Structures and adsorption of binary hard-core Yukawa mixtures in a slitlike pore: grand canonical Monte Carlo simulation and density-functional study

The grand canonical ensemble Monte Carlo simulation and density-functional theory are applied to calculate the structures, local mole fractions, and adsorption isotherms of binary hard-core Yukawa mixtures in a slitlike pore as well as the radial distribution functions of bulk mixtures. The excess Helmholtz energy functional is a combination of the modified fundamental measure theory of Yu and Wu [J. Chem. Phys. 117, 10156 (2002)] for the hard-core contribution and a corrected mean-field theory for the attractive contribution. A comparison of the theoretical results with the results from the Monte Carlo simulations shows that the corrected theory improves the density profiles of binary hard-core Yukawa mixtures in the vicinity of contact over the original mean-field theory. Both the present corrected theory and the simulations suggest that depletion and desorption occur at low temperature, and the local segregation can be observed in most cases. For binary mixtures in the hard slitlike pore, the present corrected theory predicts more accurate surface excesses than the original one does, while in the case of the attractive pore, no improvement is found in the prediction of a surface excess of the smaller molecule.     

Structure of inhomogeneous attractive and repulsive hard-core yukawa fluid: grand canonical Monte Carlo simulation and density functional theory study

A density functional theory is proposed for an inhomogeneous hard-core Yukawa (HCY) fluid based on Rosenfeld's perturbative method. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the hard-core repulsion and a quadratic functional Taylor expansion for the long-ranged attractive or repulsive interactions. To test the established theory, grand canonical ensemble Monte Carlo simulations are carried out to simulate the density profiles of attractive and repulsive HCY fluid near a wall. Comparison with the results from the Monte Carlo simulations shows that the present density functional theory gives accurate density profiles for both attractive and repulsive HCY fluid near a wall. Both the present theory and simulations suggest that there is depletion for attractive HCY fluid at low temperature, but no depletion is found for repulsive HCY fluid. The calculated results indicate that the present density functional theory is better than those of the modified version of the Lovett-Mou-Buff-Wertheim and other density functional theories. The present theory is simple in form and computationally efficient. It predicts accurate radial distribution functions of both attractive and repulsive HCY fluid except for the repulsive case at high density, where the theory overestimates the radial distribution function in the vicinity of contact.     

Storage of hydrogen at 303 K in graphite slitlike pores from grand canonical Monte Carlo simulation

Grand canonical Monte Carlo (GCMC) simulations were used for the modeling of the hydrogen adsorption in idealized graphite slitlike pores. In all simulations, quantum effects were included through the Feynman and Hibbs second-order effective potential. The simulated surface excess isotherms of hydrogen were used for the determination of the total hydrogen storage, density of hydrogen in graphite slitlike pores, distribution of pore sizes and volumes, enthalpy of adsorption per mole, total surface area, total pore volume, and average pore size of pitch-based activated carbon fibers. Combining experimental results with simulations reveals that the density of hydrogen in graphite slitlike pores at 303 K does not exceed 0.014 g/cm(3), that is, 21% of the liquid-hydrogen density at the triple point. The optimal pore size for the storage of hydrogen at 303 K in the considered pore geometry depends on the pressure of storage. For lower storage pressures, p < 30MPa, the optimal pore width is equal to a 2.2 collision diameter of hydrogen (i.e., 0.65 nm), whereas, for p congruent with 50MPa, the pore width is equal to an approximately 7.2 collision diameter of hydrogen (i.e., 2.13 nm). For the wider pores, that is, the pore width exceeds a 7.2 collision diameter of hydrogen, the surface excess of hydrogen adsorption is constant. The importance of quantum effects is recognized in narrow graphite slitlike pores in the whole range of the hydrogen pressure as well as in wider ones at high pressures of bulk hydrogen. The enthalpies of adsorption per mole for the considered carbonaceous materials are practically constant with hydrogen loading and vary within the narrow range q(st) congruent with 7.28-7.85 kJ/mol. Our systematic study of hydrogen adsorption at 303 K in graphite slitlike pores gives deep insight into the timely problem of hydrogen storage as the most promising source of clean energy. The calculated maximum storage of hydrogen is equal to approximately 1.4 wt %, which is far from the United States Department of Energy (DOE) target (i.e., 6.5 wt %), thus concluding that the total storage amount of hydrogen obtained at 303 K in graphite slitlike pores of carbon fibers is not sufficient yet.     

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.     

