Determination of interfacial tension of binary mixtures from perturbative approaches

We determine the interfacial properties of mixtures of spherical Lennard-Jones molecules from direct simulation of the vapour–liquid interface. We consider mixtures with same molecular size but different dispersive energy parameter values. We use the extensions of the improved version of the inhomogeneous long-range corrections of Janecek, presented recently by MacDowell and Blas and Martínez-Ruiz et al., to deal with the interaction energy and microscopic components of the pressure tensor. We have performed Monte Carlo simulations in the canonical ensemble to obtain the interfacial properties of mixtures of Lennard-Jones molecules with a cut-off distance rc = 3σ in combination with the inhomogeneous long-range corrections. The pressure tensor is obtained using the mechanical (virial) and thermodynamic route. The vapour–liquid interfacial tension is also evaluated using three different procedures, the Irving–Kirkwood method, the difference between the macroscopic components of the pressure tensor, and the test-area methodology. This allows to check the validity of the recent extensions presented to deal with the contributions due to long-range corrections for intermolecular energy and pressure tensor in the case of binary mixtures. In addition to the pressure tensor and the surface tension, we also obtain density profiles, coexistence densities, and interfacial thickness as functions of pressure, at a given temperature. According to our results, the main effect of increasing the ratio between the dispersive energy parameters of the mixture, ε22/ε11, is to sharpen the vapour–liquid interface and to increase the width of the biphasic coexistence region. Particularly interesting is the presence of a relative maximum in the density profiles of the less volatile component at the interface. This maximum is related with adsorption or accumulation of these molecules at the interface, a direct consequence of stronger attractive interactions between these molecules in comparison with the rest of intermolecular interactions. In addition to that, the interfacial thickness decreases, the width of the tangential microscopic component of the pressure tensor profile increases, and the surface tension increases as ε22/ε11 is larger.The authors would like to acknowledge helpful discussions with A.I. Moreno-Ventas Bravo. Further financial support from Junta de Andalucía and Universidad de Huelva is also acknowledged. This work was supported by Ministerio de Ciencia e Innovación [grant number FIS2010-14866]; Ministerio de Economía y Competitividad [grant number FIS2013- 46920-C2-1-P].This work was supported by Ministerio de Ciencia e Innovacion [grant number FIS2010-14866]; Ministerio de Economia y Competitividad [grant number FIS2013-46920-C2-1-P]

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

Universal scaling behaviour of surface tension of molecular chains

We use and extend the universal relationship recently proposed by Galliero [G. Galliero, J. Chem. Phys. 133, 074705 (2010)], based on a combination of the corresponding-states principle of Guggenheim [E. A. Guggenheim, J. Chem. Phys. 13, 253 (1945)] and the parachor approach of Macleod [J. Macleod, Trans. Faraday Soc. 19, 38 (1923)], to predict the vapour-liquid surface tension of fully flexible chainlike Lennard-Jones molecules. In the original study of Galliero, the reduced surface tension of short-chain molecules formed by up to five monomers is expressed as a unique function of the difference between the liquid and vapour coexistence densities. In this work, we extend the applicability of the recipe and demonstrate that it is also valid for predicting the surface tension of two different chainlike molecular models, namely, linear tangent chains that interact through the Lennard-Jones intermolecular potential and fully flexible chains formed by spherical segments inter- acting through the square-well potential. Computer simulation data for vapour-liquid surface tension of fully flexible and rigid linear Lennard-Jones, and fluid flexible square-well chains is taken from our previous works. Our results indicate that the universal scaling relationship is able to correlate short- and long-chain molecules with different degrees of flexibility and interacting through different inter- molecular potentials.The authors would like to acknowledge helpful discus- sions with B. Mendiboure, D. Bessières, F. Plantier, M. M. Piñeiro, and J. M. Míguez. This work was supported by Ministerio de Ciencia e Innovación (MICINN, Spain) through Grants Nos. FIS2010-14866 and FIS2010-22047-C05-05. Further financial support from Proyecto de Excelencia from Junta de Andalucía (Grant No. P07-FQM02884), Comunidad Autónoma de Madrid (Grant No. MODELICO-P2009EPS-1691), and Universidad de Huelva are also acknowledged

