Resonant forcing

A wide variety of measurements can now be made on single molecules, including electrical (e.g. scanning tunnelling microscopy), magnetic (e.g. spin resonance), force (e.g. atomic force microscopy), optical (e.g. near-field and far-field fluorescence microscopies) and hybrid teclmiques. This contribution addresses only Arose teclmiques tliat are at least partially optical. Single-particle electrical and force measurements are discussed in tire sections on scanning probe microscopies (B1.19) and surface forces apparatus (B1.20). 

Dynamic techniques are used to determine storage and loss moduli, G and G respectively, and the loss tangent, tan 5. Some instmments are sensitive enough for the study of Hquids and can be used to measure the dynamic viscosity T 7 Measurements are made as a function of temperature, time, or frequency, and results can be used to determine transitions and chemical reactions as well as the properties noted above. Dynamic mechanical techniques for sohds can be grouped into three main areas free vibration, resonance-forced vibrations, and nonresonance-forced vibrations. Dynamic techniques have been described in detail (242,251,255,266,269—279). A number of instmments are Hsted in Table 8. Related ASTM standards are Hsted in Table 9. 

Resonance-Forced Vibration. Resonance-forced vibration devices drive the vibration of the specimen. This can be over a range of frequencies that includes the resonant frequency, which is detected as a maximum in the ampHtude, or the instmment can be designed to detect the resonant frequency and drive the specimen at that frequency. An example of the resonance-forced vibration technique is the vibrating reed. A specimen in... 

Here the reactants can combine to form the ground state of the supposed intermediate. Since the ionization potentials of N (14.54 e.v.) and NO (9.25 e.v.) are very different, any resonance force of the type suggested by Giese (8) will be repulsive but weak. Thus, there should be no barrier to reaction (7), and it is known to be fast at low ion energies (23). 

Simpson WT, Peterson DL (1957) Coupling strength for resonance force transfer of electronic energy in Van der Waals solids. J Chem Phys 26 588-593... 

This fundamental relation can be extended to the many-body case, and a correlation between the interatomic force in the attractive-force regime and the tunneling conductance can be established. For metals, an explicit equation between two sets of measurable quantities is derived. Of course, the simple relation between the measured force and measured tunneling conductance is not valid throughout the entire distance range. First, the total force has three components, namely, the van der Waals force, the resonance force, and the repulsive force. Second, the actual measurement of the force in STM and... 

AFM is further complicated by the deformation of the tip and sample near the gap region (Teague, 1978 Coombs and Pethica, 1985 Chen and Hamers, 1991a). At very short tip-sample distances, the reading from the z piezo no more represents the gap displacement. Nevertheless, in the normal working distance range of STM, the dominant force is the resonance force, and the simple relation is valid. 

Fig. 7.1. Three regimes of interaction in the hydrogen molecular ion. (a) At large distances, R>16 a.u., the. system can be considered as a neutral hydrogen atom plus a proton. The polarization of the hydrogen atom due to the field of the proton generates a van der Waals force, (b) At intermediate distances, 16>/ >4 a.u. the electron can tunnel to the vicinity of another proton, and vice versa. A resonance force is generated, which is either attractive or repulsive, (c) At short distances, R<4 a.u., proton-proton repulsion becomes important. (Reproduced from Chen, 1991c, with permission.)...

Second, the sensitivity of AFM. In a typical AFM (Binnig et al., 1986), the force sensitivity is about 0.01 nN. In the range of 4-10 a.u., the resonance force in the hydrogen molecular ion is 4 nN to 0.01 nN. Therefore, the resonance force (attractive atomic force) of a single chemical bond, extended over a distance of 3 A, can be detected. On the other hand, the van der Waals force of a pair of neutral atoms, when it is distinguishable from the total force. 

Magnetic resonance force microscopy would allow direct chemical imaging of samples to depths of about 100 nm for a system providing 1 nm lateral resolution. In such experiments, depth resolution is obtained by scanning the radio frequency employed to flip the electron or nuclear spins in the sample. 

Rugar, D., R. Budakian, H.J. Mamin, and B.W. Chui. 2004. Single spin detection by magnetic resonance force microscopy. Nature 430 329-332. 

As an example of principle number 4 above, consider a locally excited large panel on which resonant bending waves account for most of the vibratory response. However, assume that these resonant waves have a wavelength shorter than that of free waves in the surrounding air. In such a case the resonant waves are poorly coupled to the air, and radiate very little sound. What radiation there is can be dominated by non-resonant forced motion around the drive point (and at other discontinuities). As a result, applied damping can reduce the resonant response, but not the forced motion and the radiation of sound. 

How can a phenomenon of orbital dynamics and celestial mechanics, such as the Laplace resonance, result in distinctive tectonic patterns on a planetary body The linking process is tides. The orbital resonance forces orbital eccentricities. Thus, as a satellite orbits Jupiter, even if its... 

P. Coullet and K. Emilsson. Pattern formation in the strong resonant forcing of spatially distributed oscillators. Physica A, 188 190-200, 1992. 

Thus, the velocity of the resonant drift induced by the periodic modulation is determined by the ratio h/Tm- Under resonant forcing, ujm = the drift is along a straight line whose direction depends on the initial orientation of the spiral wave o and on the constant ip. More generally, if the parameter modulation is given by... 

Mamin HJ, Budakian R, Chui BW, Rugar D et al. (2005) Magnetic resonance force microscopy of nuclear spins Detection and manipulation of statistical polarization. Phys. Rev. B 72 24,413-24,419. 

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