Reactant diffusion process potential

Absolute reaction rates can be affected by molecular diffusion processes that dictate the rates at which collisional encounter complexes occur before reaction. This affect usually shows up in the way reaction rates depend on the physical form of the reactants (gas, liquid, solid, solution, etc.), particularly on concentrations for reactants in gas or hquid phases. Adsorption of reactants onto surfaces can enhance the effective concentrations of reactive species and/or reduce the dimensionahty of the diffusion process. Classic work by Eigen and Richter (14) showed how restricting diffusion to one or two dimensions can dramatically increase potential reaction rates, and this principle has been applied to the kinetics of protein translocation along DNA chains, for example. See References 15 and 16 for more information. 

If the repulsion between the two reactants is strong, the relative motion before the proton transfer can be considered as a translation with a mean velocity v in the solvent medium through a diffusion process, which is governed by a periodic potential, as already dicussed in Sec,1.III. The rate constant can then be expressed by equation (23.IV)... 

Diffusion process at a constant electrode potential. Assuming that Reaction (2-II) is a totally reversible reaction, and the reductant is insoluble (CR(0,f) = 1). According to the Nernst Eqn (2.24), the oxidant s surface concentration should be constant if the electrode potential is held as a constant. In this case, Co(0, t) = Cq = constant (Cq is the reactant concentration at electrode surface). Using the other three conditions as (1) the diffusion coefficient (Do) is constant, independent on the reactant concentration (2) at the beginning of reaction (t=0), the reactant concentration is uniform across the entire electrolyte solution, that is,Co(x,0)= C and (3) at any time, the reactant concentration at unlimited distance is not changed with reaction process, that is, Co(°o,t) = C, Eqn (2.40) can be resolved to give the expression of Co(x,t) ... 

This first chapter to Volume 2 Interfadal Kinetics and Mass Transport introduces the following sections, with particular focus on the distinctive feature of electrode reactions, namely, the exponential current-potential relationship, which reflects the strong effect of the interfacial electric field on the kinetics of chemical reactions at electrode surfaces. We then analyze the consequence of this accelerating effect on the reaction kinetics upon the surface concentration of reactants and products and the role played by mass transport on the current-potential curves. The theory of electron-transfer reactions, migration, and diffusion processes and digital simulation of convective-diffusion are analyzed in the first four chapters. New experimental evidence of mechanistic aspects in electrode kinetics from different in-situ spectroscopies and structural studies are discussed in the second section. The last... 

The UBI-QEP scheme is fairly simple to use, both for diatom and polyatom surface interactions. It is an attempt to include a large body of experimental data in the same theoretical framework. It has mainly been used to predict activation barriers for reactions and diffusion processes. However a few molecular dynamics studies using the UBI potentials for dissociative reactions on metal surfaces were reported in ref. [145]. However, in order to treat evenhandedly the reactant and product state, a modified potential function containing more parameters is suggested (see Appendix G of ref. [145]). 

The characteristic feature of solid—solid reactions which controls, to some extent, the methods which can be applied to the investigation of their kinetics, is that the continuation of product formation requires the transportation of one or both reactants to a zone of interaction, perhaps through a coherent barrier layer of the product phase or as a monomolec-ular layer across surfaces. Since diffusion at phase boundaries may occur at temperatures appreciably below those required for bulk diffusion, the initial step in product formation may be rapidly completed on the attainment of reaction temperature. In such systems, there is no initial delay during nucleation and the initial processes, perhaps involving monomolec-ular films, are not readily identified. The subsequent growth of the product phase, the main reaction, is thereafter controlled by the diffusion of one or more species through the barrier layer. Microscopic observation is of little value where the phases present cannot be unambiguously identified and X-ray diffraction techniques are more fruitful. More recently, the considerable potential of electron microprobe analyses has been developed and exploited. 

The relation between E and t is S-shaped (curve 2 in Fig. 12.10). In the initial part we see the nonfaradaic charging current. The faradaic process starts when certain values of potential are attained, and a typical potential arrest arises in the curve. When zero reactant concentration is approached, the potential again moves strongly in the negative direction (toward potentials where a new electrode reaction will start, e.g., cathodic hydrogen evolution). It thus becomes possible to determine the transition time fiinj precisely. Knowing this time, we can use Eq. (11.9) to find the reactant s bulk concentration or, when the concentration is known, its diffusion coefficient. 

As demonstrated in Section 5.2, the electrode potential is determined by the rates of two opposing electrode reactions. The reactant in one of these reactions is always identical with the product of the other. However, the electrode potential can be determined by two electrode reactions that have nothing in common. For example, the dissolution of zinc in a mineral acid involves the evolution of hydrogen on the zinc surface with simultaneous ionization of zinc, where the divalent zinc ions diffuse away from the electrode. The sum of the partial currents corresponding to these two processes must equal zero (if the charging current for a change in the electrode potential is neglected). The potential attained by the metal under these conditions is termed the mixed potential Emix. If the polarization curves for both processes are known, then conditions can be determined such that the absolute values of the cathodic and anodic currents are identical (see Fig. 5.54A). The rate of dissolution of zinc is proportional to the partial anodic current. 

Concentration Polarization As a reactant is consumed at the electrode by electrochemical reaction, there is a loss of potential due to the inability of the surrounding material to maintain the initial concentration of the bulk fluid. That is, a concentration gradient is formed. Several processes may contribute to concentration polarization slow diffusion in the gas phase in the electrode pores, solution/dissolution of reactants/products into/out of the electrolyte, or diffusion of reactants/products through the electrolyte to/from the electrochemical reaction site. At practical current densities, slow transport of reactants/products to/from the electrochemical reaction site is a major contributor to concentration polarization ... 

A poorly balanced water distribution in the fuel cell can severely impair its performance and cause long-term effects due to structural degradation. If PEMs or CLs are too dry, proton conductivity will be poor, potentially leading to excessive joule heating, which could affect the structural integrity of the cell. Too much water in diffusion media (CLs and GDLs) blocks the gaseous supply of reactants. As these examples show, all processes in PEECs are linked to water distribution and the balance of water fluxes. 

The theory for cyclic voltammetry was developed by Nicholson and Shain [80]. The mid-peak potential of the anodic and cathodic peak potentials obtained under our experimental conditions defines an electrolyte-dependent formal electrode potential for the [Fe(CN)g] /[Fe(CN)g]" couple E°, whose meaning is close to the genuine thermodynamic, electrolyte-independent, electrode potential E° [79, 80]. For electrochemically reversible systems, the value of7i° (= ( pc- - pa)/2) remains constant upon varying the potential scan rate, while the peak potential separation provides information on the number of electrons involved in the electrochemical process (Epa - pc) = 59/n mV at 298 K [79, 80]. Another interesting relationship is provided by the variation of peak current on the potential scan rate for diffusion-controlled processes, tp becomes proportional to the square root of the potential scan rate, while in the case of reactants confined to the electrode surface, ip is proportional to V [79]. 

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