Title: Application of the static structure factor for efficient characterization of finite-size particle-films

Abstract

Monolayers of micro- and nanoparticles on solid substrates have many practical applications. They include electrochemical, piezoelectric, and plasmonic sensors; catalysts; antimicrobial and antireflective surfaces; or substrates for spectroscopy. Once produced, the particle systems usually need to be tested to ensure their high quality and functionality. The main objective of our research has been to develop a cheap and accurate method for efficient characterization of particle films. We have demonstrated that the multidimensional function of static structure factor is a promising candidate for this purpose. To compute Its continuous, ensemble averaged approximation, we may Fourier transform the radial distribution function calculated over an appropriate range of interparticle distance and system parameters. To calculate a discrete approximation of the structure factor for a sample monolayer image, on the other hand, we need to compute the squared modulus of the discrete Fourier transform of the digital image. Then, performing a least-squares fit of the continuous approximation to the discrete data, we can estimate the system parameters, with no identification of individual particles. To validate our approach, we have first determined parameters of a dense array of monodisperse hard spheres, generated by event-driven molecular dynamics. The particle radius, surface coverage, and size of analyzed area have been found with standard errors on the order of 1%. Then, using images of monolayers published in the literature, we have demonstrated a practical application of the approach to determine important parameters of random particle ensembles at lower surface coverage. For that, we have used a 4D structure-factor function of the waive number, particle surface coverage, and diameter of analyzed area, computed for hard disk systems generated with the model of random sequential adsorption. Our results suggest that the novel approach can be generalized for films of charged particles by simply increasing the dimensionality of the structure-factor function.