Vapour–liquid interfacial properties of square-well chains from density functional theory and Monte Carlo simulation

The statistical associating fluid theory for attractive potentials of variable range (SAFT-VR) density functional theory (DFT) developed by [Gloor et al., J. Chem. Phys., 2004, 121, 12740–12759] is used to predict the interfacial behaviour of molecules modelled as fully-flexible square-well chains formed from tangentially-bonded monomers of diameter s and potential range l = 1.5s. Four different model systems, comprising 4, 8, 12, and 16 monomers per molecule, are considered. In addition to that, we also compute a number of interfacial properties of molecular chains from direct simulation of the vapour–liquid interface. The simulations are performed in the canonical ensemble, and the vapour– liquid interfacial tension is evaluated using the wandering interface (WIM) method, a technique based on the thermodynamic definition of surface tension. Apart from surface tension, we also obtain density profiles, coexistence densities, vapour pressures, and critical temperature and density, paying particular attention to the effect of the chain length on these properties. According to our results, the main effect of increasing the chain length (at fixed temperature) is to sharpen the vapour–liquid interface and to increase the width of the biphasic coexistence region. As a result, the interfacial thickness decreases and the surface tension increases as the molecular chains get longer. The interfacial thickness and surface tension appear to exhibit an asymptotic limiting behaviour for long chains. A similar behaviour is also observed for the coexistence densities and critical properties. Agreement between theory and simulation results indicates that SAFT-VR DFT is only able to predict qualitatively the interfacial properties of the model. Our results are also compared with simulation data taken from the literature, including the vapour–liquid coexistence densities, vapour pressures, and surface tension.Francisco José Martínez-Ruiz, Felipe J. Blas and A.Ignacio Moreno-Ventas Bravo acknowledge Ministerio de Economía y Competitividad of Spain for financial support from project FIS2013-49620-C2-1-P, co financed with EU Feder funds. We also acknowledge financial support from project number FIS2015-71749-REDT ‘‘Red de Simulación Molecular’’, Acciones de Dinamización Redes de Excelencia del Ministerio de Economía y Competitividad. Additional support from Universidad de Huelva and Junta de Andalucía is also acknowledged

Propiedades interfaciales y equilibrio de fase de mezclas fluidas mediante simulación Monte Carlo

