Field-frequency plot

Fig. 8. The water-proton spin-lattice relaxation rates vs. magnetic field strength plotted as the Larmor frequency at 282 K for hexacyanochromate(II) ion ( ), trioxalatochromate(III) ion ( ), and trimalonatochromate(III) ion (A). The lines were computed using translational diffusion models developed by Freed with and without the inclusion of electron spin relaxation effects 54,121).

Fig. 18. The proton spin-lattice relaxation rate recorded as a function of the magnetic field strength plotted as the proton Larmor frequency for lysozyme samples. Dry ( ), hydrated to 8.9% ( ), 15.7% (O). 23.1% (A), and cross-linked in a gel ( ). The solid lines were computed from the theory. The solid lines are fits to the data using Eq. (4) with Rs given by Eq. (6). The two parameters adjusted are Rsl and b (97). The small peaks most apparent in the dry samples are caused by cross-relaxation to the peptide nitrogen spin (90,122).

The first measurements of microwave ionization in any atom were carried out with a fast beam of H by Bayfield and Koch1, who investigated the ionization of a band of approximately five n states centered at n = 65. Using microwave and rf fields with frequencies of 9.9 GHz, 1.5 GHz, and 30 MHz, to ionize the atoms they found that the same field was required at 30 MHz and 1.5 GHz to ionize the atoms, but that a smaller field was required at 9.9 GHz. The measurements showed that at n = 65 frequencies up to 1.5 GHz are identical to a static field. Later, more systematic measurements have confirmed the initial measurements and have allowed significant refinements of our understanding. In Fig. 10.16 we show the ionization threshold fields (in this case the field at which there is 10% ionization) of H in a 9.9 GHz field.21 The ionization fields are plotted as n4E vs n3a>, and they bring out two factors. First, at low frequencies the field required is l/9n4, the static field required to ionize the red n Stark state of m n. Second, as shown by the scaling of the horizontal axis, the required field drops below l/9n4 as the microwave frequency approaches the interval between adjacent n states, 1 In3. 

Fig. 9. A rotation spectrum is produced by observing the motion of a cell in a rotating electric field of constant amplitude and plotting the rotation speed of the cell against frequency of the field. In solutions of low conductivity, the cell rotates in the opposite direction to the field (anti-field rotation) at low frequencies. This rotation reaches a peak when the field frequency corresponds to the charge relaxation time of the membrane. The position of this peak therefore contains information about membrane permittivity and conductivity. As the frequency increases further, the rate of cell spinning falls, becoming zero at about 1 MHz. Above this frequency, the cell starts to spin with the field (co-field rotation) and a second peak is reached. The frequency at which this peak occurs depends in practice mainly on the conductivity of the interior of the cell. It may be used for non-destructive determination of cytosolic electrolyte concentration.

Figure 8.10 (a) G versus frequency w for an ER fluid composed of 20 wt% alumina particles in poly(dimethylsiloxane) at an ac field frequency of 500 Hz. (b) Master plot superposing the data of (a). E 5 is the root-mean-square field strength at 500 Hz. (From Parthasarathy et al. 1994, with kind permission from Elsevier Science-NL, Sara Burgerhartstraat 25, 1066 KV Amsterdam, The Netherlands.). 

The energy quantum used in NMR is much smaller than that needed for electron spectroscopy,but the response is less sensitive, and a large sample is needed also the interpretation is even less straightforward. Supported metal catalysts are very suitable for study and the Pt nucleus has been extensively examined (Section 2.4.2). This dependence of NMR amplitude on field/frequency shows separate, if not well resolved, peaks at 1.138 and 1.10 G kHz, corresponding respectively to Knight shifts of-3.34 and zero percent and thus to bulk and surface atoms. The plots have been imaginatively deconvoluted, but no use... 

Figure 2 Precision of the initial stabilization of the evolution field. The plot represents the voltage transient recorded with a Hall probe (6 iJ.T/mV) and a 16 bit analogue-to-digital converter. The field level corresponds to a proton Larmor frequency of 3.5 kHz. The fieldcycling relaxometer is described below. This plot demonstrates that the evolution field can be stabilized within 1 digital unit in a ring-down time less than 1 ms.

A good discussion of plasma waves and a tabulation of their characteristics is available (12). Useful plots of the dispersion relations for various frequencies, field conditions, geometries, and detailed mathematical relationships are given in Reference 13. 

Fig. 52. (a) The frequency swept dipole-dipole driven NMR spectra of thioanisole recorded at a variety of magnetic fields, (b) The NMR and sideband transitions observed in the thioanisole data presented as a plot of magnetic field versus transition frequency. The transitions are defined in fig. 51. 

Clearly for titration purposes, it is low-dielectric constant conducting solutions which will be important, and addition of a suitable reagent to such a solution permits the plotting of a titration curve from which the end point can be deduced as described in Section 13.7. It should be noted that in view of the enhanced conductance in the high-frequency field, the maximum concentration of reagents is much smaller than with normal conductimetric titrations, and the maximum concentration will depend on the frequency chosen. It is found that... 

Fig. 1.24 Two examples of frequency-depen-dent relaxation times - 7"i is plotted as a function of the proton resonance frequency V = ou/2 JI, which was obtained from measurements at different magnetic fields strengths. Left polyisoprene (PI) melts and solutions of the same samples at 19wt-% concentration in cyclohexane. Numbers indicate the average molecular weight. The difference between the melt and solution increases towards lower magnetic fields strengths, the frequency dependence is more pronounced for melts.

FIGURE 9.3 Spectra of the mixture of canthaxanthin (2mM) and A1C13 (2mM) in CH2C12 measured at 60 K at the field B0=3349G and microwave frequency 9.3757 GHz (a) superimposed plot of a set of three-pulse ESEEM spectra as the modulus Fourier transform and (b) HYSCORE spectrum measured with a x=152ns. (From Konovalova, T.A., J. Phys. Chem. B, 105, 8361, 2001. With permission.)... 

HYSCORE spectra of zeaxanthin radicals photo-generated on silica-alumina were taken at two different magnetic fields B0=3450G and B0=3422G, respectively. In order to combine the data from the two spectra, the field correction was applied (Dikanov and Bowman 1998). The correction consists of a set of equations that allow transformation of spectra to a common nuclear Zeeman frequency. The set of new frequencies was added to that of the former spectrum and plotted as the squares of the frequencies v2a and v2p. Examples of these plots can be found in Focsan et al. 2008. 

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