Simulation of chemical reaction equilibria by the reaction ensemble Monte Carlo method: a review†

Understanding the mechanism and kinetics of the formation and breaking of ring structures during silica polymerization: a computational study

Ring structures are ubiquitous in porous materials and play a crucial role in the functioning of these materials. Understanding the ring formation and breaking mechanism is essential for designing and controlling the porosity, framework density, channels, and cage formation in porous materials. The current work attempts to understand the formation, breaking, and survival of rings using a computational approach. We have used the reaction ensemble Monte Carlo simulation technique and studied silica polymerization starting from monomers to inter-connected large silica clusters in dilute and concentrated silica systems. We calculated various properties of representative smaller and bigger rings at different stages of polymerization. We found that smaller rings form in the initial polymerization stages and larger ring sizes appear at later stages. The smaller rings have a larger residence time than the bigger rings in the silica system, and the residence time changes with the polymerization stage. Both smaller and bigger rings have a shorter residence time in the dilute system than the concentrated silica system. As a result, ring formation and breaking kinetics are faster in the dilute silica system, which causes reorganization within the silica cluster leading to a dense cluster. A slow reorganization of rings in the concentrated silica system is observed, due to which clusters retain their random, branched configuration and porous region within the cluster. We also investigated a series of ring formation and breaking steps to understand the formation mechanism of isolated and grouped rings in the studied silica systems. We found that rings form and break by all possible reactions during ring-formation and cluster-aggregation stages. In contrast, only one reaction is dominant in the initial and aging stages of polymerization. The concentration of silica affects the formation of isolated rings, whereas the kinetics of a grouped ring is not significantly altered. Detailed insights into the reaction dynamics of rings at various stages of polymerization would be helpful in the rational design of porous silica polymorphs.

Accelerated simulation method for charge regulation effects

The net charge of solvated entities, ranging from polyelectrolytes and biomolecules to charged nanoparticles and membranes, depends on the local dissociation equilibrium of individual ionizable groups. Incorporation of this phenomenon, charge regulation (CR), in theoretical and computational models requires dynamic, configuration-dependent recalculation of surface charges and is therefore typically approximated by assuming constant net charge on particles. Various computational methods exist that address this. We present an alternative, particularly efficient CR Monte Carlo method (CR-MC), which explicitly models the redistribution of individual charges and accurately samples the correct grand-canonical charge distribution. In addition, we provide an open-source implementation in the large-scale Atomic/Molecular Massively Parallel Simulator molecular dynamics (MD) simulation package, resulting in a hybrid MD/CR-MC simulation method. This implementation is designed to handle a wide range of implicit-solvent systems that model discreet ionizable groups or surface sites. The computational cost of the method scales linearly with the number of ionizable groups, thereby allowing accurate simulations of systems containing thousands of individual ionizable sites. By matter of illustration, we use the CR-MC method to quantify the effects of CR on the nature of the polyelectrolyte coil-globule transition and on the effective interaction between oppositely charged nanoparticles.

Conformation and Ionization Behavior of Charge-Regulating Polyelectrolyte Brushes in a Poor Solvent

Understanding the structural response of weak polyelectrolyte brushes upon external stimuli is crucial for their applications ranging from modifying surface properties to the development of smart and intelligent materials. In this work, coarse-grained molecular dynamics simulations were carried out to investigate the conformation and ionization behavior of charge-regulating polyelectrolyte brushes under poor solvent conditions, using an implicit solvent model. The results show that, while the thickness of a sparse polyelectrolyte brush shows a similar behavior to that of a single chain, namely, a monotonic change as a function of solvent quality (modeled by an effective segment-segment attraction strength parameter) and solution pH, a dense polyelectrolyte brush exhibits more complex behavior. An unexpected reexpansion is observed when the effective segment-segment attraction strength is further increased, especially in the case of a high pH. In the latter case, strong attraction in polymer segments promotes the formation of large, interchain, cylindrical aggregates, leading to an increase in brush thickness.

