AM-AFM

The simple textbook solution of a harmonic damped oscillator becomes complex when the vibrating tip interacts with the surface of a sample, e.g., in tapping mode AFM. Although the different imaging modes and the experimental observables may vary, the underlying physics is similar. Amplitude and frequency modulated AFMs are most commonly used, labeled by AM-AFM (amplitude modulation or tapping) and FM-AFM. For a detailed review of this topic several reviews are available, e.g., [15]. 

The oscillation amplitude A is the primary variable in AM-AFM. Its representation as a function of the average tip-surface separation d is called amplitude curve. The numerical solution of the weakly perturbed oscillator shows in some situations two different solutions for the vibration amplitude, a low (L) and high amplitude (H) solution. If the tip-surface separation and the external parameters are unchanged, the initial conditions will determine which solution is realized. 

For a weakly perturbed, harmonic damped driven oscillator, the resonance is shifted on the frequency scale depending on the sign of the interaction forces (Fig. 1.13). The availability of analytical expressions facilitates the applications of the weakly perturbed harmonic oscillator models for AM-AFM. Such harmonic models may be useful to illustrate the concepts used in AM-AFM well enough however, in most practical imaging cases, they do not describe the experiments [15]. 

The results demonstrate the relationship between the phase angle and energy dissipation. From a physics point of view, the action of attractive and repulsive, nonlinear tip-surface interactions contribute to the coexistence of two stable oscillation states in AM-AFM. The jump in the amplitude curve corresponds to transition from the attractive to the repulsive regime, near point b, where the phase changes sign. This will later be important for interpretations of phase images. 

Phase contrast in AM AFM can be observed primarily due to inelastic contributions and some elastic ones (topography, contact-noncontact transitions, and variation of elasticity if dissipative channels are present). Attractive (low amplitude, L branch) and repulsive (high amplitude, H branch) regimes are shown below (Fig. 1.15 and 1.16). 

In the past two decades AM-AFM has emerged as a powerful tool to study the morphology of liquid drops with nanometer resolution. Various imaging modes have been developed, and the conditions and parameters necessary to ensure reliable, nonperturbative imaging have been identified. The science of wetting phenomena on the nanoscale has greatly benefited from these advancements. Extensive AFM studies of the morphology of nanoscale droplets on a variety... 

In 1991, Albrecht et al. invented frequency modulation atomic force microscopy (FM-AFM) for operating d3mamic-mode AFM in vacuum environments. Before this invention, it was common to operate d3mamic-mode AFM with the amplitude detection method, which is referred to as amplitude modulation AFM (AM-AFM). In AM-AFM, the tip-sample distance is regulated such that the oscillation amplitude of the cantilever (A) is kept constant. 

AM-AFM was mainly used in air and liquid, and its applications in vacuum were very limited. This is because of the high Q factor in vacuum. For a t3q>ical cantilever, Q = 1,000-100,000 in vacuum, Q = 100-1,000 in air and Q = 1-10 in liquid. In dynamic-mode AFM, a high Q factor provides higher force sensitivity. In addition, the vacuum environment provides a clean surface and a well-defined environment, which are essential for the surface science studies. Thus, there were strong demands for operating d3mamic-mode AFM in vacuum. However, the time response of A is inversely proportional to the Q factor, so the use of AM-AFM in vacuum was difficult in most of the applications because of the slow time response. 

To resolve this issue, Albrecht et al. proposed to detect the frequency shift A/ of the cantilever resonance instead of A. In FM-AFM, the cantilever is always oscillated at its resonance frequency using a self-oscillation circuit. Thus, the A/ induced by the tip-sample interaction results in the frequency shift of the cantilever vibration. The A/ is detected from the cantilever deflection signal and used for the tip-sample distance regulation feedback. As the time response of A/ is free from the influence of Q, the time response of FM-AFM in vacuum is much faster than that of AM-AFM. Owing to the high force sensitivity obtained by the high Q factor and the atomically well-defined environment provided by vacuum, true atomic-resolution imaging by dynamic-mode AFM has become possible in 1995. ... 

Figure 20 presents am AFM image of the Ni deposit on A1 from IL-Ni-sulfate system. The presence of spherical, cluster tike formations can be clearly observed. A coating thickness of about 4 pm and a roughness around of 430 nm have been estimated, probably due to the initial non-homogeneities of the A1 metallic substrate. 

