含义Meaning
高分子稀溶液的特性黏数与分子量的幂律关系。指数 a 反映链构象：θ 溶剂中无规线团 0.5，良溶剂 0.6–0.8，刚性棒约 1.8。黏度法是最简便的分子量测定方法。
A power law between intrinsic viscosity and molar mass; the exponent reflects conformation: 0.5 for random coils in θ solvent, 0.6–0.8 in good solvents, ~1.8 for rigid rods. Viscometry is the simplest molar-mass method.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \([\eta]\) | 特性黏数intrinsic viscosity | mL·g⁻¹ |
| \(K, a\) | 与高分子–溶剂–温度相关的常数constants for polymer–solvent–temperature | |
| \(\bar M_v\) | 黏均分子量viscosity-average molar mass | g·mol⁻¹ |
推导Derivation
弗洛里–福克斯：线团视为不可穿透的球，\([\eta] = \Phi\langle r^2\rangle^{3/2}/M\)。
Flory–Fox: \([\eta] = \Phi\langle r^2\rangle^{3/2}/M\) for impermeable coils.
θ 条件下 \(\langle r^2\rangle \propto M\)，所以 \([\eta] \propto M^{1/2}\)；良溶剂中线团溶胀 \(\langle r^2\rangle \propto M^{1.2}\)，a ≈ 0.8。
In θ conditions \(\langle r^2\rangle \propto M\) → a = 0.5; swollen coils give a ≈ 0.8.
适用条件与局限Assumptions & limitations
K、a 需用已知分子量的窄分布标样标定；只适用于标定所用的分子量范围。
K and a must be calibrated with narrow standards in the relevant mass range.
例题Worked example
聚苯乙烯/甲苯 25 °C：K = 7.5×10⁻³ mL/g，a = 0.75；[η] = 50 mL/g → M_v ≈ 1.2×10⁵ g/mol。
PS/toluene, 25 °C: [η] = 50 mL/g → M_v ≈ 1.2×10⁵ g/mol.