An Introduction to
Polymer Chemistry
BY

D. MARGERISON, B. Sc9 Ph. D.
Lecturer in Inorganic, Physical and Industrial
Chemistry, University of Liverpool
AND

G. C. EAST, B. Sc, Ph. D.
Lecturer in High Polymer Chemistry, Department
of Textile Industries, University of Leeds

PERGAMON

PRESS

OXFORD - LONDON · EDINBURGH . NEW YORK
TORONTO - SYDNEY . PARIS · BRAUNSCHWEIG


Pergamon Press Ltd., Headington Hill Hall, Oxford
4 & 5 Fitzroy Square, London W.l
Pergamon Press (Scotland) Ltd., 2 & 3 Teviot Place, Edinburgh 1
Pergamon Press Inc., 44-0121st Street, Long Island City, New York 11101
Pergamon of Canada Ltd., 6 Adelaide Street East, Toronto, Ontario
Pergamon Press (Aust.) Pty. Ltd., 20-22 Margaret Street, Sydney,
New South Wales
Pergamon Press S.A.R.L., 24 rue des Écoles, Paris 5 e
Vieweg & Sohn GmbH, Burgplatz 1, Braunschweig
Copyright © 1967 Pergamon Press Ltd.

First edition 1967
Library of Congress Catalog Card No. 66-18393

This book is sold subject to the condition
that it shall not, by way of trade, be lent,
resold, hired out, or otherwise disposed
of without the publisher's consent,
in any form of binding or cover
other than that in which
it is published.
(2853/67)

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PREFACE
book is concerned with the fundamental chemistry of
synthetic organic polymers of high molecular weight. It is
intended for those commencing the study of Polymer Chemistry for the first time and should be of interest not only to
university and technical college students attending their first
lecture course on the subject but also to more elementary
students who wish to broaden their knowledge of chemistry.
We have assumed that our readers possess no prior acquaintance
with the concepts of polymer chemistry but possess a reasonable
knowledge of elementary chemistry, physics and mathematics.
Since our object is to explain the basic principles of the
subject, we have confined the major part of our discussion to
the more important methods of molecular weight determination
and to the simpler mechanisms of polymerization. Thus osmotic, light scattering and viscosity methods of molecular weight
determination have been dealt with in some detail together

with the kinetics of selected examples of condensation and
free-radical addition polymerization. The main features of
ionic polymerization have also received a reasonable amount of
attention. Wherever possible, we have attempted to clarify our
discussion with numerical examples. Several topics of considerable importance have been omitted; we have not dealt with the
thermodynamics of polymer solutions or the methods of structure determination since these subjects require a knowledge
of statistical thermodynamics and spectroscopic techniques.
We hope that our discussion of what we have chosen to regard
as the basic ideas of polymer chemistry will compensate for
these omissions.
THIS

vii

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Vili

PREFACE

Like most authors, we owe a debt of gratitude to our
teachers and colleagues who have so materially contributed to
our understanding of the subject. In particular, we wish to
thank Professor C. E. H. Bawn, F. R. S. for continued advice
and encouragement. We also wish to thank Dr. T. B. Grimley
for clarifying many aspects of the subject and Messrs. S. G.
Canagaratna, P. McBride and R. G. M. Mirrlees for their
comments on the manuscript. Any errors found in this book
are, however, the responsibility of the authors. Our thanks are

due to the Sociộtộ franỗais d'instruments de contrôle et d'analyse for the photograph of their light scattering instrument and
for permission to use some of their experimental data. Finally,
we wish to acknowledge the help given by our respective
wives.
D. MARGERISON
G. C. EAST

