The bioavailability of poorly water-soluble active pharmaceutical ingredients (APIs) can be improved via the formulation of an amorphous solid dispersion (ASD), where the API is incorporated into a suitable polymeric carrier. Optimal carriers that exhibit good compatibility (i.e., solubility and miscibility) with given APIs are typically identified through experimental means, which are routinely labor- and cost-inefficient. Therefore, the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state, a popular thermodynamic model in pharmaceutical applications, is examined in terms of its performance regarding the computational pure prediction of API-polymer compatibility based on activity coefficients (API fusion properties were taken from experiments) without any binary interaction parameters fitted to API-polymer experimental data (that is, kij = 0 in all cases). This kind of prediction does not need any experimental binary information and has been underreported in the literature so far, as the routine modeling strategy used in the majority of the existing PC-SAFT applications to ASDs comprised the use of nonzero kij values. The predictive performance of PC-SAFT was systematically and thoroughly evaluated against reliable experimental data for almost 40 API-polymer combinations. We also examined the effect of different sets of PC-SAFT parameters for APIs on compatibility predictions. Quantitatively, the total average error calculated over all systems was approximately 50% in the weight fraction solubility of APIs in polymers, regardless of the specific API parametrization. The magnitude of the error for individual systems was found to vary significantly from one system to another. Interestingly, the poorest results were obtained for systems with self-associating polymers such as poly(vinyl alcohol). Such polymers can form intramolecular hydrogen bonds, which are not accounted for in the PC-SAFT variant routinely applied to ASDs (i.e., that used in this work). However, the qualitative ranking of polymers with respect to their compatibility with a given API was reasonably predicted in many cases. It was also predicted correctly that some polymers always have better compatibility with the APIs than others. Finally, possible future routes to improve the cost-performance ratio of PC-SAFT in terms of parametrization are discussed.

Department of Physical Chemistry Faculty of Chemical Engineering University of Chemistry and Technology Prague Technická 5 166 28 Prague 6 Czech Republic

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Brouwers J.; Brewster M. E.; Augustijns P. Supersaturating Drug Delivery Systems: The Answer to Solubility-Limited Oral Bioavailability?. J. Pharm. Sci. 2009, 98, 2549–2572. 10.1002/jps.21650. PubMed DOI

Alonzo D. E.; Zhang G. G. Z.; Zhou D. L.; Gao Y.; Taylor L. S. Understanding the Behavior of Amorphous Pharmaceutical Systems during Dissolution. Pharm. Res. 2010, 27, 608–618. 10.1007/s11095-009-0021-1. PubMed DOI

Zografi G.; Newman A. Interrelationships Between Structure and the Properties of Amorphous Solids of Pharmaceutical Interest. J. Pharm. Sci. 2017, 106, 5–27. 10.1016/j.xphs.2016.05.001. PubMed DOI

Flory P. J.Principles of Polymer Chemistry ;Cornell University Press: Ithaca, NY, USA, 1953.

Thakral S.; Thakral N. K. Prediction of Drug-Polymer Miscibility Through the Use of Solubility Parameter Based Flory-Huggins Interaction Parameter and the Experimental Validation: PEG as Model Polymer. J. Pharm. Sci. 2013, 102, 2254–2263. 10.1002/jps.23583. PubMed DOI

Bansal K.; Baghel U. S.; Thakral S. Construction and Validation of Binary Phase Diagram for Amorphous Solid Dispersion Using Flory-Huggins Theory. AAPS PharmSciTech 2016, 17, 318–327. 10.1208/s12249-015-0343-8. PubMed DOI PMC

Erlebach A.; Ott T.; Otzen C.; Schubert S.; Czaplewska J.; Schubert U. S.; Sierka M. Thermodynamic Compatibility of Actives Encapsulated into PEG-PLA Nanoparticles: In Silico Predictions and Experimental Verification. J. Comput. Chem. 2016, 37, 2220–2227. 10.1002/jcc.24449. PubMed DOI

