Resonance Instruments

As mentioned above in the context of forced oscillations, resonance occurs at a frequency given by Eq. (7.24) if the phase angle is small. From the resonance frequency, (o, the storage modulus is readily calculated  

In this case, measurements of the amplitudes of displacement and force, as well as the phase angle, are not required. The frequency of the force is varied while its amplitude is kept constant (ref. 6 p. 34-48). The frequency at which the amplitude of the displacement is maximum is taken as the resonance frequency. Usually several relatively decreasing maxima are obtained. 

The loss tangent can be obtained from the half-width of the resonance peak according to the expression 

The half-width Ago is the difference between two frequencies for which the amplitude of the motion is half as large as it is at resonance. See also Problem 17.3. 

The resonance method is useful when the data are required at only one frequency or at a small number of frequencies. In a typical device used to measure the dynamic tensile storage modulus, the rod, which has a circular or rectangular cross section, is hung by threads at nodal points. An oscillating force is applied at one end of the rod by means of a piezolectric transducer. The response is detected at the other end by a capacitive transducer. To achieve that, it is very convenient to paint the extremities of the rod in front of the transducers with cooloidal silver or another conductive paint. 

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The performance of the classifier has been verified using a number of practical applications, such as civil engineering [3], inspection of aerospace composite structures, ball bearings and aircraft multi-layer structures. Here we present shortly some results, focusing on detection of disbonds in adhesively joint multi-layer aerospace structures using Fokker Bond Tester resonance instrument, details can be found in [1]. 

To find explosives Gas analyzers, chromatography instruments, drift-spectrometers, neutron defectosopes, nuclear-magnetic and nuclear-quadrupole resonant instruments... 

Commercial mass analyzers are based almost entirely on quadrupoles, magnetic sectors (with or without an added electric sector for high-resolution work), and time-of-flight (TOE) configurations or a combination of these. There are also ion traps and ion cyclotron resonance instruments. These are discussed as single use and combined (hybrid) use. 

An added consideration is that the TOF instruments are easily and quickly calibrated. As the mass range increases again (m/z 5,000-50,000), magnetic-sector instruments (with added electric sector) and ion cyclotron resonance instruments are very effective, but their prices tend to match the increases in resolving powers. At the top end of these ranges, masses of several million have been analyzed by using Fourier-transform ion cyclotron resonance (FTICR) instruments, but such measurements tend to be isolated rather than targets that can be achieved in everyday use. 

A simple mass spectrometer of low resolution (many quadrupoles, magnetic sectors, time-of-flight) cannot easily be used for accurate mass measurement and, usually, a double-focusing magnetic/electric-sector or Fourier-transform ion cyclotron resonance instrument is needed. 

Fig. 2.3.2 A wire frame drawing and photograph of a Mark I GARFieid magnet as manufactured by Resonance Instruments Ltd. The third picture is a close up of the sample space.

There are two kinds of Type (2) ion trap mass spectrometers the quadrupole ion trap and the ion cyclotron resonance instruments. 

Ion conducting glasses, 12 585-586 Ion-cut process, 14 448-449 Ion cyclotron (ICR) analyzers, 15 663-664 Ion cyclotron resonance instrument, 15 664 Ion-dipole interactions, 14 411-418 Ion doping, in photocatalysis, 19 94-95 Ion doses, measuring, 14 444—445 Ion engines, cesium application, 5 705 Ion exchange, 14 380-426... 

Fig. 1.29 Diagram of an ion cyclotron resonance instrument. The magnetic field is oriented along the z-axis and ions ( ) are trapped according the same axis. Due to the cyclotronic motion the ions rotate around the z-axis in the x-y plane.

The most commonly used mass separators are quadrupoles, ions traps and time-of-flight analyzers, for which the principle of mass separation is discussed below. Additionally, other types such as magnetic sector field or Fourier-trans-form cyclotron-resonance instruments are available. 

Figure 16.13—Resolution. The figure on the left defines the parameters used to calculate resolution. To the right a low-resolution spectrum of a sample of lead is shown. The highest mass resolutions are achieved with cyclotron resonance instruments (see Fig. 16.8). The resolution greatly depends on the compound chosen for the calculation. For instruments in which Am is a constant, the upper mass limit theoretically corresponds to the maximum resolution, i.e. this the value at which masses m and m + 1 can no longer be distinguished from one another.

Nuclear Magnetic Resonance (NMR). This technique is essentially based on the same principle as ESR, but NMR is capable of detecting nuclei (MHz) instead of electrons (GHz). (Lack of a standardized nomenclature has resulted in numerous modifiers in connection with magnetic resonance instrumentation—electron, proton, nuclear, etc, plus apphcaaon-related terms, such as silicon-29, oxygen-17, nC S,P NMR, elc.)... 

