Diffusion-limited exchange kinetics

Reaction-Limited Versus Diffusion-Limited Exchange Kinetics... 

The key to obtaining pore size information from the NMR response is to have the response dominated by the surface relaxation rate [19-26]. Two steps are involved in surface relaxation. The first is the relaxation of the spin while in the proximity of the pore wall and the other is the diffusional exchange of molecules between the pore wall and the interior of the pore. These two processes are in series and when the latter dominates, the kinetics of the relaxation process is analogous to that of a stirred-tank reactor with first-order surface and bulk reactions. This condition is called the fast-diffusion limit [19] and the kinetics of relaxation are described by Eq. (3.6.3) ... 

In any case, exceptions to the FIAM have been pointed out [2,11,38,44,74,76,78]. For example, the uptake has been shown to depend on the Cj M or rMI (e.g. in the case of siderophores [11] or hydrophobic complexes [43,50]), rather than on the free c M. Several authors [11,12,15] showed that a scheme taking into account the kinetics of parallel transfer of M from several solution complexes to the internalisation transporter ( ligand exchange ) can lead to exceptions to the FIAM, even if there is no diffusion limitation. Adsorption equilibrium has been assumed in all the models discussed so far in this chapter, and the consideration of adsorption kinetics is kept for Section 4. Within the framework of the usual hypotheses in this Section 3, we would expect that the FIAM is less likely to apply for larger radii and smaller diffusion coefficients (perhaps arising from D due to the labile complexation of M with a large macromolecule or a colloid particle, see Section 3.3). 

Also, in the late 1950s and 1960s some particularly seminal papers on ion exchange kinetics appeared by Helfferich (1962b, 1963, 1965) that are classics in the field. In this research it was definitively shown that the rate-limiting steps in ion exchange phenomena were film diffusion (FD) and/ or particle diffusion (PD). Additionally, the Nernst-Planck theories were explored and applied to an array of adsorbents (Chapter 5). 

Quantification and Elucidation of Rate-Limiting Steps 109 Chemical Reaction and Diffusion 112 Rates of Ion Exchange on Soils and Soil Constituents 113 Mineralogical Composition 114 Ion Charge and Radius 116 Binary Cation and Anion Exchange Kinetics 117... 

The overall permeation rate of a material is determined by both ambipolar conductivity in the bulk and interfacial exchange kinetics. For -> solid electrolytes where the electron - transference numbers are low (see -> electrolytic domain), the ambipolar diffusion and permeability are often limited by electronic transport. 

For many energy transfer processes, the interaction takes place when the partners are separated by more than the sum of the gas-kinetic collision radii. For example, energy transfer between excited singlet states of hydrocarbons occurs as fast as spontaneous decay at concentrations in benzene corresponding to a distance, r, between exchanging molecules of about 5 nm, or about 10 times the collision diameter. The measured rate constants for transfer of excitation in the hydrocarbons also seem greatly to exceed the diffusion-limited rate, and do not depend on solvent viscosity. 

The efficiency of electron-transfer reduction of Cgo can be expressed by the selfexchange rates between Coo and the radical anion (Ceo ), which is the most fundamental property of electron-transfer reactions in solution. In fact, an electrochemical study on Ceo has indicated that the electron transfer of Ceo is fast, as one would expect for a large spherical reactant. This conclusion is based on the electroreduction kinetics of Ceo in a benzonitrile solution of tetrabutylammonium perchlorate at ultramicroelectrodes by applying the ac admittance technique [29]. The reported standard rate constant for the electroreduction of Ceo (0.3 cm s ) is comparable with that known for the ferricenium ion (0.2 cm s l) [22], whereas the self-exchange rate constant of ferrocene in acetonitrile is reported as 5.3 x 10 s , far smaller than the diffusion limit [30, 31]. 

Further, the kinetics of Ca binding are quite different with water exchange rates close to the coUision diffusion limits of 10 ° s unlike much slower rates of 10 s for Mg. Ca can interact with neutral oxygen donors, like carbonyls and ethers, unlike Mg in aqueous media, as well as with anions, which avoids compehhon with Na. ... 

The limits at which one or the othertype of diffusion is controlling have been determined by Tsai.When > 50, the rate is controlled by film diffusion. When Klc b < 0.005, the rate is controlled by particle diffusion. In these relationships, K is the distribution coefficient, Ic is the diffusivity ratio (Dp/Df), 8 is the relative film thickness on a resin particle with a radius of a. Between these two limits, the kinetic description of ion exchange processes must include both phenomenon. 

Feedback. When an oxidoreductase enzyme is immobilized at the specimen surface, a redox mediator present in solution may be recycled by the diffusion-limited electrochemical process at the tip and electron exchange with the enzyme active site as described in Sec. I.C. The mass transport rate is defined by the tip radius and height of the tip above the specimen. The tip current depends on the mass transport rate and the enzyme kinetics. Kinetic information may therefore be obtained from the dependence of tip current on height, i.e., an approach curve. When the mediator is fed... 

More related to general photochemistry are the papers which have appeared on wholly or partly diffusion-controlled reactions. The effect of a very short lifetime of the donor on the calculation of fluorescence quantum yields and lifetimes has been analysed by Viriot et al. Andre et al. analyse the kinetics of energy transfer to an acceptor when there are two different excited states capable of acting as donors and when interaction between these states is possible. The exchange interaction contribution to energy transfer between ions in the rapid diffusion limit... 

The substitution reaction of (NPCI2) with phenol is a sequential reaction [40. 42]. The experimental results can easily demonstrate the relationship between the reaction kinetic limitation and the particle diffusion limitation. In a triphasc reaction, the overall kinetic cycle can be broken up into two steps by virtue of the presence of two practically insoluble liquid phases a chemical conversion step in which the active catalyst sites (Resin" with phenolatc ions) react with the hexachlorocyclotriphospha/cne in the organic solvent, and an ion-exchange step in which the attached catalyst sites are in contact with the aqueous phase. 

The apparent diffusion coefficient, Da in Eq. (11) is a mole fraction-weighted average of the probe diffusion coefficient in the continuous phase and the microemulsion (or micelle) diffusion coefficient. It replaces D in the current-concentration relationships where total probe concentration is used. Both the zero-kinetics and fast-kinetics expressions require knowledge of the partition coefficient and the continuous-phase diffusion coefficient for the probe. Texter et al. [57] showed that finite exchange kinetics for electroactive probes results in zero-kinetics estimates of partitioning equilibrium constants that are lower bounds to the actual equilibrium constants. The fast-kinetics limit and Eq. (11) have generally been considered as a consequence of a local equilibrium assumption. This use is more or less axiomatic, since existing analytical derivations of effective diffusion coefficients from reaction-diffusion equations are approximate. 

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