Effect of pressure on the carbon dioxide hydrate-water interfacial free energy along its dissociation line.

We investigate the effect of pressure on the carbon dioxide (CO2) 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 bars using the TIP4P/Ice and TraPPE molecular models for water and CO2, respectively, in combination with two different extensions of the Mold Integration technique [J. Colloid Interface Sci. 623, 354 (2022) and J. Chem. Phys. 157, 134709 (2022)]. Results obtained from computer simulation, 29(2) and 30(2) mJ/m2, are found to be in excellent agreement with the only two measurements that exist in the literature, 28(6) mJ/m2 determined by Uchida et al. [J. Phys. Chem. B 106, 8202 (2002)] and 30(3) mJ/m2 determined 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 bars. 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.

Simulation of the CO2 hydrate-water interfacial energy: The mold integration-guest methodology.

The growth pattern and nucleation rate of carbon dioxide hydrate critically depend on the precise value of the hydrate-water interfacial free energy. There exist in the literature only two independent experimental measurements of this thermodynamic magnitude: one obtained by Uchida et al. [J. Phys. Chem. B 106, 8202 (2002)], 28(6) mJ/m2, and the other by Anderson and co-workers [J. Phys. Chem. B 107, 3507 (2003)], 30(3) mJ/m2. Recently, Algaba et al. [J. Colloid Interface Sci. 623, 354 (2022)] have extended the mold integration method proposed by Espinosa and co-workers [J. Chem. Phys. 141, 134709 (2014)] to deal with the CO2 hydrate-water interfacial free energy (mold integration-guest or MI-H). Computer simulations predict a value of 29(2) mJ/m2, in excellent agreement with experimental data. The method is based on the use of a mold of attractive wells located at the crystallographic positions of the oxygen atoms of water molecules in equilibrium hydrate structures to induce the formation of a thin hydrate slab in the liquid phase at coexistence conditions. We propose here a new implementation of the mold integration technique using a mold of attractive wells located now at the crystallographic positions of the carbon atoms of the CO2 molecules in the equilibrium hydrate structure. We find that the new mold integration-guest methodology, which does not introduce positional or orientational information of the water molecules in the hydrate phase, is able to induce the formation of CO2 hydrates in an efficient way. More importantly, this new version of the method predicts a CO2 hydrate-water interfacial energy value of 30(2) mJ/m2, in excellent agreement with experimental data, which is also fully consistent with the results obtained using the previous methodology.

Density functional theory for the prediction of interfacial properties of molecular fluids within the SAFT-γ coarse-grained approach.

Recently, we have proposed the SAFT-VR Mie MF DFT approach [Algaba et al., Phys. Chem. Chem. Phys., 2019, 21, 11937-11948] to investigate systems that exhibit fluid-fluid interfaces. This formalism is based on the combination of the Statistical Associating Fluid Theory for attractive potentials of variable range using Mie intermolecular potential (SAFT-VR Mie) and a Density Functional Theory (DFT) treatment of the free energy. A mean-field approach is used to evaluate the attractive term, neglecting the pair correlations associated to attractions. This theory has been combined with reported SAFT-γ Coarse-Grained (CG) Mie force fields to provide an excellent description of the vapor-liquid interface of carbon dioxide and water pure fluids. The present work is a natural and necessary extension of this previous study. We assess the adequacy of the proposed methodology for dealing with inhomogeneous fluid systems of large complex molecules, in particular carbon tetrafluoride and sulfur hexafluoride greenhouse gases, the refrigerant 2,3,3,3-tetrafluoro-1-propene, and the long-chain n-decane and n-eicosane hydrocarbons. The obvious diversity of these fluids, their chemical and industrial interest, and the fact of that SAFT-γ CG Mie force fields have been reported for them justify such choice. With the aim of testing the theory, we perform Molecular Dynamics simulations in the canonical ensemble using the direct coexistence technique for the same models. We focus both on bulk, such as coexistence diagrams and vapor pressure curves, as well as interfacial properties, including surface tension. The comparison of the theoretical predictions with the computational results as well as with experimental data taken from the literature demonstrates the reliability and generalization of this method for dealing simultaneously with vapor-liquid equilibrium and interfacial phenomena. Hence, it appears as a potential tool for the interface analysis, with the main advantage over molecular simulation of low computational cost, and solving the experimental difficulties in accurately measuring the surface tension of certain systems.

Simulation of the carbon dioxide hydrate-water interfacial energy.

