Efficient Application of Continuous Fractional Component Monte Carlo in the Reaction Ensemble

The Impact of Metal Centers in the M-MOF-74 Series on Formic Acid Production

The confinement effect of porous materials on the thermodynamical equilibrium of the CO2 hydrogenation reaction presents a cost-effective alternative to transition metal catalysts. In metal-organic frameworks, the type of metal center has a greater impact on the enhancement of formic acid production than the scale of confinement resulting from the pore size. The M-MOF-74 series enables a comprehensive study of how different metal centers affect HCOOH production, minimizing the effect of pore size. In this work, molecular simulations were used to analyze the adsorption of HCOOH and the CO2 hydrogenation reaction in M-MOF-74, where M = Ni, Cu, Co, Fe, Mn, Zn. We combine classical simulations and density functional theory calculations to gain insights into the mechanisms that govern the low coverage adsorption of HCOOH in the surrounding of the metal centers of M-MOF-74. The impact of metal centers on the HCOOH yield was assessed by Monte Carlo simulations in the grand-canonical ensemble, using gas-phase compositions of CO2, H2, and HCOOH at chemical equilibrium at 298.15-800 K, 1-60 bar. The performance of M-MOF-74 in HCOOH production follows the same order as the uptake and the heat of HCOOH adsorption: Ni > Co > Fe > Mn > Zn > Cu. Ni-MOF-74 increases the mole fraction of HCOOH by ca. 105 times compared to the gas phase at 298.15 K, 60 bar. Ni-MOF-74 has the potential to be more economically attractive for CO2 conversion than transition metal catalysts, achieving HCOOH production at concentrations comparable to the highest formate levels reported for transition metal catalysts and offering a more valuable molecular form of the product.

Sequestration of Small Ions and Weak Acids and Bases by a Polyelectrolyte Complex Studied by Simulation and Experiment

Mixing of oppositely charged polyelectrolytes can result in phase separation into a polymer-poor supernatant and a polymer-rich polyelectrolyte complex (PEC). We present a new coarse-grained model for the Grand-reaction method that enables us to determine the composition of the coexisting phases in a broad range of pH and salt concentrations. We validate the model by comparing it to recent simulations and experimental studies, as well as our own experiments on poly(acrylic acid)/poly(allylamine hydrochloride) complexes. The simulations using our model predict that monovalent ions partition approximately equally between both phases, whereas divalent ones accumulate in the PEC phase. On a semiquantitative level, these results agree with our own experiments, as well as with other experiments and simulations in the literature. In the sequel, we use the model to study the partitioning of a weak diprotic acid at various pH values of the supernatant. Our results show that the ionization of the acid is enhanced in the PEC phase, resulting in its preferential accumulation in this phase, which monotonically increases with the pH. Currently, this effect is still waiting to be confirmed experimentally. We explore how the model parameters (particle size, charge density, permittivity, and solvent quality) affect the measured partition coefficients, showing that fine-tuning of these parameters can make the agreement with the experiments almost quantitative. Nevertheless, our results show that charge regulation in multivalent solutes can potentially be exploited in engineering the partitioning of charged molecules in PEC-based systems at various pH values.

Interfacial Tensions, Solubilities, and Transport Properties of the H2/H2O/NaCl System: A Molecular Simulation Study

Data for several key thermodynamic and transport properties needed for technologies using hydrogen (H2), such as underground H2 storage and H2O electrolysis are scarce or completely missing. Force field-based Molecular Dynamics (MD) and Continuous Fractional Component Monte Carlo (CFCMC) simulations are carried out in this work to cover this gap. Extensive new data sets are provided for (a) interfacial tensions of H2 gas in contact with aqueous NaCl solutions for temperatures of (298 to 523) K, pressures of (1 to 600) bar, and molalities of (0 to 6) mol NaCl/kg H2O, (b) self-diffusivities of infinitely diluted H2 in aqueous NaCl solutions for temperatures of (298 to 723) K, pressures of (1 to 1000) bar, and molalities of (0 to 6) mol NaCl/kg H2O, and (c) solubilities of H2 in aqueous NaCl solutions for temperatures of (298 to 363) K, pressures of (1 to 1000) bar, and molalities of (0 to 6) mol NaCl/kg H2O. The force fields used are the TIP4P/2005 for H2O, the Madrid-2019 and the Madrid-Transport for NaCl, and the Vrabec and Marx for H2. Excellent agreement between the simulation results and available experimental data is found with average deviations lower than 10%.

