Force is measured in an SFM by collecting a force
curve, which is a plot of cantilever deflection, dc, as a function of
sample position along the z-axis (i.e. towards or away from the probe
tip; the z-piezo position). It assumes a simple relationship (i.e.
Hooke’s Law) between the force, F, and the cantilever deflection:
F = - k dc
where k is the spring constant of the cantilever.
Some other forces included in tip-sample interaction under dc approach
or retracting motion are presented on the figure left [1].
Used definitions see below. The interpretation of AFM force curves
relies almost entirely on established force laws, particularly those
determined using the SFA [2].
These force laws describe force as a function of the probe–sample
separation distance (D) rather than as a function of the z-piezo
position. Thus, to be useful, the force curves must be transformed into
descriptions of force as a function of distance, F(D). However, current
SFMs do not have an independent measure of D. Instead, the
transformation to D is achieved by subtracting the cantilever
deflection from the z-piezo movement.
For a very hard surface, zero
separation is defined as the region in the force curve in which the
cantilever deflection is coupled 1:1 with the sample movement; this
appears in the force curve as a straight line of unit slope. A
corrected curve is called a force–distance curve. Notice that
determining D by this approach requires that the tip make contact with
the sample. In practice, there are two factors (long-range forces and
sample elasticity) that can make determining the point of contact very
difficult. A complete force curve includes the forces measured as the
probe approaches the sample and is retracted to its starting position.
Because the forces on the tip can vary as it is moved toward or away
from the sample, for the purposes of presentation, we will divide the
force curve into approach and retraction portions and consider them
separately.
References
TIBTECH 17, 143 (1999).
Israelashvili, J.N. (1992) Intermolecular and Surface Forces, Academic Press.