La comprensión, desde un punto de vista molecular, del equilibrio de fase y las propiedades interfaciales de sistemas condensados ha crecido enormemente en las últimas décadas. Sin embargo, la determinación de propiedades termodinámicas y estructurales de sistemas inhomogéneos formados por mezclas complejas (cadenas moleculares, sustancias asociantes, ...), como anchura interfacial, adsorción y tensión superficial entre otras, es limitada en comparación con la de sistemas homogéneos. El conocimiento preciso de las propiedades interfaciales es esencial en el diseño de procesos de enorme interés teórico e industrial. Hoy en día se puede determinar el diagrama de fases completo y las propiedades interfaciales de un determinado modelo haciendo uso de la simulación molecular, debido en gran parte al vertiginoso aumento de la potencia computacional y al gran número algoritmos que se han desarrollado en estos últimos años. En esta tesis se combinan diferentes técnicas de simulación Monte Carlo para entender desde el punto de la Mecánica Estadística cómo los parámetros microscópicos de un modelo molecular determinan las propiedades interfaciales de sistemas que exhiben equilibrio líquido-vapor y líquido-líquido. Especial importancia tiene el análisis del efecto de las correcciones de largo alcance sobre el comportamiento del sistema, debido al truncamiento de potenciales continuos, por lo que en esta tesis se extiende y mejora una metodología para determinar dichas correcciones. Especial énfasis tiene el cálculo de la tensión superficial, así como la incorporación a dicho cálculo de las correcciones de largo alcance, extendiendo y mejorando el método estándar basado en el cálculo del tensor de presiones del sistema inhomogéneo mediante el cálculo del virial. Este cálculo es fácil de implementar en sistemas sencillos, pero no tanto en sistemas moleculares complejos, por lo que se han utilizado otras metodologías basadas en la ruta termodinámica: perturbaciones de volumen, Test-Area (TA) y el Wandering Interface Method (WIM). Se ha determinado la tensión interfacial líquido-vapor y líquido-líquido de mezclas binarias de modelos esféricos sencillos, y la tensión superficial líquido-vapor de cadenas flexibles de monómeros que interaccionan mediante los potenciales de Lennard-Jones y de pozo cuadrado (Square Well). La aproximación Soft-SAFT, basada en la teoría de Wertheim, ha permitido calcular el diagrama de fases completo de las mezclas con objeto de validar las metodologías de simulación Monte Cario implementadas. En el caso de cadenas flexibles Lennard-Jones se ha estudiado el efecto de la longitud de cadena y flexibilidad sobre las propiedades interfaciales. Se ha determinado la presión de vapor en el equilibrio líquido-vapor de cadenas SW de forma indirecta mediante la combinación de la simulación Monte Cario e integración termodinámica, así como su incertidumbre haciendo uso del Método Sintético. Por último, se han explorado relaciones de escalado universal para correlacionar cadenas moleculares con diferente grado de flexibilidad que interaccionan bajo el potencial intermolecular de Lennard-Jones y de Square-Well.The understanding, from a molecular perspective, of the phase equilibria and interfacial properties of condensed systems, has increased in the last years. However, the determination of the thermodynamic and structural properties of inhomogeneous systems of complex mixtures (molecular chains, associating systems...), such as the interfacial thickness, adsorption, and surface tension, among others, is limited compared with that of homogenous systems. The precise knowledge of the interfacial properties is essential from a theoretical point of view and for the design of process of industrial interest. Nowadays, it is possible to determine the global phase diagram and the interfacial properties of a given model using molecular simulation. This is probably due to the enormous increasing of the available computational resources and also due to the development of new and more effective computational methods during the last years. In this Thesis, we combine different Monte Carlo simulation techniques to understand, from the Statistical Mechanics point of view, how the microscopic parameters of a given molecular model determine the interfacial properties of systems that exhibit vapour-liquid and liquid-liquid equilibria. The analysis on how the long-range corrections affect the behaviour of the system, particularly due to the discontinuities existing in continuous potential that are truncated at a given distance, is an important and delicate issue. In this Thesis, we extend and improve an existing methodology in the literature to account for these long-range corrections. We put special emphasis on how these corrections affect to the interfacial tension and extend and improve the standard method for determining the pressure tensor in inhomogeneous systems (virial or mechanical route). This methodology is easy to apply and implement in systems form from spherically symmetric molecules, but this is not the case of complex molecular systems. In this Thesis, we use alternative methods, based on the thermodynamic route, such as the volume perturbation technique, the Test-Area (TA) methodology, and the Wandering Interface Method (WIM). We have determined the vapour-liquid and liquid-liquid interfacial tension of binary mixtures of spherical systems, and the vapour-liquid surface tension of flexible chains form from monomers that interact through the Lennard- Jones and Square-Well intermolecular potentials, among many other interfacial properties. The Soft-SAFT approach, based on Wertheim’s theory, is used to calculate the global phase diagram of the mixtures studied in order to compare the simulation results obtained in this Thesis. In the case of flexible Lennard-Jones chains, we have studied the effect of chain length and flexibility on the phase equilibria and interfacial properties. We have also calculated the vapour pressure of Square-Well chains along the vapour-liquid coexistence combining Monte Carlo simulations of the interface and the thermodynamic integration technique, as well as the associated error from the Sinthetic Method. Finally, we have also analysed some universal scaling relationships for Lennard-Jones and Square-Well molecular chains with different degrees of flexibility

Liquid-liquid interfacial properties of a symmetrical Lennard-Jones binary mixture

