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The theory of interfacial properties in liquid-liquid or liquid-vapour systems is nearly 200 years old. The advent of computational tools has greatly advanced the field, mainly through the use of Molecular Dynamics simulations. Despite the successes and advances in the theory of interfacial phenomena for liquid-liquid systems, the study of solid-liquid interfaces remains a challenge both theoretically and experimentally. The main reason why the treatment of solid-liquid systems has fallen behind that of liquid-liquid systems is that there are complications that arise whenever an interface involving solid systems is considered involving both theory of the solid-liquid interface and the calculations using MD simulations. An example of the former is that, contrary to the liquid-liquid case, the interfacial properties of solids depend on the lattice orientation. The main complications in these calculations arise from the fact that for solids the ``mechanical route'' cannot be used. To overcome this problem, several numerical approaches were proposed. The main purpose of this review is to provide an overview of these different methodologies and to discuss their strengths and weaknesses. We classify these methodologies into two main groups: direct and indirect methods. Direct methods are those that can calculate directly the properties of interfaces, while in indirect approaches the properties of the interface are not the primary result of the simulations. We also included a discussion on the origin of the difficulties in considering solid interfaces from a thermodynamic point of view. In the second part of the review, we discuss two key related topics: nucleation theory and curved interfaces. They both represent an important problem in the study of interfaces and in the context of solid-liquid ones for which the research is still extremely active., Comment: 111 pages, 14 figures

We investigate the effect of pressure on the carbon dioxide (CO$_{2}$) hydrate-water interfacial free energy along its dissociation line using advanced computer simulation techniques. In previous works, we have determined the interfacial energy of the hydrate at $400 \,\text{bar}$ using the TIP4P/ice and TraPPE molecular models for water and CO$_{2}$, respectively, in combination with two different extensions of the Mold Integration technique [J. Chem. Phys. 141, 134709 (2014)]. Results obtained from computer simulation, $29(2)$ and $30(2)\,\text{mJ/m}^{2}$, are found to be in excellent agreement with the only two measurements that exist in the literature, $28(6)\,\text{mJ/m}^{2}$ determined by Uchida et al. [J. Phys. Chem. B 106, 8202 (2002)] and $30(3)\,\text{mJ/m}^{2}$ by Anderson et al. [J. Phys. Chem. B 107, 3507 (2002)]. Since the experiments do not allow to obtain the variation of the interfacial energy along the dissociation line of the hydrate, we extend our previous studies to quantify the effect of pressure on the interfacial energy at different pressures. Our results suggest that there exists a correlation between the interfacial free energy values and the pressure, i.e., it decreases with the pressure between $100$ and $1000\,\text{bar}$. We expect that the combination of reliable molecular models and advanced simulation techniques could help to improve our knowledge of the thermodynamic parameters that control the interfacial free energy of hydrates from a molecular perspective., Comment: 7 pages, 4 figures

In this paper, the solubility of carbon dioxide (CO$_{2}$) in water along the isobar of 400 bar is determined by computer simulations using the well-known TIP4P/Ice force field for water and TraPPE model for CO$_{2}$. In particular, the solubility of CO$_{2}$ in water when in contact with the CO$_{2}$ liquid phase, and the solubility of CO$_{2}$ in water when in contact with the hydrate have been determined. The solubility of CO$_{2}$ in a liquid-liquid system decreases as temperature increases. The solubility of CO$_{2}$ in a hydrate-liquid system increases with temperature. The two curves intersect at a certain temperature that determines the dissociation temperature of the hydrate at 400 bar ($T_{3}$). We compare the predictions with the $T_{3}$ obtained using the direct coexistence technique in a previous work. The results of both methods agree and we suggest 290(2)K as the value of $T_{3}$ for this system using the same cutoff distance for dispersive interactions. We also propose a novel and alternative route to evaluate the change in chemical potential for the formation of hydrate along the isobar. The new approach is based on the use of the solubility curve of CO$_{2}$ when the aqueous solution is in contact with the hydrate phase. It considers rigorously the non-ideality of the aqueous solution of CO$_{2}$, providing reliable values for driving force for nucleation of hydrates in good agreement with other thermodynamic routes used. It is shown that the driving force for hydrate nucleation at 400 bar is larger for the methane hydrate than for the carbon dioxide hydrate when compared at the same supercooling. We have also analyzed and discussed the effect of the cutoff distance of the dispersive interactions and the occupancy of CO$_{2}$ on the driving force for nucleation of the hydrate., Comment: 25 pages, 19 figures

Averaged local bond order parameters based on spherical harmonics, also known as Lechner and Dellago order parameters, are routinely used to determine crystal structures in molecular simulations. Among different options, the combination of the $\overline{q}_{4}$ and $\overline{q}_{6}$ parameters is one of the best choices in the literature since allows one to distinguish, not only between solid- and liquid-like particles but also between different crystallographic phases, including cubic and hexagonal phases. Recently, Algaba et al. [J. Colloid Interface Sci. 623, 354, (2022)] have used the Lechner and Dellago order parameters to distinguish hydrate- and liquid-like water molecules in the context of determining the carbon dioxide hydrate-water interfacial free energy. According to the results, the preferred combination previously mentioned is not the best option to differentiate between hydrate- and liquid-like water molecules. In this work, we revisit and extend the use of these parameters to deal with systems in which clathrate hydrates phases coexist with liquid phases of water. We consider carbon dioxide, methane, tetrahydrofuran, nitrogen, and hydrogen hydrates that exhibit sI and sII crystallographic structures. We find that the $\overline{q}_{3}$ and $\overline{q}_{12}$ combination is the best option possible between a large number of possible different pairs to distinguish between hydrate- and liquid-like water molecules in all cases., Comment: 18 pages, 8 figures

