SAFT

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The following SAFT variants are available in TP-Cloud:

• SPC-SAFT
• PC-SAFT
• PCP-SAFT
• SAFT-VR Mie
• SAFT-VRQ Mie

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Introduction to SAFT

Statistical Associating Fluid Theory has a basis in statistical thermodynamics, thermodynamic perturbation theory, and a molecular description of the fluid interactions. The molecular fluid interactions can be leveraged in molecular simulations to extract thermodynamic properties. The connection between molecular simulations, EoS and experiments is very useful in cases where few experiments are available, or the experiments are very challenging. The molecular basis of SAFT EoS will in some cases give excellent extrapolative properties. Barker and Henderson showed in their pioneering paper that the reduced, residual Helmholtz energy of the system can be written as an expansion around a system consisting of hard spheres (superscript HS), where $\alpha=A/RT$. The expansion of the residual Helmholtz energy presented by Baker and Henderson is:

$$\alpha^r = \alpha^{\text{HS}}+\frac{1}{T}\alpha_1+\frac{1}{T^2}\alpha_2+\frac{1}{T^3}\alpha_3+...$$

where $\alpha_j$ is the jth-order perturbation terms that take into account attraction between the particles. The SAFT variants differ both in the sophistication of the molecular interaction potential, and how the perturbation terms are modelled.

SPC-SAFT

The simplfied PC-SAFT (SPC-SAFT) in TP-Cloud uses the simplified PC-SAFT (SPC-SAFT) EoS presented by von Sloms et al. ¹. For pure components it has the same form as the original PC-SAFT by Gross and Sadowski ², but uses simplified mixing rules for the radial distribution function and hard-sphere terms; it has in all considered cases been found to have accuracy comparable to the original PC-SAFT.

PC-SAFT

TP-Cloud has the PC-SAFT model presented by Gross and Sadowski ². In the EoS, molecules are conceived to be chains composed of spherical segments. The pair potential for the segment of a chain is given by a modified square-well potential.

PCP-SAFT

The PCP-SAFT model ³ extends PC-SAFT EoS by explicitly modeling Helmholtz energy contributions due to dipole-dipole (DD), quadrupole-quadrupole (QQ), and dipole-quadrupole (DQ) interactions:

$$A^{r} = A^{\text{HS}} + A^{\text{disp}} + A^{\text{QQ}} + A^{\text{DD}} + A^{\text{DQ}}.$$

SAFT-VR Mie

TP-Cloud contains the SAFT-VR-Mie EoS presented by Lafitte et al. ⁴. This SAFT variant uses the Mie-potential to describe interactions between monomers, which is a more flexible and realistic description of molecular interactions than the modified square-well potential used in SPC-SAFT,PC-SAFT and PCP-SAFT.

SAFT-VRQ Mie

Molecular interactions described by Mie potentials do not capture the quantum-mechanical nature of hydrogen, helium, deuterium and neon at low temperatures. These effects can be approximated semi-classically by Feynman-Hibbs-corrected Mie potentials, which are temperature-dependent. SAFT-VRQ Mie is a SAFT EoS for pure fluids ⁵ and mixtures ⁶ that exhibit strong quantum effects, described by Feynman-Hibbs corrected Mie potentials of first and second order. The EoS gives a very accurate representation of hydrogen as shown below (dashed line), which reproduces molecular simulation results (filled dots), and agrees with the multiparameter EoS for hydrogen by Leachman et al. (solid line) ⁷.

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References

Footnotes

1. von Solms, Nicolas, Michael L. Michelsen, and Georgios M. Kontogeorgis. "Computational and physical performance of a modified PC-SAFT equation of state for highly asymmetric and associating mixtures." Industrial & engineering chemistry research 42.5 (2003): 1098-1105. ↩

2. Gross, Joachim, and Gabriele Sadowski. "Perturbed-chain SAFT: An equation of state based on a perturbation theory for chain molecules." Industrial & engineering chemistry research 40.4 (2001): 1244-1260. ↩ ↩²

3. Gross, Joachim. "An equation‐of‐state contribution for polar components: Quadrupolar molecules." AIChE journal 51.9 (2005): 2556-2568. ↩

4. Lafitte, Thomas, et al. "Accurate statistical associating fluid theory for chain molecules formed from Mie segments." The Journal of chemical physics 139.15 (2013). ↩

5. Aasen, Ailo, et al. "Equation of state and force fields for Feynman–Hibbs-corrected Mie fluids. I. Application to pure helium, neon, hydrogen, and deuterium." The Journal of Chemical Physics 151.6 (2019). ↩

6. Aasen, Ailo, et al. "Equation of state and force fields for Feynman–Hibbs-corrected Mie fluids. II. Application to mixtures of helium, neon, hydrogen, and deuterium." The Journal of Chemical Physics 152.7 (2020). ↩

7. Leachman, Jacob W., et al. "Fundamental equations of state for parahydrogen, normal hydrogen, and orthohydrogen." Journal of Physical and Chemical Reference Data 38.3 (2009): 721-748. ↩