Some years ago, I had a similar problem. In the end I used the OWRK-method. For that, one needs to measure the contact angle of at least two different liquids with different hydrophobicity.
Then, one can do a linear regression to get the free surface energy out of an equation [D.K. Owens et al. Estimation of the surface free energy of polymers. journal of applied polymer science, 13:1741, 1969], where the data points are the measured contact angles in combination with the corresponing liquid-vapor free energies (the latter have to be found in literature).