mse 2001- chapter 6 ppt
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1
Chapter 6
Noncrystalline and Semicrystalline Materials
• Introduction
• Glass Transition Temperature
• Viscous Deformation
• Structure and Properties of Amorphous and Semi-crystalline Polymers
• Structure and Properties of Glasses
• Structure and Properties of Rubbers and Elastomers
2
Introduction
• The emphasis thus far has been on crystalline materials.
• There are numerous engineering materials that lack the long range translational periodicity of a crystalline material.
• These non-crystalline materials are referred to as either amorphous, glassy, or super-cooled liquids.
• Theoretically, any material can form an amorphous structure if the cooling rate from the melt is sufficiently rapid to suppress crystal formation.
• This chapter will emphasize the structural considerations that facilitate the development of an amorphous structure.
3
Glass Transition Temperature
Glassy State
A state of material in the absence of long-range order below the glass
transition temperature � large scale mobility is frozen� atomic movement
requires time.
Rubbery State
A state of material in the absence of long-range order above the glass
transition temperature� atomic movement takes shorter time.
Window glass vs. Rubber band
What if you give them a good blow using a hammer?
Glass transition temperature: the temperature below which the physical
properties of amorphous materials vary in a manner similar to those of a
solid phase (glassy state), and above which amorphous materials behave
like liquids (rubbery state).
4
Specific Volume for a Variety of Materials
Liquid to glass solid transformation in a
pure substance. The glass transition
temperature, Tg, is not an equilibrium
transformation temperature.
Liquid to crystalline solid transformation
for a pure substance. The melting
temperature, Tm, is an equilibrium
transformation temperature
Glass Transition
The slope normalized by the volume V is the volumetric thermal expansion
coefficient (αv)
dT
dV
Vv
1=α
Decrease of specific volume of liquid with decreasing temperature
5
Glass Transition
Below Tm, material tends to crystallize.
The crystal formation (crystallization)
occurs over a period of time because
the establishment of long-range order
(LRO) requires atomic rearrangement
by diffusion.
It is possible to avoid crystallization by
cooling at a sufficiently high rate so as
to suppress the diffusion necessary to
establish LRO in the crystal.
The volume of the collection of atoms
continues to decrease with the slope
characteristic of the liquid below the
melting temperature, forming a super-
cooled liquid.
6
Liquid to Semi-crystalline Solid Transformation
T>Tm: Liquid state, molecular motion is very large.
Tg<T<Tm: Rubbery state (super-cooled liquid), molecular motion is relatively large.
T<Tg: Glassy state, molecular motion is very small. � Frozen state
Many polymers are
semicrystalline
7
Comparison of the Response of a Solid and a Liquid to a
Shear Stress
F dy
A dx
G
τ γ
τ γ
∝
∝
=
( )
( )
dyd
dt
dx
dyd
dx
dt
τ
τ
∝
∝
d
dt
γτ η ηγ= = &
Viscous Deformation
G: shear modulusη: shear viscosity
Unit of viscosity: poise, P
P=g/(cm s)
Time independent Time dependent
8
Temperature Dependence of Viscosity
Fluidity
expo
Q
RTφ φ
− =
1exp
o
Q
RTη η
φ
+ = =
Viscous Deformation
Viscosity
Question) Calculate the viscosity of molasses at 100 °C assuming an activation energy of 30 kJ/mol. It is known that the viscosity at 25°C is
Solution)( )( )
( )( )
−==
1210
20
1
2 11exp
/exp
/exp
TTR
Q
RTQ
RTQ
T
T
η
η
η
η
( ) PC 5025 =°η
( ) ( ) PKKKmolJ
molJPC 41.4
298
1
373
1
)/(314.8
/30000exp50100 =
−=°η
9
Example: Temperature-dependent viscosity of ordinary window glass
10
Classification of Polymers
• The degree of polymerization
• The nature of the bond– Thermoplastics (TP), possible secondary bonds
between chains
– Thermoset (TS), cross-links between chains
• Molecular weight– Molecular weight
– Number average molecular weight
– Weight average molecular weight
– Polydispersity
– Conformation
– Configuration- Tacticity and branching
11
Structure and Properties of Amorphous and
Semicrystalline Polymers
Ethylene
building block
Poly (ethylene)
monomer
Poly (ethylene)
chain
Poly (ethylene) chains pack well because the side groups are only hydrogen
Formation (polymerization) of Poly (ethylene) from a Basic
Chemical Unit of C2H4
C=C
H H
H H
C=C
H H
H H
C C
H H
H H
.. C C
H H
H H
C C
H H
H H
.. C C
H H
H H
C C
H H
H H
C C
H H
H H
… .. C C
H H
H H
C C
H H
H H
C C
H H
H H
…C C
H H
H H
C C
H H
H H
C C
H H
H H
C C
H H
H H
C C
H H
H H
C C
H H
H H
… ..
