Determination of Solid Surface Tension by Contact Angle



In this chapter, approaches to determine solid surface tension by contact angle are briefly reviewed and assessed. These approaches include the Zisman method, various versions of the surface tension component methods, and the equation of state methods. The Zisman method is an empirical approach based on the relationship between the cosine of the contact angle and the surface tensions of the test liquids. The approach allows the determination of the critical surface tension of the solid. However, it is limited to low surface energy surfaces as data points from high surface tension liquids deviate from linearity due to polar and H-bonding interactions. The surface tension component approach is pioneered by Fowkes who assumed that (1) surface tension can be partitioned into individual independent components and (2) the work of adhesion can be expressed as the geometric means of the surface tension components. The original Fowkes method only considered dispersion interaction, and the methodology has been extended to include polar and H-bonding interactions in the extended Fowkes method or electron donor and acceptor interactions in the vOCG method. The equation of state assumes that the interfacial liquid–solid surface tension depends on the surface tension of the liquid and solid only. The interface surface tension was obtained by curve fitting with contact angle data and adjustable parameters. While the equation of state approach has been improved and three different versions have been developed, the basic thermodynamic assumption and the methodology were seriously challenged by many researchers in the field. It is important to note that both surface tension component methods and equation of state methods are semiempirical and that there are many assumptions in each methodology. Both approaches inherit a reversible work-of-adhesion assumption from Dupre. Specifically, for two immiscible liquids, the free energy change at the interface is equated to the interfacial tension of the newly formed interface subtracted by the surface tensions of the precursor liquids. The validity of this assumption is always questionable when one of the components is solid as the surface molecules or segments in solid have no mobility during any interfacial interaction. In view of this questionable assumption and the semiempirical nature of the contact angle approach, we propose a simpler and more direct approach to move forward. Since the motivation of determining surface tension is to be able to predict surface wettability and adhesion, we suggest measuring the advancing and receding angle of the solid surface instead. They have recently been shown to correlate to wettability and adhesion, respectively, by force measurements.


Solid surface tension Solid surface energy Contact angle Work of adhesion Zisman method Surface tension component method Fowkes method Owens–Wendt–Rabel–Kaelble method Extended Fowkes method Equation of state 