Calculating Thermodynamic Factors for Diffusion Using the Continuous Fractional Component Monte Carlo Method

Thermodynamic factors for diffusion connect the Fick and Maxwell-Stefan diffusion coefficients used to quantify mass transfer. Activity coefficient models or equations of state can be fitted to experimental or simulation data, from which thermodynamic factors can be obtained by differentiation. The accuracy of thermodynamic factors determined using indirect routes is dictated by the specific choice of an activity coefficient model or an equation of state. The Permuted Widom's Test Particle Insertion (PWTPI) method developed by Balaji et al. enables direct determination of thermodynamic factors in binary and multicomponent systems. For highly dense systems, for example, typical liquids, it is well known that molecular test insertion methods fail. In this article, we use the Continuous Fractional Component Monte Carlo (CFCMC) method to directly calculate thermodynamic factors by adopting the PWTPI method. The CFCMC method uses fractional molecules whose interactions with their surrounding molecules are modulated by a coupling parameter. Even in highly dense systems, the CFCMC method efficiently handles molecule insertions and removals, overcoming the limitations of the PWTPI method. We show excellent agreement between the results of the PWTPI and CFCMC methods for the calculation of thermodynamic factors in binary systems of Lennard-Jones molecules and ternary systems of Weeks-Chandler-Andersen molecules. The CFCMC method applied to calculate the thermodynamic factors of realistic molecular systems consisting of binary mixtures of carbon dioxide and hydrogen agrees well with the NIST REFPROP database. Our study highlights the effectiveness of the CFCMC method in determining thermodynamic factors for diffusion, even in densely packed systems, using relatively small numbers of molecules.

A New Force Field for OH- for Computing Thermodynamic and Transport Properties of H2 and O2 in Aqueous NaOH and KOH Solutions

The thermophysical properties of aqueous electrolyte solutions are of interest for applications such as water electrolyzers and fuel cells. Molecular dynamics (MD) and continuous fractional component Monte Carlo (CFCMC) simulations are used to calculate densities, transport properties (i.e., self-diffusivities and dynamic viscosities), and solubilities of H2 and O2 in aqueous sodium and potassium hydroxide (NaOH and KOH) solutions for a wide electrolyte concentration range (0-8 mol/kg). Simulations are carried out for a temperature and pressure range of 298-353 K and 1-100 bar, respectively. The TIP4P/2005 water model is used in combination with a newly parametrized OH- force field for NaOH and KOH. The computed dynamic viscosities at 298 K for NaOH and KOH solutions are within 5% from the reported experimental data up to an electrolyte concentration of 6 mol/kg. For most of the thermodynamic conditions (especially at high concentrations, pressures, and temperatures) experimental data are largely lacking. We present an extensive collection of new data and engineering equations for H2 and O2 self-diffusivities and solubilities in NaOH and KOH solutions, which can be used for process design and optimization of efficient alkaline electrolyzers and fuel cells.

Effect of Branching on Mutual Solubility of Alkane-CO2 Systems by Molecular Simulations

Mutual solubilities of hydrocarbon-CO₂ systems are important in a broad range of applications. Experimental data and theoretical understanding of phase behavior of large hydrocarbon molecules and CO₂ are limited. This is especially true in relation to the molecular structure of hydrocarbons when the carbon number exceeds 12. In this work, the continuous fractional component Gibbs ensemble Monte Carlo simulations are used to investigate mutual solubility of different alkane and CO₂ systems and the molecular structure. We investigate the mutual solubility of n-decane, n-hexadecane, n-eicosane, and the corresponding structural isomers in the CO₂-rich and hydrocarbon-rich phase. The focus will be solubility of the heavy normal alkanes and their structural isomers in CO₂. The simulation results are verified by comparing the experimental data when measurements are available. The simulation of phase behavior of the n-decane-CO₂ system agrees with the experiments. We also present simulation results of n-hexadecane-CO₂ and n-eicosane-CO₂ systems away from the critical region partly due to the finite size effect. We establish that solubility of the hydrocarbons in CO₂ is improved by change of the molecular structure in heavier alkanes. The enhanced solubility is limited in decane isomers, but the isomers of hexadecane and eicosane show 2- to 3-time solubility enhancement. The molecular dynamics simulations suggest that the improvement is from a higher coordination number of CO₂ for methyl (CH₃) rather than for methylene (CH₂) groups. This study sets the stage for molecular engineering and synthesis of hydrocarbons that are soluble in CO₂ not only by considering functionality but also by changing the molecular structure. The solubility enhancement is the first step in viscosification of CO₂ which broadens the use of CO₂.

