An examination of the vapour-liquid interface of associating fluids using a SAFT-DFT approach

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.

Comparison of the vapour–liquid surface tensions for substances studied in this work as obtained from SAFT-VR Mie DFT and experiments.

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.

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

Vapour–liquid surface tension for tangent (open symbols) and vibrating (filled symbols) square-well chains.

Corresponding-states behavior of an ionic model fluid with variable dispersion interactions

Guggenheim's corresponding-states approach for simple fluids leads to a remarkably universal representation of their thermophysical properties. For more complex fluids, such as polar or ionic ones, deviations from this type of behavior are to be expected, thereby supplying us with valuable information about the thermodynamic consequences of the interaction details in fluids. Here, the gradual transition of a simple fluid to an ionic one is studied by varying the relative strength of the dispersion interactions compared to the electrostatic interactions among the charged particles. In addition to the effects on the reduced surface tension that were reported earlier [F. Leroy and V. C. Weiss, J. Chem. Phys. 134, 094703 (2011)], we address the shape of the coexistence curve and focus on properties that are related to and derived from the vapor pressure. These quantities include the enthalpy and entropy of vaporization, the boiling point, and the critical compressibility factor Zc. For all of these properties, the crossover from simple to characteristically ionic fluid is seen once the dispersive attraction drops below 20%-40% of the electrostatic attraction (as measured for two particles at contact). Below this threshold, ionic fluids display characteristically low values of Zc as well as large Guggenheim and Guldberg ratios for the reduced enthalpy of vaporization and the reduced boiling point, respectively. The coexistence curves are wider and more skewed than those for simple fluids. The results for the ionic model fluid with variable dispersion interactions improve our understanding of the behavior of real ionic fluids, such as inorganic molten salts and room temperature ionic liquids, by gauging the importance of different types of interactions for thermodynamic properties.

Liquid-vapor interfaces of patchy colloids

We investigate the liquid-vapor interface of a model of patchy colloids. This model consists of hard spheres decorated with short-ranged attractive sites ("patches") of different types on their surfaces. We focus on a one-component fluid with two patches of type A and nine patches of type B (2A9B colloids), which has been found to exhibit reentrant liquid-vapor coexistence curves and very low-density liquid phases. We have used the density-functional theory form of Wertheim's first-order perturbation theory of association, as implemented by Yu and Wu [J. Chem. Phys. 116, 7094 (2002)], to calculate the surface tension, and the density and degree of association profiles, at the liquid-vapor interface of our model. In reentrant systems, where AB bonds dominate, an unusual thickening of the interface is observed at low temperatures. Furthermore, the surface tension versus temperature curve reaches a maximum, in agreement with Bernardino and Telo da Gama's mesoscopic Landau-Safran theory [Phys. Rev. Lett. 109, 116103 (2012)]. If BB attractions are also present, competition between AB and BB bonds gradually restores the monotonic temperature dependence of the surface tension. Lastly, the interface is "hairy," i.e., it contains a region where the average chain length is close to that in the bulk liquid, but where the density is that of the vapor. Sufficiently strong BB attractions remove these features, and the system reverts to the behavior seen in atomic fluids.

Using fundamental measure theory to treat the correlation function of the inhomogeneous hard-sphere fluid

We investigate the value of the correlation function of an inhomogeneous hard-sphere fluid at contact. This quantity plays a critical role in statistical associating fluid theory, which is the basis of a number of recently developed classical density functionals. We define two averaged values for the correlation function at contact and derive formulas for each of them from the White Bear version of the fundamental measure theory functional, using an assumption of thermodynamic consistency. We test these formulas, as well as two existing formulas, against Monte Carlo simulations and find excellent agreement between the Monte Carlo data and one of our averaged correlation functions.

Predicting gas adsorption in complex microporous and mesoporous materials using a new density functional theory of finely discretized lattice fluids

We introduce a nonlocal on-lattice version of density functional theory (DFT) that allows for efficient modeling of fluids in complex inhomogeneous materials. In its previous implementations, classical DFT has required fine discretization of the fluid density. As a result, in studies of gas adsorption it has been used only in idealized pore models with high symmetry. Our new lattice DFT dramatically reduces the computational demand required to model simple fluids and hence can be efficiently applied to complex materials with multiple directions of asymmetry. We apply our new lattice DFT to study nitrogen adsorption in a slit pore with open ends and directly obtain the correct desorption hysteresis. We also apply our DFT to predict hydrogen adsorption accurately in an atomistic model of a metal-organic framework.

