Cluster Origin of the Solubility of Single-Wall Carbon Nanotubes

Abstract

The possibility of the existence of single-wall carbon nanotubes (SWNT) in organic solvents, in the form of clusters containing a number of SWNTs, is discussed. A theory is developed based on a bundletmodel for clusters, which enables describing the distribution function of clusters by size. Comparison of the calculated values of solubility with experimental data would permit obtaining energetic parameters characterizing the interaction of an SWNT with its surrounding in a solid phase or solution. Fullerenes and SWNTs are unique objects, whose behavior in many physical situations is characterized by remarkable peculiarities. Peculiarities in solutions show up in that fullerenes and SWNTs represent the only soluble forms of carbon, what is primary related to the originality in the molecular structure of fullerenes and SWNTs. The fullerene molecule is a virtually uniform closed spherical or spheroidal surface, having no sharp ridges or dents. Similarly, an SWNT is a smooth cylindrical unit. Both structures give rise to the relatively weak interaction between the neighbouring molecules in a crystal, and promote effective interaction of the molecules with those of a solvent. Another peculiarity in solutions is related to their tendency to form clusters, consisting of a number of fullerene molecules or SWNTs. The energy of interaction of a fullerene molecule or SWNT with solvent molecules is proportional to the surface of the former molecule, and roughly independent of the relative orientation of solvent molecules. A unified treatment is proposed in the framework of the bundlet model of a cluster, in accordance with which the free energy of an SWNT involved in a cluster consists of two components: a volume one proportional to the number of molecules n in a cluster and a surface one proportional to n1/2.

Cluster nature of the solvent features of single‐wall carbon nanohorns

“…The equations are modeled in a home-built program. Previously reported cases are comparative studies of the cluster nature of the solvent features of fullerene C 60 , SWNT, SWNT with -correction [7][8][9][10] and their extrapolation n 3 ϱ [11]. The software is available from the authors.…”

“…In earlier publications, the bundlet model for clusters of SWNTs was presented [7]. The aim of this report is to perform a comparative study of the properties of fullerenes, SWNTs, and SWNCs.…”

Asymptotic Coagulation-Fragmentation Equations

“…The equality is valid for SWNT clusters. The free energy of a cluster is made up of two parts: the volume part, proportional to the number of SWNTs n in the cluster, and the surface one, proportional to n 1/2 [1][2][3][4]. The model assumes that clusters consisting of n >> 1 particles have a cylindrical bundlet shape and permits the Gibbs energy G n for a cluster of size n to be G n = G 1 n G 2 n 1 2…”

Asymptotic Analysis of Coagulation–Fragmentation Equations of Carbon Nanotube Clusters

“…Relaxation of the stability criterion allows invention of sphere packings of even lower density, including ones with 95.5 and 95.8% void space. In earlier publications the bundlet model for clusters of SWNTs was presented [ 20 - 22 ]. The aim of the present report is to perform a comparative study of the properties of fullerenes (droplet model) and SWNTs (bundlet model).…”