C C
H H
H H
C C
H H
H H
C C
H H
H H
C C
H H
H H
… …C C
H H
H H
C C
H H
H H
C C
H H
H H
C C
H H
H H
C C
H H
H H
C C
H H
H H
C C
H H
H H
C C
H H
H H
C C
H H
H H
C C
H H
H H
C C
H H
H H
C C
H H
H H
… …
C C
H H
H H
C C
H H
H H
C C
H H
H H
C C
H H
H H
… …C C
H H
H H
C C
H H
H H
C C
H H
H H
C C
H H
H H
C C
H H
H H
C C
H H
H H
C C
H H
H H
C C
H H
H H
C C
H H
H H
C C
H H
H H
C C
H H
H H
C C
H H
H H
… …
Glass transition temperature: -78 °C. Melting temperature: 100 °C. Amorphous density at 25 °C: 0.855 g/cm3. Crystalline density at 25 °C: 1.00 g/cm3. Molecular weight of repeat unit: 28.05 g/mol
Widely used in making translucent,
lightweight, and tough plastics, films,
containers, insulation, etc.
12
C
H
H
C
H
H
C C C C
H
H
H
H
H
H
H
H
... ...
C
H
H
C
H
H
n
Degree of Polymerization (DP)
n: the number of monomeric unit
~10,000 to ~1,000,000
The degree of polymerization
C C
H
H
H
Cl
C C
H
H
H
Cl
C
C
C
C
C
C
C
C
C
C
Cl Cl Cl Cl Cl
H H H H HH H H H H
H H H H H
n
Another Example:
Poly (vinyl chloride)
C C
H H
H H
.. C C
H H
H H
C C
H H
H H
..
13
Poly (ethylene terephthalate), PET or PETE, one of the polyesters
Film, fibers, clothing, drink bottle
Density 1370 kg/m3
Young modulus (E) 2800–3100 MPa
Tensile strength (σt) 55–75 MPa
Glass temperature 75 °Cmelting point 260 °C
Poly (styrene), PS
Density 1050 kg/m³
Specific Gravity 1.05
Young's modulus (E) 3000-3600 MPa
Tensile strength (st) 46–60 MPa
Glass temperature 95 °CMelting point 240 °C
Containers and toys
14
CH
2
C
H2
CH
2
C
H2
CH
2
C
H2
NH
NH
C
O
CH
2
C
H2
CH
2
C
H2
C
O
n
Nylon 66, one of the polyamides
Carpet fiber, apparel, airbags, tires,
ropes, conveyor belts, and hoses
Poly (p-phenyleneterephthalamide), PPTA or Kevlar
Fibers and bulletproof vests
One of the most strong polymers
C
F
F
C
F
F
n
Poly (tetrafluoroethylene), PTFE (Teflon)bearings, bushings, gears, slide plates
One of the most hydrophobic polymers
With the lowest frictional coefficient
15
Thermoplastic Polymer and Thermoset Polymer
Thermoplastic polymer: capable of softening or fusing (melting) when
heated and of hardening again when cooled
e.g.) various linear polymers (no chemical crosslinking)poly (ethylene), poly (propylene), and Poly (ethylene terephthalate)
Thermoset polymer: not capable of softening or fusing (melting) when
heated and of hardening again when cooled � The curing (crosslinking)
process makes three-dimensional network structure in polymeric material
e.g.) various polymers with chemical crosslinkingVulcanized rubber