Surface tension of the most popular models of water by using the test-area simulation method

We consider the calculation of the surface tension from simulations of several models of water, such as the traditional TIP3P, SPC, SPC/E, and TIP4P models, and the new generation of TIP4P-like models including the TIP4P/Ew, TIP4P/Ice, and TIP4P/2005. We employ a thermodynamic route proposed by Gloor et al. [J. Chem. Phys. 123, 134703 (2005)] to determine the surface tension that involves the estimate of the change in free energy associated with a small change in the interfacial area at constant volume. The values of the surface tension computed from this test-area method are found to be fully consistent with those obtained from the standard mechanical route, which is based on the evaluation of the components of the pressure tensor. We find that most models do not reproduce quantitatively the experimental values of the surface tension of water. The best description of the surface tension is given by those models that provide a better description of the vapor-liquid coexistence curve. The values of the surface tension for the SPC/E and TIP4P/Ew models are found to be in reasonably good agreement with the experimental values. From the present investigation, we conclude that the TIP4P/2005 model is able to accurately describe the surface tension of water over the whole range of temperatures from the triple point to the critical temperature. We also conclude that the test area is an appropriate methodological choice for the calculation of the surface tension not only for simple fluids, but also for complex molecular polar fluids, as is the case of water.

Density functional theory for inhomogeneous associating chain fluids

We propose a nonlocal density functional theory for associating chain molecules. The chains are modeled as tangent spheres, which interact via Lennard-Jones (12,6) attractive interactions. A selected segment contains additional, short-ranged, highly directional interaction sites. The theory incorporates an accurate treatment of the chain molecules via the intramolecular potential formalism and should accurately describe systems with strongly varying external fields, e.g., attractive walls. Within our approach we investigate the structure of the liquid-vapor interface and capillary condensation of a simple model of associating chains with only one associating site placed on the first segment. In general, the properties of inhomogeneous associating chains depend on the association energy. Similar to the bulk systems we find the behavior of associating chains of a given length to be in between that for the nonassociating chains of the same length and that for the nonassociating chains twice as large.

Monte Carlo study of interfacial properties of associating fluids

Canonical Monte Carlo Simulations have been performed to calculate liquid-vapor properties of the associating square well and Lennard-Jones fluids with one and two sites. Simulations were carried out by using several values of reduced temperatures and association energies. The orthobaric densities, as well as the surface tension of associating square well fluids, were calculated and compared with those reported previously in literature; a good agreement was found among them. Results of surface tension of two-sites associating Lennard-Jones fluids are presented here for the first time.

Examination of the Excess Thermodynamic Properties of n-Alkane Binary Mixtures: A Molecular Approach

A modification of the statistical associating fluid theory, the so-called Soft-SAFT equation of state, is proposed to predict the excess thermodynamic properties of binary mixtures of n-alkanes. n-Alkane molecules are modeled as fully flexible Lennard-Jones chains. This molecular model accounts for the most important microscopic features of real chainlike molecules: attractive and repulsive interactions between different chemical groups and the connectivity of the segments that form the molecules. In this work we consider an additional microscopic effect that can profoundly affect certain thermodynamic properties, namely, the conformational changes when two different n-alkane molecules are mixed. We propose, following the work of Vega and co-workers [J. Chem. Phys. 1999, 111, 3192], a simple model to account for the conformational changes in molecules. The resulting free energy is combined with the SAFT free energy to describe the excess thermodynamic properties of binary mixtures of n-alkanes. Predictions from the theory are compared with experimental data taken from the literature. The agreement between the experiments and the theoretical predictions is excellent in all cases. This work shows that although minor microscopic effects, such as the conformational changes in the molecules that form the mixtures, have only a very small effect on the usual thermodynamic properties, such as pressure, chemical potential, phase equilibria, and excess volumes, they can contribute significantly to other thermodynamic properties. In fact, one of the main conclusions of this work is that it is essential that conformational effects be taken into account in molecular-based theories if an accurate description of certain excess properties (excess enthalpy for instance) is desired.

Molecular simulation study of effect of molecular association on vapor-liquid interfacial properties

Vapor-liquid interfacial properties of square-well associating fluids are studied via transition-matrix Monte Carlo simulation. Results for one-site and two-site association models are presented. Coexistence properties, surface tension, cluster distribution, density profile, and orientation profile are presented. Molecular association affects the interfacial properties and cluster fractions more than it affects the bulk densities. We observe that the surface tension exhibits a maximum with respect to association strength. This behavior is in agreement with the recent study of Peery and Evans for one site system using a square-gradient approach.

