Free Energy Approaches for Modeling Atomic Force Microscopy in Liquids

High resolution atomic force microscopy (AFM) in liquids offers atomic scale insight into the structure at water/solid interfaces and is perhaps the only tool capable of resolving the nature of formed hydration layers. However, convolution between the imaging signal and the tip/surface interactions and hydration layers means that interpretation is far from straightforward. Modeling the complex imaging mechanism of atomic force microscopy in liquids requires calculation of the free energy profile as a function of the distance between AFM tip and surface. Its derivative is the best approximation for the force acting on the AFM tip, including entropic contributions from interactions with water molecules in hydration layers over the surface and around the tip apex. In order to establish a reliable approach for these simulations, we compare two methods of calculating free energy profiles from atomistic molecular dynamics simulations, umbrella sampling and free energy perturbation, on two model surfaces, calcium fluoride and calcium carbonate. Our results demonstrate that both methods effectively provide equivalent free energy profiles but offer different possibilities in terms of efficiency, constraints, and analysis of the free energy components.