In this work, we determine the dissociation line of the nitrogen (N$_2$) hydrate by computer simulation using the TIP4P/Ice model for water and the TraPPE force field for N$_2$. We use the solubility method proposed recently by some of us to evaluate the dissociation temperature of the hydrate at different pressures, from 500 to 1500 bar. Particularly, we calculate the solubility of N$_2$ in the aqueous solution when it is in contact with a N$_2$-rich liquid phase and when in contact with the hydrate phase via planar interfaces as functions of temperature. Since the solubility of N$_2$ decreases with temperature in the first case and increases with temperature in the second case, both curves intersect at a certain temperature that determines the dissociation temperature at a given pressure. We find a good agreement between the predictions obtained in this work and the experimental data taken from the literature in the range of pressures considered in this work. From our knowledge of the solubility curves of N$_2$ in the aqueous solution, we also determine the driving force for nucleation of the hydrate, as a function of temperature, at different pressures. In particular, we use two different thermodynamic routes to evaluate the change in chemical potential for hydrate formation. Although the driving force for nucleation slightly decreases (in absolute value) when the pressure is increased, our results indicate that the effect of pressure can be considered negligible in the range of pressures studied in this work. To the best of our knowledge, this is the first time the driving force for nucleation of a hydrate that exhibits crystallographic structure sII, along its dissociation line, is studied from computer simulation., Comment: 15 pages, 9 figures. arXiv admin note: text overlap with arXiv:2408.03257

In this work, the tetrahydrofuran (THF) hydrate-water interfacial free energy is determined at $500\,\text{bar}$, at one point of the univariant two-phase coexistence line of the THF hydrate, by molecular dynamics simulation. The Mold Integration-Host methodology, an extension of the original Mold Integration technique to deal with hydrate-fluid interfaces, is used to calculate the interfacial energy. Water is described using the well-known TIP4P/Ice model and THF is described using a rigid version of the TraPPE model. We have recently used the combination of these two models to accurately describe the univariant two-phase dissociation line of the THF hydrate, in a wide range of pressures, from computer simulation [J. Chem. Phys. 160, 164718 (2024)]. The THF hydrate-water interfacial free energy predicted in this work is compared with the only experimental data available in the literature. The value obtained, $27(2)\,\text{mJ/m}^{2}$, is in excellent agreement with the experimental data taken from the literature, $24(8)\,\text{mJ/m}^{2}$. To the best of our knowledge, this is the first time that the THF hydrate-water interfacial free energy is predicted from computer simulation. This work confirms that the Mold Integration technique can be used with confidence to predict solid-fluid interfaces of complex structures, including hydrates that exhibit sI and sII crystallographic structures., Comment: 11 pages, 6 figures

In this work, we determine the dissociation line of the nitrogen (N$_{2}$) hydrate by computer simulation using the TIP4P/Ice model for water and the TraPPE force field for N$_{2}$. This work is the natural extension of our previous paper in which the dissociation temperature of the N$_2$ hydrate has been obtained at $500$, $1000$, and $1500\,\text{bar}$ [\emph{J. Chem. Phys.} \textbf{159}, 224707 (2023)] using the solubility method and assuming single occupancy. We extend our previous study and determine the dissociation temperature of the N$_2$ hydrate at different pressures, from $500$ to $4500\,\text{bar}$, taking into account single and double occupancy of the N$_{2}$ molecules in the hydrate structure. We calculate the solubility of N$_2$ in the aqueous solution, as a function of temperature, when it is in contact with a N$_{2}$-rich liquid phase and when in contact with the hydrate phase with single and double occupancy via planar interfaces. Both curves intersect at a certain temperature that determines the dissociation temperature at a given pressure. We observe a negligible effect of the occupancy on the dissociation temperature. Our findings are in very good agreement with the experimental data taken from the literature. We have also obtained the driving force for nucleation of the hydrate as a function of the temperature and occupancy at several pressures. As in the case of the dissociation line, the effect of the occupancy on the driving force for nucleation is negligible. To the best of our knowledge, this is the first time that the effect of the occupancy on the driving force for nucleation of a hydrate that exhibits sII crystallographic structure is studied from computer simulation., Comment: 15 pages, 13 figures

In this work, the univariant two-phase coexistence line of the hydrate of tetrahydrofuran (THF) is determined from 100 to 1000 bar by molecular dynamics simulations. The study is carried out by putting in contact a THF hydrate phase with a stoichiometric aqueous solution phase. Following the direct coexistence technique, the pressure has been fixed, and the coexistence line has been determined by analyzing if the hydrate phase grows or melts at different values of temperature. The model of water used is the well-known TIP4P/Ice model. We have used two different models of THF based on the transferable parameters for phase equilibria-united atom approach (TraPPE-UA), the original (flexible) TraPPe-UA model as well as a rigid and planar version of it. Overall, at high pressures, small differences have been observed in the results obtained by both models. Also, large differences have been observed in the computational efforts required by the simulations performed using both models, being the rigid and planar version much faster than the original one. The effect of the unlike dispersive interactions between the water and THF molecules has been also analyzed at 250 bar using the rigid and planar THF model. In particular, we have modified the Berthelot combining rule by adding a factor ({\xi}O-THF) that modifies the unlike water-THF dispersive interactions and we have analyzed the effect on the dissociation temperature when {\xi}O-THF is modified from 1.0 (original Berthelot combining rule) to 1.4 (modified Berthelot combining rule). We have extended the study using {\xi}O-THF = 1.4 and the rigid THF model to the rest of the pressures considered in this work, finding an excellent agreement with the scarce experimental data taken from the literature., Comment: 10 pages, 5 figures