Cluster model expanded to C-nanostructures: Fullerenes, tubes, graphenes and their buds

The existence of nanographene (GR) and GR-fullerene bud (GR-BUD) in cluster form is discussed in organic solvents. Theories are developed based on columnlet, bundlet and droplet models describing size-distribution functions. The phenomena present a unified explanation in columnlet model, in which free energy of GR involved in cluster comes from its volume, proportional to number of molecules n in cluster. Columnlet model enables describing distribution function of GR stacks by size. From purely geometrical considerations, columnlet (GR/GR-BUD), bundlet [single-wall carbon nanotube (SWNT) (CNT) (NT) and NT-fullerene bud (NT-BUD)] and droplet (fullerene) models predict dissimilar behaviours. Interaction-energy parameters of GR/GR-BUD are taken from C60. An NT-BUD behaviour or further is expected. Solubility decays with temperature result smaller for GR/GR-BUD than SWNT/NT-BUD than C60, in agreement with lesser numbers of units in clusters. Discrepancy between experimental data of the heat of solution of fullerenes, CNT/NT-BUDs and GR/GR-BUDs is ascribed to sharp concentration dependence of the heat of solution. Diffusion coefficient drops with temperature result greater for GR/GR-BUD than SWNT/NT-BUD than C60, corresponding to lesser number of units in clusters. Aggregates (C60)13, SWNT/NT-BUD7 and GR/GR-BUD3 are representative of droplet, bundlet and columnlet models.