Rapid quantitative chemical mapping of surfaces with sub-2 nm resolution

We present a theory that exploits four observables in bimodal atomic force microscopy to produce maps of the Hamaker constant H. The quantitative H maps may be employed by the broader community to directly interpret the high resolution of standard bimodal AFM images as chemical maps while simultaneously quantifying chemistry in the non-contact regime. We further provide a simple methodology to optimize a range of operational parameters for which H is in the closest agreement with the Lifshitz theory in order to (1) simplify data acquisition and (2) generalize the methodology to any set of cantilever-sample systems.