1-5 polymers & ceramics 12

2010-2011 S1MP2004, MP2304, MP3104, MP3304

Manufacturing & Materials

A/P Zhou Wei

Web: http://www3.ntu.edu.sg/home/mwzhou/

http://www3.ntu.edu.sg/home/mwzhou/

School of MAEResearch and teaching organized into

Knowledge Domains (KD’s). MP2004 is aligned with KD of Manufacturing Engineering Division:

• Materials,• Forming,• Joining/assembly,• Machining.

Lathe

Mild Steel


tool

Interplay

between

machining &

materials

Arc Welding

Mild Steel


seam

Interplay

between

welding &

materials

Metals

Ceramics Polymers

Metal-PolymerCompositesMetal-Ceramic

Composites

Ceramic-Polymer Composites

Materials

Lecture 1

Revision of key concepts

Allotropic - PolymorphicCarbon.

Graphite Diamond Buckminster- fullerene

Periodic Table

http://en.wikipedia.org/wiki/Periodic_table

BondingThree types of primary bonding:(1) Ionic (I) – metals – nonmetals (2) Covalent (C) – nonmetals-nonmetals,(3) Metallic (M) – metals.

Secondary bonding(1) Van der Waal’s (VDW) (2) Dipolar (D)(3) Hydrogen –Bonding (HB).

Nobel Gases – energetically stableGases Electron Orbits Electrons per shell

2 (K-shell)

10 (K, L-shells)

18 (K, L, M-shells)

e-

e-

e-

He42

Ne2010

Ar4018

Primary Bonding(1) I

(2) C

Na Cl Na+ Cl-

(Ne) (Ar)

Strong electrostatic force

O O O2

(Ne) (Ne)

Primary Bonding(3) M

Na

Valence e-

Na Na Na

Valence e-

(conduction e-)(Ne)

Secondary Bonding(1) VDWAs atoms vibrate may temporarily loose

electrical symmetry → dipole.

(2) DPermanent dipoles due to asymmetry.

+ -

HCl

+ -

Secondary Bonding(3) HB• Strongest secondary bonding type.• Occurs when H covalently bonded to F, O,

and N.• High melting point of H20 due to HB.

+

+-

+

+-

Defects

For effective bonding atoms (ions) need to be surrounded by maximum number of nearest neighbors.

Unit cell

∞ Single Crystal, defect free

Each atom has max. no. of nearest neighbors & optimum separaration. (no strain ). Min. energy.

⊥

Single Crystal - defectsSurface Vacancy Interstitial Substitution

Dislocation

High energy

Poly-Crystalline -diffusion

Grain boundary

High energy

Boundary EnergySolid Solution

•Atoms without max. no. of nearest neighbors in state of high energy.•Also elastic strain.

Boundary EnergyOrdered Phase at 30 °C

Boundary area=69 units

Boundary Energy


Ordered Phase at120 °C

Boundary energy decreases sinceoriginally high.

Boundary Energy


Coherent Phase at30 °C

Boundary Energy


Coherent Phase at 120 °C

Boundary energy unchanged sinceoriginally low.

Stress (σ) – Strain (ε)

Brittle

σ

εDuctile

ε

σ

TS

ToughnessToughness

××

Actual strength of metals less than theoretical strength. Why?

Plastic Deformation

Plastic Deformation

σ

σ

Slipplane

Six bonds break at same time!

Dislocations

σ

σ Slip plane

σ

σ

Only one bond break!

Two main deformation mechanisms:(1) Dislocation motion(2) Twinning

Plastic Deformation

Crystallography• Seven crystal systems.• Metals mainly Body Centered Cubic (BCC),

Face Centred Cubic (FCC), or Hexagonal Close Packed (HCP).

• Ceramics rarely simple structures.

a a a

cBCC FCC HCP

Slip Systems• Generally, dislocations move in directions

where atom separation is small.• All permutations of these “easy”

directions - part of slip system.• Greater number of (active) slip systems,

greater ductility of material.

BCC – [111]

Ductile or Brittle?• Energy required to move dislocation

depends exponentially on distance moved.• Almost all FCC metals are ductile (many

active slip-systems).• Almost all HCP metals are brittle (few

active slip-systems).• For BCC it depends on temperature and

metal.

A Cu-60wt% Ag alloy is prepared.

• What phases present at RT?• What are phase compositions?• What are relative amounts of each phase present?

Binary Phase Diagram Revision

×

Composition (wt % Ag)0 20 40 60 80 100

1000

800

600

400

200

α+β

α+Lβ+L

L

αβ8.0 91.271.9

Tempe

ratu

re (

°C)

×

6 wt% Ag 95 wt% Ag

α=8 wt% Ag - 92 wt% Cuβ=91.2 wt %Ag – 8.8 wt% Cu

Composition (wt % Ag)0 20 40 60 80 100

1000

800

600

400

200

α+β

α+Lβ+L

L

αβ

8.0 91.271.9

Tempe

ratu

re (

°C)

%3882.91602.91% =

−−=α

×

6 wt% Ag 95 wt% AgComposition (wt % Ag)0 20 40 60 80 100

1000

800

600

400

200

α+β

α+Lβ+L

L

αβ

8.0 91.271.9

Tempe

ratu

re (

°C)

Summary. α + β phases present at RT. α=8 wt% Ag, β=91.2 wt % Ag.. α=38%, β=62%

α-phase

β−phase

∀≡ phase (takes as long as is necessary)

• Almost no diffusion in solid state.

