Grand-canonical Transition-matrix Monte Carlo Research Articles

Efficient Modeling of Water Adsorption in MOFs Using Interpolated Transition Matrix Monte Carlo.

With the specter of accelerating climate change, securing access to potable water has become a critical global challenge. Atmospheric water harvesting (AWH) through metal-organic frameworks (MOFs) emerges as one of the promising solutions. The standard numerical methods applied for rapid and efficient screening for optimal sorbents face significant limitations in the case of water adsorption (slow convergence and inability to overcome high energy barriers). To address these challenges, we employed grand canonical transition matrix Monte Carlo (GC-TMMC) methodology and proposed an efficient interpolation scheme that significantly reduces the number of required simulations while maintaining accuracy of the results. Through the example of water adsorption in three MOFs: MOF-303, MOF-LA2-1, and NU-1000, we show that the extrapolation of the free energy landscape allows for prediction of the adsorption properties over a continuous range of pressure and temperature. This innovative and versatile method provides rich thermodynamic information, enabling rapid, large-scale computational screening of sorbents for adsorption, applicable for a variety of sorbents and gases. As the presented methodology holds strong applicative potential, we provide alongside this paper a modified version of the RASPA2 code with a ghost swap move implementation and a Python library designed to minimize the user's input for analyzing data derived from the TMMC simulations.

Phase behaviour of confined associating fluid in a functionalized slit pore: a Monte Carlo study

Vapour-liquid phase equilibria of associating fluids under confinement are investigated using Grand-Canonical Transition Matrix Monte Carlo (GC-TMMC) method. Various properties of coexistence phases and critical properties are estimated for multiple associating fluids at different slit widths. The structural features of coexistence phases are examined through monomer fraction, density profile, and orientation profile. The role of surface sites on the phase behaviour under confinement is critically examined. It has a significant effect on the structural behaviour of coexistence phases, leading to a change in the properties of coexistence phases. In particular, the orientation of associating fluid molecules near the functionalized surface is entirely different than in the case of a smooth surface. The orientation of two sites associating (when sites are located oppositely to each other) fluid molecules is normal to surface, forming bonds with surface sites in one direction and another bond with molecules in an adjacent layer.

Prediction of Vapor–Liquid Coexistence Data for p-Cymene Using Equation of State Methods and Monte Carlo Simulations

A naturally occurring aromatic organic compound, p-cymene, finds applications as reaction intermediate, solvent in production of pharmaceuticals, fragrances, and fine chemicals. The experimental vapor liquid equilibria (VLE) data of p-cymene is available at pressures up to 537.4 kPa. In this study, the thermodynamic properties of p-cymene are determined using structure property correlations combined with equations of state (EoS) and molecular simulation techniques. Two molecular simulation techniques, Gibbs ensemble Monte Carlo (GEMC) and grand canonical-transition matrix Monte Carlo (GC-TMMC) have been employed for prediction of VLE. The estimates of properties, including vapor pressures, heats of vaporization, coexistence densities, and critical properties have been compared with available experimental data. The thermodynamic properties predicted by molecular simulations and also that obtained from Peng–Robinson (PR) and volume translated Peng–Robinson (VTPR) EoS are generally, in broad agreement with the experimental data. Further, GEMC results for coexistence densities and saturation vapor pressures are compared with that from GC-TMMC technique.

Use of the Grand Canonical Transition-Matrix Monte Carlo Method to Model Gas Adsorption in Porous Materials

We present grand canonical transition-matrix Monte Carlo (GC-TMMC) as an efficient method for simulating gas adsorption processes, with particular emphasis on subcritical gas adsorption in which capillary phase transitions are present. As in other applications of TMMC, the goal of the simulation is to compute a particle number probability distribution (PNPD), from which thermophysical properties of the system can be computed. The key advantage of GC-TMMC is that, by appropriate use of histogram reweighting, one can generate an entire adsorption isotherm, including those with hysteresis loops, from the PNPD generated by a single GC-TMMC simulation. We discuss how to determine various thermophysical properties of an adsorptive system from the PNPD, including the identification of capillary phases and capillary phase transitions, the equilibrium phase transition, other free energies, and the heat of adsorption. To demonstrate the utility of GC-TMMC for studies of adsorption, we apply the method to various sy...

