Supramolecular Magnetic Brushes: The Impact of Dipolar Interactions on the Equilibrium Structure

The equilibrium structure of supramolecular magnetic filament brushes is analyzed at two different scales. First, we study the density and height distributions for brushes with various grafting densities and chain lengths. We use Langevin dynamics simulations with a bead-spring model that takes into account the cross-links between the surface of the ferromagnetic particles, whose magnetization is characterized by a point dipole. Magnetic filament brushes are shown to be more compact near the substrate than nonmagnetic ones, with a bimodal height distribution for large grafting densities. This latter feature makes them also different from brushes with electric dipoles. Next, in order to explain the observed behavior at the filament scale, we introduce a graph theory analysis to elucidate for the first time the structure of the brush at the scale of individual beads. It turns out that, in contrast to nonmagnetic brushes, in which the internal structure is determined by random density fluctuations, magnetic forces introduce a certain order in the system. Because of their highly directional nature, magnetic dipolar interactions prevent some of the random connections to be formed. On the other hand, they favor a higher connectivity of the chains' free and grafted ends. We show that this complex dipolar brush microstructure has a strong impact on the magnetic response of the brush, as any weak applied field has to compete with the dipole-dipole interactions within the crowded environment.
This research has been partially supported by the Austrian Research Fund (FWF): START-Projekt Y 627-N27. The authors are grateful to the Ural Federal University stimulating programme. S.S.K, E.S.P., and E.V.N. are supported by RFBR mol-a-ved 15-32-20549. The work of E.V.N. was partially supported by the President of RF, Grant NO MK-5216.2015.2. S.S.K. is supported by the Ministry of Education and Science of the Russian Federation (Contract 02.A03.21.000, Project 3.12.2014/K) and EU-Project 642774 ETN-Colldense. P.A.S. acknowledges financial support from the Universitat de les Illes Balears within its Programa de foment de la recerca. T.S. and J.J.C. were supported by the project FIS2012-30634 (funded by the Spanish Mineco). J.J.C. and T.S. also acknowledge funding from a grant awarded by the Conselleria d’Educació, Cultura i Universitats del Govern de les Illes Balears and the European Social Fund (ESF).