Grand-canonical Transition-matrix Monte 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.

Role of site–site interaction on the phase equilibria of multiple-site associating fluids in a functionalized slit pore

Vapor–liquid phase equilibria for multiple sites associating fluids with different associating strengths are investigated in a slit pore using grand-canonical transition matrix Monte Carlo method. The increase of critical temperature from two-site to four-site associating fluids at constant site strength is quite significant as compared to that of the one-site to two-site associating fluids, which is more pronounced at higher associating strength (ϵ* = 6). Monomer fraction and cluster size distribution are used to investigate the association of fluid particles in coexistence phases. The monomer fraction for both phases decreases with increased associating sites on the fluid particles due to more site–site interaction with neighboring fluid particles and forming a larger cluster. Therefore, the number of associating sites and their distribution play a vital role in the association of fluid particles. Moreover, the saturation chemical potential changes with the arrangement of the sites. For two-site associating fluids, we observe early vapor–liquid transition when the sites are oppositely placed, and when the sites are placed at 90°, the vapor–liquid transition is observed at the higher chemical potential. Moreover, four-site associating fluids with a square arrangement show early vapor–liquid phase transition, mainly because these arrangements of sites effectively interact with surface sites and the molecules in the next layer.

Effect of shape anisotropy on the precipitation of dimeric nanoparticles.

We use grand canonical transition matrix Monte Carlo simulations to study the precipitation of dimeric nanoparticles. The dimers are composed of two particles having different chemical features and separated by a fixed distance. The non-attractive and attractive parts of the dimer are modeled using hard-sphere and square-well potentials, respectively. The shape anisotropy is altered by changing the relative sizes of the two particles. We observe that the stability of the nanosuspension increases with the increase in the size of the non-attractive part of the dimer. The precipitates of dimers having larger non-attractive parts have lower packing densities, contain large cavities, and show evidence of self-assembly in the bulk and on the surface. We also use the results from our simulations and the classical nucleation theory to study the kinetics of precipitation. At a given temperature and relative supersaturation, the rate of homogeneous nucleation increases with the increase in the size of the non-attractive parts. Finally, we use an example to show how our results can guide the design of nanosuspensions containing chemically anisotropic dimers that are stable under particular conditions.

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 Thermodynamic Properties of Levulinic Acid via Molecular Simulation Techniques.

Second-generation biofuels are a complex mixture of organic compounds that can be further processed to hydrocarbon fuels and other valuable chemicals. One such chemical is levulinic acid (IUPAC name: 4-oxo pentanoic acid), which is a highly versatile ketoacid obtained from cellulose present in agricultural byproducts. For oxygen-containing compounds that decompose at elevated temperatures and pressures, determining the vapor–liquid equilibria data at high temperatures via the experimental route may be challenging. The molecular simulation approach is a cost-effective tool to obtain the necessary data while also allowing us to understand the microscopic origins of macroscopic observable properties. We have employed the transferable potential for phase equilibria-united atom force field to describe the interactions in this system with the parameters for a torsional interaction that are not reported in the literature (levulinic acid is a ketoacid) being determined from density functional theory calculations. We have verified our parameterization via density computations in the isothermal–isobaric ensemble and by comparing our simulation results with the corresponding data from experiments reported in the literature. We have performed grand-canonical transition-matrix Monte Carlo simulations in the temperature range from 580 to 690 K to estimate the vapor–liquid coexistence curves in the temperature–density plane and the Clapeyron plots. From this data, the critical point (TC = 755 K, ρC = 285.4 kg/m3, and PC = 30.57 bar) has been estimated, and this may be used as input to the equations of state employed in process simulation software for design of industrial separation processes including those for “biorefining”. As levulinic acid is a “ketoacid”, hydrogen bonding occurs, and the liquid phase structure has also been studied using radial distribution functions.

Study of fluid phase equilibria of triangle-well mixtures in bulk and under confinement using grand canonical transition matrix Monte Carlo

