Reactive Monte Carlo Simulations Research Articles

Titration in Canonical and Grand-Canonical Ensembles.

We discuss problems associated with the notion of pH in heterogeneous systems. For homogeneous systems, standardization protocols lead to a well-defined quantity, which, although different from Sørensen's original idea of pH, is well reproducible and has become accepted as the measure of the "hydrogen potential". On the other hand, for heterogeneous systems, pH defined in terms of the chemical part of the electrochemical activity is thermodynamically inconsistent and runs afoul of the Gibbs-Guggenheim principle that forbids splitting of the electrochemical potential into separate chemical and electrostatic parts, since only the sum of two has any thermodynamic meaning. The problem is particularly relevant for modern simulation methods which involve charge regulation of proteins, polyelectrolytes, nanoparticles, colloidal suspensions, and so forth. In this paper, we show that titration isotherms calculated using semigrand canonical simulations can be very different from the ones obtained using canonical reactive Monte Carlo simulations.

Non-equilibrium transport of nanoparticles across the lipid membrane.

Development of effective strategies for the internalization of nanoparticles is essential in many applications, such as drug delivery. Most, if not all, previous studies are based on equilibrium considerations. In this work, inspired by the recent development of a pro-drug delivery strategy based on reversible esterification, we consider a non-equilibrium transport mechanism for nanoparticles of a 6 nm diameter across the lipid membrane. We divide the transport process into insertion and ejection steps, which are studied with coarse-grained models using free energy and reactive Monte Carlo simulations, respectively. The simulations show that the non-equilibrium transport efficiency is relatively insensitive to the fraction of reactive surface ligands once a modest threshold is surpassed, while the distribution pattern of different (hydrophilic, reactive and permanent hydrophobic) ligands on the nanoparticle surface has a notable impact on both the insertion and ejection steps. Our study thus supports a novel avenue for designing nanoparticles that are able to be efficiently internalized and provides a set of relevant guidelines for surface functionalization.

Theory of Charge Regulation of Colloidal Particles in Electrolyte Solutions

We present a theory that enables us to (i) calculate the effective surface charge of colloidal particles and (ii) efficiently obtain titration curves for different salt concentrations. The theory accounts for the shift of pH of solution due to the presence of 1:1 electrolyte. It also accounts self-consistently for the electrostatic potential produced by the deprotonated surface groups. To examine the accuracy of the theory, we have performed extensive reactive Monte Carlo simulations, which show excellent agreement between theory and simulations without any adjustable parameters.

Reactive Monte Carlo simulations for charge regulation of colloidal particles.

We use a reactive Monte Carlo simulation method and the primitive model of electrolyte to study acid-base equilibrium that controls charge regulation in colloidal systems. The simulations are performed in a semi-grand canonical ensemble in which colloidal suspension is in contact with a reservoir of salt and strong acid. The interior of colloidal particles is modeled as a low dielectric medium, different from the surrounding water. The effective colloidal charge is calculated for different numbers of surface acidic groups, pH, salt concentrations, and types of electrolyte. In the case of potassium chloride, the titration curves are compared with the experimental measurements obtained using potentiometric titration. A good agreement is found between simulations and experiments. In the case of lithium chloride, the specific ionic adsorption is taken into account through the partial dehydration of lithium ion.

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.

Enhanced replica exchange reactive Monte Carlo simulations for constructing zeolite frameworks

We investigate the ability of a reactive model of silica to build crystalline zeolite frameworks with an enhanced sampling approach based on replica exchange Monte Carlo (REMC) simulations. In our implementation of REMC, the silica hydrolysis/condensation equilibrium constant controlling network formation is chosen as the index parameter characterising each replica. We show that improving the performance of the REMC method by increasing its efficiency in producing zeolite crystals allows zeolites with larger unit cells to be constructed. In particular, we perform an efficiency case study on the sodalite structure, containing 12 tetrahedra per unit cell and then apply the resulting enhancements to construct a significantly larger zeolite. We have improved our simulations in two ways; first, we have analysed the roles of the Monte Carlo parameters on the efficiency of this REMC method. Second, we have implemented an adaptive protocol that resets the values of the hydrolysis/condensation equilibrium constants among the replicas, ‘on the fly’ of each simulation, to optimise replica exchange for the purpose of constructing zeolite crystals. Finally, we show that by applying these enhancements, the REMC method can produce the crystal structure of zeolite AWW, a nanoporous material with 24 tetrahedra per unit cell.

A coarse-grained molecular dynamics – reactive Monte Carlo approach to simulate hyperbranched polycondensation

A coarse-grained molecular dynamics (CG-MD) and reactive Monte Carlo (RMC) hybrid method (CG-MD + RMC) has been developed to investigate the hyperbranched polycondensation of 3,5-bis(trimethylsiloxy)benzoyl chloride to poly(3,5-dihydroxybenzoic acid). The CG force field to describe the formation of the hyperbranched macromolecules has been extracted from all-atom molecular dynamics simulations by the mapping technology of iterative Boltzmann inversion. In the mapping process branched poly(3,5-dihydroxybenzoic acid) in an all-atom description has been employed as a target object to derive the CG force field for hyperbranched polymers. In the RMC simulations, the reactivity ratio of the functional groups has been optimized by fitting experimental data with the iterative dichotomy method (Macromolecules, 2003, 36, 97). Using such a simulation framework, detailed information including the molecular weight, the molecular weight distribution and the branching degree of a specific polymerization process has been derived. Radial distribution functions of the atomistic and coarse-grained systems are in excellent agreement. A good agreement between the present simulations and experiment has been demonstrated, too. Especially, the intramolecular cyclization fraction has been reproduced quantitatively. This work illustrates that the present reactive CG-MD + RMC model can be used for quantitative studies of specific hyperbranched polymerizations.

