Configurational-bias Monte Carlo Simulations Research Articles

In silico screening of zeolite membranes for CO 2 capture

The separation of CO 2/H 2, CO 2/CH 4, and CO 2/N 2 mixtures is of practical importance for CO 2 capture and other applications in the processing industries. Use of membranes with microporous layers of zeolites, metal–organic frameworks (MOFs), and zeolitic imidazolate frameworks (ZIFs) offer considerable promise for use in such separations. In view of the extremely wide variety of available microporous structures, there is a need for a systematic screening of potential candidates in order to obtain the best permeation selectivities, S perm. The permeation selectivity is a product of the adsorption selectivity, S ads, and the diffusion selectivity, S diff, i.e. S perm = S ads × S diff. For maximizing S perm, we need to choose materials for which S ads and S diff complement each other. For a wide variety of zeolites, we have used Configurational-Bias Monte Carlo (CBMC) simulations of mixture adsorption isotherms, along with Molecular Dynamics (MD) simulations of diffusivities for three binary mixtures, CO 2/H 2, CO 2/CH 4, and CO 2/N 2, to calculate S ads, S diff, and S perm. These simulation results provide insights into the influence of pore size, pore topology and pore connectivity that influences each of the three selectivities. In particular, we emphasize the important role of correlations in the diffusion behaviors within microporous materials. Furthermore, we have constructed Robeson plots for each of the separations in order to provide generic guidelines to the choice of materials that offer the appropriate compromise between S perm and the membrane permeability.

Hydrogen Bonding Effects in Adsorption of Water−Alcohol Mixtures in Zeolites and the Consequences for the Characteristics of the Maxwell−Stefan Diffusivities

This work highlights a variety of peculiar characteristics of adsorption and diffusion of polar molecules such as water, methanol and ethanol in zeolites. These peculiarities are investigated with the aid of configurational-bias Monte Carlo (CBMC) simulations of adsorption isotherms, and molecular dynamics (MD) simulations of diffusivities in FAU, MFI, DDR, and LTA zeolites. Because of strong hydrogen bonding, significant clustering of the guest molecules occurs in all investigated structures. Because of molecular clustering, the inverse thermodynamic factor 1/Gamma(i) identical with (d[ln c(i)])/(d[ln f(i)]) exceeds unity for a range molar concentrations c(i) within the micropores. The degree of clustering is lowered as the temperature is increased. For the concentration ranges for which 1/Gamma(i) > 1, the Fick diffusivity, D(i), for unary diffusion is often lower than both the Maxwell-Stefan, D(i), and the self-diffusivity, D(i,self). For water-alcohol mixtures, the hydrogen bonding between water and alcohol molecules is much more predominant than for water-water, and alcohol-alcohol molecule pairs. Consequently, the adsorption of water-alcohol mixtures shows significant deviations from the predictions of the ideal adsorbed solution theory (IAST). The water-alcohol bonding also leaves its imprint on the mixture diffusion characteristics. The Maxwell-Stefan diffusivity, D(i), of either component in water-alcohol mixtures is lower than the corresponding values of the pure components; this behavior is distinctly different from that for mixtures of nonpolar guest molecules. The binary exchange coefficient D(12) for water-alcohol mixtures is also significantly lower than either self-exchange coefficients D(11) and D(22) of the constituent species. This implies that correlation effects are significantly stronger in water-alcohol mixtures than for the constituent species. Correlation effects are found to be significant for water-alcohol mixture diffusion in DDR and LTA zeolites, even though such effects are negligible for the pure constituents. The major conclusion to emerge from this investigation is that, unlike mixtures of nonpolar molecules, it is not possible to estimate water-alcohol mixture adsorption and diffusion characteristics on the basis of pure component data.

Application of a coarse-grained model for DNA to homo- and heterogeneous melting equilibria

Configurational-bias Monte Carlo simulations were carried out on deoxyribonucleic acid (DNA) decamers using a coarse-grained molecular model. The effects of single mutations on the melting transition were investigated as were heterogeneous systems with immobilization of one strand on a surface, both with and without a spacer. The destabilizing effect of an internal mutation is attributed to a lack of cooperativity, which acts through a hydrogen bonding nucleotide’s restriction of the conformational freedom of neighboring bases. A surface-oligomer spacer is necessary for duplex stability with the destabilizing effect of the surface coinciding with the volume it excludes.

