CHAPTER 4:
POLYMER STRUCTURES
Spherulite, rubber specimen. Chain-folded lamellar crystallites, ~10 nm thick, 30,000×
Chapter 4 -
ISSUES TO ADDRESS...
• What are the general structural and chemical
characteristics of polymer molecules?
• What are some of the common polymeric
materials, and how do they differ chemically?
• How is the crystalline state in polymers different
from that in metals and ceramics ?
2
4.1 Structures of Polymers
• Introduction and Motivation
– Polymers are extremely important materials (i.e. plastics)
– Have been known since ancient times – cellulose, wood, rubber,
etc..
– Biopolymers – proteins, enzymes, DNA …
– Last ~50 years – tremendous advances in synthetic polymers
– Just like for metals and ceramics, the properties of polymers
• Thermal stability
• Mechanical properties
Are intimately related to their molecular structure …
4.1 Ancient Polymers
Originally natural
polymers were used:
– Wood
– Rubber
– Cotton
– Wool
– Leather
Oldest known use:
– Silk
Rubber balls used by Incas
Noah used pitch (a natural polymer) for the ark
Noah's pitch
Genesis 6:14 "...and cover it inside
and outside with pitch."
gum based resins
extracted from
pine trees
Chapter 4 - 4
4.2 Polymer Composition
Most polymers are hydrocarbons
– i.e., made up of H and C
• Saturated hydrocarbons
– Each carbon singly bonded to four other atoms
– Example:
• Ethane, C2H6
H
H
C
H
H
C
H
H
Chapter 4 - 5
4.2 Unsaturated Hydrocarbons
• Double & triple bonds somewhat unstable
• Thus, can form new bonds
– Double bond found in ethylene or ethene - C2H4
H
H
C C
H
H
– Triple bond found in acetylene or ethyne - C2H2
H C C H
Chapter 4 - 6
4.2 Structures of Polymers
• about hydrocarbons
– Why? Most polymers are hydrocarbon (e.g. C, H) based
– Bonding is highly covalent in hydrocarbons
– Carbon has four electrons that can participate in bonding,
hydrogen has only one
– Saturated versus unsaturated
H
•
H
C
C
H
H
H
H
H
Ethylene
C
C
H
H
C
C
H
Acetylene
Unsaturated
H
H
Ethane
Saturated
•
Unsaturated – species contain
carbon-carbon double/triple
bonds
• Possible to substitute
another atom on the carbon
Saturated – carbons have four
atoms attached
• Cannot substitute another
atom on the carbon
Chapter 4 -
4.2 Hydrocarbon Molecules
Ethylene
Ethene
Acetylene
Ethyne
Hydrocarbons have strong chemical bonds, but
interact only weakly with one another (van der
Waals’ forces)
(normal) butane
isobutane
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4.2 Isomerism
compounds with same chemical formula can have
quite different structures
for example: C8H18
• normal-octane
H H H H H H H H
H C C C C C C C C H
= H3C CH2 CH2 CH2 CH2 CH2 CH2 CH3
H H H H H H H H

H3C ( CH2 ) CH3
6
Isomerism – compounds of the
same chemical composition but
different atomic arrangements (i.e.
bonding connectivity)
2,4-dimethylhexane
CH3
H3C CH CH2 CH CH3
CH2
CH3
4.2
Chapter 4 - 10
4.3 Polymer Molecules
Molecules are gigantic
Macromolecules
Repeat units
Monomer
4.3 Polymers
• Polymer molecules
– what is a polymer?
– Polymers are molecules (often called
macromolecules) formed from a series of building
units (monomers) that repeat over and over again
H H
C
• polymers can have a range of
molecular weights
• There are many monomers
• Can make polymers with
different monomers, etc..
