polymer properties
TRANSCRIPT
FF
Tensile
F
Bending
FF
Compressive
F
Shear
F
stress forcearea
strain lengthlength
The slope of the stress-strain curve in the elastic region. Hooke’s law: E = /
A measure of the stiffness of the material.
Larger the value of E, the more resistant a material is to deformation.
Note: ET = Eo – bTe-To/T where Eo and b are
empirical constants, T and To are temperatures Units:
E: [GPa] or [psi]: dimensionless
Elastic deformationReversible:
( For small strains)Stress removed material returns to original
size
Plastic deformationIrreversible: Stress removed material does not return to
original dimensions.
Yield Strength (y) The stress at which plastic deformation
becomes noticeable (0.2% offset).
P the stress that divides the elastic and plastic behavior of the material.
True stress = F/A True strain =
ln(l/l0) = ln (A0/A)(A must be used
after necking)0
0
0
strain gEngineerin
stress gEngineerin
lll
AF
Apparent softening
True Strain t dl
lL o
L
lnL
Lo
True Stress t Load
A
Load
A0
AL A oLo
t ln 1
t 1
The total area under the true stress-strain curve which measures the energy absorbed by the specimen in the process of breaking.
Toughness d
The total elongation of the specimen due to plastic deformation, neglecting the elastic stretching (the broken ends snap back and separate after failure).
Essentials of Materials Science & EngineeringSecond Edition
Authors: Donald R. Askeland & Pradeep P. Fulay
Materials Science and Engineering: An IntroductionSixth Edition, Author: William D. Callister, Jr.
The Science and Engineering of MaterialsFourth Edition, Authors: Askeland and Phule (Fulay ?)
Introduction to Materials Science for EngineersSixth Edition, Author: James F. Shackelford
• Stress and strain: These are size-independent measures of load and displacement, respectively.
• Elastic behavior: This reversible behavior often shows a linear relation between stress and strain. To minimize deformation, select a material with a
large elastic modulus (E or G).• Plastic behavior: This permanent deformation
behavior occurs when the tensile (or compressive) uniaxial stress reaches y.
• Toughness: The energy needed to break a unit volume of material.
• Ductility: The plastic strain at failure.
Note: materials selection is critically related to mechanical behavior for design
applications.
Polymers have unique mechanical properties vs. metals & ceramics.Why?
Bonding, structure, configurations
Polymers and inorganic glasses exhibit viscoelastic behavior (time and temperature dependant behavior)
Polymers may act as an elastic solid or a viscous liquidi.e. Silly Putty (silicon rubber)
- bounces, stretches, will flatten over long times
Low Strain RateHigh extension - failure
resilient rubber ballElastic behavior rapid deformation
Very low Strain rate - FlattenFlow like a viscous fluid
PolymersPolymer : Materials are made up of many (poly) identical chemical units (mers) that are joined together to construct giant molecules.
Plastics - deformable, composed of polymers plus additives. E.g. a variety of films, coatings, fibers, adhesives, and foams. Most are distinguished by their chemical form and composition.
The properties of polymers is related to their structures, which in turn, depend upon the chemical composition. Many of these molecules contain backbones of carbon atoms, they are usually called "organic" molecules and the chemistry of their formation is taught as organic chemistry.
The most common types of polymers are lightweight, disposable, materials for use at low temperatures. Many of these are recyclable. But polymers are also used in textile fibers, non-stick or chemically resistant coatings, adhesive fastenings, bulletproof windows and vests, and so on.
Polymers
Polymer : Materials are made up of many (poly) identical chemical units (mers) that are joined together to construct giant molecules. Carbon – 1s22s22p2
It has four electrons in its outermost shell, and needs four more to make a complete stable orbital. It does this by forming covalent bonds, up to 4 of which can be formed.
The bonds can be either single bonds, ie one electron donated by each participating element, or double bonds (2 e- from each), or triple bonds (3 from each)
C X1
X2
X4
X4
Xi can be any entity ex H, O, another C, or even a similar monomer
C X1
X2
X4
X4
Polymers – many repeating units
C X1
X2
X4
X4 + C X1
X2
X4
X4 +…
CCCC CAnd so on… if the bonds can keep getting formed, entire string-like structures (strands, or chains) of the repeating units are created. C is the most common element in polymers. Occasionally, Si may also participate in such bonding.
Classes of PolymersThermoplastics:
Consist of flexible linear molecular chains that are tangled together like a plate of spaghetti or bucket
of worms. They soften when heated.
Thermosets:
Remain rigid when heated & usually consist of a highly cross-linked, 3D network.
Elastomers:
Consist of linear polymer chains that are lightly cross-linked. Stretching an elastomer causes chains to partially untangle but not deform permanently
(like the thermoplastics). Of all the materials, polymers are perhaps the most versatile, not only because the properties can be drastically modified by simple chemistry, but the behavior is also
dependent on the architecture of the chains themselves.
From proteins to bullet-proof jackets to bottles, polymers are INDISPENSIBLE to life as we know it
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a) & b) 3 dimensional models,
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backbone
side-group
Polymer Synthesis - I
Addition in which one “mer” is added to the structure at a time.
