Charge Inversion at Minute Electrolyte Concentrations

Anionic dimyristoylphosphatidic acid monolayers spread on ${\mathrm{LaCl}}_3$ solutions reveal strong cation adsorption and a sharp transition to surface overcharging at unexpectedly low bulk salt concentrations. We determine the surface accumulation of ${\mathrm{La}}^{3+}$ with anomalous x-ray reflectivity and find that ${\mathrm{La}}^{3+}$ compensates the lipid surface charge by forming a Stern layer with $\approx 1$ ${\mathrm{La}}^{3+}$ ion per 3 lipids below a critical bulk concentration, $c_t\approx 500\mathrm{n}M$. Above $c_t$, the surface concentration of ${\mathrm{La}}^{3+}$ increases to a saturation level with $\approx 1$ ${\mathrm{La}}^{3+}$ per lipid, thus implying that the total electric charge of the ${\mathrm{La}}^{3+}$ 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 contribute to the charge inversion.

Figure 1

DMPA monolayer isotherms for different ${\mathrm{La}}^{3+}$ subphase concentrations.

Figure 2

Fresnel-normalized x-ray reflectivities, $R/R_F$, of DMPA monolayers at $E=8.0\mathrm{keV}$ (off resonance) and 5.486 keV (La $L_{\mathrm{III}}$ resonance) on aqueous ${\mathrm{LaCl}}_3$ solutions. For clarity, subsequent pairs of data sets are offset by a factor of 100 each. Solid lines derive from model fits.

Figure 3

VRDF electron density profiles derived from fits to the experimental data. The off-resonance and on-resonance data shown in Fig. 2 were corefined with consistent sets of parameters that deviated only in the effective electron numbers and absorption cross sections of the ${\mathrm{La}}^{3+}$ component. Subsequent ED pairs are offset by $0.2e^{-}/{\AA }^3$ for clarity. Similar ED profiles were derived from a modified box model as described in the text. The number density of ${\mathrm{La}}^{3+}$ at the interface was subsequently obtained from such models via Eq. (2).

Figure 4

Number of adsorbed ${\mathrm{La}}^{3+}$ per DMPA in surface monolayers as a function of bulk ${\mathrm{LaCl}}_3$ concentration. Red plot symbols indicate results at $15\mathrm{mN}/\mathrm{m}$ derived from the anomalous reflectivity data pairs shown in Fig. 2 and ED profiles similar to those shown in Fig. 3. The results indicated by blue symbols were derived from independent data measured at 8.0 keV alone.