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A Machine Learning Study of Polymer-Solvent Interactions

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Abstract

Polymer-solvent interaction is a fundamentally important concept routinely described by the Flory-Huggins interaction (χ), Hildebrand solubility(✉δ) and the relative energy difference (RED) determined from Hansen solubility in experimental, theoretical and simulation studies. Here we performed a machine learning study based on a comprehensive and representative dataset covering the interaction pairs from 81 polymers and 1221 solvents. The regression models provide the coefficients of determination in the range of 0.86–0.94 and the classification models deliver the area under the receiver operating characteristic curve (AUCs) better than 0.93. These models were integrated into a newly developed software polySML-PSI. Important features including LogP, molar volume and dipole are identified, and their non-linear, nonmonotonic contributions to polymer-solvent interactions are presented. The widely known “like-dissolve-like” rule and two broadly used empirical equations to estimate χ as a function of temperature or Hansen solubility are also evaluated, and the polymer-specified constants are presented. This study provides a quantitative reference and a tool to understand and utilize the concept of polymer-solvent interactions.

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References

  1. Flory, P. J. Thermodynamics of high polymer solutions. J. Chem. Phys. 1942, 10, 51–61.

    Article  CAS  Google Scholar 

  2. Flory, P. J. Thermodynamics of high polymer solutions. J. Chem. Phys. 1941, 9, 660–660.

    Article  CAS  Google Scholar 

  3. Huggins, M. L. Some properties of solutions of long-chain compounds. J. Phys. Chem. 1942, 46, 151–158.

    Article  CAS  Google Scholar 

  4. Huggins, M. L. The viscosity of dilute solutions of long-chain molecules. IV. Dependence on concentration. J. Am. Chem. Soc. 1942, 64, 2716–2718.

    Article  CAS  Google Scholar 

  5. Blanks, R. F.; Prausnitz, J. Thermodynamics of polymer solubility in polar and nonpolar systems. Ind. Eng. Chem. Fundam. 1964, 3, 1–8.

    Article  CAS  Google Scholar 

  6. Bae, Y. H.; Okano, T.; Kim, S. W. Temperature dependence of swelling of crosslinked poly(N, N′-alkyl substituted acrylamides) in water. J. Polym. Sci., Part B: Polym. Phys. 1990, 28, 923–936.

    Article  CAS  Google Scholar 

  7. Schweizer, K. S.; Yethiraj, A. Polymer reference interaction site model theory: new molecular closures for phase separating fluids and alloys. J. Chem. Phys. 1993, 98, 9053–9079.

    Article  CAS  Google Scholar 

  8. Zhuang, B.; Ramanauskaite, G.; Koa, Z. Y.; Wang, Z. G. Like dissolves like: a first-principles theory for predicting liquid miscibility and mixture dielectric constant. Sci. Adv. 2021, 7, eabe7275.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  9. Geoghegan, M.; Krausch, G. Wetting at polymer surfaces and interfaces. Prog. Polym. Sci. 2003, 28, 261–302.

    Article  CAS  Google Scholar 

  10. Chen, J.; Zhuang, H.; Zhao, J.; Gardella, J. A. Solvent effects on polymer surface structure. Surf. Interface Anal. 2001, 31, 713–720.

    Article  CAS  Google Scholar 

  11. Guillen, G. R.; Pan, Y.; Li, M.; Hoek, E. M. V. Preparation and characterization of membranes formed by nonsolvent induced phase separation: a review. Ind. Eng. Chem. Res. 2011, 50, 3798–3817.

    Article  CAS  Google Scholar 

  12. König-Mattern, L.; Linke, S.; Rihko-Struckmann, L.; Sundmacher, K. Computer-aided solvent screening for the fractionation of wet microalgae biomass. Green Chem. 2021, 23, 10014–10029.

    Article  Google Scholar 

  13. Xia, J.; Guo, H.; Travesset, A. On the thermodynamic stability of binary superlattices of polystyrene-functionalized nanocrystals. Macromolecules 2020, 53, 9929–9942.

    Article  CAS  Google Scholar 

  14. Chen, J.; Zha, L.; Hu, W. Effect of solvent selectivity on crystallization-driven fibril growth kinetics of diblock copolymers. Polymer 2018, 138, 359–362.

