Semi-Experimental Methods for Determination of Flory-Huggins Interaction Parameter in Polymeric Mixtures: A Review
Subject Areas :
1 - Sahand University of Technology
Keywords: Flory-Higgins interaction parameter, Melting point depression, Equilibrium swelling, Contact angle, Phase diagram, Vapor pressure, Inverse gas chromatography,
Abstract :
The Flory-Huggins interaction parameter (χ) is a crucial factor affecting the miscibility and morphology of components in polymer mixtures and their final properties and applications. The reliable measurement of the interaction parameter is worthwhile in fundamental understanding and quantitative determination of structure-performance relation and finally in practical applications of polymers in different fields. Different methods are used for evaluation of this parameter. In this study, six semi-experimental methods are reviewed: measurement of melting point depression, equilibrium swelling, contact angle, phase separation points, vapor pressure, and inverse gas chromatography. In these methods, equilibrium melting temperatures of pure polymer and its mixtures, degree of equilibrium swelling of the cross-linked polymer in the presence of swelling agent, surface energy of components in the polymeric mixtures, equilibrium components composition in the two-phase system, the ratio of partial vapor pressure of solvent to its saturated one and retention volume are experimentally measured, respectively. Then a proper equation is fitted on the data and the interaction parameter is obtained. In some methods, such as measurement of contact angle, only a positive interaction parameter at temperature of the test is obtained. But in some others, such as measurement of melting point depression, there is no constraint for the sign of interaction parameter. In addition, some methods can determine the composition dependency of the interaction parameter, such as determination of phase separation points.
1. Gao M., Liang Z., Geng Y., Ye L., Significance of Thermodynamic Interaction Parameters in Guiding the Optimization of Polymer: Nonfullerene Solar Cells, Chemical Communications, 56, 12463-12478, 2020.
2. Ye L., Collins B.A., Jiao X.C., Zhao J. B., Yan H., Ade H., Miscibility-Function Relations in Organic Solar Cells: Significance of Optimal Miscibility in Relation to Percolation, Advanced Energy Materials, 8, 1703058, 2018.
3. Ségolène A., Zhishuai G., Everett S. Zofchak M.C., Fredrickson G.H., Ganesan V., Hawker C.J., Lynd N.A., Non-Intuitive Trends in Flory–Huggins Interaction Parameters in Polyether-Based Polymers, Macromolecules, 54, 6670–6677, 2021.
4. Aid S., Eddhahak A., Khelladi S., Ortega Z., Chaabani S., Tcharkhtchi A., On the Miscibility of PVDF/Pmma Polymer Blends: Thermodynamics, Experimental and Numerical Investigations, Polymer Testing, 73, 222-231, 2019.
5. Ma R., Li G., Li D., Liu T., Luo Z., Zhang G., Zhang M., Wang Z., Luo S., Yang T., Liu F., Yan H., Tang B., Understanding the Effect of End Group Halogenation in Tuning Miscibility and Morphology of High-Performance Small Molecular Acceptors, Solar RRL, 4, 2000250, 2020.
6. Paulin J.A., Lopez-Aguilar J.E., Fouconnier B., Vargas R.O., Lopez-Serrano F., Revisiting the Flory–Rehner Equation: Taking a Closer Look at the Flory–Huggins Interaction Parameter and Its Functionality with Temperature and Concentration with Nipa as a Case Example, Polymer Bulletin, 79, 6709–6732, 2022.
7. Liu Y., Xian K., Peng Z., Gao M., Shi Y., Deng Y., Geng Y., Ye L., Tuning the Molar Mass of P3ht Via Direct Arylation Polycondensation Yields Optimal Interaction and High Efficiency in Nonfullerene Organic Solar Cells, Journal of Materials Chemistry A, 9, 19874-19885, 2021.
8. Friedrich C., Riemann R.E., Rheological and Thermodynamic Study of the Miscible Blend Polystyrene/Poly(Cyclohexyl Methacrylate), Polymer, 37, 2499-2507, 1996.
9. Chopra D., Kontopoulou M., Vlassopoulos D., Hatzikiriakos S. G., Effect of Maleic Anhydride Content on the Rheology and Phase Behavior of Poly(Styrene-Co-Maleic Anhydride)/Poly(Methyl Methacrylate) Blends, Rheologica Acta, 41, 10-24, 2002.
10. Huang Y., Jiang S., Li G., Chen D., Effect of Fillers on the Phase Stability of Binary Polymer Blends: A Dynamic Shear Rheology Study, Acta Materialia, 53, 5117–5124, 2005.
11. Lee J.H., Balsara N.P., Chakraborty A.K., Krishnamoorti R., Hammouda B., Thermodynamics and Phase Behavior of Block Copolymer/Homopolymer Blends with Attractive and Repulsive Interactions, Macromolecules, 35, 7748–7757, 2002.