*
*
C
H
n
H
H H
poly-ethylene
C
mer unit :
C
H
H
n is often a very large number!
e.g. can make polyethylene with MW > 100,000! ~3600 mers ~7200 carbons
Chemistry of polymer molecules
Example: ethylene
• Gas at STP
• To polymerize ethylene, typically increase T, P and/or add an initiator
H
C
R
+
C
R
H
H
H
C
+
C
H
H
H
C
Initiation
C
H
H
H
H
R
H
H
C
H
H
H
R
C
H
C
H
H
H
C
C
H
H
H
Propagation
C
H
H H
After many additions of monomer to the growing chain…
R* = initiator; activates the monomer to begin chain growth
Initiator: example - benzoyl peroxide
H
C O O C
H
H
2
*
*
H
H
C
C O =2R
H
C
H
n
H
poly-ethylene
4.4 Polymer chemistry
• Polymers are chain molecules. They are built
up from simple units called monomers.
• E.g. polyethylene is built from ethylene units:
which are assembled into long chains:
Polyethylene or polythene (IUPAC name poly(ethene)) is a
thermoplastic commodity heavily used in consumer products
(notably the plastic shopping bag). Over 60 million tons of the
material are produced worldwide every year.
Tetrafluoroethylene monomer polymerize to form PTFE or
polytetrafluoroethylene
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poly(tetrafluoroethene) or poly(tetrafluoroethylene) (PTFE) is a synthetic
fluoropolymer. PTFE is the DuPont brand name Teflon. Melting: 327C
Vinyl chloride monomer leads to poly(vinyl chloride) or PVC
PVC: manufacturing toys,
packaging, coating, parts in motor
vehicles, office supplies,
insulation, adhesive tapes,
furniture, etc. Consumers: shoe
soles, children's toys, handbags,
luggage, seat coverings, etc.
Industrial sectors: conveyor belts,
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printing rollers. Electric and
electronic equipment: circuit
boards, cables, electrical boxes,
computer housing.
Chemistry and Structure of Polyethylene
Adapted from Fig.
4.1, Callister &
Rethwisch 3e.
Note: polyethylene is a long-chain hydrocarbon
- paraffin wax for candles is short polyethylene
• Polymer = many mers
17
Chapter 4 -
Adapted from Fig. 14.2, Callister 6e.
Polymer chemistry
– In polyethylene (PE) synthesis, the monomer is ethylene
– Turns out one can use many different monomers
H H
• Different functional groups/chemical composition – polymers have very
different properties!
F F
C
*
*
C
n
C
*
C
n
Monomers
H
H
*
F
F
poly(ethylene)
(PE)
poly(tetrafluoroethylene)
(PTFE, teflon)
H
H
C
C
C
H
H
C
C
*
C
Cl
F
C
H H
H H
*
F
n
H
poly(vinylchloride)
(PVC)
*
F
F
*
C
n
H
C
H
Cl
poly(styrene)
(PS)
H
C
H
H
C
H
C
H
Homopolymer and Copolymer
• Polymer chemistry
– If formed from one monomer (all the repeat units are
the same type) – this is called a homopolymer
– If formed from multiple types of monomers (all the
repeat units are not the same type) – this is called a
copolymer
• Also note – the monomers shown before are
referred to as bifunctional
– Why? The reactive bond that leads to polymerization
(the C=C double bond in ethylene) can react with two
other units
– Other monomers react with more than two other units
– e.g. trifunctional monomers
The Top 10 Bulk or Commodity
Chapter 4 -
4.5 MOLECULAR WEIGHT
Molecular weight, M: Mass of a mole of chains.
low M
high M
Not all chains in a polymer are of the same length
i.e., there is a distribution of molecular weights
Chapter 4 - 21
Molecular weight
– The properties of a polymer depend on its
length
– synthesis yields polymer distribution of
lengths
– Define “average” molecular weight
– Two approaches are typically taken
• Number average molecular weight (Mn)
• Weight-average molecular weight (Mw)
Chapter 4 -
MOLECULAR WEIGHT DISTRIBUTION
Adapted from Fig. 4.4, Callister & Rethwisch 3e.
