Polymer Physics

and theweight-average molecular weightby

MW

P

WiMi

P

Wi

¼

P

NiM^2 i

P

NiMi

(2.18)

Here the molecular weight commonly means the molar mass of polymers, in
units of grams per mole (g/mol). In practice, the molecular weight is also used with
reference to the molar mass of C^12 as divided by 12, given the units of Dalton (Da).
Theindex of polydispersity dcan be used to characterize the width of molecular
weight distributions, which is defined by

d

MW

MN

(2.19)

For a monodisperse polymer sample,d¼1. The ranges ofdvalues change
drastically with the different mechanisms of polymerization. The values ofdare
1.01–1.05 in living polymerization (anionic, cationic, living free radical, etc.),
around 1.5 in condensation polymerization or coupling termination of polymeriza-
tion, around 2 in disproportionation reactions on polymerization, 2–5 for
high-conversion olefins, 5–10 in self-acceleration on common free radical poly-
merization, 8–30 in coordination polymerization, and 20–50 in branching reactions
on polymerization.
Another often used characterization of molecular weight is theviscosity-average
molecular weight

M



SWiMai

SWi

 1 =a

(2.20)

which is obtained from the viscosity measurement of polymer dilute solutions
(according to Mark-Houwink equation, the intrinsic viscosity []¼KMa, where
Kis constant. See (5.18) in Sect.5.1). Whena¼1,

M¼



SNi

SNiMi

 1

¼MN (2.21)

and whena¼1,

M¼

SWiMi

SWi

¼MW (2.22)

Conventionally,a¼0.5 ~ 1, thus

MN<MMW (2.23)

2.4 Molecular Weights and Their Distributions 25