Approximate Corona Phase Hamiltonian for Individual Cylindrical Nanoparticle-Polymer Interactions.

Nanoparticle surfaces, such as cylindrical nanowires and carbon nanotubes, are commonly coated with adsorbed polymer corona phases to impart solution stabilization and to control molecular interactions. These adsorbed polymer molecules (biological or otherwise), also known as the corona phase, are critical to engineering particle and molecular interactions. However, the prediction of its structure and the corresponding properties remains an unresolved problem in polymer physics. In this work, we construct a Hamiltonian describing the adsorption of an otherwise linear polymer to the surface of a cylindrical nanorod in the form of an integral equation summing up the energetic contributions corresponding to polymer bending, confinement, solvation, and electrostatics. We introduce an approximate functional that allows for the solution of the minimum energy configuration in the strongly bound limit. The functional is shown to predict the pitch and surface area of observed helical corona phases in the literature based on the surface binding energy and persistence length alone. This approximate functional also predicts and quantitatively describes the recently observed ionic strength-mediated phase transitions of charged polymer corona at carbon nanotube surfaces. The Hamiltonian and the approximate functional provide the first theoretical link between the polymer's mechanical and chemical properties and the resulting adsorbed phase configuration and therefore should find widespread utility in predicting corona phase structures around anisotropic nanoparticles.