AnisotropyPolycrystalline metal with equal sized grains (equiaxed) – isotropic.

Isotropic Anisotropic

KIC - materials susceptibility to brittle fracture.

Fracture Toughness, KIC

Critical stress material can withstand before fracture:

KIC-Steel ~90, KIC-Al ~25, KIC-Glass~0.8, KIC-

plastic ~1 MPa√m

aK IC

c πσ

1.1≤

2a

a

σc

σc

What is creep?• Creep - time-dependent (permanent) deformation of materials subjected to constant stress.

• Limiting factor in lifetime of devices.

• Important for metals when operating-temperature > 0.4 Tm (Tm =absolute melting temperature).

What is creep?

time

ε.

×

Secondary

Primary

Tertiary

Operation preferred in secondary (steady-state) creep.

Rupture

What is creep?Creep reduce by:

1. Increasing Tm.2. Increasing elastic modulus, E.3. Increasing grain-size.4. Alloys - have substitutional impurities with low-diffusivity at high-temperatures (such as W).

Metastable

Examples• Fe3C (cementite),• Martensite,• Amorphous materials.

EE

Stable Metastable

Lecture 2

Polymers

How Plastic Bottles are Made

http://www.youtube.com/watch?v=T01i_vp2mJE

Polymer Molecules• Atoms bonded by covalent bond. • Gigantic molecules made from repeating structural units.

Monomer unit

Polymer

-c-c-c-c-c-c-c-c-c-c-c-c-| | | | | | | | | | | |H H H H H H H H H H H H

| | | | | | | | | | | |H Cl H Cl H Cl H Cl H Cl H Cl

Polymer Molecules

Macro-Molecule (PVC)

Small-Molecule (CH4)

H – C - H|H

H|

– C - C|H

H|

|H

Cl|– C - C

|H

H|

|H

Cl|

– C - C|H

H|

|H

Cl|– C - C

|H

H|

|H

Cl|

– C - C|H

H|

|H

Cl|– C - C

|H

H|

|H

Cl|

|H

H|

– C -

5-atoms

10,000-atoms

MonomersMonomers must have multi-functional reactive bonds or chemical groups (minimum functionality is two, i.e. di-functional)

• Mono-functional:– Ethanol CH3CH2-OH

• Di-functional:– Ethylene diol HO-CH2CH2-OH

• Tri-functional– Glycerol HO-CH2-CH(OH)-CH2-OH

Condensation Reaction

Small molecule eliminated (e.g. H2O).

HO-CH2CH2-OH + HO-CH2CH2-OH→ HO-CH2CH2-O-CH2CH2-OH + H2O

HO-CH2CH2-OH + HO-CH2CH2-O-CH2CH2-OH →HO-CH2CH2-O-CH2CH2-O-CH2CH2-OH + H2O

Plastics?Plastics fall into two categories.

(1) Pure polymer (e.g. high density poly-ethylene).

(2) Multiple-blends with fillers, additives, etc.

Mers

C HHH

CH

HCR

H

HPolyethylene (PE)

General vinyl polymer – Poly vinyl mer

Polypropylene (PP)Polystyrene (PS)

when R is → ClPolyvinyl chloride (PVC)

MorphologyMaterials categorized according to their morphologies.AmorphousNo long-range order, i.e. random coils or irregular packing of chains.

Morphology

Perfectly Crystalline

Regular 3-D arrangement of molecular chains.

MorphologySemi-Crystalline

Regions of amorphous & perfectly crystalline in co-existence.

crystallite

(1) Linear

• Repeat units held by strong covalent bonds.• Chains long & flexible (1-D).• Different molecules held together by weaker secondary forces.Examples PE, PVC, PS, PMMA.

(2) Branched

•Introduced during side polymerisation.•Chains packing efficiency ↓ due to steric (size) effects.•Polymer density ↓

Thermoplastics• Polymers soften upon heating & made to flow when a stress is applied. • When cooled, they will solidify to a solid or rubbery solid.

Can be recycled.

Solidheating

Liquid (melt)cooling

Forming Processes•Widely used in manufacturing plastic products by •Injection molding•Thermoforming•Extrusion

(3a) Cross-linked

• Adjacent linear chains joined to one another by strong covalent bonds.• Achieved by growth at high temperature (irreversible).

Example Rubber elastic material cross-linked by a method known as vulcanization.

(3b) Network• Tri-functional (or more) monomer units form three or more covalent bonds resulting in a 3-D networks.• Achieved by growth at elevated temperature.

Example: Epoxies.

Thermoset• Polymers which become hard and rigid upon heating (irreversible).

• Chain motion restricted by high degrees of cross-linking.

• Harder, stronger, more brittle but with better dimensional stability compared with Thermoplastic Polymers.

Elastomers• Mechanical properties like natural rubber.• Linear or cross-linked.• Chains extended upon deformation but are prevented from flow by cross-links or physical domains.•Returns to original shape on removal of σ.

Domain

LinearChain

Classification

Homopolymer:

• One type of monomer (A) used to build polymer.

