Recently, deep eutectic solvents (DES) have been considered as possible electrolytes for the electrochemical reduction of CO2 to value-added products such as formic and oxalic acids. The applicability of pure DES as electrolytes is hindered by high viscosities. Mixtures of DES with organic solvents can be a promising way of designing superior electrolytes by exploiting the advantages of each solvent type. In this study, densities, viscosities, diffusivities, and ionic conductivities of mixed solvents comprising DES (i.e., reline and ethaline), methanol, and propylene carbonate were computed using molecular simulations. To provide a quantitative assessment of the affinity and mass transport of CO2 and oxalic and formic acids in the mixed solvents, the solubilities and self-diffusivities of these solutes were also computed. Our results show that the addition of DES to the organic solvents enhances the solubilities of oxalic and formic acids, while the solubility of CO2 in the ethaline-containing mixtures are in the same order of magnitude with the respective pure organic components. A monotonic increase in the densities and viscosities of the mixed solvents is observed as the mole fraction of DES in the mixture increases, with the exception of the density of ethaline-propylene carbonate which shows the opposite behavior due to the high viscosity of the pure organic component. The self-diffusivities of all species in the mixtures significantly decrease as the mole fraction of DES approaches unity. Similarly, the self-diffusivities of the dissolved CO2 and the oxalic and formic acids also decrease by at least 1 order of magnitude as the composition of the mixture shifts from the pure organic component to pure DES. The computed ionic conductivities of all mixed solvents show a maximum value for mole fractions of DES in the range from 0.2 to 0.6 and decrease as more DES is added to the mixtures. Since for most mixtures studied here no prior experimental measurements exist, our findings can serve as a first data set based on which further investigation of DES-containing electrolyte solutions can be performed for the electrochemical reduction of CO2 to useful chemicals.

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Deep eutectic solvents (DESs) have emerged as a cheaper and greener alternative to conventional organic solvents. Choline chloride (ChCl) mixed with urea at a molar ratio of 1:2 is one of the most common DESs for a wide range of applications such as electrochemistry, material science, and biochemistry. In this study, molecular dynamics simulations are performed to study the effect of urea content on the thermodynamic and transport properties of ChCl and urea mixtures. With increased mole fraction of urea, the number of hydrogen bonds (HBs) between cation-anion and ion-urea decreases, while the number of HBs between urea-urea increases. Radial distribution functions (RDFs) for ChCl-urea and ChCl-ChCl pairs shows a significant decrease as the mole fraction of urea increases. Using the computed RDFs, Kirkwood-Buff Integrals (KBIs) are computed. KBIs show that interactions of urea-urea become stronger, while interactions of urea-ChCl and ChCl-ChCl pairs become slightly weaker with increasing mole fraction of urea. All thermodynamic factors are found larger than one, indicating a non-ideal mixture. Our results also show that self- and collective diffusivities increase, while viscosities decrease with increasing urea content. This is mainly due to the weaker interactions between ions and urea, resulting in enhanced mobilities. Ionic conductivities exhibit a non-monotonic behavior. Up to a mole fraction of 0.5, the ionic conductivities increase with increasing urea content and then reach a plateau.

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The Kirkwood–Buff (KB) theory is one of the most rigorous solution theories that connects molecular structure to macroscopic behaviour. The key quantity, the so–called KB Kirkwood–Buff Integrals (KBIs), are defined either in terms of fluctuations in the number of molecules or integrals over radial distribution functions over open subvolumes. In the grand–canonical ensemble, KBIs of infinitely large and open systems are directly related to thermodynamic properties such as partial derivatives of chemical potentials and partial molar volumes. Using molecular simulations, it is only possible to study small systems with a finite number of molecules, and therefore finite–size effects should be considered.@en

Kirkwood–Buff (KB) integrals provide a connection between microscopic properties and thermodynamic properties of multicomponent fluids. The estimation of KB integrals using molecular simulations of finite systems requires accounting for finite size effects. In the small system method, properties of finite subvolumes with different sizes embedded in a larger volume can be used to extrapolate to macroscopic thermodynamic properties. KB integrals computed from small subvolumes scale with the inverse size of the system. This scaling was used to find KB integrals in the thermodynamic limit. To reduce numerical inaccuracies that arise from this extrapolation, alternative approaches were considered in this work. Three methods for computing KB integrals in the thermodynamic limit from information of radial distribution functions (RDFs) of finite systems were compared. These methods allowed for the computation of surface effects. KB integrals and surface terms in the thermodynamic limit were computed for Lennard–Jones (LJ) and Weeks–Chandler–Andersen (WCA) fluids. It was found that all three methods converge to the same value. The main differentiating factor was the speed of convergence with system size L. The method that required the smallest size was the one which exploited the scaling of the finite volume KB integral multiplied by L. The relationship between KB integrals and surface effects was studied for a range of densities.

