Curvature effect on the surface-patterning of end-tethered polymers under nanoconfinement

Surface-patterning of end-tethered polymers is of fundamental importance in polymer physics. Understanding the effect of nanoconfinement on such patterning is crucial for the functionalization of nanochannels/pores for a wide range of applications from biosensing to molecular filtering. On the other hand, the confinement also imposes a great challenge for in-vivo experimental analysis of the polymer behavior. Here we use a molecular theory to study the molecular organization of polymeric materials grafted to the inner surface of solid-state nanochannels/pores. Our theory shows that nanoconfined end-tethered polymers can microphase-separate into rich morphologies in bad solvent. These morphologies and their broken symmetries depend on many factors including the solvent quality, the grafting density of the polymer, the shape of the channel and so on. By investigating the nanoconfinement effect in a larger geometrical context covering flat, convex and concave topologies, we reveal a generic curvature effect on the thermodynamics of the surface-patterning. Furthermore, our theory predicts a strong coupling between such curvature-dependent morphology and external stimuli such as an in-channel flow. Our insights can be used to guide the rational design of smart nanochannels.