Mass-transport-controlled processes

The information required to predict electrochemical reaction rates (i.e., experimentally determined by Evans diagrams, electrochemical impedance, etc.) depends upon whether the reaction is controlled by the rate of charge transfer or by mass transport. Charge transfer controlled processes are usually not affected by solution velocity or agitation. On the other hand, mass transport controlled processes are strongly influenced by the solution velocity and agitation. The influence of fluid velocity on corrosion rates and/or the rates of electrochemical reactions is complex. To understand these effects requires an understanding of mixed potential theory in combination with hydrodynamic concepts. 

If we consider again the equation of charge transfer, but for a mass transport-controlled process, the change in the current distribution at a radius r will be... 

If we want to solve the diffusion problem for electrodes where the potential varies with time, then we must add to equations 3.44-3.47 an expression which relates the electrode potential E to the concentration at the electrode surface. Since we are dealing in this section with mass-transport controlled processes, we shall use a modified form of the Nernst equation. At zero current the potential is given by... 

In this chapter we shall focus our attention on the use of transients for the separation between activation and mass-transport-controlled processes. 

The simplest approach used for autocatalyst modelling is the so-called look up table (Laing et al., 1999). Essentially, the model is populated with a database of conversions for various species as a function of temperature and space velocity, from which conversions can be predicted by interpolation. This, coupled with a simple thermal model for catalyst temperature and some way of allowing for mass transport control, constitutes the simplest type of model. Once this sort of model has been written, adapting to another formulation is a relatively quick process of measuring new conversion curves and adding these to the model. 

Such a sharp drop in surface area of the noble metals does not result in a corresponding activity decrease. As measured by various empirical criteria, such as conversion at a certain temperature, it is found that activity loss is initially not nearly as steep as the indicated loss in site accessibility. The reason is that such measurements are usually carried out under conditions of mass transport control, when the vast majority of the active surface is not utilized in the catalytic process. However, once the active surface has dropped below a certain value, catalytic activity diminishes rapidly (66). These results emphasize that to begin with, a huge reserve of activity is required if the statutory service life of 50,000 miles is to be achieved. How large this reserve has to be is determined to a large extent by the poison levels. 

This equivalence between the charge of surface-bound molecules and the current of solution soluble ones is due to two main reasons first, in an electro-active monolayer the normalized charge is proportional to the difference between the total and reactant surface excesses ((QP/QP) oc (/> — To)), and in electrochemical systems under mass transport control, the voltammetric normalized current is proportional to the difference between the bulk and surface concentrations ((///djC) oc (c 0 — Cq) [49]. Second, a reversible diffusionless system fulfills the conditions (6.107) and (6.110) and the same conditions must be fulfilled by the concentrations cQ and cR when the process takes place under mass transport control (see Eqs. (2.150) and (2.151)) when the diffusion coefficients of both species are equal. 

The effect of altering the rate of mass transport to the electrode surface was also studied (see Fig. 2.20). At low rotation rates, the reaction is mass transport-controlled but as the rotation speed is increased, the current tends to a rotation speed-independent value indicating that the current becomes limited by some other process. 

It is assumed that all electrons transfers from the particle conduction band and surface states to the electrode take place under conditions where the current is mass transport controlled. The first order rate constant kg describes electron promotion either by thermal or photonic processes, and the rate constant k describes the loss of the electrons from the conduction band or surface states by a process which is first order in electron concentration. The validity of this assumption will be discussed later. There will be an equation similar to equation (71) for each value of m. If each equation is multiplied by its value of m and the engendered set of equations summed, it is possible to obtain the simple result that ... 

Convective diffusion — The electrochemical - mass transport controlled by both -> convection and - diffusion is called a process by convective diffusion [i]. Convection is caused by externally controlled force or spontaneous force. Convective diffusion has been conventionally used in a strict sense for well-controlled flow such as for -> rotating disk electrodes [ii], - channel elec-... 

