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.This work was sponsored by the ERC advanced grant Failflow (27769). This financial support is gratefully acknowledged. This work was supported by Acción Integrada España-Francia from Ministerio de Ciencia e Innovación and Picasso Project (Project Nos. FR2009-0056 and PHC PI- CASSO2010). F.J.B. would like to acknowledge financial support from Ministerio de Ciencia e Innovación (Project No. FIS2010-14866), Junta de Andalucía, and Universidad de Huelva. C. Malheiro would like to acknowledge the ISIFOR Carnot institute for her mobility grant

Effect of dispersive long-range corrections to the pressure tensor: The vapour-liquid interfacial properties of the Lennard-Jones system revisited

We propose an extension of the improved version of the inhomogeneous long-range corrections of Janecek [J. Phys. Chem. B 110, 6264–6269 (2006)], presented recently by MacDowell and Blas [J. Chem. Phys. 131, 074705 (2009)] to account for the intermolecular potential energy of spherical, rigid, and flexible molecular systems, to deal with the contributions to the microscopic components of the pressure tensor due to the dispersive long-range corrections. We have performed Monte Carlo simulations in the canonical ensemble to obtain the interfacial properties of spherical Lennard-Jones molecules with different cutoff distances, rc = 2.5, 3, 4, and 5σ . In addition, we have also considered cutoff distances rc = 2.5 and 3σ in combination with the inhomogeneous long-range corrections proposed in this work. The normal and tangential microscopic components of the pressure tensor are obtained using the mechanical or virial route in combination with the recipe of Irving and Kirkwood, while the macroscopic components are calculated using the Volume Perturbation thermodynamic route proposed by de Miguel and Jackson [J. Chem. Phys. 125, 164109 (2006)]. The vapour-liquid interfacial tension is evaluated using three different procedures, the Irving-Kirkwood method, the difference between the macroscopic components of the pressure tensor, and the Test-Area methodology. In addition to the pressure tensor and the surface tension, we also obtain density profiles, coexistence densities, vapour pressure, critical temperature and density, and interfacial thickness as functions of temperature, paying particular attention to the effect of the cutoff distance and the long- range corrections on these properties. According to our results, the main effect of increasing the cutoff distance (at fixed temperature) is to sharpen the vapour-liquid interface, to decrease the vapour pressure, and to increase the width of the biphasic coexistence region. As a result, the interfacial thickness decreases, the width of the tangential microscopic component of the pressure tensor profile increases, and the surface tension increases as the cutoff distance is larger. We have also checked the effect of the impulsive contribution to the pressure due to the discontinuity of the intermolecular interaction potential when it is cut. If this contribution is not accounted for in the calculation of the microscopic components of the pressure tensor, incorrect values of both components as well as a wrong structure along the vapour-liquid interface are obtained.The authors would like to acknowledge helpful discus- sions with J. M. Míguez, L. G. MacDowell, and M. M. Piñeiro. This work was supported by Ministerio de Ciencia e Innovación (MICINN, Spain) (Grant No. FIS2010-14866) and by Ministerio de Economía y Competitividad (MINECO) (Grant No. FIS2013-46920-C2-1-P). Further financial sup- port from Junta de Andalucía and Universidad de Huelva is also acknowledged

Adsorption and interfacial phenomena of a Lennard-Jones fluid adsorbed in slit pores: DFT and GCMC simulations

Confinement of fluids in porous media leads to the presence of solid–fluid (SF) interfaces that play a key role in many different fields. The experimental characterisation of SF interfacial properties, in par- ticular the surface tension, is challenging or not accessible. In this work, we apply mean-field density functional theory (DFT) to determine the surface tension and also density profile of a Lennard-Jones fluid in slit-shaped pores for realistic amounts of adsorbed molecules. We consider the pore walls to interact with fluid molecules through the well-known 10-4-3 Steele potential. The results are com- pared with those obtained from Monte Carlo simulations in the Grand Canonical Ensemble (GCMC) using the test-area method. We analyse the effect on the adsorption and interfacial phenomena of volume and energy factors, in particular, the pore diameter and the ratio between SF and fluid–fluid dispersive energy parameters, respectively. Results from DFT and GCMC simulations were found to be comparable, which points to their reliability.The authors would like to acknowledge helpful discussions with A. I. Moreno-Ventas Bravo. We also acknowledge Centro de Supercomputación de Galicia (CESGA, Santiago de Compostela, Spain) and MCIA (Mésocentre de Calcul Intensif Aquitain) of the Universités de Bordeaux and Pau et Pays de l’Adour (France), for providing access to computing facilities