We determine the interfacial properties of a symmetrical binary mixture of equal-sized spherical Lennard-Jones molecules, σ11 = σ22, with the same dispersive energy between like species, ϵ11 = ϵ22, but different dispersive energies between unlike species low enough to induce phase separation. We use the extensions of the improved version of the inhomogeneous long-range corrections of Jane˘cek [J. Phys. Chem. B 110, 6264 (2006)], presented recently by MacDowell and Blas [J. Chem. Phys. 131, 074705 (2009)] and Martínez-Ruiz et al. [J. Chem. Phys. 141, 184701 (2014)], to deal with the interaction energy and microscopic components of the pressure tensor. We perform Monte Carlo simulations in the canonical ensemble to obtain the interfacial properties of the symmetrical mixture with different cut-off distances rc and in combination with the inhomogeneous long-range corrections. The pressure tensor is obtained using the mechanical (virial) and thermodynamic route. The liquid-liquid interfacial tension is also evaluated using three different procedures, the Irving- Kirkwood method, the difference between the macroscopic components of the pressure tensor, and the test-area methodology. This allows to check the validity of the recent extensions presented to deal with the contributions due to long-range corrections for intermolecular energy and pressure tensor in the case of binary mixtures that exhibit liquid-liquid immiscibility. In addition to the pressure tensor and the surface tension, we also obtain density profiles and coexistence densities and compositions as functions of pressure, at a given temperature. According to our results, the main effect of increasing the cut-off distance rc is to sharpen the liquid-liquid interface and to increase the width of the biphasic coexistence region. Particularly interesting is the presence of a relative minimum in the total density profiles of the symmetrical mixture. This minimum is related with a desorption of the molecules at the interface, a direct consequence of a combination of the weak dispersive interactions between unlike species of the symmetrical binary mixture, and the presence of an interfacial region separating the two immiscible liquid phases in coexistenceThe authors would like to acknowledge helpful discussions with J. M. Garrido, J. M. Miguez, M. M. Pineiro, and E. de Miguel. This work was supported by Ministerio de Economia y Competitividad through Grant No. FIS2013-46920-C2-1-P (confinanced with EU Feder funds). Further financial support from Junta de Andalucia and Universidad de Huelva is also acknowledged

Effect of molecular flexibility of Lennard-Jones chains on vapor-liquid interfacial properties

We have determined the interfacial properties of short fully flexible chains formed from tangentially bonded Lennard-Jones monomeric units from direct simulation of the vapor-liquid interface. The results obtained are compared with those corresponding to rigid-linear chains formed from the same chain length, previously determined in the literature [F. J. Blas, A. I. M.-V. Bravo, J. M. Míguez, M. M. Piñeiro, and L. G. MacDowell, J. Chem. Phys. 137, 084706 (2012)]. The full long-range tails of the potential are accounted for by means of an improved version of the inhomogeneous long-range corrections of Janeček [J. Phys. Chem. B 129, 6264 (2006)] proposed recently by MacDowell and Blas [J. Chem. Phys. 131, 074705 (2008)] valid for spherical as well as for rigid and flexible molecular systems. Three different model systems comprising of 3, 5, and 6 monomers per molecule are considered. The simulations are performed in the canonical ensemble, and the vapor-liquid interfacial tension is evaluated using the test-area method. In addition to the surface tension, we also obtained density profiles, coexistence densities, critical temperature and density, and interfacial thickness as functions of temperature, paying particular attention to the effect of the chain length and rigidity on these properties. According to our results, the main effect of increasing the chain length (at fixed temperature) is to sharpen the vapor-liquid interface and to increase the width of the biphasic coexistence region. As a result, the interfacial thickness decreases and the surface tension increases as the molecular chains get longer. Comparison between predictions for fully flexible and rigid-linear chains, formed by the same number of monomeric units, indicates that the main effects of increasing the flexibility, i.e., passing from a rigid-linear to a fully flexible chain, are: (a) to decrease the difference between the liquid and vapor densities; (b) to decrease the critical temperature and to increase the critical density; (c) to smooth the density profiles along the interfacial region; (d) to increase the interfacial thickness; and (e) to decrease the vapor-liquid surface tension.The authors would like to acknowledge helpful discussions with C. Vega, A. Galindo, J. M. Miguez, and M. M. Pineiro. This work was supported by Ministerio de Ciencia e Innovacion (MICINN, Spain) through Grant Nos. FIS2011-13119-E, FIS2010-14866 (F. J. B. and F. J. M. R.), and FIS2010-22047-C05-05 (L. G. M. D.). Further financial support from Proyecto de Excelencia from Junta de Andalucia (Grant No. P07-FQM02884), Comunidad Autonoma de Madrid (Grant No. MODELICO- P2009/EPS-1691), and Universidad de Huelva is also acknowledged