Rate-limiting diffusion metal

SOME IMPLICATIONS OF A RATE-LIMITING DIFFUSION 7.5.1 Bioavailability of Colloidal Bound Metal... 

The reductive nitrosylation of a synthetic iron porphyrin by HNO (193) proceeds with a reported rate constant of 1 x 107 A/-1 s However, this value was estimated based on a HNO dimerization rate constant of 8 x 109 M-1 s-1 (210), which is now considered to be 1000-fold lower [(8 x 106 A/-1 s-1 (106)]. The recalculated constant for the reaction of HNO with the porphyrin (3 x 10s AT V1) is similar to the estimated value of HNO addition to metMb. Synthetic porphyrins generally react 30-fold faster with NO (1 x 109M 1 s-1) than ferrous Mb [for a recent, thorough review see (44)] due to rate-limiting diffusion of NO through the protein. The similarity in rate constants for HNO with metMb and the ferric porphyrin suggests that the rate-limiting step in reductive nitrosylation is likely addition of HNO to the ferric metal, with little influence from the protein structure. 

Mechanistically, in approximately neutral solutions, solid state diffusion is dominant. At higher or lower pH values, iron becomes increasingly soluble and the corrosion rate increases with the kinetics approaching linearity, ultimately being limited by the rate of diffusion of iron species through the pores in the oxide layer. In more concentrated solutions, e.g. pH values of less than 3 or greater than 12 (relative to 25°C) the oxide becomes detached from the metal and therefore unprotective . It may be noted that similar Arrhenius factors have been found at 75 C to those given by extrapolation of Potter and Mann s data from 300°C. 

Since, in both these reactions (i.e. KI or Rbl and Agl), product formation occurs on both sides of the original contact interface, it is believed that there is migration of both alkali metal and silver ions across the barrier layer. Alkali metal movement is identified as rate limiting and the relatively slower reaction of the rubidium salt is ascribed to the larger size and correspondingly slower movement of Rb+. The measured values of E are not those for cation diffusion alone, but include a contribution from... 

Figure 3.6. Spatial variation of the electrochemical potential, jl02-, of O2 in YSZ and on a metal electrode surface under conditions of spillover (broken lines A and B) and when equilibrium has been established. In case (A) surface diffusion on the metal surface is rate limiting while in case (B) the backspillover process is controlled by the rate, I/nF, of generation of the backspillover species at the three-phase-boundaries. This is the case most frequently encountered in electrochemical promotion (NEMCA) experiments as shown in Chapter 4.

Equations 4.31 and 4.32 also suggest another important fact regarding NEMCA on noble metal surfaces The rate limiting step for the backspillover of ions from the solid electrolyte over the entire gas exposed catalyst surface is not their surface diffusion, in which case the surfacediffusivity Ds would appear in Eq. 4.32, but rather their creation at the three-phase-boundaries (tpb). Since the surface diffusion length, L, in typical NEMCA catalyst-electrode film is of the order of 2 pm and the observed NEMCA time constants x are typically of the order of 1000 s, this suggests surface diffusivity values, Ds, of at least L2/t, i.e. of at least 4 10 11 cm2/s. Such values are reasonable, in view of the surface science literature for O on Pt(l 11).1314 For example this is exactly the value computed for the surface diffusivity of O on Pt(lll) and Pt(100) at 400°C from the experimental results of Lewis and Gomer14 which they described by the equation ... 

Upon formation of a metal chelate or complex, the next rate-limiting step in delivering iron to the cell is the diffusion of iron complexes through the. soil in response to diffusion gradients. In the vicinity of plant roots, metal chelates and complexes may also move by bulk flow in the transpiration stream as water moves from the soil into the plant. However, depending on their charge characteristics and hydrophobicity, metal chelators and complexes can become adsorbed to clay and organic matter, which may then decrease their mobility and bioavail-... 

Limiting currents are usually associated with cathodic reactions (e.g., in metal deposition), although anodic reactions are by no means excluded. Whenever the supply of a dissolved species from the solution to the electrode surface becomes the rate-limiting factor, limiting-current phenomena may be observed. Anodic limiting currents can be obtained, for example, in the oxidation of ferrous to ferric ion, or ferro- to ferricyanide ion (El). Diffusion of H20 limits 02 evolution in fused NaOH (A2). In these examples the limiting current is caused by depletion of the reactant species at the anode. 

Full catalyst formulations consist of zeolite, metal and a binder, which provides a matrix to contain the metal and zeolite, as well as allowing the composite to be shaped and have strength for handling. The catalyst particle shape, size and porosity can impact the diffusion properties. These can be important in facile reactions such as xylene isomerization, where diffusion of reactants and products may become rate-limiting. The binder properties and chemistry are also key features, as the binder may supply sites for metal clusters and affect coke formation during the process. The binders often used for these catalysts include alumina, silica and mixtures of other refractory oxides. 

In our second example we look at the reduction of chlorinated ethenes at a nickel electrode and at the surfaces of two zero-valent metals [Fe(0), Zn(0)]. To gain insight into the rate-limiting process(es) in these cases, we consider how the relative overall reduction rates (relative to PCE) of PCE, TCE, and the three DCE isomers (see Fig. 14.15 for structures) vary as a function of two common descriptors used in QSARs, the one-electron reduction potential (EJ Fig- 14.17a) and the bond dissociation energy (DR X Fig. 14.176). In all these systems, the reduction rates were found to be significantly slower than diffusion of the compounds to the respective surfaces. Therefore, the large differences in the relative reactivities of the compounds between the systems reflect differences in the actual reaction at the metal surface. 

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