Calculating Gibbs free energies of transfer from Gibbs ensemble Monte Carlo simulations

The partitioning of the ternary systems n-pentane/n-heptane/(helium or argon) at ambient conditions is investigated using configurational-bias Monte Carlo simulations in the Gibbs ensemble. The results demonstrate that this approach yields very precise partition constants and free energies of transfer. Simulations are carried out to study the dependence of the n-pentane partitioning with respect to the carrier gas, the system size, and the overall solute concentrations. None of the changes of variables, within the ranges used here, has a significant effect on the alkane partitioning. However, chemical potentials calculated via Widom's ghost particle insertions show a strong number dependence for phases containing relatively few molecules of a given type. This problem originates from the fact that the chemical potential is calculated for a concentration of real particles plus one ghost particle that is systematically larger than the equilibrium concentration. A simple correction term is suggested to account for this problem. Received: 13 May 1998 / Accepted: 18 June 1998 / Published online: 4 September 1998     

Monte Carlo simulations of squalane in the Gibbs ensemble

We investigate the liquid–vapour coexistence curve of 2,6,10,15,19,23-hexamethyltetracosane (squalane) near the critical point with a new Lennard–Jones parameter set and compare our results to existing simulation data as well as to recent experimental vapour pressure data. Comparison of the liquid–vapour coexistence curve to previous simulation data reveals that this new force field, which includes tail corrections to the truncation of the non-bonded interactions increases the liquid density. We determine the critical temperature to 829 K and 825 K (with roughly 1% error) for two different system sizes, 72 and 108 molecules, and the critical density to 0.211 g/cm³ and 0.228 g/cm³, respectively. We extrapolate experimental vapour pressure data by use of Antoine's law to the temperature range covered by simulation and yield good agreement between simulation and experiment. We note that the vapour pressure in simulation is essentially governed by the ideal vapour pressure.     

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 separation in mixtures of Yukawa and charged Yukawa particles from Gibbs ensemble Monte Carlo simulations and the mean spherical approximation

The phase equilibrium of mixtures of Yukawa and charged Yukawa particles is studied by means of Gibbs ensemble Monte Carlo (GEMC) simulation method and the mean spherical approximation (MSA). The strength of the Coulomb energy compared to that of the Yukawa attraction is characterized by a coupling constant. For low coupling constants a classical vapor--liquid phase separation appears with a good agreement between GEMC and the MSA. For high coupling constant, a phase separation between a salt poor and a salt rich phase occurs that resembles the phase equilibrium behavior of the solvent primitive model.     

Optimized ensemble Monte Carlo simulations of dense Lennard-Jones fluids

We apply the recently developed adaptive ensemble optimization technique to simulate dense Lennard-Jones fluids and a particle-solvent model by broad-histogram Monte Carlo techniques. Equilibration of the simulated fluid is improved by sampling an optimized histogram in radial coordinates that shifts statistical weight towards the entropic barriers between the shells of the liquid. Interstitial states in the vicinity of these barriers are identified with unprecedented accuracy by sharp signatures in the quickly converging histogram and measurements of the local diffusivity. The radial distribution function and potential of mean force are calculated to high precision.     

Symmetric diblock copolymers in nanopores: Monte Carlo simulations and strong-stretching theory

We have performed lattice Monte Carlo simulations to study the self-assembled morphology of symmetric diblock copolymers in nanopores. The pore diameter and surface preference are systematically varied to examine their effects on the chain conformations, structures of various morphologies, and their phase transition. Various ensemble-averaged profiles and quantities are used to provide detailed information about the system. The simulation results are also compared with the predictions of a strong-stretching theory commonly used in the literature. Such comparisons reveal the deficiencies of this theory in describing the morphologies under cylindrical confinement, and call for further theoretical studies using more accurate formalisms.     

Bubble point pressure estimates from Gibbs ensemble simulations

Bubble pressure points of ethanol–1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea refrigerant) mixtures from the third Industrial Fluid Properties Simulation Challenge are computed using publicly available molecular simulation software. Several published force fields are compared against the known answers provided in the contest guidelines and the best force fields are used to make predictions for the unknown results.     

Convergence of Monte Carlo simulations of liquid water in the NPT ensemble

Long Monte Carlo simulations of liquid water at 25° and 1 atm have been carried out to study the convergence characteristics of the calculations. The recently reported TIPS2 potential was employed with system sizes of 125 and 216 monomers. The enthalpy, volume and radial distribution functions converge rapidly and show little size dependence. However, the rates of convergence are much slower for the fluctuation properties and are in the order: heat capacity (Cp) ? isothermal compressibility (?) ? coefficient of thermal expansion (α). In fact,the weak coupling of the enthalpy and volume allows only crude estimates for α. In addition, the estimation of statistical error bounds for the thermodynamic properties is analyzed. It is found that very long (2500-3500 k) simulations are needed to yield valid estimates of the errors for the enthalpy, volume and C_p, while the erros for ? and α would still be elusive.     

