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Asymptotic Analysis of Coagulation–Fragmentation Equations of Carbon Nanotube Clusters

Francisco Torrens1* and Gloria Castellano2

Author Affiliations

1 Institut Universitari de Ciència Molecular, Universitat de València, Edifici d’Instituts de Paterna, P.O. Box 22085, Valencia, 46071, Spain

2 Instituto Universitario de Medio Ambiente y Ciencias Marinas, Universidad Católica de Valencia San Vicente Mártir, Guillem de Castro-94, Valencia, 46003, Spain

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Nanoscale Research Letters 2007, 2:337-349  doi:10.1007/s11671-007-9070-8

Published: 27 June 2007


The possibility of the existence of single-wall carbon nanotubes (SWNTs) in organic solvents in the form of clusters is discussed. A theory is developed based on abundletmodel for clusters describing the distribution function of clusters by size. The phenomena have a unified explanation in the framework of the bundlet model of a cluster, in accordance with which the free energy of an SWNT involved in a cluster is combined from two components: a volume one, proportional to the number of moleculesnin a cluster, and a surface one, proportional ton1/2. During the latter stage of the fusion process, the dynamics were governed mainly by the displacement of the volume of liquid around the fusion site between the fused clusters. The same order of magnitude for the average cluster-fusion velocity is deduced if the fusion process starts with several fusion sites. Based on a simple kinetic model and starting from the initial state of pure monomers, micellization of rod-like aggregates at high critical micelle concentration occurs in three separated stages. A convenient relation is obtained for <n> at transient stage. At equilibrium, another relation determines dimensionless binding energy α. A relation with surface dilatational viscosity is obtained.

Solubity of carbon nanotubes; Bundletmodel for clusters; Droplet model for clusters; Membrane biophysics; Nanotube; Fullerene