Adsorption and the Chemical Reaction N2O4 ↔ 2NO2 in the Presence of N2 in a Gas Phase Connected with a Carbon Nanotube

The paper shows, by molecular simulations, that a CNT (9,9) carbon nanotube allows very efficient separation of nitrogen oxides (NO _x ) from N₂, that has in good approximation properties of the complete air mixture. Gibbs ensemble Monte Carlo simulations are used to describe the adsorption. The permanent chemical reaction between N₂O₄ and NO₂, which occurs simultaneously to adsorption, is treated by the reactive Monte Carlo simulation. A very high selectivity has been found. For a low pressure and at T = 298 K, an adsorption/reaction selectivity between NO _x and N₂ can reach values up to 3 × 10³.

Unfolding of the chromatin fiber driven by overexpression of noninteracting bridging factors

Nuclear molecules control the functional properties of the chromatin fiber by shaping its morphological properties. The biophysical mechanisms controlling how bridging molecules compactify chromatin are a matter of debate. On the one side, bridging molecules could cross-link faraway sites and fold the fiber through the formation of loops. Interacting bridging molecules could also mediate long-range attractions by first tagging different locations of the fiber and then undergoing microphase separation. Using a coarse-grained model and Monte Carlo simulations, we study the conditions leading to compact configurations both for interacting and noninteracting bridging molecules. In the second case, we report on an unfolding transition at high densities of the bridging molecules. We clarify how this transition, which disappears for interacting bridging molecules, is universal and controlled by entropic terms. In general, chains are more compact in the case of interacting bridging molecules because interactions are not valence limited. However, this result is conditional on the ability of our simulation methodology to relax the system toward its ground state. In particular, we clarify how, unless using reaction dynamics that change the length of a loop in a single step, the system is prone to remain trapped in metastable, compact configurations featuring long loops.

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.

Learnings from the Relation between the Number of Forward and Reverse Reactions (Transfer Cycles) Required to Converge to Equilibrium and the Ratio of the Forward to the Reverse Rate Constants in Simple Chemical Reactions

In simple, reversible, chemical reactions of the type A ⇋ B, chemical equilibrium is related to chemical kinetics via the equality between the equilibrium constant and the ratio of the forward to the reverse rate-constant, i.e., K _eq = k _f/k _r, where K _eq is the equilibrium constant and k _f and k _r denote the rate constants for the forward (A → B) and reverse (B → A) reactions, respectively. We review and examine the relation between the number of forward and reverse reactions required to take place for the aforementioned system to reach equilibrium and the ratio of the forward to the reverse rate constant. Each cycle of reactants becoming products and the products becoming reactants is defined as the transfer cycle (TC). Therefore, we underscore the relation between the number of TCs required for the system to equilibrate and k _f/k _r. We also vary the initial concentrations of the reactants and products to examine their dependency of the relation between the number of TCs required to reach equilibrium and k _f/k _r. The data reveal a logarithmic growth-type relation between the number of TCs required for the system to achieve equilibrium and k _f/k _r. The results of this relation are discussed in the context of several scenarios that populate the trajectory. We conclude by introducing students and researchers in the area of chemistry and biochemistry to physical phenomena that relate the initial concentrations of the reactants and products and k _f/k _r to the number of TCs necessary for the system to equilibrate.

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.

Combined Adsorption and Reaction in the Ternary Mixture N2, N2O4, NO2 on MIL-127 Examined by Computer Simulations

A high selectivity of NO _x over N₂ (simulating air) is found in silico when studying the adsorption of the ternary mixture N₂O₄/NO₂/N₂ on the metal-organic framework MIL-127(Fe) by molecular simulations under consideration of the recombination reaction N₂O₄ ↔ 2NO₂. The number of N atoms in nitrogen oxides NO _x and that in N₂ is used to define a selectivity of the combined adsorption and chemical recombination that can reach values of about 1000.