    Article  CAS  Google Scholar 

  15. Tao, Y.; Olsen, B. D.; Ganesan, V.; Segalman, R. A. Domain size control in self-assembling rod-coil block copolymer and homopolymer blends. Macromolecules 2007, 40, 3320–3327.

    Article  CAS  Google Scholar 

  16. Danquah, M.; Fujiwara, T.; Mahato, R. I. Self-assembling methoxypoly(ethylene glycol)-b-poly(carbonate-co-L-lactide) block copolymers for drug delivery. Biomaterials 2010, 31, 2358–2370.

    Article  CAS  PubMed  Google Scholar 

  17. Jimenez, J.; Ford, E. Mapping wet vs gel spinning in Hansen space. Polymer 2021, 230, 124079.

    Article  CAS  Google Scholar 

  18. Robinson, J. Solvent flux through dense polymeric nanofiltration membranes. J. Membr. Sci. 2004, 230, 29–37.

    Article  CAS  Google Scholar 

  19. Orwoll, R. A.; Arnold, P. A., Polymer-solvent interaction parameter χ. In Physical properties of polymers handbook, Mark, J. E., Ed. Springer: 2007; pp. 233–257.

  20. Venkatram, S.; Kim, C.; Chandrasekaran, A.; Ramprasad, R. Critical assessment of the hildebrand and hansen solubility parameters for polymers. J. Chem. Inf. Model. 2019, 59, 4188–4194.

    Article  CAS  PubMed  Google Scholar 

  21. Hansen, C. Hansen Solubility Parameters: A User’s Handbook. CRC Press: 2007, p. 546.

  22. Khansary, M. A. Vapor pressure and Flory-Huggins interaction parameters in binary polymeric solutions. Korean J. Chem. Eng. 2016, 33, 1402–1407.

    Article  CAS  Google Scholar 

  23. Schwahn, D.; Willner, L. Phase Behavior and Flory- Huggins interaction parameter of binary polybutadiene copolymer mixtures with different vinyl content and molar volume. Macromolecules 2002, 35, 239–247.

    Article  CAS  Google Scholar 

  24. Sun, Z.; Wang, C. H. Determination of Flory-Huggins interaction parameter and self-diffusion coefficients in ternary polymer solutions by quasielastic light scattering. J. Chem. Phys. 1995, 103, 3762–3766.

    Article  CAS  Google Scholar 

  25. DiPaola-Baranyi, G.; Guillet, J. Estimation of polymer solubility parameters by gas chromatography. Macromolecules 1978, 11, 228–235.

    Article  CAS  Google Scholar 

  26. Deshpande, D.; Tyagi, O. Gas chromatographic behavior of poly(vinyl acetate) at temperatures encompassing Tg: determination of Tg and η. Macromolecules 1978, 11, 746–751.

    Article  CAS  Google Scholar 

  27. Emerson, J. A.; Toolan, D. T. W.; Howse, J. R.; Furst, E. M.; Epps, T. H. Determination of solvent-polymer and polymer-polymer Flory-Huggins interaction parameters for poly(3-hexylthiophene) via solvent vapor swelling. Macromolecules 2013, 46, 6533–6540.

    Article  CAS  Google Scholar 

  28. Errede, L. Polymer swelling. 5. Correlation of relative swelling of poly(styrene-co-divinylbenzene) with the Hildebrand solubility parameter of the swelling liquid. Macromolecules 1986, 19, 1522–1525.

    Article  CAS  Google Scholar 

  29. Sweere, A. J.; Fraaije, J. G. Prediction of polymer-solvent miscibility properties using the force field based quasi-chemical method PAC-MAC. Polymer 2016, 107, 147–153.

    Article  CAS  Google Scholar 

  30. Cui, F.; Chen, W.; Kong, X.; Liu, L.; Shi, C.; Li, Y. Anomalous dynamics of water in polyamide matrix. J. Phys. Chem. B 2019, 123, 3086–3095.

    Article  CAS  PubMed  Google Scholar 

  31. Chen, W.; Cui, F.; Liu, L.; Li, Y. Assembled structures of perfluorosulfonic acid ionomers investigated by anisotropic modeling and simulations. J. Phys. Chem. B 2017, 121, 9718–9724.

