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Cantilevers

Cantilevers are very often made of silicon or silicon nitride. The basic lever with a tip is mounted on a rectangular chip, which enables easy handling (Fig. 3.2).

(a) An image of a silicon nitride chip with several cantilevers

Figure 3.2 (a) An image of a silicon nitride chip with several cantilevers

characterized by various spring constants (MLCT cantilevers type C, D and E with the corresponding spring constant of 0.01, 0.03 and 0.1 N/m). Inset: (b) The electron microscope image of a probing tip at the end of the cantilever. Image of the cantilever tip—courtesy of Piotr Bobrowski.

Each single cantilever is characterized by its material properties and geometry: length, width, thickness, and shape (it can be rectangular or triangular one). These parameters define cantilevers’ elastic properties that are quantitatively described by a spring constant expressed in N/m. Typical geometries of the silicon nitride cantilevers are shown in Table 3.1. At the end of the cantilever, a probing tip is located. Very frequently, the probing tip possesses the pyramid-like shape (Fig. 3.2b), however, it can also be in a form of a cone or a sphere. Independently of the tip shape, the radius of curvature is defined as the radius of a circular sphere that best approximates the tip end. Typically it ranges from 2 to 50 nm.

Table 3.1 Geometrical parameters of exemplary silicon nitride cantilevers (MLCT type), frequently used in the measurements of biological samples

Probe Type—MLCT

Cantilever type

A

B

C

D

E

F

Nominal spring constant [N/m]

0.07

0.02

0.01

0.03

0.1

0.6

Resonant frequency [kHz]

22

15

7

15

38

125

Length [pm]

175

210

310

225

140

85

Width [pm]

22

20

20

20

18

180

Note: The nominal cantilever thickness is 0.55 pm; however, according to manufacturer's data, thickness varies from 0.5 to 0.6 pm.

It has always been clear that the tip shape of the AFM probe influences the recorded images. Thus, acquired images are a convolution of the properties of the sample and the AFM probe. This is illustrated in Fig. 3.3, showing an idealized contact-mode AFM experiment carried out in two extreme conditions.

The influence of the AFM probing tip geometry on recorded images

Figure 3.3 The influence of the AFM probing tip geometry on recorded images. If the radius of curvature is much smaller than the size of the studied surface structures, the measured AFM profile (red dash lines) follows the real shape of the studied structure. In opposite conditions, the resulting image follows the shape of the probing tip.

If the radius of curvature is much smaller than the structures’ size on an investigated surface, the AFM probe traces the real shape of the studied structures (red dash line in Fig. 3.3, recorded by the AFM).

If the radius of curvature is much larger than the surface structures, the AFM profile reveals the shape of the probing tip. In reality, the AFM image reflects both the shape of the surface structures and the shape of the probe. The use of the sharpest possible probes can minimize erroneous features generated due to such a convolution but, simultaneously, can induce surface damages if the sample is delicate.

The effect of the AFM probe size on the imaged surface structures can be easily illustrated during the imaging single protein molecules like concanavalin A (Con A, unpublished data of the author, Fig. 3.4a).

(a) The effect of the AFM probe (a four-sided pyramid with

Figure 3.4 (a) The effect of the AFM probe (a four-sided pyramid with

open angle of 35° and radius of curvature of 50 nm) on single protein molecule (Con A, concanavalin A from Canavalia ensiformis), attached to mica surface and recorded in phosphate buffered saline (pH = 7.4) using a home build AFM system working at the IFJ PAN, Krakow, Poland). (b) The idea of the molecule diameter de-convolution.

Concanavalin A is a glycoprotein isolated from Canavalia ensiformis, which was dissolved in phosphate buffered saline (PBS buffer, pH = 7.4). At pH > 7.0, Con A is a globular/ellipsoidal tetramer with a single molecule dimensions of 6.7 nm x

11.3 nm x 12.2 nm [2]. Clearly visible rectangular shape of Con A indicates the effect of tip shape on the recorded images of molecule topography. In case of globular structures, the deconvolution of the tip shape, and thereby, the determination of real dimensions can be obtained from the following equation [3] (Fig. 3.4b):

where FWHM is the full width taken at half maximum, R is the radius of the curvature of the AFM probe, and D is the diameter of the studied molecule.

 
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