On the isobaric thermal expansivity of liquids.

The temperature and pressure dependence of isobaric thermal expansivity, α(p), in liquids is discussed in this paper. Reported literature data allow general trends in this property that are consistent with experimental evidence to be established. Thus, a negative pressure dependence is to be expected except around the critical point. On the other hand, α(p) exhibits broad regions of negative and positive temperature dependence in the (T, p) plane depending on the nature of the particular liquid. These trends are rationalized here in terms of various molecular-based equations of state. The analysis of the Lennard-Jones, hard sphere square well and restricted primitive model equations allows understanding the differences in the α(p) behavior between liquids of diverse chemical nature (polar, nonpolar, and ionic): broader regions of negative temperature and positive pressure dependencies are obtained for liquids characterized by larger ranges of the interparticle potential. Also, using the statistical associating fluid theory (SAFT) allowed the behavior of more complex systems (basically, those potentially involving chain and association effects) to be described. The effect of chain length is rather simple: increasing it is apparently equivalent to raise the interaction range. By contrast, association presents a quite complex effect on α(p), which comes from a balance between the dispersive and associative parts of the interaction potential. Thus, if SAFT parameters are adjusted to obtain low association ability, α(p) is affected by each mechanism at clearly separate regions, one at low temperature, due to association, and the other to dispersive forces, which has its origin in fluctuations related with vapor-liquid transition.

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).

Thermodynamic properties of the Mie n-6 fluid: a comparison between statistical associating fluid theory of variable range approach and molecular dynamics results.

Molecular dynamics (MD) simulations of direct and derivative thermodynamic properties of the Mie n-6 fluid (n=8, 10, and 12) have been performed for liquid to supercritical states. Using the results, an in depth test of the monomer-monomer interaction estimation of a recently derived statistical associating fluid theory of variable range (SAFT-VR) equation of state [Lafitte et al., J. Chem. Phys., 124, 024509 (2006)] has been carried out based on the Mie n-6 potential. For pure fluids, using an appropriate scaling, MD simulations show that density and isometric heat capacity are nearly independent of n, whereas sound velocity and thermal pressure coefficient tend to increase with n. In addition, the results show that predictions provided by the equation of state are consistent with those coming from MD and catch correctly the trends of each property with n except for the heat capacity. The comparison is next extended to binary mixtures with components differing only in the value of the n parameter and which demonstrate the reliability of the scheme (MX1b) used by Lafitte et al. to deal with this parameter in the SAFT-VR equation of state. In addition, a new empirical one-fluid approximation of the n parameter is proposed thanks to MD simulations, which very favorably compare with the one-fluid model on n previously proposed in the literature. The consistency of this approximation is addressed by making use of it in combination with the SAFT-VR Mie equation of state. It is shown that using such an approach, which is easier to handle than the MX1b one, yields slightly improved results compared to those of the MX1b.

A comprehensive description of chemical association effects on second derivative properties of alcohols through a SAFT-VR approach.

A recently derived version of the statistical associating fluid theory (SAFT), denoted as SAFT-VR Mie, which incorporates the Mie potentials within the SAFT-VR framework to model the monomer segment interactions (Lafitte et al. J. Chem. Phys. 2006, 124, 024509), is used for the study of second-order derivative properties and phase equilibria of alcohols and 1-alcohol + n-alkane binary mixtures. For this purpose, a variable repulsive potential is used to induce nonconformal interactions in the reference nonbonded fluid. These features have a significant influence on the chain and association contributions through the contact value of the radial distribution function, and they enhance the SAFT theory performance in the application to associating substances. When dealing with pure alcohols and 1-alcohol + n-alkane binary mixtures, an accurate description of both phase equilibria and second-order derivatives is obtained with a single set of molecular parameters. To explore the predictive ability limit of the model we have particularly focused our attention on secondary derivative properties, which display singularities due to the formation of aggregates. With this approach, we have found that the model is able to reproduce accurately the complex behavior of the isobaric heat capacity of alcohols as, for instance, the maximum versus temperature in the compressed liquid region. Furthermore, in the case of 1-hexanol + n-hexane binary mixtures, the proposed equation is found to capture the association effects on the pressure and temperature dependence of the isobaric thermal expansivity. These two special features, which to our knowledge have never been described by a theoretical model, emphasize both the validity of the changes in the model proposed and the physical meaning of the molecular parameters obtained in this study.

Heat capacity of associated systems. Experimental data and application of a two-state model to pure liquids and mixtures.

The predictions from a recently reported (J. Chem. Phys. 2004, 120, 6648) two-state association model (TSAM) have been tested against experimental data. The temperature, T, and pressure, p, dependence of the isobaric heat capacity, C(p), for three pure alcohols and the temperature dependence at atmospheric pressure of the excess heat capacity, C(p)(E), for four alcohol + ester mixtures have been measured. The branched alcohols were 3-pentanol, 3-methyl-3-pentanol, and 3-ethyl-3-pentanol, and the mixtures were 1-butanol and 3-methyl-3-pentanol mixed with propyl acetate and with butyl formate. These data, together with literature data for alcohol + n-alkane and alcohol + toluene mixtures, have been analyzed using the TSAM. The model, originally formulated for the C(p) of pure liquids, has been extended here to account for the C(p)(E) of mixtures. To evaluate its performance, quantum mechanical ab initio calculations for the H-bond energy, which is one of the model parameters, were performed. The effect of pressure on C(p) for pure liquids was elucidated, and the variety of C(p)(E)(T) behaviors was rationalized. Furthermore, from the C(p) data at various pressures, the behavior of the volume temperature derivative, (deltaV/deltaT)(p), was inferred, with the existence of a (deltaV/deltaT)(p) versus T maximum for pure associated liquids such as the branched alcohols being predicted. It is concluded that the TSAM captures the essential elements determining the behavior of the heat capacity for pure liquids and mixtures, providing insight into the macroscopic manifestation of the association phenomena occurring at the molecular level.

Simultaneous estimation of phase behavior and second-derivative properties using the statistical associating fluid theory with variable range approach.

A modified statistical associating fluid theory (SAFT) with variable range version is presented using the family of m-n Mie potentials. The use of this intermolecular potential for modeling repulsion-dispersion interactions between the monomer segments, together with a new method for optimizing the molecular parameters of the equation of state, is found to give a very accurate description of both vapor-liquid equilibria and compressed liquid bulk properties (volumetric and derivative properties) for long-chain n-alkanes. This new equation improves other SAFT-like equations of state which fail to describe derivative properties such as the isothermal compressibility and the speed of sound in the condensed liquid phase. Emphasis is placed on pointing out that the key for modeling the latter properties is the use of a variable repulsive term in the intermolecular potential. In the case of the n-alkanes series, a clear dependence of the characteristic molecular parameters on increasing chain length is obtained, demonstrating their sound physical meaning and the consistency of the new fitting procedure proposed. This systematic method for optimizing the model parameters includes data on the saturation line as well as densities and speed of sound data in the condensed liquid phase, and the results show undoubtedly that the model performance is enhanced and its range of applicability is now widened, keeping in any case a good balance between the accuracy of the different estimated properties.