Area, under pulse shape

Shaped pulses are created from text files that have a line-by-line description of the amplitude and phase of each of the component rectangular pulses. These files are created by software that calculates from a mathematical shape and a frequency shift (to create the phase ramp). There are hundreds of shapes available, with names like Wurst , Sneeze , Iburp , and so on, specialized for all sorts of applications (inversion, excitation, broadband, selective, decoupling, peak suppression, band selective, etc.). The software sets the maximum RF power level of the shape at the top of the curve, so that the area under the curve will correspond to the approximately correct pulse rotation desired (90°, 180°, etc.). When an experiment is started, this list is loaded into the memory of the waveform generator (Varian) or amplitude setting unit (Bruker), and when a shaped pulse is called for in the pulse sequence, the amplitudes and phases are set in real time as the individual rectangular pulses are executed. 

The results to be expected from a typical TAP experiment have been simulated (35) for a simple irreversible adsorption and are shown in Fig. 2. If there is no adsorption, the pulse at the reactor outlet is represented by curv e A. For > 0, some of the inlet pulse (N a moles of A) remains on the catalyst, and the amount is proportional to the difference between the areas under curve A and curve B, for example. Figure 3 shows what happens with reversible adsorption. For fast adsorption and slow desorption, there may be two peaks as shown by curve C. After a sufficient length of time, all the gas that was initially adsorbed will have left in the exit peak. Cleaves et al. (35) also show that for values of k. and kj that are sufficiently high so that the gas and adsorbed phases are everywhere in equilibrium, the response curve has the shape of curv e A but the peak height is reduced to 1.85/(1 + Keq). 

The aim of BPS-MS approach presented here can be summarized by comparing the simulated receiver operator characteristic (ROC) curves shown in Figure 1. Each additional dimension of analysis (a distinct pulse shape, that yields distinct mass spectrum) enlarges the area under the curve and therefore the confidence of the measurement. 

The potential of the peak Ep is indicative of which species is involved. If the reduction (or oxidation) mechanism is diffusion-controlled the concentration of the species controls the Faradaic current. Since differential pulse polarography effectively displays the derivative of this current, theoretically it is the area under the peak which is proportional to the concentration. However, provided the shape of the peak does not change, the height of the peak is also proportional to concentration. The choice between the two modes of measurement will be discussed later. 

Differential pulse polarography is particulary susceptible to surface active phenomena. Adsorbed forms of the analyte and its electrode products can give rise to separate peaks. But even the adsorption of otherwise inactive third species can alter the reversibility and electrode kinetics of the process producing sometimes huge changes in the shape of peak. The area under the peak will, however, remain constant in most cases. But the height of the peak is of no use. If surfactants are likely to be present it is best to calibrate and measure the area under the peak. 

Other stimuli that can be used are a random input and a sinusoidal input. The response of a step input is an S-shaped curve see Fig. 11.20 top. The response of a pulse input is a bell-shaped curve see Fig. 11.20 bottom. The ideal pulse input is of infinitely short duration such an input is called a delta function or impulse. The normalized response to a delta function is called the C curve. Thus, the total area under the curve equals unity. 

For physical adsorption the area under the pulse is the same as the area imder the adsorption peak. The rate of desorption, which controls the shape of the desorption pulse, depends on the relative strengths of adsorption of the solute and solvent. In some instances a long time elapses before all the solute molecules are removed, and tfiis results in a desorption pulse having a long tail, making it difficult to decide when desorption is complete. 

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