Roughness spectroscopy of particle monolayer: Implications for spectral analysis of the monolayer image

Abstract

The surface roughness of a particle monolayer is one of its fundamental characteristics, conventionally described in terms of power spectral density. We derive a general equation for this function and demonstrate its similarity to those applied in the theory of scattering. To validate our analytical results, we compare them with numerical results derived for a monolayer of 450nm spherical particles, of surface coverage 0.85. We also demonstrate a practical application of our approach on the example of spectral analysis of a SEM image of a polystyrene particle monolayer of surface coverage close to 0.5. Our theoretical model provides a general framework for a cheap and easy parametrization of particle monolayers.