Grand canonical transition matrix Monte Carlo simulations are used to determine the fluid phase diagrams, at two different temperatures, in bulk and under confinement of weakly attractive slit pores, for four different types of binary mixtures: mixture 1 is symmetric, with a weakened interaction between the unlike species (unlike the other three mixtures), mixture 2 with asymmetry in size of the molecules, mixture 3 with asymmetry in the depth of the potential well and, finally, mixture 4 where both the size and well-depth are different. The triangle-well (TW) potential is employed to model the fluid-fluid and wall-fluid interactions as this potential provides simple, qualitatively accurate and practical representation of the interactions present in real systems. The simple nature of the TW models enables us to obtain a qualitative understanding of the effects of the fluid-fluid potential parameters and the effect of confinement on the vapor-liquid coexistence behavior of the four different types of TW fluid mixtures described above. Significant differences in the vapor-liquid coexistence behavior of the confined fluid from the bulk phase behavior are observed. Comparison of the bulk and confined systems indicate that the intersection of the liquid-liquid phase envelope with the vapor-liquid equilibrium (VLE) curve observed in the bulk phase of mixture 1 does not occur under confinement with the heteroazeotrope being replaced by VLE showing an azeotrope at lower pressures and liquid-liquid coexistence at higher pressure. A significant decrease in the area of the vapor + liquid coexistence region is noted for mixture 2. The supercritical behavior of component 2 is noted for the confined systems in mixtures 3 and 4 at both temperatures, however, the pressure-composition diagram in the bulk system shows supercritical behavior only at the higher temperature. Canonical Monte Carlo simulations were subsequently performed on the confined systems to obtain the energy values and the density and composition profiles along the pore width at the equilibrium points. The latter data have been utilized to explain the phase diagrams of the confined mixtures and correlate the differences in the phase diagrams to the variation in the potential parameters.

Vapor–Liquid Equilibria of Mixtures of Molecular Fluids Using the Activity Fraction Expanded Ensemble Simulation Method

The activity fraction expanded ensemble (AFEE) simulation technique has been extended to predict the vapor–liquid coexistence behavior of binary mixtures of molecular fluids. The systems of molecular mixtures studied are thiophene–n-hexane (a mixture of an aromatic compound with a n-alkane) and methane–n-hexane (mixture of n-alkanes with significant difference in size). Comparison with results from the grand canonical transition matrix Monte Carlo method and experimental data available in the literature has also been provided. Further, we have investigated the computational efficiency of the AFEE technique at temperatures where both compounds exhibit subcritical behavior (thiophene–n-hexane at 338.15 K) and where one of the components shows supercritical behavior (methane–n-hexane at 373 K). Canonical Monte Carlo simulations are also performed to obtain the radial distribution functions which have been used to study the structure of the coexisting liquid phases to gain insights into the molecular origins ...

Critical temperature estimation of bulk and confined atomic fluid using vapour−liquid interfacial free energy

The critical temperatures of bulk and confined atomic fluids are investigated using values of the vapour−liquid interfacial free energy of coexistence obtained from grand-canonical transition-matrix Monte Carlo simulations using a histogram reweighting technique. The temperature corresponding to zero interfacial free energy of coexistence is the estimated critical temperature for the system under investigation. Slit width of confined atomic fluid for this investigation is varied from 40 to 1 fluid particle diameter. The obtained critical temperatures have shown nonlinear monotonic trend with inverse of slit width. Moreover, five different linear regimes of critical temperature are observed in the studied range of slit width. Interestingly, in the slit width range of less than two fluid particle diameters, the critical temperature approaches two-dimensional value and remains approximately indifferent with a decrease in slit width up to one fluid particle diameter. This investigation also reveals that the critical temperature of bulk and confined atomic fluid estimated using the vapour−liquid interfacial free energy of coexistence is within reasonable accuracy with that obtained using the simplified form of scaling law.

Phase Equilibria and Critical Point Predictions of Mixtures of Molecular Fluids Using Grand Canonical Transition Matrix Monte Carlo

Mixtures of molecular fluids are encountered often in chemical industry, and the vapor–liquid coexistence curves are required for efficient design of separation processes. Hence, a computational scheme employing the Wang–Landau and grand canonical transition matrix Monte Carlo molecular simulation techniques is used for the first time to compute the fluid phase diagrams of molecular mixtures. Binary mixtures of n-alkanes, viz., methane–ethane, ethane–propane, propane–n-butane systems, are studied here as examples of molecular mixtures. The total molecule number probability distribution, obtained from the GC-TMMC simulations, allows us to directly calculate coexistence properties such as pressure, density, and composition. On comparison with experimental data, reported in the literature, it was observed that the predicted VLE properties, with the exception of pressure, are in close agreement with the corresponding experimental values. The deviation of calculated pressure from experiments could be attribute...