Milgram, K. E. Abatement of spectral interferences in elemental mass spectrometry design and construction of inductively coupled plasma ion sources for Fourier Transform ion cyclotron resonance instrumentation, Ph. D. Thesis, University of Florida, 1997, Diss. Abstr. Int., B 1998, 59(2), 639. 

As the name suggests, electric resonance experiments make use of electric fields to achieve molecular state selection. Figure 8.25 shows a schematic diagram of a molecular beam electric resonance instrument, which we will discuss in more detail when we describe experiments on the CsF molecule. In contrast to the magnetic resonance apparatus discussed earlier, the A, B and C fields in figure 8.25 are all electric fields. In... 

Figure 8.33. Block diagram of the molecular beam electric resonance instrument used by Freund, Fisk, Flerschbach and Klemperer [55]. Transitions induced in the C field region which obey the selection rule AM = 1 result in an increase in the number of molecules reaching the detector this is the flop-in mode of detection.

The first successful application of molecular beam electric resonance to the study of a short-lived free radical was achieved by Meerts and Dymanus [142] in their study of OH. They were also able to report spectra of OD, SH and SD. Their electric resonance instrument was conventional except for a specially designed free radical source, in which OH radicals were produced by mixing H atoms, formed from a microwave discharge in H2, with N02 (or H2S in the case of SH radicals). In table 8.24 we present a complete A-doublet data set for OH, including the sets determined by Meerts and Dymanus, with J = 3/2 to 11/2 for the 2n3/2 state, and 1/2 to 9/2 for the 2ni/2 state. Notice that, for the lowest rotational level (7 = 3/2 in 2n3/2), the accuracy of the data is higher. These transitions were observed by ter Meulen and Dymanus [143], not by electric resonance methods, but by beam maser spectroscopy, with the intention of providing particularly accurate data for astronomical purposes. This is the moment for a small diversion into the world of beam maser spectroscopy. It has been applied to a large number of polyatomic molecules, but apparently OH is the only diatomic molecule to be studied by this method. 

B5. Bible, R. H., Nuclear magnetic resonance instrumentation since the Varian A-60. Appl. Spectrosc. 24, 326-331 (1970). 

Electron Spin Resonance. Trapped free radicals in irradiated starch were studied utilizing an electron paramagnetic resonance instrument (Varian Associates Type 4500) fitted with a 100-kc. field modulation, Hi-lo power microwave bridge, and a multipurpose specimen cavity. The instrument is stated to have an accuracy of 10% and a minimum resolution of about lO spins per cc. Variants 0.1% pitch mixed with potassium chloride calibration standard containing 10 " spins per cm. of length was used as the reference curve. Samples and standard were contained in quartz tubes, 4 mm. in i.d., in sufficient depth to fill the cavity. 

H NMR measurements were performed at 20°C using a Maran NMR spectrometer (Resonance Instruments, UK) operating at resonance frequency of 23 MHz. The second moment of the FIDs was calculated using Microsoft Excel Solver. 

In analytical work, a resonance instrument can produce good results, though these will be in no case better and in some cases poorer than the results from a well-designed conventional instrument. Since many elements have a number of resonance lines with diflFerent sensitivities, and the resonance detector does not distinguish between them, the sensitivities achieved with resonance detectors are often poorer than those with monochromators. Baseline drift for single beam instrumentation is likely to be comparable. The considerations affecting the signal-to-noise ratio are complex, but the upshot is that the two types of instruments are comparable in this respect also. 

Various forms of tandem mass spectroscopy (MS/MS) have also been used in the analysis of biomolecules. Such instruments consist of an ionisation source (ESI or MALDI or other) attached to a first mass analyser followed by a gas-phase collision cell. This collison cell further fragments the selected ions and feeds these ions to a second mass detector. The final mass spectrum represents a ladder of fragment ions. In the case of peptides the collision cell usually cleaves the peptides at the amide bond. The ladder of resulting peptides reveals the sequence directly [496]. Thus, tandem MS instruments, such as the triple quadrupole and ion-trap instruments have been routinely applied in LC-MS/MS or ESI-MS/MS for peptide sequencing and protein identification via database searching. New configurations, which have been moving into this area include the hybrid Q-TOF [498], the MALDI-TOF-TOF [499] and the Fourier transform ion cyclotron resonance instruments [500]. 

The manufacturers of these lands of instruments all have a long list of appHca-tions. Most of the appHcations are similar and many are pre-packaged as specific analyzers so that they simply unpack, set up and data is acquired within an hour or so after the magnet temperature equilibrates. The instrument vendors for broadline systems are Bruker Instruments [22], Oxford Instruments [23], Praxis [24], Process Control Technology (PCT) [25] and Resonance Instruments [26]. Determination of oil and/or water content dominates the applications. Oil and water analyses are established for seeds and soil in the agriculture industry, catalysts and detergents in the chemicals industry, capsules, tablets and powders in the pharmaceutical and cosmetic industries as well as a wide variety of foodstuffs. 

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