文档介绍：PolymerPolymerPolymer PhysicsPhysicsPhysics
高分子物理高分子物理高分子物理
44 MolecularMolecular weightsweights
andand SizesSizes
高分子的分子量与尺寸
Molecular weights and molecular
weight distribution
分子量与分子量分布
Characteristics of polymer molecular weights
高分子的分子量的特点
z The molecular weights are very high, ranging
from about 25,000 to 1,000,000 g/mol or higher.
z The molecular weight of ordinary size
molecules is fixed (., benzene has a
molecular weight of 78 g/mol regardless of its
source). Most polymer molecular weights, on
the other hand, vary greatly depending on the
method of preparation.
z Most polymers are polydisperse; that is, the
sample contains more than one species.
Molecular weight averages
平均分子量
Number-average molecular weight
∑ i Ni M i ∑ i wi
M n = =
∑ i Ni ∑ i (wi / M i )
Weight-average molecular weight
2
∑ i Ni M i ∑ i wi M i
M w = =
∑ Ni M i ∑ wi
Z-average molecular weight
3 2
∑ i Ni M i ∑ i wi M i
M z = 2 =
∑ Ni M i ∑ wi M i
Viscosity-average molecular weight
1/ a
⎡ N M 1+a ⎤
∑ i i i Schematic of a simple molecular weight
M v = ⎢⎥
N M
⎣∑ i i i ⎦ distribution, showing the various averages
Molecular weight distribution
分子量分布
Number-average distribution width
2 ⎛ M ⎞
σ 2 = [()M − M ] = M 2 ⎜ w −1⎟
n n n n ⎜⎟
⎝ M n ⎠
Weight-average distribution width
2 ⎛ M ⎞
σ 2 = [()M − M ] = M 2 ⎜ z −1⎟
w w w w ⎜⎟
⎝ M w ⎠
Polydispersity
高分子分子量的多分散性
Polydispersity index M M
α= w = z
M n M w
Method Polydispersity Stereospecificity
Natural Proteins Perfect
Anionic Polymerization - None
Chain Polymerization -3 None
Step Polymerization -4 None
Ziegler-Natta Polymerization 2-40 High
Cationic Polymerization Broad None
Determination of the number-
average molecular weight
数均分子量的测定
End-group analyses
端基分析
z Many types of syntheses leave a special group on one or both
ends of the molecule, such as hydroxyl and carboxyl. These
c