Theoretical and Computational Insight into Solvent and Specific Ion Effects for Polyelectrolytes: The Importance of Local Molecular Interactions

Polyelectrolytes in solution show a broad plethora of interesting effects. In this short review article, we focus on recent theoretical and computational findings regarding specific ion and solvent effects and their impact on the polyelectrolyte behavior. In contrast to standard mean field descriptions, the properties of polyelectrolytes are significantly influenced by crucial interactions with the solvent, co-solvent and ion species. The corresponding experimental and simulation results reveal a significant deviation from theoretical predictions, which also highlights the importance of charge transfer, dispersion and polarization interactions in combination with solvation mechanisms. We discuss recent theoretical and computational findings in addition to novel approaches which help broaden the applicability of simple mean field theories.

The effects of confinement in pores built of folded graphene sheets on the equilibrium of nitrogen monoxide dimerisation reaction

In the current work we have used reactive Monte Carlo simulations to systematically study the effects of graphene folding on equilibria of NO dimerisation occurring at isolated surfaces and in porous networks built of corrugated graphene sheets. It has been demonstrated that the folding of isolated graphene sheets significantly improves the yield of reactions occurring on their surface. Then, it has also been shown that in slit-like pores formed by the folded graphene sheets the reaction yield depends on the corrugation and arrangement of the pore walls. It has been found that the reaction yield increases when the walls' corrugation is high because of the appearance of narrow regions and/or wedge-like regions in the pores. The condensation of reacting fluid in such places, where the bulges at both walls are close one to another, leads to much higher reaction yield than on the surface of isolated sheets. Thus, we recommended the highly corrugated graphene to control the chemical reactions.

Simulations of ionization equilibria in weak polyelectrolyte solutions and gels

This article recapitulates the state of the art regarding simulations of ionization equilibria of weak polyelectrolyte solutions and gels. We start out by reviewing the essential thermodynamics of ionization and show how the weak polyelectrolyte ionization differs from the ionization of simple weak acids and bases. Next, we describe simulation methods for ionization reactions, focusing on two methods: the constant-pH ensemble and the reaction ensemble. After discussing the advantages and limitations of both methods, we review the existing simulation literature. We discuss coarse-grained simulations of weak polyelectrolytes with respect to ionization equilibria, conformational properties, and the effects of salt, both in good and poor solvent conditions. This is followed by a discussion of branched star-like weak polyelectrolytes and weak polyelectrolyte gels. At the end we touch upon the interactions of weak polyelectrolytes with other polymers, surfaces, nanoparticles and proteins. Although proteins are an important class of weak polyelectrolytes, we explicitly exclude simulations of protein ionization equilibria, unless they involve protein-polyelectrolyte interactions. Finally, we try to identify gaps and open problems in the existing simulation literature, and propose challenges for future development.

Influence of weak groups on polyelectrolyte mobilities

The ionization of dissociable groups in weak polyelectrolytes does not occur in a homogenous fashion. Monomer connectivity imposes constraints on the localization of the dissociated (charged) monomers that affect the local electric potential. As a result, the mean bare charge along a weak polyelectrolyte can vary depending on the proximity to topological features (e.g. presence of crosslinks or dangling ends). Using reaction-ensemble Monte-Carlo simulations we calculate the dissociation inhomogeneities for a few selected PE configurations, linear, rod-like, flexible four-arm star, and a star with stiff arms. An ensemble preaverage is used to obtain the annealed bare charge profile for these different polymer configurations. Using molecular dynamics simulations within a Lattice-Boltzman fluid, we investigate how the electrophoretic mobility is affected by the bare charge inhomogeneities arising from the annealed weak polyelectrolytes. Surprisingly, the mobility obtained for the situations corresponding to the predicted charge profile for annealed weak polyelectrolytes are not significantly different than the mobility obtained when all the monomers have an identical charge (under the constraint that the total polyelectrolyte bare charge is the same). This is also true for the stiff rod-like variants where conformational changes induced from the localization of the monomer charges are negligible. In salty solutions, we find that counterions are affected by the electric potential modulations induced by the topological features. Since the counterions crowd in regions where the electric potential caused by the dissociated monomers is highest, they wash-out the bare charge inhomogeneities and contribute to a more uniform effective backbone charge.