Surface tension of associating fluids by Monte Carlo simulations

Canonical Monte Carlo (NVT-MC) simulations were performed to obtain surface tension and coexistence densities at the liquid-vapor interface of one-site associating Lennard-Jones and hard-core Yukawa fluids, as functions of association strength and temperature. The method to obtain the components of the pressure tensor from NVT-MC simulations was validated by comparing the equation of state of the associative hard sphere system with that coming from isothermal-isobaric Monte Carlo simulations. Surface tension of the associative Lennard-Jones fluid determined from NVT-MC is compared with previously reported results obtained by molecular dynamics simulations of a pseudomixture model of monomers and dimers. A good agreement was found between both methods. Values of surface tension of associative hard-core Yukawa fluids are presented here for the first time.

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

A Helmholtz free energy density functional is developed to describe the vapor-liquid interface of associating chain molecules. The functional is based on the statistical associating fluid theory with attractive potentials of variable range (SAFT-VR) for the homogenous fluid [A. Gil-Villegas, A. Galindo, P. J. Whitehead, S. J. Mills, G. Jackson, and A. N. Burgess, J. Chem. Phys. 106, 4168 (1997)]. A standard perturbative density functional theory (DFT) is constructed by partitioning the free energy density into a reference term (which incorporates all of the short-range interactions, and is treated locally) and an attractive perturbation (which incorporates the long-range dispersion interactions). In our previous work [F. J. Blas, E. Martin del Rio, E. de Miguel, and G. Jackson, Mol. Phys. 99, 1851 (2001); G. J. Gloor, F. J. Blas, E. Martin del Rio, E. de Miguel, and G. Jackson, Fluid Phase Equil. 194, 521 (2002)] we used a mean-field version of the theory (SAFT-HS) in which the pair correlations were neglected in the attractive term. This provides only a qualitative description of the vapor-liquid interface, due to the inadequate mean-field treatment of the vapor-liquid equilibria. Two different approaches are used to include the correlations in the attractive term: in the first, the free energy of the homogeneous fluid is partitioned such that the effect of correlations are incorporated in the local reference term; in the second, a density averaged correlation function is incorporated into the perturbative term in a similar way to that proposed by Toxvaerd [S. Toxvaerd, J. Chem. Phys. 64, 2863 (1976)]. The latter is found to provide the most accurate description of the vapor-liquid surface tension on comparison with new simulation data for a square-well fluid of variable range. The SAFT-VR DFT is used to examine the effect of molecular chain length and association on the surface tension. Different association schemes (dimerization, straight and branched chain formation, and network structures) are examined separately. The surface tension of the associating fluid is found to be bounded between the nonassociating and fully associated limits (both of which correspond to equivalent nonassociating systems). The temperature dependence of the surface tension is found to depend strongly on the balance between the strength and range of the association, and on the particular association scheme. In the case of a system with a strong but very localized association interaction, the surface tension exhibits the characteristic "s shaped" behavior with temperature observed in fluids such as water and alkanols. The various types of curves observed in real substances can be reproduced by the theory. It is very gratifying that a DFT based on SAFT-VR free energy can provide an accurate quantitative description of the surface tension of both the model and experimental systems.

Interfacial properties of Lennard-Jones chains by direct simulation and density gradient theory

We perform a series of molecular dynamics simulations of Lennard-Jones chains systems, up to tetramers, in order to investigate the influence of temperature and chain length on their phase separation and interfacial properties. Simulation results serve as a test to check the accuracy of a statistical associated fluid theory (soft-SAFT) coupled with the density gradient theory. We focus on surface tension and density profiles. The simulations allow us to discuss the success and limitations of the theory and how to estimate the only adjustable parameter, the influence parameter. This parameter is obtained by fitting the surface tension, and then used to obtain the density profiles in a predictive manner. A good agreement is found if the temperature dependence of this parameter is neglected.(c) 2004 American Institute of Physics.

Microscopic structure and properties of an interface between coexisting phases of an associating fluid adsorbed in slitlike pores

Using density functional theory, we calculate density profiles of an associating fluid in slitlike pores. These profiles characterize an interface between two coexisting, adsorbed phases, e.g., between gaseous and liquid phases formed during capillary condensation. Our study has been carried out for weakly, as well as for strongly, associated fluids confined in pores of different widths. We also investigate the role of the fluid-wall interaction.