Chirality of electrodeposits grown in a magnetic field

Abstract

Electrodeposits grown around a point cathode in a flat, horizontal electrochemical cell have fractal form. When grown in the presence of a perpendicular applied magnetic field, the deposits develop a spiral structure with chirality which reverses on switching the field direction. These structures are modeled numerically using biased variants of the diffusion limited aggregation (DLA) model. The effects of electric and magnetic fields are modeled successfully by varying the probabilities that a random walker will move in a given direction as a result of a Coulomb force and the Lorentz force-induced flow of electrolyte past the deposit surface. By contrast, a numerical model which considers only the effect of the Lorentz force on individual ions, without reference to the surface of the growing deposit, produces spiral structures with incorrect chirality. The modified DLA model is related to the differential equations for diffusion, migration, and convection. Length scales in the problem are understood by associating the step length of the random walker with the diffusion layer thickness, the lookup radius with the hydrodynamic boundary layer thickness and a point on the numerical deposit with a nucleation center for growth of a crystallite.