Xiang T. X.; Anderson B. D. Molecular Dynamics Simulation of Amorphous Hydroxypropylmethylcellulose and Its Mixtures With Felodipine and Water. J. Pharm. Sci. 2017, 106, 803–816. 10.1016/j.xphs.2016.10.026. PubMed DOI

Chakravarty P.; Lubach J. W.; Hau J.; Nagapudi K. A Rational Approach Towards Development of Amorphous Solid Dispersions: Experimental and Computational Techniques. Int. J. Pharm. 2017, 519, 44–57. 10.1016/j.ijpharm.2017.01.003. PubMed DOI

Turpin E. R.; Taresco V.; Al-Hachami W. A.; Booth J.; Treacher K.; Tomasi S.; Alexander C.; Burley J.; Laughton C. A.; Garnett M. C. In Silico Screening for Solid Dispersions: The Trouble with Solubility Parameters and χFH. Mol. Pharmaceutics 2018, 15, 4654–4667. 10.1021/acs.molpharmaceut.8b00637. PubMed DOI

Anderson B. D. Predicting Solubility/Miscibility in Amorphous Dispersions: It Is Time to Move Beyond Regular Solution Theories. J. Pharm. Sci. 2018, 107, 24–33. 10.1016/j.xphs.2017.09.030. PubMed DOI

DeBoyace K.; Wildfong P. L. D. The Application of Modeling and Prediction to the Formation and Stability of Amorphous Solid Dispersions. J. Pharm. Sci. 2018, 107, 57–74. 10.1016/j.xphs.2017.03.029. PubMed DOI

Miquelard-Garnier G.; Roland S. Beware of the Flory Parameter to Characterize Polymer-Polymer Interactions: A Critical Reexamination of the Experimental Literature. Eur. Polym. J. 2016, 84, 111–124. 10.1016/j.eurpolymj.2016.09.009. DOI

Abbott S. Solubility, Similarity, and Compatibility: A General-Purpose Theory for the Formulator. Curr. Opin. Colloid Interface Sci. 2020, 48, 65–76. 10.1016/j.cocis.2020.03.007. DOI

Niederquell A.; Wyttenbach N.; Kuentz M. New Prediction Methods for Solubility Parameters Based on Molecular Sigma Profiles Using Pharmaceutical Materials. Int. J. Pharm. 2018, 546, 137–144. 10.1016/j.ijpharm.2018.05.033. PubMed DOI

Gupta J.; Nunes C.; Vyas S.; Jonnalagadda S. Prediction of Solubility Parameters and Miscibility of Pharmaceutical Compounds by Molecular Dynamics Simulations. J. Phys. Chem. B 2011, 115, 2014–2023. 10.1021/jp108540n. PubMed DOI

Huynh L.; Neale C.; Pomes R.; Allen C. Computational Approaches to the Rational Design of Nanoemulsions, Polymeric Micelles, and Dendrimers for Drug Delivery. Nanomedicine 2012, 8, 20–36. 10.1016/j.nano.2011.05.006. PubMed DOI

Maniruzzaman M.; Morgan D. J.; Mendham A. P.; Pang J. Y.; Snowden M. J.; Douroumis D. Drug-Polymer Intermolecular Interactions in Hot-Melt Extruded Solid Dispersions. Int. J. Pharm. 2013, 443, 199–208. 10.1016/j.ijpharm.2012.11.048. PubMed DOI

Alsenz J.; Kuentz M. From Quantum Chemistry to Prediction of Drug Solubility in Glycerides. Mol. Pharmaceutics 2019, 16, 4661–4669. 10.1021/acs.molpharmaceut.9b00801. PubMed DOI

Kříž K.; Řezáč J. Benchmarking of Semiempirical Quantum-Mechanical Methods on Systems Relevant to Computer-Aided Drug Design. J. Chem. Inf. Model. 2020, 60, 1453–1460. 10.1021/acs.jcim.9b01171. PubMed DOI

