Model for the treeing process of the silver electrodeposition experiment

ANA L. PASTORE Y PIONTTI; CRISTIAN E. LA ROCCA; LIDIA A. BRAUNSTEIN

San Carlos de Bariloche-Río Negro

Workshop; IX Latin American Workshop on Nonlinear Phenomena; 2005

We simulate a model that captures all the features of the silver electrodeposition experiment in a rectangular cell. We study the bulk of the aggregates on the basis of a treeing process [1,2]. The model proposed is a diffusion limited process in 1+1 dimension where the particles are dropped from the top of a rectangular lattice and are allowed to difuse. The diffusion upwards is forbidden, whereas in the other directions the particles are allowed to diffuse with probability 1-p to the lateral nearest neighbors positions and with probability p downwards. Here p takes into account the strength of the electric field. When a newly deposit particle has a nearest neighbor which belongs to only one tree, it sticks to that tree. If the particle has more than one nearest neighbor that belongs to different trees one of them is selected at random and the particle sticks to the chosen tree. We compute the r.m.s. heights h_s and r.m.s. widths w_s as function of the mass s of the trees. We found that the scaling behavior of h_s and w_s depends very weakly on p. The values obtained for the magnitudes studied here are in perfect agreement with the ones found on the experiment [3]. [1] Z. Rácz and T. Vicsek, Phys. Rev. Lett. 51, 2382 (1983). [2] F. Romá, C. M. Horowitz and E. V. Albano, Phys. Rev. E 66, 066115 (2002). [3] C. M. Horowitz, M. A. Pasquale, E. V. Albano and A. J. Arvia, Phys. Rev. B 70, 033406 (2004).