TIP FINITE-SIZE EFFECTS ON ATOMIC-FORCE MICROSCOPY IN THE CONTACT MODE - SIMPLE GEOMETRICAL CONSIDERATIONS FOR RAPID ESTIMATION OF APEX RADIUS AND TIP ANGLE BASED ON THE STUDY OF POLYSTYRENE LATEX BALLS

Atomic force microscopy (AFM) has been developed as a tool for investigating any type of surface at an atomic scale. Since then, except for particular surfaces exhibiting an atomic roughness, we know that the finite size of the tip does not allow us to access at the whole structure of the surface. Moreover, the tip geometry radically modifies the range of the interactions. Therefore, even an approximate knowledge of the tip geometry is of particular importance. The aim of the present note is to provide a simple way to get the main parameters of a tip - its apex radius of curvature and the cone angle - by using a simple reference sample: latex balls. To do so, simple geometrical arguments are used, assuming that both the tip and the sample behave like hard samples, a reasonable assumption at a mesoscopic scale (tens of nanometres to micrometres). Using this simplifying assumption, we present a formula which could be used to rapidly evaluate the effect of the finite size of the apex of the tip in the formation of AFM images of simple objects: steps, isolated spheres or two-dimensional close-packed lattices of spheres, and cosinusoidal corrugations. Two types of tip geometry are presupposed: a conic tip truncated by a spherical apex or a parabolic tip. It is then shown that, in practice, latex balls can be used as a reference to estimate the radius of curvature of the apex, and the angle of the cone.