Zisman Plots and Surface Energy Measurements

Critical surface tension (γ_c) is estimated by extrapolating a Zisman plot, obtained by plotting the cosine of the contact angle of pure liquids on a solid surface to be studied, against the surface tension of the same series of liquids. The intercept of the curve at cos θ = 1 is known as critical surface tension. Critical surface tension is a fictitious value often used to characterise surface wettability.

Surface energy can be defined as the energy required per unit area to increase the size of the surface, and as such is often quoted in units of mN/m. Critical surface energy is the surface energy at which complete wetting occurs.

Surface energy or surface tension of a substance (γ) is often described as consisting of two components, polar (γ^p) and dispersive (γ^d), and expressed as:

When two surfaces meet, of substances i and j, the combination result can be expressed as:

The term (f(γ_i^p,γ_i^d,γ_j^p,γ_j^d)), is then studied by various researchers, and different theories have been proposed for its significance and determination. The calculation of surface energies can be done by the software using various theoretical methods according to the measurement required:

Geometric mean: This method uses the Girifalco-Goods-Fowkes-Young (GGFY) single fluid model. The GGFY model is used when the test liquid selected forms a low contact angle with the solid substrate during wetting.
Wu Harmonic Mean:This method is often used by many polymer scientists who are dealing with much less polar surfaces, and want to know the polarity of the sample. However, due to the mathematical difficulties in solving for the values, it is not as commonly utilised as the Geometric mean method.
Owens/Wendt Geometric Mean: Due to the assumptions involved, it is better utilised to deal with solid surfaces that are polar. Since most of the solids have some polarities on their surfaces, it is the most popular method.
Lewis Acid/Base method: Based on the Lewis acid and base theory, it was proposed by Good, van Oss, and Chaudhury. Due to the consideration of the bonding between the molecules, this method is more applicable for hydrogen bonding systems. Since the theory is still at its early stage of development, the usage of this method is not as wide as the Geometric mean and Harmonic mean methods.

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