ABSTRACT
Overpotentials ................................................................................. 352 15.2 Galvanostatic Conditions and Large Overpotentials ....................................................... 354
15.2.1 Galvanostatic Conditions with Negligible Current Densities (Poor Performance Catalysts) ........................................................................... 354
15.2.2 Galvanostatic Conditions with Large Current Densities (Good Performance Catalysts).......................................................................... 357
15.3 Non-Galvanostatic Conditions and Constant Overpotentials .......................................... 360 15.4 Metal Rough Growth in the Absence and Presence of Overpotentials........................... 363
15.4.1 Metal Roughness at Regular and Periodic Surfaces ........................................ 363 15.4.1.1 Cycloid Surfaces ............................................................................. 363
15.5 Metal Roughness at Non-Regular Surfaces ..................................................................... 371 15.5.1 Perturbation Theory and Linear Stability Theorem ......................................... 371
Appendix A: Resolution of the Differential Equation (15.37) by Changing Variables............... 375 Appendix B: Logarithmic Integral Function ................................................................................ 380 Appendix C: Elliptic Integral Function ........................................................................................ 382 References ..................................................................................................................................... 383
Smooth surfaces can develop roughness or even porosity during metal electrodeposition since it is a very slow process that is controlled by many factors including applied potential, electrolyte composition, substrate morphology, and temperature [1,2]. The development of a smooth metal surface during electrodeposition concerns the amount of deposited metal, morphology of the surface, compactness of the deposit, current efficiency, and cell-applied potential. Excessive roughening can lead to short-circuiting between cathode-anode systems in technologically operating
cells. Roughening can affect the mechanical stability of the anodes, thereby causing corrosion and pitting with crevice formation, and finally leading to the concentration of flux at their edges.
