Direct Observation of Charge Inversion by Multivalent Ions as a Universal Electrostatic Phenomenon

We have directly observed reversal of the polarity of charged surfaces in water upon the addition of trivalent and quadrivalent ions using atomic force microscopy. The bulk concentration of multivalent ions at which charge inversion reversibly occurs depends only very weakly on the chemical composition, surface structure, size, and lipophilicity of the ions, but is very sensitive to their valence. These results support the theoretical proposal that spatial correlations between ions are the driving mechanism behind charge inversion.

Figure 1

(a) Optical microscope images of the side (left) and top (right) of a cantilever with a silica sphere. Force versus separation measurements in different concentrations of (b) ${\mathrm{L}\mathrm{a}\mathrm{C}\mathrm{l}}_3$, (c) ${\mathrm{C}\mathrm{o}\mathrm{C}}_{12}{\mathrm{H}}_{30}{\mathrm{N}}_8{\mathrm{C}\mathrm{l}}_3$, and (d) $\mathrm{R}\mathrm{u}({\mathrm{N}\mathrm{H}}_3{)}_6{\mathrm{C}\mathrm{l}}_3$. The insets illustrate schematically the attractive (1) and repulsive (2) forces between the silica bead and the amine-terminated surface. The legend applies to all three graphs.

Figure 2

Normalized force extrapolated to zero separation obtained from fits to Eq. (1), versus multivalent ion concentration $c$ for (a) ${\mathrm{C}\mathrm{o}\mathrm{C}}_{12}{\mathrm{H}}_{30}{\mathrm{N}}_8{\mathrm{C}\mathrm{l}}_3$ (squares) and $\mathrm{R}\mathrm{u}({\mathrm{N}\mathrm{H}}_3{)}_6{\mathrm{C}\mathrm{l}}_3$ (circles) and for (b) ${\mathrm{L}\mathrm{a}\mathrm{C}\mathrm{l}}_3$ (squares) and $\mathrm{R}\mathrm{u}({\mathrm{N}\mathrm{H}}_3{)}_6{\mathrm{C}\mathrm{l}}_3$ (circles). In each case the data were obtained consecutively using the same silica bead. Lines are guides to the eye.

Figure 3

Force versus separation measurements in different concentrations of (a) ${\mathrm{K}}_4\mathrm{F}\mathrm{e}(\mathrm{C}\mathrm{N}{)}_6$ and (b) ${\mathrm{K}}_3\mathrm{F}\mathrm{e}(\mathrm{C}\mathrm{N}{)}_6$. (c) Normalized force at zero separation versus multivalent ion concentration $c$ for ${\mathrm{K}}_4\mathrm{F}\mathrm{e}(\mathrm{C}\mathrm{N}{)}_6$ (squares) and ${\mathrm{K}}_3\mathrm{F}\mathrm{e}(\mathrm{C}\mathrm{N}{)}_6$ (circles). Lines are guides to the eye.