含义Meaning
给出瞬时共聚物组成 F₁ 与单体投料组成 f₁ 的关系。竞聚率 r₁ = k₁₁/k₁₂、r₂ = k₂₂/k₂₁ 描述各自由基对同种与异种单体的偏好。
Relates instantaneous copolymer composition F₁ to feed composition f₁. Reactivity ratios r₁ = k₁₁/k₁₂ and r₂ = k₂₂/k₂₁ describe each radical’s preference for its own monomer.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(r_1, r_2\) | 竞聚率reactivity ratios | 1 |
| \(f_1\) | 单体投料中 M₁ 的摩尔分数mole fraction of M₁ in the feed | 1 |
| \(F_1\) | 共聚物中 M₁ 的摩尔分数mole fraction of M₁ in the copolymer | 1 |
推导Derivation
末端模型：链端自由基的反应性只取决于末端单元，四个增长反应 k₁₁、k₁₂、k₂₁、k₂₂。
Terminal model: four propagation steps k₁₁, k₁₂, k₂₁, k₂₂.
M₁ 消耗速率 \(k_{11}[\mathrm M_1\cdot][\mathrm M_1] + k_{21}[\mathrm M_2\cdot][\mathrm M_1]\)，M₂ 同理。
Write consumption rates for M₁ and M₂.
交叉增长稳态 \(k_{12}[\mathrm M_1\cdot][\mathrm M_2] = k_{21}[\mathrm M_2\cdot][\mathrm M_1]\)，消去自由基浓度并引入 r₁、r₂ 即得。
Steady state of cross-propagation eliminates radical concentrations.
r₁r₂ ≈ 0 倾向交替共聚（苯乙烯–马来酸酐）；r₁r₂ = 1 为理想无规共聚；r₁, r₂ > 1 倾向嵌段或均聚混合。F₁ = f₁ 的点为恒比（共沸）共聚点。
r₁r₂ ≈ 0 → alternating; r₁r₂ = 1 → ideal random; both > 1 → blocky. F₁ = f₁ is the azeotropic point.
适用条件与局限Assumptions & limitations
只给瞬时组成；转化率升高时投料组成漂移，需积分（斯克特方程）。
Instantaneous only; feed drift needs integration (Skeist).
末端模型对某些体系不足，需倒数第二单元模型。
Some systems need the penultimate model.
例题Worked example
苯乙烯 (1) – 甲基丙烯酸甲酯 (2)：r₁ = 0.52，r₂ = 0.46，近似无规偏交替，恒比点 f₁ ≈ 0.53。
Styrene–MMA: r₁ = 0.52, r₂ = 0.46; nearly random with slight alternation, azeotrope at f₁ ≈ 0.53.