    Article  CAS  PubMed  Google Scholar 

  32. Lei, Q.-L.; Ciamarra, M. P.; Ni, R. Nonequilibrium strongly hyperuniform fluids of circle active particles with large local density fluctuations. Sci. Adv. 2019, 5, eaau7423.

    Article  PubMed  PubMed Central  Google Scholar 

  33. Li, Y.; Liu, L.; Chen, W.; An, L. Materials genome: research progress, challenges and outlook. Sci. Sin. Chim. 2018, 48, 243–255.

    Article  Google Scholar 

  34. Liu, L.; Ding, F.; Li, Y. Big data approach on polymer materials: fundamental, progress and challenge. Acta Polymerica Sinica (in Chinese) 2022, 52, 1–17.

    Google Scholar 

  35. Chandrasekaran, A.; Kim, C.; Venkatram, S.; Ramprasad, R. A deep learning solvent-selection paradigm powered by a massive solvent/nonsolvent database for polymers. Macromolecules 2020, 53, 4764–4769.

    Article  CAS  Google Scholar 

  36. Greaves, T. L.; Drummond, C. J. Solvent nanostructure, the solvophobic effect and amphiphile self-assembly in ionic liquids. Chem. Soc. Rev. 2013, 42, 1096–1120.

    Article  CAS  PubMed  Google Scholar 

  37. Postel, S.; Schneider, C.; Wessling, M. Solvent dependent solute solubility governs retention in silicone based organic solvent nanofiltration. J. Membr. Sci. 2016, 497, 47–54.

    Article  CAS  Google Scholar 

  38. Sanchez-Lengeling, B.; Roch, L. M.; Perea, J. D.; Langner, S.; Brabec, C. J.; Aspuru-Guzik, A. A Bayesian approach to predict solubility parameters. Adv. Theory Simul. 2018, 2, 1800069.

    Article  CAS  Google Scholar 

  39. Mark, J. E. Physical properties of polymer handbook. Springer: 2007, Vol. 1076.

  40. Potter, C. B.; Davis, M. T.; Albadarin, A. B.; Walker, G. M. Investigation of the dependence of the Flory-Huggins interaction parameter on temperature and composition in a drug-polymer system. Mol. Pharm. 2018, 15, 5327–5335.

    Article  CAS  PubMed  Google Scholar 

  41. Van Dijk, M.; Wakker, A. Some observations on the behaviour of the thermodynamic interaction parameter in dilute polymer solutions. Polymer 1993, 34, 132–137.

    Article  CAS  Google Scholar 

  42. Lindvig, T.; Michelsen, M. L.; Kontogeorgis, G. M. A Flory-Huggins model based on the Hansen solubility parameters. Fluid Phase Equilib. 2002, 203, 247–260.

    Article  CAS  Google Scholar 

  43. Bicerano, J. Prediction of Polymer Properties. CRC Press: 2002.

  44. Barton, A. F. M. CRC handbook of solubility parameters and other cohesion parameters, second edition. CRC Press Taylor and Francis: 2017 p. 1–739.

  45. Zade, S. S.; Zamoshchik, N.; Bendikov, M. From short conjugated oligomers to conjugated polymers. Lessons from studies on long conjugated oligomers. Acc. Chem. Res. 2011, 44, 14–24.

    Article  CAS  PubMed  Google Scholar 

  46. RDKit: open-source cheminformatics. http://www.rdkit.org/. (accessed 23 Nov).

  47. Rappé, A. K.; Casewit, C. J.; Colwell, K.; Goddard III, W. A.; Skiff, W. M. UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations. J. Am. Chem. Soc. 1992, 114, 10024–10035.

    Article  Google Scholar 

  48. Stewart, J. J. P. MOPAC2016. http://OpenMOPAC.net (accessed 29 Nov).

  49. Bajusz, D.; Rácz, A.; Héberger, K. Why is Tanimoto index an appropriate choice for fingerprint-based similarity calculations. J. Cheminform. 2015, 7, 1–13.

    Article  CAS  Google Scholar 

  50. Liu, L.; Chen, W.; Liu, T.; Kong, X.; Zheng, J.; Li, Y. Rational design of hydrocarbon-based sulfonated copolymers for proton exchange membranes. J. Mater. Chem. A 2019, 7, 11847–11857.

