【作者】 李晓毅；

【导师】 吴大诚；

【作者基本信息】 四川大学 ， 材料学， 2000， 博士

【摘要】 本文通过计算机模拟，系统研究了有方向的格点和普通无方向的格点上受限高分子单链的构象性质。 Manhattan格点是有方向的格点，首先采用精确计数法，计算了二维和三维Mahattan格点上有壁限制的尾形SAW的构象数，均方末端距和均方回转半径，并用比率法和Dlog Padé近似计算了临界指数和连通常数，以及均方末端距的标度指数。同时也计算了三维Manhattan格点上自由SAW的同类性质。对三维自由SAW和尾形SAW，最长链长分别达到31和30步，是迄今为止三维格点模型中SAW链计数所达到的最长链长。 在没有方向的简立方格子上，当自避行走链起点在壁(z=0)上，其它格点都被壁限制在半空间(z≥0)，高分子链由于与壁的相互作用而使平面z=0上的点贡献一份额外的能量，而且在高分子链内部也由于最近邻相互作用而贡献额外的能量。本文运用复合Markov链法和直方图技术，研究了简立方格点上同时具有吸附作用和最近邻相互作用的自避行走模型的热力学性质，最后在相图上绘出了相边界。相图表明，存在四个相，分别是AE，DE，AC和DC，并且吸附相变和塌缩相变同时存在。 最后讨论了近壁链问题，采用解析法，精确计数和Monte Carlo模拟分别对近壁NRW和SAW在方格子和简立方格子上的构象性质等问题进行了研究和比较。研究结果表明，不论NRW还是SAW，随着起点与壁的距离逐渐增大，链球经历一个迅速收紧再逐渐扩张的过程。更多还原

【Abstract】 The conformation of restricted single polymer chain on oriented lattice and non-oriented lattice was systematically studied using computer simulation.The Manhattan lattice was an oriented lattice. The total number of self-avoiding walks terminally attached to a surface on both two-dimensional Manhattan lattice and three-dimensional Manhattan lattice, their mean square end-to-end distance, and their mean square radius of gyration, were exactly enumerated. The analysis of exact enumeration data using the ratio method and Dlog Fade approximate gave the connective constant and the critical exponents of conformation and end-to-end distance. At the same time, we got the same kinds of properties of free self-avoiding walks on three-dimensional Manhattan lattice. The length of free SAW and tail SAW on three-dimensional Manhattan lattice was up to 31 and 30 steps, which is the longest up to now.On the non-oriented simple cubic lattice, the self-avoiding walks were confined to the half-space (z>0) with the origin vertex in the plane (z=0). In the adsorption model the self-avoiding walks interacted with the plane zr=0 and contributed an additional energy term. At the same time the steps had nearest-neighbor interactions within the walk and contributed an additional energy term for the collapse model. The thermodynamic properties for self-avoiding walks on simple cubic lattice with both surface-interacting and nearest-neighbor interacting were calculated using multiple Markov chains method and histogram technique. These results gave the location of transition in the phase diagram of this r’odel. The phase diagramindicated that there were four kinds of phases. They are AE (adsorbed-expanded), DE (desorbed-expanded), AC (adsorbed-collapsed) and DC (desorbed-collapsed). It was found that both adsorption and collapse transitions were existed.We discussed the problem of polymer chains near an impenetrable plane. The conformational properties of NRW and SAW on square lattice and simple cubic lattice were studied by means of the equation, the exacted enumeration and the Monte Carlo simulation. It was shown that both NRW and SAW contracted rapidly and then extended slowly when the distance between the surface and the origin vertex of chain increased.更多还原