The lowest surface energy is not 6.7 mJ/m2, as it was reported for n-Perfluoroeicosane

In a celebrated and often cited (almost 900 citations) paper by Nishino et al. (1999) “The Lowest Surface Free Energy Based on -CF3 Alignment” Langmuir 15:4321-4323, it has been reported that the maximum possible water contact angle with a smooth solid material is 119 degrees. This was achieved for n-Perfluoroeicosan (C20F42)-coated glass. The authors state that “closest hexagonal packed -CF3 groups” provide the lowest possible surface energy. In other words, there are no chemical groups with lower surface energies. The paper further claims that the value of the solid-air surface energy for n-Perfluoroeicosan is 6.7 mJ/m2 and that “this value is much smaller than that (22 mJ/m2) of PTFE.” PTFE or Polytetrafluoroethylene better known under its commercial name “Teflon” is a famous non-sticky low adhesion polymer material consisting of the same elements – carbon and fluorine – with the formula (C2F4)n.

Note that different experimentalists reported PTFE static contact angle values between 110 degrees and 126 degrees, and even higher. The results may depend on the measurement technique and on the accuracy of the experiment as well as on smoothness of the surface.

The problem with the calculation of the solid-air surface energy by the contact angle data is that the Young equation for the contact angle, cos(CA) = (GSA – GSL)/GLA, involves three parameters: the surface energies for the solid-air, solid-water, and water-air interfaces. While the value of the latter is well known at the room temperature, GLA=72.8 mJ/m2, the two other values are unknown for the C20F42-water and C20F42-air interfaces. The only result, which can be extracted from the contact angle data, is for the difference of the surface energies:

GSA – GSWater = -35.29 mJ/m2

A measurement with another liquid, methylene iodide (CH2I2) having GLA=50.8 mJ/m2 supplied the CA=107 degrees and

GSA – GSmethylene iodide = -14.85 mJ/m2

However, the value of GSA is still unknown. To resolve this, Nishino et al. (1999) used a model by Owens & Wendt 1969 “Estimation of the surface free energy of polymers” Appl. Polym. Sci. 13:1741 (doi:10.1002/app.1969.070130815), which excludes the solid-liquid surface energy by assuming that it is a function of the solid-air and liquid-air surface energies. The model of Owens & Wendt; however, uses a large number of assumptions about the nature of intermolecular forces including that

(i) The surface energy is a sum of the dispersion and polar components
GLA = GLAD + GLAP
GSA = GSAD + GSAP.

(ii) The dependency of cos(CA) vs. GLA for homologous series of liquids on a given solid is generally a straight line.

(iii) The relationship holds
GSL = GSA + GLA – 2(GSADGLAD)1/2 – 2 (GSAPGLAP)1/2.

These are quite strong assumptions. For the dispersion component, a physical argument that the 2(GSADGLAD)1/2 approximate relationship may be valid was provided by Fowkes. For the polar (H-bond) component, the term 2 (GSAPGLAP)1/2 is merely an assumption by Owens & Wendt. This is in addition to the assumption that the dispersion and polar components are independent of each other and constitute additive terms. However, in addition, apparently there is a typo in Nishino (1999), and instead of the latter relationship, a different (and wrong) formula was suggested (their Eq. 2):

(1 + cos(CA))GLA = 2(GSADGSAP)1/2 + 2 (GLADGLAP)1/2.

As a result, a direct check of the latter relationship is not in agreement with the 6.7 mJ/m2 value.

Note also that the lowest value of the liquid-air surface energy at the room temperature, GLA=10 mJ/m was reported for perfluorohexane (C6F14), which belongs to the same CnF2n+2 series. Given all this, it is questionable whether the solid-air surface energy of the n-Perfluoroeicosane is indeed more than three times lower than that of the PTFE.

Below is a fragment from the paper, where this is discussed:
M. Nosonovsky and B. Bhushan, 2016 “Why re-entrant surface topography is needed for robust oleophobicity,” Phil. Trans. R. Soc. A 374:20160185. http://dx.doi.org/10.1098/rsta.2016.0185

UPDATE: For our publication on the topic, please see http://sites.uwm.edu/nosonovs/2017/10/27/revisiting-lowest-possible-surface-energy-of-a-solid/