Mass-Transport-Controlled Reactions

Mass transport occurs by three different modes  

The flux (J), a common measure of the rate of mass transport at a fixed point, is defined as the number of molecules penetrating a unit area of an imaginary plane in a unit of time and is expressed in units of mol cm V1. The flux to the electrode is described mathematically by a differential equation, known as the Nernst-Planck equation, given here for one dimension 

According to Fick s first law, the rate of diffusion (i.e., the flux) is directly proportional to the slope of the concentration gradient  

Combination of Eqs. (1.4) and (1.5) yields a general expression for the current response  

the current (at any time) is proportional to the concentration gradient of the electroactive species. As indicated by the equations above, the diffusional flux is time-dependent. Such dependence is described by Fick s second law (for linear diffusion)  

Mass transport occurs by tlmee different modes  

FIGURE 1-1 The tliree modes of mass transport. (Reproduced with pemiission from reference 1.) 

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In this section we consider experiments in which the current is controlled by the rate of electron transfer (i.e., reactions with sufficiently fast mass transport). The current-potential relationship for such reactions is different from those discussed (above) for mass transport-controlled reactions. 

In this chapter you will learn that proper assessment of mass transport controlled corrosion reactions requires knowledge of the concentration distribution of the reacting species in solution, certain properties of the electrolyte, and the geometry of the system. A rigorous calculation of mass transport controlled reaction rates requires detailed information concerning these parameters. Fortunately, many of the governing equations have been solved for several well-defined geometries. 

The mass transfer coefficient, K, is defined as the ratio of the mass transport controlled reaction rate to the concentration driving force. The concentration driving force will depend on both turbulent and bulk convection. Bulk convection depends on molecular diffusivity, while the turbulent component depends on eddy diffusivity (4). The mass transfer coefficient considers the combination of the two transport mechanisms, empirically. 

In the case of a mass transport-controlled reaction, we have to make the complete transformation of (13.1) into... 

Fig. 62. Crystal-electrode geometry, notation, and boundary conditions for mass transport-controlled reaction of H+ at the crystal surface.

Fig. 66. The variation in shielding factor with time for the reduction of H+ in an aqueous polymaleic acid system of concentration 7.63 mM in monomer units. The flow rate employed is 1.64 x 10 2cm3 s 1. A theoretical shielding factor of0.333 is predicted on the basis of the crystal electrode geometry, for mass transport-controlled reaction of H+ at the crystal surface. Data from the authors laboratory.

Maximizing the space-time yield, and thereby minimizing the investment cost in cells, requires the cell current to be maximized. However, different strategies must be used to scale kinetically and mass transport-controlled reactions. 

Hypochlorite reduction, reaction 15, is a mass transport controlled reaction in the absence of chromate in the electrolyte and takes place easily on most electrode materials. Chlorate reduction (reaction 16), on the other hand, is kinetically controlled and chlorate is present at a high... 

In the general case, for a mass transport controlled reaction, the values of both electrode area A will contribute to performance. Therefore, it is... 

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