Microscopic structure of liquid 1-1-1-2-tetrafluoroethane (R134a) from Monte Carlo simulation

1-1-1-2-tetrafluoroethane (R134a) is one of the most commonly used refrigerants. Its thermophysical properties are important for evaluating the performance of refrigeration cycles. These can be obtained via computer simulation, with an insight into the microscopic structure of the liquid, which is not accessible to experiment. In this paper, vapour-liquid equilibrium properties of R134a and its liquid microscopic structure are investigated using coupled-decoupled configurational-bias Monte Carlo simulation in the Gibbs ensemble, with a recent potential [J. Phys. Chem. B 2009, 113, 178]. We find that the simulations agree well with the experimental data, except at the vicinity of the critical region. Liquid R134a packs like liquid argon, with a coordination number in the first solvation shell of 12 at 260 K. The nearest neighbours prefer to be localized in three different spaces around the central molecule, in such a manner that the dipole moments are in a parallel alignment. Analysis of the pair interaction energy shows clear association of R134a molecules, but no evidence for C-HF type hydrogen bonding is found. The above findings should be of relevance to a broad range of fluoroalkanes.

Investigation of the driving forces for retention in reversed-phase liquid chromatography: Monte Carlo simulations of solute partitioning between n-hexadecane and various aqueous–organic mixtures

With the aim of learning about the solubility characteristics of retentive and mobile phases often encountered in reversed-phase liquid chromatography (RPLC) and to examine the driving forces for retention, configurational-bias Monte Carlo simulations in the Gibbs ensemble were carried out for systems consisting of three phases: an n-hexadecane retentive phase (serving as a model of the hydrophobic RPLC stationary phase), a mobile phase with varying water–acetonitrile or water–methanol composition, and a helium vapor phase (serving as an ideal gas reference state). Gibbs free energies of transfer between each of these phases were computed for a series of small alkane and alcohol solutes and from these the methylene and hydroxyl increments were determined. The results indicate that both nonpolar and polar solutes have favorable interactions with both the mobile and stationary phase thus showing that neither the solvophobic theory nor lipophilic theory alone can explain the driving forces for retention in RPLC. In addition, an analysis of the solvation environments of methylene and hydroxyl groups in the mobile and stationary phases was carried out. The methylene group is shown to be preferentially solvated by the organic component of the aqueous–organic mixture, however, clustering of the organic solvent molecules in the absence of the solute was not observed. For the hydroxyl group, hydrogen bonding was shown to be important in both the mobile and stationary phases.

A molecular simulation study of commensurate–incommensurate adsorption of n-alkanes in cobalt formate frameworks

The channels of the cobalt formate frameworks consist of one-dimensional channels that have a zig-zag configuration. Propane (C3) has a length that commensurates with the channel segment length; longer n-alkanes such as n-butane (nC4), n-pentane (nC5) and n-hexane (nC6) have conformations that straddle two channel segments. Configurational-bias Monte Carlo (CBMC) simulations show that the adsorption strength of C3 is higher than that of n-butane (nC4) and n-pentane (nC5); this unusual hierarchy is a direct consequence of the commensurate–incommensurate adsorption. CBMC simulations also reveal the possibility of separating C3–nC6, C3–nC4, nC4–nC6 and nC4–nC5 liquid mixtures for which the adsorbed phase contains predominantly the shorter alkane. Molecular dynamics simulations show that the hierarchy of self-diffusivities is non-monotonic and is the mirror image of the hierarchy of adsorption strengths.

Prediction of sound velocity in normal alkanes: A configurational-bias Monte Carlo simulation approach

We propose a Monte Carlo computational approach to obtain the velocity of sound in fluids, based on the fluctuation method [F.A. Escobedo, J. Chem. Phys. 108 (1998) 8761]. The technique involves a sequential implementation of the isobaric-isothermal and canonical ensembles in a simulation box, in which the (residual) thermodynamic derivative properties are evaluated via the fluctuation method during configurational-bias Monte Carlo simulation. We specifically tested our Monte Carlo theory to compute the velocity of sound in a number of (linear) alkane fluids (methane, n-butane, n-heptane, and n-decane). In the case of methane, we employed a united atom Lennard-Jones potential [D. Möller, J. Oprzynski, A. Möller, J. Fischer, Mol. Phys. 75 (1992) 363]. We present an analysis of the bulk pair correlation function for methane near its critical temperature, which potentially reveals structural differences to explain the extrema phenomena in heat capacities as well as sound velocity differences at such corresponding extrema states. In the case of n-butane, n-heptane, and n-decane, we used an optimized anisotropic united atom intermolecular Lennard-Jones description of Ungerer et al. [P. Ungerer, C. Beauvais, J. Delhommelle, A. Boutin, B. Rousseau, A.H. Fuchs, J. Chem. Phys. 112 (2000) 5499] along with the intramolecular parameters of Nieto-Draghi and Ungerer [C. Nieto-Draghi, P. Ungerer, J. Chem. Phys. 125 (2006) 044517]. We provided extensive comparison with the experimental data in the temperature range between 273.15 and 432.15 K and pressures up to 50 MPa. In excellent agreement with the experiment, we find the Monte Carlo technique to be capable of predicting the velocity of sound in the fluids studied in the present analysis, with improved accuracy in higher pressures at which the validity of the fluctuation theory has been established.