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LIST OF P R I N C I P A L S Y M B O L S
A
A2 and A3
A
a
a0
B
B
C
C
[C · ]
[C-]s
[C + ]
&
β+
&~
c
c
'd9


the pre-exponential factor in the Arrhenius equation; usually appears with subscript.
the second and third virial coefficients in the π/c, c
expansion.
a monomer molecule or a mer.
the total concentration of COOH groups at any
time t.
the initial concentration of COOH groups.
the second virial coefficient in the π/c, c expansion.
a monomer molecule or a mer.
the third virial coefficient in the π/c, c expansion.
a mer.
the total concentration of polymer radicals at any
time t.
the total concentration of polymer radicals at the
steady state.
the total concentration of active centres in cationic
polymerization at any time t.
the transfer constant in radical polymerization;
usually appears with subscript.
a positively charged ion or counter-ion.
a negatively charged ion or counter-ion.
the weight concentration of solute, i.e. the weight
of solute per unit volume of solution.
the velocity of light in vacuo.
one of the two alternative configurations of an
asymmetric carbon atom.
ix

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X

E
E
E0
H
H0
I0
I0
Ιθ
IQ
l'è

I
[I]
[I] 0
S?0
i
J0
j
K
K

AN INTRODUCTION TO POLYMER CHEMISTRY

the activation energy; usually appears with subscript.
the strength of the electric field at any point in
space.
the maximum strength of the electric field at any

point in space.
the strength of the magnetic field at any point in
space.
the maximum strength of the magnetic field at any
point in space.
the scattered intensity at an angle φ to the incident
beam.
the incident intensity.
the scattered intensity at an angle 0 to the incident
beam.
the scattered intensity at an angle 0 to the incident
beam from unit volume of the scattering medium.
the contribution of concentration fluctuations to
the scattered intensity at an angle 0 to the incident
beam from unit volume of the scattering medium.
an initiator molecule.
the concentration of the initiator at any time t.
the initial concentration of the initiator.
the incident intensity of photochemically active
radiation.
an integer.
the energy scattered per unit solid angle per
second at a n angle φ to the incident b e a m .
an integer.
a constant appearing in the treatment of light
scattering.
a constant of proportionality relating the limiting
viscosity n u m b e r to a power of the molecular
weight.


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LIST OF PRINCIPAL SYMBOLS

K
k

k{
kp
kt
ktr
kdp
km
ks
k'
L
7'
M

Mx
M.
M
Mw
Mv
M
[M]
[M] 0
M|
[MJ

Mj ·
[Mi - ]
N
N

9

XI

the number of 'd or 7' sequences.
a rate constant—usually appears with subscript,
the more important instances being listed below;
also an integer or a proportionality constant.
the rate constant for initiation.
the rate constant for propagation.
the rate constant for termination.
the rate constant for transfer.
the rate constant for depropagation.
the rate constant for monomer transfer.
the rate constant for spontaneous decomposition.
the Huggins' constant.
the number of A or B sequences.
one of the two alternative configurations of an
asymmetric carbon atom.
a molecular weight—usually appears with subscript, the more important instances being listed
below.
the molecular weight of the monomer or mer.
the molecular weight of the /-mer.
the number average molecular weight.
the weight average molecular weight.

the viscosity average molecular weight.
a monomer molecule.
the concentration of monomer at any time t.
the initial concentration of the monomer.
a polymer molecule containing /-mers.
the concentration of the /-mer at any time t.
a radical containing /-mers.
the concentration of the radical containing /-mers
at any time t.
the total number of molecules in an assembly.
the total number of molecules in unit volume—the
number concentration.

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Xll

Ni
N{
N0
n

n
n
n0

H

A(S)

nB(S)
P0
Ρ(β)
[P]
p
p
p

PAA.

R
Re
R90

R'Q

R·
(r 2 ) 1/8

AN INTRODUCTION TO POLYMER CHEMISTRY

the number of /-mers in a n assembly.
t h e number of /-mers in unit volume.
t h e Avogadro number.
t h e number average degree of polymerization, i.e.
the average number of m o n o m e r units in a polymer molecule.
a number of moles.
t h e refractive index of a gas or solution.
t h e refractive index of the pure solvent.


the number of sequences containing S A units.
the number of sequences containing S B units.
the incident flux.

