A method of maximum entropy modeling the aggregation kinetics

It has been demonstrated how a method of maximum entropy of the aggregation probability distribution determines the aggregate mass distribution for the Brownian aggregation occurring in three-dimensional space. The resulting distribution corresponds to the experimental data. Using the equation describing an act of aggregation, which determines the fractal dimension of formed aggregate as dependent on the sizes and fractal dimensions of constituent clusters, it is also possible to calculate the fractal dimension of formed aggregates. The obtained value D=1.82 corresponds well to theoretical predictions and measured values. This method is then employed to determine the fractal dimension and size distribution of clusters produced by the two-dimensional Brownian aggregation, as well as by the aggregation in the free molecular regime occurring in three-dimensional space. The obtained result is also close to measured and calculated values. Hence, this work confirms the validity of the maximum entropy method in aggregation kinetics. The possibility to apply the reported method to other mechanisms of aggregation is discussed.