Fullerite crystal thermodynamic characteristics and the law of corresponding states

The existence of single-wall carbon nanotubes in organic solvents in the form of clusters is discussed. A theory is developed based on a bundlet model, which enables describing the cluster-size distribution function. Comparison of calculated solubilities with experiments would permit obtaining energetic parameters, characterizing the interaction of a nanotube with its surrounding. Fullerenes and nanotubes are objects whose behaviour in many physical situations is characterized by peculiarities, which show up in that these systems represent the only soluble forms of carbon, what is related to their molecular structures. The fullerene molecule is a virtually uniform closed spherical-spheroidal surface and a nanotube is a smooth cylindrical unit. Both structures give rise to weak interactions between the neighbouring units in a crystal and promote their interaction with solvent molecules. The phenomena have a unified explanation in the bundlet model, in which the free energy of a nanotube in a cluster is combined from two components: a volume one proportional to the number of molecules n in a cluster and a surface one proportional to n1/2. Growth mechanisms of fractal clusters in fullerene solutions are analyzed along with similarity laws, determining the thermodynamic characteristics of fullerite crystals. In accordance with the similarity laws, the dimensionless Debye temperatures theta0 for all crystals belonging to the considered class should be close. Temperatures theta0 are determined by a similarity relation from experimental and estimated data. Fullerite theta0 is twice that for inert-gas crystals because, near the Debye point, the fullerite crystal is orientationally ordered so that its structure is dissimilar to face-centred cubic. A fullerene molecule whose thermal rotation is frozen cannot be considered as a spherically symmetric particle. The fulfilment of the similarity laws, which are valuable for particles with spherically symmetric interaction potential, would hardly be expected.