For imaging in IC-AFM (see Fig. 3.29), the amplitude of cantilever oscillation is used for feedback control, and the set point. Asp. is less than the free oscillation amplitude, A . This mode of operation is also referred to as amplitude modulation (AM) AFM. A convenient way to standardize the description of tapping conditions for both stiff and compliant materials is to use Ao, Asp, and Asp/Ao [108]. This ratio is called the set-point ratio r p. 

FIG. 26-9 Incident overpressure vs. scaled distance, surface hurst. The t points are from Kingery and PanniU, Memo Report ISIS BRL. Adapted fr am Department of Army, Navy, and Air- For ce TM5-1300, NAVFAC P-397, AFM 88-22.)... 

Wold DJ, Frisbie CD (2000) Formation of metal-molecule-metal tunnel junctions microcontacts to alkanethiol monolayers with a conducting AFM tip. J Am Chem Soc 122 (12) 2970-2971... 

Fig. 3. Total alkalis versus silica (TAS) and (b) AFM plot of Irvine and Baragar (1971), (c) modified Zr/Ti02-Nb/Y plot (Pearce, 1996) of Winchester and Floyd (1977), (d) Rock/chondrite-normalized REE diagram for rocks of amli-llica pluton and (e) rock/MORB-normalized spidergrams, (f) Th/Yb vsTa/Yb diagram.

Auletta T, de Jong MR, Mulder A, van Veggel FCJM, Huskens J, Reinhoudt DN, Zou S, Zapotoczny S, Schonherr H, Vancso GJ, Kuipers L. 3-Cyclodextrin host-guest complexes prohed under thermodynamic equilibrium thermodynamics and AFM force spectroscopy. J Am Chem Soc 2004 126 1577-1584. 

Zou S, Schoenherr H, Vancso GJ. Force spectroscopy of quadruple H-bonded dimers by AFM dynamic bond rupture and molecular time-temperature superposition. J Am Chem Soc 2005 127 11230-11231. 

Finally, I would like to admit that, even with such extensive reviews and revisions, the book is still neither perfect nor does it represent the last word. Especially in such an active field as STM and AFM, new concepts and new measurements come out every day. I expect that substantial progress will be made in the years to come. Naturally, I am looking forward to future editions. I am anxious to hear any comments and suggestions from readers, with whose help, the future editions of this book would be more useful, more truthful, and more accurate. Thus spake Johann Wolfgang von Goethe ... 

Schonherr, H., V. Chechik, C.J.M. Stirling, and G.J. Vansco. 2000. Monitoring surface reactions at an AFM tip An approach to follow reaction kinetics in self-assembled monolayers on the nanometer scale. J. Am. Chem. Soc. 122 3679-3687. 

Figure 15.7 Resorcin[4]arene photoswitch for self-assembly (a) and pictograms visualizing the diluted self-assembled monolayer of this photoswitch for single-molecule affinity studies by AFM (b).23 (Reprinted with permission from C. Schafer et al., J. Am. Chem. Soc. 2007,129, 1488-1489. Copyright 2007 American Chemical Society.)...

A feature of the neutron reflectivity study on polyDMDAAC and surfactant adsorption by Penfold et al. [74] was that the adsorbed layer of polyDMDAAC was remarkably robust and unaffected by the subsequent surfactant adsorption. This is not always the case, and Fielden et al. [76] reported a large increase in the thickness of the surface layer of AM-MAPTC on mica due to complex formation with SDS. Thickness increases with electrolyte and pH were reported for high molecular weight polyacrylamide adsorbed onto silica, measured by null ellip-sometry by Samoshina et al. [82] in the absence of surfactant. Complex formation at the interface, resulting in layer thickening, was also reported by Dedinaite et al. [83] for PCMA/SDS mixtures on mica from AFM measurements. 

C3A reacts with any Sufficient inner C-S-H AFt inside shell forming has formed to fill m the hexogonal plates of AFm. space behveen -am and Continuing formation of shell. The outer C-S-H... 

FIGURE 4.1.8 Tapping mode AFM topographs and 2-D GIXD patterns of 60-nm-thick pentacene films on (a) HMDS- and (b) OTS-treated Si02/Si substrates. (From Yang, H. et al., J. Am. Chem. Soc. 127, 11542, 2005. With permission.)... 

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