Free Energy of Classical Molecular Crystals by Thermodynamic Integration from a Harmonic Reference

We develop an algorithm for calculating the normal modes of vibration of mechanical systems with constraints, particularly of molecules with rigid bonds and models of rigid molecules, and use it to obtain the harmonic free energy of a crystal. The anharmonic correction is then calculated by the conventional thermodynamic integration over temperature in the NVT ensemble. Attention is paid to finite-size errors, tail corrections, thermostat choice, ergodicity, and other sources of inaccuracies. The calculated free energy of ice XIV modeled by the TIP4P/2005 potential agrees with the previously reported value and is by one order more accurate.

Carbon Nanohorns as Reaction Nanochambers - a Systematic Monte Carlo Study

Carbon nanohorns (CNHs, one of the newest carbon allotropes) have been subjected to intensive experimental and theoretical studies due to their potential applications. One of such applications can be their use as reaction nanochambers. However, experimental studies on the reaction equilibria under confinement are extremely challenging since accurate measurements of the concentrations of reacting species in pores are a very hard task. So, the main ways to examine such phenomena are theoretical methods (e.g. the reactive Monte Carlo, RxMC). We have presented the first systematic RxMC study on the influence of the CNH’s geometric parameters (the apex angle, the diameter, and the length) on reaction equilibria, taking the nitrogen monoxide dimerisation as an example. All the investigated parameters significantly affect the reaction yield at low and moderate coverages. Short and narrow CNHs have been found to be preferred. However, the key factor influencing the reaction equilibria is the presence of a conical part. Energetics of interactions between the reacting molecules in this fragment of a nanohorn maximises the effects of confinement. In consequence, CNHs have the advantage over their nanotube counterparts of the same diameter. The obtained results have confirmed that CNHs can be considered as potential reaction nanochambers.

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.

Unexpected protonation state of Glu197 discovered from simulations of tacrine in butyrylcholinesterase

Butyrylcholinesterase (BChE) has been actively involved in drug discoveries from many fields for decades. In the crystal structure of the BChE-tacrine complex, there is an unanticipated formyl-proline molecule resolved very close to tacrine, raising an essential question on how reliable it is to apply the binding pose in a crystal structure to analyze related experimental observations, in which no formyl-proline is actually involved. In this study, by performing a series of 100 ns molecular dynamics simulations, we demonstrate that it is safe to employ the structural information from this crystal structure to analyze related experimental observations. Surprisingly, Glu197 needs to be protonated to have the structures simulated appropriately. It should be noted that Glu197 has been commonly considered as deprotonated in diverse analyses due to its low pKa in aqueous solution, for which some interpretations are inconsistent or unclear. Our further investigation shows that the protonated Glu197 plays a very important role in preserving His438 within the catalytic triad through stabilizing a highly conserved water molecule. Interestingly, the catalytic triad and Glu197 have been long recognized for possibly deviating largely from the crystal structure, which might be catalytically deficient and is generally considered to result from the difference between the crystal and aqueous environment. Herein, our results suggest that the large deviations of the catalytic triad and Glu197 from the crystal structure are caused by the inappropriate protonation state of Glu197. This finding shall provide an important clue that has been long missing for a better understanding of BChE-related puzzles or even reconsideration of some BChE-catalyzed reaction mechanisms.