This process is begun by an initiator that "opens up" a C=C double bond, attaches itself to one of the resulting single bonds, & leaves the second one dangling to repeat the process
Polymer Synthesis - II
Condensation in which the ends of the precursor molecules lose atoms to form water or alcohol, leaving bonds that join with each other to form bits of the final large molecules. An example is shown in the Detail - the formation of nylon.
Molecular weight distribution
The degree of polymerization (DP) = no. of monomers per polymer. It is determined from the ratio of the average molecular weight Mw of the polymer
to the molecular weight of the repeat unit (MRP).DP = Mw / MRP
where Mw = fi Mi : Mw = weight average molecular weightMn = xi Mi : Mn = number average molecular weight
Mi = mean molecular weight of each range fi = weight fraction of polymer having chains within that range
xi = fraction of total number of chains within each range
M n xiM ii
M w wiM ii xiM i
2
i
xi ni
nii
number fraction
Degree of Polymerization
nn Mn
m ; nw Mw
m m "mer" molecular weight
Degree of polymerization (DP)- number of monomers per polymer chain, ie no. of repeat units.
Obviously, the weight (either in AMU, or in g/mol) is the same for each repeat unit. Then, the total weight of the polymer chain, ie its molecular weight is :-
mol. Wt. = N.Mm
where N is the number of monomers in that chain, ie the DP; Mm is the weight of the monomer.
In a polymer sample synthesized from monomers by either condensation or addition polymerization, one always has a distribution of DPs amongst the resulting chains.
So let us consider that we have 100 monomers. Let the weight of each monomer be 1g/mol (in reality, this is Hydrogen !) Let us see some ways in which we can arrange this:1)1 chain of N=100, ie mol. Wt. = 1002)2 chains of N=50 each, ie mol. Wt. = 503)10 chains of N=10 each, ie mol. Wt. = 104)3 chains, 2 of N=25, and 1 of N=50
3 chains, 2 of N=25, and 1 of N=50. Now, to calculate the average molecular weight, we have two methods:1) Take the simple numerical average, ie
(25+25+50)/3.0 = (2x25 + 1x50)/3.0 = 33.33. This value is according to the number fraction of each type of chain (1/3 of the chains are of N=50, and 2/3 have N = 25)
2) Take the average according to the weight fraction of each chain. What is the total weight ?
Mtotal=100Wfraction
50 = 50/100, ie ½ , Wfraction25=2*25/100 = 1/2
So, taking weight fractions, we get the average molecular weight as Mw = 50*1/2 + 25*1/2 = 25+12.5 = 37.5
So, numerical fractions, and weight fractions for mol. Wt. give different answers!Mn = SUM(niMi)/Sum(ni) , where ni = no. of chains of length Mi
Mw = SUM(wiMi), where wi = weight fraction of chains of length Mi.
But, wi = niMi/SUM(niMi) ie the weight of that polymer (i), divided by total weight.
So, in the previous example, W50 = 50/100, W251 = 25/100, W25
2 = 25/100
Suppose we want to find out the average population of each state.* We can go to each senator of each state and find out what the population of
their state is, and then divide that number by 100. This number is the number-average population for each state. This is exactly
similar to the Mn that we calculated earlier, ie no. av. Mol. wt.. Problem ?Yes, of course. What do we do about say, CA and AK ?
Now, senators are busy, so we ask congressmen from each state. Then, we take the value that each congressman/congresswoman gives us, and then divide by the number of congresscritters. What value do we get ? Certainly one different from our earlier attempt ! Problem ?
Now the value is much higher than before. This is exactly similar to the Mw that we calculated earlier, ie to weight av. mol. Wt.
Is this value MUCH more representative (eh eh !) of the average population of each state ? Well, not really. But at least, it is an average.
We learn about these differences, because different measurement techniques measure different averages, and the ratio of Mw to Mn, called the Poly Dispersity Index (PDI) often determines properties.
* taken from “Polymer Physics” by M. Rubinstein & R. H. Colby, 1st edition, OUP
• Polymer = many mers
• Covalent chain configurations and strength:
Direction of increasing strengthBranched Cross-Linked NetworkLinear
secondarybonding
C C C C C CHHHHHH
HHHHHH
Polyethylene (PE)
mer
ClCl ClC C C C C C
HHH
HHHHHH
Polyvinyl chloride (PVC)
mer
Polypropylene (PP)CH3
C C C C C CHHH
HHHHHH
CH3 CH3
mer
Structure of polymers strongly affects their properties; e.g., the ability of chains to slide past each other (breaking Van der Waals bonds) or to arrange themselves in regular crystalline patterns. Some of the parameters are: the extent of branching of the linear polymers;the arrangement of side groups. A regular arrangement (isotactic) permits the greatest regularity of packing and bonding, while an alternating pattern (syndiotactic) or a random pattern (atactic) produces poorer packing which lowers strength & melting temperature.