  1. 1.
    Cuenot S, Fretigny C, Demoustier-Champagne S, Nysten B (2004) Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy. Phys Rev B Condens Matter 69:165410CrossRefGoogle Scholar
  2. 2.
    Young T (1805) An essay on the cohesion of fluids. Philos Trans R Soc Lond 95:65–87CrossRefGoogle Scholar
  3. 3.
    Dupre A (1869) Theorie Mechanique de la Chaleur. Gauthier-Villars, Paris, p 369Google Scholar
  4. 4.
    Schrader ME (1995) Young-dupre revisited. Langmuir 11:3585–3589CrossRefGoogle Scholar
  5. 5.
    Hui CY, Jagota A (2013) Surface tension, surface energy, and chemical potential due to their difference. Langmuir 29:11310–11316CrossRefGoogle Scholar
  6. 6.
    Gray VR (1965) Surface aspects of wetting and adhesion. Chem Ind 23:969–977Google Scholar
  7. 7.
    Johnson RE (1959) Conflicts between Gibbsian thermodynamics and recent treatments of interfacial energies in solid–liquid-vapor systems. J Phys Chem 63:1655–1658CrossRefGoogle Scholar
  8. 8.
    Fox HW, Zisman WA (1950) The spreading of liquids on low energy surfaces. I. Polytetrafluoroethylene. J Colloid Sci 5:514–531CrossRefGoogle Scholar
  9. 9.
    Zisman WA (1964) Relation of the equilibrium contact angle to liquid and solid constitution. In: Fowkes F (ed) Contact angle, wettability, and adhesion, advances in chemistry. American Chemical Society, Washington, DC, pp 1–51CrossRefGoogle Scholar
  10. 10.
    Ellison AH, Fox HW, Zisman AW (1953) Wetting of fluorinated solids by H-bonding liquids. J Phys Chem 57:622–627CrossRefGoogle Scholar
  11. 11.
    Nishino T, Meguro M, Nakamae K, Matsushita M, Ueda Y (1999) The lowest surface free energy based on -CF3 alignment. Langmuir 15:4321–4323CrossRefGoogle Scholar
  12. 12.
    Shafrin EG, Zisman WA (1960) Constitutive relations in the wetting of low energy surfaces and the theory of the retraction method of preparing monolayer. J Phys Chem 64:519–524CrossRefGoogle Scholar
  13. 13.
    Chhatre SS, Guardado JO, Moore BM, Haddad TS, Mabry JM, McKinley GH, Cohen RE (2010) Fluoroalkylated silicon-containing surfaces—estimation of solid-surface energy. ACS Appl Mater Interfaces 2:3544–3554CrossRefGoogle Scholar
  14. 14.
    Fowkes FM (1962) Determination of interfacial tensions, contact angles, and dispersion forces in surfaces by assuming additivity of intermolecular interactions in surface. J Phys Chem 66:382CrossRefGoogle Scholar
  15. 15.
    Fowkes FM (1964) Attractive forces at interfaces. Ind Eng Chem 56:40–52CrossRefGoogle Scholar
  16. 16.
    Fowkes FM (1972) Donor-acceptor interactions at interfaces. J Adhes 4:155–159CrossRefGoogle Scholar
  17. 17.
    Berthelot D (1898) Sur le mélange des gaz. C R Hebd Seances Acad Sci 126:1857–1858Google Scholar
  18. 18.
    Good RJ (1992) Contact angle, wetting, and adhesion: a critical review. J Adhes Sci Technol 6:1269–1302CrossRefGoogle Scholar
  19. 19.
    Owens DK, Wendt RC (1969) Estimation of the surface free energy of polymers. J Appl Polym Sci 13:1741–1747CrossRefGoogle Scholar
  20. 20.
    Rabel W (1971) Einige Aspekte der Benetzungstheorie und ihre Anwendung auf die Untersuchung und Veränderung der Oberflächeneigenschaften von Polymeren. Farbe und Lack 77:997–1005Google Scholar
  21. 21.
    Kaelble DH (1970) Dispersion-polar surface tension properties of organic solids. J Adhes 2:66–81CrossRefGoogle Scholar
  22. 22.
    Janczuk B, Bialopiotrowicz T (1989) Surface free-energy components of liquids and low energy solids and contact angles. J Colloid Interface Sci 127:189–204CrossRefGoogle Scholar
  23. 23.
    Kitazaki Y, Hata TJ (1972) Surface-chemical criteria for optimum adhesion. J Adhes 4:123–132CrossRefGoogle Scholar
  24. 24.
    Van Oss CJ, Good RJ, Chaudhury MK (1986) The role of van der Waals forces and hydrogen bonds in “hydrophobic interactions” between biopolymers and low energy surfaces. J Colloid Interface Sci 111:378–390CrossRefGoogle Scholar
  25. 25.
    Van Oss CJ, Ju L, Chaudhury MK, Good RJ (1988) Estimation of the polar parameters of the surface tension of liquids by contact angle measurements on gels. J Colloid Interface Sci 128:313–319Google Scholar
  26. 26.
    van Oss CJ (2006) Interfacial forces in aqueous media. Taylor & Francis, New YorkGoogle Scholar
  27. 27.
    Kollman P (1977) A general analysis of noncovalent intermolecular interactions. J Am Chem Soc 99:4875–4894CrossRefGoogle Scholar
