Solid surface free energy is one of the basic physical properties like density, melting point, refractive index, dielectric constant, modulus, etc. Measuring the solid surface free energy has applications in paints, coatings, and adhesives, semiconductors, printing, aerospace, mining, pharmaceutical and many more industries. To give an insight, high surface energy material is more reactive and stickier.
It is impossible to calculate both γSL and γSV from Young Eq.!!! And we need a function like:
![\[ {{\gamma }^{SL}=f({\gamma }^S,{\gamma }^L)} \]](https://quicklatex.com/cache3/4c/ql_98f2c936898a02306f5cd0144cdcfc4c_l3.png "Rendered by QuickLaTeX.com")
N.B.:
![\[ {{\gamma }^S\approx {\gamma }^{SV} \]](https://quicklatex.com/cache3/54/ql_e8d6bf0cdc18152fdc6522d8458da554_l3.png "Rendered by QuickLaTeX.com")
and
![\[ {{\gamma }^L\approx {\gamma }^{LV} \]](https://quicklatex.com/cache3/c2/ql_e97dd7e4e03583e024c52bee16f120c2_l3.png "Rendered by QuickLaTeX.com")
This approach is called equation of state. A historical review on equation of state is provided here:
Antonow:
![\[ {{\gamma }^{SL}={\gamma }^L-{\gamma } \]](https://quicklatex.com/cache3/35/ql_a763743740657bc39a7fd4c8eb43c135_l3.png "Rendered by QuickLaTeX.com")
Rayleigh:
![\[ {{\gamma }^{SL}={\gamma }^S+{\gamma }^L-2\sqrt{{\gamma }^S{\gamma }^L} \]](https://quicklatex.com/cache3/0a/ql_2563a3ddc531ee23f2e34d301a2e710a_l3.png "Rendered by QuickLaTeX.com")
Girifalco and Good:
![\[ {{\gamma }^{SL}={\gamma }^S+{\gamma }^L-2\phi \sqrt{{\gamma }^S{\gamma }^L} \]](https://quicklatex.com/cache3/d6/ql_12cc9c9055e451643dad1a7ed54f7fd6_l3.png "Rendered by QuickLaTeX.com")
Neumann:
![\[ {{\gamma }^{SL}={\gamma }^S+{\gamma }^L-2e^{-\beta {\left({\gamma }^L-{\gamma }^S\right)}^2}\sqrt{{\gamma }^S{\gamma }^L} \]](https://quicklatex.com/cache3/71/ql_92c2bd817c47bd1afdad259182b7fa71_l3.png "Rendered by QuickLaTeX.com")
This approach is surface tension components, as forces common to both phases act across the interface.
Fowkes: Dispersion (London dispersion) + Non-dispersive (dipole-dipole interactions, H-bonding, …)
Owens and Wendt: Dispersion + H-bonding.
Rabel and Kaelble: Dispersion + Polar
Subsequent researchers called this as the OWRK method:
![\[ {{\gamma }^{SL}={\gamma }^{SV}\mathrm{+}{\gamma }^{LV}-2\sqrt{{{\gamma }^{SV}}^d.{{\gamma }^{LV}}^d}-2\sqrt{{{\gamma }^{SV}}^P.{{\gamma }^{LV}}^P} \]](https://quicklatex.com/cache3/f2/ql_7611bba99e9f56ac6454b31602a69bf2_l3.png "Rendered by QuickLaTeX.com")
Extended Fowkes method by Kitazaki et al.: Dispersion + Polar + H-bonding
![\[ {{\gamma }^{SL}={\gamma }^{SV}\mathrm{+}{\gamma }^{LV}-2\sqrt{{{\gamma }^{SV}}^d.{{\gamma }^{LV}}^d}-2\sqrt{{{\gamma }^{SV}}^P.{{\gamma }^{LV}}^P}-2\sqrt{{{\gamma }^{SV}}^h.{{\gamma }^{LV}}^h} \]](https://quicklatex.com/cache3/f6/ql_a75b410fc82a7d2077f67754e398adf6_l3.png "Rendered by QuickLaTeX.com")
van Oss: Lifshitz van der Waals (LW) + Lewis acid (+) + Lewis base (-):
![\[ {{\gamma }^{LS}={\gamma }^L+{\gamma }^S-2\sqrt{{{\gamma }^L}^{LW}{{\gamma }^S}^{LW}}-2\sqrt{{{\gamma }^L}^+{{\gamma }^S}^-}-2\sqrt{{{\gamma }^L}^-{{\gamma }^S}^+} \]](https://quicklatex.com/cache3/db/ql_28cdf9addfc85006bbc24ab2a2adaedb_l3.png "Rendered by QuickLaTeX.com")
van Oss, Chaudhury, and Good (vOCG):
short range surface tension + long range surface tension
Jikan CAG Series utilize OWRK, Wu, and Equation of State algorithms, some of which were reviewed earlier, in order to precisely measure the solid surface free energy by means of Jikan Assistant Software.