We present a detailed overview of classical molecular simulation studies examining the self-diffusion coefficient of water. The self-diffusion coefficient is directly associated with the calculations of tracer or mutual diffusion coefficient of mixtures and, therefore, is a fundamental transport property, essential for an accurate description of mass transfer processes in biological, geological (i.e. energy or environmentally related), and chemical systems. In the current review we explore two distinct research areas. Namely, we discuss the self-diffusion of water in the bulk phase and under confinement. Different aspects that affect the diffusion process, including the molecular models, the system-size effects, the temperature and pressure conditions and the type of confinement are discussed. Finally, possible directions for future research are outlined.@en

Clathrate hydrates have characteristic properties that render them attractive for a number of industrial applications. Of particular interest are the following two cases: (i) the incorporation of large amounts of gas molecules into the solid structure has resulted in considering hydrates as possible material for the storage/transportation of energy or environmental gases, and (ii) the selective incorporation of guest molecules into the solid structure has resulted in considering hydrates for gas-mixture separations. For the proper design of such industrial applications, it is essential to know accurately a number of thermodynamic, structural and transport properties. Such properties can either be measured experimentally or calculated at different scales that span the molecular scale-up to the continuum scale. By using clathrate hydrates as a particular case study, we demonstrate that performing studies at multiple length scales can be utilised in order to obtain properties that are essential to process design.@en

Clathrate hydrates have characteristic properties that render them attractive for a number of industrial applications. Of particular interest are the following two cases: (i) the incorporation of large amounts of gas molecules into the solid structure has resulted in considering hydrates as possible material for the storage/transportation of energy or environmental gases, and (ii) the selective incorporation of guest molecules into the solid structure has resulted in considering hydrates for gas-mixture separations. For the proper design of such industrial applications, it is essential to know accurately a number of thermodynamic, structural and transport properties. Such properties can either be measured experimentally or calculated at different scales that span the molecular scale-up to the continuum scale. By using clathrate hydrates as a particular case study, we demonstrate that performing studies at multiple length scales can be utilised in order to obtain properties that are essential to process design.@en

Clathrate hydrates have characteristic properties that render them attractive for a number of industrial applications. Of particular interest are the following two cases: (i) the incorporation of large amounts of gas molecules into the solid structure has resulted in considering hydrates as possible material for the storage/transportation of energy or environmental gases, and (ii) the selective incorporation of guest molecules into the solid structure has resulted in considering hydrates for gas-mixture separations. For the proper design of such industrial applications, it is essential to know accurately a number of thermodynamic, structural and transport properties. Such properties can either be measured experimentally or calculated at different scales that span the molecular scale-up to the continuum scale. By using clathrate hydrates as a particular case study, we demonstrate that performing studies at multiple length scales can be utilised in order to obtain properties that are essential to process design.@en

In this study, all available data from experiments and molecular simulations for the intra-diffusivities of H2 and O2 in H2O, and for the self-diffusivity of pure H2O are analyzed to examine the validity of the Stokes-Einstein relation. This analysis is motivated by the significant amount of work devoted through the years for improving the predictions of intra- and self-diffusivities in binary and multi-component mixtures relevant to chemical and environmental processes. Here, we calculate the slopes s and t corresponding to the ln(D)vs.ln[Formula presented] plots, respectively, where D is the intra-diffusivity, η the viscosity, and T the temperature of the systems. Our results show that s and t deviate from unity no matter if the experimental or simulation data are used. This means that the Stokes-Einstein relation is violated for the binary systems of H2 and O2 with H2O, and for pure H2O. Although prior studies mainly focused on re-evaluating the parameter A of the SE-based semi-theoretical/semi-empirical approaches expressed as [Formula presented], our results indicate that reliable predictions for the intra- and self-diffusivities can be achieved by improving the accuracy of the prediction of slopes s and t.@en

Available data from experiments and molecular simulations for the intra-diffusivities of H (Formula presented.) and O (Formula presented.) in H (Formula presented.) O, and for the self-diffusivity of pure H (Formula presented.) O (at pressure and temperature conditions in which the solvent is in the vapour phase) are compared against calculations based on the Chapman-Enskog theory or other semi-empirical/semi-theoretical methods. A novel methodology is proposed to extrapolate the intra-/self-diffusivities data computed from molecular dynamics simulations at low pressures. The extrapolated values are used to further refine the recently-proposed [Tsimpanogiannis et al., J. Chem. Eng. Data, 66, 3226-3244, (2021)], molecular simulation based correlation of intra-/self-diffusivities as a function of pressure and temperature with the solvent being in the vapour phase.@en

The translational self-diffusion coefficient and the shear viscosity of water are related by the fractional Stokes–Einstein relation. We report extensive novel molecular dynamics simulations for the self-diffusion coefficient and the shear viscosity of water. The SPC/E and TIP4P/2005 water models are used in the temperature range 220–560 K and at 1 or 1,000 bar. We compute the fractional exponents t, and s that correspond to the two forms of the fractional Stokes–Einstein relation (Formula presented.) and (Formula presented.) respectively. We analyse other available experimental and numerical simulation data. In the current analysis two temperature ranges are considered (above or below 274 K) and in both cases deviations from the Stokes–Einstein relation are observed with different values for the fractional exponents obtained for each temperature range. For temperatures above 274 K, both water models perform comparably, while for temperatures below 274 K TIP4P/2005 outperforms SPC/E. This is a direct result of the ability of TIP4P/2005 to predict water densities more accurately and thus predict more accurately the water self-diffusion coefficient and the shear viscosity.@en

Molecular dynamics simulations are carried out to compute the intradiffusion coefficients of H2 and O2 in H2O for temperatures ranging from 275.15 to 975.15 K and pressures ranging from 0.1 to 200 MPa. These conditions span vapor, liquid, and supercritical conditions. For the vast majority of the state points examined, experimental data are not available. The accuracy of six H2 and six O2 force fields is tested in reproducing the available experimentally measured densities, self-diffusivities, and shear viscosities of the pure gas and the intradiffusivity of the gas in H2O. Namely, we screen the H2 force fields developed by Buch, Vrabec and co-workers, Hirschfelder et al., Cracknell, a modified Silvera-Goldman, and Marx and Nielaba. For O2, the force fields by Bohn et al., Miyano, Coon et al., Hansen et al., Vrabec et al., and Watanabe are tested. Overall, the force fields by Buch and Bohn for H2 and O2, respectively, were found to perform the best, and combined with the TIP4P/2005 H2O force field are used to compute the intradiffusivities in the entire temperature and pressure range. The new data are used to develop an engineering model that can predict the H2 and O2 intradiffusivity in vapor, liquid, and supercritical H2O. The new model uses 11 parameters and has an accuracy of 4-11%. The model is validated with other available experimental and simulation data for H2 and O2 in H2O and pure H2O. Aside from the extensive collection of new data for the intradiffusivities of H2 and O2 in H2O, we present new data for the densities, shear viscosities, and self-diffusivities of pure TIP4P/2005 H2O in the same wide temperature and pressure range. The new data and the engineering model presented here can be used for the design and optimization of chemical processes, for which the knowledge of H2 and O2 diffusivities in H2O is important. @en