Anharmonicity, solvation forces, and resolution in atomic force microscopy at the solid-liquid interface

Solid-liquid interfaces are central to nanoscale science and technology and control processes as diverse as self-assembly, heterogeneous catalysis, wetting, electrochemistry, or protein function. Experimentally, measuring the structure and dynamics of solid-liquid interfaces with molecular resolution remains a challenge. This task can, in principle, be achieved with atomic force microscopy (AFM), which functions locally, and with nanometer precision. When operated dynamically and at small amplitudes, AFM can provide molecular-level images of the liquid solvation layers at the interfaces. At larger amplitudes, results in the field of multifrequency AFM have shown that anharmonicities in the tip motion can provide quantitative information about the solid's mechanical properties. The two approaches probe opposite aspects of the interface and are generally seen as distinct. Here it is shown that, for amplitudes A < d, the thickness of the solvation region, the tip mainly probes the interfacial liquid, and subnanometer resolution can be achieved through solvation forces. For A > d, the tip trajectory becomes rapidly anharmonic due to the tip tapping the solid, and the resolution decreases. A nonlinear transition between the two regimes occurs for A similar to d and can be quantified with the second harmonic of the tip oscillation. These results, confirmed by computer simulations, remain valid in most experimental conditions. Significantly, they provide an objective criterion to enhance resolution and to decide whether the results are dominated by the properties of the solid or of the liquid.