Solid Surface Free Energy

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:

    \[  {{\gamma }^{SL}=f({\gamma }^S,{\gamma }^L)} \]


    \[  {{\gamma }^S\approx {\gamma }^{SV} \]


    \[  {{\gamma }^L\approx {\gamma }^{LV} \]

This approach is called equation of state. A historical review on equation of state is provided here:


    \[  {{\gamma }^{SL}={\gamma }^L-{\gamma } \]


    \[  {{\gamma }^{SL}={\gamma }^S+{\gamma }^L-2\sqrt{{\gamma }^S{\gamma }^L} \]

Girifalco and Good:

    \[  {{\gamma }^{SL}={\gamma }^S+{\gamma }^L-2\phi \sqrt{{\gamma }^S{\gamma }^L} \]


    \[  {{\gamma }^{SL}={\gamma }^S+{\gamma }^L-2e^{-\beta {\left({\gamma }^L-{\gamma }^S\right)}^2}\sqrt{{\gamma }^S{\gamma }^L} \]

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:

    \[  {{\gamma }^{SL}={\gamma }^{SV}\mathrm{+}{\gamma }^{LV}-2\sqrt{{{\gamma }^{SV}}^d.{{\gamma }^{LV}}^d}-2\sqrt{{{\gamma }^{SV}}^P.{{\gamma }^{LV}}^P} \]

Extended Fowkes method by Kitazaki et al.: Dispersion + Polar + H-bonding

    \[  {{\gamma }^{SL}={\gamma }^{SV}\mathrm{+}{\gamma }^{LV}-2\sqrt{{{\gamma }^{SV}}^d.{{\gamma }^{LV}}^d}-2\sqrt{{{\gamma }^{SV}}^P.{{\gamma }^{LV}}^P}-2\sqrt{{{\gamma }^{SV}}^h.{{\gamma }^{LV}}^h} \]

van Oss: Lifshitz van der Waals (LW) + Lewis acid (+) + Lewis base (-):

    \[  {{\gamma }^{LS}={\gamma }^L+{\gamma }^S-2\sqrt{{{\gamma }^L}^{LW}{{\gamma }^S}^{LW}}-2\sqrt{{{\gamma }^L}^+{{\gamma }^S}^-}-2\sqrt{{{\gamma }^L}^-{{\gamma }^S}^+} \]

van Oss, Chaudhury, and Good (vOCG):
short range surface tension + long range surface tension

Solid Surface Free Energy

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