Short Range Attraction between Two Similarly Charged Silica Surfaces

Using an atomic force microscope we measure the interaction between two identically charged silica surfaces in the presence of a saline solution. For pure NaCl the interaction is always repulsive. Upon addition of cobalt hexamine ions, $\mathrm{Co}({\mathrm{NH}}_3{)}_6^{+3}$, the repulsion is gradually suppressed and a pronounced attraction develops at distances much shorter than the screening length. Higher concentrations of cobalt hexamine turn the attraction back into repulsion. Measurements of surface charge renormalization by the trivalent cations provide their surface density and their association constant to the negatively charged silica surface. These estimates tend to exclude interaction between two condensed Wigner crystals as an explanation for the attraction.

Figure 1

Force versus distance curves for three different cations and the same ${\mathrm{Cl}}^{-}$ anion. The ionic strength in all cases corresponds to $r_{\mathrm{DH}}=10\mathrm{nm}$. The $p\mathrm{H}$ was set to 6 by negligible addition of HCl or NaOH. Inset: Semilog plot of the force versus distance for the NaCl curve together with best fit to PB models with constant charge or constant surface potential.

Figure 2

(a) Force versus distance curves for pure NaCl and three $\mathrm{Co}({\mathrm{NH}}_3{)}_6{\mathrm{Cl}}_3:\mathrm{NaCl}$ mixtures. The ionic strength in all cases was set to give $r_{\mathrm{DH}}=10\mathrm{nm}$. The $p\mathrm{H}$ was set to 6 by negligible titrations of either HCl or NaOH. Inset: a magnified view of the $1:25$ mixture. (b) Force versus distance curves for higher concentrations of $\mathrm{Co}({\mathrm{NH}}_3{)}_6{\mathrm{Cl}}_3$ (no NaCl). Inset: At very high $\mathrm{Co}({\mathrm{NH}}_3{)}_6{\mathrm{Cl}}_3$ concentrations ($8.3\times {10}^{-2}\mathrm{M}$ curve) the short range repulsion is preceded by a small attraction (data taken with a different tip on a different sample than the main figure).

Figure 3

(a) Four attraction curves fitted with single exponents. Curves $a$, $b$, $c$, $d$ correspond, respectively, to 0.75 mM $\mathrm{NaCl}:0.03\mathrm{mM}$ $\mathrm{Co}({\mathrm{NH}}_3{)}_6{\mathrm{Cl}}_3$ mixture, 0.1 mM $\mathrm{Co}({\mathrm{NH}}_3{)}_6{\mathrm{Cl}}_3$, 0.2 mM $\mathrm{Co}({\mathrm{NH}}_3{)}_6{\mathrm{Cl}}_3$, 23.75 mM $\mathrm{NaCl}:0.1\mathrm{mM}$ $\mathrm{Co}({\mathrm{NH}}_3{)}_6{\mathrm{Cl}}_3$ mixture. Solid lines represent best exponential fit (see text). (b) Semilog plots of the same data. The calculated DH screening lengths $a$, $b$, $c$, and $d$ are 10 nm, 12.6 nm, 8.9 nm, and 2 nm. The measured decay lengths of attraction $a$, $b$, $c$, and $d$ are 2.4 nm, 2.5 nm, 1.7 nm, and 0.85 nm.

Figure 4

Extracted dimensionless potential at the edge of the diffusive layer versus CoH concentration and two sodium chloride concentrations (see text).