Charge inversion at ultra-low electrolyte concentrations*

Synchrotron x-ray reflectivity studies of the anionic phospholipid DMPA in monolayers spread on very dilute solutions of LaCl$_3$ reveal strong adsorption of the cations at nanomolar and micromolar concentrations, and a sharp transition in cation concentration at the interface as a function of ionic strength. Using anomalous X-ray reflection we determine the number of La$^{3+}$ ions per DMPA$^-$ (surface charge density, $\sigma \approx e^-/40$ \AA$^2$) over four orders of magnitude in bulk ion concentration. We find that at concentrations in the range 10--300 nM La$^{3+}$ forms a Stern layer with $\approx$ 1 La$^{3+} /$ 3 DMPA$^-$, thus neutralizing the lipid surfaces charge. At a critical bulk concentration, $C_t \approx$ 500 nM, the surface concentration of La$^{3+}$ increases steeply, up to a saturation level with $\approx$ 1 La$^{3+} /$ DMPA. The strong condensation of La$^{3+}$ above $C_t$ implies that the charge at the interface is reversed. We provide theoretical arguments that the charge reversal is facilitated by 1) strong correlations between the phosphate groups and La$^{3+}$ ions and 2) hydrogen bonding of hydroxyl groups, effectively forming the complex La$^{3+}$PO$_4^{2-} $OH$^- $.