The number of molecules used in a typical Molecular Dynamics (MD) simulations is orders of magnitude lower than in the thermodynamic limit. It is therefore essential to correct diffusivities computed from Molecular Dynamics simulations for finite-size effects. We present a comprehensive review on finite-size effects of diffusion coefficients by considering self-, Maxwell–Stefan, and Fick diffusion coefficients in pure liquids, as well as binary, ternary, and quaternary mixtures. All finite-size corrections, both analytical and empirical, are discussed in detail. The finite-size effects of rotational and confined diffusion are also briefly discussed.

Molecular Dynamics simulations were performed for the prediction of the finite-size effects of Maxwell-Stefan diffusion coefficients of molecular mixtures and a wide variety of binary Lennard-Jones systems. A strong dependency of computed diffusivities on the system size was observed. Computed diffusivities were found to increase with the number of molecules. We propose a correction for the extrapolation of Maxwell-Stefan diffusion coefficients to the thermodynamic limit, based on the study by Yeh and Hummer (J. Phys. Chem. B, 2004, 108, 15873-15879). The proposed correction is a function of the viscosity of the system, the size of the simulation box, and the thermodynamic factor, which is a measure for the nonideality of the mixture. Verification is carried out for more than 200 distinct binary Lennard-Jones systems, as well as 9 binary systems of methanol, water, ethanol, acetone, methylamine, and carbon tetrachloride. Significant deviations between finite-size Maxwell-Stefan diffusivities and the corresponding diffusivities at the thermodynamic limit were found for mixtures close to demixing. In these cases, the finite-size correction can be even larger than the simulated (finite-size) Maxwell-Stefan diffusivity. Our results show that considering these finite-size effects is crucial and that the suggested correction allows for reliable computations.

Molecular dynamics simulations were carried out to study the self-diffusion coefficients of CO₂, methane, propane, n-hexane, n-hexadecane, and various poly(ethylene glycol) dimethyl ethers (glymes in short, CH₃O–(CH₂CH₂O)_n–CH₃ with n = 1, 2, 3, and 4, labeled as G1, G2, G3, and G4, respectively) at different conditions. Various system sizes were examined. The widely used Yeh and Hummer [J. Phys. Chem. B 108, 15873 (2004)] correction for the prediction of diffusion coefficient at the thermodynamic limit was applied and shown to be accurate in all cases compared to extrapolated values at infinite system size. The magnitude of correction, in all cases examined, is significant, with the smallest systems examined giving for some cases a self-diffusion coefficient approximately 15% lower than the infinite system-size extrapolated value. The results suggest that finite size corrections to computed self-diffusivities must be used in order to obtain accurate results.

Deep Eutectic Solvents (DESs) are a new generation of green solvents, which are considered an environmentally friendly alternative to ionic liquids (ILs) and volatile organic compounds. The addition of controlled amounts of water to DESs has a signi cant e ect on their microscopic structure, and thus on their thermodynamic and transport properties. In this way DESs can be modi ed, leading to solvents with improved characteristics. In this work, molecular dynamics (MD) simulations are performed to obtain a better understanding of the relation between the microscopic structure, molecular interactions and thermophysical properties of aqueous reline and ethaline solutions at temperatures ranging from 303.15 K to 363.15 K. For both reline and ethaline solutions, the hydrogen bond (HB) networks disappear with increasing mass fraction of water, and the intensity of RDF peaks decreases. For a mass fraction of water of 40%, most of the HBs between the compounds of reline and ethaline are broken, and DESs are fully dissolved in water. Consequently, a monotonic decrease in viscosities, and an increase in self-di usion coecients are observed. Electrical conductivities show a non-monotonic behavior with increasing water content. Up to to 60% water mass fraction, the electrical conductivities increase with increasing water content. A further increase in the mass fraction of water decreases conductivities. For all studied systems, the hydrogen bond network and the peaks of RDFs show relatively small changes for water mass fractions below 5% and beyond 40%. The MD results show that viscosities decrease with temperature, while di usivities and electrical conductivities increase. The e ect of temperature on the structure of DES-water mixtures is negligible.

Direct electrochemical reduction of CO₂ to C₂ products such as ethylene is more efficient in alkaline media, but it suffers from parasitic loss of reactants due to (bi)carbonate formation. A two-step process where the CO₂ is first electrochemically reduced to CO and subsequently converted to desired C₂ products has the potential to overcome the limitations posed by direct CO₂ electroreduction. In this study, we investigated the technical and economic feasibility of the direct and indirect CO₂ conversion routes to C₂ products. For the indirect route, CO₂ to CO conversion in a high temperature solid oxide electrolysis cell (SOEC) or a low temperature electrolyzer has been considered. The product distribution, conversion, selectivities, current densities, and cell potentials are different for both CO₂ conversion routes, which affects the downstream processing and the economics. A detailed process design and techno-economic analysis of both CO₂ conversion pathways are presented, which includes CO₂ capture, CO₂ (and CO) conversion, CO₂ (and CO) recycling, and product separation. Our economic analysis shows that both conversion routes are not profitable under the base case scenario, but the economics can be improved significantly by reducing the cell voltage, the capital cost of the electrolyzers, and the electricity price. For both routes, a cell voltage of 2.5 V, a capital cost of $10,000/m², and an electricity price of <$20/MWh will yield a positive net present value and payback times of less than 15 years. Overall, the high temperature (SOEC-based) two-step conversion process has a greater potential for scale-up than the direct electrochemical conversion route. Strategies for integrating the electrochemical CO₂/CO conversion process into the existing gas and oil infrastructure are outlined. Current barriers for industrialization of CO₂ electrolyzers and possible solutions are discussed as well.