Bakelite, a Phenol Formaldehyde Resin (used in electrical insulators and plastic wear)
Urea-formaldehyde foam (used in plywood, particleboard and medium-density fibreboard)
Melamine resin (used on worktop surfaces)
Polyester Resin (used in glass-reinforced plastics/fibreglass (GRP))
Epoxy Resin
16
Structure of Cross-linked Rubber
Thermoplastic Polymer and Thermoset Polymer
C C
R H
H
C C
H H
H
C C
R H
H
C C
H H
H
… …
C C
R
H
H
C C
H
HH
C C
R
H
H
C C
H
HH
… …
Double
bonds
C C
R H
H
C C
H H
H
C C
R H
H
C C
H H
H
… …C C
R H
H
C C
H H
H
C C
R H
H
C C
H H
H
… …
C C
R
H
H
C C
H
HH
C C
R
H
H
C C
H
HH
… …
Double
bonds
…
…
C C
R H
H
C C
H H
H
C C
R H
H
C C
H H
H
…
C C
R
H
H
C C
H
HH
C C
S H
H
C C
H S
H
…
SSCross-linked
Primary Bonds
H H
C C
R H
H
C C
H H
H
C C
R H
H
C C
H H
H
…
C C
R
H
H
C C
H
HH
C C
S H
H
C C
H S
H
…
SSCross-linked
Primary Bonds
H H
Unsaturated bonds are used to form cross-links with cross-linker.
Vulcanized rubber
17
Thermoplastic Polymer and Thermoset Polymer
Polyester with saturated bonds along the chain
Polyester with unsaturated
bonds along the chain
Crosslinking with apolystyrene monomer
Thermoplastic
Thermoset polymerPET
PET
PET-based thermoset
polymer
18
Thermoplastic Polymer and Thermoset Polymer
Bakelite
Three bonding
sites in each
mer.
19
Molecular Weight of Polymers
Molecular weight
Number average molecular weight
Weight average molecular weight
Polydispersity
20
w
n
MPD
M=
Number average molecular weight Weight average molecular weight
Polydispersity
Molecular Weight of Polymers
( )
∑
∑=
i
i
i
ii
nN
MN
M
( ) ( )
∑
∑
∑
∑==
i
i
i
ii
i
ii
i
ii
wW
MW
MN
MN
M
2
iii MNW =
Mi: the molecular weight of polymer chain i
Ni: the number of polymer chains that have Mi
Wi: the product of Ni and Mi
21
Mi Ni ni Wi wi
100 5 0.25 500 0.125
200 10 0.50 2000 0.500
300 5 0.25 1500 0.375
Number average molecular weight Weight average molecular weight
Molecular Weight of Polymers
( ) ( )
∑
∑
∑
∑==
i
i
i
ii
i
ii
i
ii
wW
MW
MN
MN
M
2
iii MNW =
20020
4000
5105
3005200101005==
++
×+×+×=nM
2254000
900000
3005200101005
3005200101005 222
==×+×+×
×+×+×=wM
125.1200
225===
n
w
M
MPD
∑=
i
i
ii
N
Nn
∑=
i
ii
iii
Mn
Mnw
( )( )== ∑
∑
∑
i
ii
i
i
i
ii
n MnN
MN
M ( )=∑i
iiMw
ni: number fraction
wi: weight fraction
22
Exercise:
A batch of polyvinyl chloride has
the following molecular
distribution. Based upon the
data, calculate the number
average molecular weight
distribution, the weight average
molecular weight distribution
and the polydispersity.
