POLYMERS 3/PH/AM
Lecture 3 Make the Molecules
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This lecture is divided into three parts:
 (1) Types of Simple Polymerization
 (2) Statistics of Polymerization
 (3) Copolymerization

(1) TYPES OF SIMPLE POLYMERIZATION
Addition
Chain-Growth
Condensation
Step-Growth
‘Living’
People used to use these regularly, but they
relate to chemical processes rather than the
statistics of polymerization.
Now we use these.
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Chain Growth Polymerization
Here we have a lattice of monomer molecules (light
grey). A site is activated (by a chemical initiator, by
radiation, or whatever) – this is the very dark grey
circle.
This then adds monomer after monomer to the chain
(dark grey), while the activity (star) is transferred to the
end of the growing chain.
Some kind of process deactivates the growing end, and
then we have a polymer molecule in solution in the
monomer.
The characteristic of this type of polymerization is that
it gives complete chains in solution in monomer.
Step-Growth Polymerization
Here we have a lattice of monomer
molecules (light grey). There is no
need to activate a site: temperature
or a catalyst enables the reaction.
All the time, at various places, one
monomer adds to another forming
a dimer. Dimers can add
monomers, making trimers, or two
dimers can add, making a tetramer.
And so the process goes on.
During this type of polymerization,
we have a mass of partly grown
polymer chains, .all of which are
combining to make bigger
molecules.
Living Polymerization.
Here we have a fixed number of active sites which stay alive. The monomer may be used
up, but if we add more than these sites continue to grow. One can imagine them as corals
on a reef which only grow when they are fed.
(2) STATISTICS OF POLYMERIZATION
Why do we want to know molecular weights?
Weaker    PROPERTIES    Stronger
Lower   MOLECULAR WEIGHT   Higher
Easier    PROCESSING    Harder
Here we have an example of Step Growth Polymerization, where the reaction proceeds,
making bigger and bigger molecules. We show the accompanying change in properties.
This particular one is a condensation polymerization, because water is eliminated during
the reaction. But that is secondary. To sort that sort of distinction out, go to:
http://www.psrc.usm.edu/macrog/synth.htm
Self Condensation of HO(CH2)9COOH
Mn
Number of ester groups
Spinnability
4,170
25
Absent
5,670
33
Short fibers, no cold drawing
7,330
43
Long fibers, no cold drawing
9,330
55
Long fibers that cold draw
16,900
99
Easy to spin and cold draw
25,200
148
Spins at T>210°C and cold draws
Data from Organic Chemistry of Synthetic High Polymers, R. W. Lenz, 1967, p 66.
Step-growth statistics
Consider the self-condensation of A-B and the stoichiometric polymerization of A-A with
B-B where A may react only with B and vice-versa. This is equivalent to determining the
probability of finding a polymer molecule containing x structural units of the form
A-B [A-B]x-2 A-B
Let p = probability that a B group has reacted.
(This is equivalent to the fraction of B groups reacted.)
1 – p = probability that a B group is unreacted
In virtually all cases (except for polyurethanes) one can assume that the reaction events are
independent. Thus, the probability that an x-mer has formed is given by
p x –1 (1-p)

