Chapter 4
Highlights:
1.
Understand what a polymer is, and understand polymer shape, structure and configuration,
and copolymers
2.
Understand and be able to calculate number- and weight-average molecular weight, and
number- and weight-average degree of polymerization.
3.
Understand the factors that control the extent of crystallinity in a polymer sample.
Notes:
Naturally occurring polymers, including rubber, cotton, wood, and silk, have been used for
centuries. Synthetic polymers are widely used as plastics (polyethylene, polyvinylchloride = PVC)
synthetic fibers (nylon, polyester), and synthetic rubber. An enormous advantage of polymers
relative to other engineering materials is that they are much cheaper. An enormous disadvantage of
polymers relative to other engineering materials is that they are not as mechanically strong.
g.
Table 4.3 lists some common polymer materials, including polyethylene (kid’s toys, plastic bottles,
saran wrap, etc.), polypropylene (isotactic, many applications), polyvinyl chloride (plastic pipes,
electrical insulation), and polytetrafluoroethylene (PTFE = Teflon).
Polymers are made by connecting a large number of individual hydrocarbon (hydrogen + carbon)
molecules into a much larger, long-chain molecule. The individual hydrocarbon molecules are
called “mers,” and the longer molecule that is created is called a “polymer.”
Example: Formation of polyethylene from ethylene.
n(C 2 H 4 ) → CH 3 (CH 2 )n− 2 CH 3
Illustrations from the online text demonstrate this reaction mechanism. Figures 4.1 and 4.2 illustrate
the molecular structure of polymer chains, which contain connected tetrahedral sp3 hybridized C
atoms.
Molecular Weight
The lengths of different polymer molecules within one batch of polymers can vary substantially. A
common method to characterize such a polymer mixture is by its average molecule weight.
−
−
Unfortunately, one can do this by either the number-average  M n  or weight-average  M w 




molecular weight. These are defined as:
_
Mn =
_
Mw =
∑x M
i
∑w M
i
i
i
Mi = Mean molecular weight of size range i
xi = Fraction of the total number of polymer chains within the corresponding size range.
wi = Weight fraction of molecules within the corresponding size range.
Example:
Three polymer molecules have molecular weights of 10,000 and 30,000 and 50,000
g/mol.
x1 = x 2 = x 3 =
−
Mn =
1
3
1
(10,000) + 1 (30,000) + 1 (50,000) = 30,000
3
3
3
w1 =
10,000
= 0.11
10,000 + 30,000 + 50,000
w2 =
30,000
= 0.33
10,000 + 30,000 + 50,000
w3 =
50,000
= 0.56
10,000 + 30,000 + 50,000
−
M w = (0.11)(10,000 ) + (0.33 )(30,000 ) + (0.56 )(50,000 ) = 39,000
Similarly, we can define the average degree of polymerization (# of mer units per polymer
molecule) according to the number-average (nn) or weight-average (nn):
−
nn =
Mn
−
m
−
nw =
Mw
−
m
−
where m is the mer molecular weight. Show Figures 4.3 and 4.4.
Polymer shape, structure and configuration; copolymers
Show Figures 4.5-4.7 and 4.9, schematics of stereoisomers and geometric isomers, and explain.
Synthetic rubbers are often copolymers: automobile tires are typically made from styrene-butadiene
rubber, and gasoline hoses are made from nitrile rubber (acrylonitrile and butadiene).
sp3 hybridized C atoms
Isotactic (R all above plane of page)
Syndiotactic (R alternates above, below plane of page)
Linear (a), branched (b), cross-linked (c), and networked (d) polymers
Random (a), alternating (b), block (c),
and graft (d) copolymers.
Polymer Crystallinity
Show Figures 4.10-4.15.
Unit cell for crystalline polyethylene
Possible structure of crystalline polymer
Crystallization of polymers is much more difficult that crystallization of metals and ceramics.
Polymer crystallization is made more difficult by their chemical heterogeneity (different chain
lengths, etc.); by their long chain lengths, which make exact chain alignment difficult; and by the
weak secondary (van der Waals) bonds that hold together polymer crystals. Note that metallic and
ceramic crystals are held together by metallic and ionic bonds, respectively, and that these bonds are
much stronger. Nevertheless, polymers are often partly, but rarely completely, crystalline.
One simple way to characterize the degree of crystallinity in a polymer sample is to calculate the %
crystallinity of the sample:
% crystallinity =
ρ c (ρ s − ρ a )
x100
ρ s (ρ c − ρ a )
Here ρs, ρc, and ρa are the sample density, the density of the 100% crystalline polymer, and the
density of the 100% amorphous polymer, respectively.
Note that when ρs = ρc, % crystall. = 100%. When ρs = ρa, 100% crystal. = 0%.
Example:
The density is 2.144 g/cm3 for a polymer that is 51.3% crystalline, and 2.215 g/cm3
for a polymer that is 74.2% crystalline. Calculate the densities of the completely
crystalline and completely amorphous polymer.
Using the equation above, we can generate a 2x2 system of equations:
0.513 =
ρ c (2.144 − ρ a )
2.144(ρ c − ρ a )
0.742 =
ρ c (2.215 − ρ a )
2.215(ρ c − ρ a )
The easiest way to do this problem is to divide the second equation by the first equation:
ρ c (2.215 − ρ a )
0.742 2.215(ρ c − ρ a )
=
0.513 ρ c (2.144 − ρ a )
2.144(ρ c − ρ a )
1.4464 = 0.9879
(2.215 − ρ a )
(2.144 − ρ a )
ρ a = 1.991 g / cm 3 , ρ c = 2.313 g / cm 3
Degree of crystallinity is increased for:
1)
2)
3)
4)
5)
Slow cooling relative to fast cooling. This allows time for diffusion to occur (Chapter 6)
and align the polymer chains.
Linear > branched > cross-linked, network polymers.
Isotactic, syndiotactic > atactic polymers.
Simple mer unit > bulky side chains in mer unit.
Copolymers > simple polymers.
More crystalline polymers tend to be mechanically stronger, and more resistive to chemical
dissolution and softening by heat.