Scaling Laws for Concave polymer brushes in good solvent

While most theoretical models—including scaling analyses and self-consistent field theories—have focused on flat and convex polymer brushes, there is a significant gap in research focused on brushes with open concave curvatures. A concave brush should not be seen simply as an inverted convex brush; as the free volume changes with distance from the surface, influenced by the curvature. Furthermore, understanding the morphology of concave brushes is vital for applications involving polymer grafting on complex biological interfaces, like proteins. In this study, we aim to understand the scaling behaviors across different regimes, which are influenced by grafting density, chain length, and surface curvature. We conducted coarse-grained molecular dynamics simulations of both convex and concave cap brushes with varying spherical curvature using HOOMD-Blue. Analysis of the density profiles reveal distinctly different scaling regimes in both their density profiles and brush heights, indicating that concave brushes are both microscopically and macroscopically different compared to their convex counterparts. These results provide insights that can aid in the design of functionalized particles interactions for more complex surface and core geometries.