Simulation of atomic force microscopy of molecular structures and interplay with experiment

Atomic Force Microscope (AFM) is a multi-functional device for surface imaging, local measurements of material properties and manipulation of matter at the micron and nanometer scales. An AFM control system determines its applications as well as sensitivity, spatial resolution and accuracy of imaging and measurements of sample properties (mechanical, electromagnetic, etc.) Modeling and simulation of the tip-sample interactions is an essential part of AFM study, which can reveal critical issues of this nonlinear dynamic control system. Recent progress in the modeling led to analytical classification of imaging and spectroscopy modes and to quantitative nano-mechanical studies. These results and related algorithms allow developing a simulator of AFM images and force curves in quasi-static (contact, indentation, peak force tapping) and dynamic (amplitude/frequency modulation) modes. This paper provides a theoretical and algorithmic basis for AFM simulation, which was implemented for a number of applications. The essential features of the simulation include a description of tip and sample as the assemblies of spheres; calculation of integrated tip-sample force; conditions of contact and limited penetration that guarantee existence and, in some practically important cases, uniqueness of solution of AFM equations for different control modes; and finally, efficient solvers. Applications demonstrate how the interplay between simulation and experiment can optimize AFM study and analysis and lead to better understanding of molecular structures and properties.