• Structure can be represented by multiple repetition of a single repeat unit.

Examples : PE, PTFE, PS, PVC, ...

A AAAA n

Copolymer• Polymer structure made up of two (or more) monomer units.•Polymer has combined properties of various monomers. Types of Copolymer

Random Copolymer - poly(A-ran-B) :

Two different units (A and B) randomly dispersed along chain

ABAABAAABBAAAB

CopolymerAlternating Copolymer - poly(A-alt-B):

ABABABABABABAB

Block Copolymer - polyA-block-polyB :

AAABBBBBAAABBBBB

CopolymerGraft Copolymer:

• chains of one kind are attached to backbone of different polymer.

• known as polyA-graft-polyB.

A AA A AA A AA

BBB

BBB

BBB

BBB

BBB

Lecture Theatre • Distribution of students, ages 19-29 years. • Can talk about number fraction of

students with age in range 23-25. i.e. number of students in this age range / total number of all students present.

• Alternatively, can talk about weight fraction of students in age range 23-25. i.e. weight of students in this age range / total weight of all students present.

Molar Mass• Measures size (or weight) of polymer

molecule. • Defined as an average value with a wide

distribution of polymer chain size.• Represents statistical nature of

polymerization. Main averages:

•Number-average molar mass, Mn•Weight-average molar mass, Mw

Number versus weight averageDistribution of molecular weight

Molecular weight

Mn

Mw

Amou

nt o

f Po

lymer

s

Poly-DispersityRatio of two measures of molecular weight called Poly-Dispersity (PD):

• PD=1.0 - all molecules have same weight! Unusual for polymers.• ↑ in poly-dispersity ⇒ ↑ width of molecular weight distribution

n

W

MMPD =

Significance of Molar Mass• Chain ends considered as defects in polymers since they have no covalent bond to transmit strength.

∴ as molecular weight ↑, tensile strength ↑ rapidly and gradually levels off.

↓ in chain ends

↑ in molecular weight ↑ in chain length

Example

Calculate:(a) Mn, (b) Mw, and (c) nw (weight averaged Degree of Polymerization.

MolecularWeight Range

(g/mol)wixi

8,000-16,00016,000-24,00024,000-32,00032,000-40,00040,000-48,00048,000-56,000

0.050.160.240.280.200.07

0.020.100.200.300.270.11

(a) Calculate Mn

Molecular wt Range Mean,Mi xi xiMi

8,000-16,000 12,000 0.05 60016,000-24,000 20,000 0.16 3,20024,000-32,000 28,000 0.24 6,72032,000-40,000 36,000 0.28 10,08040,000-48,000 44,000 0.20 8,80048,000-56,000 52,000 0.07 3,640

Mn = ΣxiMi = 33,040 g/mol

Molecular wt.Range Mean,Mi wi wiMi

8,000-16,000 12,000 0.02 24016,000-24,000 20,000 0.10 200024,000-32,000 28,000 0.20 560032,000-40,000 36,000 0.30 10,80040,000-48,000 44,000 0.27 11,88048,000-56,000 52,000 0.11 5720

Mw = ΣwiMi = 36,240 g/mol

(b) Calculate Mw

For PP, molar mass of repeat unit

= 3(mC) + 6(mH)

= (3×12 g/mol) + (6×1 g/mol) = 42 g/mol

And since , nw = 863Mwnw = m

(c) Calculate nw CH

HCC

H

HHH

Configurations & ConformationsGeometric detail of how each unit is added & shape of chain are important factors.

- Refers to placement of successive repeat units into chain

Chain Configurations:

- Chain can take on ∞ number of shapes by rotation about backbone bonds, this gives rise to different conformations.

Chain Conformations:

Molecular ConfigurationArrangements of atoms fixed by covalent bonds in molecule & cannot be altered unless bonds are broken.Configurations:

• Order (head-to-head, head-to-tail, tail-to-tail) • Stereoisomerism (Isotactic, Syndiotactic, Atactic)

Order in Molecules

Three ways adjacent bonds can be formed :

Considering vinyl molecule

• Head-to-Head• Head-to-Tail•Tail-to-Tail

CH

HCR

HHead Tail

Order in Molecules

Tail-to-Tail Head-to-Tail

CR

HC

H

HCR

HCH

HCH

HCR

HCH

HCR

H

• Head-to-tail - more energetically favourable due to lack of steric effects & polar repulsion from similar side groups.• HT configuration dominates (never 100%).

CH

HC

R

HCH

HCR

H

Head-to-head

StereoisomerismIsotactic

R groups lie on same side of zig-zag plane.

Atactic R groups on random position, no regularity

R groups alternate around plane.

Syndiotactic

C C CCC C CC

HH H

H HH

HH

HR R

H HR

HR

C C CCC C CC

HH R

H HH

HR

HR H

H HR

HH

C C CCC C CC

HH R

H HH

HH

HR H

H HR

HR

Tacticity of PS

Isotactic Syndiotactic Atactic Never 100 % tactic - in a given polymer chain, usually a combination of configurations!

Molecular Shape• Once polymer molecule formed, its configuration is fixed but single polymer bonds not “rigid”.

Some degree of freedom :

Molecule shape will affect thermal + mechanical properties.

