Activation-diffusion control

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The overpotential rj in mixed activation-diffusion control is given by... 

Taking into account that the exchange current density depends on the concentration of reacting ion, it follows that the growth of dendrites12,21,22 inside the diffusion layer of the macroelectrode is in fact under mixed activation-diffusion control. Hence, it can be expected that the process on the microelectrodes placed on the surface of the inert macroelectrode can be under mixed control. This is because the charge transfer occurs on the microelectrodes, while the mass-transfer limitations are related to the diffusion layer of the macroelectrode. 

Obviously, deposition to the tip of such protrusion inside the diffusion layer is activation controlled relative to the surrounding electrolyte, but it is under mixed activation-diffusion control relative to the bulk solution. 

The activation-diffusion control of electrodeposition process is a characteristic of metals characterized by the medium exchange current density values and lower hydrogen overpotentials. Copper is the typical representative of this group of metals, and the polarization curve recorded from 0.10 M CUSO4 in 0.50 M H2SO4 is shown in Fig. 1.10a. 

Fig. 2.4 Copper deposits obtained from 0.10 M CUSO4 in 0.50 M H2SO4. Quantity of electricity, Q 20 mA h cm (a) activation-controlled electrodeposition rj = 90 mV, initial current density 3.3 mA cm, (b) mixed activation-diffusion-controlled electrodeposition rj= 140 mV, initial current density 4.2 mA cm, and (c) dominant diffusion-controlled electrodeposition ri = 210 mV, initial current density 6.5 mA cm (Reprinted from Refs. [7, 8, 13] with kind permission from Springer and Ref [16] with permission from Elsevier)...

It can also be seen from Fig. 2.6c-f that the growth of such protrasions produces carrot-like forms, another typical form obtained in copper depositimi under mixed activation-diffusion control. This happens under the condition k 1, when activation control takes place only around the tip of the protrusion, as is illustrated in Fig. 2.6c, d. In this case, Eq. (2.20) can be rewritten in the form ... 

The final form of the carrot-like protrusion is shown in Fig. 2.6e. It can be concluded from the parabolic shape that such protrusions grow as moving paraboloids in accordance with the Barton-Bockris theory [5], the tip radius remaining constant because of the surface energy effect. It can be concluded from Fig. 2.6f that thickening of such a protrusion is under mixed activation-diffusion control because the deposit is seen to be of the same quality as that on the surrounding macroelectrode surface. It can be seen from the Fig. 2.6d that activation control takes place only at the very tip of the protrusion. 

In summary, deposition under nuxed activation-diffusion control causes the formation of a number of growth forms and the increase of surface coarseness, this increase being more pronounced at higher current densities. It should be noted that electrodeposition at a periodically changing rate can change considerably the morphology of the deposits [13, 25]. 

The current density under a mixed activation-diffusion-controlled electrodeposition is given by Eq. (1.13), and substitution of the corresponding limiting diffusion current density from Eqs. (2.62) and (2.63) into the Eq. (1.13) produces after rearrangement ... 

Dendritic Growth Inside Diffusion Layer of the Active Macroelectrode and Ohmic Diffusion and Activation-Diffusion-Controlled Deposition and Determination of tji and tjc... 

For metals characterized by io < A (electrodeposition under mixed activation-diffusion control e.g., Cu), both rji and rjc increase with increasing concentration of the depositing ions, indicating a decrease of the ioHi. ratios with the increasing concentration of metal ions [111]. The difference between i/c and //j (see Eqs. (2.46) and (2.47)) is given by ... 

For metals characterized by io Jl (electrodeposition in mixed ohmic-diffusion control of the electrodeposition e.g., Pb and Ag), increasing concentration of metal ions causes a decrease in both and [111]. Simultaneously, opposite to electrodeposition of metals in mixed activation-diffusion control, increasing the concentration of depositing ions leads to a strong increase in the io/t r tio. 

An increase in leads to a decrease of and, at sufficiently large Tn, the electrodeposition comes under mixed activation-diffusion control, i.e., when ... 

The hydrogen evolution influences the hydrodynamic conditions inside electrochemical cell [6-8]. The increase in hydrogen evolution rate leads to the decrease of the diffusion layer thickness and hence to the increase of limiting diffusion current density of electrode processes. It was shown [6] that if the rate of gas evolutimi at the electrode is larger than 100 cm /cm min (>5 A cm ), the diffusion layer becomes only a few micrometers thick. A coverage of an electrode surface with gas bubbles can be about 30 % [6]. If the thickness of the diffusion layer in conditions of natural convection is 5 10 cm and in strongly stirred electrolyte 5 10 cm [9], it is clear that gas evolution is the most effective way of the decrease of mass transport limitations for electrochemical processes in mixed activation-diffusion control. 

For electrochemical process in mixed activation-diffusion control, the overpotential t] and the current density i are related by Eq. (1.31) [10] ... 

Fig. 1.4 Copper deposits obtained from 0.30 M C11SO4 in 0.50 M H2SO4 by electrodeposition under mixed activation-diffusion control. Deposition overpotential 220 mV (a) Quantity of electricity 40 mAh cm (b) The same as in (a), and (c) and (d) quantity of electricity 20 mAh cm (Reprinted from [7, 10] with permission from Springer and [13] with pmnission from the Serbian Chemical Society.)...

Ohmic-Diffusion and Activation-Diffusion Controlled Deposition... 

The overpotential of electrodeposition, rj, in the region of mixed activation-diffusion control is given by Eq. (3.19) ... 

A different approach to impedance measurements of electrodes in CP conditions was assumed by Juchniewicz and Jankowski (1993). They elaborated a quantitative method, allowing the determination of the partial anodic current of polarized electrodes. They proposed an electric equivalent circuit of a polarized electrode describing the impedance characteristic of an electrode as a function of the applied potential. It has been assumed that on the electrode one activation controlled anodic reaction and one cathodic reaction with mixed activation-diffusion control proceeds. The adopted electric equivalent circuit is presented in Fig. 8-11. 

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