### Abstract

There has recently been great interest in fullerene molecular solutions, and especially in their possible medical and biological applications. In almost all fullerene solutions, the problem arises of describing cluster formation and growth. The theoretical description of these is at present still restricted to chemical thermodynamics or to simple phenomenological models. In the present work, a first attempt is made to provide a consistent description of the kinetics of cluster growth in fullerene molecular solutions. The Frenkel-Zeldovich equation of nucleation theory (the Fokker-Plank equation) is used as the basis for this theoretical model. Two simple models are used for describing the growth of clusters: a solution-liquid drop model and a model of confined growth for unsaturated and supersaturated concentrations of solution. Numerical solutions for the system of kinetic equations describing the evolution of the cluster size distribution function f(n, t) are obtained. The time dependence of the characteristics of the cluster state, the mean size of the cluster, and the cluster concentration in solution are obtained and compared with the analytical estimates. In the case of unsaturated solutions, we find for both models that the fullerenes are solved mostly in the form of free monomers. In the case of super-saturated (metastable) solutions, the processes of cluster formation and growth take place. If the liquid drop model is used, we find that the mean size of the cluster decreases as the solution concentration increases. If the confined growth model is used, we find that the mean cluster size does not depend on the initial supersaturation. Experiments with fullerene solutions in toluene and carbon disulfide, for which we have the most complete data for estimating the model parameters, are analyzed with respect to our results.

Original language | English |
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Pages (from-to) | S52-S61 |

Journal | Physics of Particles and Nuclei |

Volume | 36 |

Issue number | SUPPL. |

Publication status | Published - nov. 24 2005 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Physics of Particles and Nuclei*,

*36*(SUPPL.), S52-S61.