Exact Analytical Solutions of Charged Monomer and Dimer Deposition Models in One and Two Dimensions

Abstract

Our work is motivated by the manufacturing process of self-assembled antireflective coatings using silica and titania nanoparticles. During the manufacturing process, it is highly desirable to know the time dependent analytical relationship between the index of refraction of the coating and the particle density of the jammed state. We present exact analytical results of one-dimensional cooperative sequential adsorption (CSA) models for two cases: monomer and dimer deposition of charged particles. We extend our study to two-dimensional deposition models on Cayley trees for charged monomers and dimers. Using standard linear algebra techniques, we introduce the general methodology for finding the exact analytical solutions for the monomer and dimer deposition of charged particles and discuss the time dependence of particle density (surface coverage) for some special cases of particle-particle interaction.