A simple model for the barrier properties of brushes with an arbitrary chain length distribution

Polymer brushes can form protective barriers on surfaces, reducing fouling and adsorption of foreign entities. Predicting how the properties of such surfaces depend on physical brush parameters has technological implications for the applications of these coatings. However, most theoretical models require in-depth knowledge or advanced mathematical and computational skills, which prevents their broad use. Here, we present a simple model extending the Alexander-De Gennes ansatz for arbitrary chain length distributions, allowing us to easily rationalize the effect of polydispersity, which is a feature of all realistic brushes. This model can predict the interaction of a brush with nanoparticles or an opposing wall, as demonstrated by good qualitative agreement with molecular dynamics simulations. An open-source Python implementation of our model is freely available on GitHub, and the model allows for efficient screening of brush designs to reach technological applications.