I'd like to know how a deformation value of a hypothetical repulsive F-D will be calculated in the Peak-Force tapping mode (QNM mode). Since the cantilever never comes in contact with a the sample (or at least not during a minimal deflection value, from where "deformation" is extracted) I dont see how to get this mechanical property.

How do you define the contact point, e.g Tip-sample distance = 0 for repulsive force curves.

These curves could occur in liquid in low electrolyte buffers (no screening effect) and by an interaction btw. a negatively charged tip and a negatively charged surface.

Lets start with the first part of your question. Bede's Applications note#138 (under "Bruker media" on top of page) has a diagram explaining the various parameters that can get extracted. I am not sure if I understand you correctly but why you think that the tip never contacts the surface? If the tip indeed never contacts the surface one could not measure nanomechanical properties. In order to accurately measure e.g. sample modulus the tip indeed has to indent the sample a few nm.

Well, the value for the deformation is extracted at about 10% of the peak force (depending of the deformation fit region), at which - when assuming no attractive forces are present - the tip is not in contact with the surface. Repulsion is due DLVO forces (double layer repulsion etc) at large distance or non-DLVO forces at small distances (<5nm). The sample will be definitely deformed, but in order to extract a deformation value as schemed by the manual you need to know tip-sample distance and therefore a contact point.

In cases such as the one that you describe, it is difficult to determine the true deformation. The simple algorithm that we use to calculate the deformation may not match the true deformation, but it has the advantages that it is easy to describe and calculate in real-time. As the application note states:

"Maximum sample deformation is calculated from the difference in separation from the point where the force is zero to the peak force point along the approach curve (see figure 1(iv)). There may be some error in this measurement due to the fact that the tip first contacts the surface at the jump-to-contact point (figure 1(i), point B) rather than at the zero crossing."

Actually, there is an additional parameter, "Deformation Force Level", that allows you to choose the % force (on the approach curve) where the deformation will be calculated (described in the online help). The deformation is just the difference in separation between that point and the peak force.

As you say, DLVO forces will provide an additional complication, but maybe you can choose the deformation force level to be higher than the maximum force from the DLVO repulsion?

If you want to apply your own algorithm to get a better estimate of teh deformation, you could use matlab with the matlab toolbox provided in Nanoscope Analysis v1.40r3 or later. Please let us know if you find a better algorithm!