Molecular weight Range
(g/mole)
ni
5,000-10,000
0.05
10,000-15,000
0.16
15,000-20,000
0.22
20,000-25,000
0.27
25,000-30,000
0.20
30,000-35,000
0.08
35,000-40,000
0.02
Answer:
Mean MW ni niMi
7500 0.05 375
12500 0.16 2000
17500 0.22 3850
22500 0.27 6075
27500 0.2 5500
32500 0.08 2600
37500 0.02 750
21150
wi = niWi/21150
Number Average Molecular Weight
Weight Average Molecular Weight
Mean MW wi wiMi
7500 0.0177 132.98
12500 0.0946 1182
17500 0.182 3185.6
22500 0.2872 6462.8
27500 0.26 7151.3
32500 0.1229 3995.3
37500 0.0355 1329.8
23440
PD = 23440 / 21150 = 1.108
( ) ==∑i
iin MnM
( ) ==∑i
iiw MwM
23
Molecular Weight Distribution for Typical Polymers
Number average
Weight average
Number average
Weight average
Am
ount
of po
lym
er
Molecular weight
Am
ount
of po
lym
er
Molecular weight
Nu
mb
er
of
po
lym
er
ch
ain
Fra
cti
on
of
po
lym
er
ch
ain
If the distribution is broadened to have more contribution from larger molecular weight, the difference between Mn and Mw becomes increased.� The polydispersity increases.
PD=1.0 � monodisperse distribution
The importance of the molecular weight (MW) and its distribution (MWD)
� MW and MWD influence most of the properties of any polymers such as
mechanical, thermal, electrical, optical, transport, solution, interfacial and
thermodynamic properties.
24
Chain configuration (configurational isomer)determined by tacticity of polymer.
Tacticity is simply the way pendant groups are arranged along the
backbone chain of a polymer
Example: Tacticity in Polystyrene
Isotactic
(same side)
Syndiotactic
(alternating sides)
Atactic
(random)
25
isotactic PMMA syndiotactic PMMA atactic PMMA
Once polymer chain has a specific tacticity, it cannot have other tacticities
through the rotation of bond in backbone.
If you really want, You need to break the bonds.
CH2 n
C
CH3
O
O
CH3
Another example polymer of tacticity:
Poly(methylmethacrylate), PMMA
26
Tacticity in Polyvinylchloride
Isotactic Syndiotactic
Atactic
Cl
27
A chain branch is a location on the main-chain backbone where a side group has
been removed and replaced with another “branch” of backbone atoms.
Example: Chain branching in polyvinylchloride
Chain Branching in Polymers
28
Factors Affecting Crystallinity in Polymers (packing polymer chains to form a parallel array)
• The size of the side groups (Polymers with large, bulky side groups
cannot be packed efficiently to form crystals.)
• The extent of chain branching (Hard to form crystals with branched chains)
• Tacticity (easier to establish LRO in isotactic and syndiotactic polymers)
• The complexity of the repeat unit (Polymers with long repeat units are
hard to crystalize because they require more extensive chain segment
motion to establish LRO)
• The degree of secondary bonding (polar side groups provide additional
“driving force” and aid in the formation of polymer crystals)
C
H
H
C
H
H
n
C
H
H
C
H
H
n
CH3
CH2
CHn
Easy to crystallize Relatively easy to c.
Very
hard to c.
29
Tacticity
crystallizable
The complexity of the repeat unit
C
H
H
C
H
H
n
V.S.
The degree of secondary bonding
C
H
H
C
H
H
n
CH3
V.S.
C
O
O CH2
CH2
C
O
On
C
H
H
C
H
H
n
Cl
30
Semicrystalline Polymers
Schematic
Spherulites, aggregates of crystalline and noncrystalline regions. The
Maltese cross is a pattern that develops because of the imagining technique.
Even polymers for which factors are favorable for crystallization such as
polyethylene are never fully crystalline.
Because the macromolecules are highly entangled in the melt and
diffusion rates are low, the chains do not have sufficient time to completely
disentangle during solidification.