Thermodynamics of adsorption of light alkanes and alkenes in single-walled carbon nanotube bundles

The thermodynamics of adsorption of light alkanes and alkenes (CH4, C2H6, C2H4, C3H8, and C3H6) in single-walled carbon nanotube bundles is studied by configurational-bias grand canonical Monte Carlo simulation. The bundles consist of uniform nanotubes with diameters in the range 11.0 < D (A) < 18.1, arranged in the usual close-packed hexagonal lattice. The phase space is systematically analyzed with calculations for adsorption at room temperature and reduced pressure range of 8.7 x 10-9 < (p/p0) < 0.9. The simulation results are interpreted in terms of the molecular nature of the adsorbate and the corresponding solid-fluid interactions. It is shown that confinement in the internal volume of the bundle (interstitial and intratubular) is energetically more favorable than physisorption on the external surface (grooves and exposed surfaces of peripheral tubes), as indicated by the curves of isosteric heat as a function of reduced pressure. However, the zero-loading properties suggest a crossover point to this behavior for D = 18 - 19 A. When interstitial confinement is not inhibited by geometrical considerations, it is possible to establish the following ordering of the zero-loading isosteric heat by type of adsorption site.

Microscopic Structure and Interaction Analysis for Supercritical Carbon Dioxide−Ethanol Mixtures: A Monte Carlo Simulation Study

Configurational-bias Monte Carlo simulations in the isobaric-isothermal ensemble using the TraPPE-UA force field were performed to study the microscopic structures and molecular interactions of mixtures containing supercritical carbon dioxide (scCO(2)) and ethanol (EtOH). The binary vapor-liquid coexisting curves were calculated at 298.17, 333.2, and 353.2 K and are in excellent agreement with experimental results. For the first time, three important interactions, i.e., EtOH-EtOH hydrogen bonding, EtOH-CO(2) hydrogen bonding, and EtOH-CO(2) electron donor-acceptor (EDA) bonding, in the mixtures were fully analyzed and compared. The EtOH mole fraction, temperature, and pressure effect on the three interactions was investigated and then explained by the competition of interactions between EtOH and CO(2) molecules. Analysis of the microscopic structures indicates a strong preference for the formation of EtOH-CO(2) hydrogen-bonded tetramers and pentamers at higher EtOH compositions. The distribution of aggregation sizes and types shows that a very large EtOH-EtOH hydrogen-bonded network exists in the mixtures, while only linear EtOH-CO(2) hydrogen-bonded and EDA-bonded dimers and trimers are present. Further analysis shows that EtOH-CO(2) EDA complex is more stable than the hydrogen-bonded one.

Diffusion of n-butane/ iso-butane mixtures in silicalite-1 investigated using infrared (IR) microscopy

Adsorption and diffusion of n-butane/ iso-butane mixtures in individual silicalite-1 crystals has been investigated using infrared (IR) microscopy. The equilibrium sorption isotherm for an equimolar gas phase mixture is calculated using Configurational Bias Monte-Carlo simulations. The comparison between simulation results and the experimental data enabled the determination of absolute values of concentration in the IR experiments. n-Butane uptake under presence of iso-butane and, vice versa, iso-butane uptake under presence of n-butane have been studied experimentally. It is shown that the n-butane counter-uptake is not limited by the n-butane diffusivity, but by the availability of free sites, which is, in turn, determined by the mobility of iso-butane. A site-percolation threshold, given by the number of iso-butane molecules blocking the ‘traffic junctions’ of the channel network, has been employed for explaining the occurrence of network regions which are initially inaccessible for n-butane in the counter-uptake process.

