Transcript Slide 1

EBB 220/3
Polymer Physics
INTRODUCTION

Characteristics of;
 Thermoplastic
(amorphous & semicrystalline)

thermoset
 rubber
Linear & crosslink system?
 Differences between
vulcanizing and curing?

INTRODUCTION
Structure
The structural properties of a polymer
relate to the physical arrangement of
monomers along the backbone of the
chain.
 Structure has a strong influence on the
other properties of a polymer.

Structure



The simplest form of polymer molecule is a straight chain
or linear polymer, composed of a single main chain. The
flexibility of an unbranched chain polymer is
characterized by its persistence length.
A branched polymer molecule is composed of a main
chain with one or more substituent side chains or
branches.
A cross-link suggests a branch point from which four or
more distinct chains emanate. A polymer molecule with a
high degree of crosslinking is referred to as a polymer
network
Monomer arrangement in
copolymers




Monomers within a copolymer may be organized along the
backbone in variety of ways.
Alternating copolymers possess regularly alternating monomer
residues
Random copolymers have a random sequence of monomer
residue types
Block copolymers have two or more homopolymer subunits linked
by covalent bonds. Block copolymers with two or three distinct
blocks are called diblock copolymers and triblock copolymers,
respectively.
Tacticity in polymers
 This property describes the relative stereochemistry of
chiral centers in neighboring structural units within a
macromolecule. There are three types: isotactic, atactic,
and syndiotactic.
 Precise knowledge of tacticity of a polymer also helps
understanding at what temperature a polymer melts, how
soluble it is in a solvent and its mechanical properties.
Melting point



The term "melting point" when applied to polymers
suggests not a solid-liquid phase transition but a
transition from a crystalline or semi-crystalline phase to a
solid amorphous phase.
Though abbreviated as simply "Tm", the property in
question is more properly called the "crystalline melting
temperature".
Among synthetic polymers, crystalline melting is only
discussed with regards to thermoplastics, as
thermosetting polymers will decompose at high
temperatures rather than melt.
Glass transition temperature (Tg)


A parameter of particular interest in synthetic polymer manufacturing
is the glass transition temperature (Tg), which describes the
temperature at which amorphous polymers undergo a second order
phase transition from a rubbery, viscous amorphous solid to a brittle,
glassy amorphous solid.
The glass transition temperature may be engineered by altering the
degree of branching or cross-linking in the polymer or by the
addition of plasticizer.
The Space Shuttle Challenger disaster was caused
by rubber O-rings that were below their glass transition
temperature on an unusually cold Florida morning, and
thus could not flex adequately to form proper seals
between sections of the two solid-fuel rocket boosters.
Polymer Structure/Property
relationships

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

Chain length
Increasing chain length tends to decrease chain mobility,
increase strength and toughness, and increase the glass
transition temperature (Tg).
This is a result of the increase in chain interactions such
as Van der Waals attractions and entanglements that
come with increased chain length.
These interactions tend to fix the individual chains more
strongly in position and resist deformations and matrix
breakup, both at higher stresses and higher
temperatures.
Polymer Structure/Property
relationships
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Branching
Branching of polymer chains also affect the bulk properties of polymers.
Long chain branches may increase polymer strength, toughness, and Tg
due to an increase in the number of entanglements per chain.
Random length and atactic short chains, on the other hand, may reduce
polymer strength due to disruption of organization.
Short side chains may likewise reduce crystallinity due to disruption of the
crystal structure. Reduced crystallinity may also be associated with
increased transparency due to light scattering by small crystalline regions. A
good example of this effect is related to the range of physical attributes of
polyethylene.
High density polyethylene (HDPE) has a very low degree of branching, is
quite stiff, and is used in applications such as milk jugs. Low density
polyethylene (LDPE), on the other hand, has significant numbers of short
branches, is quite flexible, and is used in applications such as plastic films.
Polymer Structure/Property
relationships

