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高分子链的构象统计算法对于高斯链概念的理解至关重要,同时也是高分子统计理论的基础。目前常用教材的推导过程各不相同,通常采用Kuhn的计算方法,但这个方法不仅过程复杂繁琐,易使学生望而却步,而且还存在瑕疵,不利于学生对高斯链概念的理解。本文以学生所学数理统计知识为基础,对经典的Kuhn统计算法进行修订,介绍了一种柔性高分子链均方末端距的统计算法。这种方法过程简单明了,易于接受,有助于学生对高斯链概念的理解。针对不同数理基础的学生,还提出了一种更为简单的均方末端距计算方法。
The conformational statistics of polymer chains are crucial for the understanding of the Gaussian chain concept and are also the basis for the theory of polymer statistics. At present, the derivation process of commonly used textbooks varies. Kuhn’s calculation method is usually adopted. However, the method is not only complicated and cumbersome but also discourages students from being flawed, which is not conducive to students’ understanding of the concept of Gaussian chain. Based on the mathematical statistics students learned, this paper revised the classical Kuhn statistical algorithm and introduced a statistical algorithm of mean square end distance of flexible polymer chains. The process of this method is simple, easy to accept, and helps students to understand the concept of Gaussian chain. For students with different mathematical basis, a simpler mean-square-end distance calculation method is also proposed.