Figure 1

AM-AFM imaging of the surface of calcite in water as a function of $A_0$ and $S$. Images acquired in soft conditions ($S\sim 0.8$) are presented in (a)–(e) for selected $A_0$ values. In each case, a full cycle of the tip trajectory recorded during the image acquisition is given (solid curve) together with the free trajectory, recorded away from the surface in identical operating conditions (dotted black curve). The curves presented have been averaged over >1000 cycles (always preserving the phase), but the motion of the base of the cantilever has not been subtracted. Significant anharmonicities arise when the tip reaches the surface for $A_0>1.14\mathrm{nm}$ (arrows). The total anharmonicity $H$ is given in (f) for each imaging condition over all the $A_0$ studied. The fits of the experimental data were obtained with the Hill equation which provided transition amplitude values of $A_{0,t}=1.8\pm 0.3\mathrm{nm}$ (medium), $A_{0,t}=1.6\pm 0.2\mathrm{nm}$ (soft), and $A_{0,t}=1.8\pm 0.2\mathrm{nm}$ (ultrasoft). The $H$ values were obtained by summing the intensities of the harmonics peaks in the fast Fourier transform spectra of the tip trajectory (see the Supplemental Material [25] for an example of the analysis). An abrupt increase in $H$ is visible for $A_0\gtrsim 1.5$ nm regardless of the imaging condition used, although lower $S$ tend to yield higher $H$. (g) The inset provides the $S$ values measured experimentally for each $A_0$ and each imaging condition. The curves are linear fits of the experimental data. The differences between imaging conditions are less marked for larger $A_0$. This is due to the large anharmonicities making it difficult to fully control the amplitude at the fundamental frequency. The color scale of the topography (blue) is always 5 Å in (a)–(e), and the color scale of the phase (yellow) is adjusted in each case to provide the best contrast.Reuse & Permissions

Figure 2

AM-AFM imaging of the surface of bilayers stacks (a) and (b) and mica (c) and (d) in water as a function of $A_0$. All images were acquired with a soft set point. As for Fig. 1, the topography is presented on the left (blue color scale), and the phase is presented on the right (yellow color scale). (a) When imaged with small amplitude (that is, below the $H$ transition), the tip probes the interfacial liquid and can distinguish between molecular solvation structures. These differences are interpreted as molecular-level signatures of the type of lipid images: The more strongly hydrated PG headgroups (black arrow) appear higher in topography and darker in phase than the PC (white arrow). The phase contrast reflects the magnitude of the local solvation forces [13]. Different structural arrangements of the PC and PG headgroups might also play a role (see the Supplemental Material [25] for further discussions) (b) At higher amplitudes (above the $H$ transition), the lipid headgroups can still be resolved but without a clear distinction between DPPG and DPPC. Similar results on mica show atomic-level imaging of the solvation structure at small amplitude (c) and complete loss of resolution with apparition of noise at larger amplitudes (d). (e) Evolution of $H$ as a function of $A_0$ for all three solids in soft imaging conditions. (The data for medium and ultrasoft set points is available for both systems in the Supplemental Material [25] together with control experiments for the lipids). The color scales for the images (a)–(d) are as in Fig. 1.Reuse & Permissions

Figure 3

(a) Simulation of the oscillation anharmonicity $H$, (b) the maximum force experienced by the tip during an oscillation cycle (peak force), and (c) the tip energy dissipation per oscillation cycle as a function of $A_0$ for several set point values and solvation decay lengths. In (a), the transition amplitudes $A_{0,t}$ were obtained from fits with the Hill equation: For $\delta =0.25\mathrm{nm}$ [light gray curves (orange)], $A_{0,t}^{S=0.75}=0.7\pm 0.1$, $A_{0,t}^{S=0.85}=0.7\pm 0.1$, and $A_{0,t}^{S=0.95}=0.6\pm 0.1\mathrm{nm}$ ($S=0.95)$; for $\delta =0.5\mathrm{nm}$ [gray curves (green)], $A_{0,t}^{S=0.75}=1.6\pm 0.2$, $A_{0,t}^{S=0.85}=1.7\pm 0.2$, and $A_{0,t}^{S=0.95}=2.1\pm 0.9\mathrm{nm}$ ($S=0.95)$; for $\delta =1.0\mathrm{nm}$ [black curves (blue)], $A_{0,t}^{S=0.75}=8\pm 5$, $A_{0,t}^{S=0.85}$, and $A_{0,t}^{S=0.95}\mathrm{nm}$ did not converge properly. The dark horizontal line in (c) marks the energy necessary to fully remove water from 0.5×0.5 nm${}^2$ of calcite.Reuse & Permissions