The pulse experiment

The frequency function is a Lorentzian with linewidth at half height of (jt72)-i(= Ri/n). The same, of course, holds in the continuous wave experiment. R2 is a measure of the uncertainty of the energy levels, which gives the linewidth in every spectroscopy. The uncertainty principle, according to which the uncertainty in energy of a level is inversely proportional to the lifetime, tells us that T2 is a measure of the lifetime of the energy levels. 

If the frequency of the pulse is different from the resonating frequency, nothing changes as long as the pulse contains the latter frequency as a component. It 

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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. 

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. 

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

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. 

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.

The pulse experiments using orthovanadates and V/y-AFCb catalysts showed that high selectivity for dehydrogenation of butane could be obtained by reaction of butane with lattice oxygen. This has also been demonstrated with other oxides, including Mg-Mo oxide (43, 44). 

An optical consideration specific to the use of the TOF-MS with high-intensity sources is the removal of background ions, plasma gas ions, and matrix ions to prevent detector saturation. To date, this has been accomplished with parallel-plate deflection in the flight path, which is depicted in Fig. 12.6. Removal of specific m/z ions is accomplished by the application of a time-dependent potential to one, or both, of the plates at some time delayed with respect to the repeller pulse. In this way, those ions between the plates at the time of the pulse experience a field transverse to the flight axis and are removed from the flight path. The voltage pulses employed here must have fast rise and fall times (<10-20 nsec), and be applied at precise delay intervals to ensure that mass resolution is not compromised, and to allow for the unimpeded passage of the previous and subsequent masses. Also, the... 

In contrast to the pulsed experiments, the main problem for many years in cw experiments was to observe any signal at all. However, this is not apparent from simple feasibility estimates, as we now show. We assume for simplicity that one excites the atoms using two counter-propagating plane-polarized gaussian beams each with the... 

Figure 6c, d shows the results simulated for a case in which Wetu 0 but E = 0, i.e., only GSA/ETU is active. The pulsed experiment. Fig. 6c, shows the characteristic delayed maximum observed in Fig. 4b. When E = 0, N2 has a value of exactly zero at time zero, and so the rise of the upconversion transient truly begins at zero. Comparison to Fig. 6 a, b shows that this rise derives from the decay rate constant of the upper state, k2 = A 2a + A 2b- Since N2 is proportional to Nf in ETU (Eqs. 7 and 10), the decay of the transient N2 population lasts substantially longer than the natural decay of the upper state, and has a rate constant exactly twice that of Ni under these low-power conditions when all of the above assumptions are met. Figure 6d shows the corresponding data following a square pulse. The decay again proceeds with a rate constant exactly twice that of Nj under the assumed conditions, with a small deviation at short times where k2 is still consequential. Based on this comparison, it is clear that ESA and ETU mechanisms are readily distinguishable using either square-wave or pulsed excitation modes under these conditions (see below for k2 < ki).

Pulse NMR techniques allow one to not only measure the NMR spectrum of the sample but also to evaluate the relaxation times of the nuclei present. The relaxation information is not readily obtainable from the continuous-wave experiment, and, therefore, in addition to being much faster, the pulse experiment also yields more information than the continuous-wave experiment. 

Rabo, Risch, and Poutsma (58) extended these measurements to cobalt and ruthenium, and moreover varied the temperature of the hydrogenation. Their results clearly demonstrate that at room temperature C ds is much more reactive then CO ds- However, at higher temperatures both C ds and COjds are converted (Table V). In their concise discussion the authors state The pulse experiments at 200-300°C suggest that surface carbon is more reactive than non-dissociated CO. No conclusive proof regarding the relative reactivities of these two species could be obtained, however, because both of these species are present, and they both react with hydrogen in this temperature range (58, p. 307). As we know that, whatever the rate may be, CO converts under actual synthesis conditions, this remark raises the crucial question whether it is CO ds or C js that is the source of the reaction products in actual synthesis. 

Evidence yielded by the pulsed experiments for predominance of N2O in the prompt product detected fi om CO pulse contact with NO//0.5% Rh02/Ce02 could likewise be understood in terms of the C 0 pulse having scavenged oxygens from the N 0-covered surface, thereby facilitating N2O formation through N + - N2O reaction events. 

Cumene is cracked in a recycle reactor over commercial H-ZSM5 extrudates during a pulse experiment. The results are compared to those obtained from steady state measurements. A linear model for diffusion, adsorption and reaction rate is applied to reactants and products. In contrast to literature it is shown that if the Thiele modulus is greater than 5, the system becomes over parameterised. If additionally adsorption dynamics are negligible or not measurable, only one lumped parameter can be extracted, which is the apparent reaction constant found from steady state experiments. The pulse experiment of cumene is strongly diffusion limited showing no adsorption dynamics of cumene. However, benzene adsorbed strongly on the zeolite and could be used to extract transient model parameters. 

The rate of CO2 injection corresponds to an average amoimt of C (in the form of CO2) of 0.0135 pmol/sec, i.e. 0.162 pg/sec. Taking into accoimt that the specific surface area of the La203 is 10 m /g, and that the mass of catalyst used in the pulse experiment was 20 mg, the injection rate corresponds to 0.81 pg/secW. At this rate, the catalyst is still able to adsorb and desorb the CO2 reaching a pseudo steady state with an oscillation of constant amplitude. 

The re-oxidation of Tb203 has also been studied in the same manner as that of ceria, i.e. by combining oxygen pulses at 298 K and TPO [333]. Re-oxidation mainly occurs during the TPO run (890 fimole 02 g ), the oxygen uptake associated with the pulse experiment at 298 K being much smaller (5 (imole 02.g ). As already noted, under the TPO conditions (P02 38 Torr) re-oxidation to dioxide is far from completion (theoretical uptake for full re-oxidation to dioxide 1340 pmole 02.g ). 

In both Equations 60 and 61, it has been assumed that T T2, so that exp(-T/T2) can be ignored with respect to one. Substituting Equations 60 and 61 into Equation 59 gives the maximum attainable S/N in the pulse experiment ... 

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