| The author presents the theory of the conformational statistics and the computer simulation of the restricted polymer chain, as an important topic in polymer materials sciences. In particular it is shown that behaviors of a polymer chains are strongly dependant on the confined geometry, i.e., the chain is closed to the wall, or adsorbed to the wall, even crossed through the wall. The conformation distribution and the probability function of restricted polymer are derived. Meanwhile, the author discusses the theory of polymer solution and its thermodynamical quantity based on the basic model. The relationship between the glass transition of polymers under high pressure and the conformation behavior of the polymer chain is also discussed.Besides of the Introduction as the first chapter, there are three parts in this thesis, including Computation Method, Theoretical Analysis and Simulation, and Application Study. First the computational models and methods in the classic theory of polymer physics are introduced. Then the conformational behavior of the restricted polymer chains and their probability functions under different conditions are studied. Finally the author tries to analysis the solution theory of polymer and the conformation behavior of polymer in high pressure.Actually, the results of computer simulations are often different from those ofexperiments. The reason is as follows. First, the theories and the simulations are from experiments in a high abstract way and always become simple in comparison with the real questions. Second, the simulation models generally do not agree with the theory models. So there must be some differences in three results of theories, experiments and computer simulations. To avoid to this, the author choose the computation models, which agree with the theory model, and do his best to decrease the hypothesis in the models, which could make the computer model more agree with the theoretical model. The direct count number method (DCM), the statistic count number method (SCM) and the dynamics Monte Carlo method are chosen to simulate the conformation of polymer chain in this thesis, in which three elementary moves are introduced in dynamics Monte Carlo algorithm, including flip moves, crankshaft moves and pivot moves in order to make the results exactly. In the part of studies of the conformational behaviors of the polymer chain near the wall, the combination method and mathematical analysis methods are introduced into the derivation of conformation probability of the polymer chain near the wall. Monte Carlo method is used to simulate the conformational numbers of the chain with the different distance from the wall. It is proved that the results of Monte Carlo method are similar as that of mathematic analysis, also the combination method takes the right results after modifying the data for the parity of the chain length, origin position and the end-group position of the chain.The results show that the wall has obvious effect on the conformation of the polymer chain near it. The origin position of the polymer chain is important parameter to measure the effect of the wall. Meanwhile, the function of conformational number is monotone and there is not any valley in the curve of the conformation numbers vs. the distance of the chain from the wall.The author introduces a new parameter of xc presented the minimum distance of the chain from the wall, at which the wall has no effect on the chain. The results show that the xc is larger than the end-to-end distance of polymer chain l/2, and also has the same scaling relationship with it, i.e. xc~1/2~N1/2. And xc is much smaller than the length N for the long chain. At the same time, it introduces anenhancement factor in the formula of the conformational number of the chain near the wall with the distance. This factor changes from 0.5 to 1.0 rapidly, which is appeared as an error function for the probability function of the conformation of the polymer chain with the different distance.In the study of the conformati...
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