Most Probable Distribution: Number Fraction
P.J. Flory, Principles of Polymer Chemistry, 1953, p 32
Number Average Molecular Weight, Mn
Most Probable Distribution: Weight Fraction
P.J. Flory, Principles of Polymer Chemistry, 1953, p 32
Weight Average Molecular Weight, Mw
The breadth of the Distribution is usually characterized by the value
Mw / M n
Otherwise known as the Polydispersity
For step-growth polymers, the equations imply that:
 as p tends to 1,
 the polydispersity tends to 2.
Chain-growth Polymerization
Consider a chain growing until random something stops it.
Let p = probability that it keeps on going.
1 – p = probability that it gets stopped
Thus, the probability that an x-mer formsS is given by
p x –1 (1-p)
Most Probable Distribution: Number
Fraction
Number Average Molecular Weight, Mn
Most Probable Distribution: Weight
Fraction
Weight Average Molecular Weight, Mw
the Polydispersity
Mw / M n
Which is the same as we got for step-growth polymerization. However, things other than
simple stoppage can happen in chain growth polymerization: two growing chains can join
their two active ends, etc., and these can give rise to different statistics.
Notice that in ideal chain growth polymerization, the average molecular weights stay the
same, while the number of polymer molecules goes on increasing;
while in step growth polymerization, the average molecular weight keeps on increasing, while
the total number of molecules goes down.
(a) This shows the number and weight distributions for a chain growth polymer, with
random statistics. Stem length is taken relative to the number average chain length.
The number distribution falls away from the left, while the weight distribution rises to a peak
and then falls off. These curves are practically identical to the step-growth one, so why
bother? In the chain-growth polymerization, the mean stem length, ideally, remains the
same all through, while the total mass of polymer increases at the expense of monomer. In
the chain growth weight distribution, the peak continuously shifts to higher values.
(b) This shows the mass distribution plotted as a function of log molecular weight. This
approximates to a log-normal distribution with a polydispersity of 2 (again!)
This shows a cumulative distribution for the
above statistics. Only 27% of the mass of
material is made of molecules shorter than
the number average (rel. stem length = 1)
while 40% is longer than the number
average (r.s.l. = 2).
Living Polymers
Each living site receives monomer molecules adding at random, rather like a puddle
receiving random raindrops (we assume that the area of the puddle remains constant!).
Systems like these tend to follow a:
Poisson Distribution:
For largeµ, the Poisson distribution looks very much like the Gaussian. However, it has
this special feature, in that the mean and variance are equal, so:
Molecular Weight Distributions achieved in Practice
Method
Polydispersity
Stereospecificity
Natural Proteins
1.0
Anionic Polymerization
‘Living’ Polymers
1.02 – 1.5
None
Ordinary Chain Polymerization
1.5 – 3
None
Ziegler-Natta
(with catalyst particles)
2 – 40
High
Metallocene
(directive molecular catalysts)
2 – 2.5
High
Cationic
Broad
None
Step Polymerization
2.0 – 4
None
Modified after Sperling, p. 95
Perfect

COPOLYMERIZATION
First we will deal with ‘light’ copolymerization, where one monomer is in the
overwhelming majority. A very common example of this is so-called linear low density
polyethylene. Here a small percentage of a comonomer is added, for example hexane (C6)
is added to the ethylene giving a polyethylene with butyl (C4) branches.
Four models of ‘light’ copolymerization, for example ethylene copolymerized with a few %
of a heavier monomer.
a: uniformly placed branches: too
good to be true!
(b) statistical random branching –
the ideal distribution. All
molecules are similar, and branch
free lengths are distributed in a
similar fashion to molecular
lengths in chain growth. Modern
metallocene catalysed PEs
approach this ideal.
(c) Each molecule is statistically
randomly branched, but each
molecule has a different average
comonomer content. This is
typical of Ziegler PEs.
(d) Different parts of the
molecule different. Not found in
theory and/or practice?
Different Types of Copolymer
Random: This is a ‘heavy’ version of
what we studied in the page above. Very
common.
Alternating: Found where each
monomer insists on adding to the other.
Rather than a copolymer of A and B, it
can be regarded as a homopolymer of
AB.
Block: These are almost always living
polymers, where one changes the
monomer once or twice during the
polymerization.
Graft: Here one takes polymer one, and
with a help of a graft agent produces
active sites along the chain for monomer
two to grow.
Here we show the rate constants for M1
and M2 adding to chains with active ends
M1* or M2*. These are used in the law of
mass action. In general, if A is adding to B,
then:
d(AB)/dt= k[A][B]
here we compare chains with either M1 or
M2 at the end.
Here we show the disappearance of each
type of monomer: it is the sum of adding to
M1* and M2*.
What determines the composition is not the
four k’s separately, but the two reactivity ratios.
Of course, if the k’s are very low, the reaction
will take till the cows come home, and if
they’re too high, things will go off like a bomb.
This is the easiest situation
to envisage.
r1×r2 = 1 is called the ideal
polymerization, because it
resembles ideal solutions in
behaviour. But we won’t
worry you with that one.
This makes alternating
copolymers.
If both r1 and r2 were very
high, this would make a
block copolymer. But this
does not occur in practice,
so block copolymers are
made by living
polymerizations.
Crosslinked Polymers
This is a schematic of an Epoxy Resin
This is a (very) schematic of Rubber
before and after Crosslinking