\[\nu = \frac{R_p}{R_i} = \frac{k_p[\mathrm M]}{2(fk_dk_t[\mathrm I])^{1/2}},\qquad \bar X_n = 2\nu\ (\text{偶合终止}),\ \ \nu\ (\text{歧化终止})\]\[\nu = \frac{R_p}{R_i} = \frac{k_p[\mathrm M]}{2(fk_dk_t[\mathrm I])^{1/2}},\qquad \bar X_n = 2\nu\ (\text{combination}),\ \ \nu\ (\text{disproportionation})\]
梅奥方程（链转移）Mayo equation (chain transfer)
\[\frac{1}{\bar X_n} = \frac{1}{\bar X_{n,0}} + C_\mathrm M + C_\mathrm S\frac{[\mathrm S]}{[\mathrm M]} + C_\mathrm I\frac{[\mathrm I]}{[\mathrm M]}\]含义Meaning
每个引发的自由基在终止前平均加成的单体数。引发剂越多，速率越快但分子量越低——工业上必须权衡。
The average number of monomers added per initiating radical before termination. More initiator speeds polymerisation but lowers molar mass — an industrial trade-off.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(\nu\) | 动力学链长kinetic chain length | 1 |
| \(C_\mathrm M, C_\mathrm S, C_\mathrm I\) | 向单体、溶剂、引发剂的链转移常数chain-transfer constants to monomer, solvent, initiator | 1 |
推导Derivation
链长 = 增长速率 / 引发（= 终止）速率。
Chain length = propagation rate / initiation (= termination) rate.
代入稳态自由基浓度即得 \(\nu \propto [\mathrm M][\mathrm I]^{-1/2}\)。
With steady-state radicals, \(\nu \propto [\mathrm M][\mathrm I]^{-1/2}\).
偶合终止一条死链含两段动力学链；链转移使每条动力学链产生多条死链，降低 \(\bar X_n\)（梅奥方程）。
Combination joins two kinetic chains; chain transfer splits one into several (Mayo).
适用条件与局限Assumptions & limitations
同自由基聚合速率的稳态假设。
Same steady-state assumptions as the rate law.