Study On The Aggregation And Breakup Of Fractal Clusters Through Monte Carlo Simulation

The fractal aggregation is a common phenomenon in nature,such as snowflake formation,growth of crystalline thin films and so on.The fractal dispersion is also a common phenomenon,such as scouring by water,fragmentation of soil clusters and so on.The aggregation and dispersion of clusters belong to nonlinear processes,which exhibit self-organization phenomena and self-similarity in stochastic processes.And these features have given rise to a series of thoughts among scholars.Such as the process of cluster aggregation and dispersion,the influence of the external environment on the aggregation and dispersion process,etc.For these issues,scholars have never stopped exploring.In traditional experimental methods,scholars use instruments to conduct research,but in many environments traditional experiments are not easy to perform and the experiments are too dependent on the instruments.And with the development of computers,the advantages of studying the structure and behavior of cluster aggregation and dispersion through computer simulations are gradually emerging.The use of computer simulation methods,you can reasonably adjust the control parameters according to demand,and the use of the computer's own advantages can quickly obtain information related to aggregation and dispersion.Among them,Monte Carlo simulation is a suitable method for studying such stochastic processes,which can shield the properties of the particles themselves and construct probabilistic models of fractal aggregation and dispersion by generating the corresponding random variables from the probability distribution of the particles.Therefore,this study uses Monte Carlo simulation methods to construct fractal aggregation and dispersion models for different scenarios to investigate the kinetic processes.Most of the previous studies were conducted in closed systems without considering the influence of the external environment on the kinetic process,thus failing to realistically describe the particle motion process,and the classical clusters aggregation model was used to describe the process of particle aggregation in closed systems.The relevant works are as follow:(1)A dispersion model under an open system based on the clusters aggregation model is constructed.In open systems,the clusters become unstable and disperse due to the influence of external environment.For example,solvent injection,temperature change,etc.Therefore,A "dichotomous" dispersion model based on the idea of "dimerization" of clusters aggregation model was proposed by analyzing the dispersion characteristics of clusters in open systems.The model can be viewed as the inverse process of clusters aggregation,that is,randomly selected clusters are always dispersed into two small clusters.Secondly,two cases of fast dispersion and slow dispersion are studied using the model,and the difference between them is mainly reflected in the setting of the dispersion probability.Finally,the dispersion form of the proposed dispersion model can be divided into two cases,erosive dispersion and collapse dispersion,depending on the location where dispersion is likely to occur.(2)A fractal aggregation model based on the cluster's aggregation model with the combined effect of gravity and evaporation is constructed.Based on the different characteristics of the two,this paper studies the model under the combined action of gravity and evaporation,and implements the model using Java language.It was found that when evaporation is small,the gravitational effect of clusters dominates,and more large clusters sink as the aggregation process proceeds.When the cluster sinks to the bottom,gravity will limit the random diffusion of the underlying clusters,causing the system to enter a stable state in advance.At this time,the particles in the system are not aggregate into a cluster,and all clusters are laid flat at the bottom of the system.When evaporation is large,evaporation can reduce the restriction of gravity on the random diffusion of the underlying large clusters,and eventually all particles in the system coalesce into one large cluster.Under the combined effect of evaporation and gravity,the final cluster structure formed in the system is denser and the aggregation rate of the whole system is larger.(3)A fractal aggregation model based on the cluster's aggregation model for different electrolyte solution concentration regimes was constructed.Based on the analysis of the influence of electrolyte concentration on the cluster aggregation process,The Java language was used to realize the fractal aggregation model in the electrolyte solution system,and study the aggregation kinetics process in this system.Studies have shown that there is a transition point between the fast condensation and the slow condensation of this model,that is,the critical concentration.The ratio of the critical concentration of electrolyte solutions of different valences is a fixed value.Secondly,the influence of electrolyte solution on the particle aggregation process behaves differently in different aggregation mechanisms.In the fast aggregation mechanism,the electrolyte solution has almost no effect on the aggregation process.In the slow aggregation mechanism,the aggregation rate of the system increases as the concentration of the electrolyte solution increases.And when the concentration of the electrolyte solution reaches the critical concentration,the aggregation rate will no longer change and the system becomes fast aggregation.Finally,the clusters formed by fast aggregation are loose and porous,while the clusters formed by slow aggregation are denser.Since the larger the fractal dimension,the denser the cluster structure is,the critical concentration of the electrolyte solution is also the turning point of the fractal dimension change.In summary,two kinetic processes of nanocluster aggregation and dispersion in the open system are analyzed in this paper.And based on the clusters aggregation model,three models of fractal dispersion model under open system,aggregation model under evaporation and gravity system,and aggregation model under electrolyte solution system were implemented using Monte Carlo simulation method.This paper is a useful attempt and complement to the theoretical study of the kinetic process of nanocluster aggregation and dispersion.A new idea for the construction of aggregation and dispersion models of clusters in open systems is proposed methodologically.Practically,the developed simulation software is cross-platform and highly interactive,which can provide technical support for related research scholars to study particle stability.