FracVAL: An improved tunable algorithm of cluster-cluster aggregation for generation of fractal structures formed by polydisperse primary particles

In this study, the tunable algorithm of cluster-cluster aggregation developed by Filippov et al. (2000) for generating fractal aggregates formed by monodisperse spherical primary particles is extended to polydisperse primary particles. This new algorithm, termed FracVAL, is developed by using an innovative aggregation strategy. The algorithm is able to preserve the prescribed fractal dimension (D_f) and prefactor (k_f) for each aggregate, regardless of its size, with negligible error for lognormally distributed primary particles with the geometric standard deviation being as large as 3. In contrast, for polydisperse primary particles the direct use of Filippov et al. (2000) method, as is done by Skorupski et al. (2014), does not ensure the preservation of D_f and k_f for individual aggregates and it is necessary to generate a large number of aggregates to achieve the prescribed D_f and k_f on an ensemble basis. The performance of FracVAL is evaluated for aggregates consisting of 500 and 1000 monomers and for fractal dimension variation over the entire range of D_f between 1 and 3 and k_f between 0.1 and 2.7. Aggregates consisting of 500 monomers are generated on average in less than 2.4 min on a common laptop, illustrating the efficiency of the proposed algorithm.本研究将Filippov等人（2000年）提出的、用于生成由单分散球形初级粒子（monodisperse spherical primary particles）构成的分形聚集体（fractal aggregates）的团簇-团簇聚集（cluster-cluster aggregation）可调算法，拓展至多分散初级粒子（polydisperse primary particles）场景。该全新算法被命名为FracVAL，其依托创新的聚集策略开发而成。本算法可针对每个聚集体维持预设的分形维数（fractal dimension, D_f）与前置因子（prefactor, k_f），不受聚集体尺寸影响；对于几何标准差（geometric standard deviation）高达3的对数正态分布（lognormally distributed）初级粒子，其误差可忽略不计。与之形成对比的是，若直接沿用Filippov等人（2000年）的方法（如Skorupski等人（2014年）的做法），则无法保证单个聚集体的D_f与k_f符合预设要求，仅能在系综层面（ensemble basis）通过生成大量聚集体来实现预设的D_f与k_f。本研究针对由500和1000个初级粒子构成的聚集体，以及分形维数D_f在1至3、前置因子k_f在0.1至2.7的全区间变化场景中，对FracVAL的性能进行了评估。在普通笔记本电脑上，生成包含500个初级粒子的聚集体平均耗时不足2.4分钟，充分体现了所提算法的高效性。