HYPOTHESIS: Carbon dioxide hydrates are ice-like nonstoichiometric inclusion solid compounds with importance to global climate change, and gas transportation and storage. The thermodynamic and kinetic mechanisms that control carbon dioxide nucleation critically depend on hydrate-water interfacial free energy. Only two independent indirect experiments are available in the literature. Interfacial energies show large uncertainties due to the conditions at which experiments are performed. Under these circumstances, we hypothesize that accurate molecular models for water and carbon dioxide combined with computer simulation tools can offer an alternative but complementary way to estimate interfacial energies at coexistence conditions from a molecular perspective. CALCULATIONS: We have evaluated the interfacial free energy of carbon dioxide hydrates at coexistence conditions (three-phase equilibrium or dissociation line) implementing advanced computational methodologies, including the novel Mold Integration methodology. Our calculations are based on the definition of the interfacial free energy, standard statistical thermodynamic techniques, and the use of the most reliable and used molecular models for water (TIP4P/Ice) and carbon dioxide (TraPPE) available in the literature. FINDINGS: We find that simulations provide an interfacial energy value, at coexistence conditions, consistent with the experiments from its thermodynamic definition. Our calculations are reliable since are based on the use of two molecular models that accurately predict: (1) The ice-water interfacial free energy; and (2) the dissociation line of carbon dioxide hydrates. Computer simulation predictions provide alternative but reliable estimates of the carbon dioxide interfacial energy. Our pioneering work demonstrates that is possible to predict interfacial energies of hydrates from a truly computational molecular perspective and opens a new door to the determination of free energies of hydrates.

An accurate density functional theory for the vapor-liquid interface of chain molecules based on the statistical associating fluid theory for potentials of variable range for Mie chainlike fluids.

A new Helmholtz free energy density functional is presented to predict the vapor-liquid interface of chainlike molecules. The functional is based on the last version of the statistical associating fluid theory for potentials of variable range for homogeneous Mie chainlike fluids (SAFT-VR Mie). Following the standard formalism, the density functional theory (SAFT-VR Mie DFT) is constructed using a perturbative approach in which the free energy density contains a reference term to describe all the short-range interactions treated at the local level, and a perturbative contribution to account for the attractive perturbation which incorporates the long-range dispersive interactions. In this first work, we use a mean-field version of the theory in which the pair correlations are neglected in the attractive term. The SAFT-VR Mie DFT formalism is used to examine the effect of molecular chain length and the repulsive exponent of the intermolecular potential on density profiles and surface tension of linear chains made up of up to six Mie (λr - 6) segments with different values of the repulsive exponent of the intermolecular potential. Theoretical predictions from the theory are compared directly with molecular simulation data for density profiles and surface tension of Mie chainlike molecules taken from the literature. Agreement between theory and simulation data is good for short-chain molecules under all thermodynamic conditions of coexistence considered. Once the theory has proven that it is able to predict the interfacial properties, and particularly interfacial tension, the SAFT-VR Mie DFT formalism is used to predict the interfacial behavior of two new coarse-grained models for carbon dioxide and water recently proposed in the literature. In particular, the theoretical formalism, in combination with the coarse-grained models for carbon dioxide and water, is able to predict the interfacial properties of these important substances in a reasonable way.

Density functional theory for the description of spherical non-associating monomers in confined media using the SAFT-VR equation of state and weighted density approximations.

As a first step of an ongoing study of thermodynamic properties and adsorption of complex fluids in confined media, we present a new theoretical description for spherical monomers using the Statistical Associating Fluid Theory for potential of Variable Range (SAFT-VR) and a Non-Local Density Functional Theory (NLDFT) with Weighted Density Approximations (WDA). The well-known Modified Fundamental Measure Theory is used to describe the inhomogeneous hard-sphere contribution as a reference for the monomer and two WDA approaches are developed for the dispersive terms from the high-temperature Barker and Henderson perturbation expansion. The first approach extends the dispersive contributions using the scalar and vector weighted densities introduced in the Fundamental Measure Theory (FMT) and the second one uses a coarse-grained (CG) approach with a unique weighted density. To test the accuracy of this new NLDFT/SAFT-VR coupling, the two versions of the theoretical model are compared with Grand Canonical Monte Carlo (GCMC) molecular simulations using the same molecular model. Only the version with the "CG" approach for the dispersive terms provides results in excellent agreement with GCMC calculations in a wide range of conditions while the "FMT" extension version gives a good representation solely at low pressures. Hence, the "CG" version of the theoretical model is used to reproduce methane adsorption isotherms in a Carbon Molecular Sieve and compared with experimental data after a characterization of the material. The whole results show an excellent agreement between modeling and experiments. Thus, through a complete and consistent comparison both with molecular simulations and with experimental data, the NLDFT/SAFT-VR theory has been validated for the description of monomers.

Extension of the Test-Area methodology for calculating solid-fluid interfacial tensions in cylindrical geometry.

We extend the well-known Test-Area methodology of Gloor et al. [J. Chem. Phys. 123, 134703 (2005)], originally proposed to evaluate the surface tension of planar fluid-fluid interfaces along a computer simulation in the canonical ensemble, to deal with the solid-fluid interfacial tension of systems adsorbed on cylindrical pores. The common method used to evaluate the solid-fluid interfacial tension invokes the mechanical relation in terms of the tangential and normal components of the pressure tensor relative to the interface. Unfortunately, this procedure is difficult to implement in the case of cylindrical geometry, and particularly complex in case of nonspherical molecules. Following the original work of Gloor et al., we perform free-energy perturbations due to virtual changes in the solid-fluid surface. In this particular case, the radius and length of the cylindrical pore are varied to ensure constant-volume virtual changes of the solid-fluid surface area along the simulation. We apply the modified methodology for determining the interfacial tension of a system of spherical Lennard-Jones molecules adsorbed inside cylindrical pores that interact with fluid molecules through the generalized 10-4-3 Steele potential recently proposed by Siderius and Gelb [J. Chem. Phys. 135, 084703 (2011)]. We analyze the effect of pore diameter, density of adsorbed molecules, and fluid-fluid cutoff distance of the Lennard-Jones intermolecular potential on the solid-fluid interfacial tension. This extension, as the original Test-Area formulation, offers clear advantages over the classical mechanical route of computational efficiency, easy of implementation, and generality.