Effect of pore morphology on vapor–liquid phase transition and crossover behavior of critical properties from 3D to 2D

Grand-canonical transition-matrix Monte Carlo (GC-TMMC) simulation, is used to investigate the effect of pore shape and surface-fluid strength on the vapor–liquid phase transition and crossover behavior of critical properties from 3D to 2D of a square well (SW) fluid. We present the vapor–liquid coexistence phase diagram in hard and attractive cylindrical pores of varying slit width from 4 to 50 molecular diameters. This investigation indicates that having same pore shape but different surface nature can significantly alter the coexistence envelopes and hence the critical point. Critical temperature is found to approach the 3D bulk value monotonically irrespective of the pore shape and surface nature. However, the rate of approach of critical point towards the 3D bulk value decreases as the effective confinement increases. On the other hand, approach of pore critical density towards the bulk 3D value follows a non-monotonic path, irrespective of pore shape and surface strength. Interestingly, with the same pore shape, attractive wall surface follows an opposite trend to approach the bulk critical density as compared to that of hard wall surface. Crossover from 3D to 2D behavior in the hard cylindrical pores is observed around 28 molecular diameters, which is significantly larger than that observed by earlier workers for hard and attractive slit pores.

Prewetting transitions of one site associating fluids

Prewetting transitions are studied for Lennard-Jones (LJ) based dimer forming associating fluids, on a structureless surface represented by LJ 9-3 type potential, for various association strengths using grand-canonical transition matrix Monte Carlo (GC-TMMC) and histogram reweighting techniques. Occurrences of prewetting transition are observed for association strengths: epsilon(af)=2.0, 4.0, 6.0, 8.0, and 10.0. Structural properties, monomer fraction, and orientation order profile of thin-thick film of one-site associating fluids are presented. Wetting temperature, T(w), and prewetting critical temperature, T(pwc), increases with increasing association strength, which is in agreement with the results of the density functional theory (DFT). Length of prewetting line, on the other hand, is found to decrease first with increasing association energy until epsilon(af)=8.0 and subsequently found to increase substantially for epsilon(af)=10. This behavior is contrary to the prediction from the DFT. We observe that the boundary tension of thin-thick film via GC-TMMC and finite size scaling exhibits a maximum with respect to association strength.

Quasi-2D and prewetting transitions of square-well fluids on a square-well substrate

Molecular simulation methodologies are employed to study the first-order transition of variable square-well (SW) fluids on a wide range of weak attractive surfaces. Surface phase diagram of SW fluids of attractive well diameter λ ff = 1.5, 1.75, 2.0 on a smooth, structureless surface modelled by a SW potential is reported via grand-canonical transition-matrix Monte Carlo (GC-TMMC) and histogram reweighting techniques. Fluids with λ ff = 1.5 and 1.75 show quasi-2D vapour–liquid phase transition; on the other hand, prewetting transition is visible for a SW fluid with larger well-extent λ ff = 2.0. The prewetting line, its length, and closeness to the bulk saturation curve are found to depend strongly on the nature of the fluid–fluid and fluid–wall interaction potentials. Boundary tension of surface coexistence films is calculated by two methods. First, the finite size scaling approach of Binder is used to evaluate the boundary tension via GC-TMMC. Second, the results of the boundary tension are verified by virtue of its relation to the pressure tensor components, which are calculated using a NVT-Monte Carlo approach. The results from the two methods are in good agreement. Boundary tension is found to increase with the increase in the wall–fluid interaction range for the quasi-2D system; conversely, boundary tension for thin–thick film, at prewetting transition, decreases with the increase in the wall–fluid interaction range.

Surface tension and vapour–liquid phase coexistence of variable-range hard-core attractive Yukawa fluids

The vapour–liquid phase coexistence and surface tension of hard-core Yukawa fluids with short attraction range, λ = 8.0, 9.0 and 10.0, are reported using grand-canonical transition-matrix Monte Carlo (GC-TMMC) with the histogram reweighting method. Surface tension is calculated using finite-size scaling approach of Binder. We also compare GC-TMMC results with the available literature data for Yukawa fluids with λ = 1.8, 3.0 and 4.0. Critical properties obtained from rectilinear diameter approach and least square-technique are also reported. GC-TMMC results are found to be more precise than the previous reported values. We also present the corresponding state of surface tension for extremely short-range attractive Yukawa fluids.

