Contact angle is just an express of the surface tension, but I want to know the value (N/m), just like liquid.
In general and simply explained you should not only measure the surface tension. The polar and disperse part of it are important, too.
Use at least two known liquids with a high polar or disperse surface tension like water and diiod-methane, respectively and measure the contact angles of droplets on your surface.
Then you can use e.g. Owens-Wendt-Rabel-Kaelble to calculate the surface energy including dispers and polar part in N/m.
This paper gives an overview regarding measurement, calculation and different models on the example of SAMs: http://www.sciencedirect.com/science/article/pii/S0040609006005372
What are you attempting to do with this? From the point of view that solids are just very slow liquids one could get an average deformation of the solid from such a surface tension but the timescale for these rearrangements are likely so long and the durations of them are so short that they can likely be considered zero on the timescale of your observations. There are electronic edge state effects that could lead to local bond changes, premelting layers, etc that give strong near surface effects but little interior stress or rearrangement effects as you might expect for a liquid droplet with surface tension.
For compliant solids there are some interesting new results. http://phys.org/news/2013-08-rethinking-surface-tension.html
JKR is the only solid method and it is still highly dependent on roughness,surface contaminations etc.
Chaudhury, Whitesides, Langmuir 7 (1991) 1013
de Gennes, Brochard-Wyart, Quere, Capillarity and Wetting Phenomena 2002, chapter 2.6.4
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