Lateral phase separation of mixed polymer brushes on planar and spherical surfaces

A mixed polymer brush consists of two (or more) polymer species grafted to a surface at a high density, inducing the polymers to highly stretch to maximize favorable solvent interactions while minimizing polymer overlap. The enthalpic and entropic interactions between the different polymers give rise to lateral phase behavior on the surface. Understanding this phase separation behavior is interesting for applications in nanotemplating and controlled protein adsorption. In this work, we present a novel theoretical model to quickly predict lateral phase separated morphologies of mixed polymer brushes on planar, cylindrical and spherical surfaces. The model combines a Flory-Huggins model for enthalpic interactions between the polymer components with an Alexander-de Gennes model for the entropy of the brush layers. When there is a length difference between the polymer components, these two interactions along with the conformational entropy of the system lead to a range of morphologies including stripes, dimples, mixing, and complete phase separation. The computational efficiency of this model allows for phase diagrams to be generated with great accuracy. The results of our model thus allow for the fast prediction of lateral morphologies on different geometries.