A modified SAFT equation of state is developed by applying the perturbation theory of Barker and Henderson to a hard-chain reference fluid. With conventional one-fluid mixing rules, the equation of state is applicable to mixtures of small spherical molecules such as gases, nonspherical solvents, and chainlike polymers. The three pure-component parameters required for nonassociating molecules were identified for 78 substances by correlating vapor pressures and liquid volumes. The equation of state gives good fits to these properties and agrees well with caloric properties. When applied to vapor−liquid equilibria of mixtures, the equation of state shows substantial predictive capabilities and good precision for correlating mixtures. Comparisons to the SAFT version of Huang and Radosz reveal a clear improvement of the proposed model. A brief comparison with the Peng−Robinson model is also given for vapor−liquid equilibria of binary systems, confirming the good performance of the suggested equation of state. ...

Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules

Efficient estimation of free energy differences from Monte Carlo data

Recent theoretical work on the microscopic structure and surface tension of the liquid-vapour interface of simple (argon-like) fluids is critically reviewed. In particular, the form of pairwise intermolecular correlations in the liquid surface and the capillary wave treatment of the interface are examined in some detail. It is argued that conventional capillary wave theory, which leads to divergences in the width of the density profile, is unsatisfactory for describing all the equilibrium aspects of the interface. The density functional formalism which has been developed to study the liquid-vapour interface can also be profitably applied to other problems in the statistical mechanics of non-uniform fluids; here a new generalization of the ‘linear’ theory of spinodal decomposition is formulated and by considering a ‘nearly uniform’ fluid, some useful results for the long-wavelength behaviour of the liquid structure factor of various monatomic liquids are obtained. Some other topics of current inte...

The nature of the liquid-vapour interface and other topics in the statistical mechanics of non-uniform, classical fluids

An equation of state for associating liquids is presented as a sum of three Helmholtz energy terms: Lennard-Lones (LJ) segment (temperature-dependent hard sphere + dispersion), chain (increment due to chain formation), and association (increment due to association). This equation of state has been developed by extending Wertheim’s theory obtained from a resummed cluster expansion. Pure component molecules are characterized by segment diameter, segment-segment interaction energy, for example, Lennard-Jones u and E, and chain length expressed as the number of segments. There are also two association parameters, the association energy and volume, characteristic of each site-site pair. The agreement with molecular simulation data is shown to be excellent at all the stages of development for associating spheres, mixtures of associating spheres, and nonassociating chains. The model has been shown to reproduce experimental phase equilibrium data for a few selected real pure compounds.

New reference equation of state for associating liquids

http://static.sif.it/SIF/resources/public/files/va2012/likos_0710.pdf

Effective interactions in soft condensed matter physics

The perturbation theory previously shown to give good results for the equation of state of a square‐well fluid at liquid densities and temperatures is applied to more realistic potentials with soft repulsion, in particular the 6:12 potential. For an arbitrary potential function a modified potential is defined involving three parameters, namely a hard‐sphere diameter, an inverse‐steepness parameter for the repulsive region, and a depth parameter for the attractive region. When the latter parameters are zero, the modified potential becomes the hard‐sphere potential; when they are one, it becomes the original potential. The configuration integral is expanded in a double‐power series in the inverse‐steepness and depth parameters, the hard‐sphere diameter being chosen so that the first‐order term in the inverse‐steepness parameter is zero. The first‐order term in the depth parameter is evaluated essentially exactly and the second‐order term approximately: other second‐order terms and all higher‐order terms are neglected. The resulting equation of state is in good agreement with molecular dynamics, Monte Carlo results, and experimental data for argon at all temperatures and densities relevant for fluids.

D. Henderson

Papers

Perturbation Theory and Equation of State for Fluids. II. A Successful Theory of Liquids