Inhibition coefficient

These definitions, formally different with respect to those reported in eqn (14.10), approach each other in the case of negligible inhibition. This approach is very useful because, with this choice, CPC is directly related to the flux reduction due only to external mass transfer resistance and not to the inhibition phenomenon. Moreover, the polarization and inhibition effect are able to be separately identified and split into their own different contributions, which can thus be analyzed to provide a better understanding of the coupled influence of these two phenomena. This is done by defining another coefficient, i.e. the inhibition coefficient, IC, which is on the other hand a quantitative indicator of the inhibition phenomenon only (see next section). 

As anticipated in the previous section, an inhibition coefficient is necessary in order to evaluate conveniently the inhibition effect only without the polarization one. Analogously to what was done for CPC, an inhibition eoefficient, IC, was defined according to eqn (14.14), where the superscript clean and on permeance indicates that membrane is not affected by inhibition  

This definition, applied in the specific case to the inhibition by CO, is general and reflects the deep difference existing between the effect of polarization and inhibition on permeation. In fact, polarization acts outside the membrane, whereas inhibition affects its intrinsic permeance by competitively occupying the adsorption site and decreasing the effective nominal membrane area. 

However, the two phenomena are strongly linked to each other, since polarization favors the inhibiting species towards the membrane surface and, on the other hand, inhibition tends to reduce the permeating flux decreasing to a certain extent the polarization itself. This is the reason why coefficients by which to decouple polarization and inhibition are useful to represent easily this complex membrane behavior. 

The effect of inhibition by CO on hydrogen permeation has recently become the object of several investigations, since CO is typically present in significant amounts in the hydrogen streams to be separated. In particular, a macroscopic model equation was developed to describe the influence of CO on permeation. This equation modifies Sieverts law to take into account the permeance reduction due to CO as reported in eqn (14.15), where the quantities a, and 6co represent a coefficient accounting for other additional effects of CO on adsorbed hydrogen and the membrane surface coverage by CO, respectively  

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Change the operating variables and note their influence on the reaction rate for given values of the inhibition coefficient, Kj. 

High values of the inhibition coefficient (/= 12-28) were detected for the first time in the oxidation of cyclohexanol [1] and butanol [2] inhibited by 1-naphthylamine. For the oxidation of decane under the same conditions, /= 2.5. In the case of oxidation of the decane-cyclohexanol mixtures, the coefficient / increases with an increase in the cyclohexanol concentration from 2.5 (in pure decane) to 28 (in pure alcohol). When the oxidation of cyclohexanol was carried out in the presence of tetraphenylhydrazine, the diphenylaminyl radicals produced from tetraphenylhydrazine were found to be reduced to diphenylamine [3]. This conclusion has been confirmed later in another study [4]. Diphenylamine was formed only in the presence of the initiator, regardless of whether the process was conducted under an oxygen atmosphere or under an inert atmosphere. In the former case, the aminyl radical was reduced by the hydroperoxyl radical derived from the alcohol (see Chapter 6), and in the latter case, it was reduced by the hydroxyalkyl radical. 

The oxidation of primary and secondary alcohols in the presence of 1-naphthylamine, 2-naphthylamine, or phenyl-1-naphthylamine is characterized by the high values of the inhibition coefficient / > 10 [1-7], Alkylperoxyl, a-ketoperoxyl radicals, and (3-hydroxyperoxyl radicals, like the peroxyl radicals derived from tertiary alcohols, appeared to be incapable of reducing the aminyl radicals formed from aromatic amines. For example, when the oxidation of tert-butanol is inhibited by 1-naphthylamine, the coefficient /is equal to 2, which coincides with the value found in the inhibited oxidation of alkanes [3], However, the addition of hydrogen peroxide to the tert-butanol getting oxidized helps to perform the cyclic chain termination mechanism (1-naphthylamine as the inhibitor, T = 393 K, cumyl peroxide as initiator, p02 = 98 kPa [8]). This is due to the participation of the formed hydroperoxyl radical in the chain termination ... 

Table 16.1 presents the inhibition coefficients / and the termination rate constants kn in systems with the cyclic chain termination mechanism with aromatic amines. Naturally, these are apparent rate constants, which characterize primarily the rate-limiting step of the chain termination process. 

Inhibition Coefficients f and Rate Constants k for the Reactions of Peroxyl Radicals with Aromatic Amines in Systems with a Cyclic Mechanism of Chain Termination (Experimental Data)... 

The processes of oxidation of cyclohexadiene, 1,2-substituted ethenes, and aliphatic amines are decelerated by quinones, hydroquinones, and quinone imines by a similar mechanism. The values of stoichiometric inhibition coefficients / and the rate constants k for the corresponding reactions involving peroxyl radicals (H02 and >C(0H)00 ) are presented in Table 16.3. The/coefficients in these reactions are relatively high, varying from 8 to 70. Evidently, the irreversible consumption of quinone in these systems is due to the addition of peroxyl radicals to the double bond of quinone and alkyl radicals to the carbonyl group of quinone. 

Rate Constants and Inhibition Coefficients for Chain Termination by Quinones and... 

