Modeling directed self-assembly of nanoparticles under perpendicular electric fields

We design and model an experiment to study the effect of electric bias on particle-coverage densities produced during ionic nanoparticle self-assembly. The experiment involves the application of a uniform external electric field parallel to a glass substrate during the self-assembly of silica nanoparticles. We refer to this procedure as directed self-assembly of monolayers (DSAM). In our theoretical analysis, we modify existing cooperative sequential adsorption models to account for diffusion under an applied electric field. We use the mean field approximation to solve for particle-coverage densities. To ascertain the validity of this method, we compare our solutions to Monte Carlo simulations of the system. We also discuss particular experimental implementations of an ionic self-assembled monolayer under the influence of perpendicular external electric fields.