Formation of Knots of Carbon Nanotubes in Isotactic Polypropylene Matrix due to the Results of Small-Angle Neutron Scattering and Lattice Numerical Simulation

— Data on the morphology of carbon allotrope nanoparticles in an isotactic polypropylene (IPP) matrix are analyzed. They are obtained using the small-angle neutron scattering method and a YuMO spectrometer at the IBR2 reactor of the Frank Laboratory for Neutron Physics, Joint Institute for Nuclear Physics (Dubna, Russian Federation). The fractal dimensionality is calculated, the form is reconstructed, and the geometric dimensions of the obtained particles and aggregates of single-wall carbon nanotubes (SWCNTs) in the IPP volume taken in concentrations of 1.2, 2.6, and 8 wt % are determined using ATSAS software. It is established that nanotubes form fractal nanoobjects with a rough surface in the IPP volume. Composite IPP/SWCNT systems are polydisperse to a significant degree; nanotubes twist into coils and knots and become more densely packed; in the polymer volume, the dimensions of the formed nanoparticles and their aggregates are several times larger than the initial ones used during synthesis. A model of knot formation in polymer materials based on calculating the asymptotic Hopf invariant and the lattice fractal dimensionality is used in this paper to interpret the results and predictions of the possible morphology forming in samples of such a type. The energies and probabilities of knot formation are estimated qualitatively using the Monte Carlo method.