Using a hard sphere model and numerical calculations, the effect of the hydration force between a conical tip and a flat surface in the atomic 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 ( approximately 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 the remarkably high resolution achieved with contact-mode AFM. To disrupt 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 independent of the radius of curvature. This latter conclusion suggests that there should be no penalty for the use of sharper tips if hydration force is the dominant interaction between the tip and the specimen, which might be realizable under certain conditions. Furthermore, the calculated hydration energy near the specimen surface compares well with experimentally determined values with an atomic force microscope, providing further support to the validity of these calculations.
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