### An Algorithm for Evaluating Fractal Parameters of a Single Soot Aggregate

##### Egor Demidov and Alexei Khalizov

Soot is a major component of atmospheric aerosols and a potent climate-warming agent. The climate forcing properties of soot change as the particles age in the atmosphere. This change is partly due to morphological compaction of soot particles that occurs upon acquisition of liquid coatings. Freshly formed soot particles are lacey aggregates of complex morphology, which is commonly characterized using fractal theory, as these aggregates have been shown to statistically conform to the fractal scaling law. Accordingly, two parameters, fractal dimension, and pre-exponential factor, are often used to correlate climate-forcing properties of soot to its morphology. Determining the fractal parameters is trivial for an ensemble of aggregates of different sizes, but these parameters cannot be calculated directly in a straightforward manner for a single aggregate. As we are developing a model for soot restructuring, we need to be able to evaluate the fractal parameters of a single aggregate at any step of the compaction process. We hypothesize that since soot aggregates statistically conform to the fractal scaling law, they should be self-similar and we may be able to determine the fractal parameters by extracting sub-aggregates from a single aggregate instead of analyzing an ensemble of individually generated aggregates of different sizes. Preliminary results are promising and we have been able to determine the fractal parameters of aggregates generated numerically with reasonable accuracy. However, more work is needed to optimize the method and formulate its constraints. The algorithm will be verified on both deterministic fractals with well-defined fractal parameters and disordered fractals, such as soot aggregates