A Molecular Dynamics investigation of the influence of framework flexibility on self-diffusivity of ethane in Zn(tbip) frameworks

Configurational-Bias Monte Carlo simulations of the adsorption isotherm of ethane in Zn(tbip) (H 2tbip = 5-tert-butyl isophthalic acid), a representative of metal-organic frameworks, show an inflection at a loading, q i = 6 molecules per unit cell. This inflection causes the inverse thermodynamic factor, 1/ Γ i, to display a minimum at q i = 6, along with a maximum at q i ≈ 10. Molecular Dynamics (MD) simulations of the self-diffusivity D i,self, taking account of the framework flexibility of Zn(tbip) show that the D i,self − q i dependence follows that of 1/ Γ i − q i, with a minimum at q i = 6. Remarkably, MD simulations assuming a rigid framework yield significantly lower values of the self-diffusivities, and show a monotonic decrease of D i,self with q i.

Analysis of Diffusion Limitation in the Alkylation of Benzene over H-ZSM-5 by Combining Quantum Chemical Calculations, Molecular Simulations, and a Continuum Approach

A continuum model based on the Maxwell−Stefan (M-S) equations in combination with the ideal adsorbed solution theory has been used to analyze the influence of adsorption thermodynamics and intraparticle diffusional transport on the overall kinetics of benzene alkylation with ethene over H-ZSM-5. The parameters appearing in the M-S equations were obtained from molecular dynamics simulations, and pure component adsorption isotherms were obtained from configurational-bias Monte Carlo simulations in the grand canonical ensemble. Rate coefficients for the elementary steps of the alkylation were taken from quantum chemical calculations. The intrinsic kinetics of two different reaction schemes were analyzed. The simulations show that all apparent rate parameters of the alkylation are strongly dependent on the reaction conditions. By taking diffusional limitation into account, experimentally determined reaction rates and the orders in the partial pressures of reactants can be reproduced. The results of this study show that empirical power law rate expressions become inappropriate when used to correlate kinetic data over a broad range of conditions. In addition, it is demonstrated that the usual approaches to determine effectiveness factors for reactions in porous media, which assume a constant effective diffusivity, may lead to substantial deviations from rigorous simulations, whereas the simulation model developed here can be used to predict the effectiveness factor for zeolite particles for any set of reaction conditions.

Inflection in the loading dependence of the Maxwell–Stefan diffusivity of iso-butane in MFI zeolite

Configurational-bias Monte Carlo simulations of the adsorption isotherm for iso-butane (iC4) in MFI zeolite shows a strong inflection at a loading Θ = 4 molecules per unit cell. The consequence of the isotherm inflection on the loading dependence of the Maxwell–Stefan (M–S) diffusivity, Ð, was investigated using infra-red microscopy (IRM). The experimental data show that Ð decreases nearly linearly as Θ is increased to 4; further increase in Θ results in a sharp increase in Ð, with a cusp at Θ = 4. Kinetic Monte Carlo (KMC) simulations are used to rationalize the experimental observations. The simulations indicate that significant inter-molecular repulsions are present for Θ > 4.

Size Effects on the Solvation of Anions at the Aqueous Liquid−Vapor Interface

The presence of certain anions at the aqueous liquid−vapor interface is often attributed to polarization effects. This work shows that the size of the ion also plays an important role in driving monovalent inorganic ions to the surface. Configurational-bias Monte Carlo simulations in the Gibbs ensemble were performed to investigate the liquid−vapor interface for neat water and ionic solutions at 298 K. The total ion concentration is about 1.2 M, but the solutions contained a mixture of anions of varying size all having the same fixed charge and Lennard-Jones well depth (i.e., the same polarizability). Results show that as the size of the anion increases so does the propensity for interfacial solvation. The largest anions are consistently found closer to the interface than smaller anions. We also find that large anions, which may prefer a surface location on their own, can be excluded from the interfacial region by inclusion of even larger anions in a mixture.

Application of the TraPPE Force Field for Predicting the Hildebrand Solubility Parameters of Organic Solvents and Monomer Units

Configurational-bias Monte Carlo simulations in the isothermal-isobaric and Gibbs ensembles using the transferable potentials for phase equilibria (TraPPE) force field were carried out to compute the liquid densities, the Hildebrand solubility parameters, and the heats of vaporization for a set of 32 organic molecules with different functional groups at a temperature of 298.15 K. In addition, the heats of vaporization were determined at the normal boiling points of these compounds. Comparison to experimental data demonstrates that the TraPPE force field is significantly more accurate than predictions obtained from molecular dynamics simulations with the Dreiding force field [Belmares et al. J. Comput. Chem. 2004, 25, 1814] and an equation of state approach [Stefanis et al. Fluid Phase Equil. 2006, 240, 144]. For the TraPPE force field, the mean unsigned percent errors for liquid density, the Hildebrand solubility parameter, and the heat of vaporization at 298.15 K are 1.3, 3.3, and 4.5%, respectively.

