An introduction to stochastic self-assembly: theory, simulation and experimental applications

We introduce three stochastic cooperative models for particle deposition and evaporation relevant to ionic self-assembly of nanoparticles with applications in surface fabrication and nanomedicine. We present a method for mapping a stochastic model onto the Ising model, which allows us to use the established results for the Ising model to describe the properties of the system. After completing the mapping process, we investigate the time dependence of particle density using the mean field approximation. We complement this theoretical analysis with Monte Carlo simulations that support our models. These techniques, which can be used separately or in combination, are useful as pedagogical tools because they are tractable mathematically and they apply equally well to many other physical systems with nearest-neighbor interactions including voter and epidemic models.