Simultaneous application of the gradient theory and Monte Carlo molecular simulation for the investigation of methane/water interfacial properties.

This work is dedicated to the simultaneous application of the gradient theory of fluid interfaces and Monte Carlo molecular simulations for the description of the interfacial behavior of the methane/water mixture. Macroscopic (interfacial tension, adsorption) and microscopic (density profiles, interfacial thickness) properties are investigated. The gradient theory is coupled in this work with the SAFT-VR Mie equation of state. The results obtained are compared with Monte Carlo simulations, where the fluid interface is explicitly considered in biphasic simulation boxes at both constant pressure and volume (NPT and NVT ensembles), using reliable united atom molecular models. On one hand, both methods provide very good estimations of the interfacial tension of this mixture over a broad range of thermodynamic conditions. On the other hand, microscopic properties computed with both gradient theory and MC simulations are in very good agreement with each other, which confirms the consistency of both approaches. Interfacial tension minima at high pressure and prewetting transitions in the vicinity of saturation conditions are also investigated.

Interfacial properties of water/CO2: a comprehensive description through a Gradient Theory-SAFT-VR Mie approach.

The Gradient Theory of fluid interfaces is for the first time combined with the SAFT-VR Mie EOS to model the interfacial properties of the water/CO(2) mixture. As a preliminary test of the performance of the coupling between both theories, liquid-vapor interfacial properties of pure water have been determined. The complex temperature dependence of the surface tension of water can be accurately reproduced, and the interfacial thickness is in good agreement with experimental data and simulation results. The water/CO(2) mixture presents several types of interfaces as the liquid water may be in contact with gaseous, liquid, or supercritical CO(2). Here, the interfacial tension of the water/CO(2) mixture is modeled accurately by the gradient theory with a unique value of the crossed influence parameter over a broad range of thermodynamic conditions. The interfacial density profiles show a systematic adsorption of CO(2) in the interface. Moreover, when approaching the saturation pressure of CO(2), a prewetting transition is highlighted. The adsorption isotherm of CO(2) is computed as well in the case of a gas/liquid interface and compared with experimental data. The good agreement obtained is an indirect proof of the consistency of interfacial density profiles computed with the gradient theory for this mixture and confirms that the gradient theory is suitable and reliable to describe the microstructure of complex fluid interfaces.

Interfacial properties of the Mie n-6 fluid: Molecular simulations and gradient theory results.

In a first part, interfacial properties of a pure monoatomic fluid interacting through the Mie n-6 potential (n=8, 10, 12, and 20) have been studied using extensive molecular simulations. Monte Carlo and molecular dynamics simulations have been employed, using, respectively, the test area approach and the mechanic route. In order to yield reference values, simulations have been performed with a cutoff radius equal to 10sigma, which is shown to be sufficient to avoid long range corrections. It is shown that both approaches provide results consistent with each other. Using the molecular simulations results, it is demonstrated that a unique scaling law is able to provide an accurate estimation of the surface tension whatever the repulsive exponent n, even far from the critical point. Furthermore, it is shown that the surface tension of the Mie n-6 fluid is as well accurately described by a unique Parachor's law. Density profiles are shown to be well represented by the tanh mean field profile, with slight deviations for the lowest temperatures and the smallest n. In addition, the interfacial width is shown to increase when n decreases (for a given reduced temperature) and to follow the usual scaling behavior for not too low temperature. In a second part, interfacial properties of the Mie n-6 fluid computed by the gradient theory, coupled with an equation of state based on the Barker-Henderson perturbation theory, have been compared with those obtained by molecular simulations. It is demonstrated that, even far from the critical point, the gradient theory is efficient to compute surface tensions and density profiles of this model fluid, provided the equation of state accurately model the phase behavior of the fluid involved (which is not the case for n=8 in this study).

Modeling of the linear viscoelastic properties of oil-in-water emulsions.

The aim of this work is to use a recently developed statistical model of dispersions with nonhydrodynamic interactions to describe the linear viscoelastic properties of emulsions of Newtonian liquids. None of the existing models can describe the rheological behavior of such systems, particularly the elastic properties, in the linear regime. We first present the results of numerical simulations of our model applied to emulsions. We show that taking nonhydrodynamic interactions into account allows to predict that emulsions of two purely viscous liquids have a complex viscoelastic behavior. We then compare the model to experimental results on oil/water emulsions, stabilized with ionic and nonionic surfactants. We find out that our statistical mechanical approach gives a much better description of the viscoelastic behavior of these samples than purely hydrodynamic models do. However, the elasticity observed is underestimated by our model. We indicate further theoretical developments which could improve the description of the viscoelastic properties of emulsions.