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Chemical cross-linking
Cross linking tends to increase Tg and increase strength
and toughness.
Cross linking consists of the formation of chemical bonds
between chains.
Among other applications, this process is used to
strengthen rubbers in a process known as vulcanization,
which is based on cross linking by sulfur. Car tires, for
example, are highly cross linked in order to reduce the
leaking of air out of the tire and to toughen their
durability. Eraser rubber, on the other hand, is not cross
linked to allow flaking of the rubber and prevent damage
to the paper.
Polymer Structure/Property
relationships
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Inclusion of plasticizers
Inclusion of plasticizers tends to lower Tg and increase polymer
flexibility.
Plasticizers are generally small molecules that are chemically similar
to the polymer and create gaps between polymer chains for greater
mobility and reduced interchain interactions.
A good example of the action of plasticizers is related to
polyvinylchlorides or PVCs.
A uPVC or unplasticized polyvinylchloride is used for things such as
pipes. A pipe has no plasticizers in it because it needs to remain
strong and heat resistant. Plasticized PVC is used for clothing for a
flexible quality. Plasticizers are also put in some types of cling film to
make the polymer more flexible.
Polymer Structure/Property
relationships
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Degree of crystallinity
Increasing degree of crystallinity tends to make
a polymer more rigid. It can also lead to greater
brittleness.
Polymers with degree of crystallinity
approaching zero or one will tend to be
transparent, while polymers with intermediate
degrees of crystallinity will tend to be opaque
due to light scattering by crystalline / glassy
regions.
Example of Thermoplastic
Polymers
Example of Thermoplastic
Polymers
EBB 220/3
PRINCIPLE OF
VISCO-ELASTICITY
INTRODUCTION

The differences between the polymeric
materials behaviour and materials with
totally elastic behaviours are :

Time dependent characteristics
 Temperature dependent characteristics

Polymeric materials will show the properties
that dependent on stress & strain  that
will influence when the loading being
applied.

The response of polymeric materials with
stress or strain that been applied
dependent on :
1.
2.

Loading rate
Loading time
The
differences
behaviour are :
1.
2.
3.
between
Elastic materials
Viscous materials
Visco-elasticity
materials
Behaviour of elastic material

Elastic behaviour is instantaneous/immediate.

The total deformation (or strain) occurs the
instant the stress is applied or release.

Upon release of the external stress – the
deformation is totally recovered (deformation
is reversible)

The specimens
deformation
assumes
its
original
Elastic materials



The spring (in the following figure) represents
the elastic portion (usually short term) of a
plastic material's response to load.
When a load is applied to the spring, it instantly
deforms by an amount proportional to the load.
When the load is removed, the spring instantly
recovers to its original dimensions.
As with all elastic responses, this response is
independent of time and the deformation is
dependent on the spring constant.
Behaviour of viscous material

Deformation
or
instantaneously.

In response to an applied stressdeformation is delayed or dependent
with time.

This deformation is not reversible or
completely recovered after stress is
released.
strain
is
not
Viscous Behavior



The dash-pot in the following figure represents the viscous portion of
a plastic's response.
The dash-pot consists of a cylinder holding a piston immersed in a
viscous fluid. The fit between the piston and cylinder is not tight.
When a load is applied, the piston moves slowly in response. The
higher the loading, the faster the piston moves. If the load is
continued at the same level, the piston eventually bottoms out
(representing failure of the part). The viscous response is generally
time- and rate-dependent.
 
de
dt
= viscosity
de/dt = strain rate
Summary: Hooke’s law (elastic) &
Newton’s Law (plastic)
The behaviour of linear elastic were given by Hooke’s
law:
•
  Ee
•
or
The behaviour of linear
viscous were given by
Newton’s Law:
de
 
dt
d
de
E
dt
dt
E= Elastic modulus
 = Stress
e= strain
de/dt = strain rate
d/dt = stress rate
= viscosity
** This equation only applicable at low strain
Visco elastic behaviour
•
Behaviour of most polymer is in between
behaviour of elastic and viscous materials.
1.
At low temperature & high strain rate,

2.
At high temperature & low strain rate,

3.
Polymer demonstrate elastic behaviour,
Polymer demonstrate viscous behaviour
At intermediate temperatures & rate of
strain