t h e particle scattering factor for t h e angle 0.
t h e total concentration of polymer.
t h e magnitude of t h e induced dipole moment.
the extent of reaction.
t h e planar configuration of t h e carbon a t o m
associated with the unpaired electron in a polymer
radical.
^ probability that a n A unit in a copolymer of
A a n d B is followed by another A unit ; p A B ,
PBB * PBA a r e defined similarly.
t h e gas constant.
t h e reduced intensity at a n angle 0 to t h e incident
beam.
t h e reduced intensity at 90° t o t h e incident b e a m ;
this is termed t h e Rayleigh ratio for a gas or a
pure liquid.
the contribution of concentration fluctuations to
the reduced intensity at a n angle Θ t o t h e incident
beam.
a primary radical.
t h e r o o t mean square end-to-end distance of the
polymer chains.

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LIST OF PRINCIPAL SYMBOLS

r
r± and r2
S
SA and SB
S
T
Tc
TH
t
W
wi
z
a
a
Γ2 and Γ3
r\x
η2
[η]
Θ
0
λ
λ'
π
ρ
a

Xlll


the distance of a representative point in space from
a scattering source.
reactivity ratios in copolymerization.
the number of units in a sequence.
the average number of A and B units in a sequence.
a solvating species.
the absolute temperature.
the ceiling temperature.
a transfer agent.
time—occasionally appears with subscript.
the total weight of a mixture of polymer molecules
of all sizes.
the total weight of /-mers in a mixture.
the dissymmetry coefficient.
the polarizability.
the exponent in the limiting viscosity number
—molecular weight relation.
the second and third virial coefficients in the π/c, c
expansion.
the viscosity of the solvent.
the viscosity of a polymer solution.
the limiting viscosity number (formerly called the
intrinsic viscosity).
the Theta temperature.
an angle.
the wavelength of light in vacuo.
the wavelength of light in a medium of refractive
index n.
the osmotic pressure of a solution.
the density of a liquid; usually appears with

subscript.
the probability that a given asymmetric carbon
atom is followed by another of the same configuration.

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Xiv

t
r
φ
ω

AN INTRODUCTION TO POLYMER CHEMISTRY

the turbidity of a pure liquid.
the average lifetime of a polymer radical at the
steady state.
an angle.
a solid angle.
NOTE
1. Except in the case of the limiting viscosity number, the
symbol [ ] indicates molar concentration, i.e. the number
of moles of the species indicated per litre of solution.
2. The summation sign Σ has been used throughout the text
to indicate a summation taken from one to infinity over
the parameter in question unless otherwise stated.

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CHAPTER 1

INTRODUCTION
book is concerned with some of the simpler aspects of
the chemistry and physics of high molecular weight compounds. The molecules of these substances are usually between
5000 and 2,000,000 times as heavy as a simple hydrogen atom
and consequently are composed of many hundreds or thousands of atoms joined together. The arrangement of the atoms
in such molecules is not, however, entirely random since their
molecular formulae can always be represented as an integral
multiple of simple atomic groupings. That is to say, molecules of the type under discussion contain a large number of
simple sub-units joined together by covalent bonds. These subunits or building blocks are termed mers and hence high molecular weight compounds are often referred to as polymers
(many mers). Polymer molecules are usually derived from the
compound or compounds containing only one mer—the
monomer or monomers, as they are called; for this reason, we
shall often use the terms, monomer unit or monomer residue,
in place of the term, mer. Molecules which contain only a few
of these sub-units joined together are termed oligomers (few
mers); particular instances are the terms, dimer, trimer, etc.,
which are used for molecules containing two, three, etc., of
the sub-units found in the polymer. It is generally more convenient, however, to use the single term, polymer, to describe
all molecules containing more than one mer.
Before proceeding with further generalities, let us consider
a simple case, poly(û)-hydroxy undecanoic acid). This polymer
THIS

1

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2

AN INTRODUCTION TO POLYMER CHEMISTRY

is formed from ω-hydroxy undecanoic acid, HO(CH 2 ) 10 COOH,
with the simple repeating structure
H^-OiCH^ioC-fOCCH^ioC-l-OfCH^ioC-i-. . . 4-O(CH2)10C4-OH
ί

IM

o

II ;

Il :

o

o

;

Il !

o

or more briefly


I il.

