SAFT

References

These are some of the key papers which describe in detail the current versions of SAFT from the MSE team.

SAFT-γ-Mie 
This is our Opus Magna, the seminal paper on the EoS: Papaioannou et al. "Group contribution methodology based on the statistical associating fluid theory for heteronuclear molecules formed from Mie segments"  J. Chem. Phys. 140, 054107 (2014) . link

SAFT-VR-Mie
This paper present the theory for homonuclear chains. it is a subset of the one above. Lafitte et al. "Accurate statistical associating fluid theory for chain molecules formed from Mie segments"  J. Chem. Phys. 139, 154504 (2013) link

Simple version (easy to code) 
An abridged (simple ) version of the theory is presented in Avendaño et al. “SAFT-γ Force Field for the Simulation of Molecular Fluids: 2. Coarse-Grained Models of Greenhouse Gases, Refrigerants, and Long Alkanes.” J. Phys. Chem. B 117,  2717–33 (2013). link

Parametrization 
The Mie potential can be expressed in terms of the corresponding state principle ( see Ramrattan et al. “A Corresponding-States Framework for the Description of the Mie Family of Intermolecular Potentials.” Mol Physics 113,932–47  (2015) link ). Following that idea, the paper of Mejia et al. (“Force Fields for Coarse-Grained Molecular Simulations From a Corresponding States Correlation.” Ind. Eng. Chem. Res 53, : 4131–41. (2014) link ) presents the M&M correlation that links the molecular parameters of the equation of state to critical properties, hence allowing a very rapid evaluation of parameters.

Open Access code ( to download)  
The following publication provides the details of an open-access code for SAFT- γ ( and a density gradient theory code to calculate interfacial tensions): Mejía, A., Müller, E. A. & Maldonado, G. C. SGTPy: A Python Code for Calculating the Interfacial Properties of Fluids Based on the Square Gradient Theory Using the SAFT-VR Mie Equation of State. J. Chem. Information Mod 61, 1244–1250 (2021). See also the GitHub. link

Reviews

These are links to some of the review papers written about the SAFT theory and applications

  1. Molecular-based equations of state for associating fluids: A review of SAFT and related approaches; Muller and Gubbins, Ind. Eng. Chem. Res. 40, 2193 ( 2001)  paper
  2. SAFT associating Fluids and Fluid Mixtures; McCabe and Galindo Chapter 8 of Applied Thermodynamics of Fluids (2010) paper
  3. Force-Field parameters from the the SAFT-g Equation of state for use in coarse grained Molecular simulations; Muller and Jackson, Annu. Rev. Chem. Biomol. Eng. 5, 405-25 ( 2014) paper

Tables of SAFT parameters

Picture
We are working on this...
In the meantime, check out the Bottled SAFT site, where you can obtain coarse-grained parameters for thousands of molecules ; www.bottledsaft.org. The story behind it is in this paper. (alternative download here)

Coarse grained SAFT intermolecular potentials

 We have developed the SAFT-γ CG force fields based on the Mie potential, using the SAFT-γ Mie EoS as a platform to estimate the parameters of the interaction from macroscopic fluid-phase equilibrium and single-phase thermodynamic data. The accuracy of the theory allows one to develop molecular models that are appropriate not only for simple rigid and polar/quadrupolar or associating molecules, such as carbon dioxide or water, but also for long-chain fluids and polymers, heteronuclear molecules such as surfactants, and mixtures of these components. A representation of the thermodynamic, phase equilibrium, and structural properties of these systems is challenging owing to the nonisotropic nature of the molecular interactions, giving rise to unusual features in the balance of the repulsive and attractive contributions to the intermolecular potential that cannot be captured with a simple Lennard-Jones spherical or homonuclear representation of the molecules. The SAFT-γ force-field parameters estimated from experimental data using the EoS provide an excellent description of the fluid-phase equilibria without the need for further refinement. The entire fluid-phase diagram of mixtures, including properties that are not considered in the parameter-estimation procedure, is represented well with our simple CG models. Furthermore, the direct molecular simulation of the SAFT-γ molecular models provides a reliable route to properties that are not accessible from the EoS, such as the structure (radial distribution functions), the self-assembly into mesophases, the interfacial tension, the adsorption on surfaces, and the transport properties. The group-contribution nature of the methodology allows for the description of the behavior of a wide range of complex fluids in a consistent and quantitative way. The one-to-one correspondence of the force fields to the EoS provides a unique avenue to the multiscale modeling of complex fluids.