total wt of polymer
Mn 
total # of molecules
M n  x i M i
M w  w i M i
Mi = mean (middle) molecular weight of size range i
xi = number fraction of chains in size range i
wi = weight fraction of chains in size range i
Chapter 4 - 23
Molecular weight
Are the two different? Yes, one is essentially based
on mole fractions, and the other on weight fractions
They will be the same if all the chains are exactly of the
same MW! If not Mw > Mn
Get Mn
from this
Get Mw from
this
Molecular weight
– Other ways to define polymer MW
– Degree of polymerization
• Represents the average number of mers in
a chain. The number and weight average
degrees of polymerization are
Mn
nn 
m
Mw
nw 
m
m is the mer MW in both cases. In the case of a
copolymer (something with two or more mer units), m
is determined by
m
f jmj

fj and mj are the chain fraction and molecular
weight of mer j
Example Problem 4.1
– Given the following data determine the
• Number average MW
• Number average degree of polymerization
• Weight average MW
How to find Mn?
1. Calculate xiMi
Number average MW (Mn)
2. Sum these!
MW range (g/mol)
Min
5000
10000
15000
20000
25000
30000
35000
Mean (Mi)
Max
10000
15000
20000
25000
30000
35000
40000
xi
0.05
0.16
0.22
0.27
0.20
0.08
0.02
(g/mol) x iMi (g/mol)
375
7500
2000
12500
3850
17500
6075
22500
5500
27500
2600
32500
750
37500
M n  21,150 g / mol
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Example Problem 4.1
Number average degree of polymerization
– (MW of H2C=CHCl is 62.50 g/mol)
M n 21,150 g / mol
nn 

 338
62.50 g / mol
m
Weight average molecular weight (Mw)
M w 23,200 g / mol

 1.10
M n 21,150 g / mol
MW range (g/mol)
Min
5000
10000
15000
20000
25000
30000
35000
How to find Mw?
1. Calculate wiMi
2. Sum these!
M w  23,200 g / mol
Mean (Mi)
Max
10000
15000
20000
25000
30000
35000
40000
wi
0.02
0.10
0.18
0.29
0.26
0.13
0.02
(g/mol) wiMi (g/mol)
7500
150
12500
1250
17500
3150
22500
6525
27500
7150
32500
4225
37500
750
c04tf04b
Degree of Polymerization, DP
DP = average number of repeat units per chain
H H H H H H H H H H H H
H C C (C C ) C C C C C C C C H
DP = 6
H H H H H H H H H H H H
Mn
DP 
m
where m  average molecular weight of repeat unit
for copolymers this is calculated as follows :
m  fi mi
Chain fraction
mol. wt of repeat unit i
Chapter 4 - 30
4.6 Polymers – Molecular Shape
Molecular Shape (or Conformation) – chain
bending and twisting are possible by rotation
of carbon atoms around their chain bonds
– note: not necessary to break chain bonds
to alter molecular shape
Adapted from Fig.
4.5, Callister &
Rethwisch 3e.
– C-C bonds are typically 109° (tetrahedral, sp3 carbon)
– If you have a macromolecule with hundreds of C-C bonds, this
will lead to bent chains
Chapter 4 - 31
Structures of Polymers
• Molecular shape
– Taking this idea further, can also have rotations about bonds
• Leads to “kinks”, twists
• “the end-to-end distance of a polymer chain in the solid state
(or in solution) is usually much less than the distance of the
fully extended chain!
• This is not even taking into account that you have numerous
chains that can become entangled!
Chapter 4 -
 4.7 Molecular structure
 Physical properties of polymers depend
not only on their molecular weight/shape,
but also on the difference in the chain
structure
 Four main structures
• Linear polymers
• Branched polymers
• Crosslinked polymers
• Network polymers
4.7 Molecular Structures for
Polymers
secondary
bonding
Linear
Branched
Cross-Linked
Network
Adapted from Fig. 4.7, Callister & Rethwisch 3e.
Chapter 4 - 34
Linear polymers
 – polymers in which the mer units are connected endto-end along the whole length of the chain
 These types of polymers are often quite flexible
• Van der waal’s forces and H-bonding are the two
main types of interactions between chains
• Some examples – polyethylene, teflon, PVC,
polypropylene
Branched polymers
• Polymer chains can branch:
• Or the fibers may aligned parallel, as in fibers and some
plastic sheets.
