Class of cooperative stochastic models: Exact and approximate solutions, simulations, and experiments using ionic self-assembly of nanoparticles.

We present exact and approximate results for a class of cooperative sequential adsorption models using matrix theory, mean-field theory, and computer simulations. We validate our models with two customized experiments using ionically self-assembled nanoparticles on glass slides. We also address the limitations of our models and their range of applicability. The exact results obtained using matrix theory can be applied to a variety of two-state systems with cooperative effects.

Cooperative sequential-adsorption model in two dimensions with experimental applications for ionic self-assembly of nanoparticles.

Self-assembly of nanoparticles is an important tool in nanotechnology, with numerous applications, including thin films, electronics, and drug delivery. We study the deposition of ionic nanoparticles on a glass substrate both experimentally and theoretically. Our theoretical model consists of a stochastic cooperative adsorption and evaporation process on a two-dimensional lattice. By exploring the relationship between the initial concentration of nanoparticles in the colloidal solution and the density of particles deposited on the substrate, we relate the deposition rate of our theoretical model to the concentration.