Page 564 - Carrahers_Polymer_Chemistry,_Eighth_Edition

Reactions on Polymers 527

P = 1
gel
DP n,o (16.12)
The degree of cross-linking can be expressed in terms of cross-links per gram or per unit vol-
ume. If C is the moles of cross-links per unit volume, n is the number of network chains per unit
volume, d is the density of cross-linked polymer, and M is the number-average molecular weight
c
of the polymer segments between cross-links, then
n d
C = =
2 2M c (16.13)

.
such that the number of moles of cross-links per gram of network polymer is 1/2 M c
Swelling and mechanical measurements are generally employed to experimentally determine the
degree of cross-linking.

16.5 REACTIVITIES OF END GROUPS
Polymers containing one reactive end group are often referred to as macromolecular monomers or
macromers. They can be represented as

M–M–M–M–M–M–M–M–M–M–M–M–M–M–M–M–M–M–M–M–M–M–Reactive group (16.14)

They are used in the formation of a number of products, including star polymers and some graft
polymers.
Polymers that contain two active end groups are referred to as telechelic polymers. These are
then of the form

Reactive group–M–M–M–M–M–M–M–M–M–M–M–M–M–M–M–M–M–Reactive group (16.15)

Telechelic polymers are also used in the synthesis of many products, including segmented poly-
urethane and polyester products.
Macromers are then “short” polymers that contain an active end group. This end group can be
a site of unsaturation, heterocycle, or other group that can further react. Macromers are usually
designed as intermediates in the complete synthesis of a polymeric material. These macromers can
be introduced as side chains (grafts) or they may serve as the backbones (comonomer) of polymers.
The macromers can also act as separate phases.
Macromers have been used to produce thermoplastic elastomers. Generally, the backbone serves
as the elastomeric phase while the branches serve as the hard phases. These structures are often
referred to as “comb”-shaped because of the similarity between the rigid part of the comb and its
teeth and the structure of these graft polymers.
−M−M−M−M−M−M−M−M−M−M−M−M−M−M−M−M−M−M−M−M−M−M−M−M−M−M−
| | | | | | |
N N N N N N N
N N N N N N N
N N N N N N N
N N N N N N (16.16)
N N N N N
N N N N
N N N
N N N
N N

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