Download here the a review paper on the use of SAFT for coarse grained simulations ( Force-Field parameters from the the SAFT-g Equation of state for use in coarse grained Molecular simulations; Muller and Jackson, Annu. Rev. Chem. Biomol. Eng. 5, 405-25 ( 2014) , and a beautiful video of a micelle separating from an air-water interface. A recent discussion on the method as applied to polymers is written by  A. K. Pervaje, C. C. Walker, and E. E. Santiso, “Molecular simulation of polymers with a SAFT-γ Mie approach,” Mol. Simulation,  45, (2019) 1223–1241.

Parameters for the SAFT force field can be easily derived for any molecule for which the critical constants are known using the scheme put forward in this  paper ( the M&M correlation )  Mejía, A., Herdes, C., & Müller, E. A. (2014). Force Fields for Coarse-Grained Molecular Simulations from a Corresponding States Correlation. Ind. Eng. Chem. Res, 53(10), 4131–4141. . They can also be obtained from Bottled SAFT (see above). This tool allows you to obtain SAFT-Mie coarse grained parameters for homonuclear models for over 6000 different chemical compounds at a click of a button. If you want to run SAFT force fields simulations in Gromacs and/or HOOMD, please see this paper on raaSAFT, (Ervik, Å., Serratos, G. J., & Müller, E. A. (2017). raaSAFT: A framework enabling coarse-grained molecular dynamics simulations based on the SAFT-γ Mie force field. Computer Physics Communications, 212, 161–179. doi:10.1016/j.cpc.2016.07.035) a framework enabling coarse-grained molecular dynamics simulations based on the SAFT-γ Mie force field.

A series of papers have  been devoted to the development and application of the SAFT-γ CG force fields:

  1. Carbon dioxide (CO2) Avendaño, Carlos, Thomas Lafitte, Amparo Galindo, Claire S Adjiman, George Jackson, and Erich A Müller. “SAFT-Γ Force Field for the Simulation of Molecular Fluids. 1. a Single-Site Coarse Grained Model of Carbon Dioxide.”  J.  Phys. Chem. B 115, (2011): 11154–69. doi:10.1021/jp204908d. We have now an improved 2-site models for CO2 here:  L. Zheng, F. Bresme, J. P. M. Trusler, and E. A. Müller, “Employing SAFT Coarse-Grained Force Fields for the Molecular Simulation of Thermodynamic and Transport Properties of CO 2– n-Alkane Mixtures,” J.  Chem Eng. Data, 65, (2019) 1159–1171. DOI: 10.1021/acs.jced.9b00534
  2. Carbon tetrafluoride (CF4) ; Sulfur hexafluoride (SF6),  n- decane (n-C10H22) , n-eicosane (n-C20H42),  2,3,3,3-tetrafluoro-1-propene (HFO-1234yf)) Avendaño, Carlos, Thomas Lafitte, Claire S Adjiman, Amparo Galindo, Erich A Müller, and George Jackson. “SAFT-Γ Force Field for the Simulation of Molecular Fluids: 2. Coarse-Grained Models of Greenhouse Gases, Refrigerants, and Long Alkanes.”  J.  Phys. Chem. B 117, (2013): 2717–33. doi:10.1021/jp306442b.
  3. Benzene (C6H6), n-decylbenzene Lafitte, Thomas, Carlos Avendaño, Vasileios Papaioannou, Amparo Galindo, Claire S Adjiman, George Jackson, and Erich A Müller. “SAFT- Γforce Field for the Simulation of Molecular Fluids: 3. Coarse-Grained Models of Benzene and Hetero-Group Models of N-Decylbenzene.” Molecular Physics 110, (2012): 1189–1203. doi:10.1080/00268976.2012.662303.
  4. Water (H2O) Lobanova, Olga, Carlos Avendaño, Thomas Lafitte, Erich A Müller, and George Jackson. “SAFT-Γ Force Field for the Simulation of Molecular Fluids: 4. a Single-Site Coarse-Grained Model of Water Applicable Over a Wide Temperature Range.” Molecular Physics 113, (2015): 1228–49. doi:10.1080/00268976.2015.1004804.
  5. Alkanes (heteronuclear model)  S. Rahman, O. Lobanova, G. Jiménez-Serratos, C. Braga, V. Raptis, E. A. Müller, G. Jackson, C. Avendaño, and A. Galindo, “SAFT‐γ Force Field for the Simulation of Molecular Fluids. 5. Hetero- Group Coarse-Grained Models of Linear Alkanes and the Importance of Intramolecular Interactions,” J Phys. Chem. B, 122, (2018): 9161–9177. doi:10.102/acs.ppcb.8b04095.
  6. Water/CO2/alkane mixtures Lobanova, Olga, Andrés Mejía, George Jackson, and Erich A Müller. “SAFT-γ Force Field for the Simulation of Molecular Fluids 6: Binary and Ternary Mixtures Comprising Water, Carbon Dioxide, and N-Alkanes.” J. Chem. Thermodyn. 93, (2016): 320–36. doi:10.1016/j.jct.2015.10.011.
  7. CO2 - water Müller, Erich A, and Andrés Mejía. “Resolving Discrepancies in the Measurements of the Interfacial Tension for the CO 2+ H 2O Mixture by Computer Simulation.”  J.  Phys. Chem Letters 5 (2014): 1267–71. doi:10.1021/jz500417w.
  8. Contact angle of water Santiso, Erik, Carmelo Herdes, and Erich Muller. “On the Calculation of Solid-Fluid Contact Angles From Molecular Dynamics.” Entropy 15 (2013): 3734–45. doi:10.3390/e15093734.
  9. Light Gases and crude oils Herdes, Carmelo, Tim S Totton, and Erich A Müller. “Coarse Grained Force Field for the Molecular Simulation of Natural Gases and Condensates.” Fluid Phase Equilibria 406 (2015): 91–100. doi:10.1016/j.fluid.2015.07.014.
  10. Perfluorooctane ( adsoprtion on carbons) Herdes, Carmelo, Forte, Esther, George Jackson, and Erich A Müller  " Predicting the adsorption of n-perfluorohexane in BAM P109 standard activated carbon by molecular simulation using SAFT-γ Mie coarse-grained force fields" Adsorp. Sci. Technol. , 34 (2016)
  11. Light-switching surfactants Herdes, Carmelo, Erik E Santiso, Craig James, Julian Eastoe, and Erich A Müller. “Modelling the Interfacial Behaviour of Dilute Light-Switching Surfactant Solutions.” J. Colloid  Interf. Sci. 445, (2015): 16–23. doi:10.1016/j.jcis.2014.12.040.
  12. Super spreading surfactants, including parameters for trisiloxanes Theodorakis, Panagiotis E, Erich A Müller, Richard Craster, and Omar K Matar. “Superspreading: Mechanisms and Molecular Design.” Langmuir 31,(2015): 2304–9. doi:10.1021/la5044798.; See also Theodorakis, Panagiotis E, Erich A Müller  Richard Craster, and Omar K Matar  “Modelling the Superspreading of Surfactant-Laden Droplets with Computer Simulation.” Soft Matter 11 (2015): 9254–61. doi:10.1039/C5SM02090E.