• chains off the main chain (backbone)
– This leads to inability of chains to pack very closely together
» These polymers often have lower densities
• These branches are usually a result of side-reactions during
the polymerization of the main chain
– Most linear polymers can also be made in branched forms
Crosslinked polymers
• Molecular structure
– adjacent chains attached via covalent bonds
• Carried out during polymerization or by a non-reversible reaction
after synthesis (referred to as crosslinking)
• Materials often behave very differently from linear polymers
• Many “rubbery” polymers are crosslinked to modify their mechanical
properties; in that case it is often called vulcanization
• Generally, amorphous polymers are weak and
cross-linking adds strength: vulcanized rubber is
polyisoprene with sulphur cross-links:
Network polymers
– polymers that are “trifunctional” instead of bifunctional
– There are three points on the mer that can react
– This leads to three-dimensional connectivity of the polymer
backbone
• Highly crosslinked polymers can also be classified as network
polymers
• Examples: epoxies, phenol-formaldehyde polymers
POLYMER MICROSTRUCTURE
• Covalent chain configurations and strength:
Direction of increasing strength
Adapted from Fig. 14.7, Callister 6e.
2
4.8 Molecular configurations
Classification scheme for the
characteristics of polymer
molecules
isomerism – different molecular
configurations for molecules (polymers) of
the same composition
Stereoisomerism
Geometrical Isomerism
4.8 Molecular Configurations
Repeat unit
R = Cl, CH3, etc
Configurations – to change must break bonds
Stereoisomers are mirror
images – can’t superimpose
without breaking a bond
A
A
C E E C
B D
D B
mirror
plane
H
H
C C
H
H H
C C
R
H R
H R
or
C C
H H
Head to-tail
Typically the head-to-tail
configuration dominates
Head to-head
Structures of Polymers
• Stereoisomerism
– Denotes when the mers are linked together in the same way
(e.g. head-to-tail), but differ in their spatial arrangement
– This really focuses on the 3D arrangement of the side-chain
groups
– Three configurations most prevalent
• Isotactic
• Syndiotactic
• Atactic
ISOTACTIC
• Stereoisomerism
– Isotactic polymers
– All of the R groups are on the same side of the chain
H
R
H
H
C
H
Isotactic configuration
C
C
C
H
R
C
C
C
H
R
H
R
H
H
H
• Note: All the R groups are head-to-tail
• All of the R groups are on the same side of the chain
• Projecting out of the plane of the slide
• This shows the need for 3D representation to understand
stereochemistry!
SYNDIOTACTIC
• Stereoisomerism
– Syndiotactic polymers
– The R groups occupies alternate sides of the chain
H
R
H
H
C
H
Syndiotactic configuration
C
C
C
R
H
C
C
C
H
R
R
H
H
H
H
• Note: The R groups are still head-to-tail
• R groups alternate – one of out of the plane, one into the plane
ATACTIC
• Stereoisomerism
– Atactic polymers
– The R groups are “random”
H
R
H
H
C
H
Atactic configuration
C
C
C
H
R
C
C
C
R
H
H
R
H
H
H
• R groups are both into and out of the plane, no real registry
• Two additional points
• Cannot readily interconvert between stereoisomers – bonds
must be broken
• Most polymers are a mix of stereoisomers, often one will
predominate
Stereoisomerism—Head-to-tail
isotactic configuration
Syndiotactic
conformation
Atactic conformation
cis/trans Isomerism
CH3
H
CH3
C C
CH2
CH2
C C
CH2
CH2
H
cis
trans
cis-isoprene
(natural rubber)
trans-isoprene
(gutta percha)
H atom and CH3 group on
same side of chain
H atom and CH3 group on
opposite sides of chain
Chapter 4 - 48
Geometrical Isomerism
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4.9 Plastics
• variety of properties due to their rich chemical makeup
• They are inexpensive to produce, and easy to mold,
cast, or machine.
• Their properties can be expanded even further in
composites with other materials.
