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

Based on small angle neutron-scattering data from a nanocomposite composed of fullerene C₆₀ (16.5 wt %) in an isotactic polypropylene matrix, we receive information on the clusterization of nanoparticles and define their geometric parameters and dimensionality. This study proposes an interpretation of the aggregation of particles with surface fractal properties in the size range up to 80 nm, as observed in a small-angle-neutron-scattering experiment. Based on well-known theories about the defect structure of the fullerene C₆₀ molecule in non-Euclidean metrics, specifically disclinations and monopoles in the two-dimensional spherical space of Gödel type, we formulate a lattice version of the monopole gas model. Within this framework, we use the Monte Carlo method on a lattice with the Abelian projection to estimate the energies of monopole currents at various monopole concentrations. The proposed model enables the calculation of the fractal properties of C₆₀ nanoparticles in a polymer composite, as well as the interpretation of the evolution of disclinations.