Corresponding states vapour–liquid phase equilibria of confined square–well fluid

Corresponding states vapour–liquid phase equilibria of confined square-well fluid are studied by means of grand-canonical transition-matrix Monte Carlo simulation and histogram reweighting method. In this study, square-well fluid is considered under hard and attractive slit pore confinements ranging from 1.5 to 40 molecular diameters. Corresponding states vapour–liquid phase coexistence envelopes display insignificant effect of wall−fluid interaction for slit pore confinements ranging from 1.5 to 3 molecular diameters. On the other hand, significant effect of wall−fluid interaction on the corresponding state coexistence envelope is observed for slit pore confinements ranging from 4 to 40 molecular diameters. Moreover, at a given slit width, shrinking in corresponding state coexistence envelope is observed with increase in the wall−fluid interaction. However, in the larger slit pore width of 30 to 40 molecular diameters, shrinking in the corresponding state vapour–liquid coexistence envelopes become indifferent with the stronger wall−fluid interactions studied in this work. Structural behaviour of coexisting phases in slit pores are also investigated through local density profiles, to understand the overall behaviour of corresponding states coexistence envelopes. Fluctuating positive and negative deviations in the corresponding state spreading pressure with respect to corresponding bulk value is observed for studied wall−fluid interactions and slit pore confinements.

Prediction of fluid-phase behavior of symmetrical binary Yukawa fluids using transition matrix Monte Carlo

Binary fluid mixtures display a wide array of fluid phase behavior ranging from simple vapor-liquid equilibrium diagrams to more complicated topology like azeotropy and heteroazeotropy. As a first step towards understanding the phenomena of equilibrium of binary molecular systems, the properties of binary monoatomic fluids have been studied in this work. An additional simplification made in this work is that of a symmetrical binary system where all similar molecules interact via the hard-core Yukawa (HCY) potential, u(r), while the dissimilar molecules interact via a potential, δu(r) where δ is a scalar parameter. The value of δ here is 0.75, which leads to the dissimilar molecules showing a tendency to dislike one another and the resulting phase diagram is such that the mixing-demixing line intersects the vapor-liquid equilibrium curve away from the vapor-liquid critical point. The effect of the variable potential range parameter of the HCY potential on the topology of the phase diagrams is investigated using grand canonical transition matrix Monte Carlo simulations and the conditions of temperature and pressure at which the system exhibits azeotropy and heteroazeotropy are ascertained. We find that the densities of the mixtures, as predicted by our simulation at equimolar concentrations, are in close agreement with the self-consistent Ornstein-Zernike approximation results of Schöll-Paschinger and co-workers.

Relation between pore size and the compressibility of a confined fluid.

When a fluid is confined to a nanopore, its thermodynamic properties differ from the properties of a bulk fluid, so measuring such properties of the confined fluid can provide information about the pore sizes. Here, we report a simple relation between the pore size and isothermal compressibility of argon confined in such pores. Compressibility is calculated from the fluctuations of the number of particles in the grand canonical ensemble using two different simulation techniques: conventional grand-canonical Monte Carlo and grand-canonical ensemble transition-matrix Monte Carlo. Our results provide a theoretical framework for extracting the information on the pore sizes of fluid-saturated samples by measuring the compressibility from ultrasonic experiments.

Effect of surface-screening parameter of the Yukawa potential model on vapour–liquid phase coexistence and critical-point properties of confined Yukawa fluid

We report the effect of surface-screening parameter of Yukawa potential model on vapour–liquid phase coexistence and critical-point properties of slit–pore-confined Yukawa fluid, using grand canonical transition-matrix Monte Carlo along with the histogram reweighting method. The effect of surface-screening parameter on the vapour–phase coexistence density is insignificant for the studied system. On the other hand, significant effect of surface-screening parameter is observed on liquid phase coexistence density. With increasing surface-screening parameter, liquid phase coexistence density decreases. Critical-point properties have shown monotonic decreasing trends with increase in surface-screening parameter. Moreover, the effect of change of surface-screening parameter is least on critical temperature changes as compared to critical density and critical pressure changes for the studied Yukawa system in this work.

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...

A comparative study of critical temperature estimation of atomic fluid and chain molecules using fourth-order Binder cumulant and simplified scaling laws

Grand-canonical transition-matrix Monte Carlo simulation with histogram reweighting and finite-size scaling technique are used to calculate fourth-order Binder cumulant of order parameter along the vapour–liquid coexistence line to calculate the critical temperature of bulk and confined square-well fluid in slit pore of two pore sizes. Further, this approach is utilised to estimate the critical temperatures of relatively more complex fluids such as n-alkanes confined in graphite and mica slit pores of different slit widths. The estimated critical temperatures are compared with the critical temperature obtained for the same systems using simplified form of the scaling law. This investigation reveals that critical temperatures of simple and complex fluids in bulk state and under confinement, estimated using the scaling law, are within reasonable accuracy with that obtained using more accurate and rigorous approach of fourth-order Binder's cumulant.