•Rotation•Bending

Rotation & Bending

Bending

Rotation

109°

C-C bond length, d=0.154nm

Bending & RotationRotation & bending depends on :(1) Type of bond

(2) Type of main chain

• single bond - can rotate• double/triple bond - rigid

• bulky main chain restricts rotation

O C CO

C CC C

Bending & Rotation

(3) Type of side group

• bulky side groups act as stearic (size) hindrance. • restricts rotation.

C CC C

Shape• Each single bond capable of rotation.• Chain length less useful to characterise polymer shape.

r

Shape

• for linear flexible chains, distance separating chain ends is end-to-end distance, r.

• More useful descriptor for polymer shape as it describes both size & shape of chain.

End-to-End distance, , where N – number of C atoms in polymer backbone

Ndr =

Man in the Mirror

http://www.youtube.com/watch?v=KtT78oI3zDw

Lecture 3

Polymers

Crystalline Polymer

In very large molecules (polymers), ability to crystallise depends on

•Regularity of structure

•Intermolecular bonding groups.

Single Crystal of PE:

• Requires very special growth conditions.• Engineering polymers not single crystal.

Single Crystals

5 µm

Amorphous Polymer• Polymer that is completely non-crystalline.

• Structure can be thought of as simply frozen polymer liquids.

• Many engineering polymers are amorphous.

Examples: are rubber, atactic PS, epoxies.

Semi-Crystalline (SC) Polymers• Most polymer molecules partially crystallize due to size, stereo-regularity, geometrical reason.• Crystalline regions mixed within amorphous material.

Crystallite

Amorphous Most engineering

polymers SC.

SC Polymers• Bulk polymers - generally partially crystalline.• Consist of small crystalline regions (crystallites) & amorphous regions.

Reasons:• Polymer are macromolecules (long chains), hence low diffusion rates. • Macromolecules highly entangled in melt & do not have time to disentangle during solidification.

SC Polymers - spherulites

CrystalliteAmorphous

Nucleus

• 10 nm thick radial layers.• Chains oriented ⊥ to radius of structure.

Polymer CrystalinityAmorphous

polymerSC

polymerCrystalline

polymer↑ in crystallinity

Density : crystalline polymer > amorphous polymer (chains closely packed in crystalline polymer).

s, c & a refer to specimen, totally crystalline polymer & totally amorphous polymer.

% Crystallinity ( )( ) 100×

−−=

acs

asc

ρρρρρρ

Melting Temperature

• Melting - transformation of polymer crystal from solid with highly ordered structure of aligned molecular chains to a viscous liquid with highly random molecular chains.• Occurs at melting temperature, Tm.• Takes place over range of temperatures, not possible to define single melting temperature for a polymer.

Melting CharacteristicsCharacteristics of polymer melting different from other materials :

• Melting depends upon specimen history & temperature of crystallization.• Melting depends upon rate at which specimen is heated.• Differences due to peculiar morphology of polymer crystals.

Annealing

T(°C)

time0

Crystallite

Amorphous

Annealing : temperature below melting point of material

• Crystallites very thin.• Strong dependence of Tm on crystal thickness.• Surface energy ↑ with decreasing crystallite size.• Tm ↓ with decreasing size

Melting Characteristics

Melting

25% chainunbonded

5% chainunbonded

Melting

Annealing

T(°C)

time0

Crystallite

Amorphous

Annealing : as crystallites grow, their melting points increase

T(°C)

t0.1 hrs

Effect of Heating Rate

T(°C)

t 10 hrs

(a) has lower melting point compared to (b) due to annealing. This is very unusual behavior.

(a) (b)

Effect of Heating RateMelting dependent on heating rate since annealing takes place when crystalline polymer heated and melted. Decrease in heating rate

• Increase in annealing effect• Increase in lamellae thickness• Increase Tm

Annealing : heat treatment providing movement of polymer chains by diffusion (depends on temperature & time).

Glass Transition

• As polymer is cooled it becomes rubbery, then a relatively hard and/or elastic polymer glass is obtained!• Temperature at which polymer changes from rubber to glass is Glass Transition Temperature, Tg.

•Polymers that can easily deform will have low Tg.

Polymer CrystallinityAbility of polymer to crystallize depends on molecular ordering of polymer chains.

(1) Side group (bulky, polar, branches)(2) Molecular structure (type of polymer, isomerism)(3) Thermal history (cooling rate) and applied stress.

Factors affecting chain alignment:

Side Groups Chains with bulkier side groups will have less tendency towards crystallization.

Crystallize easilyCH

HCH

H

PE

CF

FCF

F

PTFE

difficult tocrystallize

PSCH CH2

Chains with hydrogen bonding promote crystallization.

CH2 CN CH2 CH2 CH2 CH2 CH2N

CH2 NC CH2 CH2 CH2 CH2CH2 C

O H O

H O H

CH2 CN CH2 CH2 CH2 CH2 CH2N

CH2 NC CH2 CH2 CH2 CH2CH2 C

O H O

H O H

Repeat unitNylon

Side Groups

Molecular StructureCrystallinity ↑ with increasing regularity (i.e. reduced randomness) in structural arrangement.

• Linear Polymers → Crystallizes easily

•Branched Polymers → Partially crystalline

•Network & Cross-linked Polymers → Amorphous

Molecular Structure

• isotactic & syndiotactic polymer - crystalline.• atactic polymers - amorphous.

