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Fig. 11. The polarization curve for silver electrodeposition from nitrate solution on a graphite electrode. Fig. 10. The polarization curve for copper deposition on the electrode from Fig. 9.

Figure 11 The polarization curve for silver electrodeposition from nitrate solution on a graphite electrode. Fig. 10. The polarization curve for copper deposition on the electrode from Fig. 9.

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Fig. 2. The dependences jn calculated using Eq. (1), (jo/j.)=1 and 0.01, f. = 107/120 fx =10-™120), y =0.5 and j, =50 mA/cm?, and ones modified using Eq. (4), L=0.2 cm and «=0.1Scm"!. due to the JR error [3], where Lis the length of the electrolyte column between the tip of a liquid capillary and the electrode and x is the specific conductivity of the electrolyte.
Fig. 2. The dependences jn calculated using Eq. (1), (jo/j.)=1 and 0.01, f. = 107/120 fx =10-™120), y =0.5 and j, =50 mA/cm?, and ones modified using Eq. (4), L=0.2 cm and «=0.1Scm"!. due to the JR error [3], where Lis the length of the electrolyte column between the tip of a liquid capillary and the electrode and x is the specific conductivity of the electrolyte.
Fig. 1. The dependence j-n calculated using Eq. (1), (jo/j.)=100, f.=10"/'20 fa = 10-120), y =0.5 and j, =50 mA/cm2, and one modified using Eq. (4), L=0.2cm and «=0.1 Sem,
Fig. 1. The dependence j-n calculated using Eq. (1), (jo/j.)=100, f.=10"/'20 fa = 10-120), y =0.5 and j, =50 mA/cm2, and one modified using Eq. (4), L=0.2cm and «=0.1 Sem,
Fig. 4. The dependences (j/j,)-n calculated using Eq. (1), (jo/jt)=10, fe=107/?°, fa = 107/120), y = 0.5, andj, = 10 mA/cm? and j, = 50 mA/cm2, and ones modified using Eq. (4), L=0.2 cm and x =0.033Scm7!. In the case under consideration, complete ohmic control of the deposition process can be expected for (jg/j,) => 100 up to a current
Fig. 4. The dependences (j/j,)-n calculated using Eq. (1), (jo/jt)=10, fe=107/?°, fa = 107/120), y = 0.5, andj, = 10 mA/cm? and j, = 50 mA/cm2, and ones modified using Eq. (4), L=0.2 cm and x =0.033Scm7!. In the case under consideration, complete ohmic control of the deposition process can be expected for (jg/j,) => 100 up to a current
Fig. 3. The dependences j-n calculated using Eq. (1), (jo/j.)=10, fe=10%!2°, fa = 10-20), y =0.5, and j, = 50 mA/cm2, and ones modified using Eq. (4), L=0.2 cm, «=0.1 and 0.033Scm"!.
Fig. 3. The dependences j-n calculated using Eq. (1), (jo/j.)=10, fe=10%!2°, fa = 10-20), y =0.5, and j, = 50 mA/cm2, and ones modified using Eq. (4), L=0.2 cm, «=0.1 and 0.033Scm"!.
Fig. 5. Model of a paraboloidal surface protrusion; h is the height of the protrusion relative to the flat portion of the surface, r is the radius of the protrusion tip and 6 is the thickness of the diffusion layer. a OS 9 Ei — a eT, rs, a Obviously, deposition to the tip of such a protrusion inside the diffusion layer is activation controlled relative to the surround- ing electrolyte, but it is under mixed diffusion-activation control relative to the bulk solution.
Fig. 5. Model of a paraboloidal surface protrusion; h is the height of the protrusion relative to the flat portion of the surface, r is the radius of the protrusion tip and 6 is the thickness of the diffusion layer. a OS 9 Ei — a eT, rs, a Obviously, deposition to the tip of such a protrusion inside the diffusion layer is activation controlled relative to the surround- ing electrolyte, but it is under mixed diffusion-activation control relative to the bulk solution.
Fig. 6. The polarization curves for copper electrodeposition obtained on: (a) the initial surface, obtained by deposition of copper ona copper wire electrode for 10 min at 300 mV; (b) electrode surface obtained by deposition of copper on the substrate (a) at 650 mV for 32 min; (c) the same as in (b) but for 38 min; (d) the same as in (b) but for 92 min.
Fig. 6. The polarization curves for copper electrodeposition obtained on: (a) the initial surface, obtained by deposition of copper ona copper wire electrode for 10 min at 300 mV; (b) electrode surface obtained by deposition of copper on the substrate (a) at 650 mV for 32 min; (c) the same as in (b) but for 38 min; (d) the same as in (b) but for 92 min.
