模型高分子尾型链的构象统计理论

CONFIGURATIONAL STATISTICS OF MODEL POLYMER TAIL CHAIN

基于金刚石格点上受限于半空间的随机行走，借概率论中的反射原理推导出了模型高分子尾型链的构象分布．得到了链长为Ｎ的模型尾型链的允许构象数Ｃ１（Ｎ）和末端距分布函数．在四选择模型中，发现Ｃ１（Ｎ）／４Ｎ与Ｎ－１／２成正比．模型尾型链在与壁正交方向上的均方末端距分布与平行方向比较扩张至２倍，而后者与自由链对应的分量相等．这些解析结果得到了精确计数和ＭｏｎｔｅＣａｒｌｏ模拟计算机“实验”的支持．

The conformational distributions of a model polymer tail chain was deduced based on the diamond lattice walk confined in the half space by means of the reflection principle.The relationship of the available conformational number C 1(N) with the chain length N and the distribution function of end to end distance were obtained for this model tail chain.In the case of 4 choices diamond lattice walk,it was found that C 1(N)/4 N is proportional directly to N -1/2 .The component of the mean square end to end distance normal to the wall for the model tail extends to two times in comparison with the parallel components which is same as the components for the corresponding free chain.These analytical results were confirmed in computer experiments including the exact enumeration and Monte Carlo simulation.