Polar and Dispersion Contributions to Solid Surface Tension a Reconsideration of Their Mathematical Evaluation

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Abstract
One technique for the experimental determination of the dispersion and polar contributions to solid tension, γs d and γs p , is to measure the contact angle θ of a set of m liquids of known dispersion and polar contributions to surface tension on the solid and then to calculate γs d and γs p . There are two common techniques for this calculation, graphically1 or analytically.2,3 The graphical technique is limited in that it only considers dispersion forces (i.e., nonpolar systems) and so only isolates γs d . For this reason the analytical procedures which isolate both γs d and γs p are more commonly used, and they can be expressed in matrix notation as: where A is a 2 × 2 matrix containing information about the characterizing liquids and their contact angles, and the vector ◯ is related to γs d and γs p . Equation (1) is solved for all mC2 different liquid pairs to give a set of values for γs d and γs p which can then be subjected to statistical analysis.

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