Aryl phosphites inhibit the initiated oxidation of hydrocarbons and polymers by breaking chains on the reaction with peroxyl radicals (see Table 17.3). The low values of the inhibition coefficient / for aryl phosphites are explained by their capacity for chain autoxidation [14]. Quantitative investigations of the inhibited oxidation of tetralin and cumene at 338 K showed that with increasing concentration of phosphite /rises tending to 1 [27]. 

For initiated oxidation, the inhibitory criterion could be defined as the ratio v0/v or (v0/ v — v/v0), where v0 and v are the rates of initiated oxidation in the absence and presence of the fixed concentration of an inhibitor, respectively. Another criterion could be defined as the ratio of the inhibition coefficient of the combined action of a few antioxidants / to the sum of the inhibition coefficients of individual antioxidants when the conditions of oxidation are fixed (fx = IfiXi where f, and x, are the inhibition coefficient and molar fraction of z th antioxidant terminating the chain). It should, however, be noted that synergism during initiated oxidation seldom takes place and is typical of autoxidation, where the main source of radicals is formed hydroperoxide. It is virtually impossible to measure the initial rate in the presence of inhibitors in such experiments. Hence, inhibitory effects of individual inhibitors and their mixtures are usually evaluated from the duration of retardation (induction period), which equals the span of time elapsed from the onset of experiment to the moment of consumption of a certain amount of oxygen or attainment of a certain, well-measurable rate of oxidation. Then three aforementioned cases of autoxidation response to inhibitors can be described by the following inequalities (r is the induction period of a mixture of antioxidants). 

This equation agrees with the experimental data (see Table 20.1). The chain termination on the surface of MoS2 occurs catalytically with a very high inhibition coefficient / 3 x 105. 

The values of k were 0.18, 1.98 and 1.16 x 10 (moldm s basis) for Soils A, B and C in Figure 3.15, respectively. These values are more than four times k for the solution system. The values of the inhibition coefficients-a = —1686, = 6.13, c = 3854—were smaller than in the solution system. As a result the concentrations of P and DOC required to halve the rate of precipitation were 10 times those in the solution system. Also the interaction between [Pl] and [Cl] was negligible in the solution system but important in the soils. Figure 3.16 shows plots of Equation (3.54) for different valnes of [Pl] and [Cl] and w = 0.75 gdm. For the values used, which are realistic for submerged-soil solutions, the combined inhibitory effect of P and DOC was snch that an order of magnitude greater degree of supersaturation [(Ca +)(C03 )/A sp] is necessary to produce the same rate of precipitation as in the absence of inhibitors. 

The inhibiting influence of cyclodextrins on the Cd(II)/Cd(Hg) electrode processes was studied [56]. It was found that the inhibition coefficient increases in the series a-cyclodextrin < y-cyclodextrin <... 

In order to demonstrate the viability of the approach, protein phosphatase inhibition was first performed with the enzyme in solution and detected by colorimetric methods. Two microcystin variants, microcystin-LR and microcystin-RR, were used. Both enzymes were inhibited by these toxins, although to a different extent. The 50% inhibition coefficients (IC50) towards microcystin-LR were 0.50 and 1.40 pgL 1 (concentrations in the microtitre well) for the Upstate and the GTP enzymes, respectively. Hence, the Upstate enzyme was more sensitive. The IC50 towards microcystin-RR were 0.95 and 2.15 pgL-1 for the Upstate and the GTP enzymes, respectively. As expected, microcystin-LR was demonstrated to be a more potent inhibitor. 

All the reactions mentioned above make the inhibiting coefficient f much more than 2, when amines are used as inhibitors. At present we do not know either the role of alkyl radicals in such reactions or the stages of quinoneimine reduction to amino-phenol. ... 

Earlier, we found that heavy-atom effect can also be observed in bioluminescent systems 3,4 bioluminescence inhibition coefficients were found to decrease in the series potassium halides KC1, KBr, and KI. Two mechanisms can be responsible for the change of the intensity of bioiuminescence in the presence of heavy ions the physicochemical effect of external heavy atom mentioned above, and the biochemical effect, i.e. interactions with the enzymes resulting in changes in enzymatic activity. A series of model experiments was conducted to evaluate the contribution of the physicochemical mechanism. These involved the photoexcitation of model fluorescent compounds close to bioiuminescence emitters in chemical nature and fluorescent properties - flavin mononucleotide, firefly luciferin and coelenteramide. These results are clear evidence of the smaller contribution of the physicochemical mechanism to the decrease in the bioiuminescence intensity for the three bioluminescent systems under study.4... 

In the following sub-section, concentration polarization coefficient (CPC) and inhibition coefficient (IC) will be introduced separately in order to show their different contribution on the overall permeance reduction. 

The expression reported in eqn (14.16) allows the inhibition coefficient to be expressed explicitly. In fact, comparing eqns (14.14) to (14.16), it is possible to note that IC assumes the form reported in eqn (14.17), where the subscript "Membrane has been added to the hydrogen and CO partial pressures to highlight that all the variables should be evaluated in correspondence of the membrane surface and not of the fluid bulk ... 

According to their definition, these coefficients - namely, concentration polarization coefficient CPC), inhibition coefficient IC) and the overall... 

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