Topological Defects in Aggregation of the C60 Fullerene in the Isotactic Polypropylene Matrix

Basing on the data of small-angle neutron scattering for the nanocomposite composed of fullerene C60 (16.5 wt. %) in the matrix of isotactic polypropylene, we received information on clusterization of nanoparticles and defined their geometric parameters and dimensionality. In this paper, we propose interpretation of particle aggregation possessing the properties of surface fractal in the size range up to 80 nm observed using small-angle neutron scattering method. Basing on the well-known theories of defect structures of a fullerene molecule C60 in non-Euclidean metrics, in particular, of disclinations and monopole in two-dimensional spherical Gödel space—time, we formulate a lattice version for the action of monopole gas, in which with the lattice Monte Carlo method, using abelian projection, we estimate the energy of monopole currents at different monopole concentrations. In frames of the proposed model, it is possible to calculate fractal properties of the fullerene C60 in a polymer composite and also to interpret evolution of disclinations.