Geometric Features of Structuring of Amphiphilic Macromolecules on the Surface of a Spherical Nanoparticle

The self-assembly of amphiphilic homopolymers tightly grafted to the spherical nanoparticle and immersed in a selective solvent is studied by the computer experiment method. Conditions under which macromolecules form thin membrane-like layers surrounding the nanoparticle are determined. It is first shown that the emerging polymer structures may be approximated by complete embedded minimal surfaces satisfying the Weierstrass representation, namely, helicoid, catenoid, and Enneper and Costa surfaces. Mathematical constructions defining these minimal surfaces highlight a new type of ordering of polymer structures and determine its symmetry classification similar to crystal classification by Fedorov groups. Calculations for the two considered sets of parameters show that structures approximated by a helicoid are energetically more favorable than structures approximated by other minimal surfaces.