Isomerism:

Copolymer:More irregular & random monomer arrangement is less crystalline.• Alternating & Block copolymer → Crystallisation• Random & Graft copolymer → Amorphous

Important Point

•Tm only relevant to Crystalline Polymers

•Tg only relevant to Amorphous Polymers. •If both Tg & Tm are observed, polymer must be Semi-crystalline.

Factors affecting Tm High melting points associated with

• highly regular structures • rigid molecules • close packing capability • strong inter-chain attraction

Examples• Aromatic polyesters: high Tm because of relatively high chain stiffness.• Polyamides: high Tm because of inter-chain HB.

Factors Affecting Tm

Tm dependent on:

(1) Molecular Weight(2) Backbone (3) Side groups

• At Tm, whole polymer chains are able to translate from one position to another. • Factors affecting interaction between chains will affect Tm.

Molecular Weight↓ molecular weight ⇒ ↓ chain length

↑ in chain ends ⇒ ↑ in defects ⇒ ↓ in Tm

High Tm Low Tm

BackboneMost important factor affecting Tm.

Chemical Structure:

(1) Nature of backbone

• Determines stiffness of main polymer chain.• Controls ease at which rotation can occur about chemical bonds along chain.

Backbone

Flexibility decreasing groups:

⇒ ↑ Tm

• Bulky main chain:

• Unsaturated bonds:

• Polar groups:

phenyl

NHCOamide

C C C Cdiene

Flexibility increasing groups:O , O O , CO O

⇒ ↓ Tm

Backbone

Repeat Unit Tm/KCH2 CH2

CH2 CH2 O

CH2 CH2 CO O

CH2 CH2

CH2 CH2 CO NH

410340395

670603

Side GroupsType & size of side groups affects rotation about bonds in main chain.

Consider vinyl polymer:

CH2 CHR

If R = H, (a flexible group) i.e PE,

(CH2CH- H)-

Flexibility restricting groups:

CH3

⇒ ↑ Tm

Cl CN

Polar side groups

Bulky side groups

Side Groups

Repeat Unit Tm/KCH2 CHR

CH2 CH3

CH3

CH2 CH2 CH3

CH2 CH(CH3)2

460398351508450

Side group (R)

Side Groups

410H

Not as clear cut: balance betweenflexibility and size

Chain BranchingIncrease in branching • ↑ in defects (↓ in packing)• ↓ in intermolecular forces between polymer chains• ↓ in Tm

Example: HDPE has a higher Tm than LDPE.

Glass Transition, Tg• Tg depends upon rate at which temperature is changed, i.e. rate of heating /cooling.• Lower heating rate, lower Tg

•At Tg, polymer chains frozen in position become free to rotate & translate. • Factors that affect chain rotation(molecular rigidity) & move will affect Tg.

T(°C)

t0.1 hrs

Effect of Heating Rate

T(°C)

t 10 hrs

(a) has higher Tg compared to (b). This is very common behavior.

(a) (b)

Factors affecting, Tg

Tg depends on:

(1) Backbone

(2) Side groups

(3) Molecular weight

(4) Molecular structure (Isomerism and type of polymer)

(5) Additives

Nature of Backbone• Chain flexibility governed by nature of chemical groups which constitute main chain (similar to Tm).• Groups that reduce ease of rotation will increase Tg.

Repeat Unit Tg/KCH2 CH2

CH2 CH2 O O

140-270206357

353CH2 CH2

Side Groups(i) Bulky side group:• Large side groups give greatest stiffening effect.• Flexible side groups have less stiffening effect.(ii) Secondary bonding:

• Polar groups increase Tg because of restriction in rotation due to dipole interactions.

Tg(PVC)>Tg(PP)

• HB & VDW forces between chain ↓ flexibility & increase Tg.

Side GroupsRepeat Unit Tg/K

CH2 CHRCH2 CH3

CH3

CH2 CH2 CH3

CH2 CH(CH3)2

250249233323373

Side group (R)

ClOHCN

354358370

Not as clear cut: balance betweenflexibility and size

BranchingSmall number of branches

• Small number of branches tend to ↓ Tg • Increase in free volume ⇒ increase in rotation

Branching

• Long branches tend to ↑ Tg

• Long branches hinder rotation ⇒ ↑ in chain rigidity ⇒ increase Tg

Generally

Molecular Weight

↑ in molecular weight ⇒ ↑ in Tg

• Polymer of low molecular weight have greater number of chain ends in given volume compared to high molecular weight.

• Since chain ends are less restrained, they have greater mobility at a given temperature.

Molecular StructureCross-linking• Slight cross-linking will have no effect on chain rigidity.

• High density of cross-links results in decrease in chain flexibility ⇒↑ Tg

•Tg may not occur in highly cross-linked materials!

Plasticisers

• Small molecules which get in between

polymer chains.

• Molecules that space out chains from one

other ⇒Tg is lowered by use of

plasticizers.

•How do plasticizers affect Tm?

Lecture 4

Polymers

σ-ε of Brittle PolymerTypical σ-ε curve for glassy polymer, e.g. PS:

CompressionTension

Stre

ss

Strain

• Initially elastic deformation, σ proportional ε.