Polymer
behaviour
demonstrate
visco-elastic
Polymer is called visco- elastic because:
•
•
Showing both behaviour
behaviour
•
Instantaneously elastic strain
viscous time dependent strain
elastic & viscous
followed
by
Mechanical Model
•
Methods that used to predict the behaviour of viscoelasticity.
•
They consist of a combination of between elastic
behaviour and viscous behaviour.
•
Two basic elements that been used in this model:
•
1.
Elastic spring with modulus which follows Hooke’s
law
2.
Viscous dashpots with viscosity 
Newton’s law.
which follows
The models are used to explain the phenomena creep
and stress relaxation of polymers involved with different
combination of this two basic elements.
CREEP
Constant stress is applied
 the strain relaxes as
function of time
STRESS RELAXATION
Constant strain is applied
 the stress relaxes as
function of time
The common mechanical model that use to
explain the viscoelastic phenomena are:
•
1.
•
2.
•
3.
•
Maxwell
Spring and dashpot  align in series
Voigt
Spring and dashpot  align in parallel
Standard linear solid
One Maxwell model and one spring  align
in parallel.
Maxwell Model
•
Maxwell model consist of spring and dashpot in series
and was developed to explain the mechanical
behaviour on tar.
•
On the application of stress, the strain in each elements
are additive.
•
The total strain is the sum of strain in spring & dashpot.
The stress each elements endures is the same.
Viscous dashpot
Elastic spring
•
Overall stress , overall strain e in the system is given
by:
e  e s  ed
es = strain in spring and ed = strain in dashpot dashpot
•
Because the elements were in series  the stress is the
same for all elements,
 s d
•
Equations for spring and dashpot can be written as:
de s
d
E
dt
dt
and
ded
 
dt
•
For Maxwell model, the strain rate is given as
de 1 d 


dt E dt 
•
In creep case, the stress at   0 therefore
d/dt = 0. The equations can be written as:
de  0

dt 
•
Maxwell model can predict the Newtonian
behaviour  the strain is predict to increase
with time
.
• The behavior of Maxwell
model during creep loading
(constant stress, 0 strain
is predicted to increased
linearly with time
This is not the viscoelastic
behaviour of polymeric
materials  de/dt decreased
with time
•
May be this model is useful to predict the behaviour of
polymeric materials during stress relaxation.
•
In this case, the strain is constant e=e0 applied to the
system given de/dt =0
de 1 d 


dt E dt 
•
then
d

•

E


1 d 
0

E dt 
dt
Integration at t=0  0 given
 0
 Et 
eksp   
 
o= earlier stress
•
•
The term /E is constant
for Maxwell model and
sometimes can be refered as time relaxation, t0 written
as:
 t 
   0 eksp  
 t0 
The exponential decreased in stress can be predicted 
give a better representation of polymeric materials
behaviour.
•Stress
were
predicted
completely relaxed with time
period  it is not the normal
case for polymer
Voigt Model
•
Can also known as the Kelvin model.
•
It consists of a spring and dashpot in parallel.
•
In application of strain, the stress of each element
is additive, and the strain in each element is the
same.
Elastic spring
Viscous dashpot
•
The parallel arrangement of spring and dashpot gives
the strain e are the same for the system given by:
e  es  ed
es = strain in spring and ed = strain in dashpot
•
Because the elements in parallel  stress  d in every
elements are additive and the overall stress are
   s  d
•
Equation for spring and dahpot can be written as:
 s  Ee
and
de
d 
dt
•
For Voigt model, the strain rate are
de  Ee
 
dt  
•
•
The accuracy of prediction the mechanical behaviour of
Voigt model can be confirm.
In creep case, stress is   o so d/dt = 0. The equation
can be written as:
de Ee  0


dt 

•
The simple differential equation given by:
0 
 Et 
e
1  eksp   
E 
  
•
•
Constant ratio /E can be replace with time
relaxation, t0.
Changes in strain with time
having creep are given by:
0 
e
1  eksp
E 
for Voigt model that
 t 
  
 t 0 
Figure shows polymer
behavior under creep
deformation strain rate
decreased with time
e o /.E and t=