Glass-rubber-liquid
• Amorphous plastics have a complex thermal profile with
3 typical states:
Glass phase (hard plastic)
9
8
Log(stiffness)
Pa
Leathery phase
7
6
Rubber phase (elastomer)
5
4
Liquid
3
Temperature
THERMOPLASTICS
• Thermosetting and thermoplastic polymers
– Another way to categorize polymers – how do they respond to
elevated temperatures?
– Thermoplastics – these materials soften when heated, and
harden when cooled – this process is totally reversible
• This is due to the reduction of secondary forces between polymer
chains as the temperature is increased
• Most linear polymers and some branched polymers are
thermoplastics
THERMOSETS
• Thermosetting and thermoplastic polymers
– Thermosets – these materials harden the first time they are
heated, and do not soften after subsequent heating
• During the initial heat treatment, covalent linkages are formed
between chains (i.e. the chains become cross-linked)
• Polymer won’t melt with heating – heat high enough it will degrade
• Network/crosslinked polymers are typically thermosets
•
•
•
•
•
Polymers which irreversibly change when heated are called thermosets.
Most often, the change involves cross-linking which strengthens the
polymer (setting).
Thermosets will not melt, and have good heat resistance.
They are often made from multi-part compounds and formed before setting
(e.g. epoxy resin).
Setting accelerates with heat, or for some polymers with UV light.
Thermoplastics
• Polymers which melt and solidify without chemical
change are called thermoplastics.
• They support hot-forming methods such as injectionmolding and FDM.
THERMOPLASTICS VS THERMOSETS
• Thermoplastics:
--little cross linking
--ductile
--soften w/heating
--polyethylene (#2)
polypropylene (#5)
polycarbonate
polystyrene (#6)
T
mobile
liquid
viscous
liquid
crystalline
solid
Callister,
rubber
Fig. 16.9
tough
plastic
Tm
Tg
partially
crystalline
solid
Molecular weight
• Thermosets:
Adapted from Fig. 15.18, Callister 6e. (Fig. 15.18 is from F.W.
Billmeyer, Jr., Textbook of Polymer Science, 3rd ed., John Wiley
and Sons, Inc., 1984.)
--large cross linking
(10 to 50% of mers)
--hard and brittle
--do NOT soften w/heating
--vulcanized rubber, epoxies,
polyester resin, phenolic resin
3
4.10 Structures of Polymers
• Copolymers
– Idea – polymer that contains more than one mer unit
– Why? If polymer A has interesting properties, and polymer B has
(different) interesting properties, making a “mixture” of polymer
should lead to a superior polymer
“Random” copolymer – exactly what it sounds like
“Alternating” copolymer – ABABABA…
Structures of Polymers
• Copolymers
– Idea – polymer that contains more than one mer unit
– Why? If polymer A has interesting properties, and polymer B has
(different) interesting properties, making a “mixture” of polymer
should lead to a superior polymer
“Block” copolymers. Domains of “pure” mers
“Graft” copolymers. One mer forms
backbone, another mer is attached to
backbone and is a sidechain (it is “grafted” to
the other polymer)
Copolymers
two or more monomers
polymerized together
• random – A and B randomly
positioned along chain
• alternating – A and B
alternate in polymer chain
• block – large blocks of A
units alternate with large
blocks of B units
• graft – chains of B units
grafted onto A backbone
A–
B–
Adapted from Fig.
4.9, Callister &
Rethwisch 3e.
random
alternating
block
graft
Chapter 4 - 58
Copolymers
• Polymers often have two different monomers along
the chain – they are called copolymers.
• With three different units, we get a terpolymer. This
gives us an enormous design space…
Chapter 4 -
4.11 Polymer structure
• The polymer chain layout determines a lot of material
properties:
• Amorphous:
• Crystalline:
Crystallinity in Polymers
Adapted from Fig.
4.10, Callister &
Rethwisch 3e.