Revisiting poromechanics in the context of microporous materials

International audiencePoromechanics offers a consistent theoretical framework for describing the mechanical response of porous solids, fully or partially saturated with a fluid phase. When dealing with fully saturated microporous materials, which exhibit pores of the nanometre size, aside from the fluid pressure acting on the pore walls additional effects due to adsorption and confinement of the fluid molecules in the smallest pores must be accounted for. From the mechanical point of view, these phenomena result into volumetric deformations of the porous solid: the so-called "swelling" phenomenon. The present work investigates how the poromechanical theory should be refined in order to describe adsorption and confinement induced swelling in microporous solids. Firstly, we report molecular simulation results that show that the pressure and density of the fluid in the smallest pores are responsible for the volumetric deformation of the material. Secondly, poromechanics is revisited in the context of a microporous material with a continuous pore size distribution. Accounting for the thermodynamic equilibrium of the fluid phase in the overall pore space, the new formulation introduces an apparent porosity and an interaction free energy. We use a prototype constitutive relation relating these two quantities to the Gibbs adsorption isotherm, and then calculate the induced deformation of the solid matrix. Agreement with experimental data found in the literature is observed. As an illustrating example, we show the predicted strains in the case of adsorption of methane on activated carbon

Understanding the Phase Behavior of Tetrahydrofuran + Carbon Dioxide, + Methane, and + Water Binary Mixtures from the SAFT-VR Approach

The high-pressure phase diagrams of the tetrahydrofuran(1) + carbon dioxide(2), + methane(2), and + water(2) mixtures are examined using the SAFT-VR approach. Carbon dioxide molecule is modeled as two spherical segments tangentially bonded, water is modeled as a spherical segment with four associating sites to represent the hydrogen bonding, methane is represented as an isolated sphere, and tetrahydrofuran is represented as a chain of m tangentially bonded spherical segments. Dispersive interactions are modeled using the square-well intermolecular potential. In addition, two different molecular model mixtures are developed to take into account the subtle balance between water–tetrahydrofuran hydrogen-bonding interactions. The polar and quadrupolar interactions present in water, tetrahydrofuran, and carbon dioxide are treated in an effective way via square-well potentials of variable range. The optimized intermolecular parameters are taken from the works of Giner et al. (Fluid Phase Equil. 2007, 255, 200), Galindo and Blas (J. Phys. Chem. B 2002, 106, 4503), Patel et al. (Ind. Eng. Chem. Res. 2003, 42, 3809), and Clark et al. (Mol. Phys. 2006, 104, 3561) for tetrahydrofuran, carbon dioxide, methane, and water, respectively. The phase diagrams of the binary mixtures exhibit different types of phase behavior according to the classification of van Konynenburg and Scott, ranging from types I, III, and VI phase behavior for the tetrahydrofuran(1) + carbon dioxide(2), + methane(2), and + water(2) binary mixtures, respectively. This last type is characterized by the presence of a Bancroft point, positive azeotropy, and the so-called closed-loop curves that represent regions of liquid–liquid immiscibility in the phase diagram. The system exhibits lower critical solution temperatures (LCSTs), which denote the lower limit of immiscibility together with upper critical solution temperatures (UCSTs). This behavior is explained in terms of competition between the incompatibility with the alkyl parts of the tetrahydrofuran ring chain and the hydrogen bonding between water and the ether group. A minimum number of unlike interaction parameters are fitted to give the optimal representation of the most representative features of the binary phase diagrams. In the particular case of tetrahydrofuran(1) + water(2), two sets of intermolecular potential model parameters are proposed to describe accurately either the hypercritical point associated with the closed-loop liquid–liquid immiscibility region or the location of the mixture lower- and upper-critical end-points. The theory is not only able to predict the type of phase behavior of each mixture, but also provides a reasonably good description of the global phase behavior whenever experimental data are availabl