Han R.; Xiong H.; Ye Z. Y. F.; Yang Y. L.; Huang T. H.; Jing Q. F.; Lu J. H.; Pan H.; Ren F. Z.; Ouyang D. F. Predicting Physical Stability of Solid Dispersions by Machine Learning Techniques. J. Controlled Release 2019, 311, 16–25. 10.1016/j.jconrel.2019.08.030. PubMed DOI

Gao H. L.; Wang W.; Dong J.; Ye Z. Y. F.; Ouyang D. F. An Integrated Computational Methodology with Data-Driven Machine Learning, Molecular Modeling and PBPK Modeling to Accelerate Solid Dispersion Formulation Design. Eur. J. Pharm. Biopharm. 2021, 158, 336–346. 10.1016/j.ejpb.2020.12.001. PubMed DOI

Gross J.; Sadowski G. Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules. Ind. Eng. Chem. Res. 2001, 40, 1244–1260. 10.1021/ie0003887. DOI

Gross J.; Sadowski G. Application of the Perturbed-Chain SAFT Equation of State to Associating Systems. Ind. Eng. Chem. Res. 2002, 41, 5510–5515. 10.1021/ie010954d. DOI

Ruether F.; Sadowski G. Modeline the Solubility of Pharmaceuticals in Pure Solvents and Solvent Mixtures for Drug Process Design. J. Pharm. Sci. 2009, 98, 4205–4215. 10.1002/jps.21725. PubMed DOI

Spyriouni T.; Krokidis X.; Economou I. G. Thermodynamics of Pharmaceuticals: Prediction of Solubility in Pure and Mixed Solvents with PC-SAFT. Fluid Phase Equilib. 2011, 302, 331–337. 10.1016/j.fluid.2010.08.029. DOI

Klajmon M. Investigating Various Parametrization Strategies for Pharmaceuticals within the PC-SAFT Equation of State. J. Chem. Eng. Data 2020, 65, 5753–5767. 10.1021/acs.jced.0c00707. DOI

Klajmon M. Purely Predicting the Pharmaceutical Solubility: What to Expect from PC-SAFT and COSMO-RS?. Mol. Pharmaceutics 2022, 19, 4212–4232. 10.1021/acs.molpharmaceut.2c00573. PubMed DOI

Laube F. S.; Sadowski G. Predicting the Extraction Behavior of Pharmaceuticals. Ind. Eng. Chem. Res. 2014, 53, 865–870. 10.1021/ie403284y. DOI

Brinkmann J.; Becker I.; Kroll P.; Luebbert C.; Sadowski G. Predicting the API Partitioning Between Lipid-Based Drug Delivery Systems and Water. Int. J. Pharm. 2021, 595, 120266.10.1016/j.ijpharm.2021.120266. PubMed DOI

Veith H.; Schleinitz M.; Schauerte C.; Sadowski G. Thermodynamic Approach for Co-Crystal Screening. Cryst. Growth. Des. 2019, 19, 3253–3264. 10.1021/acs.cgd.9b00103. DOI

Prudic A.; Ji Y. H.; Sadowski G. Thermodynamic Phase Behavior of API/Polymer Solid Dispersions. Mol. Pharmaceutics 2014, 11, 2294–2304. 10.1021/mp400729x. PubMed DOI

Prudic A.; Ji Y.; Luebbert C.; Sadowski G. Influence of Humidity on the Phase Behavior of API/Polymer Formulations. Eur. J. Pharm. Biopharm. 2015, 94, 352–362. 10.1016/j.ejpb.2015.06.009. PubMed DOI

Luebbert C.; Huxoll F.; Sadowski G. Amorphous-Amorphous Phase Separation in API/Polymer Formulations. Molecules 2017, 22, 296.10.3390/molecules22020296. PubMed DOI PMC

Dohrn S.; Luebbert C.; Lehmkemper K.; Kyeremateng S. O.; Degenhardt M.; Sadowski G. Solvent Influence on the Phase Behavior and Glass Transition of Amorphous Solid Dispersions. Eur. J. Pharm. Biopharm. 2021, 158, 132–142. 10.1016/j.ejpb.2020.11.002. PubMed DOI

