Figure 2: Adsorption isotherm of Rb⁺ ions at the surface of mica measured by IDM in solution.

The isotherms (a) comprise measurements conducted with two types of cantilevers that exhibit different spring constants (k_s~0.1 N m⁻¹ for the softer lever and k_s~0.5 N m⁻¹ for the stiffer lever) but a same tip design. The solid lines represent data fits with the Frumkin isotherm, which allows for ion–ion correlations. The dashed lines provide fits without correlations (Langmuir isotherm) (see Supplementary Methods for details). The apparent surface coverage derived from IDM measurements with the softer cantilever is larger than for the stiffer cantilever, consistent with the expected smaller mechanical perturbation (and hence smaller ) of the Stern layer by the softer cantilever. The results indicate a relatively small mechanical perturbation energy by the measuring IDM tip ( kJ mol⁻¹ for the softer lever, Supplementary Fig. 11) but a substantially larger electrostatic perturbation of ~7 kJ mol⁻¹ for both cantilevers. Control experiments with gold-coated tips confirm the dominance of the electrostatic perturbation (Supplementary Fig. 5). Representative topographic images of the IDM measurements are shown in b for the stiffer lever (see also Supplementary Fig. 4 and Supplementary Methods for a full set of data). Scale bar, 5 nm (b).