MSE 2001- Chapter 6 Ppt

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