Monte Carlo Simulation Of Linear And Ring Polymers And Their Blends

Since the concept of polymer was first proposed in the 1920 s,its scientific research has entered a stage of rapid development,and many polymer materials with unique properties have been synthesized.Polymers are composed of a large number of basic units connected by covalent bonds.The main chain usually contains a large number of degrees of freedom and many strong interactions.These factors make the polymers exhibit some special physical properties.Research on polymer melts and blends can make the research and application of polymer materials more directional,and have certain reference value for electronics,medical,chemical production and other aspects.The research of polymers can be carried out through theory and experiments,and can also be simulated by computers.The research object starts from linear polymer chains and gradually expands to ring polymers,H-shaped polymers,star polymers,polymer blends,etc.The model used in computer simulation is gradually improved on the basis of theory,and it is closer to the real polymer.We conducted a computer simulation study using the Monte Carlo method and the improved BondFluctuation model.The model places polymer chain units on the lattice points of a cubic lattice with periodic boundary conditions,and each chain unit occupies one lattice point.By setting appropriate excluded volume condition,finite bond length condition and chain non-crossing condition to simulate the motion of the real chain,where the chain non-crossing condition is realized by introducing the secondary lattice where the bond midpoints are located.The first chapter firstly introduces the basic concepts of polymers,then introduces the properties related to polymer chains,and briefly summarizes the development of computer simulation research and related issues.In the second chapter,we introduce the theoretical basis of polymer and the model used in this research.In the third chapter,we investigate the statistical and dynamics properties of linear and circular polymer melts,and introduce H-shaped and star polymer melts for comparative analysis.Based on the intersection of the mean-square monomer displacement in the center-of-mass frame and the mean-square center-of-mass displacement,the end-to-end correlation function,the mean-square radius of gyration,and the maximum mean-square end-to-end distance,we obtain four kinds of relaxation times,and find that polymers with different architectures satisfy a universal relationship when relaxation times defined by maximum mean-square end-to-end distance as a function of corresponding mean-square radius of gyration.We then use the mean-square monomer displacement to verify the correctness of this relationship.Chapter four mainly studies the physical properties of the ring polymers when the ends of linear chains are free or fixed in linear-ring blends.It is found that in the two cases,the physical properties such as the end-to-end correlation function,mean-square monomer displacement,mean-square center-of-mass displacement,diffusion coefficient,and relaxation time of the ring polymers show basically opposite trends with the increase of the linear chain length,and there is large differences in the performance of the corresponding physical properties of ring polymer melts.In addition,we also obtained four kinds of relaxation times through calculation in this study,and find that when the end of the linear chain is fixed and the length of the chain is short,the relaxation time obtained by the end-to-end correlation function is significantly less than the relaxation times defined by other methods.This is because the end-to-end correlation function includes tumble-rotation mechanism,which accelerates the relaxation of the ring polymers.