  28. 28.
    Hobza P, Zahradnik R (1980) Weak intermolecular interactions in chemistry and biology. Elsevier, New YorkGoogle Scholar
  29. 29.
    Wu S (1971) Calculation of interfacial tension in polymer system. J Polym Sci C 34:19–30CrossRefGoogle Scholar
  30. 30.
    Wu S (1973) Polar and nonpolar interactions in adhesion. J Adhes 5:39–55CrossRefGoogle Scholar
  31. 31.
    Schultz J, Tsutsumi K, Donnet JB (1977) Surface properties of high-energy solids I. Determination of the dispersive component of the surface free energy of mica and its energy of adhesion to water and n-alkanes. J Colloid Interface Sci 59:272–277CrossRefGoogle Scholar
  32. 32.
    Schultz J, Tsutsumi K, Donnet JB (1977) Surface properties of high-energy solids determination of the nondispersive component of the surface free energy of mica and its energy of adhesion to polar liquids. J Colloid Interface Sci 59:278–282CrossRefGoogle Scholar
  33. 33.
    Sell PJ, Neumann AW (1966) The surface tension of solids. Angew Chem Int Ed 5:299–307CrossRefGoogle Scholar
  34. 34.
    Neumann AW, Good RJ, Hope CJ, Sejpal M (1974) An equation-of-state approach to determine surface tensions of low-energy solids from contact angles. J Colloid Interface Sci 49:291–304CrossRefGoogle Scholar
  35. 35.
    Li D, Neumann AW (1990) A reformulation of the equation of state for interfacial tensions. J Colloid Interface Sci 137:304–307CrossRefGoogle Scholar
  36. 36.
    Kwok DY, Neumann AW (1999) Contact angle measurement and contact angle interpretation. Adv Colloid Interface Sci 81:167–249CrossRefGoogle Scholar
  37. 37.
    Kwok DY, Neumann AW (2000) Contact angle interpretation in terms of solid surface tension. Colloids Surf A Physicochem Eng Asp 161:31–48CrossRefGoogle Scholar
  38. 38.
    Girifalco LA, Good RJ (1957) A theory for the estimation of surface and interfacial energies. I. Derivation and application to interfacial tension. J Phys Chem 61:904–909CrossRefGoogle Scholar
  39. 39.
    Van Oss CJ, Good RJ, Chaudhury MK (1988) Additive and nonadditive surface tension components and the interpretation of contact angles. Langmuir 4:884–891CrossRefGoogle Scholar
  40. 40.
    Fowkes FM, Riddle FL, Pastore WE, Weber AA (1990) Interfacial interactions between self-associated polar liquids and squalane used to test equations for solid–liquid interfacial interactions. Colloids Surf 43:367–387CrossRefGoogle Scholar
  41. 41.
    Good RJ, Elbing E (1971) Generalization of theory for estimation of interfacial energies. Chem Phys Interfaces 2:72–96Google Scholar
  42. 42.
    Morrison I (1991) Does the phase rule for capillary systems really justify an equation of state for interfacial tensions? Langmuir 7:1833–1836CrossRefGoogle Scholar
  43. 43.
    Zenkiewicz M (2007) Comparative study on the surface free energy of a solid calculated by different methods. Polym Test 26:14–19CrossRefGoogle Scholar
  44. 44.
    Della Volpe C, Maniglio D, Brugnara M, Siboni S, Morra M (2004) The solid surface free energy calculation I. In defense of the multicomponent approach. J Colloid Interface Sci 271:434–453CrossRefGoogle Scholar
  45. 45.
    Siboni S, Della Volpe C, Maniglio D, Brugnara M (2004) The solid surface free energy calculation II. The limits of the Zisman and of the “equation-of-state” approaches. J Colloid Interface Sci 271:454–472CrossRefGoogle Scholar
  46. 46.
    Cwikel D, Zhao Q, Liu C, Su X, Marmur A (2010) Comparing contact angle measurements and surface tension assessments of solid surfaces. Langmuir 26:15289–15294CrossRefGoogle Scholar
  47. 47.
    Della Volpe C, Maniglio D, Morra M, Siboni S (2002) The determination of a “stable equilibrium” contact angle on heterogeneous and rough surfaces. Colloids Surf A Physicochem Eng Asp 206:47–67CrossRefGoogle Scholar
  48. 48.
    Samuel B, Zhao H, Law KY (2011) Study of wetting and adhesion interactions between water and various polymer and superhydrophobic surfaces. J Phys Chem C 115:14852–14861CrossRefGoogle Scholar

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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Founder & CEO at Research and Innovative SolutionsPenfieldUSA
  2. 2.School of Engineeing, Mechanical and Nuclear EngineeringVirginia Commonwealth UniversityRichmondUSA

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