31
Structure of Glasses
Example: silica glass
The basic building block
in silicate structures,
amorphous and
crystalline, is the (SiO4)4-
tetrahedron
In the crystal, the tetrahedra are
arranged on a periodic lattice
In glass, the tetrahedra are joined at
the corners. Each oxygen is shared
by two tetrahedra but the resulting
structure lacks long-range three-
dimensional ordering.
32
2-Dimensional Representations of Silicate Structures
Silica glass Crystalline silica
A random network A crystalline structure
33
X-Ray Diffraction for crystalline silica and silica glass
Inte
nsity
0.160.120.080.04 0.20 0.24
Crystalline silica: diffraction
peaks tell crystal structure
Silica glass: no distinct
diffraction peaks because
of the absence of LRO
sin � /�
34
Some Glass Forming Systems
• Elements S, Se, P
• Oxides SiO2, B2O3, P2O5, GeO2, AsO2
• Halides BF2, AlF3, ZnCl2, Ag(Cl,Br,I),Pb(Cl2,Br2,I2)
• Sulfides As2S3, Sb2S3, etc.
• Selenides Various compounds of Tl, Sn, Pb, As, Sb, Bi, Si, P
• Tellurides Various compounds of Tl, Sn, Pb, As, Sb, Bi, Ge
• Nitrides KNO3-Ca(NO3)2 and many mixtures containing alkali and alkaline earth nitrates
• Sulfates KHSO4 and many other binary and ternary mixtures
• Carbonates K2CO3-MgCO3
• Polymers Polystyrene, PMMA, polycarbonate, PET
• Metallic Alloys Au4Si, Pd4Si, (Fe-Si-B) alloys, Al-transition metal rare earths
Requirement: the material should be cooled from the liquid rapidly
enough that crystal structures are given insufficient time to develop.
35
Zachariasen’s Rules for Oxide Glass Formation
• Oxide glass networks are composed of oxygen polyhedra.
• Coordination number of each oxygen atom in the network should be 2.
• Coordination number of each metal atom in the network should be 3 or 4.
• Oxide polyhedra share corners, not edges or faces.
• Each polyhedron should share at least 3 corners.
Example 1: Check whether SiO2 satisfies all the rules
Example 2: Check the B2O3 system
triangular
polyhedron
(BO3)3-
sharing an edge
(not allowed)
sharing a corner
(angle � � 180°)
sharing a corner
(angle � � 180°; it becomes a crystal)�
36
Network Formers and Modifiers
• Network Formers
– SiO2
– GeO2
– B2O3
– P2O5
– As2O5
• Network Modifiers– Li2O
– K2O
– Na2O
– Cs2O
– MgO
– BaO
– CaO
– ZnO
– PbO
Network modifiers tend to break up the 3-D
primary bond network and, decrease the primary
bond density, and therefore, decrease the glass
transition temperature. This helps to reduce the
production cost of glass.
37
Rubbers
CH
2
C
CH3
CCH
2
n
H
Cis-1,4-poly (isoprene)
Natural Rubber
Synthetic Rubber
CH2
CH CH CH2 n
CH2
CH CH CH2 n
CH2
CH CH CH2
CH2
CH CH CH2
CH2
CH CH CH2
S S
S S
CH2
CH CH CH2
Poly (butadiene)
Sulfur bridge
Sulfur cross-link
38
Rubbers and Elastomers
Most rubbers are elastomers, materials that can be deformed several
hundred percent and recover completely.
Thermoset Elastomer Thermoplastic Elastomer
Conventional thermoset polymer
1 cross-linking /1000 mers
� Light cross-linking
�Flexible rubber
�e.g., rubber band
1 cross-linking / 10 mers
� Heavy cross-linking
� Hard & brittle material
� e.g., automobile tires
CH2
CHx
CH2
CH CH CH2 y
CH2
CHz
Poly (styrene)
block
Poly (styrene)
block
Poly (butadiene)
block
Morphology
SBS triblock copolymer
No chemical cross-linking
� It can be melted and
solidified.
Islands of hard styrene
blocks take the role as
crosslinking points.
