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Equation of state

In general, an equation of state is a thermodynamic equation which describes the given state of a system as a function of state variables such as pressure, temperature, volume and number of particles. The equation of state proposed by Neumann is used to calculate the surface free energy of a solid by measuring the contact angle with a single liquid with known surface tension.


According to Young's equation, there is a relationship between the contact angle θ, the surface tension of the liquid σl, the interfacial tension σsl between liquid and solid and the surface free energy σs of the solid:

In order to be able to calculate the surface free energy from the contact angle, the second unknown variable σsl must be determined.

Neumann has proposed the following equation for calculating the interfacial tension:

A value of 0.0001247 has been determined empirically for the constant β.


Unlike the methods for determining the surface free energy based on Fowkes, the type of interactions affecting the interfacial tension (polar part and disperse part of the surface tension) are not taken into account.



  • R. J. Good, Contact Angle, Wetting and Adhesion: a Critical Review. In: K. L. Mittal (Hrg.): Contact Angle, Wettability and Adhesion. Festschrift in Honor of Professor Robert J. Good. Utrecht 1993, S. 3-36.
  • D. Li; A. W. Neumann, Equation of State for Interfacial Tensions of Solid-Liquid systems. In: Advances in Colloid and Interface Science 39 (1992), S. 299-345.
  • E. Moy; A. W. Neumann, Solid/Liquid Interfacial Tensions from Contact Angle Data and Direct Force Measurements. In: J. Coll. Interf. Sci. 119,1 (1987), S. 296-297.
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