Vapor-liquid phase coexistence and transport properties of two-dimensional oligomers

Grand-canonical transition-matrix Monte Carlo and histogram reweighting techniques are used herein to study the vapor-liquid coexistence properties of two-dimensional (2D) flexible oligomers with varying chain lengths (m = 1-8). The phase diagrams of the various 2D oligomers follow the correspondence state (CS) principle, akin to the behavior observed for bulk oligomers. The 2D critical density is not influenced by the oligomer chain length, which contrasts with the observation for the bulk oligomers. Line tension, calculated using Binder's formalism, in the reduced plot is found to be independent of chain length in contrast to the 3D behavior. The dynamical properties of 2D fluids are evaluated using molecular dynamics simulations, and the velocity and pressure autocorrelation functions are investigated using Green-Kubo (GK) relations to yield the diffusion and viscosity. The viscosity determined from 2D non-equilibrium molecular dynamics simulation is compared with the viscosity estimated from the GK relations. The GK relations prove to be reliable and efficient for the calculation of 2D transport properties. Normal diffusive regions are identified in dense oligomeric fluid systems. The influence of molecular size on the diffusivity and viscosity is found to be diminished at specific CS points for the 2D oligomers considered herein. In contrast, the viscosity and diffusion of the 3D bulk fluid, at a reduced temperature and density, are strongly dependent on the molecular size at the same CS points. Furthermore, the viscosity increases and the diffusion decreases multifold in the 2D system relative to those in the 3D system, at the CS points.

Surface phase transitions of multiple-site associating fluids

Surface phase transitions of Lennard–Jones (LJ) based two- and four-site associating fluids have been studied for various associating strengths using grand-canonical transition matrix Monte Carlo simulations. Our results suggest that, in the case of a smooth surface, represented by a LJ 9-3-type potential, multiple-site associating fluids display a prewetting transition within a certain temperature range. However, the range of the prewetting transition decreases with increasing associating strength and increasing number of sites on the fluid molecules. With the addition of associating sites on the surface, a quasi-2D vapor–liquid transition may appear, which is observed at a higher surface site density for weaker associating fluids. The prewetting transition at lower associating strength is found to shift towards the quasi-2D vapor–liquid transition with increasing surface site density. However, for highly associating fluids, the prewetting transition is still intact, but shifts slightly towards the lower temperature range. Adsorption isotherms, chemical potentials and density profiles are used to characterize surface phase transitions.

Surface Phase Transition of Associating Fluids on Functionalized Surfaces

Surface phase transitions are studied for Lennard-Jones (LJ) based dimer forming associating fluids on modified surfaces with active sites for various association strengths using grand-canonical transition matrix Monte Carlo. We examine adsorption isotherm, density, energy, and monomer profiles to differentiate layering, quasi-2D vapor–liquid and prewetting transitions. Prewetting transition is found for association strengths: εaf = 8 and 10, whereas, for weaker associating fluids, εaf = 4 and 6, we observe quasi-2D vapor–liquid transition. The growth of thick films in the case of quasi-2D vapor liquid transitions is found to suppress with decrease in temperature and eventually splits in layering transitions. For systems exhibiting prewetting transition, wetting temperature and prewetting critical temperature increase with increasing association strength. In addition, we examine boundary tension of quasi-2D and prewetting transitions using finite size scaling formalism of Binder. Our results indicate that the quasi-2D boundary tension is lower than that of the prewetting transition. Surface sites are found to reduce the boundary tension; however, the effect of active sites diminishes with stronger fluid–fluid associating strength.

Vapour–liquid phase equilibria of simple fluids confined in patterned slit pores

We present the influence of surface heterogeneity on the vapour–liquid phase behaviour of square-well fluids in slit pores using grand-canonical transition-matrix Monte Carlo simulations along with the histogram-reweighting method. Properties such as phase coexistence envelopes, critical properties and local density profiles of the confined SW fluid are reported for chemically and physically patterned slit surfaces. It is observed that in the chemically patterned pores, fluid–fluid and surface attraction parameters along with the width of attractive and inert stripes play fundamentally different roles in the phase coexistence and critical properties. On the other hand, pillar gap and height significantly affect the vapour–liquid equilibria in the physically patterned slit pores. We also present the effect of chemically and physically patterned slit surfaces on the spreading pressure.

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.