Solid State Properties

Chapter 4

AmorphousGlassy

Semi-CrystallineElastomericPolyisoprene Tg = -73 °CPolybutadiene, Tg = -85 °CPolychloroprene, Tg = -50 °CPolyisobutylene, Tg = -70 °C

Viscous Liquid

Polymer Phases

Polystyrene Tg = 100 °CPolymethyl methacrylate, Tg = 105 °C

Nylon 6,6, Tg = 50 °C; Tm = 265 °CPoly ethylene terephthalate, Tg = 65 °C; Tm =270 °C

Polydimethylsiloxane Tg = -123°C; Tm = -40 °C

Glass-rubber-liquid

• Amorphous plastics have a complex thermal profile with 3 typical states:

Log(stiffness)Pa

Temperature

3

9

6

7

8

4

5

Glass phase (hard plastic)

Rubber phase (elastomer)

Liquid

Leathery phase

Polystyrene

Tg

Tygon (plasticized PVC)

PDMS

polyisobutylene

Phase diagram for semi-crystalline polymer

Temperature

Tg Tm Tb

Vol

ume

Glassy Solid

Crystalline Solid

Glassy SolidsPolystyrene Tg 100 °CPMMA Tg 105 °CPolycarbonate Tg 145 °CRubber Tg -73 °C

Crystalline SolidsPolyethylene Tm 140 °CPolypropylene Tm 160 °CNylon 6,6 Tm 270 °C

Polymers don’t exist in gas state; RT for boiling is higher than bond energies

Liquid

LiquidsInjection molding & extrusionPolydimethylsiloxane Tm -40 °C

Polymer Phases

Differential Scanning Calorimetry (DSC)

Modulus versus temperature

Viscous Response of Newtonian Liquids

AF

s =σ

A

A

y

Fx

tx

v

=

There is a velocity gradient (v/y) normal to the area. The viscosity relates the shear stress, σs, to the velocity gradient.

ytx

yv

s

σ ==

The viscosity can thus be seen to relate the shear stress to the shear rate:

γγ

σ &====tty

xyt

xs

ΔΔΔ

The top plane moves at a constant velocity, v, in response to a shear stress:

v

has S.I. units of Pa s.

The shear strain increases by a constant amount over a time interval, allowing us to define a strain rate:

tγ

γ =& Units of s-1

Measuring viscosities

Requires standards10-100,000 cP

1 pascal second = 10 poise = 1,000 millipascal second

Viscosity of Polymer Melts

Poly(butylene terephthalate) at 285 ºC

For comparison: for water is 10-3 Pa s at room temperature.

Shear thinning behaviour

Scaling of Viscosity: ~ N3.4

~ TGP

~ N3.4 N0 ~ N3.4

Universal behaviour for linear polymer melts

Applies for higher N: N>NC

Why?Data shifted

for clarity!

G.Strobl, The Physics of Polymers, p. 221

3.4

Viscosity is shear-strain rate dependent. Usually measure in the limit of a low shear rate: o

Concept of “Chain” Entanglements If the molecules are sufficient long (N >100 - corresponding to the entanglement mol. wt., Me), they will entangle with each other.

Each molecule is confined within a dynamic “tube”.

Tube G.Strobl, The Physics of Polymers, p. 283

Network of Entanglements

There is a direct analogy between chemical crosslinks in rubbers and “physical” crosslinks that are created by the entanglements.

The physical entanglements can support stress (for short periods up to a time T), creating a “transient” network.

An Analogy!

There are obvious similarities between a collection of snakes and the entangled polymer chains in a melt.

The source of continual motion on the molecular level is thermal energy, of course.

“Memory” of Previous State

Poly(styrene)

Tg ~ 100 °C

Development of Reptation Scaling Theory

Sir Sam Edwards (Cambridge) devised tube models and predictions of the shear relaxation modulus.

In 1991, de Gennes was awarded the Nobel Prize for Physics.

Pierre de Gennes (Paris) developed the concept of polymer reptation and derived scaling relationships.

There once was a theorist from Francewho wondered how molecules dance.“They’re like snakes,” he observed, “As they follow a curve, the large onesCan hardly advance.”

D ~ M -2

P.G. de GennesScaling Concepts in Polymer Physics

Cornell University Press, 1979

de Gennes

Entanglement Molecular Weights, Me, for Various Polymers

Poly(ethylene) 1,250

Poly(butadiene) 1,700

Poly(vinyl acetate) 6,900

Poly(dimethyl siloxane) 8,100

Poly(styrene) 19,000

Me (g/mole)

Amorphous Glasses (< Tg)

Tg: 40 carbons in backboneStarting moving in concert

Glass transition temperature

Rate of cooling affects Tg

Polymer Tg ( °C)

Polymer Tg ( °C)

Factors that affect Tg

Polar groups increase packing density; more thermal energy is needed to created volume

Factors that affect Tg

**

OHn

**

CNn

**

FnOther polar vinyl polymer:

Factors that affect Tg

Factors that affect Tg

Main chain stiffness: reduced flexibility

N

O

O

*

O

NH

H2C

npolyamide imide (Torlon)

Tg = 550-600 °C

O

*NH

n

polybenzamide

Tg = 500+ °C

N

NH

*

N

HN

n

polybenzimidazole (PBI)

Tg = 700-775 °C

Polyarylenes

Nylon-3Tg = 110-200 °C

* NH

*

O

n

Nylon-6Tg = 52 °C

*

HN *

O

n * NH

*

O

n

Nylon-11Tg = 42 °C

O

*NH

n

polybenzamide

Tg = 500+ °C

Nylons or polyamides

Side Chain Rigidity

Long chains plasticize

Factors that affect Tg

Anchors to movement

Long chains plasticize movements

Factors that affect Tg

OOMe

n

poly(methyl methacrylate)

Me

OMeO

OMeOO

MeOOMeOO

MeO

Tg = 47 °C (isotactic)

OMeO

OMeOO

MeOOMeOO

MeO

Tg = 120-140 °C (syndiotactic)

Tg = 110 °C (atactic > 50 % syndiotactic)

poly(methyl methacrylate)

Factors that affect Tg

Tacticity

Factors that affect Tg

Symmetry of substituents

**

Fn

**

Fn

F

Tg = -39 °CTg = -20 °C

**

Cln

**

Cln

Cl

Tg = -17 °CTg = 87 °C

asymmetric symmetric

Asymmetric have higher Tg’s

Factors that affect Tg: Mw

Factors that affect Tg: Crosslinking

Factors that affect Tg: Plasticizer

Phthalates

O

O

O

O

Immiscible (Two phase) and miscible (blends) polymers

Tg as a function of film thickness

Glass Transition

• Rigid group in backbone

• Flexible polymer backbone

• Steric Hinderance

• Long plasticizing side groups

• Symmetrical substituents

• Polar functionalities

• Plasticizers

O*O

O

*

n

polyether ketone (PEEK)Tg = 119 °C

O*O

O

*

n

polyether ketone (PEEK)Tg = 225 °C

Additional Kinds of Transitions

Amorphous Polymers Thermo-mechanical properties