Boundary-Monte Carlo Method for Neutral and Charged Confined Fluids

In this work, we describe a new Monte Carlo (MC) simulation method to investigate highly coupled fluids in confined geometries at a constant chemical potential. This method is based on so-called multi-scale Hamiltonian methods, wherein the chemical potential is determined using a more amenable Hamiltonian for a fluid in an "outer" region, which facilitates standard methods, such as grand canonical MC simulations or Widom's particle insertion method. The (inner region) fluid of interest is placed in diffusive contact with the simpler outer fluid via a boundary zone wherein the Hamiltonian is transformed. The current method utilizes an ideal fluid for the outer regions, which allows for implicit rather than explicit simulations. Only the boundary and inner region need explicit consideration; hence, the nomenclature used is boundary-Monte Carlo. We illustrate the utility of the method for simple neutral and charged fluids in cylindrical and planar pores. In the latter case, we use a dense room-temperature ionic liquid model and illustrate how the boundary zone establishes a proper Donnan equilibrium between inner and outer fluids in the presence of charged planar electrodes. Thus, the method allows direct calculation of properties such as the differential capacitance, without the need for additional difficult calculations of the requisite Donnan potential.

Vapor pressures and vapor phase compositions of choline chloride urea and choline chloride ethylene glycol deep eutectic solvents from molecular simulation

Despite the widespread acknowledgment that deep eutectic solvents (DESs) have negligible vapor pressures, very few studies in which the vapor pressures of these solvents are measured or computed are available. Similarly, the vapor phase composition is known for only a few DESs. In this study, for the first time, the vapor pressures and vapor phase compositions of choline chloride urea (ChClU) and choline chloride ethylene glycol (ChClEg) DESs are computed using Monte Carlo simulations. The partial pressures of the DES components were obtained from liquid and vapor phase excess Gibbs energies, computed using thermodynamic integration. The enthalpies of vaporization were computed from the obtained vapor pressures, and the results were in reasonable agreement with the few available experimental data in the literature. It was found that the vapor phases of both DESs were dominated by the most volatile component (hydrogen bond donor, HBD, i.e., urea or ethylene glycol), i.e., 100% HBD in ChClEg and 88%-93% HBD in ChClU. Higher vapor pressures were observed for ChClEg compared to ChClU due to the higher volatility of ethylene glycol compared to urea. The influence of the liquid composition of the DESs on the computed properties was studied by considering different mole fractions (i.e., 0.6, 0.67, and 0.75) of the HBD. Except for the partial pressure of ethylene glycol in ChClEg, all the computed partial pressures and enthalpies of vaporization showed insensitivity toward the liquid composition. The activity coefficient of ethylene glycol in ChClEg was computed at different liquid phase mole fractions, showing negative deviations from Raoult's law.

New Features of the Open Source Monte Carlo Software Brick-CFCMC: Thermodynamic Integration and Hybrid Trial Moves

We present several new major features added to the Monte Carlo (MC) simulation code Brick-CFCMC for phase- and reaction equilibria calculations (https://gitlab.com/ETh_TU_Delft/Brick-CFCMC). The first one is thermodynamic integration for the computation of excess chemical potentials (μ^ex). For this purpose, we implemented the computation of the ensemble average of the derivative of the potential energy with respect to the scaling factor for intermolecular interactions (). Efficient bookkeeping is implemented so that the quantity is updated after every MC trial move with negligible computational cost. We demonstrate the accuracy and reliability of the calculation of μ^ex for sodium chloride in water. Second, we implemented hybrid MC/MD translation and rotation trial moves to increase the efficiency of sampling of the configuration space. In these trial moves, short Molecular Dynamics (MD) trajectories are performed to collectively displace or rotate all molecules in the system. These trajectories are accepted or rejected based on the total energy drift. The efficiency of these trial moves can be tuned by changing the time step and the trajectory length. The new trial moves are demonstrated using MC simulations of a viscous fluid (deep eutectic solvent).

Competitive Adsorption of Xylenes at Chemical Equilibrium in Zeolites

The separation of xylenes is one of the most important processes in the petrochemical industry. In this article, the competitive adsorption from a fluid-phase mixture of xylenes in zeolites is studied. Adsorption from both vapor and liquid phases is considered. Computations of adsorption of pure xylenes and a mixture of xylenes at chemical equilibrium in several zeolite types at 250 °C are performed by Monte Carlo simulations. It is observed that shape and size selectivity entropic effects are predominant for small one-dimensional systems. Entropic effects due to the efficient arrangement of xylenes become relevant for large one-dimensional systems. For zeolites with two intersecting channels, the selectivity is determined by a competition between enthalpic and entropic effects. Such effects are related to the orientation of the methyl groups of the xylenes. m-Xylene is preferentially adsorbed if xylenes fit tightly in the intersection of the channels. If the intersection is much larger than the adsorbed molecules, p-xylene is preferentially adsorbed. This study provides insight into how the zeolite topology can influence the competitive adsorption and selectivity of xylenes at reaction conditions. Different selectivities are observed when a vapor phase is adsorbed compared to the adsorption from a liquid phase. These insight have a direct impact on the design criteria for future applications of zeolites in the industry. MRE-type and AFI-type zeolites exclusively adsorb p-xylene and o-xylene from the mixture of xylenes in the liquid phase, respectively. These zeolite types show potential to be used as high-performing molecular sieves for xylene separation and catalysis.

