Reactivity quotients

As shown by TalkneP there is a direct connection between the Rayleigh quotient method and the reactive flux method. Two conditions must be met. The first is that phase space regions of products must be absorbing. In different terms, the trial function must decay to zero in the products region. The second condition is that the reduced barrier height pyl" 1. As already mentioned above, differences between the two methods will be of the order e P. ... 

Let us now consider what we mean by the reactivity of a hydrocarbon in autoxidation. One measure is how fast it oxidizes by itself at unit concentration and unit rate of initiation. (Rates of thermal oxidation at unknown rates of initiation are not useful enough to be considered.) The first two columns of figures in Table VII give such comparisons in terms of kp/(2kt)l/l at 30° and 60°C. and determine the order in which hydrocarbons are listed in the table. The results of Ingold and Sajus agree fairly well the orders of reactivity are identical except for a trivial difference with the xylenes. The stated quotients at 60°C. are uniformly 2 to 3 times as large as at 30°C. for sec-butylbenzene and more reactive hydrocarbons but 3 to 6 times as large for less reactive hydrocarbons. 

NACs in a laboratory column system containing aquifer material from the banks of a river-groundwater infiltration site (Fig. 14.11). The columns were run under ferrogenic conditions. Note that zero-order kinetics suggests that the reactive sites were always saturated such as encountered in enzyme kinetics at saturation (Box 12.2). In this system, all model compounds as well as other NACs including again TNT, ADNTs, and DANTs (data not shown, see Hofstetter et al., 1999) reacted at virtually the same rate. However, when present in mixtures, the compounds showed competition for the reactive sites. A competition quotient, Qc (competition with the reference compound 4-C1-NB present at about equal concentrations) was determined for all model compounds ... 

Specificity To determine the cross reactivity, pooled serum with an hFSH content of 0 or 15 U/1 was given additions of different quantities of hormones as listed below. The percentage cross reactivity is the quotient from the average hFSH concentration and the concentration of the cross-reacting substance that is required to achieve the same degree of binding to the antibody. 

Copolymerization. In free-radical copolymerization (qv), the composition of the copolymer is controlled by the comonomer reactivity ratios (23). The monomer reactivity ratio is defined as the quotient of the rate constants for chain homopropagation to the rate constant for chain cross-propagation. 

Since a nuclear reactor is a statistical system, it will show fluctuations in neutron intensity. These fluctuations, or pile noise, are not commonly considered of interest in themselves, but only as interference to other experiments. However, since the nature of the pile noise depends strongly on important reactor parameters, its study can enable the determination of quantities less easily accessible by other means. In particular, Moore (f) points out that the noise spectrum of such a system, that is, the mean square noise amplitude per unit band width, is proportional to the square modulus of the transfer function or to the Fourier cosine transform of the autocorrelation function. Thus, observation of the noise spectrum of a reactor could yield information about the shape of its transfer function. To test this technique, pile noise analyses were done on various low-power experimental reactors at Argonne National J aboratory. Since these reactors operate at such a low level that power effects on reactivity do not appear, the shape of the low-frequency portions of their transfer functions would depend only on fairly well-known delayed neutron parameters, and thus would be of little interest. However, the high-frequency rolloff portion of the transfer function is strongly dependent on the quotient of the effective delayed neutron fraction over the prompt neutron... 

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