Vapor-liquid critical and interfacial properties of square-well fluids in slit pores

Vapor-liquid phase equilibria of square-well (SW) fluids of variable interaction range: lambdasigma=1.25, 1.75, 2.0, and 3.0 in hard slit pores are studied by means of grand-canonical transition-matrix Monte Carlo (GC-TMMC) simulation. Critical density under confinement shows an oscillatory behavior as slit width, H, reduced from 12sigma to 1sigma. Two linear regimes are found for the shift in the critical temperature with the inverse in the slit width. The first regime is seen for H>2.0sigma with linear increase in the slope of shift in the critical temperature against inverse slit width with increasing interaction range. Subsequent decrease in H has little consequence on the critical temperature and it remains almost constant. Vapor-liquid surface tensions of SW fluids of variable well extent in a planar slit pore of variable slit width are also reported. GC-TMMC results are compared with that from slab based canonical Monte Carlo and molecular dynamics techniques and found to be in good agreement. Although, vapor-liquid surface tension under confinement is found to be lower than the bulk surface tension, the behavior of surface tension as a function of temperature is invariant with the variable pore size. Interfacial width, xi, calculated using a hyperbolic function increases with decreasing slit width at a given temperature, which is contrary to what is being observed recently for cylindrical pores. Inverse scaled interfacial width (xi/H), however, linearly increases with increase in the scaled temperature (T(c,bulk)-T)/T(c,bulk).

The effects of interaction range, porosity and molecular association on the phase equilibrium of a fluid confined in a disordered porous media

Grand-canonical transition-matrix Monte Carlo (GC-TMMC) is employed to analyse the effects of range of interaction, packing fraction and molecular association on phase coexistence properties of square-well (SW) based fluids in disordered pores. The nature of the phase equilibria were studied inside a repulsive disordered porous media with packing fractions, η m = 0.05 and 0.10. Three values of the SW attractive well range parameter were studied: λ = 1.5, 1.75, and 2.0. Coexistence number probability distribution reflects the signature of the disordered structure of the porous matrix. Yet, no multiple fluid–fluid transition was observed. The effect of strength of molecular association on coexistence densities, density profile, saturation pressure, and monomer fraction for the SW based dimerizing fluids inside a repulsive disordered media is reported. Association is found to increase as the packing fraction of the matrix increase. Critical properties of these confined fluids are calculated via a rectilinear diameter approach. Fractional shift in the critical temperature linearly decreases with the increase in the attractive well width for non-associating fluids. The rate of decrease in the critical temperature shift increases with the increase in packing fraction. Associating sites are found to suppress the shift in the critical temperature.

Comparing the Use of Gibbs Ensemble and Grand-Canonical Transition-Matrix Monte Carlo Methods to Determine Phase Equilibria

We present results from a computational study investigating the use of Gibbs ensemble and grand-canonical transition-matrix Monte Carlo (GC-TMMC) methods to determine the liquid−vapor phase coexistence properties of pure molecular fluids of varying degrees of complexity. The molecules used in this study were ethane, n-octane, cyclohexane, 2,5-dimethylhexane, 1-propanol, and water. We first show that the GC-TMMC method can reproduce Gibbs ensemble results found in the literature. Given the excellent agreement for each molecule, we then compare directly the performance of Gibbs ensemble and GC-TMMC simulations at both low and high reduced temperatures by monitoring the relative uncertainties in the saturation properties as a function of computational time. In general, we found that the GC-TMMC method yielded limiting uncertainties in the saturated vapor density and pressure that were significantly smaller, by an order of magnitude in some instances, than those of the Gibbs ensemble method. Limiting Gibbs ensemble uncertainties for these properties were generally in the 0.8−5.0% range. However, both methods yielded comparable limiting uncertainties in the saturated liquid density, which fell within the range of 0.1−1.0%. In the case of water at 300 K, we found that the Gibbs ensemble outperformed GC-TMMC. The relatively poor performance of the GC-TMMC method in this situation was tied to the slow convergence of the density probability distribution at this low temperature. We also discuss strategies for improving the convergence rate under these conditions.

