Statistical associating fluid theory (SAFT) is a

chemical A chemical substance is a unique form of matter with constant chemical composition and characteristic properties. Chemical substances may take the form of a single element or chemical compounds. If two or more chemical substances can be combin ...

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 middle ...

, 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. Sometimes called statistical physics or statistical thermodynamics, its applicatio ...

to explain how complex

fluids In physics, a fluid is a liquid, gas, or other material that may continuously move and deform (''flow'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot res ...

and fluid mixtures form associations through

hydrogen bonds In chemistry, a hydrogen bond (H-bond) is a specific type of molecular interaction that exhibits partial covalent character and cannot be described as a purely electrostatic force. It occurs when a hydrogen (H) atom, covalently bonded to a mo ...

. 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 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 energ ...

term that can be used in

equations of state In physics and chemistry, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal energy. Most mod ...

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 th ...

and phase equilibrium properties of pure fluids and fluid mixtures. SAFT was developed using

statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applicati ...

. 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 ene ...

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 Sir John Edward Lennard-Jones (27 October 1894 – 1 November 1954) was a British mathematician and professor of theoretical physics at the University of Bristol, and then of theoretical chemistry, theoretical science at the University of C ...

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,

polymers A polymer () is a substance or material that consists of very large molecules, or macromolecules, that are constituted by many repeating subunits derived from one or more species of monomers. Due to their broad spectrum of properties, b ...

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 can flow like a liquid, but its molecules may be oriented in a common direction as i ...

electrolytes An electrolyte is a substance that conducts electricity through the movement of ions, but not through the movement of electrons. This includes most soluble salts, acids, and bases, dissolved in a polar solvent like water. Upon dissolving, t ...

surfactant Surfactants are chemical compounds that decrease the surface tension or interfacial tension between two liquids, a liquid and a gas, or a liquid and a solid. The word ''surfactant'' is a Blend word, blend of "surface-active agent", coined in ...

solutions, and

refrigerants A refrigerant is a working fluid used in the cooling, heating, or reverse cooling/heating cycles of air conditioning systems and heat pumps, where they undergo a repeated phase transition from a liquid to a gas and back again. Refrigerants are ...

Development

SAFT evolved from thermodynamic theories, including perturbation theories developed in the 1960s, 1970s, and 1980s by John Barker and Douglas Henderson, Keith Gubbins and Chris Gray, and, in particular, Michael Wertheim's first-order, thermodynamic perturbation theory (TPT1) outlined in a series of papers in the 1980s. The SAFT equation of state was developed using statistical mechanical methods (in particular the

of Wertheim) to describe the interactions between molecules in a system. The idea of a SAFT equation of state was first proposed by Walter G. Chapman and by Chapman et al. in 1988 and 1989. Many different versions of the SAFT models have been proposed, but all use the same chain and association terms derived by Chapman et al. One of the first SAFT papers (1990) titled "New reference equation of state for associating liquids" by Walter G. Chapman, Keith Gubbins, George Jackson, and Maciej Radosz, was recognized in 2007 by '' Industrial and Engineering Chemistry Research'' as one of the most highly cited papers of the previous three decades. SAFT is one of the first theories to accurately describe (in comparison with molecular simulation) the effects on fluid properties of molecular size and shape in addition to association between molecules.

Variations

Many variations of SAFT have been developed since the 1990s, including HR-SAFT (Huang-Radosz SAFT), PC-SAFT (perturbed chain SAFT), Polar SAFT, PCP-SAFT (PC-polar-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 Cubic Equation of state, equations of state are a specific class of thermodynamic models for modeling the pressure of a gas as a function of temperature and density and which can be rewritten as a cubic function of the molar volume. Equations of ...

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 In physics, lattice field theory is the study of lattice models of quantum field theory. This involves studying field theory on a space or spacetime that has been discretised onto a lattice. Details Although most lattice field theories are not ...

References

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