12. Huang J.C., Determination of Polymer–Polymer Interaction Parameters Using Inverse Gas Chromatography, Journal of Applied Polymer Science, 671-680, 90, 2003.
13. Ugraskan V., Isik B., Yazici O., Cakar F., Thermodynamic Characterization of Sodium Alginate by Inverse Gas Chromatography, Journal of Chemical & Engineering Data, 65, 1795-1801, 2020.
14. Emerson J.A., Toolan D.T., Howse J.R., Furs E. M., Thomas H. Epps I., Determination of Solvent−Polymer and Polymer−Polymer Flory− Huggins Interaction Parameters for Poly(3-Hexylthiophene) Via Solvent Vapor Swelling, Macromolecules, 46, 6533−6540, 2013.
15. Zhang L., Yi N., Zhou W., Yu Z., Liu F., Chen Y., Miscibility Tuning for Optimizing Phase Separation and Vertical Distribution toward Highly Efficient Organic Solar Cells, Advanced Science, 6, 1900565, 2019.
16. Ai Q., Zhou W., Zhang L., Huang L., Yin J., Yu Z., Liu S., Ma W., Zeng J., Chen Y., Ternary Organic Solar Cells: Compatibility Controls for Morphology Evolution of Active Layers, Journal of Materials Chemistry C, 5, 10801-10812, 2017.
17. Flory P.J., Principles of Polymer Chemistry, Cornell University Press, USA, 1953.
18. Ghasemi M., Ye L., Zhang Q., Yan L., Kim J.H., Awartani O., You W., Gadisa A., Ade H., Panchromatic Sequentially Cast Ternary Polymer Solar Cells, Advanced Materials, 29, 1604603, 2017.
19. Kim J. Y., Order–Disorder Phase Equilibria of Regioregular Poly (3-Hexylthiophene-2, 5-Diyl) Solution, Macromolecules, 51, 9026-9034, 2018.
20. Wang Q., Li M., Peng Z., Kirby N., Deng Y., Ye L., Geng Y., Calculation Aided Miscibility Manipulation Enables Highly Efficient Polythiophene:Nonfullerene Photovoltaic Cells, Science China Chemistry, 64, 478-487, 2021.
21. Dowland S.A., Salvador M., Perea J.D., Gasparini N., Langner S., Rajoelson S., Ramanitra H.H., Lindner B.D., Osvet A., Brabec C.J., Suppression of Thermally Induced Fullerene Aggregation in Polyfullerene-Based Multiacceptor Organic Solar Cells, ACS Applied Materials & Interfaces, 9, 10971-10982, 2017.
22. Liang Z., Li M., Wang Q., Qin Y., Stuard S.J., Peng Z., Deng Y., Ade H., Ye L., Geng Y., Optimization Requirements of Efficient Polythiophene: Nonfullerene Organic Solar Cells, Joule, 1278-1295, 2020.
23. Kouijzer S., Michels J.J., van den Berg M., Gevaerts V.S., Turbiez M., Wienk M. M., Janssen R. A.J., Predicting Morphologies of Solution Processed Polymer:Fullerene Blends, Journal of the American Chemical Society, 135, 12057-12067, 2013.
24. Lv J., Tang H., Huang J., Yan C., Liu K., Yang Q., Hu D., Singh R., Lee J., Lu S., Additive-Induced Miscibility Regulation and Hierarchical Morphology Enable 17.5% Binary Organic Solar Cells, Energy & Environmental Science, 14, 3044-3052, 2021.
25. Nilsson S., Bernasik A., Budkowski A., Moons E., Morphology and Phase Segregation of Spin-Casted Films of Polyfluorene/Pcbm Blends, Macromolecules, 40, 8291-8301, 2007.
26. Li D., Neumann A., A Reformulation of the Equation of State for Interfacial Tensions, Journal of Colloid and Interface Science, 137, 304-307, 1990.
27. Li D., Neumann A., Contact Angles on Hydrophobic Solid Surfaces and Their Interpretation, Journal of Colloid and Interface Science, 148, 190-200, 1992.
28. Kim D.Y., Park J.W., Lee D.Y., Seo K.H., Correlation between the Crosslink Characteristics and Mechanical Properties of Natural Rubber Compound Via Accelerators and Reinforcement, Polymers, 12, 2020, 2020.
29. Riedl B., Prud'homme R. E., The Determination of the Thermodynamic Interaction Parameter Χ in Polymer Blends, Polymer Engineering & Science, 24, 1291-1299, 1984.
30. Mohammadi-Jam S., Waters K.E., Inverse Gas Chromatography Applications: A Review, Advances in Colloid and Interface Science, 212, 21-44, 2014.
31. Fernandez-Berridi M.J., Eguiazabal J.I., Elorza J.M., Iruin J.J., Vapor-Pressure Osmometry and Inverse Gas Chromatography in the Analysis of Thermodynamic Properties of Polymer Solutions, Journal of Polymer Science Part B: Polymer Physics, 21, 859-868, 1983.