Approaches to Determine Solid Surface Tension by Contact Angle

Similarly, when two cylinders of immiscible liquids are brought together (Fig. 7. lb), the free energy change per unit area would be AG and is equaled to the negative of work of adhesion. More importantly, the free energy change can be equated as the interfacial tension of the newly formed interface subtracted by the surface tensions of the precursor liquids. 

Now if one assumes that L, is a liquid and L2 is a solid (5) and combines Eqs. (7.1) and (7.3), the work of adhesion between a liquid and a solid surface (11 is given by Eq. (7.4), which becomes known as the Young-Dupre equation [4]  

2 Approaches to Determine Solid Surface Tension by Contact Angle 

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In summary, there are three basic approaches to use contact angle data to determine the surface tensions of solid surfaces. These approaches are the Zisman method, the surface tension component methods, and the equation of state. Within these three approaches, there are many variants. It is reasonable to wonder the merit, accuracy, and limitation of some of the methods. The Zisman method is an empirical approach based on the correlation between the cosines of the contact angles on a solid surface versus the surface tensions of the test liquids. With alkanes, linear plots are usually obtained, and the critical solid surface tension (yc) is determined by extrapolating... 

Thus by contact angle measurements using three different liquids (L), of which two must be polar, with known y Y and y values, the ys", Ys and ys of any solid (S) can, in principle, be determined. The value of yl must be known or determined independently [108]. The apolar component of the surface tension of solids (yj" ) can be determined by contact angle measurements using strictly apolar liquids for which yL = y These surface tension components can be related to experimentally determined pull-off forces between chemically modified AFM tips and an oxyfluorinated isotactic polypropylene surface in CFM approaches [110]. It was observed that the pull-off force measured with carboxylic acid tips in ethanol depended hnearly on the basic term of the surface tension (y,") on the modified polymer surface. 

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