How to estimate the surface coverage of polymer grafted planar substrates and spherical nanoparticles

Surface coverage is an important parameter in describing the kinetics of adsorption in interface science, the adsorption theory of macromolecules (<i>e.g.</i>, proteins, DNA) on biomaterial surface, the stability of colloids with surface modifications and the application of surfactants at interfaces. In this work, we focus on nanoparticles (NPs) with polymer coatings and, with a mean-field approach, propose a universal theoretical model for calculating the coverage of polymers on planar or spherical substrates at different solvent qualities. Validated by molecular dynamics simulations, our model is applicable to a wide range of polymer morphologies - from partially occluded to completely covered NPs - and provides a novel quantitative approach to characterize this type of polymer patchy particles.