高分子链构象统计算法教学的探讨

Discussion on Teaching in Conformational Statistical Algorithm of Polymeric Chains

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。

Conformation statistical theory of polymeric chains is essential to the understanding of the concept of Gaussian chain. It is the base of the statistical theory in polymer science. Kuhn^s method is the mostly described one in textbooks of polymer physics. But the mathematical steps are complex, which is hard to be comprehended by the students. Meanwhile, some flaws exist in it which hinders the understanding of the concept of Gaussian chain and has a negative impact on the study of statistical theory of polymer dilute solution and rubber elasticity. The Kuhn^s method is modified based on central limit theorem. Two methods for calculating the mean square end-to-end distance are introduced. These methods are concise and explicit, which are easy to understand and be beneficial for the students to catch on the concept of Gaussian chain.