Statistical associating fluid theory (SAFT) is a

chemical A chemical substance is a form of matter having constant chemical composition and characteristic properties. Some references add that chemical substance cannot be separated into its constituent elements by physical separation methods, i.e., wit ...

theory, based on

perturbation theory In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middl ...

, that uses

statistical thermodynamics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic be ...

to explain how complex

fluids In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear ...

and fluid mixtures form associations through

hydrogen bonds In chemistry, a hydrogen bond (or H-bond) is a primarily electrostatic force of attraction between a hydrogen (H) atom which is covalently bound to a more electronegative "donor" atom or group (Dn), and another electronegative atom bearing a ...

. Widely used in industry and academia, it has become a standard approach for describing complex mixtures. Since it was first proposed in 1990, SAFT has been used in a large number of molecular-based equation of state models for describing the Helmholtz energy contribution due to association.

Overview

SAFT is a Helmholtz energy term that can be used in equations of state that describe the

thermodynamic Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of t ...

and phase equilibrium properties of pure fluids and fluid mixtures. SAFT was developed using statistical mechanics. SAFT models the

Helmholtz free energy In thermodynamics, the Helmholtz free energy (or Helmholtz energy) is a thermodynamic potential that measures the useful work obtainable from a closed thermodynamic system at a constant temperature ( isothermal). The change in the Helmholtz e ...

contribution due to association, i.e. hydrogen bonding. SAFT can be used in combination with other Helmholtz free energy terms. Other Helmholtz energy contributions consider for example Lennard-Jones interactions,

covalent A covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs. The stable balance of attractive and repulsive forces between atom ...

chain-forming bonds, and association (interactions between segments caused by, for example, hydrogen bonding). SAFT has been applied to a wide range of fluids, including

supercritical fluids A supercritical fluid (SCF) is any substance at a temperature and pressure above its critical point, where distinct liquid and gas phases do not exist, but below the pressure required to compress it into a solid. It can effuse through porous s ...

polymers A polymer (; Greek ''poly-'', "many" + '' -mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic an ...

liquid crystals Liquid crystal (LC) is a state of matter whose properties are between those of conventional liquids and those of solid crystals. For example, a liquid crystal may flow like a liquid, but its molecules may be oriented in a crystal-like way. The ...

electrolytes An electrolyte is a medium containing ions that is electrically conducting through the movement of those ions, but not conducting electrons. This includes most soluble salts, acids, and bases dissolved in a polar solvent, such as water. Upon d ...

surfactant Surfactants are chemical compounds that decrease the surface tension between two liquids, between a gas and a liquid, or interfacial tension between a liquid and a solid. Surfactants may act as detergents, wetting agents, emulsifiers, fo ...

solutions, and

refrigerants A refrigerant is a working fluid used in the refrigeration cycle of air conditioning systems and heat pumps where in most cases they undergo a repeated phase transition from a liquid to a gas and back again. Refrigerants are heavily regulated ...

Development

SAFT evolved from thermodynamic theories, including perturbation theories developed in the 1960s, 1970s, and 1980s by John Barker and Douglas Henderson,

Keith Gubbins Keith E. Gubbins (born January 27, 1937) is a British-born American chemical engineer who is the W.H. Clark Distinguished University Professor of Chemical Engineering at North Carolina State University North Carolina State University (NC Sta ...

and Chris Gray, and, in particular, Michael Wertheim's first-order, thermodynamic perturbation theory (TPT1) outlined in a series of papers in the 1980s. SAFT was originally proposed in a 1990 paper titled "New reference equation of state for associating liquids" by Walter Chapman, Keith Gubbins, George Jackson, and Maciej Radosz, which, in 2007, was recognized by '' Industrial and Engineering Chemistry Research'' as one of the most highly cited papers of the previous three decades. SAFT improved on earlier, over-simplified theories, which were based on hard spherical molecules that do not associate, by focusing on molecular chain length and association.

Variations

Many variations of SAFT have been developed since the 1990s, including HR-SAFT (Huang-Radosz SAFT), PC-SAFT (perturbed chain SAFT), PCP-SAFT (polar PC-SAFT), soft-SAFT, polar soft-SAFT, SAFT-VR (variable range), SAFT VR-Mie. Also, the SAFT term was used in combination with cubic equations of state for describing the dispersive-repulsive interactions, for example in the Cubic-Plus-Association (CPA) equation of state model and the SAFT + cubic model and non-random-lattice (NLF) models based on lattice field theory.

References

{{reflist Equations of physics Engineering thermodynamics Mechanical engineering Equations of state Thermodynamic models Perturbation theory