PC-SAFT

PC-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 statistical mechanical methods (in particular perturbation theory).[1] 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.[2] The name perturbed chain SAFT (PC-SAFT) is thus somewhat misleading.

PC-SAFT was developed by Joachim Gross and Gabriele Sadowski, and was first presented in their 2001 article.[2] Further research extended PC-SAFT for use with associating and polar molecules, and it has also been modified for use with polymers.[3][4][5][6] A version of PC-SAFT has also been developed to describe mixtures with ionic compounds (called electrolyte PC-SAFT or ePC-SAFT).[7][8]

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 Helmholtz energy because all other thermodynamic properties can be easily found by taking the appropriate derivatives of the Helmholtz energy.[2]

${\displaystyle a=a^{\text{hc}}+a^{\text{disp}}+a^{\text{assoc}}+a^{\text{dipole}}+a^{\text{ion}}}$

Here ${\displaystyle a}$ is the molar residual Helmholtz energy.

Hard Chain Term

${\displaystyle {\frac {a^{\text{hc}}}{kT}}={\overline {m}}\cdot a^{\text{hs}}-\sum _{i=1}^{NC}{x_{i}\cdot (m_{i}-1)\cdot \ln(g_{i,i}^{\text{hs}})}}$

where

• ${\displaystyle NC}$ is the number of compounds;
• ${\displaystyle x_{i}}$ is the mole fraction;
• ${\displaystyle {\overline {m}}=\sum _{i=1}^{NC}{x_{i}m_{i}}}$ is the average number of segments in the mixture;
• ${\displaystyle a^{\text{hs}}}$ is the Bloublík-Mansoori-Leeland- Carnahan-Starling hard sphere equation of state;[9][10][11]
• ${\displaystyle g_{i,i}^{\text{hs}}}$ is the hard sphere radial distribution function at contact.[9]

References

1. Chapman, Walter G., et al. "SAFT: Equation-of-state solution model for associating fluids." Fluid Phase Equilibria 52 (1989): 31-38.
2. 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.
3. 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.
4. 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.
5. 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.
6. Gross J, Vrabec J. An equation‐of‐state contribution for polar components: Dipolar molecules. AIChE Journal. 2006 Mar 1;52(3):1194-204.
7. 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.
8. 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.
9. Boublík, T. Hard Sphere Equation of State, J. Chem. Phys. 1970;53(3):471-2.
10. 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
11. Carnahan-Starling equation of state, http://www.sklogwiki.org/SklogWiki/index.php/Carnahan-Starling_equation_of_state