Fig. 5
Velocity-dependent frictional strength in LS, IS and HS regimes and corresponding lateral forces as a function of the sliding distance. a Rate-strengthening frictional strength (shown as the friction force divided by the applied load) of a single-asperity contact between calcite and an AFM tip in a 100 mM CaCl2 solution at low ( ≤ 200 MPa, blue circles, LS), intermediate (200–400 MPa, green squares, IS) and high normal stresses ( > 400 MPa, red diamonds, HS), with the schematics showing the three identified friction mechanisms. The black symbols represent the frictional strength of the dry single-asperity contact (Fig. 4) for comparison. At low contact stresses (LS regime), the brine lubricates the single-asperity contact causing a significant decrease in friction when compared to the dry contact (black). By further increasing the stress (200–400 MPa, IS regime); the response to shear in this regime is described as a shear-promoted thermally activated slip of the localized hydrated ions on the surface, which leads to a logarithmic dependence of friction on velocity over the investigated range ( ≤ 10 µm s–1). At high contact stresses ( > 400 MPa, HS regime), the pronounced weakening of the single-asperity contact results from pressure-induced dissolution of calcite, if the contact time is sufficiently large. The red dashed line gives the calculated friction force according to Eq. (2), as in the IS regime, and extrapolated to lower velocities; the arrows illustrate the decrease in the frictional strength provided by pressure solution. b–d Representative lateral force as a function of the sliding distance in the three regimes at selected slip rates. The color scheme is the same as in a, i.e., blue for LS regime, green for IS regime, and red for HS regime. Note the different scale on the Y-axis
