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 investi gating any type of surface at an atomic scale. Since then, except for particular surfaces exhibiting an atomic roughness, we know that the f inite size of the tip does not allow us to access at the whole structu re of the surface. Moreover, the tip geometry radically modifies the r ange of the interactions. Therefore, even an approximate knowledge of the tip geometry is of particular importance. The aim of the present n ote is to provide a simple way to get the main parameters of a tip - i ts apex radius of curvature and the cone angle - by using a simple ref erence sample: latex balls. To do so, simple geometrical arguments are used, assuming that both the tip and the sample behave like hard samp les, a reasonable assumption at a mesoscopic scale (tens of nanometres to micrometres). Using this simplifying assumption, we present a form ula which could be used to rapidly evaluate the effect of the finite s ize of the apex of the tip in the formation of AFM images of simple ob jects: steps, isolated spheres or two-dimensional close-packed lattice s of spheres, and cosinusoidal corrugations. Two types of tip geometry are presupposed: a conic tip truncated by a spherical apex or a parab olic 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 th e angle of the cone.