•
Voigt model fails to predict the stress relaxation
behaviour of polymer
•
When the strain is constant at e0 and de/dt = 0 the
equation shows:
 Ee0



or
  Ee0
 The linear response is shown in the figure:
Behavior of Voigt model
at different loading 
Stress relaxation
Standard linear solid
As shown:
•
•
Maxwell model can accurately predict the
phenomenon stress relaxation to a first
approximation.
•
Voigt Model can accurately predict the
phenomenon
creep
to
a
first
approximation.
•
Standard linear solid model was
developed to combined the Maxwell and
Voigt model  to describe both creep &
stress relaxation to a first approximation.
Elastic spring
Viscous dashpot
•
In consist  one Maxwell elements in parallel with a
spring.
•
The presence on this second spring will stop the
tendency of Maxwell element undergoing viscous flow
during creep loading  but will still allow the stress
relaxation to occur
General time dependent behaviour

The true mechanical properties that appropriate
with time for polymeric materials dependent on
 types of stress or cycle of strain that been
used.

Changes in stress an strain with time (t), can be
shown in simple schema of polymer tensile.

It can be categorized based on 4 different
deformation behaviour as:
a) creep
b) Stress relaxation
c) Constant stress rate
d) Constant strain rate
INTRODUCTION

It is difficult to predict the creep and stress relaxation
for polymeric materials.

It is easier to predict the behaviour of polymeric
materials with the assumption  it behaves as linear
viscoelastic behaviour.

Deformation of polymeric materials can be divided to
two components:


Elastic component – Hooke’s law

Viscous component – Newton’s law
Deformation of polymeric materials  combination of
Hooke’s law and Newton’s law.
CREEP
Constant stress is applied
 the strain relaxes as
function of time
STRESS RELAXATION
Constant strain is applied
 the stress relaxes as
function of time
(a) Creep




During Creep loading:
A constant load were applied to the specimen at
t = 0,
The strain increased quickly at the beginning but
become slowly with time after a long period of
deformation.
For elastic solid  the strain rate is constant
Constant stress
(b) Stress Relaxation




During stress relaxation:
Strain is constant
Stress decreased slowly with time.
For elastic solid  the stress is constant
(c) Constant stress rate


The increasing strain with time is not linear.
It becoming more steep with:
1. Increasing time
2. Increasing stress rate
(d) Constant strain rate
•
•
•
The increasing stress with time is not linear.
The slope of the curve decreased with time
The slope become more steep with the increasing
strain rate
Creep phenomenon

It were the general behaviour of polymeric materials
and very important in engineering.

It can estimates the strength or the ability to
sustained the stress that been applied permanently or
constant.

Creep  polymer is stressed at a constant level for a
given a time and the strain increases during that time
periods.

Creep can be used to estimate the life times of
materials
Frequently run at temperatures where thermal
degradation is significant  data can be used to
estimate of the elevate-temperature life of materials.

3 creep stages

There were 3 stages of creep:
1.
Primary Creep– The slope of strain vs
time decreased with time.
2.
Secondary creep – Constant strain
rate.
3.
Tertiary creep – the strain rate
increased
rapidly
until
rupture
(formation of crack, yielding and etc).
Creep strain, e
Rupture
Time, t
Graph for strain curve at constant loading.

After beginning of strain, specimen will
having a slowly shape changes with
time until the yielding occur that caused
a rupture.

At primer area 

Area of early stage of deformation
when creep rate is decreased with
time (slope of the curve decreased
with time).

Polymeric materials having the
increased in creep resistance or
strain hardening.

Secondary area 



Area where the creep rate where almost constant
Creep rate were explained by the equilibrium in
between strain hardening and the ability to
maintain/ retain its shape.
Tertier area 




Where creep accelerate and rupture occurred.
Creep happens due to changes in microstructure.
Happen at higher stress for ductile materials.
Decreased in cross-section that make the rupture
or creep rate increased rapidly.

