A series of well-defined hydrophilic and hydrophobic polyelectrolytes of various chain lengths $N$ and effective charge fractions $f_{eff}$ have been adsorbed onto oppositely charged solid surfaces immersed in aqueous solutions. \emph{In situ} high energy X-ray reflectivity has provided the thickness $h$, the electron density and the roughness of the adsorbed layer in its aqueous environment. In the case of hydrophobic polyelectrolytes, we have found $h∝ N^0 f_{eff}^{-2/3}$, in agreement with a pearl-necklace conformation for the chains induced by a Rayleigh-like instability.