Sea of soft butadiene part
has elastomeric property.
39
The Influence of Temperature on the Elastic
Modulus of a Glassy Polymer
Amorphous
uncrosslinked polymer
Influence of increasing
percent crystallinityInfluence of increasing
crosslink density
With the glassy-rubbery transition at �, the
modulus reduces by
several orders of
magnitude.
The modulus of the plateau at � �increases with crystallinity
density, and modulus
remains high until �.
The modulus of the plateau at � � increases with
crosslink density, and
modulus remains high until
degradation.
40
Origin of Rubber Elasticity
L = distance between chain ends.
�: length of a carbon-carbon bond
�: number of C-C bonds in the chain
� � 70.5°
Random coil
configuration
An elastomer is capable of sustaining a tensile deformation
perhaps 10 or more times its original length. Why?
���� � �� cos�
2
� � � �1 � cos �
1 � cos �
maximumstrain ������� 1. The value can range from 10 to 300
�/2
41
Why rubber elastomers like to stay as random coils?
Consider the entropy ' (a measure of randomness of a system). The (Gibbs
free) energy of the entire system ( � ) � ' should reach the minimal value
for the thermodynamically favored state.
Only one conformation is
possible for the fully
stretched structure
→ lower-entropy
→ higher energy
→ not stable
Many equivalent
conformations for the
same ends separation
→ higher-entropy
→ low energy
→ more stable
Positive force is required to extend the length of a rubber band.
Removal of the force → rubber molecules return to their coiled conformation.
42
Homework problems for Chapter 6
1. Consider a sample of polyvinylchloride (PVC) that is composed of only two types of chains. 90% of the chains in this sample have a degree of polymerization (n) of 10,000, and 10% of the chains have n = 100,000. Calculate the polydispersity (PD) for this polymer sample.
2. Which polymer is more likely to be crystalline: [-CH2-CF2-]n or [-CH2-CHF-]n?
3. Predict which polymer in each pair listed is a better glass former (i.e., a worse crystal former): (a) Isotactic [C2H3(CH3)]n vs. syndiotactic [C2H3F]n; (b) Atactic[C2H3(CH3)]n vs. isotactic [C2H3Cl]n?
4. Calculate the molecular weight of a mer of cellulose. If the molecular weight of cotton were 9000 g/mol, how many mers would be joined? The structure of cellulose is shown.
Please make sure that you understand the exercises on p.8, p.21 and p.22.
43
5. How much weight can an initially 10-kg sample of polybutadiene rubber gain by complete reaction with oxygen? Assume that on average a single crosslink consists of a chain of two oxygen atoms. The structure of polybutadiene before crosslink is shown.
6. Why are CaO and Na2O added to SiO2 in most commercial oxide glasses, such as window and beverage glasses?
7. A glassy sample of unoriented atactic polystyrene has a molecular weight of 150,000 g/mol. What is the approximate separation of a molecule’s chain ends? The
C-C bond length is 1.54 +, and the structure of polystyrene is given below.
[C2H3(C6H5)]n
44
Solutions to Homework problems for Chapter 6
1.
2.
(Note: ,- in this solution means .- in lecture slides)
45
3.
4.
46
5.
6.
47
47
7.
Atactic polystyrene does not crystallize. It is a vinyl polymer with a backbone of
all C and a side group of benzene ring. The chain end separation is governed by
the random coil of long molecule.
The molecular weight of the mer [C2H3(C6H5)] is 12x8+1x8 = 104 g/mol. So for a
molecular weight of 150,000 g/mol, the number of mers in a long chain is
150,000/104 = 1442.
For each mer there are two C-C bonds. Using the formula
we find the end-to-end separation is roughly:� � � �
1 � cos �
1 � cos �
� � � �/0123 4
/5123 4� 165 +
� �1.54 +: length of a carbon-carbon bond
� � 1442 × 2 � 2884: number of C-C bonds in the chain
� � 70.5°, so /0123 4
/5123 4� 2
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