Self-assembly of charged particles on nanotubes and the emergence of particle rings, chains, ribbons and chiral sheets

A diverse range of supramolecular assembly processes arise from the competition between directional and isotropic intermolecular interactions. Directional interactions often have a charge origin or form local patchy interactions associated with a chemically heterogeneous particle surface, hydrogen bonding, π–π interactions and metal–ligand group complexation, or alternatively, interaction anisotropy can arise geometrically from the shape of the assembling particles or the presence of a curved surface on which the self-assembly occurs. In the present work, we focus on the nature of the self-assembly of spherical charged particles with competing van der Waals interactions bound to cylindrical surfaces, a system inspired by the self-assembly patterns found in kinesin-13 and dynamin proteins on microtubules and the self-assembled layers of DNA that organize about single wall carbon nanotubes. As in bulk fluids, we find a general tendency of positive and negative ions to form dipoles and other low energy multipolar clusters having a vanishing net charge whose directional interactions give rise to the self-assembly of ribbon and chain structures at low particle concentrations and chiral sheet structures at high particle concentrations. These chiral patterns are characterized by rectangular and hexagonal local packing symmetries, respectively, when the charge or van der Waals interactions are predominant. The chirality of these patterns is induced from a competition between the scales of the particle size and the diameter of the cylinder on which they are confined. Interesting defective layers of particles involving sheet perforations are seen when the van der Waals and charge interactions compete strongly so that no single morphology then predominates. The self-assembly of the charged particles into chains and sheets at low particle concentrations exhibits ‘reentrancy’, meaning that the extent of particle ordering into extended structures varies non-monotonically with temperature, as has been observed in a number of experimental systems. A transition from a ribbon to string morphology is also observed as the mass of the self-assembled particle clusters exceeds a critical mass.