Diffusion-limited complex formation

Takahashi et al. [220] first reported the formation of Bi-Te alloy films with varying chemical composition by means of cathodic electrodeposition from aqueous nitric acid solutions (pH 1.0-0.7) containing Bi(N03)3 and Te02. The electrodeposition took place on Ti sheets at room temperature under diffusion-limited conditions for both components. In a subsequent work [221], it was noted that the use of the Bi-EDTA complex in the electrolyte would improve the results, since Bi " is easily converted into the hydrolysis product, Bi(OH)3, a hydrous polymer, thus impairing the reproducibility of electrodeposition. The as-produced films were found to consist of mixtures of Te and several Bi-Te alloy compounds, such as Bi2Tc3, Bi2+xTe3 x, Bi Tee, and BiTe. Preparation of both n- and p-type Bi2Te3 was reported in this and related works [222]. 

The selectivity here is directly proportional to complex formation constants and can be estimated, once the latter are known. Several methods are now available for determination of the complex formation constants and stoichiometry factors in solvent polymeric membranes, and probably the most elegant one is the so-called sandwich membrane method [31], Two membrane segments of different known compositions are placed into contact, which leads to a concentration polarized sensing membrane, which is measured by means of potentiometry. The power of this method is not limited to complex formation studies, but also allows one to quantify ion pairing, diffusion, and coextraction processes as well as estimation of ionic membrane impurity concentrations. 

All in all, the tritium data present something of a mystery, but at least they set a lower limit for the effective diffusion coefficient in the range 400-500°C, a limit rather higher than some estimates that have been given in the literature for similar temperatures but which we shall not discuss until Section 3 because thay are based on experiments in which hydrogen-acceptor complex formation was clearly important. 

In this equation, kjy is the rate constant for the diffusion-limited formation of the encounter complex, d is the rate constant for diffusion apart, and ka is that for the activation step, i.e. M-L bond formation. Based on the steady-state approximation for the encounter complex concentration, the apparent rate constant for the on reaction is kon = k kj (k - ,+ka), and the activation volume is defined as... 

For the biological limitation of trace metal internalisation, complex formation will invariably decrease the concentration of free metal ion and thus decrease the biouptake fluxes and carrier-bound metal (FIAM, BLM). In the case of a diffusion-limited internalisation, complex labilities and mobilities become much more pertinent when determining uptake fluxes. As shown earlier, few experiments have been designed to identify diffusion limitation of metal uptake fluxes, despite the fact that such a limitation is possible (Figure 10). Competition experiments that can distinguish a kinetic from a thermodynamic control are rare. In these areas, an important research focus is... 

B.l.a. Water eocchange rates. Water-exchange rates are key guides of chemical reactivity in aqueous coordination compounds. Aqueous metal-ligand complexation reactions take place through the diffusion-limited formation of an electrostatic ion pair,... 

The rate of complex formation of dimethylsilylene with a variety of Lewis bases was found to be close to the diffusion limit in cyclohexane at room temperature.33,34 The results of Yamaji et al.34 indicate that the rate of this reaction is governed not so much by electronic factors such as the HOMO energy of the Lewis base as by steric hindrance around the heteroatom center. In contrast, Baggott et al.35 found a satisfying correlation between rate constants and ionization energies of the nucleophile for the reaction of dimethylsilylene with various oxygen-containing substrates in the gas phase. 

Nevertheless, even under conditions for which diffusion limitations could be excluded, MCHA was still converted directly to MCH. By adding substantial partial pressures of H2S, it was shown that the formation of MCH resulted from the nucleophilic substitution of MCHA to give 2-methylcyclo-hexylthiol and subsequent fast hydrogenolysis to give MCH. These results mean that the network of the HDN of anilines is quite complex the network of o-methylaniline (o-toluidine) is shown in Scheme 19. 

Bimolecular reactions are frequently described as diffusion-limited , meaning that the limiting step in reaction is the rate of formation of a reactive complex. This situation often applies in ILs, as they are highly viscous media. A number of studies [246, 247] have found activation energies for reactions in ILs that are equivalent to the activation energies for viscous flow in the liquid, a feature of diffusion-limited kinetics. 

Suppose that the rate of formation of product (k c t) is much faster than the rate of dissociation of the ES complex (A . j). The value of k jyi then approaches k j. Thus, the ultimate limit on the value of k JK is set by A j, the rate of formation of the ES complex. This rate cannot be faster than the diffusion-controlled encounter of an enzyme and its substrate. Diffusion limits the value of j so that it cannot be higher than between 10 and 10 s l M-f Hence, the upper limit on k. JK jyj is between 10 and 10 s i M f... 

The diffusion limit will obscure very fast rates of electron transfer (/cobs = for et d) [16]. Even if electron transfer is slow with respect to diffusion ( obs = et), work accompanies the formation of the precursor complex and/or separation of the successor complex (this is especially prevalent when the reactants and/or products are charged). Work term contributions to the observed rate of reaction can overwhelm the intrinsic factors that govern the electron transfer event [19]. For this reason, excluding special circumstances [20-26], intermolecular reactions are not ideal systems for examining the mechanistic details of electron transfer. 

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