Understanding the Reactive Adsorption of H2 S and CO2 in Sodium-Exchanged Zeolites

Purifying sour natural gas streams containing hydrogen sulfide and carbon dioxide has been a long-standing environmental and economic challenge. In the presence of cation-exchanged zeolites, these two acid gases can react to form carbonyl sulfide and water (H₂ S+CO₂ ⇌H₂ O+COS), but this reaction is rarely accounted for. In this work, we carry out reactive first-principles Monte Carlo (RxFPMC) simulations for mixtures of H₂ S and CO₂ in all-silica and Na-exchanged forms of zeolite beta to understand the governing principles driving the enhanced conversion. The RxFPMC simulations show that the presence of Na⁺ cations can change the equilibrium constant by several orders of magnitude compared to the gas phase or in all-silica beta. The shift in the reaction equilibrium is caused by very strong interactions of H₂ O with Na⁺ that reduce the reaction enthalpy by about 20 kJ mol^-1 . The simulations also demonstrate that the siting of Al atoms in the framework plays an important role. The RxFPMC method presented here is applicable to any chemical conversion in any confined environment, where strong interactions of guest molecules with the host framework and high activation energies limit the use of other computational approaches to study reaction equilibria.

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.

Polymerization kinetics of a multi-functional silica precursor studied using a novel Monte Carlo simulation technique

Silica polymerization has been extensively used to synthesize various fascinating materials for industrial and technological applications. The polymerization protocol is modified by altering several parameters (such as the concentration of the precursor, temperature, pH) heuristically to obtain the desired end product. To properly understand the effect of such parameters, knowledge of molecular events occurring during the process of polymerization is essential. In this work, we developed algorithms to capture molecular events such as translation, rotation, and reactions using the reaction ensemble Monte Carlo (REMC) technique. Our algorithms simulate molecular events in accordance with physical time by correctly scaling the movements of a cluster with the monomer, thereby capturing the kinetics of the process. We studied the polymerization of the four coordinated silica (f₄) precursor using our algorithm and observed excellent agreement between simulation results and experimental data. The algorithm was also used to study the polymerization of the three coordinated silica (f₃) precursor and it was found that our simulations capture experimental kinetics well, thereby confirming that the developed algorithms are robust. We studied the effect of the functionality of the precursor on polymerization kinetics and the resulting structure by simulating silica systems having a mixture of two, three and four functional (f₂, f₃, and f₄) silica precursors. We observed that network formation and cluster size decrease with the increase in the concentration of the f₂ precursor. The radius of gyration (R_g) of the system initially increases due to network formation and decreases later due to the collapse of a large cluster. The R_g is directly correlated with the total number of primitive rings present in the system. The molecular level understanding obtained will be useful in the design of tailored silica nanoparticles.

Computer Simulations of Static and Dynamical Properties of Weak Polyelectrolyte Nanogels in Salty Solutions

We investigate the chemical equilibria of weak polyelectrolyte nanogels with reaction ensemble Monte Carlo simulations. With this method, the chemical identity of the nanogel monomers can change between neutral or charged following the acid-base equilibrium reaction HA ⇌ A- + H⁺. We investigate the effect of changing the chemical equilibria by modifying the dissociation constant K a . These simulations allow for the extraction of static properties like swelling equilibria and the way in which charge-both monomer and ionic-is distributed inside the nanogel. Our findings reveal that, depending on the value of K a , added salt can either increase or decrease the gel size. Using the calculated mean-charge configurations of the nanogel from the reaction ensemble simulation as a quenched input to coupled lattice-Boltzmann molecular dynamics simulations, we investigate dynamical nanogel properties such as the electrophoretic mobility μ and the diffusion coefficient D.

Confinement Effects on Carbon Dioxide Methanation: A Novel Mechanism for Abiotic Methane Formation

An important scientific debate focuses on the possibility of abiotic synthesis of hydrocarbons during oceanic crust-seawater interactions. While on-site measurements near hydrothermal vents support this possibility, laboratory studies have provided data that are in some cases contradictory. At conditions relevant for sub-surface environments it has been shown that classic thermodynamics favour the production of CO2 from CH4, while abiotic methane synthesis would require the opposite. However, confinement effects are known to alter reaction equilibria. This report shows that indeed thermodynamic equilibrium can be shifted towards methane production, suggesting that thermal hydrocarbon synthesis near hydrothermal vents and deeper in the magma-hydrothermal system is possible. We report reactive ensemble Monte Carlo simulations for the CO2 methanation reaction. We compare the predicted equilibrium composition in the bulk gaseous phase to that expected in the presence of confinement. In the bulk phase we obtain excellent agreement with classic thermodynamic expectations. When the reactants can exchange between bulk and a confined phase our results show strong dependency of the reaction equilibrium conversions, [Formula: see text], on nanopore size, nanopore chemistry, and nanopore morphology. Some physical conditions that could shift significantly the equilibrium composition of the reactive system with respect to bulk observations are discussed.