Vapor-liquid equilibrium properties for confined binary mixtures involving CO2, CH4, and N2 from Gibbs ensemble Monte Carlo simulations

The effects of solid-fluid interactions on the vapor-liquid phase diagram,coexistence density,relative volatility and vaporization enthalpy have been investigated for confined binary systems of CO 2-CH 4,CO 2-N 2 and CH 4-N 2.The Gibbs ensemble Monte Carlo(GEMC) simulation results indicate that the confinement and the solid-fluid interaction have significant influences on the vapor-liquid equilibrium properties.The confinement and the strength of the solid-fluid interaction make the p-x i phase diagram move to higher pressure regions.They also make the two-phase region become narrower for each binary mixture.The strength of the solid-fluid interactions can cause increases in the coexistence liquid and vapor densities,and cause the decrease of the relative volatility and the vaporization enthalpy for the systems studied.As the pore width is decreased,the two-phase region of the binary mixture becomes narrower.     

Gibbs ensemble Monte Carlo simulation of adsorption for model surfactant solution in confined slit pores

An isobaric-isothermal Gibbs ensemble Monte Carlo simulation has been carried out to study the adsorption of a model surfactant/solvent mixture in slit nanopores. The adsorption isotherms, the density distributions, and the configuration snapshots were simulated to illustrate the adsorption and self-assembly behaviors of the surfactant in the confined pores. The adsorption isotherms are stepwise: a two-step curve for the smaller (30 A) pore and a three-step one for the larger (50 A) pore. The adsorption isotherms and the interfacial aggregate structure of the surfactants in the pores with various sizes show a qualitatively consistent performance with the previous experimental observation. The micelle size distributions of the adsorbed surfactant aggregates have been analyzed in order to understand the adsorption mechanism, which suggests that the step rise in the surfactant adsorption is associated with the considerable formation of the micelle aggregates in the confined pores. The effect of the interaction between the pore surface and the surfactant on the adsorption behavior has also been investigated. The simulation results indicate that a change in the interaction can modify the shape of adsorption isotherms. A nonlinear mathematical model was used to represent the multistep adsorption isotherms. A good agreement between the model fitting and the simulation data was obtained for both the amount of adsorption and the jump point concentration.     

Acceleration of Monte Carlo simulations through spatial updating in the grand canonical ensemble

A new grand canonical Monte Carlo algorithm for continuum fluid models is proposed. The method is based on a generalization of sequential Monte Carlo algorithms for lattice gas systems. The elementary moves, particle insertions and removals, are constructed by analogy with those of a lattice gas. The updating is implemented by selecting points in space (spatial updating) either at random or in a definitive order (sequential). The type of move, insertion or removal, is deduced based on the local environment of the selected points. Results on two-dimensional square-well fluids indicate that the sequential version of the proposed algorithm converges faster than standard grand canonical algorithms for continuum fluids. Due to the nature of the updating, additional reduction of simulation time may be achieved by parallel implementation through domain decomposition.     

Thermodynamics of hydrogen adsorption in slit-like carbon nanopores at 77 K. Classical versus path-integral Monte Carlo simulations

Hydrogen in slit-like carbon nanopores at 77 K represents a quantum fluid in strong confinement. We have used path-integral grand canonical Monte Carlo and classical grand canonical Monte Carlo simulations for the investigation of the "quantumness" of hydrogen at 77 K adsorbed in slit-like carbon nanopores up to 1 MPa. We find that classical simulations overpredict the hydrogen uptake in carbon nanopores due to neglect of the quantum delocalization. Such disagreement of both simulation methods depends on the slit-like carbon pore size. However, the differences between the final uptakes of hydrogen computed from both classical and quantum simulations are not large due to a similar effective size of quantum/classical hydrogen molecules in carbon nanospaces. For both types of molecular simulations, the volumetric density of stored energy in optimal carbon nanopores exceeds 6.4 MJ dm(-3) (i.e., 45 kg m(-3); Department of Energy target for 2010). In contrast to the hydrogen adsorption isotherms, we found a large reduction of isosteric enthalpy of adsorption computed from the quantum Feynman's path-integral simulations in comparison to the classical values at 77 K and pressures up to 1 MPa. Depression of the quantum isosteric enthalpy of adsorption depends on the slit-like carbon pore size. For the narrow pores (pore width H in [0.59-0.7] nm), the reduction of the quantum isosteric enthalpy of adsorption at zero coverage is around 50% in comparison to the classical one. We observed new phenomena called, by us, the quantum confinement-inducing polymer shrinking. In carbon nanospaces, the quantum cyclic polymers shrink, in comparison to its bulk-phase counterpart, due to a strong confinement effect. At considered storage conditions, this complex phenomenon depends on the size of the slit-like carbon nanopore and the density of hydrogen volumetric energy. For the smallest nanopores and a low density of hydrogen volumetric energy, the reduction of the polymer effective size is the highest, whereas an increase of the pore size and the density of hydrogen volumetric energy causes the polymer swelling up to a value slightly below the one computed from the bulk phase. Quantum confinement-inducing polymer shrinking is of great importance for realizing the potential of quantum molecular sieves.     

