Pulsed experiments

As long as the strong B] field is on, the magnetization continues to rotate, or precess, around B. The strength of the B field is such that, when it is on, precession occurs preferentially around its direction (y), rather than around the natural direction of B (z). Consequently, the primary field present at the nuclei is B, so the expression for the precession frequency becomes co = yB. More precisely, this equation holds at the resonance frequency (Oo = 7 0. Farther and farther from the resonance frequency, the effect of B wanes, and precession around Bq returns. A full mathematical treatment requires the inclusion of terms in both Bq and B, but, qualitatively, our interest focuses on the events at the resonance frequency. 

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With the advent of short pulsed lasers, investigators were able to perfonn time resolved coherent Raman scattering. In contrast to using femtosecond pulses whose spectral widtii provides the two colours needed to produce Raman coherences, discussed above, here we consider pulses having two distinct centre frequencies whose difference drives the coherence. Since the 1970s, picosecond lasers have been employed for this purpose [113. 114], and since the late 1980s femtosecond pulses have also been used [115]. Flere we shall briefly focus on the two-colour femtosecond pulsed experiments since they and the picosecond experiments are very similar in concept. 

Figure Bl.15.11. Fomiation of electron spin echoes. (A) Magnetization of spin packets i,j, /rand / during a two-pulse experiment (rotating frame representation). (B) The pulse sequence used to produce a stimulated echo. In addition to this echo, which appears at r after the third pulse, all possible pairs of the tluee pulses produce primary echoes. These occur at times 2x, 2(x+T) and (x+2T).

The electron-spm echo envelope modulation (ESEEM) phenomenon [37, 38] is of primary interest in pulsed EPR of solids, where anisotropic hyperfme and nuclear quadnipole interactions persist. The effect can be observed as modulations of the echo intensity in two-pulse and three-pulse experiments in which x or J is varied. In liquids the modulations are averaged to zero by rapid molecular tumbling. The physical origin of ESEEM can be understood in tenns of the four-level spin energy diagram for the S = I = model system... 

The F-eurve ean also be determined from the E-eurve obtained by a pulse experiment aeeording to Equation 8-3. For a plug flow reaetor, the step is extremely sharp, and in the limit it would approaeh a Heaviside funetion at the mean residenee time. The Heaviside unit funetion H(t - t j is... 

Sofer and Hagel, 1997). The result should, in theory, be identical to the pulse experiment. This method is used frequently in industrial laboratories. 

A pulse of a racemic mixture (5 g each enantiomer) was carried out to check the adsorption model and to predict the mass transfer coefficient. The other model parameters used in simulation were = 0.4 and Pe = 1000. The mass transfer coefficient used to fit experimental and model predictions in the pulse experiment was k = 0.4 s k Model and experimental results are compared in Figs. 9-16 and 9-17. 

Two additional systematic errors may arise in selective pulse experiments associated with pulse selectivity and relaxation during excitation. Pulse... 

However, the relaxation contributions obtained from Eq. 22 were not satisfactorily compared with those obtained from specific, deuterium-substitution experiments and single- and double-selective relaxation-rates. Moreover, the errors estimated for the triple-pulse experiments were very much larger than those observed for the other techniques. This point will be discussed next. 

Multiple-pulse experiment An experiment in which more than one pulse is applied to the nuclei. 

Garcia-Araez N, Climent V, Feliu JM. 2008. Evidence of water reorientation on model electrocatalytic surfaces from nanosecond-laser-pulsed experiments. J Am Chem Soc 130 3824-3833. 

Results at (T 0.002-0.004 N/m are found to be in good qualitative agreement with the short pulse experiments [104] with jSexper ranging from 0.018 to 0.036. 

Highly sophisticated pulse sequences have been developed for the extraction of the desired information from ID and multidimensional NMR spectra [172]. The same techniques can be used for high-resolution 1-NMR, s-NMR and NQR. Pulse experiments are commonly used for the measurement of relaxation times [173], for the study of diffusion processes [174] and for the investigation of chemical reactions [175]. Davies et al. [176] have described naming and proposed reporting of common NMR pulse sequences (IUPAC task group). An overview of pulse sequence experiments has been given [177],... 

Another advantage of frequency response analysis is that one can identify the process transfer function with experimental data. With either a frequency response experiment or a pulse experiment with proper Fourier transform, one can construct the Bode plot using the open-loop transfer functions and use the plot as the basis for controller design.1... 

The pulse experiment is not crucial for our understanding of frequency response analysis and is provided on our Web Support, but we will do the design calculations in Section 8.3. 

At the very beginning of our discussion in 1.1.1, we mentioned that any pulse experiment begins with a delay period. This is necessary so that the spins can return to equilibrium before they are excited. After excitation (when the pulse is turned off) we observe the FID, the free induction decay What decays The induced magnetization of the spins, and this process is known as relaxation. It may be slow or fast, as we shall see, and can also occur via a number of processes, which are discussed in detail in the monographs we have recommended for further reading. We will only treat relaxation very briefly here. 

It is assumed that the reactive gas A has adsorption characteristics similar to those of the gas used in the pulse experiment. 

In spite of the apparent simplicity of the method, its drawback comes from the fact that a two-spin system has been assumed. It provides merely global information spanning all protons prone two interact by dipolar coupling with the considered carbon. Selective information requires pulsed experiments stemming from the general solution of Equation (14) given below. 

The pulse experiments demonstrated that active sites for propane dehydrogenation are formed upon exposure of the oxide form of gallium modified ZSM-5 to propane itself. A constant 1 1 ratio of hydrogen produced to propane consumed is attained after a number of pulses with little propene formation, which suggests that, after propane dehydrogenation to propane, aromatization proceeds through hydrogen transfer reactions. 

In a typical pulse experiment, a pulse of known size, shape and composition is introduced to a reactor, preferably one with a simple flow pattern, either plug flow or well mixed. The response to the perturbation is then measured behind the reactor. A thermal conductivity detector can be used to compare the shape of the peaks before and after the reactor. This is usually done in the case of non-reacting systems, and moment analysis of the response curve can give information on diffusivities, mass transfer coefficients and adsorption constants. The typical pulse experiment in a reacting system traditionally uses GC analysis by leading the effluent from the reactor directly into a gas chromatographic column. This method yields conversions and selectivities for the total pulse, the time coordinate is lost. 

Figures 7-9 show the fractional conversion of methanol in the pulse as a function of temperature for the three catalysts and the three methanol feeds. Evidently the kinetic isotope effect is present on all three catalysts and over the complete temperature range, indicating that the rate limiting step is the breaking of a carbon-hydrogen bond under all conditions. From these experiments, the effect cannot be determined quantitatively as in the case of the continuous flow experiments, but to obtain the same conversion of CD,0D, the temperature needs to be 50-60° higher. This corresponds to a factor of about three in reaction rate. The difference in activity between PfoCL and Fe.(MoO.), is larger in the pulse experiments compared to tHe steady stateJ results.

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