On the pearl size of hydrophobic polyelectrolytes

Hydrophobic polyelectrolytes have been predicted to adopt an unique pearl-necklace conformation in aqueous solvents. We present in this Letter an attempt to characterise quantitatively this conformation with a focus on $D_p$, the pearl size. For this purpose polystyrenesulfonate (PSS) of various effective charge fractions $f_{eff}$ and chain lengths $N$ has been adsorbed onto oppositely charged surfaces immersed in water in condition where the bulk structure is expected to persist in the adsorbed state. \emph{In situ} ellipsometry has provided an apparent thickness $h_{app}$ of the PSS layer. In the presence of added salts, we have found: $h_{app}\sim aN^{0}f_{eff}^{-2/3}$ ($a$ is the monomer size) in agreement with the scaling predictions for $D_p$ in the pearl-necklace model if one interprets $h_{app}$ as a measure of the pearl size. At the lowest charge fractions we have found $h_{app}\sim aN^{1/3}$ for the shorter chains, in agreement with a necklace/globule transition.