Probing the Mechanism of Silica Polymerization at Ambient Temperatures using Monte Carlo Simulations

We have developed a model for silica polymerization at ambient temperatures and low densities and have studied this using reactive Monte Carlo simulations. The model focuses on SiO4 coordination with the energetics of hydrolysis and condensation reactions treated via the reaction ensemble. The simplicity of the model makes large system sizes accessible on a modest computation budget, although it is necessary to make additional assumptions in order to use the reactive Monte Carlo method as a simulation of the system dynamics. Excellent agreement for the evolution of the Qn distribution is obtained upon comparing the simulation results to experimental observations. The analysis of simulation trajectories provides mechanistic insight into the polymerization process, showing the following three regimes: oligomerization (0−1 h), ring formation (1−2.6 h), and cluster aggregation (2.6−5.6 h).

Replica Exchange for Reactive Monte Carlo Simulations

A new application of the replica exchange technique is demonstrated for use in reactive Monte Carlo simulations. The technique allows the system to traverse barriers in the free energy landscape through configuration swaps of higher temperature replicas, replicas with scaled potential energy parameters, or replicas existing at modified values of the reaction driving force (free energy of reaction). Acceptance rules are derived for the swap moves among the replicas, and the application of the replica exchange method is shown to be straightforward. We demonstrate the accuracy and efficiency of this technique by simulating the conversion of a model reaction. We find large increases in efficiency when performing simulations at computationally challenging conditions, such as high densities, particularly when a preconverged configuration reservoir is incorporated. It is possible to extend this replica exchange approach to systems involving multiple simultaneous reactions and to systems with more complex multisite reacting species.

Monte Carlo Simulation of Equilibrium Reactions at Modified Vapor−Liquid Interfaces

The equilibrium conversion of a chemical reaction is known to be affected by its local environment. Various factors may alter reaction equilibria, including shifts in pressure or temperature, solvation, adsorption within porous materials, or the presence of an interface. Previously, reactive Monte Carlo simulations have been used to predict the equilibrium behavior of chemical reactions at vapor-liquid interfaces. Here, a route is tested for tuning the interfacial conversion of a Lennard-Jones dimerization reaction by adding surfactants to the vapor-liquid interface. Several temperatures are explored as well as several different surfactant models. Even with the addition of a small concentration of surfactants, the simulations predict significant shifts in the conversion at the interface. In general, the shifts in the conversion tend to be related to the values of the interfacial tension.

Does solvent density play a role in the keto–enol tautomerism of acetylacetone?

FTIR was used to investigate the effect of solvent and solvent density on the keto–enol tautomeric equilibrium in compressed and supercritical carbon dioxide as well as ethane. The effect of the solvent (CO 2 and ethane) density on the tautomerism was found to be insignificant. These experimental results are in good agreement with modeling studies, which combine ab initio calculations of isolated acetylacetone with reactive Monte Carlo simulations of the CO 2 and ethane solvation effects.

Effects of supercritical clustering and selective confinement on reaction equilibrium: A molecular simulation study of the esterification reaction

We explore the effects of different molecular surroundings on the equilibrium conversion of ethanol and acetic acid to ethyl acetate and water. While the equilibrium conversion of this reaction is limited from 66% to 68% in the liquid phase, experimental measurements have found that the reaction yield can be enhanced within a supercritical carbon dioxide solvent and within microporous carbons. The reactive Monte Carlo simulations presented mirror these experimental findings, and provide the molecular-level information needed to explain the experimental observations. The simulations demonstrate that selectivity is the driving force for the enhanced conversion in carbon slit-pores and in the supercritical carbon dioxide solvent. Ethyl acetate tends to be selectively adsorbed within carbon slit-pores in the range of 1.0 to 2.0 nm in width, and is selectively solubilized within carbon dioxide clusters near the critical point of the fluid.

A density functional approach to chemical reaction equilibria in confined systems: Application to dimerization

The effect of confinement on chemical equilibria is investigated within the framework of a density functional theory for chemical reactions in slit pores in equilibrium with a bulk reservoir. Factors like pore size, temperature, bulk pressure, external field, and capillary condensation are known to have considerable impact on the phase equilibria of a confined system. We analyze the impact of these factors on the composition (hence conversion) of a model reacting system, from a chemical equilibria perspective. Canonical Monte Carlo simulations are performed to compare with the theoretical findings for the spatial distribution of the reactants and products in the pore. Enhanced adsorption leads to significantly higher conversions in reactions occurring in the pore phase than in the bulk phase. The validity of this framework for reacting systems is then further tested on a real system, viz., dimerization of nitric oxide in graphite micropores (size <3 nm). The results obtained are in very good agreement with the reactive Monte Carlo simulations results reported for the same system by Turner, Johnson, and Gubbins [J. Chem. Phys. 114, 1851 (2001)].

Influence of chemical and physical surface heterogeneity on chemical reaction equilibria in carbon micropores

Recent simulation results are presented for the equilibrium yield of the ammonia synthesis reaction in various model microporous carbons. It is found that the reaction equilibria within the micropores is affected by many factors, including pore size, pore shape, connectivity, surface roughness, and surface chemical activation. In order to probe these effects, reactive Monte Carlo simulations of the reaction were performed in several microporous carbon models: smooth slit-shaped carbon pores, a realistic carbon model generated from experimental diffraction data, single-walled carbon nanotubes, and smooth slit-shaped pores activated by carboxyl surface groups. The simulations show that the ammonia conversion is most sensitive to the carbon pore width and to the amount of surface chemical activation. Effects of surface corrugation and pore connectivity on the equilibrium reaction yield are minimal.