Plateau-type reaction conditions

Turner has described two reaction-type extremes, plateau-type and point-type reactions, based on the reaction yield vs. optimum reaction conditions. While the reaction conditions first disclosed by Weiss were an improvement over the existing methods to assemble the bicyclo[3.3.0] scaffold, the overall yield was low and very sensitive to reaction conditions, i.e., a point-type reaction. To increase the synthetic utility of this chemistry, reaction conditions were investigated to transition it to a plateau-type reaction. 

The unimodality constraint allows the presence of only one maximum per profile (see Figure 11.7) [42, 55, 60], This condition is fulfilled by many peak-shaped concentration profiles, like chromatograms or some types of reaction profiles, and by some instrumental signals, like certain voltammetric responses. It is important to note that this constraint does not only apply to peaks, but to profiles that have a constant maximum (plateau) or a decreasing tendency. This is the case for many monotonic reaction profiles that show only the decay or the emergence of a compound [47, 48, 51, 61], such as the most protonated and deprotonated species in an acid-base titration, respectively. 

Figure 12.5 shows the characteristic signal temperature plots obtained with these systems. It can be seen that a plateau is reached for types (a) and (b). At this point the output of the device is independent of temperature, indicating that the reaction is diffusion-controlled at a point remote from the sensor, that is, the sinter in type (a) and the chimney entry in type (b). No such plateau exists for the type (c) system. Operation of the detector under diffusion-controlled conditions limits the response time to several seconds, but offers several advantages ... 

As stated in section 12.4, it is usual to mount the sensing elements in a diffusion head of the type shown in Figure 12.4a. In such an assembly the characteristic plateau in the signal as a function of temperature (Figure 12.5a) is reached when the rate of reaction becomes controlled by the rate of diffusion of gas through the sinter. Under these conditions, the signal is directly dependent on gas concentration and independent of both element temperature and oxygen concentration. 

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