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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.

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Knowledge on the solubility of gases, especially carbon dioxide (CO2), in monoethylene glycol (MEG) is relevant for a number of industrial applications such as separation processes and gas hydrate prevention. In this study, the solubility of CO2 in MEG was measured experimentally at temperatures of 333.15, 353.15, and 373.15 K. Experimental data were used to validate Monte Carlo (MC) simulations. Continuous fractional component MC simulations in the osmotic ensemble were performed to compute the solubility of CO2 in MEG at the same temperatures and at pressures up to 10 bar. MC simulations were also used to study the solubility of methane (CH4), hydrogen sulfide (H2S), and nitrogen (N2) in MEG at 373.15 K. Solubilities from experiments and simulations are in good agreement at low pressures, but deviations were observed at high pressures. Henry coefficients were also computed using MC simulations and compared to experimental values. The order of solubilities of the gases in MEG at 373.15 K was computed as H2S > CO2 > CH4 > N2. Force field modifications may be required to improve the prediction of solubilities of gases in MEG at high pressures and low temperatures.

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The Kirkwood-Buff (KB) theory provides a rigorous framework to predict thermodynamic properties of isotropic liquids from the microscopic structure. Several thermodynamic quantities relate to KB integrals, such as partial molar volumes. KB integrals are expressed as integrals of RDFs over volume but can also be obtained from density fluctuations in the grand-canonical ensemble. Various methods have been proposed to estimate KB integrals from molecular simulation. In this work, we review the available methods to compute KB integrals from molecular simulations of finite systems, and particular attention is paid to finite-size effects. We also review various applications of KB integrals computed from simulations. These applications demonstrate the importance of computing KB integrals for relating findings of molecular simulation to macroscopic thermodynamic properties of isotropic liquids.

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The Kirkwood–Buff (KB) theory provides an important connection between microscopic density fluctuations in liquids and macroscopic properties. Recently, Krüger et al. derived equations for KB integrals for finite subvolumes embedded in a reservoir. Using molecular simulation of finite systems, KB integrals can be computed either from density fluctuations inside such subvolumes, or from integrals of radial distribution functions (RDFs). Here, based on the second approach, we establish a framework to compute KB integrals for subvolumes with arbitrary convex shapes. This requires a geometric function w(x) which depends on the shape of the subvolume, and the relative position inside the subvolume. We present a numerical method to compute w(x) based on Umbrella Sampling Monte Carlo (MC). We compute KB integrals of a liquid with a model RDF for subvolumes with different shapes. KB integrals approach the thermodynamic limit in the same way: for sufficiently large volumes, KB integrals are a linear function of area over volume, which is independent of the shape of the subvolume.

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The modelling of thermodynamic properties of liquids from local density fluctuations is relevant to many chemical and biological processes. The Kirkwood–Buff (KB) theory connects the microscopic structure of isotropic liquids with macroscopic properties such as partial derivatives of activity coefficients, partial molar volumes and compressibilities. Originally, KB integrals were formulated for open and infinite systems which are difficult to access with standard Molecular Dynamics (MD) simulations. Recently, KB integrals for finite and open systems were formulated (J Phys Chem Lett. 2013;4:235). From the scaling of KB integrals for finite subvolumes, embedded in larger reservoirs, with the inverse of the size of these subvolumes, estimates for KB integrals in the thermodynamic limit are obtained. Two system size effects are observed in MD simulations: (1) effects due to the size of the simulation box and the size of the finite subvolume embedded in the simulation box, and (2) effects due to computing radial distribution functions (RDF) from a closed and finite system. In this study, we investigate the two effects in detail by computing KB integrals using the following methods: (1) Monte Carlo simulations of finite subvolumes of a liquid with an analytic RDF and (2) MD simulations of a WCA mixture for various simulation box sizes, but at the same thermodynamic state. We investigate the effect of the size of the simulation box and quantify the differences compared to KB integrals computed in the thermodynamic limit. We demonstrate that calculations of KB integrals should not be extended beyond half the size of the simulation box. For finite-size effects related to the RDF, we find that the Van der Vegt correction (J Chem Theory Comput. 2013;9:1347) yields the most accurate results.

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