数均分子量Number average molecular weight

重均分子量 M_w = ΣNᵢMᵢ² / ΣNᵢMᵢ，对大分子更敏感，总有 M_w ≥ Mₙ。二者之比 Đ = M_w/Mₙ 称为分散度（多分散性指数），衡量分子量分布宽窄：活性阴离子聚合可得 Đ < 1.1，自由基聚合通常为 1.5–2，逐步聚合在高转化率下趋于 2。黏均分子量 M_v 介于二者之间。

The weight-average M_w = ΣNᵢMᵢ² / ΣNᵢMᵢ is more sensitive to large chains, and always M_w ≥ Mₙ. Their ratio Đ = M_w/Mₙ, the dispersity (polydispersity index), measures breadth of distribution: living anionic polymerisation gives Đ below 1.1, free-radical polymerisation usually 1.5–2, and step-growth polymerisation approaches 2 at high conversion. The viscosity average M_v lies between them.

依数性方法（膜渗透压法、蒸气压渗透法）测的是分子数目，直接得到 Mₙ；端基分析也给出 Mₙ。光散射法得到 M_w；凝胶渗透色谱（GPC/SEC）按流体力学体积分离，可同时给出 Mₙ、M_w 和完整分布，是最常用的方法。MALDI-TOF 质谱可分辨单个链长。

Colligative methods (membrane and vapour-pressure osmometry) count molecules and give Mₙ directly, as does end-group analysis. Light scattering gives M_w. Gel permeation (size-exclusion) chromatography separates by hydrodynamic volume and gives Mₙ, M_w and the full distribution, and is the most widely used technique. MALDI-TOF mass spectrometry can resolve individual chain lengths.

1920 年代施陶丁格用黏度法证明高分子是真正的大分子；1930 年代卡罗瑟斯建立了缩聚反应中数均聚合度与转化率的关系（卡罗瑟斯方程 Xₙ = 1/(1−p)），说明要得到高分子量必须使转化率接近 100%。分子量影响强度、熔体黏度和加工性：Mₙ 过低时材料脆，过高时难以加工。

In the 1920s Staudinger used viscosity to show that polymers are true macromolecules; in the 1930s Carothers related the number-average degree of polymerisation to conversion in step-growth reactions (the Carothers equation Xₙ = 1/(1−p)), showing that high molar mass requires conversion close to 100%. Molar mass governs strength, melt viscosity and processability: too low an Mₙ gives brittle material, too high makes processing difficult.