Figure 2: Time evolution of adsorbed Rb⁺ ions at the surface of mica in aqueous solution.

The AFM tip repeatedly scans the same location along the (100) direction of the crystal at 40 lines/s (a). A cartoon representation of the scanned crystal surface with adsorbed ions is shown to scale on the left. The system is stable enough to follow the same atomic sites for minutes. Three distinct height levels can be identified, represented by coloured arrows (see supplementary Fig. S2). A profile taken over a selected site (white arrow in a) provides the time evolution of the apparent height over this site (b). Assuming that the height variations are induced by ions adsorbing/desorbing, thresholding analysis (dotted black line in b) derives a distribution of time intervals spent by ions on the site. Fitting of the distribution with a single exponential decay provides a timescale of typically 100 ms (inset in b). The residence probability is the normalized number of events. A homemade algorithm automatically tracked each site position with time, taking into account drift (c): white lines indicate the location of binding sites’ centre and the black lines the limit between two adjacent sites. Only a fraction of the image given in (a) is shown as an example. All the pixels associated with a given site at a given time (interval between two adjacent black lines) are then height-averaged thereby minimising the impact of mica corrugation and specific details of the tip hydration sites dominating the imaging^48,49 (d). Profile analysis conducted over every site yielded (>than 30 min ×site) reveals three distinct timescales (e). First, a rapid timescale (25 ms) coincides with the scanning frequency and is imposed as a fitting parameter. The second and third timescale (104 ± 5 ms and 610 ± 30 ms) reflect real changes occurring over the sample (The threshold value in (e) is −0.1 nm, see Supplementary Figs S4–S7 for more details about the analysis). The data in (e) combines analysis from other experiments acquired in identical conditions (supplementary Fig. S9). The colour scale in (a,c,d) is 1.5 nm and the scale bar is 3 nm.