Depth-Resolved Photocatalytic Kinetic Modeling of Glass-Supported PMMA/TiO2/Au Transparent Self-Cleaning Coatings

Abstract

This study presents a simulation-only design framework for transparent PMMA/TiO₂/Au self-cleaning coatings deposited on an optically inert glass support and evaluated through methylene-blue (MB) discoloration kinetics. A MATLAB-based effective-medium and transfer-matrix workflow is coupled with a pseudo-first-order kinetic descriptor and a depth-resolved local volumetric rate of energy absorption (LVREA) analysis to estimate how optical thickness, TiO₂ content, and Au loading affect near-surface photonic energy deposition. The model-predicted dataset identifies a photocatalytic design window centered at a coating thickness of approximately 0.65–0.75 μm and an Au loading of about 1.0–1.4 vol %, where the balance between plasmon-assisted surface activation, transparency preservation, and parasitic metallic attenuation is most favorable. At the representative optimized point (0.70 μm, 7 vol % TiO₂, and 1.2 vol % Au), the simulated apparent rate constant reaches 0.052 min^‒1, corresponding to 95.6% MB conversion after 60 min. Higher Au content intensifies near-surface loss and shortens the useful penetration depth, while off-optimum thickness reduces the effective photonic driving force. The results are presented strictly as model-predicted trends intended to guide future experimental validation of transparent photocatalytic and self-cleaning glass coatings.