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

A new formulation of the Reaction Ensemble Monte Carlo technique (RxMC) combined with the Continuous Fractional Component Monte Carlo method is presented. This method is denoted by serial Rx/CFC. The key ingredient is that fractional molecules of either reactants or reaction products are present and that chemical reactions always involve fractional molecules. Serial Rx/CFC has the following advantages compared to other approaches: (1) One directly obtains chemical potentials of all reactants and reaction products. Obtained chemical potentials can be used directly as an independent check to ensure that chemical equilibrium is achieved. (2) Independent biasing is applied to the fractional molecules of reactants and reaction products. Therefore, the efficiency of the algorithm is significantly increased, compared to the other approaches. (3) Changes in the maximum scaling parameter of intermolecular interactions can be chosen differently for reactants and reaction products. (4) The number of fractional molecules is reduced. As a proof of principle, our method is tested for Lennard-Jones systems at various pressures and for various chemical reactions. Excellent agreement was found both for average densities and equilibrium mixture compositions computed using serial Rx/CFC, RxMC/CFCMC previously introduced by Rosch and Maginn (Journal of Chemical Theory and Computation, 2011, 7, 269-279), and the conventional RxMC approach. The serial Rx/CFC approach is also tested for the reaction of ammonia synthesis at various temperatures and pressures. Excellent agreement was found between results obtained from serial Rx/CFC, experimental results from literature, and thermodynamic modeling using the Peng-Robinson equation of state. The efficiency of reaction trial moves is improved by a factor of 2 to 3 (depending on the system) compared to the RxMC/CFCMC formulation by Rosch and Maginn.

Water-Lean Solvents for Post-Combustion CO2 Capture: Fundamentals, Uncertainties, Opportunities, and Outlook

This review is designed to foster the discussion regarding the viability of postcombustion CO₂ capture by water-lean solvents, by separating fact from fiction for both skeptics and advocates. We highlight the unique physical and thermodynamic properties of notable water-lean solvents, with a discussion of how such properties could translate to efficiency gains compared to aqueous amines. The scope of this review ranges from the purely fundamental molecular-level processes that govern solvent behavior to bench-scale testing, through process engineering and projections of process performance and cost. Key discussions of higher than expected CO₂ mass transfer, water tolerance, and compatibility with current infrastructure are presented along with current limitations and suggested areas where further solvent development is needed. We conclude with an outlook of the status of the field and assess the viability of water-lean solvents for postcombustion CO₂ capture.

Surface Interactions and Confinement of Methane: A High Pressure Magic Angle Spinning NMR and Computational Chemistry Study

Characterization and modeling of the molecular-level behavior of simple hydrocarbon gases, such as methane, in the presence of both nonporous and nanoporous mineral matrices allows for predictive understanding of important processes in engineered and natural systems. In this study, changes in local electromagnetic environments of the carbon atoms in methane under conditions of high pressure (up to 130 bar) and moderate temperature (up to 346 K) were observed with ¹³C magic-angle spinning (MAS) NMR spectroscopy while the methane gas was mixed with two model solid substrates: a fumed nonporous, 12 nm particle size silica and a mesoporous silica with 200 nm particle size and 4 nm average pore diameter. Examination of the interactions between methane and the silica systems over temperatures and pressures that include the supercritical regime was allowed by a novel high pressure MAS sample containment system, which provided high resolution spectra collected under in situ conditions. For pure methane, no significant thermal effects were found for the observed ¹³C chemical shifts at all pressures studied here (28.2, 32.6, 56.4, 65.1, 112.7, and 130.3 bar). However, the ¹³C chemical shifts of resonances arising from confined methane changed slightly with changes in temperature in mixtures with mesoporous silica. The chemical shift values of ¹³C nuclides in methane change measurably as a function of pressure both in the pure state and in mixtures with both silica matrices, with a more pronounced shift when meso-porous silica is present. Molecular-level simulations utilizing GCMC, MD, and DFT confirm qualitatively that the experimentally measured changes are attributed to interactions of methane with the hydroxylated silica surfaces as well as densification of methane within nanopores and on pore surfaces.

