  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
$h\propto N^0 f_{eff}^{-2/3}$, in agreement with a pearl-necklace conformation
for the chains induced by a Rayleigh-like instability.