H (O(CH 2 ) 10 CỴ OH,

where / represents any integer from two upwards (the monomer is represented by / = 1). The mer in this case is clearly
-O(CH 2 ) 10 CII

o

TYPES OF POLYMER
The simplest types of polymer are those formed from a single
mer as in the above example. The molecular formulae of such
homopolymers, as they are called, are then always of the form
Χ{Α},Υ,
where A represents the formula of the mer, and X and Y stand
for the groups present at the beginning and end of a sequence
of i sub-units to satisfy the valence requirements. These end
groups which may or may not be identical will not be considered any further at this particular stage but will be discussed
in the later chapters. Since all sub-units are identical by definition, only two types of homopolymer are possible. These
are:
1. the linear homopolymers formed from divalent sub-units;
2. the space network homopolymers formed from sub-units
with valence greater than two.

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3


INTRODUCTION

A good example of the first case is polymethylene
CH2-CH2-CH2-CH2-CH2-CH2

-<

The wavy lines attached to the ends of the above formula
represent the remainder of the polymethylene chain. (In general, a wavy line will be used to represent a portion of a polymer
chain in those cases where the number and type of the component mers need not be specified.) One of the few homopolymers with a space network structure is diamond in which each

FIG.

1.1.

carbon atom is bonded to four other carbon atoms as shown
in Fig. 1.1. It is perhaps worth mentioning at this stage that the
typical properties of diamond, insolubility, infusibility and
hardness are encountered in more complex polymers with
space network structures.
Some of the most important polymers are built up from
more than one sub-unit. These are termed copolymers to
distinguish them from the simpler homopolymers. Just like the
latter, their molecular formulae can always be represented in
terms of the sub-units, thus

XÌAMB^CV-.Y,

where A, B, C, etc., symbolize the formulae of the various
mers incorporated into the copolymer, i, j , k, etc., stand for

any integers and X and Y are end groups. As soon as more
than one mer is involved, a wide diversity of polymer structure
and type becomes possible. For example, even with only two
mers A and B, there are several ways of forming a linear
copolymer; these are:

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o

o

o

C e—
H6

I
Λ

CeH5

I

CeHe

I


CH 3
—

I

I

I

CH3

I

I

CH 3

I

I

C—
H3

C6H6

I

I


COOCH3 COOCH3 C e H 5

I

COOCHg C6HÖ

I

CeH5

^^^CH2-CH-CH2-C-CH2-C-CH2-CH-CH2-C-CH2-CH-CH2-CH

I

CH3

3. a random copolymer formed from styrene and methyl methacrylate

CeH
~ „8

I

^^^CH2-CH-CH2-CH-CH2-CH-CH2-CH-CH2-CH=C-CH2-CH2-CH=C-CH2

2. a block copolymer formed from styrene and isoprene

o


^CH2-CH-CH2-CH2-CH2-CH-CH2-CH2-CH2-CH-CH2-CH2-CH2-CH-CH2-CH1
I I I
I
I
I
I
I
I
I
I
I
QH 5 CO CO
CeH5 CO CO
C6H5 CO CO
CeH5 CO CO
\ /
\ /
\ /
\ /

1. an alternating copolymer formed from styrene and maleic anhydride

3

H

XS1

S
H


w

*

x

g

o

O
*

H

§

§
c
H

H

-B-A-A-B-A-B-B-A-B-A-B-B-B-

_

>


-A-A-A-A-A-A-B-B-B-B-B-B-B-

-A-B-A-B-A-B-A-B-A-B-A-B-A-

One example of each of these is shown below :

