Properties of the nuclear medium M Baldo and G F Burgio-Estimating the relevance of predictions from the Skyrme-Hartree-Fock model P-G Reinhard-Recent citations Nuclear skin and the curvature of the symmetry energy Ad. R. Raduta and F. Gulminelli-Constraints on the nuclear equation of state from nuclear masses and radii in a Thomas-Fermi meta-modeling approach D. Chatterjee et al-This content was downloaded from IP address 192.93.53.6 on 17/03 Abstract We have recently addressed the problem of the determination of the nuclear surface energy for symmetric nuclei in the framework of the extended Thomas-Fermi (ETF) approximation using Skyrme functionals. We presently extend this formalism to the case of asymmetric nuclei and the question of the surface symmetry energy. We propose an approximate expression for the diffuseness and the surface energy. These quantities are analytically related to the parameters of the energy functional. In particular, the influence of the different equation of state parameters can be explicitly quantified. Detailed analyses of the different energy components (local/non-local, isoscalar/iso-vector, surface/curvature and higher order) are also performed. Our analytical solution of the ETF integral improves previous models and leads to a precision of better than 200keV per nucleon in the determination of the nuclear binding energy for dripline nuclei.