含义Meaning
线形逐步聚合在等活性假设下，x 聚体的数量分数与质量分数。数量分数随 x 单调下降（单体最多），质量分数在 \(x \approx -1/\ln p\) 处有极大值。
Number and weight fractions of x-mers in linear step growth under equal reactivity. Number fraction falls monotonically (monomer most numerous); weight fraction peaks near \(x \approx -1/\ln p\).
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(x_x, w_x\) | x 聚体的数量、质量分数number and weight fraction of x-mers | 1 |
| \(x\) | 聚合度degree of polymerisation | 1 |
推导Derivation
任取一条链，从一端起每个官能团已反应的概率为 p，未反应为 1 − p。
Walking along a chain, each group has reacted with probability p.
恰好 x 个单元的链需要连续 x − 1 个已反应键，再接一个未反应端：\(p^{x-1}(1-p)\)。
Exactly x units requires x − 1 reacted links then an unreacted end.
质量分数乘以 x 并归一化（\(\sum x\,x_x = 1/(1-p)\)）得 \(w_x\)。
Weight fractions multiply by x and renormalise.
适用条件与局限Assumptions & limitations
忽略环化、官能团活性差异；链式聚合（如自由基聚合歧化终止）也给出类似的“最概然分布”。
Ignores cyclisation and reactivity differences; radical polymerisation with disproportionation gives the same distribution.