Using a hard sphere model and numerical calculations, the effect of th
e hydration force between a conical tip and a flat surface in the atom
ic force microscope (AFM) is examined. The numerical results show that
the hydration force remains oscillatory, even down to a tip apex of a
single water molecule, but its lateral extent is limited to a size of
a few water molecules. In general, the contribution of the hydration
force is relatively small, but, given the small imaging force (similar
to 0.1 nN) typically used for biological specimens, a layer of water
molecules is likely to remain ''bound'' to the specimen surface. This
water layer, between the tip and specimen, could act as a ''lubricant'
' to reduce lateral force, and thus could be one of the reasons for th
e remarkably high resolution achieved with contact-mode AFM. To disrup
t this layer, and to have a true tip-sample contact, a probe force of
several nanonewtons would be required. The numerical results also show
that the ultimate apex of the tip will determine the magnitude of the
hydration force, but that the averaged hydration pressure is independ
ent of the radius of curvature. This latter conclusion suggests that t
here should be no penalty for the use of sharper tips if hydration for
ce is the dominant interaction between the tip and the specimen, which
might be realizable under certain conditions. Furthermore, the calcul
ated hydration energy near the specimen surface compares well with exp
erimentally determined values with an atomic force microscope, providi
ng further support to the validity of these calculations.