There is a number of methods suitable to measure the contact angle of a liquid on a solid body. The most important point in all these methods is that the experimentalist is aware that only equilibrium values can be understood thermodynamically. Moreover, one has to take into consideration, that there are in general two critical contact angles, one receding qr and one advancing angle qa. The difference between the two values is called contact angle hysteresis, which can amount to many degrees, even several tens degrees.
Theoretical Basis
Young’s equation is the basic relationship for calculating the solid surface tension gs from the contact angle q and the surface tension of the liquid gl
As one can see, the equation contains the two parameters q and gl which can readily be measured, and two other parameters gs and gsl which are unknown. Thus, the determination of the solid surface tension gs from Eq. (V.6) requires further information, i.e. an additional relationship between the two unknown parameters gs and gsl. Neumann [[i]] proposed an equation of state of the following form
[i]. A.W. Neumann, Adv. Colloid Interface Sci., 4(1974)105
Simultaneous solution of the two Eqs. (V.6) and (V.7) can yield a value of the solid surface tension gs. There are different equations of state proposed in literature. The one proposed by Rayleigh and Good [16] has the following structure
The combination of (V.6) and (V.8) results in an equation for the calculation of the solid surface tension (energy)
This equation seems to work well when both the surface tension of the solid and the liquid are small, while the value of gs becomes too small for liquids with larger surface tensions glv. Good proposed to introduce an interaction parameter F into Eq. (V.8) to account for this deviation [[i]]
[i]. R.J. Good, J. Colloid Interface Sci., 59(1977)398
which finally yields the following relationship
The specification of this parameter F has been tried by many authors. Fowkes’ approach suggests that a surface tension can be decomposed of different components
where gd is the dispersion and gh the polar component. From this ansatz together with Eq. (V.10) Fowkes arrived at the his equation [[i]]
[i]. F.M. Fowkes, Ind. Eng. Chem., (1964)40
which differs from Eq. (V.8) only by using the dispersion part gd of the two tensions instead of the whole tension value. Combined again with (V.6) we obtain
This equation is frequently used for the interpretation of contact angle data to obtain the solid surface tension. A generalisation of the Fowkes approach was proposed by Owens and Wendt [[i]]. The Lifshitz-van-der-Waals /acid-base approach given by van Oss et al. [[ii]] provides more components of the solid surface tension: , and .
[i]. D.K. Owens and R.C. Wendt, J. Appl. Polymer Sci., 13(1969)1741 [ii]. C.J. van Oss, M.K. Chaudhury and R.J. Good, Chem. Rev., 88(1988)927
Another equation of state for the parameter F has been proposed by Li and Neumann [[i]]
[i]. D. Li and A.W. Neumann, J. Colloid Interface Sci., 148(1992)190
The value of b has been determined from a large number of experimental contact angle data and has the values of b=0.0001247 (m/mN)². Together with Young’s equation (V.6) we obtain an implicit relationship for the solid surface tension gs in the following form
For measured values of q and gl the value of gs can be calculated by an iterative method via Eq. (V.16). The following Fig. V.4 demonstrates how the contact angle depends on the surface energy of the solid when a respective pure solvent is used (with hypothetical surface tensions of 70, 50 and 30 mN/m surface tensions, respectively).
