Editing Equation of state (section)

=== Statistical associating fluid theory (SAFT) ===
An important contribution for physically based equations of state is the [[statistical associating fluid theory]] (SAFT) that contributes the [[Helmholtz free energy|Helmholtz energy]] that describes the association (a.k.a. [[hydrogen bond]]ing) in fluids, which can also be applied for modelling chain formation (in the limit of infinite association strength). The SAFT equation of state was developed using [[Statistical mechanics|statistical mechanical]] methods (in particular the [[perturbation theory]] of Wertheim<ref>{{Cite journal|last=Wertheim|first=M. S.|date=April 1984|title=Fluids with highly directional attractive forces. I. Statistical thermodynamics|url=http://dx.doi.org/10.1007/bf01017362|journal=Journal of Statistical Physics|volume=35| issue=1–2|pages=19–34|doi=10.1007/bf01017362|bibcode=1984JSP....35...19W|s2cid=121383911|issn=0022-4715}}</ref>) to describe the interactions between molecules in a system.<ref name="ChapmanGubbins1989">{{cite journal|last1=Chapman|first1=Walter G.|last2=Gubbins|first2=K.E.|last3=Jackson|first3=G.| last4=Radosz|first4=M.| title=SAFT: Equation-of-state solution model for associating fluids|journal=Fluid Phase Equilibria|date=1 December 1989|volume=52|pages=31–38|doi=10.1016/0378-3812(89)80308-5|s2cid=53310898 | language=en|issn=0378-3812}}</ref><ref name="Chapman1988">{{cite journal|last1=Chapman|first1=Walter G.|date=1988| title=Theory and Simulation of Associating Liquid Mixtures|journal=Doctoral Dissertation, Cornell University|language=en}}</ref><ref name="ChapmanGubbins1988">{{cite journal|last1=Chapman|first1=Walter G.|last2=Jackson|first2=G.| last3=Gubbins| first3=K.E.| date=11 July 1988|title=Phase equilibria of associating fluids: Chain molecules with multiple bonding sites| journal=Molecular Physics|language=en|volume=65|pages=1057–1079|doi=10.1080/00268978800101601}}</ref> The idea of a SAFT equation of state was first proposed by Chapman et al. in 1988 and 1989.<ref name="ChapmanGubbins1989" /><ref name="Chapman1988" /><ref name="ChapmanGubbins1988" />  Many different versions of the SAFT models have been proposed, but all use the same chain and association terms derived by Chapman et al.<ref name="Chapman1988" /><ref name="ChapmanGubbins1990">{{cite journal| last1=Chapman|first1=Walter G.|last2=Gubbins|first2=K.E.|last3=Jackson|first3=G.|last4=Radosz|first4=M.|title=New Reference Equation of State for Associating Liquids|journal=Ind. Eng. Chem. Res.|date=1 August 1990|volume=29|issue=8| pages=1709–1721| doi=10.1021/ie00104a021|language=en }}</ref><ref>{{Cite journal | doi=10.1063/1.473101|title = Statistical associating fluid theory for chain molecules with attractive potentials of variable range| journal=The Journal of Chemical Physics| volume=106| issue=10| pages=4168–4186|year = 1997|last1 = Gil-Villegas|first1 = Alejandro| last2=Galindo| first2=Amparo| last3=Whitehead| first3=Paul J.| last4=Mills| first4=Stuart J.| last5=Jackson| first5=George| last6=Burgess| first6=Andrew N.|bibcode = 1997JChPh.106.4168G}}</ref>