Atomic Force Microscopy

Abstract

Abstract In this chapter we review the microscopic and macroscopic theories that model interatomic (as well as intermolecular) forces, and present theoretical applications for, and experimental results of, atomic force microscopy. Interatomic forces act between any two atoms or molecules and can be classified according to whether they are repulsive or attractive, short or long range. In equilibrium, typical interatomic spacings are on the order of 2 to 3 A, below which interatomic forces are always repulsive and short range. At larger atomic separations, however, the long-range interatomic forces can be either repulsive or attractive. The theory involving the short-range repulsive forces is the more difficult one, because at close proximity, two atoms sense mainly each other, and the interaction is atom specific. In contrast, when the distances involved are large relative to atomic distances, only averages of atomic properties must be taken into account. At large distances, therefore, one can model the interaction as if it were between two macroscopic bodies, and the theory is simpler. A significant simplification in the calculation of short-range interatomic forces can be obtained by realizing that (through the Hellman-Feynman theorem) once the distribution of electronic charges is known for each of the molecules separately, the interaction between any two can be calculated using classical electromagnetic theory. One can, therefore, come up with a simplified picture of electronic charge distributions and, in quite a straightforward manner, deduce the main features of interatomic interactions using classical methods.