Improving the accuracy of computing chemical potentials in CFCMC simulations

Mutual Diffusivities of Mixtures of Carbon Dioxide and Hydrogen and Their Solubilities in Brine: Insight from Molecular Simulations

H2-CO2 mixtures find wide-ranging applications, including their growing significance as synthetic fuels in the transportation industry, relevance in capture technologies for carbon capture and storage, occurrence in subsurface storage of hydrogen, and hydrogenation of carbon dioxide to form hydrocarbons and alcohols. Here, we focus on the thermodynamic properties of H2-CO2 mixtures pertinent to underground hydrogen storage in depleted gas reservoirs. Molecular dynamics simulations are used to compute mutual (Fick) diffusivities for a wide range of pressures (5 to 50 MPa), temperatures (323.15 to 423.15 K), and mixture compositions (hydrogen mole fraction from 0 to 1). At 5 MPa, the computed mutual diffusivities agree within 5% with the kinetic theory of Chapman and Enskog at 423.15 K, albeit exhibiting deviations of up to 25% between 323.15 and 373.15 K. Even at 50 MPa, kinetic theory predictions match computed diffusivities within 15% for mixtures comprising over 80% H2 due to the ideal-gas-like behavior. In mixtures with higher concentrations of CO2, the Moggridge correlation emerges as a dependable substitute for the kinetic theory. Specifically, when the CO2 content reaches 50%, the Moggridge correlation achieves predictions within 10% of the computed Fick diffusivities. Phase equilibria of ternary mixtures involving CO2-H2-NaCl were explored using Gibbs Ensemble (GE) simulations with the Continuous Fractional Component Monte Carlo (CFCMC) technique. The computed solubilities of CO2 and H2 in NaCl brine increased with the fugacity of the respective component but decreased with NaCl concentration (salting out effect). While the solubility of CO2 in NaCl brine decreased in the ternary system compared to the binary CO2-NaCl brine system, the solubility of H2 in NaCl brine increased less in the ternary system compared to the binary H2-NaCl brine system. The cooperative effect of H2-CO2 enhances the H2 solubility while suppressing the CO2 solubility. The water content in the gas phase was found to be intermediate between H2-NaCl brine and CO2-NaCl brine systems. Our findings have implications for hydrogen storage and chemical technologies dealing with CO2-H2 mixtures, particularly where experimental data are lacking, emphasizing the need for reliable thermodynamic data on H2-CO2 mixtures.

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.

Phase diagrams-Why they matter and how to predict them

Understanding the thermodynamic stability and metastability of materials can help us to, for example, gauge whether crystalline polymorphs in pharmaceutical formulations are likely to be durable. It can also help us to design experimental routes to novel phases with potentially interesting properties. In this Perspective, we provide an overview of how thermodynamic phase behavior can be quantified both in computer simulations and machine-learning approaches to determine phase diagrams, as well as combinations of the two. We review the basic workflow of free-energy computations for condensed phases, including some practical implementation advice, ranging from the Frenkel-Ladd approach to thermodynamic integration and to direct-coexistence simulations. We illustrate the applications of such methods on a range of systems from materials chemistry to biological phase separation. Finally, we outline some challenges, questions, and practical applications of phase-diagram determination which we believe are likely to be possible to address in the near future using such state-of-the-art free-energy calculations, which may provide fundamental insight into separation processes using multicomponent solvents.

Solubility of CO2 in Aqueous Formic Acid Solutions and the Effect of NaCl Addition: A Molecular Simulation Study

There is a growing interest in the development of routes to produce formic acid from CO₂, such as the electrochemical reduction of CO₂ to formic acid. The solubility of CO₂ in the electrolyte influences the production rate of formic acid. Here, the dependence of the CO₂ solubility in aqueous HCOOH solutions with electrolytes on the composition and the NaCl concentration was studied by Continuous Fractional Component Monte Carlo simulations at 298.15 K and 1 bar. The chemical potentials of CO₂, H₂O, and HCOOH were obtained directly from single simulations, enabling the calculation of Henry coefficients and subsequently considering salting in or salting out effects. As the force fields for HCOOH and H₂O may not be compatible due to the presence of strong hydrogen bonds, the Gibbs-Duhem integration test was used to test this compatibility. The combination of the OPLS/AA force field with a new set of parameters, in combination with the SPC/E force field for water, was selected. It was found that the solubility of CO₂ decreases with increasing NaCl concentration in the solution and increases with the increase of HCOOH concentration. This continues up to a certain concentration of HCOOH in the solution, after which the CO₂ solubility is high and the NaCl concentration has no significant effect.

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).

Effect of Water Content on Thermodynamic Properties of Compressed Hydrogen

Force field-based molecular simulations were used to calculate thermal expansivities, heat capacities, and Joule-Thomson coefficients of binary (standard) hydrogen-water mixtures for temperatures between 366.15 and 423.15 K and pressures between 50 and 1000 bar. The mole fraction of water in saturated hydrogen-water mixtures in the gas phase ranges from 0.004 to 0.138. The same properties were calculated for pure hydrogen at 323.15 K and pressures between 100 and 1000 bar. Simulations were performed using the TIP3P and a modified TIP4P force field for water and the Marx, Vrabec, Cracknell, Buch, and Hirschfelder force fields for hydrogen. The vapor-liquid equilibria of hydrogen-water mixtures were calculated along the melting line of ice Ih, corresponding to temperatures between 264.21 and 272.4 K, using the TIP3P force field for water and the Marx force field for hydrogen. In this temperature range, the solubilities and the chemical potentials of hydrogen and water were obtained. Based on the computed solubility data of hydrogen in water, the freezing-point depression of water was computed ranging from 264.21 to 272.4 K. The modified TIP4P and Marx force fields were used to improve the solubility calculations of hydrogen-water mixtures reported in our previous study [Rahbari A.;J. Chem. Eng. Data2019, 64, 4103-4115] for temperatures between 323 and 423 K and pressures ranging from 100 to 1000 bar. The chemical potentials of ice Ih were calculated as a function of pressure between 100 and 1000 bar, along the melting line for temperatures between 264.21 and 272.4 K, using the IAPWS equation of state for ice Ih. We show that at low pressures, the presence of water has a large effect on the thermodynamic properties of compressed hydrogen. Our conclusions may have consequences for the energetics of a hydrogen refueling station using electrochemical hydrogen compressors.

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.