3. the random copolymer

2. the block copolymer

1. the alternating copolymer


INTRODUCTION

5

One small point, perhaps, ought to be mentioned; it is quite
permissible to classify the perfectly alternating copolymer as a
homopolymer, the mer being AB.
As in the case of homopolymers, non-linear structures may
also be formed. Perhaps the simplest of the many possibilities
are the branched copolymers which are composed predominantly of a single type of mer, thus :
-A-A-A-A-A-B-A-A-A-A-B-A-AI
I
A
A
I
I
A

A
I
I
A
A
I
I
A
I
AI

In such structures, the longest linear sequence of mers is
referred to as the "polymer backbone" and the trivalent subunits B as the branch points. For a given ratio of the numbers
of A and B, a large number of different structures are possible
according to the length of the branches and the way in which
the branch points are distributed along the polymer backbone.
A simple example of a branched polymer of this type is the
polyethylene formed at high temperatures and pressures, in
which the majority t of the branches are short chains containing
three or four carbon atoms. Its structure is:
CHf-CH2-CH-CH2-CH2

CH2-CH2-CH-CH2^MMW-

I
CH2
I
CH2
II
v^rd

CH32

I
CH2
I
CH2
I
C-/XI3

t A few branches are much longer than those shown but since the
occur at about one-tenth of the frequency of the short chain branchesy
they do not merit special consideration at this stage.
,

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6

AN INTRODUCTION TO POLYMER CHEMISTRY

Under the usual conditions of preparation, these branches
occur with frequencies ranging from one in twenty to one in a
hundred backbone CH2 units. It must be admitted that, where
the number of branch points is a very small fraction of a large
number of identical mers, there is a strong case for classifying
these polymers as homopolymers. Indeed in the example
chosen, few polymer chemists would regard high pressure
polyethylene as a copolymer even though it can be regarded
formally as built up from two mers CH2 and CH ; our purpose

in imposing a rather rigid classification is simply to draw
attention to the fact that the structure of the mer at the branch
point is not identical with the structure of the main repeating
unit.
These minor difficulties of definition disappear entirely if the
branch is composed of different mers from those making up
the backbone chain. Such polymers are termed graft copolymers, their structures being represented symbolically below:
-A-A-A-A-B-A-A-A-A-A-B-AI
I

c

c

c

c

c

c

c

c

I
I

I


I

I

I

I

cI
I

The structure of the branch point is usually closely related to
the structure of the mer making up the polymer backbone as
in the case just discussed —in fact, B is most commonly formed
by the loss of an atom or group from A during the formation
of the branch. An example of a graft copolymer is that formed
from methyl methacrylate and polystyrene.

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INTRODUCTION

C H

^βΗ 5
I

2


- C H - C H

C6H5
I

2

- C H - C H

C6H5
I

2

- C - C H

C6H5
I

2

- C H - C H

C6H
I

2

- C H N


I
CH 2
I
CH3-C-COOCH3
I
CH 2
I
CH3-C-COOCH3
I
CH 2
I
CH3-C-COOCH3

Two other types of non-linear polymer are the cross-linked
and space network polymers. The structures described by these
terms are represented in Figs. 1.2 and 1.3.
There is no essential difference between these two types of
polymer—merely increasing the number of cross-links in what
1

c
I

c

I
-A—A—A-B—A—A-A—A—A—A—A—B—A—A—A—A—AI

c

I
c
I

c

I
-A—A-A—A-A—B—A-*A—A—A—A—A—A-B-A—A—A—A—A-A—B-A-A-AI
I

c
I
c

c
I
c

I
I
-A-B-A-A-B-A-A-A-A-A-A—B-AI

?
c
I

?c
I

c


I
—A—A—A—A—A—A-A—A—B-A—A—A—A—A—

FIG. 1.2. A cross-linked polymer

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8

AN INTRODUCTION TO POLYMER CHEMISTRY

we have termed the cross-linked polymer results in the formation of the space network. An example of the former type of
polymer is to be found in partially vulcanized rubber where a
limited number of short chains of sulphur atoms link together
^Β-Λ'

