The Modeling of Polymer Brushes by a Three-Dimensional Classical Density Functional Theory and Its Predictions f or Brush–Nanoparticle Systems

Polymer brushes are widely used materials for surface modification, whereas traditional theoretical approaches such as molecular simulations are computationally expensive. In this work, a three-dimensional classical density functional theory (CDFT) is employed to investigate the structural and energetic properties of a polymer brush–nanoparticle system. Unlike conventional models, in which the polymer is constrained by an external potential and the binding site can move freely on the substrate, a three-dimensional (3D) fixed model is developed by fixing the density profile of the grafting segment. Compared with the traditional model, the 3D fixed model exhibits stronger repulsive interactions and yields more physically realistic density profiles. The Green’s function and reference ideal gas model are employed to calculate the configuration and energy of the polymer. The model indicates that polymer chains may either avoid or bypass the nanoparticle, depending on the chain length, the nanoparticle–surface separation distance, and the grafting density, thereby leading to the formation of a potential of mean force (PMF) well. The effects of other factors, including particle size, grafting density, and hydrophilicity, are also investigated, providing insights into the design and application of polymer brushes.