Charge inversion at minute electrolyte concentrations
  Anionic DMPA monolayers spread on LaCl$_3$ solutions reveal strong cation adsorption and a sharp transition to surface overcharging at unexpectedly low bulk salt concentrations. We determine the surface accumulation of La$^{3+}$ with anomalous x-ray reflectivity and find that La$^{3+}$ compensates the lipid surface charge by forming a Stern layer with $\approx 1$ La$^{3+}$ ion per 3 lipids below a critical bulk concentration, $c_t \approx 500 \mathrm{nM}$. Above $c_t$, the surface concentration of La$^{3+}$ increases to a saturation level with $\approx 1$ La$^{3+}$ per lipid, thus implying that the total electric charge of the La$^{3+}$ exceeds the surface charge. This overcharge is observed at $\approx$ 4 orders of magnitude lower concentration than predicted in ion-ion correlation theories. We suggest that transverse electrostatic correlations between mobile ions and surface charges (interfacial Bjerrum pairing) may account for the charge inversion observed in this dilute regime. 
J. Pittler, W. Bu, D. Vaknin, A. Travesset, D. J. McGillivray, and M.   Losche