■A^N,

s
A

\ỵ

A Λχ

Mr

X


Β<

,B

FIG. 1.3. A space network polymer

a large number of polyisoprene molecules ; a specific structure
of this type is shown below.
CH3
CH3
I
I
CH2-C-CH=CH-CH2-C=CH-CH,
I
S
I

s
I

s
I

s

I
CH2-C-CH2-CH2-CH2-C=CH-CH2
I
I

CH3
CH3

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9

INTRODUCTION

The space network structures are exemplified by the ureaformaldehyde polymers, a portion of whose structure is given
below.
NH2
I
CO
I
-N-CH2-N-CH2-N
I
I
CO
CO
I
I
NH
CH 2 -NH
I
CH2
I

NH-CH2-N-CH2-N


I
CO

I
NH
2

I
CO

I
CO

I*
NI H - C H 2 - N

Table 1.1 lists a few examples of the wide variety of polymeric materials known. It will be seen that many chemical
types are represented from the purely organic polymers based
on carbon and hydrogen to the purely inorganic formed from
phosphorus, nitrogen and chlorine. Many of the organic polymers will be recognized as natural products of great biochemical or technological importance. Equally well represented are
the synthetic polymers which are the mainstay of the new
technologies of the "man-made" fibre, the plastics and the
synthetic rubber industries.
TABLE 1.1

Cellulose
Starch
Chitin
Pepsin

Insulin
Egg albumin
Desoxyribose nucleic acid
Bakelite

Rubber
Nylon
Terylene
Polythene
Polystyrene
Perspex
Polyphosphorus chloronitride
Polysiloxane

In this book, we shall confine our attention almost entirely
to synthetic linear polymers based on carbon whose structures
are relatively simple. Table 1.2 shows a few of the polymers

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OOCCHg

Polyvinyl acetate

CH 2 =CH

Vinyl acetate
1


Polyvinyl chloride
(PVC)

Polyethylene
(polythene)

CH 2 =CH
1
1
Cl

CH 2 =CH 2

Ethylene

Vinyl chloride

HOOC(CH2)4COOH

Polyhexamethylene
adipamide
(nylon 6.6)

Polystyrene

H 2 N(CH 2 ) 6 NH 2

Hexamethylene
diamine

Adipic acid

Polyethylene
terephthalate
(terylene)

Polymer

CH 2 =CH
1
1
C6H5

HO(CH2)2OH
HOOCC6H4COOH

Ethylene glycol
Terephthalic
acid

1

1.2

Styrene

Formula(e)

Monomer(s)


TABLE

OOCCH 3

1

Cl
—CH2CH—

1

—CH2CH—

—CH2CH—
1
1
C6H5

v^xl 2 ^ x 1 2

—HN(CH2)6NHCO(CH2)4CO—

—0(CH 2 ) 2 OOCC 6 H 4 CO—

Mer

g
H

O

X
m

<

r

O

hd

H
O

%

H
O

d

u
o

O

H

2


>


INTRODUCTION

11

X

se

!

g a?

I

a? 3 - C = ü |

I

W|

x

u
I

<υ


^

α

cd
υ

t?
2 d

§

3
X)

x
o

ο

g Λ α
o g 8
pu,
3

ο

PU

OH

υ
II

j·

υ

S-a-8

Ο

«

o-ro

»

gw
ι

g.

υ

"S G

c
0)

3
X)

o

HH

c
<υ

T3

co
D

PQ

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Isoprene

Monomer

CHe=xC—CH=CH2
1 2
3
4

1

CH,

Formula

Polyisoprene

Polymer

c=/

/
\
H
—CH2
(trans 1,4 structure)

x

/ C _ C \
—CH2
CH2—
(eis 1,4 structure)

CH2
(3,4 structure)
H
CH3

II

C—CH3

1

CH2
(1,2 structure)
—CH2—CH—

II

CH

1

—CH2—C—

|

CH3

Mer

Table 1.2 (continued)