Typical σ-ε curve of PP (in tension):Elastic Deformation:

• Hooke’s law obeyed.

σ increase with ε up to yield point.

Yield:

Yield Pt

Stre

ss

StrainYield of polymers is ~ 5 – 10 % (metals ~ 0.1 %)

σ-ε of Tough Polymer

Plastic Deformation:

TensileStrength

Stre

ss

Strain

• Deformation cannot be fully recovered.• Cold drawing (extension at constant stress)• Polymer strain hardens and ruptures.

Strain hardening

Cold draw

σ-ε of Tough Polymer

• Mechanical properties controlled by molecular structure.• Material made up of network of cross-linked polymer chains with individual lengths of chain in random conformations.

Stre

ss

Strain

• Elastomeric • Rubber-like elasticity• Large recoverable ε at low σ level.

σ-ε curve (in tension):

σ-ε of Elastomers

Deformation of Single Phase Polymer Crystals

Elastic Deformation

(1) Polymer glasses: (Modulus ~106 Nm-2)

Involves bending & stretching of strong covalent bonds on polymer backbone as well as displacement of adjacent molecules which is opposed by relatively weak secondary (VDW) bonding.

•Elastic Deformation

(2) Polymer crystals:(Modulus ~1011 Nm-2 // to chain direction, Modulus ~106 Nm-2 ⊥ to chain direction)

// to chains:• Deformation involves stretching of strong covalent bonds and changing of bond angles.


(2) Polymer crystals:(Modulus ~1011 Nm-2 // to chain direction, Modulus ~106 Nm-2 ⊥ to chain direction)

⊥ to chains:• Deformation opposed only by weak secondary VDW or HB.


Plastic Deformation

• Polymer molecules remain relatively undistorted.• Deformation involves sliding of molecules in directions // or ⊥ to chain axis (breaking only VDW forces).


Elastic Deformation

(3) Elastomers: (Modulus ~106 Nm-2)

Amorphous polymer (>Tg) will behave like viscous liquid & normally flow under its own weight.

Unstressed state:

Elastomer is amorphous & composed of molecular chains that are highly twisted, kinked and coiled.


Upon application of load:• Partial uncoiling, untwisting, straightening & elongation of chains in stress direction.• Viscous flow takes place by uncoiling of chains in cross-linked network & extent of flow depends on degree of cross-linking.• Properties controlled by nature of cross-linked network.


Deformation of Multi-Phase Polymers – SC Polymers

• Most SC polymers behave like composites (two-phase materials)

• Increase in modulus due to combined effect of amorphous & crystalline regions.

• Effective crystal modulus depends on (a) proportion of crystalline material, (b) size, (c) shape & (d) distribution of crystals.

Mode of Fracture:

• Thermoset - Brittle (covalent bonds in network/cross-linked structure severed.)

• Thermoplastic - Ductile & brittle

Ductile-to-brittle transition occurs when:

• ↓ in temperature (significantly < Tg)• ↑ in strain rate

Fracture

Mechanical Properties

(1) Polymer structure (Molecular weight, cross-linking, chain

stiffness)(2) Processing

(Mechanical & thermal treatment)(3) Application / Testing conditions

(temperature & strain rate dependence)

Depend on:

Degree of Crystalinity• Crystalline regions ⇒ chains aligned• Extensive secondary bonding (intermolecular bonding)

• Amorphous regions ⇒ Chains misaligned• Secondary bonding less prevalent.

Semi-crystalline polymers:

• TS ↑ with ↑ degree of crystallinity

Degree of Cross-linkingCross-linking involves formation of strong covalent bonds between individual polymer chains.

Natural Rubber:

Cross-linking ↑ strength of rubber

PropertyRaw

RubberX-linkedRubber

Tensile StrengthElongation at break (%)

3001200

3000800

Chain StiffeningPolymers with stiff chains are stronger than those with flexible chains.

Stiffen methods:

• Double or triple bonds• Bulky group on backbone

1.Stiff backbone

• Bulky side groups• Polar bonds

2.Side Groups

Testing ConditionsPlastic deformation - strong dependence on testing rate & temperature.

Temperature:At constant , yield stress decreases with ↑ temperature because chains flow/slip.

• reduction in tensile strength• enhancement of ductility• decrease in elastic modulus

↑ in temperature

ε̇

For amorphous polymer, yield stress falls ~ linearly to zero at Tg (polymer glass becomes rubber)

Temperature:

• Yield stress → 0 at Tm for SC polymer.

• Above Tg, material gains strength from crystalline regions.

SC polymer:

Testing

Temperature

SCCross-linked

TmTg

Rubbery plateau

Log

Mod

ulus

Amorphous

Strain Rate:

At constant temperature, ↑ in will lead to ↑ in yield stress due to ↓ in response time for chains.

Environment such as water, oxygen, organic solvents, etc.

Other:

Testing

ε̇

Viscoelasticity• Viscoelasticity distinctive to polymers.

• Mechanical behaviour in between that of an elastic solid and a viscous liquid.

Low temperature or high strain rates:→ Elastic

High temperature or low strain rates:

→ Viscous

Creep LoadingConstant σ applied to a polymer at time t = 0 & ε increase rapidly at first, slowing down over longer time period.

time

σ

Stress system Strain system

time

ε

Elastic solid

Polymer Viscous liquid

Stress Relaxationε in polymer held constant & σ decays slowly with time.

