Monte Carlo simulation of gold nano-colloids aggregation morphologies on a heterogeneous surface

After one hour immersion (adsorption) in nano-colloidal suspensions, mesoscopic (μm scale) aggregation networks of gold nanoparticles (25 nm) are formed on a methyl/amine terminated surface (CH3/NH2) and followed by the substrate drying. A Monte Carlo simulation is then performed to model these patterns in microscopic scale. It is revealed that a two-state Pott-like model allows to reproduce these structures if some inactive sites are introduced at the interface between (CH3/NH2) and Au nano-colloids. The purpose of this study is to estimate the number of inactive sites by an inverse method based on an original multi-fractal formalism. Multi-fractal measures are defined like the quantity of information contained at different scales in surface morphology. After, parameters are estimated to minimise the norm between the experimental multi-fractal and simulated spectra. The robustness of this multi-scale analysis is tested by a statistical bootstrap protocol that gives computing confidence intervals of the physical coefficients.