Journal of Mathematical Chemistry

, Volume 43, Issue 3, pp 1032–1051 | Cite as

Principal component analysis and multicomponent surface free energy theories

  • C. Della Volpe
  • S. Siboni

The same underlying mathematical structure characterizes some of the most popular multicomponent models for the prediction of surface free energies and adhesion works. After a brief illustration of the general methods for the computation of liquid and solid components in typical multicomponent theories, it is shown that both model definition and component estimate may take great advantage from application of Principal Component Analysis techniques, owing to the very peculiar structure of adhesion work equations. It is also put into evidence that a problem of scale multiplicity arises as a consequence of the symmetries involved in the model equations for adhesion work and surface free energy. A special discussion is devoted to the specific cases of van Oss–Chaudhury–Good acid–base theory, Qin–Chang model and extended Drago theory, which constitute the most common multicomponent models usually applied in the analysis of adhesion phenomena.


multicomponent acid-base theories van Oss–Chaudhury–Good theory Principal Component Analysis (PCA) 

AMS classification

80A17 80A99 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. van Oss C.J., Good R.J., Chaudhury M.K. (1986). J. Protein Chem. 5: 385CrossRefGoogle Scholar
  2. van Oss C.J., Chaudhury M.K., Good R.J. (1987). Adv. Coll. Interf. Sci. 28: 35CrossRefGoogle Scholar
  3. van Oss C.J., Good R.J., Chaudhury M.K. (1988). Langmuir 4: 884CrossRefGoogle Scholar
  4. R.J. Good and M.K. Chaudhury, in: Fundamentals of Adhesion, ed. L.H. Lee (Plenum Press, New York, 1991) Chapt. 3.Google Scholar
  5. R.J. Good and C.J. van Oss, in: Modern Approach to Wettability: Theory and Application eds. M.E. Schrader and G. Loed (Plenum Press, New York, 1991) Chapt. 1.Google Scholar
  6. van Oss C.J. (1994). Interfacial Forces in Aqueous Media. Marcel Dekker, New YorkGoogle Scholar
  7. Owens D.K., Wendt R.C. (1969). J. Appl. Polym. Sci. 13: 1741CrossRefGoogle Scholar
  8. Barber A.H., Cohen S.R., Wagner H.D. (2004). Phys. Rev. Lett. 92: 186103CrossRefGoogle Scholar
  9. Qin X., Chang W.V. (1995). J. Adhesion Sci. Technol. 9: 823Google Scholar
  10. Qin X., Chang W.V. (1996). J. Adhesion Sci. Technol. 10: 963CrossRefGoogle Scholar
  11. W.V. Chang and X. Qin, in: Acid–base Interactions: Relevance to Adhesion Science and Technology, ed. K.L. Mittal (VSP, Utrecht, 2000) Vol. 2, pp. 3–54.Google Scholar
  12. Drago R.S. (1973). Struct. Bond. 15: 73Google Scholar
  13. Drago R.S., Vogel G.C., Needham T.E. (1971). J. Amer. Chem. Soc. 93: 6014CrossRefGoogle Scholar
  14. Drago R.S., Parr L.B., Chamberlain C.S. (1977). J. Amer. Chem. Soc. 99: 3203CrossRefGoogle Scholar
  15. Edwards J.O. (1954). J. Amer. Chem. Soc. 76: 1540CrossRefGoogle Scholar
  16. Mulliken R.S. (1952). J. Phys. Chem 56: 801CrossRefGoogle Scholar
  17. Foss A. (1947). Acta Chem. Scand. 1: 8Google Scholar
  18. Peterson I.R. (2005). Surface Coatings Int. Part B: Coatings Trans. 88(1): 1CrossRefGoogle Scholar
  19. Lee L.H. (1996). Langmuir 12: 1681CrossRefGoogle Scholar
  20. Della Volpe C., Siboni S. (1997). J. Coll. Interf. Sci. 195: 121CrossRefGoogle Scholar
  21. Kamlet M.J., Abboud J.M., Abraham M.H., Taft R.W. (1983). J. Org. Chem. 48: 2877CrossRefGoogle Scholar
  22. Abraham M.H. (1993). Chem. Soc. Rev. 22:73CrossRefGoogle Scholar
  23. Wu S. (1971). J. Polym. Sci., Part C 34:19Google Scholar
  24. Wu S. (1982). Polymer Interface and Adhesion. Marcel Dekker, New YorkGoogle Scholar
  25. C. Della Volpe and S. Siboni, J. Adhesion Sci. Technol. 14(2) (2000) 235. Reprinted in: Apparent and Microscopic Contact Angles eds. J. Drelich, J.S. Laskowsky and K.L. Mittal (VSP, New York, 2000).Google Scholar
  26. Stewart G.W. (1973). Introduction to Matrix Computations. Academic press, Orlando FlaGoogle Scholar
  27. Wise B.M., Gallagher N. (1996). J. Proc. Cont. 6: 329CrossRefGoogle Scholar
  28. Geladi P., Kowalsky B.R. (1986). Anal. Chimica Acta 185: 1CrossRefGoogle Scholar
  29. Press W.H., Flannery B.P., Teukolsky S.A., Vetterling W.T. (1989). Numerical Recipes. Cambridge University Press, CambridgeGoogle Scholar
  30. Gilmore R. (1974). Lie Groups, Lie Algebras, and Some of Their Applications. Wiley New York, N.Y.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Materials Engineering and Industrial TechnologiesUniversity of TrentoPovoItaly

Personalised recommendations