Strain system Stress system

time

ε σ

time

Elastic solid

Polymer

Viscous liquid

Viscoelastic Stress Relaxation

Size of σ relaxation modulus dependent on temperature & time:

• E(t) decreases with increasing t.• E(t) decreases with increasing T.

• σ required to maintain a constant ε found to decrease with time.• Under isothermal condition, at constant ε0.time dependent stress relaxation modulus given by: ( ) ( )

0εσ ttEr =

Viscoelastic Creep• Deformation significant even at room temperature & under modest σ < yield strength.

• Under isothermal condition, constant stress applied, σ0, time dependent creep modulus given by:

( ) ( )ttE oc ε

σ=time dependent strain

Viscoelastic Creep

Creep modulus dependent on:

Temperature - Ec(t) → 0 with ↑ temperature ⇒ creep ↑

Crystallinity – Ec(t) ↑ with ↑ crystallinity⇒ creep ↓

Temperature Dependency of ErFive regions:(1) Glassy• At lowest T, material glassy & brittle.

• Er ~ equal to elastic modulus.

(2) Leathery (Glass transition)

• Er ↓ by 103 in 20 oC.• Deformation is time dependent & not totally recoverable on release of applied load.

Temperature (°C)

E r

Glassy

Leathery

RubberyRubber flow

Viscous flow (L) TmTg

104

103

102

10

1

10-1

10-2

10-3

10-460 80 100 120 140 160 180 200

(3) Rubbery Plateau

• Deforms in rubbery manner.• Consist of viscous & elastic components

(4) Rubbery Flow• Gradual transition into soft rubbery state(5) Viscous Flow

• Modulus ↓ dramatically with ↑ temperature• Chain segment vibration is independent of rotational motion.

Temperature Dependency

Example 1Is it possible to have a PolyMethyl MethAcrylate (PMMA) homopolymer with the following molecular weight data and a weight-average degree of polymerization of 585? Please justify your answer.

Example 1

Example 1MW Range

(g/mol)Mi wi Mi wi

8,000-20,000 14,000 0.01 140

20,000-32,000 26,000 0.05 1,300

32,000-44,000 38,000 0.12 4,560

44,000-56,000 50,000 0.25 12,500

56,000-68,000 62,000 0.27 16,740

68,000-80,000 74,000 0.21 15,540

80,000-92,000 86,000 0.09 7,740

molgwwMi

ii /520,58=Σ

Σ

Example 1Weight-average degree of polymerisation is 585, ∴molecular weight of this polymer mer is 100 g/mol.

molgnMmw

w /100585

58,520 ===

Example 1

Examine the mer.

( ) ( ) ( )( )100

21681512=

×+×+×=m

Yes, possible!

Example 2

An experimental poly-propylene sample has only ten polymer chains present. Four molecules have a degree of polymerization of 2, three molecules have a degree of polymerization of 3, and three molecules have a degree of polymerization of 7.

Example 2Sketch the mer unit.

C

H

Weight of one PP mer is (12g/mol × 3) + (1g/mol × 6) = 42 g/mol

Example 2Calculate number average molecular weight.

two mers

Example 2Calculate number average molecular weight.

Mean Molecular Weight, Mi

Number Fraction, xi

xiMi

2 × 42 g/mol = 84 g/mol 0.4 33.63 × 42 g/mol= 126 g/mol 0.3 37.87 × 42 g/mol= 294 g/mol 0.3 88.2

∑ xiMi = 159.6 g/mol

CERAMICSCERAMICS

Lecture 5Lecture 5

CeramicsMetal-Nonmetal Compounds

Oxides nitrides carbides borides silicates

Insulator of heat & electricity

Resistant to high temperatureand corrosion

Hard butvery brittle

Atomic Bonding: Ionic, Ionic+Covalent, Covalent

Ceramic Structure• Composed of at least two elements.• Bonding: ionic to covalent (very strong)• More complex than metals.

Crystalline

Amorphous

Crystal Structure

Ceramics withionic bonding

Metallic ions (+) - Cation

TwoFactors:

(1) Magnitude of electrical charge (positive = negative charges to maintain electrically neutral)

Nonmetallic ions (-) - Anion

(2) Relative size of cations to anions (Cation must make contact with surrounding anions)

Examples: (1) Charge effect (reflected in chemical formula)

CaF2 Ca2+

2F-Al2O3

2Al3+ 3O2-

Electroneutrality must be maintained in a ceramic material

Crystal Structure

(2) Size Effect: Cation contact with surrounding anions(a) Ionic radius: Cation rC < Anion rA(b) Cation has maximum contacting anion neighborsExamples:

A A

AA

A A

AA

Unstable Stable

A A

AA

Stable

Crystal Structure

(c) larger cation radius, more contacting

anions. Smaller anion radius, more

contacting cation

(d) rC/rA ratio: determines Coordination

Number (CN)

Crystal Structure

CN & rC/rA RatioCN rC/rA Geometry CN rC/rA Geometry

2 < 0.155

3 0.155- 0.225

4 0.225- 0.414

6 0.414 - 0.732

8 0.732- 1.000

Coordination Number & rC/rA Ratio

•Consider simple AX-type structure such as NaCl, MgO, FeO, CsCl, ZnS, SiC.

