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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
van Oss C.J., Good R.J., Chaudhury M.K. (1986). J. Protein Chem. 5: 385
van Oss C.J., Chaudhury M.K., Good R.J. (1987). Adv. Coll. Interf. Sci. 28: 35
van Oss C.J., Good R.J., Chaudhury M.K. (1988). Langmuir 4: 884
R.J. Good and M.K. Chaudhury, in: Fundamentals of Adhesion, ed. L.H. Lee (Plenum Press, New York, 1991) Chapt. 3.
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.
van Oss C.J. (1994). Interfacial Forces in Aqueous Media. Marcel Dekker, New York
Owens D.K., Wendt R.C. (1969). J. Appl. Polym. Sci. 13: 1741
Barber A.H., Cohen S.R., Wagner H.D. (2004). Phys. Rev. Lett. 92: 186103
Qin X., Chang W.V. (1995). J. Adhesion Sci. Technol. 9: 823
Qin X., Chang W.V. (1996). J. Adhesion Sci. Technol. 10: 963
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.
Drago R.S. (1973). Struct. Bond. 15: 73
Drago R.S., Vogel G.C., Needham T.E. (1971). J. Amer. Chem. Soc. 93: 6014
Drago R.S., Parr L.B., Chamberlain C.S. (1977). J. Amer. Chem. Soc. 99: 3203
Edwards J.O. (1954). J. Amer. Chem. Soc. 76: 1540
Mulliken R.S. (1952). J. Phys. Chem 56: 801
Foss A. (1947). Acta Chem. Scand. 1: 8
Peterson I.R. (2005). Surface Coatings Int. Part B: Coatings Trans. 88(1): 1
Lee L.H. (1996). Langmuir 12: 1681
Della Volpe C., Siboni S. (1997). J. Coll. Interf. Sci. 195: 121
Kamlet M.J., Abboud J.M., Abraham M.H., Taft R.W. (1983). J. Org. Chem. 48: 2877
Abraham M.H. (1993). Chem. Soc. Rev. 22:73
Wu S. (1971). J. Polym. Sci., Part C 34:19
Wu S. (1982). Polymer Interface and Adhesion. Marcel Dekker, New York
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).
Stewart G.W. (1973). Introduction to Matrix Computations. Academic press, Orlando Fla
Wise B.M., Gallagher N. (1996). J. Proc. Cont. 6: 329
Geladi P., Kowalsky B.R. (1986). Anal. Chimica Acta 185: 1
Press W.H., Flannery B.P., Teukolsky S.A., Vetterling W.T. (1989). Numerical Recipes. Cambridge University Press, Cambridge
Gilmore R. (1974). Lie Groups, Lie Algebras, and Some of Their Applications. Wiley New York, N.Y.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Della Volpe, C., Siboni, S. Principal component analysis and multicomponent surface free energy theories. J Math Chem 43, 1032–1051 (2008). https://doi.org/10.1007/s10910-007-9247-5
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10910-007-9247-5