Brick-CFCMC: Open Source Software for Monte Carlo Simulations of Phase and Reaction Equilibria Using the Continuous Fractional Component Method

We present a new molecular simulation code, Brick-CFCMC, for performing Monte Carlo simulations using state-of-the-art simulation techniques. The Continuous Fractional Component (CFC) method is implemented for simulations in the NVT/NPT ensembles, the Gibbs Ensemble, the Grand-Canonical Ensemble, and the Reaction Ensemble. Molecule transfers are facilitated by the use of fractional molecules which significantly improve the efficiency of the simulations. With the CFC method, one can obtain phase equilibria and properties such as chemical potentials and partial molar enthalpies/volumes directly from a single simulation. It is possible to combine trial moves from different ensembles. This enables simulations of phase equilibria in a system where also a chemical reaction takes place. We demonstrate the applicability of our software by investigating the esterification of methanol with acetic acid in a two-phase system.

Multiple Free Energy Calculations from Single State Point Continuous Fractional Component Monte Carlo Simulation Using Umbrella Sampling

We introduce an alternative method to perform free energy calculations for mixtures at multiple temperatures and pressures from a single simulation, by combining umbrella sampling and the continuous fractional component Monte Carlo method. One can perform a simulation of a mixture at a certain pressure and temperature and accurately compute the chemical potential at other pressures and temperatures close to the simulation conditions. This method has the following advantages: (1) Accurate estimates of the chemical potential as a function of pressure and temperature are obtained from a single state simulation without additional postprocessing. This can potentially reduce the number of simulations of a system for free energy calculations for a specific temperature and/or pressure range. (2) Partial molar volumes and enthalpies are obtained directly from the estimated chemical potentials. We tested our method for a Lennard-Jones system, aqueous mixtures of methanol at T = 298 K and P = 1 bar, and a mixture of ammonia, nitrogen, and hydrogen at T = 573 K and P = 800 bar. For pure methanol (N = 410 molecules), we observed that the estimated chemical potentials from umbrella sampling are in excellent agreement with the reference values obtained from independent simulations, for ΔT = ±15 K and ΔP = 100 bar (with respect to the simulated system). For larger systems, this range becomes smaller because the relative fluctuations of energy and volume become smaller. Without sufficient overlap, the performance of the method will become poor especially for nonlinear variations of the chemical potential.

Local Grand Canonical Monte Carlo Simulation Method for Confined Fluids

We describe a new local grand canonical Monte Carlo method to treat fluids in pores in chemical equilibrium with a reference bulk. The method is applied to Lennard-Jones particles in pores of different geometry and is shown to be much more accurate and efficient than other techniques such as traditional grand canonical simulations or Widom's particle insertion method. It utilizes a penalty potential to create a gas phase, which is in equilibrium with a more dense liquid component in the pore. Grand canonical Monte Carlo moves are employed in the gas phase, and the system then maintains chemical equilibrium by "diffusion" of particles. This creates an interface, which means that the confined fluid needs to occupy a large enough volume so that this is not an issue. We also applied the method to confined charged fluids and show how it can be used to determine local electrostatic potentials in the confined fluid, which are properly referenced to the bulk. This precludes the need to determine the Donnan potential (which controls electrochemical equilibrium) explicitly. Prior approaches have used explicit bulk simulations to measure this potential difference, which are significantly costly from a computational point of view. One outcome of our analysis is that pores of finite cross-section create a potential difference with the bulk via a small but nonzero linear charge density, which diminishes as ∼1/ln(L), where L is the pore length.