Creep test normally run in extension/ tension test.
(but can be done in shear, compression or flexural
test)

Creep rate of polymeric materials were dependent
on loading, time and temperatures.

Polymeric components will deformed rapidly at
higher temperatures.

Creep results can been shown as:
1.
Isometric curve – stress versus time
2.
Modulus creep curve – modulus versus time
3.
Isochronous curve – stress versus strain
Isometric curve



Stress that being applied will dependent on time.
At beginning  stress is higher due to bonding
forces between atoms is higher.
After a few moments  slippage between atoms
occur and the polymer crystallization rate
decreased then the strain were increased with
time.
Modulus curve

The elasticity of certain materials exists due to the materials
decomposition of chain to become more order.

If the measurements is taken in the short periods the
decomposition of chain folding had not happened  polymer
are more like persistent materials.

This graph is very useful in determination of materials rigidity
and persistent  based on the life span of the materials.
Isochronous curve

The slope of the graph is equivalent to the modulus
Young, E which is the determination the resistance
towards the neighbouring separation of the atoms.

Modulus is the rigidity or the resistance of materials
towards shapes changes.

The high modulus values  resulting from small strain
changes due to the applied stress.
The use of creep graph

The knowledge of knowing to interpret
of creep graphs are useful for materials
engineer.

Data from creep graph gives us the
information about:

1.
The rupture/deformation of the materials
2.
Yield and
materials.
3.
Can estimating the life time of the
materials
shape
change
of
the
Can choose the materials based on
materials applications.
Isochronous curve

Can comparing various types of
polymeric materials during design
because:
 The stress for materials were plotted at time
for the specific loading being applied.
Example of the problem

One of the engineer has to design rigid structure
can sustained the continuous load for 1000
hours with the strain not more than 2 %.

Question:
 What is the maximum stress can be allowed?

Solution:
 Need to make a comparison from graph strain
versus time for different stress for 1000 hours.
 strain at different stress can be resolved.

Graph stress versus strain at 1000 hours can
be plotted  the maximum stress allowed
can be obtained.
Modulus curve

From graph  creep modulus decreased with
increasing time showing the visco-elastic
behaviour.

This graph were useful because modulus were
needed in engineering deflection.
Example of the application

To chosen the life span of component that being
designing at modulus curve  the modulus value is
called design modulus.

The stress of the modulus is determine according to
the alternative :

If stress being determine  The values should be
taken from the modulus curve with the stress
value is nearly to the value that needed.

If the stress needed not yet been determine 
Need to choose the modulus curve with the
conservative stress value and need to be
checked before starting the calculation.
Isometric curve

With observing materials behaviour during stress
relaxation  can estimate the long term materials
behaviour.

Materials long term service can be estimate when
the certain stress being applied not more than the
rupture of the materials.
Example of application

For one bottle lid under constant strain for very long
period  low stress relaxation is needed.

That bottle lid will fail if the stress decreased
instantly.

Time is a the main factor that will influenced the
mechanical properties of the bottle lid because :

At very short loading time  higher stresses is
needed for particular strain.

At long term loading  lower stresses is needed to
get the particular strain.
Example of the exams question

What is definition of visco-elasticity?

Please gives the differences between
visco-elastic behavior and totally
elastic behavior.

Gives the advantages of creep
properties in materials engineering?
Effect of glass transition and
temperature on creep
Below Tg?
 In the Tg region?
 Above Tg?

Summary
•
There were a lots of attempts to discover more
complex model that can give a good
approximation to predict viscoelastic behaviour
of polymeric materials.
•
When the elements used is increased 
mathematical can be more complex.
•
It can be emphasis that mechanical models can
only gives mathematical representations for
mechanical behaviour only  it not much
help to predict the behaviour of viscoelasticity at
molecular level.
Example of the exams question

What is the purpose of mechanical model
in visco-elasticity theories?

Gives a brief description how the chosen
mechanical model can be used to estimate
the creep or stress relaxation behavior for
polymeric materials?
Thank you