monte Carlo simulation study

Monte Carlo simulations were used to investigate the solvation of naphthalene in supercritical carbon dioxide at a temperature of 308.38 K just above the solvent's critical temperature and at pressures of 74.6, 79.7, 87.8, and 310.2 bar covering a range from just below to far above the solvent's critical pressure and at a slightly elevated temperature of 318.15 K and a pressure of 93.0 bar. The Monte Carlo simulations were carried out in the isobaric-isothermal ensemble and employed the transferable potentials for phase equilibria (TraPPE) force field. Systems containing 2000 carbon dioxide molecules and from 0 to 4 solute molecules were used for all five state points, and additional simulations with 16 000 solvent molecules were carried out at the lower temperature and p = 79.7 bar. In agreement with experiment, the simulations yield large, negative partial molar volumes of naphthalene near the critical pressure at 79.7 bar, with values of -4340 +/- 750 and -3400 +/- 620 cm(3) mol(-1) for the 2000 and 16 000 molecule systems, respectively. Structural analysis through radial distribution functions and the corresponding number integrals yields good agreement with neutron diffraction data and shows evidence for a long-range density enhancement around solutes but lacking any specific solute-solvent clustering. Solvatochromic shifts estimated from the local solvent structure correlate well with the experimental data over the entire pressure range.     

Modified Monte Carlo simulation of adsorption in a spatially inhomogeneous porous system

A modified Monte Carlo method in conjunction with the canonical and grand canonical ensembles is proposed for simulating adsorption in spatially inhomogeneous porous systems. Unlike the traditional Monte Carlo simulation in terms of the grand canonical ensemble, the simulation for the regions of pore space having no direct communication with the bulk phase is performed in local conditions of the canonical ensemble.     

Application of kinetic Monte Carlo method to equilibrium systems: vapour-liquid equilibria

Kinetic Monte Carlo (kMC) simulations were carried out to describe the vapour-liquid equilibria of argon at various temperatures. This paper aims to demonstrate the potential of the kMC technique in the analysis of equilibrium systems and its advantages over the traditional Monte Carlo method, which is based on the Metropolis algorithm. The key feature of the kMC is the absence of discarded trial moves of molecules, which ensures larger number of configurations that are collected for time averaging. Consequently, the kMC technique results in significantly fewer errors for the same number of Monte Carlo steps, especially when the fluid is rarefied. An additional advantage of the kMC is that the relative displacement probability of molecules is significantly larger in rarefied regions, which results in a more efficient sampling. This provides a more reliable determination of the vapour phase pressure and density in case of non-uniform density distributions, such as the vapour-liquid interface or a fluid adsorbed on an open surface. We performed kMC simulations in a canonical ensemble, with a liquid slab in the middle of the simulation box to model two vapour-liquid interfaces. A number of thermodynamic properties such as the pressure, density, heat of evaporation and the surface tension were reliably determined as time averages.     

Chain conformation and solvent partitioning in reversed-phase liquid chromatography: Monte Carlo simulations for various water/methanol concentrations

Many structural models for the stationary phase in reversed-phase liquid chromatography (RPLC) systems have been suggested from thermodynamic and spectroscopic measurements and theoretical considerations. To provide a molecular picture of chain conformation and solvent partitioning in a typical RPLC system, a particle-based Monte Carlo simulation study is undertaken for a dimethyl octadecyl (C(18)) bonded stationary phase on a model siliceous substrate in contact with mobile phases having different methanol/water concentrations. Following upon previous simulations for gas-liquid chromatography and liquid-liquid phase equilibria, the simulations are conducted using the configurational-bias Monte Carlo method in the Gibbs ensemble and the transferable potentials for phase equilibria force field. The simulations are performed for a chain surface density of 2.9 micromol/m(2), which is a typical bonded-phase coverage for mono-functional alkyl silanes. The solvent concentrations used here are pure water, approximately 33 and 67% mole fraction of methanol and pure methanol. The simulations show that the chain conformation depends only weakly on the solvent composition. Most chains are conformationally disordered and tilt away from the substrate normal. The interfacial width increases with increasing methanol content and, for mixtures, the solvent shows an enhancement of the methanol concentration in a 10 Angstrom region outside the Gibbs dividing surface. Residual surface silanol groups are found to provide hydrogen bonding sites that lead to the formation of substrate bound water and methanol clusters, including bridging clusters that penetrate from the solvent/chain interfacial region all the way to the silica surface.