• Ordered atomic
arrangements involving
molecular chains
• Crystal structures in terms
of unit cells
• Example shown
– polyethylene unit cell
– Polymers can be crystalline (i.e.
have long range order)
– However, given these are large
molecules as compared to
atoms/ions (i.e. metals/ceramics)
the crystal structures/packing
will be much more complex
Chapter 4 - 61
Structures of Polymers
• Polymer crystallinity
– (One of the) differences between small molecules and
polymers
– Small molecules can either totally crystallize or
become an amorphous solid
– Polymers often are only partially crystalline
• Why? Molecules are very large
• Have crystalline regions dispersed within the remaining
amorphous materials
• Polymers are often referred to as semicrystalline
Structures of Polymers
• Polymer crystallinity
– Another way to think about it is that these are two
phase materials (crystalline, amorphous)
– Need to estimate degree of crystallinity – many ways
• One is from the density
%crystallin ity 
 c  s   a 
100
 s  c   a 
Structures of Polymers
4.11 Polymer crystallinity
– What influences the degree of crystallinity
• Rate of cooling during solidification
• Molecular chemistry – structure matters
– Polyisoprene – hard to crystallize
– Polyethylene – hard not to crystallize
• Linear polymers are easier to crystallize
• Side chains interfere with crystallization
• Stereoisomers – atactic hard to crystallize (why?); isotactic,
syndiotactic – easier to crystallize
• Copolymers – more random; harder to crystallize
4.11 Polymer Crystallinity (cont.)
Polymers rarely 100% crystalline
• Difficult for all regions of all chains to
become aligned
crystalline
region
• Degree of crystallinity
expressed as % crystallinity.
-- Some physical properties
depend on % crystallinity.
-- Heat treating causes
crystalline regions to grow
and % crystallinity to
increase.
amorphous
region
Adapted from Fig. 14.11, Callister 6e.
(Fig. 14.11 is from H.W. Hayden, W.G. Moffatt,
and J. Wulff, The Structure and Properties of
Materials, Vol. III, Mechanical Behavior, John Wiley
and Sons, Inc., 1965.)
Chapter 4 - 65
4.11 MOLECULAR WEIGHT &
CRYSTALLINITY
• Molecular weight, Mw: Mass of a mole of chains.
• Tensile strength (TS):
--often increases with Mw.
--Why? Longer chains are entangled (anchored) better.
• % Crystallinity: % of material that is crystalline.
--TS and E often increase
with % crystallinity.
crystalline
--Annealing causes
region
crystalline regions
amorphous
to grow. % crystallinity
region
increases.
Adapted from Fig. 14.11, Callister 6e.
(Fig. 14.11 is from H.W. Hayden, W.G. Moffatt,
and J. Wulff, The Structure and Properties of
Materials, Vol. III, Mechanical Behavior, John
Wiley and Sons, Inc., 1965.)
Chapter 4 - 4
4.12 Polymer Crystallinity
4.12 Polymer crystals
– Chain folded-model
• Many polymers crystallize as very thin platelets (or
lamellae)
• Idea – the chain folds back and forth within an individual
plate (chain folded model)
• Crystalline regions
– thin platelets with chain folds at faces
– Chain folded structure
Chapter 4 -
4.12 Single Crystals
• Electron micrograph – multilayered single crystals
(chain-folded layers) of polyethylene
• Single crystals – only for slow and carefully controlled
growth rates
Adapted from Fig. 4.11, Callister & Rethwisch 3e.
Chapter 4 - 68
4.12 Semicrystalline Polymers
Spherulite
surface
• Some semicrystalline
polymers form
spherulite structures
• Alternating chain-folder
crystallites and
amorphous regions
• Spherulite structure for
relatively rapid growth
rates
Adapted from Fig. 4.13, Callister & Rethwisch 3e.
Chapter 4 - 69
Structures of Polymers
• Polymer crystals
– More commonly, many polymers that crystallize from a melt form
spherulites
• One way to think of these – the chain folded lamellae have
amorphous “tie domains” between them
• These plates pack into a spherical shape
• Polymer analogues of grains in polycrystalline
metals/ceramics
Photomicrograph – Spherulites in
Polyethylene
Cross-polarized light used
-- a maltese cross appears in each spherulite
Adapted from Fig. 4.14, Callister & Rethwisch 3e.
Chapter 4 - 71
END of chapter 4