Title: Theoretical modeling of dendrite growth from conductive wire electropolymerization

Abstract: Electropolymerization is a bottom-up materials engineering process of micro and nano-scale that utilizes electrical signals to deposit conducting dendrites' morphologies by a redox reaction in the liquid phase. It resembles synaptogenesis in the brain, in which electrical stimulation in the brain causes the formation of synapses from the cellular neural composites. The strategy has been recently explored for neuromorphic engineering by establishing link between the electrical signals and the dendrites' shapes. Since the geometry of these structures determines their electrochemical properties, understanding the mechanisms that regulate the polymer assembly under electrically programmed conditions is an important aspect. In this manuscript, we simulate this phenomenon using mesoscale simulations, taking into account the important features of spatial-temporal potential mapping based on the time-varying signal, the motion of charged particles in the liquid due to the electric field, and the attachment of particles on the electrode. The study helps in visualizing the motion of particles in different electrical conditions, which is not possible to probe experimentally. Consistent with the experiments, the higher AC frequency of electrical activities favors linear wire-like growth, while lower frequency leads to more dense and fractal dendrites growth, and voltage offset leads to asymmetrical growth. We find that dendrites' shape and growth process systematically depend on particle concentration and random scattering. We discover that the different dendrites' architectures are associated with different Laplace and diffusion fields, which govern the monomers trajectory and subsequent dendrites' growth. Such unconventional engineering routes could have a variety of applications from neuromorphic engineering to bottom-up computing strategies.