Molecular Simulation of Chemical Reaction Equilibrium by Computationally Efficient Free Energy Minimization

The molecular simulation of chemical reaction equilibrium (CRE) is a challenging and important problem of broad applicability in chemistry and chemical engineering. The primary molecular-based approach for solving this problem has been the reaction ensemble Monte Carlo (REMC) algorithm [Turner et al. Molec. Simulation2008, 34, (2), 119-146], based on classical force-field methodology. In spite of the vast improvements in computer hardware and software since its original development almost 25 years ago, its more widespread application is impeded by its computational inefficiency. A fundamental problem is that its MC basis inhibits the implementation of significant parallelization, and its successful implementation often requires system-specific tailoring and the incorporation of special MC approaches such as replica exchange, expanded ensemble, umbrella sampling, configurational bias, and continuous fractional component methodologies. We describe herein a novel CRE algorithm (reaction ensemble molecular dynamics, ReMD) that exploits modern computer hardware and software capabilities, and which can be straightforwardly implemented for systems of arbitrary size and complexity by exploiting the parallel computing methodology incorporated within many MD software packages (herein, we use GROMACS for illustrative purposes). The ReMD algorithm utilizes these features in the context of a macroscopically inspired and generally applicable free energy minimization approach based on the iterative approximation of the system Gibbs free energy function by a mathematically simple convex ideal solution model using the composition at each iteration as a reference state. Finally, we additionally describe a simple and computationally efficient a posteriori method to estimate the equilibrium concentrations of species present in very small amounts relative to others in the primary calculation. To demonstrate the algorithm, we show its application to two classic example systems considered previously in the literature: the N₂-O₂-NO system and the ammonia synthesis system.

Reaction Ensemble Monte Carlo Simulations of CO2 Absorption in the Reactive Ionic Liquid Triethyl(octyl)phosphonium 2-Cyanopyrrolide

The absorption of CO₂ into an aprotic heterocyclic anion ionic liquid (IL) is modeled using reaction ensemble Monte Carlo (RxMC) with the semigrand reaction move. RxMC has previously been unable to sample chemical equilibrium involving molecular ions in nanostructured liquids due to the high free-energy requirements to open and close cavities and restructure the surrounding environment. Our results are validated by experiments in the modeled IL, triethyl(octyl)phosphonium 2-cyanopyrrolide ([P₂₂₂₈][cnp]), and in a close analog with longer alkyl chains on the cation. Heats of absorption and reaction from both experiment and simulation are exothermic and of comparable magnitude. Replacing experimental Henry's constants with their simulated counterparts improves the accuracy of a Langmuir-type model at moderate pressures. Nonidealities that affect chemical equilibrium are identified and calculated with high precision.

Combined Steam Reforming of Methane and Formic Acid To Produce Syngas with an Adjustable H2:CO Ratio

Syngas is an important intermediate in the chemical process industry. It is used for the production of hydrocarbons, acetic acid, oxo-alcohols, and other chemicals. Depending on the target product and stoichiometry of the reaction, an optimum (molar) ratio between hydrogen and carbon monoxide (H₂:CO) in the syngas is required. Different technologies are available to control the H₂:CO molar ratio in the syngas. The combination of steam reforming of methane (SRM) and the water-gas shift (WGS) reaction is the most established approach for syngas production. In this work, to adjust the H₂:CO ratio, we have considered formic acid (FA) as a source for both hydrogen and carbon monoxide. Using thermochemical equilibrium calculations, we show that the syngas composition can be controlled by cofeeding formic acid into the SRM process. The H₂:CO molar ratio can be adjusted to a value between one and three by adjusting the concentration of FA in the reaction feed. At steam reforming conditions, typically above 900 K, FA can decompose to water and carbon monoxide and/or to hydrogen and carbon dioxide. Our results show that cofeeding FA into the SRM process can adjust the H₂:CO molar ratio in a single step. This can potentially be an alternative to the WGS process.

Adsorption equilibrium of nitrogen dioxide in porous materials

The effect of confinement on the equilibrium reactive system containing nitrogen dioxide and dinitrogen tetroxide is studied by molecular simulation and the reactive Monte Carlo (RxMC) approach. The bulk-phase reaction was successfully reproduced and five all-silica zeolites (i.e. FAU, FER, MFI, MOR, and TON) with different topologies were selected to study their adoption behavior. Dinitrogen tetroxide showed a stronger affinity than nitrogen dioxide in all the zeolites due to size effects, but exclusive adsorption sites in MOR allowed the adsorption of nitrogen dioxide with no competition at these sites. From the study of the adsorption isotherms and isobars of the reacting mixture, confinement enhanced the formation of dimers over the full range of pressure and temperature, finding the largest deviations from bulk fractions at low temperature and high pressure. The channel size and shape of the zeolite have a noticeable influence on the dinitrogen tetroxide formation, being more important in MFI, closely followed by TON and MOR, and finally FER and FAU. Preferential adsorption sites in MOR lead to an unusually strong selective adsorption towards nitrogen dioxide, demonstrating that the topological structure has a crucial influence on the composition of the mixture and must be carefully considered in systems containing nitrogen dioxide.