Mechanism of atomic force microscopy imaging of three-dimensional hydration structures at a solid-liquid interface

Here we present both subnanometer imaging of three-dimensional (3D) hydration structures using atomic force microscopy (AFM) and molecular dynamics simulations of the calcite-water interface. In AFM, by scanning the 3D interfacial space in pure water and recording the force on the tip, a 3D force image can be produced, which can then be directly compared to the simulated 3D water density and forces on a model tip. Analyzing in depth the resemblance between experiment and simulation as a function of the tip-sample distance allowed us to clarify the contrast mechanism in the force images and the reason for their agreement with water density distributions. This work aims to form the theoretical basis for AFM imaging of hydration structures and enables its application to future studies on important interfacial processes at the molecular scale.

Figure 1

Three-dimensional $\rho$ and $F$ distributions obtained by simulation and experiment: (a) simulation model, where $z_{\mathrm{c}}$ is the $z$ component of the center-of-mass distance between the nanocluster tip and the sample slab; (b) 3D images of the simulated $\rho$ and $F$ distributions; (c) principle of 3D-SFM; and (d) 3D $F$ distribution experimentally measured by 3D-SFM. Scale bars, 0.5 nm.

Figure 2

Comparison between the simulated 3D $\rho$ and $F$ images and the experimentally measured 3D $F$ image: (a) model of ${\mathrm{CaCO}}_3$($10\overline{1}4$) surface; (b) $z$ cross sections, taken along the line A-B from (a). Scale bars, 0.3 nm. (c) and (d) $xy$ cross sections, and (e)–(g) $z$ profiles measured at Ca and ${\mathrm{CO}}_3$ sites.

Figure 3

Analysis of the $z_{\mathrm{c}}$-dependent change of the simulated 3D $\rho$ distribution during the tip approach over a Ca site: (a) model of a calcite($10\overline{1}4$) surface indicating the relevant $xy$ and $z$ cross sections [also see Fig. 2]; (b) $z$ profiles of the free energy and force $F$; (c) $z$ profiles of the tip deformation $\mathrm{\Delta }{z}_a$ and force $F$ (error bars $\pm \langle \mathrm{\Delta }{z}_a^2\rangle$); (d) $z$ cross sections of the simulated 3D $\rho$ distribution; (e) schematic diagram of the dominant processes in the contrast mechanism. The spots indicate water localized by the tip and surface (blue), with the water ordering indicated by grayscale, from highly ordered (light gray) to bulklike (dark gray). In general, as the tip approaches, ordered water is forced into the bulk region (pink arrows), producing an attractive entropic contribution. When tip and surface hydration layers match up (purple spots), the repulsive potential contribution is significantly reduced and the tip apex displaces towards the surface (green arrow). When hydration layers are forced against each other and the tip/surface (red stars), there is a strong repulsive potential contribution to the free energy and the tip apex displaces away from the surface (red arrow); (f)–(h) $xy$ cross sections of the simulated 3D $\rho$ distribution.