Wang-Landau Reaction Ensemble Method: Simulation of Weak Polyelectrolytes and General Acid-Base Reactions

We present a novel method for the study of weak polyelectrolytes and general acid-base reactions in molecular dynamics and Monte Carlo simulations. The approach combines the advantages of the reaction ensemble and the Wang-Landau sampling method. Deprotonation and protonation reactions are simulated explicitly with the help of the reaction ensemble method, while the accurate sampling of the corresponding phase space is achieved by the Wang-Landau approach. The combination of both techniques provides a sufficient statistical accuracy such that meaningful estimates for the density of states and the partition sum can be obtained. With regard to these estimates, several thermodynamic observables like the heat capacity or reaction free energies can be calculated. We demonstrate that the computation times for the calculation of titration curves with a high statistical accuracy can be significantly decreased when compared to the original reaction ensemble method. The applicability of our approach is validated by the study of weak polyelectrolytes and their thermodynamic properties.

Monte Carlo study of chemical reaction equilibria in pores of activated carbons

Systematic Monte Carlo studies concerning relationships between the porous structure of activated carbons and the equilibria of reactions under confinement are presented.

First-Principles Monte Carlo Simulations of Reaction Equilibria in Compressed Vapors

Predictive modeling of reaction equilibria presents one of the grand challenges in the field of molecular simulation. Difficulties in the study of such systems arise from the need (i) to accurately model both strong, short-ranged interactions leading to the formation of chemical bonds and weak interactions arising from the environment, and (ii) to sample the range of time scales involving frequent molecular collisions, slow diffusion, and infrequent reactive events. Here we present a novel reactive first-principles Monte Carlo (RxFPMC) approach that allows for investigation of reaction equilibria without the need to prespecify a set of chemical reactions and their ideal-gas equilibrium constants. We apply RxFPMC to investigate a nitrogen/oxygen mixture at T = 3000 K and p = 30 GPa, i.e., conditions that are present in atmospheric lightning strikes and explosions. The RxFPMC simulations show that the solvation environment leads to a significantly enhanced NO concentration that reaches a maximum when oxygen is present in slight excess. In addition, the RxFPMC simulations indicate the formation of NO2 and N2O in mole fractions approaching 1%, whereas N3 and O3 are not observed. The equilibrium distributions obtained from the RxFPMC simulations agree well with those from a thermochemical computer code parametrized to experimental data.

Computer modelling of the surface tension of the gas–liquid and liquid–liquid interface

This review presents the state of the art in molecular simulations of interfacial systems and of the calculation of the surface tension from the underlying intermolecular potential.

Gas sorption in solid surfaces: a computational study using rigid and Einstein-solid models

The reactive Monte Carlo (RxMC) method was proposed to describe the sorption of gases in solid materials due to the chemical reaction A + B ⇌ C. Two models were used to simulate the solid; the first model considered simulations with rigid particles in the solid whereas in the second model the particles were allowed to vibrate inside the solid with a given spring constant, i.e. an Einstein solid was used to simulate the substrate. In both models not only physisorption but also chemisorption of the fluid was observed. Sorption curves, at different spring constants, were simulated and it was noted that sorption was always enhanced with the Einstein solid model. Moreover, an inverse dependent function of the spring constant with the temperature was found. Finally, the second model might be used to explain the unusual sorption behavior observed in actual experimental reactions such as CO2 + Li2O ⇌ Li2CO3.