  Surface sensitive synchrotron x-ray scattering studies were performed to
obtain the distribution of monovalent ions next to a highly charged interface.
A lipid phosphate (dihexadecyl hydrogen-phosphate) was spread as a monolayer at
the air-water interface to control surface charge density. Using anomalous
reflectivity off and at the $L_3 $ Cs$^{+}$ resonance, we provide spatial
counterion (Cs$^{+}$) distributions next to the negatively charged interfaces.
Five decades in bulk concentrations are investigated, demonstrating that the
interfacial distribution is strongly dependent on bulk concentration. We show
that this is due to the strong binding constant of hydronium H$_3$O$^{+}$ to
the phosphate group, leading to proton transfer back to the phosphate group and
to a reduced surface charge. The increase of Cs$^+$ concentration modifies the
contact value potential, thereby causing proton release. This process
effectively modifies surface charge density and enables exploration of ion
distributions as a function of effective surface charge-density. The
experimentally obtained ion distributions are compared to distributions
calculated by Poisson-Boltzmann theory accounting for the variation of surface
charge density due to proton release and binding. We also discuss the accuracy
of our experimental results in discriminating among possible deviations from
Poisson-Boltzmann theory.