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.We thank Pedro J. Pérez for the critical reading of the manuscript. We also acknowledge Centro de Supercomputación de Galicia (CESGA, Santiago de Compostela, Spain) and MCIA (Mésocentre de Calcul Intensif Aquitain) of the Universités de Bordeaux and Pau et Pays de l’Adour (France) for providing access to computing facilities. We thank financial support from the Ministerio de Economía, Industria y Competitividad (FIS2017- 89361-C3-1-P), Junta de Andalucía (P20-00363), and Universidad de Huelva (P.O. FEDER UHU-1255522), all three cofinanced by EU FEDER funds. J.A. acknowledges Contrato Predoctoral de Investigación from XIX Plan Propio de Investigación de la Universidad de Huelva and a FPU Grant (Ref. FPU15/03754) from Ministerio de Educación, Cultura y Deporte. J. A., J. M. M., and F. J. B. thankfully acknowledge the computer resources at Magerit and the technical support provided by the Spanish Supercomputing Network (RES) (Project QCM- 2018–2- 0042). Funding for open access charge: Universidad de Huelva / CBU

Molecular dynamics and thermodynamical modelling using SAFT-VR to predict hydrate phase equilibria : application to CO2 hydrates

This work was dedicated to the prediction of the three phase coexistence line (CO2 hydrate–liquid H2Oliquid/vapour CO2) for the H2O+CO2 binary mixture by using (i) molecular dynamics simulations, and (ii) the well known van der Waals-Platteeuw (vdWP) model combined with the SAFT-VR equation of state. Molecular dynamics simulations have been performed using the simulation package GROMACS. The temperature at which the three phases are in equilibrium was determined for different pressures, by using direct coexistence simulations. Carbon dioxide was modelled as a linear-rigid chain molecule with three chemical units, the well-known version TraPPE molecular model. The TIP4P/Ice model was used for water. To perform the thermodynamical modelling, the SAFT-VR EOS was incorporated in the vdWP framework. The values of the cell model parameters were regressed and discussed together with the influence of some assumptions of the vdWP model. Since SAFT-VR can describe most of fluids involved in hydrate modelling (inhibitors, salts…), this study is a first step in the description of hydrate forming conditions of more complex systems. Finally, the three-phase coexistence temperatures obtained with both simulations and theory at different pressures were compared with experimental result

Understanding the Phase Behavior of Tetrahydrofuran + Carbon Dioxide, + Methane, and + Water Binary Mixtures from the SAFT-VR Approach

