Microscopic diffusion model applied to $C60$ fullerene fractals in carbon disulphide solution

Using Positronium (Ps) atom as a fundamental probe that maps changes in the local electron density of the microenvironment and high resolution transmission electron microscopy, $C60$ aggregation in neat $CS2$ solvent is reported over a concentration range $0.02 to 2.16 g/dm3.$ Spontaneous formation of stable spherical $C60$ aggregates in the colloidal range (∼90–125 nm) was observed over a critical concentration range of $0.06–0.36 g/dm3,$ beyond which the clusters broke. Specific interactions of the Ps atom with the surrounding revealed the onset concentration for stable aggregate formation in this solvent to be $0.06 g/dm3.$ The solution phase $C60$ structure in the critical concentration range was analyzed to be a spherical fractal aggregate with a fractal dimension of 1.9 and the growth mode followed a diffusion limited cluster aggregation mechanism. At concentrations beyond $0.36 g/dm3,$ an entropy driven phase change was noticed leading to the formation of irregular, but oriented crystalline components. A microscopic diffusion model was applied to calculate the o-Ps lifetime density function and diffusion coefficients of o-Ps and the $C60$ aggregates in the solution. With randomly distributed $C60$ fractal clusters, the o-Ps density function resulted in a good agreement between the calculated and the experimental o-Ps lifetimes, revealing the diffusion coefficients of $C60$ fractal cluster and the o-Ps to be $2.27×10−6 cm2/s$ and $25.1×10−5 cm2/s$ respectively.