The Study On Complex Network Models Of Polymer Melts

In the real world,there are many systems,which can be represented by complex networks,such as Internet,movie actor collaboration network,metabolic networks, aviation network,and so on.In the complex network,the nodes represent individuals or organizations while edges mimic the interactions among them.And many empirical studies indicate that these various kinds of networks with different topological structures do have some common characteristics:small average path length,large clustering coefficient,power-law degree distribution.These characteristics receive the researchers' great interest and considerable attention.On the other hand,in recent years,more and more things made of plastic,rubber and fibre have been widely used in daily life which arouses our considerable interests in studying polymer melts.According to the previous conclusions,we have known that there is an instantaneous network structure in polymer melts which is also a complex network system..But till now,we are lacking of works on polymer melts utilizing theories of complex network.In this paper,we try to do this to learn more about the structure and characteristics of polymer melts,which is obviously different from the previous way of through undiluted physical methods and processing experiments.The models of complex networks are most important tools to study complex networks.This thesis introduced two different evolving network models combining with the physical properties of polymer melts.One was a network without growth while the other with growth,then to emphasize on researching the statistic characteristics of these models.From the former network model,we obtained that the node degree was following exponential distribution and the average number of entanglements was becoming smaller and smaller.From the latter network model,we knew that both the size of cluster and the node degree were obeying power-law distribution.What's more,with enlarging the size of out network,the scale-free characteristic displayed more obviously.This phenomenon indicated that larger the size of network was,realer the network model became.At the same time,the average number of entanglements was also becoming smaller and smaller,which was significant to the application of our model because this conclusion was according with the technical processing through approaches such as heating or adding pressure to make the number of entanglements smaller.In other words,the properties of polymer melts could get improved.Additionally,it's worthy to mention that for each model,besides the theoretical reasoning,we performed numerical simulation as well.The simulative result and the theoretical result were in the same approximately.Thus,it's proved that the evolving models were reliable.At last,we gave a contrastive analysis of the two models according to the theoretical results and the simulative experimental results.