Effect of surface functionalities on gas adsorption in microporous carbons: a grand canonical Monte Carlo study

In an attempt to offer a more realistic picture of adsorption in highly heterogeneous porous systems, such as oxygen functionalized porous carbons, we consider a series of carbon surfaces baring different amounts of oxygen functionalities (hydroxyl and epoxy). These surfaces are used to construct “oxidized” slit pores of varying width and functionality. With the aid of such inhomogeneous structures we study the interaction of Ar (87 K) inside “functionalized” pores and report grand canonical Monte Carlo adsorption simulations results. Based on our simulation data, we discuss the role of chemical heterogeneity on adsorbed/gas phase equilibrium properties such as density, heat of adsorption, and molecular packing within the pores. Comparisons are made with the case of the oxygen–free (completely homogeneous) slit pore models and conclusions on the suitability of Ar based pore size distributions for functionalized porous carbons are drawn.     

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.     

Quasi one-dimensional nanopores in single-wall carbon nanohorn colloids using grand canonical Monte Carlo simulation aided adsorption technique

The average interstitial nanopore structure of single-wall carbon nanohorn (SWNH) assemblies was determined using X-ray diffraction and grand canonical Monte Carlo (GCMC) simulation aided N(2) adsorption at 77 K. The interstitial nanopores of SWNH assemblies can be regarded as quasi one-dimensional pores due to the partial orientation of the SWNH particles; the average pore width of the interstitial pores is 0.6 nm. Good agreement between the GCMC simulation of a structural model with one-dimensional interstitial nanopores and an experimental adsorption isotherm below P/P(0) = 10(-4) is evidence of the quasi one-dimensionality of the interstitial nanopores. A snapshot from the GCMC simulation showed one-dimensional growth of adsorbed N(2) molecules.     

Spatial updating grand canonical Monte Carlo algorithms for fluid simulation: generalization to continuous potentials and parallel implementation

Spatial updating grand canonical Monte Carlo algorithms are generalizations of random and sequential updating algorithms for lattice systems to continuum fluid models. The elementary steps, insertions or removals, are constructed by generating points in space either at random (random updating) or in a prescribed order (sequential updating). These algorithms have previously been developed only for systems of impenetrable spheres for which no particle overlap occurs. In this work, spatial updating grand canonical algorithms are generalized to continuous, soft-core potentials to account for overlapping configurations. Results on two- and three-dimensional Lennard-Jones fluids indicate that spatial updating grand canonical algorithms, both random and sequential, converge faster than standard grand canonical algorithms. Spatial algorithms based on sequential updating not only exhibit the fastest convergence but also are ideal for parallel implementation due to the absence of strict detailed balance and the nature of the updating that minimizes interprocessor communication. Parallel simulation results for three-dimensional Lennard-Jones fluids show a substantial reduction of simulation time for systems of moderate and large size. The efficiency improvement by parallel processing through domain decomposition is always in addition to the efficiency improvement by sequential updating.     

Investigation of the adsorption behaviour of acetone at the surface of ice. A grand canonical Monte Carlo simulation study

The adsorption isotherm of acetone at the surface of I(h) ice has been determined by a set of grand canonical Monte Carlo simulations at 200 K, by varying the chemical potential of acetone in the simulations. The obtained isotherm can be described by the Langmuir theory up to a certain relative pressure value (i.e., about 0.07); above which the isotherm increasingly deviates from the Langmuir form. This deviation mainly originates from the increasing importance of the lateral dipolar interactions. Further, above this pressure the adsorption sites are no longer equivalent: the adsorbed acetone molecules are aligned in three different ways. In one of these orientations the acetone molecule forms two, while in another one it forms one hydrogen bond with the surface waters, whereas in the third preferred orientation no hydrogen bonding occurs between the adsorbed molecule and the ice surface.     

Computation of interfacial properties via grand canonical transition matrix Monte Carlo simulation

We examine two free-energy-based methods for studying the wetting properties of a fluid in contact with a solid substrate. Application of the first approach involves examination of the adsorption behavior of a fluid at a single substrate, while the second technique requires investigation of the properties of a system confined between two parallel substrates. Both of the techniques rely upon computation and analysis of the density dependence of a system's surface free energy and provide the contact angle and solid-vapor and solid-liquid interfacial tensions for substrate-fluid combinations within the partial wetting regime. Grand canonical transition matrix Monte Carlo simulation is used to obtain the required free-energy curves. The methods examined within this work are general and are applicable to a wide range of molecular systems. We probe the performance of the methods by computing the interfacial properties for two systems in which an atomistic fluid interacts with a fcc crystal. For both of the systems studied we find good agreement between our results and those obtained via the mechanical definition of the interfacial tension.     