    Article  CAS  Google Scholar 

  51. Ke, G.; Meng, Q.; Finley, T.; Wang, T.; Chen, W.; Ma, W.; Ye, Q.; Liu, T.-Y. Lightgbm: a highly efficient gradient boosting decision tree. Adv. Neural Inf. Process. Syst. 2017, 30, 3146–3154.

    Google Scholar 

  52. Liu, T.; Liu, L.; Cui, F.; Ding, F.; Zhang, Q.; Li, Y. Predicting the performance of polyvinylidene fluoride, polyethersulfone and polysulfone filtration membranes using machine learning. J. Mater. Chem. A 2020, 8, 21862–21871.

    Article  CAS  Google Scholar 

  53. Spowage, B. M.; Bruce, C. L.; Hirst, J. D. Interpretable correlation descriptors for quantitative structure-activity relationships. J. Cheminform. 2009, 1, 1–13.

    Article  CAS  Google Scholar 

  54. Shang, B. Z.; Wang, Z.; Larson, R. G. Effect of headgroup size, charge, and solvent structure on polymer—Micelle interactions, studied by molecular dynamics simulations. J. Phys. Chem. B 2009, 113, 15170–15180.

    Article  CAS  PubMed  Google Scholar 

  55. Ivanova, A.; Madjarova, G.; Tadjer, A.; Gospodinova, N. Effect of solvation and intermolecular interactions on the structure and optical properties of PANI oligomers. Int. J. Quantum Chem. 2006, 106, 1383–1395.

    Article  CAS  Google Scholar 

  56. Box, K.; Comer, J. Using measured pKa, LogP and solubility to investigate supersaturation and predict BCS class. Curr. Drug Metab. 2008, 9, 869–878.

    Article  CAS  PubMed  Google Scholar 

  57. Papanu, J.; Hess, D.; Soane, D.; Bell, A. Dissolution of thin poly(methyl methacrylate) films in ketones, binary ketone/alcohol mixtures, and hydroxy ketones. J. Electrochem. Soc. 1989, 136, 3077.

    Article  CAS  Google Scholar 

  58. Zhao, Y.; Liu, W.; Pei, X.; Yao, D. Refinement of the theoretical solubility model and prediction of solute solubility in mixed solvent systems. Fluid Phase Equilib. 2017, 437, 43–55.

    Article  CAS  Google Scholar 

  59. Song, Z.; Chiang, S. W.; Chu, X.; Du, H.; Li, J.; Gan, L.; Xu, C.; Yao, Y.; He, Y.; Li, B. Effects of solvent on structures and properties of electrospun poly(ethylene oxide) nanofibers. J. Appl. Polym. Sci. 2018, 135, 45787.

    Article  CAS  Google Scholar 

  60. Etxabarren, C.; Iriarte, M.; Uriarte, C.; Etxeberria, A.; Iruin, J. Polymer-solvent interaction parameters in polymer solutions at high polymer concentrations. J. Chromatogr. A 2002, 969, 245–254.

    Article  CAS  PubMed  Google Scholar 

  61. Chang, T. Polymer characterization by interaction chromatography. J. Polym. Sci., Part B: Polym. Phys. 2005, 43, 1591–1607.

    Article  CAS  Google Scholar 

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Acknowledgments

The work was financially supported by the National Natural Science Foundation of China (Nos. 21774128, U1832177, 22173094, 51988102), CAS Key Research Program of Frontier Sciences (No. QYZDY-SSW-SLH027). We are grateful to Network and Computing Center, Changchun Institute of Applied Chemistry for essential support.

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Authors and Affiliations

  1. State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, 130022, China

    Ting-Li Liu, Lun-Yang Liu, Fang Ding & Yun-Qi Li

  2. School of Applied Chemistry and Engineering, University of Science and Technology of China, Hefei, 230026, China

    Ting-Li Liu, Fang Ding & Yun-Qi Li

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  1. Ting-Li Liu
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  2. Lun-Yang Liu
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  3. Fang Ding
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Correspondence to Lun-Yang Liu or Yun-Qi Li.

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Liu, TL., Liu, LY., Ding, F. et al. A Machine Learning Study of Polymer-Solvent Interactions. Chin J Polym Sci 40, 834–842 (2022). https://doi.org/10.1007/s10118-022-2716-2

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