Separating n-alkane mixtures by exploiting differences in the adsorption capacity within cages of CHA, AFX and ERI zeolites

The saturation capacity of n-alkanes in CHA, AFX and ERI zeolites, that consist of cages separated by windows, decreases with increasing carbon number. The major aim of the present communication is to demonstrate the possibility of separating n-alkane mixtures relying on differences in saturation capacities. To investigate this possibility, Configurational-Bias Monte Carlo simulations for adsorption of C3– nC6, nC4– nC6, and nC5– nC6 mixtures in CHA, AFX and ERI were carried out for equimolar bulk fluid phase. These mixture simulations show that for operation at fluid phase fugacities below about 1 MPa, the adsorbed phase in equilibrium with the bulk vapor phase is predominantly the alkane with the longer chain length, i.e. nC6. However, for operation at pressures in excess of 1 MPa, the adsorbed phase in equilibrium with the bulk liquid phase is richer in the component with the smaller chain length. In some cases, the nC6 is practically excluded from the zeolite.

Understanding Adsorption and Interactions of Alkane Isomer Mixtures in Isoreticular Metal–Organic Frameworks

Novel metal-organic frameworks (MOFs) may lead to advances in adsorption and catalysis owing to their superior properties compared to traditional nanoporous materials. A combination of the grand canonical Monte Carlo method and configurational-bias Monte Carlo simulation was used to evaluate the adsorption isotherms of C4-C6 alkane isomer mixtures in IRMOF-1 and IRMOF-6. The amounts of adsorbed linear and branched alkanes increase with increasing pressure, and the amount of branched alkanes is larger than that of the linear ones. The locations of the alkane isomer reveal that the Zn4O clusters of the IRMOFs are the preferential adsorption sites for the adsorbate molecules. The interaction energy between the Zn4O cluster and the adsorbate is larger than that between the organic linker and the adsorbate. It was further confirmed that the Zn4O cluster plays a much more important role in adsorption by pushing a probe molecule into the pore at positions closer to the Zn4O cluster. It is difficult for branched alkane molecules to approach the Zn4O cluster of IRMOF-6 closely owing to strong spatial hindrance. In addition, the adsorption selectivity is discussed from the viewpoints of thermodynamics and kinetics, and the diffusion behavior of n-butane and 2-methylpropane were investigated to illustrate the relationship between diffusion and adsorption.

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.

Prediction of viscosities and vapor–liquid equilibria for five polyhydric alcohols by molecular simulation

Reverse nonequilibrium molecular dynamics in the canonical ensemble and coupled–decoupled configurational-bias Monte Carlo simulations in the Gibbs ensemble were used to predict the low-shear rate Newtonian viscosities and vapor–liquid coexistence curves for 1,2-butanediol, 1,3-butanediol, 1,4-butanediol, 2-methyl-1,3-propanediol, and 1,2,4-butanetriol modeled with the transferable potentials for phase equilibria-united atom (TraPPE-UA) force field. Comparison with available experimental data demonstrates that the TraPPE-UA force field yields very good predictions of the viscosities and vapor–liquid coexistence curves. A detailed analysis of liquid structure and hydrogen bonding is provided.

Comparative study of pure component adsorption of linear alkanes in zeolites MFI, BEA and MOR

Grand canonical Monte Carlo (GCMC) simulations and configurational-bias Monte Carlo simulations (CBMC) have been performed to compute and compare the pure component adsorption isotherms of C1–C7 linear alkanes in MFI, BEA, and MOR zeolites at 300 K. It is demonstrated that generally, the surfaces of the three zeolites available for adsorption are not energetically homogeneous; adsorption of the alkanes in the three zeolites can be divided into two steps, in the first step of which molecules are adsorbed in the strong sites and on the later of which on the weak sites; all isotherms obtained can be well described by the dual-site Langmuir equation, though the saturation loadings and the adsorption strengths are different for the three different topologic zeolites. A quantitative analysis of the isotherms shows that the Henry’s law constants in the three zeolites obey a similar linear relation to the number of carbon atoms of the alkanes.