•Determining factor: size effect.

Unit cells -2D

Unit cells -2D

Cation

AnionUnit cell – 1 anion+1 cation

1 2

1 2

4 3

• Face of unit cell (UC) – shared between two neighboring units cells.• Edge – shared 4 UC; Corner – shared 8 UC

Cesium Chloride - Structure

Coordination No.= 8;rC/rA: 0.732-1.0

Simple cubic of Cl-with Ce+ at body centre

Unit cell:1 formula unit CsCl

Cl-Ce+

Unit cell

CsCl crystal

ion81

Rock Salt (NaCl) -Structure Coordination No. = 6; rC/rA: 0.414-0.732

e.g. NaCl, MgO, MnS, LiF, FeO

Unit cell: 4 Cl- & 4 Na+

(4 formula units)

Cl-Na+

Zinc Blende (ZnS) - Structure Coordination No.= 4; rC/rA: 0.225-0.414

All ions tetrahedrallycoordinated

e.g. ZnS, ZnTe, SiC

Unit cell:4 formula unit

S-Zn+

•Many ceramic compounds have more than one type of cation (e.g. BaTiO3)

•Crystal structure becomes very complex

•But (1) Charge effect and (2) Size effect are still determining factors

AmXp-Type Structure

Ceramic Density

AC

AC

NVAAn ∑ ∑+

=)('

ρ

Formula units in unit cell

Atomic weight of allcations + anions

Unit cell volume Avogadro’s Number6.023x1023

ImperfectionsPoint Defects Interstitials: Cation

Vacancy: Cation & Anion

Cation Vacancy Cation Interstitial

Anion V acan cy

Cation impurity Cation Interstitial Impurity

Anion im

pur ityImperfections

Impurities(solid solution)

Cation: Interstitial & SubstitutionalAnion: Substitutional

(1) Frenkel defect: Cation-vacancy/ Cation interstitial pair(2) Schottky defect: Cation-vacancy/ Anion vacancy pair

Point Defects

Frenkel Schottky

Iron Oxide: Fe present in Fe2+ + Fe3+ state;Wustite-FeO: Fe2+ in perfect structure.

Point Defects

O2-

Fe2+

Destruction of neutrality: Fe3+ formation

Maintain neutrality: 2Fe3+& 1 Fe2+ vacancy

Imperfections

Fe2+ vacancy

Fe3+Fe3+

Impurities: example, NaCl (Na+, Cl-)

If impurity Ca2+ substitute for Na+, electro-

neutrality disrupted by extra + charge

To maintain neutrality: (1) Remove 1 Na+ (form a vacancy)(2) Add 1 Cl- (interstitial): highly unlikely (Cl- too big)

ImperfectionsElectro-neutrality MUST be maintained

ZrO2-CaOTe

mpe

ratu

re (

°C)

Composition (wt% CaO)

Liquid

3000

2500

2000

1500

1000

5000 10 20 30

ZrO2

CaZrO3

Cubic ZrO2

+CaZrO3

C+L L+CaZrO3

CaZr4O9

+CaZrO3

Cubic ZrO2

C+T

M +CaZr4O9

T

C+MM

ZrO2-CaO System• One eutectic, two eutectoid reactions• ZrO2: three crystal structures:

Monoclinic Tetragonal Cubic

• T → M (on cooling): volume expansion: 4% → severe cracking• Pure ZrO2 is useless.

T & % CaO dependent

Crack Prevention: add CaO (or Y2O3 or MgO) to enable formation of Cubic Phase.

Stabilising

Partially stabilising

+ 3-7%CaOC+T: > 1000oCNo M on coolingT & C stabilizedNo cracking

Fully stabilising

add more CaOCubic at high TCubic on cooling

ZrO2-CaO System

Partially Stabilised Zirconia (PSZ)

•Stabilising agents: CaO, MgO, Y2O3

•Very tough: better than other ceramics•Transformation toughening – why?

PSZ -Transformation toughening RT: C-phase + T-phase (Metastable)T-phase → M-phase by elastic energy causing expansion & compressive σ – impede crack growth.

Crack

Stress-induced T → M

C T MC T

Mechanical Properties

Fracture•Brittle•Low fracture toughness (KIC)•KIC < prediction - due to small flaws (voids, pores, cracks)

PlasticsCeramics

Composites

Metals

0.1 1 10 100KIC

• Ceramics have extremely high melting points; most not melted and formed (e.g. casting).

• Many ceramics structures processed from powder.

• Powder compressed and heated (sintered) to give net-shape structure with high density.

Ceramic Processing

• Presence of voids, defects, cracks.• Complex crystallography and small

number of slip systems.• Very strong ionic (or covalent)

bonding.• Energetically expensive for

dislocations to move.

Why are ceramics brittle?

Example 1

It is possible for ceramic to have more than one type of cation (represented by A and B) with their chemical formula designated as AmBnXp. Determine m, n, and p for barium titanate (BamTinOp) by examination of the unit cell.

Ba2+

Example 1

O2-

Ti4+

There’s 1 Ti ion, 1 Ba ion 3 O ions. →Must be BaTiO3.

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