  13. Perfluoroalkyalkanes Morgado, Pedro, Olga Lobanova, Erich A Müller, George Jackson, Miguel Almeida, and Eduardo J M Filipe. “SAFT-Γ Force Field for the Simulation of Molecular Fluids: 8. Hetero-Segmented Coarse-Grained Models of Perfluoroalkylalkanes Assessed with New Vapour–Liquid Interfacial Tension Data.” Molecular Physics, 2016, 1–18. doi:10.1080/00268976.2016.1218077.
  14. Water-oil interfacial tensions  Herdes, Carmelo, Åsmund Ervik, Andrés Mejía, and Erich A Müller. “Prediction of the Water/Oil Interfacial Tension From Molecular Simulations Using the Coarse-Grained SAFT--Gamma; Mie Force Field.” Fluid Phase Equilibria,  476, (2108) 9–15. doi:10.1016/j.fluid.2017.06.016.
  15. Polystyrene in solvents: Jiménez-Serratos, Guadalupe, Carmelo Herdes, Andrew J. Haslam, George Jackson, and Erich A Müller. “Group Contribution Coarse-Grained Molecular Simulations of Polystyrene Melts and Polystyrene Solutions in Alkanes Using the SAFT-Γ Force Field.” Macromolecules, Macromolecules, 2017, 50 (12), pp 4840–4853. doi:10.1021/acs.macromol.6b02072.
  16. Asphaltene like molecules and groups and PAH:  G. Jiménez-Serratos, T. S. Totton, G. Jackson, and E. A. Müller, “Aggregation Behavior of Model Asphaltenes Revealed from Large- Scale Coarse-Grained Molecular Simulations,” J Phys. Chem. B, 123, (2019): 2380–2396. DOI: 10.1021/acs.jpcb.8b12295 Ser also for Pyrene C. R. Wand, M. Fayaz-Torshizi, G. Jimenez-Serratos, E. A. Muller, and D. Frenkel, “Solubilities of pyrene in organic solvents: Comparison between chemical potential calculations using a cavity-based method and direct coexistence simulations,” J. Chem. Thermodynamics, 131, (2019): 620–629. https://doi.org/10.1016/j.jct.2018.11.029
  17. Cryogenic fluids, incorporating quantum corrections ( He, Ne, H2, D2 ):  A. Aasen, M. Hammer, Å. Ervik, E. A. Müller, and Ø. Wilhelmsen, “Equation of state and force fields for Feynman–Hibbs-corrected Mie fluids. I. Application to pure helium, neon, hydrogen, and deuterium,” J Chem Phys, 151 (2019) 064508. doi: 10.1063/1.5111364 and  A. Aasen, M. Hammer, E. A. Müller, and Ø. Wilhelmsen, “Equation of state and force fields for Feynman–Hibbs-corrected Mie fluids. II. Application to mixtures of helium, neon, hydrogen, and deuterium,” J Chem Phys, 152 (2020) 074507 doi: 10.1063/1.5136079
  18. Polymers  C. C. Walker, J. Genzer, and E. E. Santiso, “Development of a fused-sphere SAFT-γ Mie force field for poly(vinyl alcohol) and poly(ethylene),” J Chem Phys, 150, (2019) 034901–16.;  Fayaz‐Torshizi, M. & Müller, E. A. "Coarse‐Grained Molecular Simulation of Polymers Supported by the Use of the SAFT‐γ Mie Equation of State". Macromol Theor Simul, 31, 2100031 (2022) doi:10.1002/mats.202100031.
  19. Polyols    A. K. Pervaje, J. C. Tilly, D. L. Inglefield Jr, R. J. Spontak, S. A. Khan, and E. E. Santiso, “Modeling Polymer Glass Transition Properties from Empirical Monomer Data with the SAFT-γ Mie Force Field,” Macromolecules,  51, (2018) 9526–9537.
  20. Waxes  S. Shahruddin, G. J. X. nez-Serratos, G. J. P. Britovsek, O. K. Matar, and E. A. Müller, “Fluid-solid phase transition of n-alkane mixtures: Coarse-grained molecular dynamics simulations and diffusion-ordered spectroscopy nuclear magnetic resonance,” Sci Rep,  9, (2019) 1002, doi:/10.1038/s41598-018-37799-7
  21. Liquid Crystals T. D. Potter, J. Tasche, E. L. Barrett, M. Walker, and M. R. Wilson, “Development of new coarse-grained models for chromonic liquid crystals: insights from top-down approaches,” Liquid Crystals, 44, 1979 (2017).  doi:/10.1080/02678292.2017.1342005  Bolaamphiphiles Fayaz-Torshizi, M. & Müller, E. A. Coarse-grained molecular dynamics study of the self-assembly of polyphilic bolaamphiphiles using the SAFT-γ Mie force field. Mol Syst Des Eng 6, 594–608 (2021). doi: 10.1039/d1me00021g
  22. Three-phase systems (water-hexane) Alonso, G., Chaparro, G., Cartes, M., Müller, E. A. & Mejía, A. Probing the Interfacial Behavior of Type IIIa Binary Mixtures Along the Three-Phase Line Employing Molecular Thermodynamics. Molecules 25, 1499 (2020). doi: 10.3390/molecules25071499