Iemtsev A.; Hassouna F.; Mathers A.; Klajmon M.; Dendisová M.; Malinová L.; Školáková T.; Fulem M. Physical Stability of Hydroxypropyl Methylcellulose-Based Amorphous Solid Dispersions: Experimental and Computational Study. Int. J. Pharm. 2020, 589, 119845.10.1016/j.ijpharm.2020.119845. PubMed DOI

Mathers A.; Hassouna F.; Klajmon M.; Fulem M. Comparative Study of DSC-Based Protocols for API-Polymer Solubility Determination. Mol. Pharmaceutics 2021, 18, 1742–1757. 10.1021/acs.molpharmaceut.0c01232. PubMed DOI

Iemtsev A.; Zemánková A.; Hassouna F.; Mathers A.; Klajmon M.; Slámová M.; Malinová L.; Fulem M. Ball Milling and Hot-Melt Extrusion of Indomethacin-L-Arginine-Vinylpyrrolidone-Vinyl Acetate Copolymer: Solid-State Properties and Dissolution Performance. Int. J. Pharm. 2022, 613, 121424.10.1016/j.ijpharm.2021.121424. PubMed DOI

Iemtsev A.; Hassouna F.; Klajmon M.; Mathers A.; Fulem M. Compatibility of Selected Active Pharmaceutical Ingredients with Poly(D, L-Lactide-Co-Glycolide): Computational and Experimental Study. Eur. J. Pharm. Biopharm. 2022, 179, 232–245. 10.1016/j.ejpb.2022.09.013. DOI

Klamt A. Conductor-Like Screening Model for Real Solvents - A New Approach to the Quantitative Calculation of Solvation Phenomena. J. Phys. Chem. 1995, 99, 2224–2235. 10.1021/j100007a062. DOI

Bell I. H.; Mickoleit E.; Hsieh C. M.; Lin S. T.; Vrabec J.; Breitkopf C.; Jager A. A Benchmark Open-Source Implementation of COSMO-SAC. J. Chem. Theory Comput. 2020, 16, 2635–2646. 10.1021/acs.jctc.9b01016. PubMed DOI PMC

Pecina A.; Eyrilmez S. M.; Kopruluoglu C.; Miriyala V. M.; Lepsik M.; Fanfrlik J.; Rezac J.; Hobza P. SQM/COSMO Scoring Function: Reliable Quantum-Mechanical Tool for Sampling and Ranking in Structure-Based Drug Design. Chempluschem 2020, 85, 2360–2361. 10.1002/cplu.202000627. PubMed DOI

Thakore S. D.; Akhtar J.; Jain R.; Paudel A.; Bansal A. K. Analytical and Computational Methods for the Determination of Drug-Polymer Solubility and Miscibility. Mol. Pharmaceutics 2021, 18, 2835–2866. 10.1021/acs.molpharmaceut.1c00141. PubMed DOI

Iemtsev A.; Klajmon M.; Hassouna F.; Fulem M. Effect of Copolymer Properties on the Phase Behavior of Ibuprofen-PLA/PLGA Mixtures. Pharmaceutics 2023, 15, 645.10.3390/pharmaceutics15020645. PubMed DOI PMC

Brady J.; Dürig T.; Lee P. I.; Li J. X. In Developing Solid Oral Dosage Forms ,2nd ed.; Qiu Y., Chen Y., Zhang G. G. Z., Yu L., Mantri R. V., Eds.; Academic Press: Boston, MA, USA, 2017.

BASF, Soluplus® Technical Information (03_90801e-06). https://pharma.basf.com/products/soluplus (accessed January 10, 2023).

Prausnitz J. M.; Lichtenthaler R. N.; de Azevedo E. G.. Molecular Thermodynamics of Fluid-Phase Equilibria ,3rd ed.; Prentice Hall: Upper Saddle River, NJ, USA, 1999.