Gibbs ensemble Monte Carlo simulation of supercritical CO2 adsorption on NaA and NaX zeolites

Adsorption of supercritical carbon dioxide on two kinds of zeolites with identical chemical composition but different pore structure (NaA and NaX) was studied using the Gibbs ensemble Monte Carlo simulation. The model frameworks for the two zeolites with SiAl ratio being unity have been chosen as the solid structures in the simulation. The adsorption behaviors of supercritical CO2 on the NaA and NaX zeolites, based on the adsorption isotherms and isosteric heats of adsorption, were discussed in detail and were compared with the available experimental results. A good agreement between the simulated and experimental results is obtained for both the adsorbed amount and the bulk phase density. The intermediate configurational snapshots and the radial distribution functions between zeolite and adsorbed CO2 molecules were collected in order to investigate the preferable adsorption locations and the confined structure behavior of CO2. The structure behaviors of the adsorbed CO2 molecules show various performances, as compared with the bulk phase, due to the confined effect in the zeolite pores.     

Prediction of the bubble point pressure for the binary mixture of ethanol and 1,1,1,2,3,3,3-heptafluoropropane from Gibbs ensemble Monte Carlo simulations using the TraPPE force field

Configurational-bias Monte Carlo simulations in the Gibbs ensemble using the TraPPE force field were carried out to predict the pressure–composition diagrams for the binary mixture of ethanol and 1,1,1,2,3,3,3-heptafluoropropane at 283.17 and 343.13 K. A new approach is introduced that allows one to scale predictions at one temperature based on the differences in Gibbs free energies of transfer between experiment and simulation obtained at another temperature. A detailed analysis of the molecular structure and hydrogen bonding for this fluid mixture is provided.     

Condensation phenomena in nanopores: a Monte Carlo study

The nonequilibrium dynamics of condensation phenomena in nanopores is studied via Monte Carlo simulations of a lattice-gas model. Hysteretic behavior of the particle density as a function of the density of a reservoir is obtained for various pore geometries in two and three dimensions. The shape of the hysteresis loops depend on the characteristics of the pore geometry. The evaporation of particles from a pore can be fitted to a stretched exponential decay of the particle density. Phase-separation dynamics inside the pore is effectively described by a random walk of the non-wetting phases. Domain evolution is significantly slowed down in the presence of a random wall-particle potential and gives rise to a temperature-dependent growth exponent. A geometric roughness of the pore wall only delays the onset of a pure domain growth.     

A Monte Carlo algorithm to study polymer translocation through nanopores. I. Theory and numerical approach

The process during which a polymer translocates through a nanopore depends on many physical parameters and fundamental mechanisms. We propose a new one-dimensional lattice Monte Carlo algorithm that integrates various effects such as the entropic forces acting on the subchains that are outside the channel, the external forces that are pulling the polymer through the pore, and the frictional effects that involve the chain and its environment. Our novel approach allows us to study the polymer as a single Brownian particle diffusing while subjected to a position-dependent force that includes both the external driving forces and the internal entropic bias. Frictional effects outside and inside the pore are also considered. This Monte Carlo method is much more efficient than other simulation methods, and it can be used to obtain scaling laws for various polymer translocation regimes. In this first part, we derive the model and describe a subtle numerical approach that gives exact results for both the escape probability and the mean translocation time (and higher moments of its distribution). The scaling laws obtained from this model will be presented and discussed in the second part of this series.     

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.     

Monte Carlo simulations on short single-stranded oligonucleotides. I. Application to RNA trimers

Monte Carlo (MC) structural simulation of short RNA sequences has been carried out by random variations of the nucleotide conformational angles (i.e., phosphodiester chain torsional angles and sugar pucker pseudorotational angles). All of the chemical bond lengths and valence angles remained fixed during the structural simulation, except those of the sugar pucker ring. In this article we present the simulated structures of RNA trimers—r(AAA) and r(AAG)—obtained at 11°C and 70°C. The influence of various initial conformations (selected as starting points in the MC simulations) on the equilibrium conformations has been discussed. The simulated conformational angles have been compared with those estimated by nuclear magnetic resonance (NMR) spectroscopy. For both of the oligonucleotides studied here, the most stable structures are helical conformations with stacked bases, at 11°C and 70°C. However, when the starting point is a stretched chain, it is found that r(AAA) adopts a reverse-stacked structure at low temperature (11°C), in which the A3 base is located between the A1 and A2 bases. Although the energies of these conformations (helical and reverse stacked) are very close to each other, the potential barrier between them is extremely high (close to 30 kcal/mol). This hinders the conformational transition from one structure to the other at a given temperature (and in the course of a same MC simulation). However, it is possible to simulate this structural transition by heating the reverse-stacked structure up to 500°C and cooling down progressively to 70°C and 11°C: Canonical helical structures have been obtained by this procedure. © 1994 by john Wiley & Sons, Inc.