Fig. 7. The photomicrographs of the substrate on which the polarization curves from Fig. 6 were obtained: (a) the initial surface, obtained by deposition of copper on copper wire for 10 min at 300 mV; (b) electrode surface obtained by deposition of copper on the substrate (a) at 650 mV for 32 min; (c) the same as in (b) but for 38 min; (d) the same as in (b) but for 92 min. It can be noticed that Eq. (18) represents the crucial contribution of this paper. Eq. (18a) describes the linear part of the polarization curves for tin [19], silver [2] and lead [20] deposition and Eq. (18b) foresees the inflection point in the cases when nc; is low and the resistance of the electrolyte large. Finally, Eq. (18c) describes the part of the polarization curve after initiation of dendrite growth. In fact, dendrite propagation under such conditions is under diffusion and surface energy control and 7; is then given by [9,18]:
Fig. 7. The photomicrographs of the substrate on which the polarization curves from Fig. 6 were obtained: (a) the initial surface, obtained by deposition of copper on copper wire for 10 min at 300 mV; (b) electrode surface obtained by deposition of copper on the substrate (a) at 650 mV for 32 min; (c) the same as in (b) but for 38 min; (d) the same as in (b) but for 92 min. It can be noticed that Eq. (18) represents the crucial contribution of this paper. Eq. (18a) describes the linear part of the polarization curves for tin [19], silver [2] and lead [20] deposition and Eq. (18b) foresees the inflection point in the cases when nc; is low and the resistance of the electrolyte large. Finally, Eq. (18c) describes the part of the polarization curve after initiation of dendrite growth. In fact, dendrite propagation under such conditions is under diffusion and surface energy control and 7; is then given by [9,18]:
= The initiation of dendritic growth is followed by an increase of the deposition current density, and the overall current density will be larger than the limiting diffusion current on a flat active electrode. Based on the above discussion, the polarization curve equation in the ohmic controlled electrodeposition of metals can be determined now by: where N=N(t) is the number of dendrites and 0 =6(t) < 1, where 0 is the coverage of the electrode surface with dendrites.
= The initiation of dendritic growth is followed by an increase of the deposition current density, and the overall current density will be larger than the limiting diffusion current on a flat active electrode. Based on the above discussion, the polarization curve equation in the ohmic controlled electrodeposition of metals can be determined now by: where N=N(t) is the number of dendrites and 0 =6(t) < 1, where 0 is the coverage of the electrode surface with dendrites.
Fig. 8. A detail from Fig. 7b.
Fig. 8. A detail from Fig. 7b.
ig. 9. (a) The agglomerate of dendrites obtained by deposition of copper on the tip of a copper wire electrode at 650 mV for 20 min; (b) the outer limit of the dendrit lectrode. This means that mass transfer limitation can be completely avoided if the deposition process is carried out on dendritic elec- trodes. Naturally, the same effect can be expected if some very fast process, other than metal electrodeposition, is carried out on dendritic electrodes. It seems also that the only way to obtain an ensemble of micro- electrodes [22] working independently under activation control is to form an agglomerate of dendrites, the tips of which represent microelectrodes working in the bulk solution outside any diffusion layer, as well as outside the bulk of the agglomerated dendrites. This could be of great importance in the activation of an inert electrode surface by partial covering with dendrites of an active catalyst.
ig. 9. (a) The agglomerate of dendrites obtained by deposition of copper on the tip of a copper wire electrode at 650 mV for 20 min; (b) the outer limit of the dendrit lectrode. This means that mass transfer limitation can be completely avoided if the deposition process is carried out on dendritic elec- trodes. Naturally, the same effect can be expected if some very fast process, other than metal electrodeposition, is carried out on dendritic electrodes. It seems also that the only way to obtain an ensemble of micro- electrodes [22] working independently under activation control is to form an agglomerate of dendrites, the tips of which represent microelectrodes working in the bulk solution outside any diffusion layer, as well as outside the bulk of the agglomerated dendrites. This could be of great importance in the activation of an inert electrode surface by partial covering with dendrites of an active catalyst.
Fig. 12. The photomicrographs of the silver deposit obtained on a graphite electrode obtained after the recording of the current at different overpotentials in polarizatic measurements: (a) 100 mV; (b) 125 mV; (c) 150 mV; (d) 175 mV; (e) 200 mV; (f) 225 mV. A stationary wire cathode was placed in the middle of a cylin- drical cell of diameter 6cm. The cell surface was covered by the anode, which was made from high purity plate of the correspond- The polarization measurements were performed in the follow- ing manner. In all cases, the overpotential was increased from the previous to an increased value and held for 30s before mea-
Fig. 12. The photomicrographs of the silver deposit obtained on a graphite electrode obtained after the recording of the current at different overpotentials in polarizatic measurements: (a) 100 mV; (b) 125 mV; (c) 150 mV; (d) 175 mV; (e) 200 mV; (f) 225 mV. A stationary wire cathode was placed in the middle of a cylin- drical cell of diameter 6cm. The cell surface was covered by the anode, which was made from high purity plate of the correspond- The polarization measurements were performed in the follow- ing manner. In all cases, the overpotential was increased from the previous to an increased value and held for 30s before mea-
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