Yalkowsky S. H.; Alantary D. Estimation of Melting Points of Organics. J. Pharm. Sci. 2018, 107, 1211–1227. 10.1016/j.xphs.2017.12.013. PubMed DOI

Wyttenbach N.; Niederquell A.; Kuentz M. Machine Estimation of Drug Melting Properties and Influence on Solubility Prediction. Mol. Pharmaceutics 2020, 17, 2660–2671. 10.1021/acs.molpharmaceut.0c00355. PubMed DOI

Mathers A.Prediction of Drug Solubility in Polymer: Combined Experimental and Computational Study. Doctoral dissertation, University of Chemistry and Technology, Prague, 2022.

Paus R.; Prudic A.; Ji Y. Influence of Excipients on Solubility and Dissolution of Pharmaceuticals. Int. J. Pharm. 2015, 485, 277–287. 10.1016/j.ijpharm.2015.03.004. PubMed DOI

Štejfa V.; Pokorný V.; Mathers A.; Růžička K.; Fulem M. Heat Capacities of Selected Active Pharmaceutical Ingredients. J. Chem. Thermodyn. 2021, 163, 106585.10.1016/j.jct.2021.106585. DOI

Luebbert C.; Sadowski G. In-Situ Determination of Crystallization Kinetics in ASDs via Water Sorption Experiments. Eur. J. Pharm. Biopharm. 2018, 127, 183–193. 10.1016/j.ejpb.2018.02.028. PubMed DOI

Dinh M.Experimental Screening of Anticancer Drug-Biodegradable Polymer Compatibility; Bachelor thesis, University of Chemistry and Technology, Prague, 2022.

Neau S. H.; Bhandarkar S. V.; Hellmuth E. W. Differential Molar Heat Capacities to Test Ideal Solubility Estimations. Pharm. Res. 1997, 14, 601–605. 10.1023/A:1012148910975. PubMed DOI

Simoes R. G.; Bernardes C. E. S.; Diogo H. P.; Agapito F.; Minas da Piedade M. E. Energetics and Structure of Simvastatin. Mol. Pharmaceutics 2013, 10, 2713–2722. 10.1021/mp400132r. PubMed DOI

von Solms N.; Michelsen M. L.; Kontogeorgis G. M. Applying Association Theories to Polar Fluids. Ind. Eng. Chem. Res. 2004, 43, 1803–1806. 10.1021/ie034243m. DOI

Huang S. H.; Radosz M. Equation of State for Small, Large, Polydisperse, and Associating Molecules: Extension to Fluid Mixtures. Ind. Eng. Chem. Res. 1991, 30, 1994–2005. 10.1021/ie00056a050. DOI

Gross J.; Spuhl O.; Tumakaka F.; Sadowski G. Modeling Copolymer Systems Using the Perturbed-Chain SAFT Equation of State. Ind. Eng. Chem. Res. 2003, 42, 1266–1274. 10.1021/ie020509y. DOI

Tumakaka F.; Gross J.; Sadowski G. Modeling of Polymer Phase Equilibria Using Perturbed-Chain SAFT. Fluid Phase Equilib. 2002, 194–197, 541–551. 10.1016/S0378-3812(01)00785-3. DOI

Kleiner M.; Sadowski G. Modeling of Polar Systems Using PCP-SAFT: An Approach to Account for Induced-Association Interactions. J. Phys. Chem. C 2007, 111, 15544–15553. 10.1021/jp072640v. DOI

Cocchi G.; De Angelis M. G.; Sadowski G.; Doghieri F. Modelling Polylactide/Water/Dioxane Systems for TIPS Scaffold Fabrication. Fluid Phase Equilib. 2014, 374, 1–8. 10.1016/j.fluid.2014.04.007. DOI

Prudic A.; Lesniak A. K.; Ji Y. H.; Sadowski G. Thermodynamic Phase Behaviour of Indomethacin/PLGA Formulations. Eur. J. Pharm. Biopharm. 2015, 93, 88–94. 10.1016/j.ejpb.2015.01.029. PubMed DOI

