Electrochemical aspects of the generation of ramified metallic electrodeposits

The growth of ramified metallic deposits by electrodeposition from dilute salt solutions and in a high electric field has been considered in the geometry of a thin rectangular cell. The equations governing ion motion in the case of a dilute electrolyte have been solved numerically and analytically in a one-dimensional (1D) and a 2D approximation. It is found that ramified growth is a direct consequence of the creation of a space charge upon anion depletion in the vicinity of the cathode. The front of the ramified deposit is predicted to advance at a speed just equal to the velocity of the anions in the applied electric field. The presence of this space charge ahead of the growing front is associated with a potential drop \ensuremath{\delta}V. Resolution of the equations in the 2D case shows that the dense-parallel morphology of the deposit also results quite naturally from the existence of a space charge in the vicinity of the filament tips. The average filament spacing and sidebranch tilting angle can be directly related to the values of \ensuremath{\delta}V and of the applied electric field. The mechanism giving rise to the space charge will apply as well to any physical system involving electric conduction with two types of carriers, if one of them exhibits blocking-contact characteristics.