Thin-thick surface phase coexistence and boundary tension of the square-well fluid on a weak attractive surface

Prewetting transition is studied for the square-well fluid of attractive-well diameter lambda(ff)sigma(ff)=1.5 in the presence of a homogeneous surface modeled by the square-well potential of attractive well from 0.8sigma(ff) to 1.8sigma(ff). We investigate surface phase coexistence of thin-thick film transition using grand-canonical transition matrix Monte Carlo (GC-TMMC) and histogram reweighting techniques. Molecular dynamics (MD) and GC-TMMC are utilized to predict the properties of the fluid for various surface fluid affinities. Occurrences of prewetting transition with the variation of surface affinity are observed for a domain of reduced temperature from T(*)=0.62 to 0.75. We have used MD and GC-TMMC+finite size scaling (FSS) simulations to calculate the boundary tension as a function of temperature as well as surface affinity. Boundary tensions via MD and GC-TMMC+FSS methods are in good agreement. The boundary tension increases with the decrease of wall-fluid affinity. Prewetting critical properties are calculated using rectilinear diameter approach and scaling analysis. We found that critical temperature and density increase with the decrease of wall-fluid affinity.

Molecular Simulation Study of Vapor-Liquid Equilibrium of Morse Fluids

The Morse potential energy function (PEF) is considered regarding the characterization of interaction forces of particles with tuning parameters. Phase coexistence of Morse fluids is predicted for different steepness and range of the PEF parameters using the grand-canonical transition matrix Monte Carlo (GC-TMMC) method, with quantification of the parameter S, which is the product of a constant with a unit of reciprocal length and the equilibrium distance between two molecules. We found that a lower limit of S exists bounded by infinite critical temperature. The critical properties of the vapor-liquid equilibrium curves are estimated using a rectilinear diameter method and a scaling law approach. A Clausius-Clayperon type relation of S and critical temperature is derived in this work. Vapor-liquid surface tension of Morse fluids by finite size scaling and GC-TMMC is also reported. Surface tensions are found to be higher at lower S.

Surface tension and vapor-liquid phase coexistence of confined square-well fluid

Phase equilibria of a square-well fluid in planar slit pores with varying slit width are investigated by applying the grand-canonical transition-matrix Monte Carlo (GC-TMMC) with the histogram-reweighting method. The wall-fluid interaction strength was varied from repulsive to attractive such that it is greater than the fluid-fluid interaction strength. The nature of the phase coexistence envelope is in agreement with that given in literature. The surface tension of the vapor-liquid interface is calculated via molecular dynamics simulations. GC-TMMC with finite size scaling is also used to calculate the surface tension. The results from molecular dynamics and GC-TMMC methods are in very good mutual agreement. The vapor-liquid surface tension, under confinement, was found to be lower than the bulk surface tension. However, with the increase of the slit width the surface tension increases. For the case of a square-well fluid in an attractive planar slit pore, the vapor-liquid surface tension exhibits a maximum with respect to wall-fluid interaction energy. We also report estimates of critical properties of confined fluids via the rectilinear diameter approach.

Surface tension and vapor–liquid phase coexistence of the square-well fluid

Vapor–liquid interfacial tension of square-well (SW) fluids is calculated using three different methods viz., molecular dynamics (MD) with collision-based virial evaluation, Monte Carlo with virial computed by volume perturbation, and Binder’s density-distribution method in conjunction with grand-canonical transition-matrix Monte Carlo (GC-TMMC). Three values of the SW attractive well range parameter were studied: λ=1.5, 1.75, and 2.0, respectively. The results from MD and GC-TMMC methods are in very good mutual agreement, while the volume-perturbation method yields data of unacceptable quality. The results are compared with predictions from the statistical associating fluid theory (SAFT), and SAFT is shown to give a good estimate for the systems studied. Liquid and vapor coexistence densities and saturation pressure are determined from analysis of GC-TMMC data and the results are found to agree very well with the established literature data.