Dynamic Modes

In the dynamic modes [86-88] the cantilever is oscillated near its resonance frequency by an additional piezo crystal. The amplitude signal of the oscillating cantilever yields the information about the interaction.

A distinction between noncontact and the dynamic mode in the repulsive regime is often made. In real noncontact mode attractive forces are measured while the tip is oscillated above the sample with an amplitude of about 10 nm, never touching the sample surface.

In the dynamic mode [89], the tip is oscillated with an amplitude of 20 to 100 nm and touches the surface at some point. The feedback loop works as in contact mode maintaining a constant amplitude. Topography and roughness information are obtained as described earlier. Additionally and simultaneously, a phase image can be recorded.

In phase imaging the phase lag between the excitation frequency and the cantilever response signal is monitored. If the cantilever is oscillating freely in air, the waveform signal detected by the photodiode should be in phase with the signal driving the piezo element. This signal is sensitive to the interaction force between the cantilever and the surface. The phase contrast arises from the different amount of energy dissipated by the tip while oscillating on surface areas with different elastic properties. A short overview of experiments and theoretical descriptions is given in [90]. The mechanical properties [91-93] as well as chemical differences can yield a phase lag, which has been correlated quantitatively to the chemical interactions on chemically microstructured surfaces [90, 94].

In pulsed force mode (PFM), force distance respectively indentation curves are recorded in z-direction continuously [95]. A sinusoidal modulation far below the resonance frequency of the cantilever is applied to the z-piezo. Typical parameters are for the amplitudes 10 to 500 nm and for the frequency values between 0.1 and 2 kHz. A complete force distance cycle from the interaction free distance to the direct contact with the probe respectively the indentation is carried out. By measuring the maximum adhesion force an adhesion image is obtained; the slope in the repulsive regime is correlated with the stiffness of the substrate and long-range forces like electrostatic forces caused by surface charges influence the baseline. Accordingly it is possible to gain information about adhesive, elastic, and electrostatic sample properties. By chemical modification of the tip it is also possible to image differences between chemically different areas on a sample surface. Typical PFM images are given in Figure 6.

Electrostatic contributions to the tip-sample interaction can be isolated to yield surface charge density information. A theoretical and analytical framework for determining relative charge densities from arrays of SFM force curves without the need for an absolute measurement of the tip-sample separation is presented in [96] labeling it D-D method.

Polar interactions probed with SFM using a charged tip can lead in the future to atomic resolution of polar surfaces [97].

Magnetic interactions can be measured with magnetically coated cantilevers [98] but are, in the further investigations of biomaterials, of lesser importance.

In addition SFM is also being used for applications in which no scanning is required, where the tip is used as a sensitive force sensor (force spectroscopy) [99-101]. Loads of 1 to 1000 nN can be applied with tips that have tip radii of up to 1 /m, leading to an investigation of the first 0.1 to 10 nm [102]. Forces on a larger scale can also be measured by using the force apparatus by Israelachvili [103, 104]. This

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Figure 6. Pulsed force mode images of blends of PS/PMMA spin-coated on silicon substrate [95]: topography (a), (c) and adhesion (b), (d) images: lighter color corresponds to lower adhesive forces. The composition of PS/PMMA is 58/42 (a), (b); and 69/31 (c), (d), scan range: 10 /m.

will cover larger areas and the limitation to mica or a modification of it is given. However, absolute force values can be determined with high accuracy because the interaction area is well known.

With the setup of an SFM, surface and adhesion forces [105] between two surfaces and the elasticity respectively hardness by indentation of the substrate can be obtained. The data are investigated by plotting the bending of the cantilever versus the load applied to the sample. By indenting the surface it is possible to gain information about the elasticity and Young's modulus [28, 106] as well as time-dependent processes happening on polymers [102]. By monitoring the forces between the tip and the surface, chemical patterns on a surface can be characterized [52].

To monitor hardness by nanoindentation usually blunter tips are used to be able to relate to macroscopical hardness testing. The Berkovich tip with nominal radius of 150 nm is used to monitor the hardness, which is defined as the ratio of the maximum load to the projected contact area [107].

By force mapping, two-dimensional arrays of force curves are recorded while scanning the tip across the sample. By this the elastic properties can be monitored over the whole scan area. From the force curves Young's modulus can be calculated according to Sneddon's modification of the Hertzian model for elastic indentation [108].

Viscoelastic properties can be also monitored on a micrometer and submicrometer scale by microrheological measurements done with magnetic beads [109]. The loads applied are in the range of 10 nN. Mainly it is applied to monitor viscoelastic properties of cells using the parameters of an effective elastic constant, a viscosity, and a relaxation time. Viscoelastic properties can also be monitored via laser-tracking microrheology by looking at the Brownian motion

of individual spherical particles embedded in the viscoelastic material by monitoring the forward scattered light [110]. As particles, polystyrene beads of 0.27 /m diameter are used.

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