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.

The system-size dependence of computed mutual diffusion coefficients of multicomponent mixtures is investigated, and a generalized correction term is derived. The generalized finite-size correction term was validated for the ternary molecular mixture chloroform/acetone/methanol as well as 28 ternary LJ systems. It is shown that only the diagonal elements of the Fick matrix show system-size dependency. The finite-size effects of these elements can be corrected by adding the term derived by Yeh and Hummer (J. Phys. Chem. B2004, 108, 15873-15879). By performing an eigenvalue analysis of the finite-size effects of the matrix of Fick diffusivities we show that the eigenvector matrix of Fick diffusivities does not depend on the size of the simulation box. Only eigenvalues, which describe the speed of diffusion, depend on the size of the system. An analytic relation for finite-size effects of the matrix of Maxwell-Stefan diffusivities was developed. All Maxwell-Stefan diffusivities depend on the system size, and the required correction depends on the matrix of thermodynamic factors.

The metal–organic frameworks (MOFs) MIL-101(Cr) and NH₂-MIL-125 offer high adsorption capacities and have therefore been suggested for sustainable energy conversion in adsorption chillers. Herein, these MOFs are benchmarked to commercial Siogel. The evaluation method combines small-scale experiments with dynamic modeling of full-scale adsorption chillers. For the common temperature set 10/30/80 °C, it is found that MIL-101(Cr) has the highest adsorption capacity, but considerably lower efficiency (−19%) and power density (−66%) than Siogel. NH₂-MIL-125 increases efficiency by 18% compared with Siogel, but reduces the practically important power density by 28%. From the results, guidelines for MOF development are derived: High efficiencies are achieved by matching the shape of the isotherms to the specific operating temperatures. By only adapting shape, efficiencies are 1.5 times higher. Also, higher power density requires matching the shape of the isotherms to create high driving forces for heat and mass transfer. Second, if MOFs’ heat and mass transfer coefficients could reach the level of Siogel, their maximum power density would double. Thus, development of MOFs should go beyond adsorption capacity, and tune the structure to the application requirements. As a result, MOFs could to serve as optimal adsorbents for sustainable energy conversion.

We present a new plugin for LAMMPS for on-the-fly computation of transport properties (OCTP) in equilibrium molecular dynamics. OCTP computes the self- and Maxwell-Stefan diffusivities, bulk and shear viscosities, and thermal conductivities of pure fluids and mixtures in a single simulation. OCTP is the first implementation in LAMMPS that uses the Einstein relations combined with the order-n algorithm for the efficient sampling of dynamic variables. OCTP has low computational requirements and is easy to use because it follows the native input file format of LAMMPS. A tool for calculating the radial distribution function (RDF) of the fluid beyond the cutoff radius, while taking into account the system size effects, is also part of the new plugin. The RDFs computed from OCTP are needed to obtain the thermodynamic factor, which relates Maxwell-Stefan and Fick diffusivities. To demonstrate the efficiency of the new plugin, the transport properties of an equimolar mixture of water-methanol were computed at 298 K and 1 bar.

The conventional design of organic Rankine cycle (ORC) power systems starts with the selection of the working fluid and the subsequent optimization of the corresponding thermodynamic cycle. More recently, systematic methods have been proposed integrating the selection of the working fluid into the optimization of the thermodynamic cycle. However, in both cases, the turbine is designed subsequently. This procedure can lead to a suboptimal design, especially in the case of mini- and small-scale ORC systems, since the preselected combination of working fluid and operating conditions may lead to infeasible turbine designs. The resulting iterative design procedure may end in conservative solutions after multiple trial-and-error attempts due to the strong interdependence of the many design variables and constraints involved. In this work, we therefore present a new design and optimization method integrating working fluid selection, thermodynamic cycle design, and preliminary turbine design. To this purpose, our recent 1-stage continuous-molecular targeting (CoMT)-computer-aided molecular design (CAMD) method for the integrated design of the ORC process and working fluid is expanded by a turbine meanline design procedure. Thereby, the search space of the optimization is bounded to regions where the design of the turbine is feasible. The resulting method has been tested for the design of a small-scale high-temperature ORC unit adopting a radial-inflow turbo-expander. The results confirm the potential of the proposed method over the conventional iterative design practice for the design of small-scale ORC turbogenerators.

Mutual diffusion coefficients can be successfully predicted with models based on the Darken equation. However, Darken-based models require composition-dependent self-diffusion coefficients which are rarely available. In this work, we present a predictive model for composition-dependent self-diffusion coefficients (also called tracer diffusion coefficients or intradiffusion coefficients) in nonideal binary liquid mixtures. The model is derived from molecular dynamics simulation data of Lennard-Jones systems. A strong correlation between nonideal diffusion effects and the thermodynamic factor is observed. We extend the model by McCarty and Mason (Phys. Fluids 1960, 3, 908-922) for ideal binary gas mixtures to predict the composition-dependent self-diffusion coefficients in nonideal binary liquid mixtures. Our new model is a function of the thermodynamic factor, the self-diffusion coefficients at infinite dilution, and the self-diffusion coefficients of the pure substances, which are readily available. We validate our model with experimental data of 9 systems. For both Lennard-Jones systems and experimental data, the accuracy of the predicted self-diffusion coefficients is improved by a factor of 2 compared to the correlation of McCarty and Mason. Thus, our new model significantly expands the practical applicability of Darken-based models for the prediction of mutual diffusion coefficients.

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.