View source for PC-SAFT

'''PC-SAFT''' (perturbed chain SAFT) is an [[equation of state]] that is based on [[statistical associating fluid theory]] (SAFT). Like other SAFT equations of state, it makes use of chain and association terms developed by Chapman, et al from [[perturbation theory]].<ref name="chapman 1989">Chapman, Walter G., et al. "SAFT: Equation-of-state solution model for associating fluids." ''Fluid Phase Equilibria'' 52 (1989): 31-38.</ref> However, unlike earlier SAFT equations of state that used unbonded spherical particles as a reference fluid, it uses spherical particles in the context of hard chains as reference fluid for  the dispersion term.<ref name="gross 2001">Gross J, Sadowski G. Perturbed-chain SAFT: An equation of state based on a perturbation theory for chain molecules. Industrial & engineering chemistry research. 2001 Feb 21;40(4):1244-60.</ref> 

PC-SAFT was developed by [[Joachim Gross]] and [[Gabriele Sadowski]], and was first presented in their 2001 article.<ref name="gross 2001" /> Further research extended PC-SAFT for use with associating and polar molecules, and it has also been modified for use with polymers.<ref name="Gross 2002">Gross J, Sadowski G. Application of the perturbed-chain SAFT equation of state to associating systems. Industrial & engineering chemistry research. 2002 Oct 30;41(22):5510-5.</ref><ref name="Gross 2002 polymer">Gross J, Sadowski G. Modeling polymer systems using the perturbed-chain statistical associating fluid theory equation of state. Industrial & engineering chemistry research. 2002 Mar 6;41(5):1084-93.</ref><ref name="Jog 1999">Jog PK, Chapman WG. Application of Wertheim's thermodynamic perturbation theory to dipolar hard sphere chains. Molecular Physics. 1999 Aug 10;97(3):307-19.</ref><ref name="Gross 2006 polar">Gross J, Vrabec J. An equation‐of‐state contribution for polar components: Dipolar molecules. AIChE Journal. 2006 Mar 1;52(3):1194-204.</ref> A version of PC-SAFT has also been developed to describe mixtures with ionic compounds (called electrolyte PC-SAFT or ePC-SAFT).<ref name="Cameretti 2005 electrolyte">Cameretti LF, Sadowski G, Mollerup JM. Modeling of aqueous electrolyte solutions with perturbed-chain statistical associated fluid theory. Industrial & engineering chemistry research. 2005 Apr 27;44(9):3355-62.</ref><ref name="Held 2014 electrolyte">Held C, Reschke T, Mohammad S, Luza A, Sadowski G. ePC-SAFT revised. Chemical Engineering Research and Design. 2014 Dec 1;92(12):2884-97.</ref>

==Form of the Equation of State==
The equation of state is organized into terms that account for different types of intermolecular interactions, including terms for
* the hard chain reference
* dispersion
* association
* polar interactions
* ions
The equation is most often expressed in terms of the [[Residual property (physics)|residual]] [[Helmholtz free energy|Helmholtz energy]] because all other thermodynamic properties can be easily found by taking the appropriate derivatives of the Helmholtz energy.<ref name="gross 2001" />

:<math>a = a^\text{hc} + a^\text{disp} + a^\text{assoc} + a^\text{dipole} + a^\text{ion}</math>

Here <math>a</math> is the molar residual Helmholtz energy.

==Hard Chain Term==
:<math>\frac{a^\text{hc}}{kT} = \overline{m} \cdot a^\text{hs} - \sum_{i=1}^{NC} {x_i \cdot (m_i-1) \cdot \ln(g^\text{hs}_{i,i}) }</math>

where
* <math>NC</math> is the number of compounds;
* <math>x_i</math> is the [[mole fraction]];
* <math>\overline{m} = \sum_{i=1}^{NC} {x_i m_i} </math> is the average number of segments in the mixture;
* <math> a^\text{hs} </math> is the Boublík-Mansoori-Leeland-[[Norman F. Carnahan | Carnahan]]-Starling ''hard sphere'' equation of state;<ref name="Boublik1970">Boublík, T. Hard Sphere Equation of State, J. Chem. Phys. 1970;53(3):471-2.</ref><ref>Mansoori GA, Carnahan NF, Starling KE, Leland TW. Equilibrium Thermodynamic Properties of the Mixture of Hard Spheres, J. Chem. Phys. 1971; 54(4):1523-25</ref><ref>''Carnahan-Starling equation of state'', http://www.sklogwiki.org/SklogWiki/index.php/Carnahan-Starling_equation_of_state</ref>
* <math> g^\text{hs}_{i,i} </math> is the ''hard sphere'' [[radial distribution function]] at contact.<ref name="Boublik1970" />

==References==
<references/>

[[Category:Engineering thermodynamics]]