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A simple approximation for forces exerted on an AFM tip in liquid
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Image of FIG. 1.
FIG. 1.

Simplifying the model system, reducing the computational effort by several orders of magnitude: (a) The actual experimental setup, inaccessible to atomistic simulations; (b) free energy calculations with a fully solvated nanocluster tip; (c) free energy calculations with a single water molecule as tip model; (d) local water density calculation from equilibrium simulations.

Image of FIG. 2.
FIG. 2.

Tip models extracted from molecular dynamics simulations that expose a flexible OH group to the environment. Bulk solvent molecules are shown as transparent “v” shapes with O red and H white. Atoms shown as larger balls are the tip terminus and its local environment. Silicon is yellow, oxygen is red, calcium is turquoise, and fluorine is pink. Upper figures show overall views of the nanoclusters, lower figures zoom in on the area of interest. (a) Silanol group –Si–OH on a silica cluster; (b) two neighbouring (vicinal) silanol groups on a silica cluster (geminal Si(OH)2 groups are also possible); (c) water molecule adsorbed on a silica cluster; (d) water molecule adsorbed on a CaF2 cluster.

Image of FIG. 3.
FIG. 3.

The local water density at the fluorite (111)/water interface. The local water density ρ(r) is the time average of counts of water molecules within a 0.1 × 0.1 × 0.1 nm3 cube centered at position r. The red, green, and blue curves indicate the local water densities over the calcium (Ca), protruding fluorine (Fh), and sub-surface fluorine (Fl) sites, respectively. The dashed black curve shows the laterally averaged water density. The inset shows that the areas of high water density (dark) within the first (1), second (2), and third (3) hydration layer, match the sub-lattices of Ca (red), Fh (green), and Fl (blue) in the surface.

Image of FIG. 4.
FIG. 4.

Comparison of the free energy curves for water molecules above CaF2 with those obtained from the water density using Eq. (1) . Density derived curves are dashed, and those from free energy perturbation calculations are shown as solid curves.

Image of FIG. 5.
FIG. 5.

Comparison of the simple model and simulations with an explicit nanocluster tip: Free energy curves over Ca (red), Fh (green), and Fl sites (blue) in a fluorite surface. Curves obtained from the local water density are solid, curves obtained from FEP with a sharp CaF2 nanocluster tip are dashed.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A simple approximation for forces exerted on an AFM tip in liquid