Prudic A.; Kleetz T.; Korf M.; Ji Y. H.; Sadowski G. Influence of Copolymer Composition on the Phase Behavior of Solid Dispersions. Mol. Pharmaceutics 2014, 11, 4189–4198. 10.1021/mp500412d. PubMed DOI

Paus R.; Ji Y. H.; Vahle L.; Sadowski G. Predicting the Solubility Advantage of Amorphous Pharmaceuticals: A Novel Thermodynamic Approach. Mol. Pharmaceutics 2015, 12, 2823–2833. 10.1021/mp500824d. PubMed DOI

Aceves-Hernandez J. M.; Hinojosa-Torres J.; Nicolas-Vazquez I.; Ruvalcaba R. M.; Garcia R. M. L. Solubility of Simvastatin: A Theoretical and Experimental Study. J. Mol. Struct. 2011, 995, 41–50. 10.1016/j.molstruc.2011.03.048. DOI

Pokorný V.; Štejfa V.; Klajmon M.; Fulem M.; Růžička K. Vapor Pressures and Thermophysical Properties of 1-Heptanol, 1-Octanol, 1-Nonanol, and 1-Decanol: Data Reconciliation and PC-SAFT Modeling. J. Chem. Eng. Data 2021, 66, 805–821. 10.1021/acs.jced.0c00878. DOI

Press W. H.; Teukolsky S. A.; Vetterling W. T.; Flannery B. P.. Numerical Recipes: The Art of Scientific Computing ,3rd ed.; Cambridge University Press: Cambridge, UK, 2007.

Marsac P. J.; Shamblin S. L.; Taylor L. S. Theoretical and Practical Approaches for Prediction of Drug-Polymer Miscibility and Solubility. Pharm. Res. 2006, 23, 2417–2426. 10.1007/s11095-006-9063-9. PubMed DOI

Marsac P. J.; Li T.; Taylor L. S. Estimation of Drug-Polymer Miscibility and Solubility in Amorphous Solid Dispersions Using Experimentally Determined Interaction Parameters. Pharm. Res. 2009, 26, 139–151. 10.1007/s11095-008-9721-1. PubMed DOI

Mathers A.; Hassouna F.; Malinová L.; Merna J.; Růžička K.; Fulem M. Impact of Hot-Melt Extrusion Processing Conditions on Physicochemical Properties of Amorphous Solid Dispersions Containing Thermally Labile Acrylic Copolymer. J. Pharm. Sci. 2020, 109, 1008–1019. 10.1016/j.xphs.2019.10.005. PubMed DOI

Mathers A.Various API–Polymer Solubility Datasets Determined via Differential Scanning Calorimetry; Unpublished raw data, University of Chemsitry and Technology, Prague, 2022.

Mathers A.; Pechar M.; Hassouna F.; Fulem M. API Solubility in Semi-Crystalline Polymer: Kinetic and Thermodynamic Phase Behavior of PVA-Based Solid Dispersions. Int. J. Pharm. 2022, 623, 121855.10.1016/j.ijpharm.2022.121855. PubMed DOI

Bao Y.; Huang X. B.; Xu J.; Cui S. X. Effect of Intramolecular Hydrogen Bonds on the Single-Chain Elasticity of Poly(Vinyl Alcohol): Evidencing the Synergistic Enhancement Effect at the Single-Molecule Level. Macromolecules 2021, 54, 7314–7320. 10.1021/acs.macromol.1c01251. DOI

Li H. B.; Zhang W. K.; Xu W. Q.; Zhang X. Hydrogen Bonding Governs the Elastic Properties of Poly(Vinyl Alcohol) in Water: Single-Molecule Force Spectroscopic Studies of PVA by AFM. Macromolecules 2000, 33, 465–469. 10.1021/ma990878e. DOI

Paradossi G.; Finelli I.; Natali F.; Telling M. T. F.; Chiessi E. Polymer and Water Dynamics in Poly(Vinyl Alcohol)/Poly(Methacrylate) Networks. A Molecular Dynamics Simulation and Incoherent Neutron Scattering Investigation. Polymers 2011, 3, 1805–1832. 10.3390/polym3041805. DOI

