Kinetic wave

The Hydrodynamic Theory of fluidized bed stability was proposed by Foscolo and Gibilaro who adapted the stability principle of Wallis. They postulated that a fluidized bed is composed of two interpenetrating fluids. One fluid is the gas phase, and the solids phase is also considered as a continuous fluid phase. In this theory, voidage disturbances in the bed propagate as dynamic and kinetic waves. The stability of the fluidized bed depends upon the relative velocities of these two waves. The velocities of the kinetic wave (ue) and the dynamic wave (nj are ... 

S. G. Mairanovskii, Catalytic and Kinetic Waves in Polarography, Plenum Press, New York, 1968. 

Kolthoff, I. M., and E. P. Parry Catalytic polarographic waves of hydrogen peroxide I. The kinetic wave for the ferric iron-hydrogen peroxide system. J. Am. Chem. Soc. 73, 3718 (1951). 

In aqueous methanol, indomethacin exhibits a half-wave potential (E.,-) at the droning mercury electrode which is dependent upon pH. In 0.1M methanolic lithium chloride, indomethacin has two waves between -1.4v and -1.6v (vs. S.C.E.). The first step height is diffusion controlled and corresponds to a two electron reduction of the amide carbonyl. The second wave is believed to be a kinetic wave. The method as described is specific for nonhydrolyzed indomethacin and is suitable for analysis of capsules, suppositories and suspensions with precision of +1.2%, +0.7% and +1.2% for the respective formulations(43). 

Refs. [i] StradipS J, Mairanovskii VG (1992) J Electroanal Chem 340 1 (Orbituary) [ii] Mairanovskii SG (1966) Catalytic and kinetic waves in polarography. Nauka, Moscow (Engl transl Mairanovskii SG (1968) Catalytic and kinetic waves in polarography. Plenum Press, New York) [iii] Mairanovskii SG, Stradips J, Bezuglyi VD (1975) Polarography in organic chemistry. Khimia, Leningrad... 

The measurement of peak potentials during LSV neglects much of the information present in the wave. For purely kinetic waves, the wave shape is dependent upon the mechanism of the process and can be used to distinguish between mechanisms. Although conclusions can be drawn by the direct comparison of the shape of the current-potential curve with theoretical data, such a comparison is subjective. Several procedures have been developed to analyse LSV wave shapes quantitatively for mechanism analysis. 

A more simple analysis of LSV waves can give essentially the same information as CPSV and NPSV. Analysis of theoretical current-potential data for Nemstian and purely kinetic waves revealed that a nearly linear region... 

Parker and Bethell, 1981a. Measurements at an Hg electrode at 23°C with MejNBF (sat.) as electrolyte. The numbers in parentheses refer to the standard deviations in 5 measurements. Peak potentials are relative to a bias setting of — 1.680 V vs Ag/Ag+ in acetonitrile. It should be noted that the reduction process does not fulfill the requirements for purely kinetic waves, linear current potential analysis indicates a slope at 100 mV s" of about 80 mV rather than 69 mV for a purely kinetic wave... 

Pauchon and Banerjee (1988), in their analysis of bubbly flows, have shown that the kinematic wave velocity based on a constant interfacial friction is weakly stable. They have also obtained a functional dependence of the interfacial friction factor on the void fraction by assuming the kinetic wave velocity equal to the characteristic velocity (kinetic waves are neutrally stable). They have assumed that turbulence provides the stabilizing mechanism through axial dispersion of the void fraction. 

In 6-carbonylnitroalkanes the nitro group is more easily reducible than the carbonyl group [68,69], whereas in 2-bromo-2-nitroacetophenone [68] the bromine is most easily reduced. A pH < 5, 2-nitroacetophenone shows a kinetic polarographic wave followed by another wave the sum of the waves corresponds to n = 4. The kinetic wave is unusual in that its height grows with pH. The explanation is that the more easily reducible species is the enolate, which is favored by a higher pH at low pH the nitro ketone is reduced as in ... 

Mairanovskil, S. G. (1961). Izv. Akad. NaukSSSR, Otd. Khim. Nauk 2140. Mairanovskil, S. G. (1966). Catalytic and Kinetic Waves in Polarography (in Russian). Nauka, Moscow. 

The rate of the chemical reaction is crucial. An extremely slow reaction would show up as a slowly rising conventional diffusion-controlled wave. However if the rate of chemical production is faster than the rate of diffusion, the limiting current will be diffusion controlled. For a kinetic wave to form, the rate of the chemical reaction must be relatively rapid but significantly slower than the rate of diff-ision. 

With a proportional relationship between the current and the concentration, kinetic waves might seem suitable for analytical application. However, because kinetic currents are so sensitive to temperature and pH, sufficient reproducibilty and accuracy can rarely be obtained, even with the best temperature control generally available. 

The key difference lies in the fact that the species of interest is regenerated and not consumed in the overall electrode process of the catalytic wave. In the kinetic wave the species of interest is consumed by the preceding chemical reaction. Hence catalytic waves are very large and conventional kinetic waves small. Strictly speaking a catalytic wave is a kinetic wave with regeneration of the species of interest. But usually the term kinetic is applied to processes without regeneration. 

Kinetic waves are common in organic polarography. Carbonyl compounds and carbohydrates result in... 

The acyclic tautomeric form of the carbohydrate is polarographically active, hence relatively weak kinetic waves only are obtained. 

With increase in the ionic strength of the solution the first kinetic wave (pH 6.0) increases in height and the second wave (pH 3.5 ) decreases. Evidently both waves have surface character. The protonation rate constant of the benzophenonetetracarboxylate anions was evaluated formally on the assumption that the principal proton donor is the hydrogen ion and with allowance for the change in concentration of charged particles at the electrode surface under the influence of its field. In these calculations account was not taken of the variation in the acid dissociation constant during its adsorption on the electrode surface (see Section 1, Point f). 

So far only diffusion waves for the reduction of undissociated molecules or anions have been observed on polarograms for o/-halo-gen-substituted carboxylic acids, and it has not been possible to observe a kinetic wave limited by the protonation rate of the anions [63, 64]. With o -bromopalmitic acid in buffered aqueous ethanolic solutions, however, there is a kinetic wave with a clearly defined surface character [44], and its height falls with increase in the pH value of the medium (Fig. 10). 

Fig. 23. Relationship between normalized height [i j /(id kinetic wave for cobalt and ratio of...

The first step on the cobalt wave ("prewave ") corresponds to discharge of Co (II) from its complex with cysteine. The height of this wave is limited by the formation rate of complexes between adsorbed cysteine anions and Co (II) ions in the layer adjacent to the electrode (henceforth written as [CoJs). Under these conditions cysteine is clearly present in excess with respect to [Co]. Reduction of the complex Co (ID ions (compared with the free ions) evidently arises from increase in their concentration near the electrode owing to adsorption of the complexes. The decrease in the height of this surface kinetic wave with increase in ionic strength is due both to a reduction in the rate constant of the ionic reaction (salt effect) and to a decrease in [Co]5 resulting from a decrease in the absolute value... 

The amine catalysts facilitate transfer of protons not only to complex nitro alcohols but also to simple aliphatic nitro compounds and to ketones [114]. Thus, for example, addition of diethylaniline and particularly of pyridine appreciably increases the height of the kinetic waves of acetophenone and propiophenone (Fig. 26) caused by their inhibited protonation. Pyridine has a greater effect than diethylaniline (Fig. 26). 

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