A grand canonical Monte Carlo study of capillary condensation in mesoporous media: effect of the pore morphology and topology

We study by means of Grand Canonical Monte Carlo simulations the condensation and evaporation of argon at 77 K in nanoporous silica media of different morphology or topology. For each porous material, our results are compared with data obtained for regular cylindrical pores. We show that both the filling and emptying mechanisms are significantly affected by the presence of a constriction. The simulation data for a constricted pore closed at one end reproduces the asymmetrical shape of the hysteresis loop that is observed for many real disordered porous materials. The adsorption process is a quasicontinuous mechanism that corresponds to the filling of the different parts of the porous material, cavity, and constriction. In contrast, the desorption branch for this pore closed at one end is brutal because the evaporation of Ar atoms confined in the largest cavity is triggered by the evaporation of the fluid confined in the constriction (which isolates the cavity from the gas reservoir). This evaporation process conforms to the classical picture of "pore blocking effect" proposed by Everett many years ago. We also simulate Ar adsorption in a disordered porous medium, which mimics a Vycor mesoporous silica glass. The adsorption isotherm for this disordered porous material having both topological and morphological defects presents the same features as that for the constricted pore (quasicontinuous adsorption and steep desorption process). However, the larger degree of disorder of the Vycor surface enhances these main characteristics. Finally, we show that the effect of the disorder, topological and/or morphological, leads to a significant lowering of the capillary condensation pressure compared to that for regular cylindrical nanopores. Also, our results suggest that confined fluids isolated from the bulk reservoir evaporate at a pressure driven by the smallest size of the pore.     

Effects of confinement on the molar enthalpy of argon adsorption in graphitic cylindrical pores: a grand canonical Monte Carlo (GCMC) simulation study

Using a grand canonical Monte Carlo simulation, we study argon adsorption in graphitic cylindrical pores to investigate the differences between the isosteric heat and the integral molar enthalpy under subcritical and supercritical conditions and compare these results against those for a flat graphite surface to investigate the role of confinement on the enthalpy change of adsorption. The isosteric heat curve is finite under subcritical conditions, but for supercritical adsorption, it becomes infinite at the pressure where the excess concentration versus pressure is maximum. This can be circumvented using the integral molar enthalpy, which is a better variable to describe the energy change for supercritical adsorption. Finally, the effects of pore geometry (radius and length) on argon adsorption under subcritical and supercritical conditions are discussed.     

Adsorption of benzene and propene in zeolite MCM-22: a grand canonical Monte Carlo study

The GCMC (grand canonical Monte Carlo) simulation technique was used to predict the competition adsorption characteristics of benzene and propene in different pore systems of MCM-22. The nine-site model of benzene was used, which proved to be effective and efficient. The zeolite was divided into three adsorption sites following a simulated annealing method. It is found that benzene and propene have the same preferential adsorption site and a similar adsorption order in different sites. Moreover, the pure and mixture isotherms of the three sites are drawn. From the isotherms, we obtained a selectivity reversal of the mixture isotherms of benzene and propene in different sites. It is also noted that the competition adsorption in the three adsorption sites for the two adsorbates can fall into three successive steps and the adsorption order of propene in mixture in these three sites is S3→S1→S2. A new model is presented to predict the benzene and propene adsorption equilibrium in MCM-22. This approach yields better multicomponent equilibrium predictions than ideal adsorbed solution theory (IAST). Isotherms at different mole fraction of benzene in gas phase indicate an advantage to increase the feed radio of benzene and propene. Thus, this work is helpful for a better understanding of the adsorption mechanism of benzene and propene in MCM-22 and hence the relation of the catalytic properties of the zeolite to its structure.     

Determination of the adsorption isotherm of methanol on the surface of ice. An experimental and grand canonical Monte Carlo simulation study

The adsorption isotherm of methanol on ice at 200 K has been determined both experimentally and by using the Grand Canonical Monte Carlo computer simulation method. The experimental and simulated isotherms agree well with each other; their deviations can be explained by a small (about 5 K) temperature shift in the simulation data and, possibly, by the non-ideality of the ice surface in the experimental situation. The analysis of the results has revealed that the saturated adsorption layer is monomolecular. At low surface coverage, the adsorption is driven by the methanol-ice interaction; however, at full coverage, methanol-methanol interactions become equally important. Under these conditions, about half of the adsorbed methanol molecules have one hydrogen-bonded water neighbor, and the other half have two hydrogen-bonded water neighbors. The vast majority of the methanols have a hydrogen-bonded methanol neighbor, as well.     