Wu Q.; Wang Y. S. Research Status of Polyvinyl Alcohol-Based Chelating Materials. IOP Conf. Ser. Earth Env. Sci. 2019, 330, 04204410.1088/1755-1315/330/4/042044. DOI

Tesei G.; Paradossi G.; Chiessi E. Poly(Vinyl Alcohol) Oligomer in Dilute Aqueous Solution: A Comparative Molecular Dynamics Simulation Study. J. Phys. Chem. B 2012, 116, 10008–10019. 10.1021/jp305296p. PubMed DOI

Arai K.; Okuzono M.; Shikata T. Reason for the High Solubility of Chemically Modified Poly(Vinyl Alcohol)s in Aqueous Solution. Macromolecules 2015, 48, 1573–1578. 10.1021/ma502602r. DOI

Avlund A. S.; Kontogeorgis G. M.; Chapman W. G. Intramolecular Association within the SAFT Framework. Mol. Phys. 2011, 109, 1759–1769. 10.1080/00268976.2011.589990. DOI

Avlund A. S.; Kontogeorgis G. M.; Michelsen M. L. Application of Simplified PC-SAFT to Glycol Ethers. Ind. Eng. Chem. Res. 2012, 51, 547–555. 10.1021/ie2011406. DOI

Gross J.; Vrabec J. An Equation-of-State Contribution for Polar Components: Dipolar Molecules. AIChE J. 2006, 52, 1194–1204. 10.1002/aic.10683. DOI

Nezbeda I. On Molecular-Based Equations of State: Perturbation Theories, Simple Models, and SAFT Modeling. Front. Phys. 2020, 8, 287.10.3389/fphy.2020.00287. DOI

Lehmkemper K.; Kyeremateng S. O.; Heinzerling O.; Degenhardt M.; Sadowski G. Impact of Polymer Type and Relative Humidity on the Long-Term Physical Stability of Amorphous Solid Dispersions. Mol. Pharmaceutics 2017, 14, 4374–4386. 10.1021/acs.molpharmaceut.7b00492. PubMed DOI

Luebbert C.; Sadowski G. Moisture-Induced Phase Separation and Recrystallization in Amorphous Solid Dispersions. Int. J. Pharm. 2017, 532, 635–646. 10.1016/j.ijpharm.2017.08.121. PubMed DOI

Ge K.; Ji Y. H. Novel Computational Approach by Combining Machine Learning with Molecular Thermodynamics for Predicting Drug Solubility in Solvents. Ind. Eng. Chem. Res. 2021, 60, 9259–9268. 10.1021/acs.iecr.1c00998. DOI

Kuentz M.; Bergstrom C. A. S. Synergistic Computational Modeling Approaches as Team Players in the Game of Solubility Predictions. J. Pharm. Sci. 2021, 110, 22–34. 10.1016/j.xphs.2020.10.068. PubMed DOI

Habicht J.; Brandenbusch C.; Sadowski G. Predicting PC-SAFT Pure-Component Parameters by Machine Learning Using a Molecular Fingerprint as Key Input. Fluid Phase Equilib. 2023, 565, 113657.10.1016/j.fluid.2022.113657. DOI

Felton K.; Rasßpe-Lange L.; Rittig J.; Leonhard K.; Mitsos A.; Meyer-Kirschner J.; Knösche C.; Lapkin A.. ML-SAFT: A Machine Learning Framework for PCP-SAFT Parameter Prediction. ChemRxiv 2023,10.26434/chemrxiv-2023-j1z06. DOI

Kaminski S.; Leonhard K. SEPP: Segment-Based Equation of State Parameter Prediction. J. Chem. Eng. Data 2020, 65, 5830–5843. 10.1021/acs.jced.0c00733. DOI

COSMOPharm: Drug-Polymer Compatibility of Pharmaceutical Amorphous Solid Dispersions from COSMO-SAC