\[Đ = \frac{\bar M_w}{\bar M_n} \ge 1\]
典型值typical values
\[Đ = 1 + p\ (\text{逐步聚合，弗洛里分布}) \to 2;\qquad Đ \approx 1 + \frac{1}{\bar X_n}\ (\text{理想活性聚合，泊松分布})\]\[Đ = 1 + p\ (\text{step growth , Flory distribution}) \to 2;\qquad Đ \approx 1 + \frac{1}{\bar X_n}\ (\text{ideal living polymerisation , Poisson distribution})\]含义Meaning
衡量分子量分布宽度。Đ = 1 为单分散；逐步聚合高转化率时趋于 2；活性/可控聚合可得 1.01–1.2。
Measures the breadth of the distribution: 1 for monodisperse, → 2 for step growth at high conversion, 1.01–1.2 for living/controlled polymerisation.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(Đ\) | 分散度dispersity | 1 |
| \(p\) | 官能团反应程度extent of reaction | 1 |
| \(\bar X_n\) | 数均聚合度number-average degree of polymerisation | 1 |
推导Derivation
按定义取比值。
By definition.
弗洛里分布中 \(\bar X_n = 1/(1-p)\)，\(\bar X_w = (1+p)/(1-p)\)，所以 Đ = 1 + p。
For the Flory distribution \(\bar X_w/\bar X_n = 1 + p\).
活性聚合中每条链同时引发、以相同速率增长，链长服从泊松分布：\(Đ = 1 + \bar X_n/(\bar X_n + 1)^2 \approx 1 + 1/\bar X_n\)。
In living polymerisation chain lengths are Poissonian: Đ ≈ 1 + 1/X̄n.
适用条件与局限Assumptions & limitations
Đ 只是分布的一个特征量，不能区分双峰与宽单峰分布；需看完整 GPC 曲线。
Đ cannot distinguish bimodal from broad unimodal distributions; inspect the full GPC trace.