CC
HH
R H
CC
HH
R H
CC
HH
R H
CC
HH
R H
CC
HH
R H
CC
HH
R H
CC
HH
H R
CC
HH
R H
CC
HH
H R
CC
HH
R H
CC
HH
R H
CC
HH
H R
CC
HH
R H
CC
HH
R H
CC
HH
R H
Isotactic
Syndiotactic
Atactic Can’t Crystallize
Isomerism – different structures, but same chemical composition
Random
Alternating
Branched
If you have some red beads and some black beads, how can you make polymers out of them ?
Blocky
We have discussed polymers comprised of a single kind of a monomer, ie just one repeating entity. However, this is not unique: we can synthesize polymers that consist of different repeating units, and such polymers are called copolymers
The combination of different mers allows flexibility in selecting properties, but the way in which the mers are combined is also important. Two different mers can be alternating, random, or in blocks along the backbone or grafted on as branches.
• Thermoplastics: --little cross-linking --ductile --soften w/heatingEx: grocery bags, bottles• Thermosets: --large cross-linking (10 to 50% of mers) --hard and brittle --do NOT soften w/heating --vulcanized rubber, epoxies, polyester resin, phenolic resinEx: car tyres, structural plastics
cross-linking
In thermoset, the network is inter-connnected in a non-regular fashion. Elastomers belong to the first category. Polyisoprene, the hydrocarbon that constitutes raw natural
rubber, is an example. It contains unsaturated C=C bonds, and when vulcanizing rubber, sulfur is added to promote crosslinks. Two S atoms are required to fully saturate a pair of –C=C— bonds and link a pair of adjacent molecules (mers) as indicated in the
reaction. Without vulcanization, rubber is soft and sticky and flows viscously even at room temperature. By crosslinking about 10% of the sites, the rubber attains mechanical
stability while preserving its flexibility. Hard rubber materials contain even greater sulfur additions.
• Molecular weight Mw: Mass of a mole of chains.
• Tensile strength (TS): --often increases with Mw.
--Why? Longer chains are entangled (anchored) better.• % Crystallinity: % of material that is crystalline. --TS and E often increase with % crystallinity. --Annealing causes crystalline regions to grow. % crystallinity increases.
crystalline regionamorphous region
smaller Mw larger Mw
Molecular weight, Crystallinity and Properties
~10 nm spacing
Oriented chains with long-range order
Amorphous disordered polymer chains in the “intercrystalline” region
Random arrangement = High Entropy Stretched = Low Entropy
Entropy is a measure of randomness: The more ordered the chains are, the lower is the entropy. Spontaneous processes always tend to increase the entropy, whichmeans that after stretching, the chains will tend to return to a high-entropy state
Elastic Deformation
creep
Cross-linking stops the sliding of chains
random
Slow Deformation
Low entropy state
Elastic
ViscousViscoelastic
VISCOELASTIC RESPONSE
Temperature & Strain Dependence:
Low T & high strain rates = rigid solids
High T & low strain rates = viscous
Rubber-like ElasticDeformation
Slow relaxation
Glassy (Elastic-high modulus)
Leathery(Elastic-low modulus)
Thermoplastic (uncrosslinked)
Tg Tm
Mod
ulus
of e
last
icity
Temp.
Rubbery Plateau Elastic at high strain rateViscous at low strain rate
medium times
Long times
Crosslinked Branched
Effect of crosslinkingThermoset
Heavy Crosslinking
ElastomerLight crosslinking
Effect of crystallinity
Tg Tm
Log
Mod
. Of E
last
icity
amorphous
50 % Crystalline
100 % crystalline
Tm
Log
Mod
. Of E
last
icity
ThermoplasticNo crosslinking
Tg
Branched polymer
Crystals act like crosslinksStrain Induced Crystallization in NR
• Compare to responses of other polymers: --brittle response (aligned, cross linked & networked case) --plastic response (semi-crystalline case)
initial: amorphous chains are kinked, heavily cross-linked.
final: chains are straight,
still cross-linked
0
20
40
60
0 2 4 6
(MPa)
8
x
x
x
elastomer
plastic failure
brittle failure
Deformation is reversible!
• Decreasing T... --increases E --increases TS
--decreases %EL
• Increasing strain rate...
--same effects as decreasing T. 20
40
60
80
00 0.1 0.2 0.3
4°C
20°C
40°C
60°C to 1.3
(MPa)
Data for the semicrystalline polymer: PMMA (Plexiglas)
• Stress relaxation test:
Er(t)
(t)o
--strain to and hold.--observe decrease in stress with time.
• Relaxation modulus:
• Data: Large drop in Er for T > Tg.
(amorphouspolystyrene)
103
101
10-1
10-3
105
60 100 140 180
rigid solid (small relax)
viscous liquid (large relax)
transition region
T(°C)Tg
Er(10s) in MPa
time
straintensile test
ot( )
Time-Temperature Superposition
Log Time
Log
Rel
axat
ion
Mod
ulus
Rel
axat
ion
Mod
ulus
Hi T
Lo T
time
Stre
ss,
10 s
10
L
fixed LLo
Er(0)= E, Young’s ModulusEr( )= 0
Glass-like elasticity
Rubber-likeelasticity
Fluid-likeViscous
Viscoelstic modulus
Modulus of elasticity E r (10s) = (10) fixed
Relaxation Modulus