Multi-barrier kinetics

The oxygen/water half-cell reaction has been one of the most challenging electrode systems for decades. Despite enormous research, the detailed reaction mechanism of this complex multi-step process has remained elusive. Also elusive has been an electrode material and surface that significantly reduces the rate-determining kinetic activation barriers, and hence shows improvements in the catalytic activity compared to that of the single-noble-metal electrodes such as Pt or Au. 

Giddings, J. C., and H. Eyeing Multi-barrier kinetics nucleation. J. Phys. Chem. 62, 305-308 (1958). 

Xian Y, Kucharski XJ, Yang Q-Z, Boulatov R (2013) Model studies of force-dependent kinetics of multi-barrier reactions. Nat Commun 2013 4... 

One can make use of (161a) and (162) in order to show the existence of the induction period in some processes involving multibarrier kinetics. For instance, the multi-barrier processes represented by Figure 10 with d /ZRT >3I(N+1) will be considered in the following discussion. 

Generally, the approach from the multi-barrier kinetics is more general than that involving partial differential equations and is advantageous over the latter in the following respects. 

The limitations in the distance and time involved in transport phenomena are small in the multi-barrier kinetics compared with conventional approaches. 

It has been reported that rates of proton transfer from carbon acids to water or hydroxide ion can be predicted by application of multi-dimensional Marcus theory to a model whereby diffusion of the base to the carbon acid is followed by simple proton transfer to give a pyramidal anion, planarization of the carbon, and adjustment of the bond lengths to those found in the final anion.124 The intrinsic barriers can be estimated without input of kinetic information. The method has been illustrated by application to a range of carbon acids having considerable variation in apparent intrinsic barrier. 

It was found, that also Ru and Os colloids can act as catalysts for the photoreduction of carbon dioxide to methane [94, 95]. [Ru(bpy)3]2+ plays a role of a photosensitizer, triethanolamine (TEOA) works as an electron donor, while bipyridinium electron relays (R2+) mediate the electron transfer process. The production of hydrogen, methane, and small amounts of ethylene may be observed in such a system (Figure 21.1). Excited [Ru(bpy)3]2+ is oxidized by bipyridinium salts, whereas formed [Ru(bpy)3]3+ is reduced back to [Ru(bpy)3]2+ by TEOA. The reduced bipyridinium salt R + reduces hydrogen and C02 in the presence of metal colloids. Recombination of surface-bound H atoms competes with a multi-electron C02 reduction. More selective reduction of C02 to CH4, ethylene, and ethane was obtained using ruthenium(II)-trisbipyrazine, [Ru(bpz)3]2+/TEOA/Ru colloid system. The elimination of hydrogen evolution is thought to be caused by a kinetic barrier towards H2 evolution in the presence of [Ru(bpz)3]2+ and noble metal catalysts [96]. 

The kinetics of the multi-channel interactions between HO2 and allyl radicals have been determined [35] and it has been established that all allyl -I-O2 reactions have high activation energy barriers [36]. 

Unfortunately, most enzymes do not obey simple Michaelis-Menten kinetics. Substrate and product inhibition, presence of more than one substrate and product, or coupled enzyme reactions in multi-enzyme systems require much more complicated rate equations. Gaseous or solid substrates or enzymes bound in immobilized cells need additional transport barriers to be taken into consideration. Instead of porous spherical particles, other geometries of catalyst particles can be apphed in stirred tanks, plug-flow reactors and others which need some modified treatment of diffusional restrictions and reaction technology. 

However, measurement of water mobility in multicomponent, multi-domained systems is not so simple. In food systems, water may be associated with different domains that control its local molecular motions. Within a specific timeframe, water molecules may migrate between two domains (of two different local mobilities). If the migration rate is slow (due to kinetic barriers) with respect to the experimental observable time frame, then the system experimental data would report multiple components in terms of water mobility. If another system has a reduced kinetic barrier, translational exchange between domains is rapid within the timeframe of the experiment. In this case, the data obtained would only report seemingly one water population (with one average mobility) leading to a misleading conclusion. Because most dynamic experiments are limited by the instrumental timeframe, it is important to select the appropriate instrument for the... 

Abstract Theoretical, experimental principles and the applications of the frequency response (FR) method for determining the diffusivities in microporous and bidispersed porous solid materials have been reviewed. Diffusivities of hydrocarbons and some other sorbates in microporous crystals and related pellets measured using the FR technique are presented, and the FR data are analysed to demonstrate the identification of the FR spectra. These results display the ability of the FR method to discriminate multi-kinetic mechanisms, including a surface resistance or surface barrier occurring simultaneously in the systems, which are difficult to be determined using other microscopic or macroscopic methods. The FR measurements also showed that the diffusivity of a system depends significantly on the subtle differences in molecular shape and size of sorbates in various... 

V vs NHE). Although this multi-electron pathway generates O2 at the lowest thermodynamic barrier, if compared to the stepwise one-electron, it poses severe kinetic and thermodynamic challenges. 

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