Self-assembly of amphiphilic homopolymers grafted onto spherical nanoparticles: complete embedded minimal surfaces and a machine learning algorithm for their recognition

By means of computer modelling, the self-assembly of amphiphilic A-graft-B macromolecules, grafted onto a spherical nanoparticle, is studied. In a solvent, that is poor for side pendants, the macromolecules self-assemble into thin membrane-like ABBA bilayers deviated from spherical nanoparticles. The bilayers form morphological structures that depend on the grafting density and macromolecular polymerization degree and can be referred to as the classical family of complete embedded minimal surfaces. The plane disk, catenoid, helicoid, Costa and Enneper surfaces as well as "double" helicoid and "complex minimal surface" were identified, and the fields of their stability were defined. The surfaces can be grouped according to the sequences of conformal transformations that transform them into each other. These surfaces arise in different experiments situationally. Results are summarized in a pie diagram constructed using a machine learning algorithm based on matching grafting points with a specially created planar graphic image. Amphiphilic macromolecules grafted onto spherical nanoparticles can self-assemble into morphological structures corresponding to the family of complete embedded minimal surfaces. They arise situationally, can coexist and transform into each other.