从反应步数推导缩聚反应聚合度计算公式

Derivation of Number Average Degree of Polycondensation from Reaction Steps

聚合度计算是缩聚反应学习的重要内容之一。本文从聚合度的定义出发,根据反应步数与聚合物分子数之间的关系,简易地推导了线型缩聚2-2型单体体系a-A-a+b-B-b、2-2+1型单体体系a-A-a+b-B-b+C-b以及2+1型单体体系a-A-b+C-b达到一定反应程度时统一形式的数均聚合度计算公式:Xn=(1+r)/(1+r-2rp)。这种推导方法思路清晰,便于理解,能够充分体现缩聚反应的逐步特性,推导过程中的数学处理也使摩尔系数r的含义更加明确、具体。

Calculation formula of degree of polymerazation is an important content in studying polycondensation theory. In this paper, the unified formula of number average degree of polymerization Xn = （1 ＋ r）/（1 ＋r-2rp） according to the definition of degree of polymerization were derived from reaction steps for linear polycondensation,including 2-2 type monomers of a-A-a ＋ b-B-b, 2-2＋ 1 type monomers of a- A- a ＋ b- B- b ＋ C- b and 2 ＋1 type monomers of a- A- b ＋ C- b. The characteristics of stepwise growth are fully reflected by this method, which is clear and easy to understand. Moreover,the implication of stoichiometric ratio ＂r＂ becomes more clear and specific in the mathematical derivation of calculation formula of degree of polymerization.