Measured spins, total number

The most popular, and also a very accurate, experimental method for measuring nonselective spin-lattice relaxation-rates is the inversion recovery (180°-r-90°-AT-PD)NT pulse sequence. Here, t is the variable parameter, the little t between pulses, AT is the acquisition time, PD is the pulse delay, set such that AT-I- PD s 5 x T, and NT is the total number of transients required for an acceptable signal-to-noise ratio. Sequential application of a series of two-pulse sequences, each using a different pulsespacing, t, gives a series of partially relaxed spectra. Values of Rj can... 

Spectral normalization Many spectral analysis procedures compare spectrum per spin, therefore the measured spectrum has to be normalized (Fig. 15.8B). Normalization is carried out by dividing the measured spectrum by its 2nd integral, which is proportional to the total number of spins. 

Figure 2. A - Experimentally measured and theoretically calculated values of dns/dt, the number of Stokes photons per unit time emitted from the atomic vapor cell. For each plot, ns = f dt dns/dt represents the total number of photons emitted from the cell. The write laser power is varied from 25 mW to 100 mW. B - Experimentally measured and theoretically calculated values of dnAs/dt, the number of anti-Stokes photons per unit time emitted from the atomic vapor cell. The experimental pulse shapes correspond to a Stokes pulse with ns 3 photons, and the theoretical curves assume an initial spin wave with nspin = 3 excitations and an optical depth of 20. Each curve is labeled with the power of the retrieve laser. Inset theoretical calculation of the number of flipped spins per unit length dnspin/dt as a function of position in the atomic cell, for nspin = 3. C - Measured anti-Stokes pulse width (full-width at half-maximum) and total photon number as a function of the retrieve laser intensity. Lines are intended only to guide the eye.

The applicability of spectroscopic methods (other than NMR) for determining functionality in humic substances is reviewed. Spectroscopic methods, like all other investigational techniques, are severely limited when applied to humic substances. This is because humic substances are comprised of complicated, ill-defined mixtures of polyelectrolytic molecules, and their spectra represent the summation of the responses of many different species. In some cases only a small fraction of the total number of molecules contributes to the measured spectrum, further complicating the interpretation of spectra. The applicability and limitations of infrared spectroscopy, Raman spectroscopy, UV-visible spectroscopy, spectrofiuorimetry, and electron spin resonance spectroscopy to the study of humic substances are considered in this chapter. Infrared spectroscopy, while still very limited when applied to humic substances, is by far the most useful of the methods listed above for determining functionality in these materials. Very little information on the functionality of humic substances has been obtained by any of the other spectroscopic methods. 

Obtain the NMR spectrum of a straight-chain alkane, such as n-octane. Identify the methyl and methylene peaks. Note the chemical shift and the spin-spin splitting. Measure the total area of the methyl and methylene peaks and correlate this with the number of methyl and methylene protons in the molecule. 

Stacked thin films were prepared as described [67]. Single ultrathin films of various thickness were prepared on glass substrates by spin coating of a toluene solution. The film was floated onto the surface of water and transferred to the top of a substrate or a stack of polymer thin films on a substrate. This procedure, using ultrathin films with the same thickness, was repeated until the total number of stacked thin layers reached several hundred for the DSC measurements and ten layers for the dielectric measurements (see Tables 1 and 2). For the dielectric measurements, the first layer of P2CS was prepared directly onto an Al-deposited... 

For Ce atoms the 4f level has the total angular momentum S = f and a total number of rotational levels N( = 2S +1 = 6. The crystal field usually splits the degeneracy, but if the level splitting is sufficiently small, all N( substates can participate in spin fluctuation. The theory of the resonance level remains qualitatively the same, but the large Nf value allows the so-call l/N approximation, which helps to simplify the calculation of the level width (Bickers et al. 1985, 1987). At zero temperature the resonance is found to have an asymmetric lineshape with a level width measured by k T. When the temperature is increased the line drops in height and shifts in energy as shown in fig. 28. Although the theory introduces a new parameters in addition... 

The bound fraction p represents the ratio of the number of segments in close contact with the surface (i.e. in trains) to the total number of segments in the polymer chain. The polymer bound fraction, p, can be directly determined using spectroscopic methods such as infrared (IR), electron spin resonance (ESR) and nuclear magnetic resonance (NMR). The IR method depends on measuring the shift in some absorption peak for a polymer and/or surface group [62-64]. The ESR and NMR methods depend on the reduction in the mobility of the segments that are in close contact with the... 

You can see from this example how NMR and NMR spectroscopy complement each other. NMR spectra provide an estimate of the electronic environment (i.e., electron rich versus electron poor) of a hydrogen nucleus under observation (S), a measure of its relative abundance (integration), and an indication of how many neighbors (and their number of types) it has (spin-spin splitting). Proton-decoupled NMR provides the total number of chemically distinct carbons, their electronic environment (5), and, in the DEPT mode, even the quantity of their attached hydrogens. Application of both techniques to the solution of a structural problem is not unlike the methods used to solve a crossword puzzle. The horizontal entries (such as the data provided by NMR spectroscopy) have to fit the vertical ones (i.e., the corresponding NMR information) to provide the correct answer. 

We therefore turn to the second triplet possibility, EJin d ). First-order spin-orbit coupling splits this orbitally degenerate state as sketched below. We include the D h symmetry labels and also values of the cylindrical quantum number which measures the total parallel angular momentum [22]. 

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