Physically Motivated Direct Non-Iterative Calculation of Surface Free Energy from Contact Angle Measurements with a Single Wetting Liquid: 1—Derivation and Demonstration of Utility

The estimation of surface free energy (SFE) of a solid is a major issue in (bio)material and (bio)interfacial research. Here, we show how combining Neumann and Gerson equations of state allows the calculation of SFE and the Girifalco–Good parameter (characterizing the interaction between the solid and the wetting liquid) analytically (in closed form) and in a physically motivated fashion solely from the surface tension of the wetting liquid and its contact angle with the solid surface. Physically meaningful interpretation is provided to the constants involved (Neumann’s “β” and Gerson’s “a” and “b”) within the framework of the density depletion theory at the interface. This is significant enhancement compared to the traditional iterative solving of the equations of state or to their empirical fitting by high-order polynomials. It is shown that the values of SFE calculated in closed-form fashion with the new Neumann-Gerson equation of state are in excellent agreement with the iteratively calculated ones. Possibilities are outlined to transparently calculate the dispersive and polar components of surface free energy from contact angle measurements with a single wetting liquid, which will be thoroughly examined in the second part of this study.