Cooperative sequential adsorption models on a Cayley tree: analytical results and applications

TL;DR

This paper introduces cooperative sequential adsorption models on Cayley trees, providing analytical solutions for surface coverage and particle configurations, with applications in nanotechnology and material science.

Contribution

It generalizes reaction-diffusion results to cooperative adsorption on Cayley trees, offering new analytical methods for complex adsorption processes.

Findings

Derived time-dependent surface coverage formulas

Calculated probabilities of particle configurations

Applicable to ionic self-assembly and nanoparticle encapsulation

Abstract

We present a class of cooperative sequential adsorption models on a Cayley tree with constant and variable attachment rates and their possible applications for ionic self-assembly of thin films and drug encapsulation of nanoparticles. Using the empty interval method, and generalizing results known from reaction-diffusion processes on Cayley trees, we calculate a variety of quantities such as time-dependent surface coverage and time-dependent probabilities of certain particle configurations.