The colloidal probe technique uses a standard AFM for the force measurements. But instead the AFM cantilever with an attached sharp tip one uses the colloidal probe. This colloidal probe is normally obtained by attaching a colloidal particle to a cantilever. By recording the deflection of the cantilever as a function of the vertical displacement of the AFM scanner one can extract the force acting between the probe and the surface as a function of the surface separation. This type of AFM operation is referred to as the force mode. With this probe, one can study interactions between various surfaces and probe particles in the sphere-plane geometry. It is also possible to study forces between colloidal particles by attaching another particle to the substrate and perform the measurement in the sphere-sphere geometry, see figure above.
The force mode used in the colloidal probe technique is illustrated in the figure on the left. The scanner is fabricated from piezoelectric crystals, which enable its positioning with a precision better than 0.1 nm. The scanner is lifted towards the probe and thereby one records the scanner displacement D. At the same time, the deflection of the cantilever ξ is monitored as well, typically with a comparable precision. One measures the deflection by focusing a light beam originating from a non-coherent laser diode to the back of the cantilever and detecting the reflected beam with a split photodiode. The lever signal S represents the difference in the photocurrents originating from the two halves of the diode. The lever signal is therefore proportional to the deflection ξ.
During an approach-retraction cycle, one records the lever signal S as a function of the vertical displacement D of the scanner. Suppose for the moment that the probe and the substrate are hard and non-deformable objects and that no forces are acting between them when they are not in contact. In such a situation, one refers to a hard-core repulsion. The cantilever will thus not deform as long not being in contact with the substrate. When the cantilever touches the substrate, its deflection will be the same as the displacement of the substrate. This response is referred to as the constant compliance or contact region. The lever signal S as a function of the scanner displacement D is shown in the figure below. This graph consists of two straight lines resembling a hockey-stick. When the surfaces are not in contact, the lever signal will be denoted as S. This value corresponds to the non-deformed lever. In the constant compliance region, the lever signal is simply a linear function of the displacement, and can be represented as a straight line
: S = a D + b
The parameters a and b can be obtained from a least-squares fit of the constant compliance region. The inverse slope a is also referred to as the optical lever sensitivity. By inverting this relation for the lever signal S, which corresponds to the non-deformed lever, one can accurately obtain the contact point from D = (S − b)/a. Depending on the substrate, the precision in determining this contact point is between 0.5–2 nm. In the constant compliance region, the lever deformation is given by
: ξ = (S − S)/a
In this fashion, one can detect deflections of the cantilever with typical resolution of better than 0.1 nm.
Let us now consider the relevant situation where the probe and the substrate interact. Let us denote by F(h) the force between the probe and the substrate. This force depends on the surface separation h.
In equilibrium, this force is compensated by the restoring force of the spring, which is given by the Hooke's law
: F = k ξ
where k is the spring constant of the cantilever. Typical spring constants of AFM cantilevers are in the range of 0.1−10 N/m. Since the deflection is monitored with a precision better 0.1 nm, one typically obtains a force resolution of 1−100 pN. The separation distance can be obtained from the displacement of the scanner and the cantilever deflection
: h = ξ + D − D
Figure below illustrates how the cantilever responds to different force profiles. In the case of a soft repulsive force, the cantilever is repelled from the surface and only slowly approaches the constant compliance region. In such situations, it might be actually difficult to identify this region correctly. When the force is attractive, the cantilever is attracted to the surface and may become unstable. From stability considerations one finds that the cantilever will be unstable provided
: dF/dh > k
This instability is illustrated in the right panel of the figure on the right. As the cantilever approaches, the slope of the force curve increases. When the slope becomes larger than the spring constant of the cantilever, the cantilever jumps into contact when the slope of the force curve exceeds the force constant of the cantilever. Upon retraction, the same phenomenon happens, but the point where the cantilever jumps out is reached at a smaller separation. Upon approach and retraction, the system will show a hysteresis. In such situations, a part of the force profile cannot be probed. However, this problem can be avoided by using a stiffer cantilever, albeit at the expense of an inferior force resolution.