Aggregation is widely seen in nanoparticles especially under conditions of high concentration and in temperature and annealing time regimes below those allowing for coalescence and sintering. A quantifiable description of aggregates has proven difficult since they are by nature disordered and show a wide dispersion in structure. The scaling of the density of aggregates with size follows mass-fractal laws and can be used to quantify one aspect of aggregates but such a description fails to quantify features such as asymmetry and branch content. In this presentation a fundamental, statistical description of aggregates is outlined based on their tortuosity and connectivity. Tortuosity is measured by the mass fractal dimension of a minimum path through the aggregate; while connectivity is related to the mass fractal dimension of a stick structure connecting branch and end points in the aggregate. These two measures can be used to calculate the mole fraction branches, the asymmetry and other aspects of the aggregate. This approach can predict the diffusion coefficient as well as the spring constant for aggregates and yields hope in predicting the overall dynamic properties of aggregates. Small angle scattering can directly measure the connectivity and tortuosity in a simple static measurement. Observed variation in aggregate structure using this description during nanoparticle growth in flames will be presented based on in situ x-ray scattering studies.

Partially supported by the US NSF through CBET 0626063 as well as by LyondellBasell Corporation and the Swiss NSF.