KJ

5*

H

g

w

E

o

K|
w

r

O

►ri

H
O

z

H
O

σ
c

o

O

H

S

>

to


INTRODUCTION

13

with which we shall be most concerned and the monomers
from which they are made.
MOLECULAR WEIGHTS AND DEGREE
OF POLYMERIZATION
As we have already said, this book is concerned with linear
molecules possessing very high molecular weights. Although it
is undesirable to be too rigid in setting a lower limit to the
molecular weight, the major part of our subsequent discussion
will be confined to substances with molecular weights above
5000. Our somewhat arbitrary choice of subject matter similarly determines an upper limit of molecular weight of around
2,000,000. The determination of molecular weights between
these limits is dealt with in detail in Chapter 2.
Molecules with molecular weights in this range are obviously

composed of many mers. If we take a homopolymer molecule
with a molecular weight of 100,000 for example, the mer
molecular weight being 100, our molecule consists of 1000
mers. This latter quantity, the number of mers in the molecule,
is termed the degree of polymerization. In the case of a copolymer molecule, this term is perhaps less informative and certainly a little more difficult to calculate. Suppose we take a
particular copolymer molecule of the same molecular weight
as above containing 25% by weight of a mer A (molecular
weight 100) and 75% by weight of a mer B (molecular weight
150). Then if we have nA mers of A and nB mers of B in this
molecule,
« A X100 = ^ X 100,000,
« B X150 = j^rX 100,000,
so that there are 250 A mers and 500 B mers ; the total number
of mers in the molecule or its degree of polymerization is thus

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14

AN INTRODUCTION TO POLYMER CHEMISTRY

750. It will be noticed that no attempt has been made in these
calculations to correct for the contribution of the end groups
to the molecular weight. This could be done, of course, if the
number and type of the end groups are known; such corrections are unimportant, however, when the polymer molecular
weight is very high. What is important is the conception that
polymer molecules are composed of many mers joined together
in long chains.
THE CONFIGURATION OF POLYMERIC

MOLECULES AND ASSOCIATED
PROPERTIES
Polymeric substances can be divided into two groups according to whether their molecules are rigid or flexible; there will
be some polymers whose molecules do not fit neatly into
either category or which pass from the first classification to the
second as the temperature is raised. Such difficulties do not,
however, lessen the utility of this classification.
Perhaps the best examples of rigid structures are to be found
in the proteins. The presence of extensive intramolecular
hydrogen bonding in these molecules is largely responsible for
their inflexibiUty and, in consequence, their definite shape. As
a rule, these shapes can be quite adequately represented by
simple geometrical shapes such as spheres, ellipsoids, rods or
discs. The dimensions of the molecules, therefore, present no
conceptual difficulties; the experimental determination of the
shape and characteristic dimensions of such molecules is,
however, by no means an easy matter.
Because of our own experience and interests, this book is
concerned mainly with synthetic linear polymers whose molecules possess a great deal offlexibility.Thisflexibilityarises as
a result of the freedom of rotation which exists about each mermer bond. In consequence molecules of this type in the solid

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15

INTRODUCTION

and liquid states and in solution tend to coil up and assume a
more compact configuration than that shown by the extended

structures given previously. To this extent, the previous formulations of the structures of linear homopolymers and copolymers are misleading for they show only the most orderly
possible arrangement of the component mers. What actually
happens is that the configuration of a particular molecule
fluctuates with time about some average. We shall understand
the problems involved better if we commence with a comparatively simple situation.

1. Flexible linear molecules in dilute solution
To simplify the problem for a typical polymer based on
carbon, let us take a long chain of carbon atoms in which free
rotation about each C—C bond is possible subject to the
C—C—C bond angle being fixed at 109°, the C—C internuclear distance being 1-54 Â. We wish to know the possible
relative positions of the nuclei of the carbon atoms making up
the chain. Relative to the first two carbon nuclei C± and C2,
the third carbon nucleus can be placed anywhere on a circle
swept out by rotating the C2—C3 bond at a constant angle of
109° to the Ci—C2 bond, as shown in Fig. 1.4. Similarly, the
?C3

•
c,

109 J

;

!

-^-*
c2 : ;

FIG.

1.4.

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