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.