Under mass transport control, an anodic layer (salt film or ion-concentrated layer) forms on the anode surface. The electrochemical dissolution process is then controlled by the diffusion and migration of mass transport limiting species in the anodic layers. In the case of Cu in concentrated phosphoric acid solution, it is said to be acceptor (water molecules) diffusion controlled. Since any arbitrary surface profile can be obtained by superimposing a series of sine waves, it is reasonable to simplify the anode surface profile to a single sine wave of wavelength a and amplitude b. Figure 10.8 shows a sinusoidal anode surface profile with anodic layer in the case of Cu in concentrated phosphoric acid solution that is, the mass transport limiting species is acceptor. Cu and acceptor concentration profiles are also illustrated in Fig. 10.8. The surface profile can be mathematically expressed as... 

There is a variety of fundamental physical and chemical principles lhat can control the deposition rate and quality of a film resulting from a CVD process. We briefly introduce them here, but refer the reader to Chapter 2 and other books on CVD for more detailed discussions. The basic processes underlying CVD can be subdivided into mass transport effects and chemical effects, each of which can occur in both the gas and solid phases. Chemical effects can be further subdivided into thermodynamic effects and kinetic effects. In some cases, a particular effect can be separated out as rate limiting, and a CVD process can be said to be mass-transport controlled or surface-kinetics controlled. In reality, transport and chemical reactions are closely coupled, with their relative importance varying with the details of the operating conditions. 

The kinetics of coating growth is basically dependent on temperatures. A CVD reaction is divided into either surface kinetic or mass transport control. Figure 11 shows a model as how the growth process depends on the surface kinetics and mass control regimes. is the concentration of the bulk gas and is the concentration at the substrate interface. The concentration of the reactants drops from the bulk to the substrate surface and the corresponding mass flux is given by,... 

So far we have concentrated our attention on activation-controlled processes. Since the rate of such processes increases exponentially with potential, it is usually possible to drive them fast enough, to ensure that mass transport becomes the limiting factor. For a measurement to be truly activation controlled, the current must be small compared to the mass-transport-controlled limiting current. The latter is given, as we have seen by... 

In order to undergo a redox process, the reactant must be present within the electrode-reaction layer, in an amount limited by the rate of mass transport of Yg, to the electrode surface. In electrolyte media, four types of mass-transport control, namely convection, diffusion, adsorption and chemical-reaction kinetics, must be considered. The details of the voltammetric procedure, e.g., whether the solution is stirred or quiet, tell whether convection is possible. In a quiet solution, the maximum currents of simple electrode processes may be governed by diffusion. Adsorption of either reactant or product on the electrode may complicate the electrode process and, unless adsorption, crystallization or related surface effects are being studied, it is to be avoided, typically... 

In applying Eq. (14) to mass transport-controlled electrolytic processes, an important step is the estimation of the effect of the imposed magnetic field strength on properties of the diffusion boundary layer. Since electrolyte density is space-variant in this layer, the right-hand side of Eq. (14) is nonzero, even if the low-Rem approximation [i.e., curl(j B) = 0] is invoked. This is clearly shown by the expanded form... 

To appreciate the impact of SECM on the study of phase transfer kinetics, it is useful to briefly review the basic steps in reactions at solid/liquid interfaces. Processes of dissolution (growth) or desorption (adsorption), which are of interest herein, may be described in terms of some, or all, of the series of events shown in Figure 1. Although somewhat simplistic, this schematic identifies the essential elements in addressing the kinetics of interfacial processes. In one limit, when any of the surface processes in Figure 1 (e.g., the detachment of ions or molecules from an active site, surface diffusion of a species across the surface, or desorption) are slow compared to the mass transport step between the bulk solution and the interface, the reaction is kinetically surface-controlled. In the other limit, if the surface events are fast compared to mass transport, the overall process is in a mass transport-controlled regime. 

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