The high-pressure phase diagrams of the tetrahydrofuran(1) + carbon dioxide(2), + methane(2), and + water(2) mixtures are examined using the SAFT-VR approach. Carbon dioxide molecule is modeled as two spherical segments tangentially bonded, water is modeled as a spherical segment with four associating sites to represent the hydrogen bonding, methane is represented as an isolated sphere, and tetrahydrofuran is represented as a chain of m tangentially bonded spherical segments. Dispersive interactions are modeled using the square-well intermolecular potential. In addition, two different molecular model mixtures are developed to take into account the subtle balance between water−tetrahydrofuran hydrogen-bonding interactions. The polar and quadrupolar interactions present in water, tetrahydrofuran, and carbon dioxide are treated in an effective way via square-well potentials of variable range. The optimized intermolecular parameters are taken from the works of Giner et al. (Fluid Phase Equil. 2007, 255, 200), Galindo and Blas (J. Phys. Chem. B 2002, 106, 4503), Patel et al (Ind. Eng. Chem. Res. 2003, 42, 3809), and Clark et al. (Mol. Phys. 2006, 104, 3561) for tetrahydrofuran, carbon dioxide, methane, and water, respectively. The phase diagrams of the binary mixtures exhibit different types of phase behavior according to the classification of van Konynenburg and Scott, ranging from types I, III, and VI phase behavior for the tetrahydrofuran(1) + carbon dioxide(2), + methane(2), and + water(2) binary mixtures, respectively. This last type is characterized by the presence of a Bancroft point, positive azeotropy, and the so-called closed-loop curves that represent regions of liquid−liquid immiscibility in the phase diagram. The system exhibits lower critical solution temperatures (LCSTs), which denote the lower limit of immiscibility together with upper critical solution temperatures (UCSTs). This behavior is explained in terms of competition between the incompatibility with the alkyl parts of the tetrahydrofuran ring chain and the hydrogen bonding between water and the ether group. A minimum number of unlike interaction parameters are fitted to give the optimal representation of the most representative features of the binary phase diagrams. In the particular case of tetrahydrofuran(1) + water(2), two sets of intermolecular potential model parameters are proposed to describe accurately either the hypercritical point associated with the closed-loop liquid−liquid immiscibility region or the location of the mixture lower- and upper-critical end-points. The theory is not only able to predict the type of phase behavior of each mixture, but also provides a reasonably good description of the global phase behavior whenever experimental data are available.We acknowledge Ministerio de Economía y Competitividad of Spain for financial support from Projects FIS2012-33621 and FIS2015-68910-P (M.M.P. and J.M.M.) and FIS2013-46920- C2-1-P (F.J.B. and J.A.), both cofinanced with EU Feder funds. J.M.M. acknowledges Xunta de Galicia for a Postdoctoral Grant (ED481B2014/117-0). The French CARNOT Institute ISIFoR is also acknowledged for the funds provided through the THEMYS Project (novel approaches in thermodynamical modelling and molecular simulation for the study of gas hydrates and their applications). Further financial support from Universidad de Huelva and Junta de Andalucía is also acknowledged

Contribution à l étude de propriétés interfaciales d alcanes confinés par simulation moléculaire de type Monte Carlo

Ce travail concerne la modélisation de propriétés interfaciales d alcanes linéaires confinés dans des pores plan/plan, telles que la quantité adsorbée ou la tension interfaciale par la simulation moléculaire de type Monte Carlo. Les calculs ont été réalisés dans les conditions thermodynamiques variées allant de pressions et températures très faibles jusqu à des valeurs élevées rencontrées typiquement dans les réservoirs. Nous avons mené une étude de sensibilité concernant trois potentiels d interaction classiquement utilisés, regardé l influence du confinement géométrique et des conditions thermodynamiques sur le méthane confiné, calculé la chaleur isostérique d adsorption et mis en évidence le phénomène de condensation capillaire. Les résultats d isotherme d adsorption obtenus par simulation ont été confrontés avec succès à des résultats expérimentaux. Cette comparaison a également permis de mettre en évidence l importance de la caractérisation du milieu poreux lors de l estimation de l isotherme d adsorption. Le comportement d alcanes linéaires de plus longue chaine a également été étudié.This work concerns the modelling of interfacial properties of linear alkanes confined in slit pores, such as adsorbed quantities or interfacial tension by the Monte Carlo molecular simulation. The simulations were performed at various thermodynamic conditions ranging from very low pressures and temperatures to higher values typical of reservoirs. We have studied the influence of three classical interaction potentials, the effect of confinement and thermodynamic conditions on confined methane, the isosteric heat of adsorption and the phenomenon of capillary condensation. Adsorption isotherms obtained with Monte Carlo simulation were successfully compared with experimental results. This study has also underlined the impact of the porous media characterization on the estimation of adsorption. The behavior of alkanes with longer chains was also determined.PAU-BU Sciences (644452103) / SudocSudocFranceF

Modélisation de l’adsorption d’eau dans des micropores par couplage des théories NLDFT et SAFT-VR

COMInternational audienc