Kinetic lattice grand canonical Monte Carlo simulation for ion current calculations in a model ion channel system

An algorithm in which kinetic lattice grand canonical Monte Carlo simulations are combined with mean field theory (KLGCMC/MF) is presented to calculate ion currents in a model ion channel system. In this simulation, the relevant region of the system is treated by KLGCMC simulations, while the rest of the system is described by modified Poisson-Boltzmann mean field theory. Calculation of reaction field due to induced charges on the channel/water and membrane/water boundaries is carried out using a basis-set expansion method [Im and Roux, J. Chem. Phys. 115, 4850 (2001)]. Calculation of ion currents, electrostatic potentials, and ion concentrations, as obtained from the KLGCMC/MF simulations, shows good agreement with Poisson-Nernst-Planck (PNP) theory predictions when the channel and membrane have the same dielectric constant as water. If the channel and membrane have a lower dielectric constant than water, however, there is a considerable difference between the KLGCMC/MF and PNP predictions. This difference is attributed to the reaction field, which is missing in PNP theory. It is demonstrated that the reaction field as well as fixed charges in the channel play key roles in selective ion transport. Limitations and further development of the current KLGCMC/MF approach are also discussed.     

Model liquid crystalline dimers in a slit pore: Monte Carlo simulation study

ABSTRACT

In this work, we present results from (isobaric–isothermal) Monte Carlo Simulation studies of liquid crystalline dimer systems confined in a slit pore. Liquid crystalline dimer systems of various spacer numbers have been considered. Surface-induced conformational and alignment properties of these systems at different pressures under homeotropic anchoring condition have been investigated. We have used easily manageable coarse grained force fields to model both monomer–monomer and monomer–substrate interaction potentials. According to the simulated result, the anchoring of dimers to the surface and orientation of mesogenic units with respect to the surface normal seem to depend on the spacer number for messogen attractive confinement. Dimers with lower spacer number are able be adsorbed to the surface and most of their mesogens are oriented along the surface normal even at lower pressure. Those with larger spacer number are distributed throughout the volume at lower pressure. In the case of mesogen repulsive confinement, most of the dimers are adsorbed to the surface and most mesogens are randomly oriented at low pressure. As the pressure gets higher, the adsorption and orientability increase depending on the type of confinement and spacer number. As a result, clear submolecular partitioning and smectic A like structure have been identified.     

Adsorption/desorption hysteresis in inkbottle pores: a density functional theory and Monte Carlo simulation study

The mechanisms of adsorption and desorption in inkbottle-shaped pores are considered for lattice models using grand canonical mean field density functional theory and Monte Carlo simulation. We find that they depend significantly on the particular pore geometry, the nature of the fluid-solid interaction, and the temperature. We find two mechanisms for desorption. One mechanism involves the emptying of the main cavity even as the density of fluid in the necks remains high, a mechanism observed recently in studies of an off-lattice model of an inkbottle. The other is a simultaneous desorption from the entire pore space, behavior that is more closely related to the traditional picture of pore blocking in the inkbottle system.     

Grand canonical Monte Carlo simulation of argon adsorption at the surface of silica nanopores: effect of pore size, pore morphology, and surface roughness

Argon adsorption (77 K) in atomistic silica nanopores of various sizes and shapes has been studied by means of grand canonical Monte Carlo simulations (GCMC). We discuss the effects of confinement (pore size), pore morphology (ellipsoidal, hexagonal, constricted pore), and surface texture (rough/smooth) on the thickness variation of the adsorbed film with pressure onto the disordered inner surface of porous materials (usually called t-plot or t-curve). We show that no confinement effect occurs when the diameter of the regular cylindrical pore is larger than 10 nm. For pores smaller than 6 nm, we find that the film thickness increases as the pore size decreases. We show that the adsorption isotherm in the rough pore can be described as the sum of an adsorbed amount similar to that found for a smooth pore (of the same radius) and a constant contribution due to atoms "trapped" in the infractuosities of the rough surface which act as a microporous texture. Simulation snapshots for Ar adsorption in hexagonal and ellipsoidal smooth pores indicate that at low pressures the gas/adsorbate interface retains memory of the pore shape and becomes cylindrical prior to the capillary condensation of the fluid in the pore. The film thickness in the hexagonal pore is close to that obtained for a cylindrical pore having a similar dimension. By contrast, we find that the film thickness for an ellipsoidal pore is always larger than that for an equivalent cylindrical pore (having the same length and volume but a circular section). We show that this effect strengthens as the pore size decreases and/or the pore asymmetry increases. Ar adsorption in a cylindrical constricted pore shows that the presence of the narrower part considerably modifies the adsorption mechanism. Finally, we report GCMC simulations of Ar adsorption (77 K) on a plane silica reference substrate for different intermolecular potentials. We discuss the effect of the interaction on the shape of the adsorption isotherm and compare our results with experiments.