Conformations And Dynamics Of Ring, Star And Knotted Polymer Chains

The changeability, diversity and excellent mechanical property cause a wide and important application of polymer materials in various fields. Therefore, further studies on the structure and performance of the polymer materials are necessary. In this dissertation, we investigate the conformational properties, the elastic behaviors and the dynamics of the polymer chains with special structure such as ring polymers, star polymers and knotted polymers.Ring polymers and star polymers have extensive applications due to their important and particular features. In Chapter 2, conformational properties and elastic behaviors of ring and star polymers in the process of tensile elongation are studied using Monte Carlo method and bond fluctuation model. Some statistical properties, such as mean-square radius of gyration and shape factor<δ*> are calculated in order to illuminate how the size and shape of the chains change in the process. At the same time, the conformational changes will lead to the changes in thermodynamic properties such as average energy and free energy A. Besides, scatting functions are also obtained for star polymer chains with different branches respectively. The impenetrability of the star cores is known to cause a discontinuity in the osmotic pressure showed through a peak in the scattering functions.In Chapter 3, we first investigate the elastic behaviors of star and linear polymer chains confined in the parallel interfaces using pruned-enriched-rosenbluth method (PERM) based on self-avoiding walk (SAW) model. The simulation results suggest that if the interfaces have the adsorptive effect on the chains, the accretion of the distance between parallel interfaces D needs acting force; while if the interfaces have no attraction, the accretion of D is a spontaneous process. Additionally, in order to understand the structure and the mechanical behavior more detailedly, we also study the microstructure of the chains:train,loop,bridge and tail. Subsequently, elastic behaviors of single polymer chains confined on rough surfaces constructed with an undersurface and some periodically tactic pillars are investigated. Beside mean-square radius of gyration and shape factor<δ*>, adsorption fraction on undersurface and on pillars are also calculated to help understand the process of desorption. Elastic force f has some plateaus during the tensile elongation for the case with strong adsorption interaction, which can explain how the chains move along z-axis and reveal that near the upper surfaces of pillars, the further adsorption of the upper surfaces is the driving mechanisms.Chapter 4 shows some dynamic behaviors of the polymer chains. First, a study of influence of a knot on the structure of a polymethylene (PM) strand and how the knot itself performs during the tensile process is presented. The work is based on the steered molecular dynamics (SMD) method. A sequence of increasing end-to-end distances R gradually results in a tighter knot and a more stretched contour. The fact that the break in a knotted rope almost invariably occurs at a point just outside the 'entrance'to the knot, which has been showed in many experiments, is further theoretically validated in our work through the calculating of some structural and thermodynamic parameters. Moreover, it is found that analysis on bond length, torsion angle and strain energy can help to study the localization and the size of a knot in the tensile process. Then, elastic behavior of 4-branched star polymer chain adsorbed on attractive surface is investigated using SMD based on the united-atom (UA) model suitable for branched alkanes. We find during the tensile process, there are three characteristic distances Zc, Z, and Zo from attractive surface, and these values vary with N. When Z=Zc, the chain is stripped from the surface, but due to the form of wall-monomer interaction, the surface remains weak influence on the chain till Z=Zt. From Z=Zt, parameters< Ua>和 respectively reach a stable value, while the shape and size of the chain still need adjustments after Z, till Zo to reach their equilibrium states. Specifically, for short chain of N=41, Z, and Z0 is incorporated. Besides, a study on the process of compact polymer chains escaping from a small sphere to a large one is also performed based on PERM. The outcome of free energy barrier is of the most significance. On the one hand, there exists a chemical potential gradient to push the polymer out of the small sphere; on the other hand, during the process of escaping, the chain must overcome a free energy barrier as the chain should stretch itself.Protein is the basic part of the life, and so it is an important topic to study the composition, structure and feature. In Chapter 5, the composition and residue-residue interactions of knotted proteins, with the comparison with that of other ones, are performed. In knotted structures, Leu occupies a maximal proportion of 9.62% among all 20 amino acids, and Leu, Phe, Trp, Gly, His, Gin, Asp, Lys and Pro may play a more important role. Also, we analyze the effects of amino acid residues on the long-range contacts. We observe a higher average number of long-range contacts in the knotted structures than in other ones, implying their furthermore important role to achieve knotting. In addition, the shape distribution of knotted structures and the contrast with the case of other ones are also presented. The comparison shows that knots will make structures more globular.