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TTTThhhheeeerrrrmmmmaaaallll TTTTrrrraaaannnnssssiiiittttiiiioooonnnnssss:::: CCCCrrrryyyyssssttttaaaalllllllliiiizzzzaaaattttiiiioooonnnn,,,,MMMMeeeellllttttiiiinnnngggg aaaannnndddd tttthhhheeee GGGGllllaaaassssssss TTTTrrrraaaannnnssssiiiittttiiiioooonnnn
• This lecture: Crystallization and Melting
• Next Lecture: The Glass Transition Temperature
• Why do polymers crystallize in a chain folded fashion?
• Why do polymers melt over a range of temperatures?
• What are the factors that affect the Tm?
Today:
Chapter 8 in CD (Polymer Science and Engineering)
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ViscoelasticViscoelasticliquidliquid
Semi-crystallineSemi-crystallineSolidSolid Glassy SolidGlassy Solid
CrystallizationCrystallization
MeltingMelting
GlassGlassTransitionTransition
TemperatureTemperature
TTTThhhheeeerrrrmmmmaaaallll TTTTrrrraaaannnnssssiiiittttiiiioooonnnnssss
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CCCCrrrryyyyssssttttaaaalllllllliiiizzzzaaaattttiiiioooonnnn aaaannnndddd tttthhhheeee GGGGllllaaaassssssss TTTTrrrraaaannnnssssiiiittttiiiioooonnnn
Vo
lum
e
Temperature
Tg Tc
Cool
Liquid or MeltGlassy
Solid
CrystallineSolid
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KKKKiiiinnnneeeettttiiiiccccssss,,,, CCCCrrrryyyyssssttttaaaalllllllliiiizzzzaaaattttiiiioooonnnnaaaannnndddd tttthhhheeee GGGGllllaaaassssssss TTTTrrrraaaannnnssssiiiittttiiiioooonnnn
Vo
lum
e
Temperature
Tg
Cool Quickly
Liquid or MeltGlassy
Solid
Does not Crystallize !
CrystallizableCrystallizable Polymer PolymerV
olu
me
Temperature
Tg
Cool Quickly
Cool Slowly
Tg
Non-Non-CrystallizableCrystallizable Polymer Polymer
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PPPPoooollllyyyymmmmeeeerrrr CCCCrrrryyyyssssttttaaaalllllllliiiizzzzaaaattttiiiioooonnnnWHAT DO WE KNOW FROM EXPERIMENTAL OBSERVATION ?
• Crystallization occurs relatively slowly
• At high undercoolings
• And results in the formation of chain folded lamellae
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PPPPoooollllyyyymmmmeeeerrrr CCCCrrrryyyyssssttttaaaalllllllliiiizzzzaaaattttiiiioooonnnn
MeltMelt
Semi-crystallineSemi-crystallineSolidSolid
TTc m
SpecificVolume
Temp
Cool
Heat
POLYMERSTTc m
SpecificVolume
Temp
Cool
Heat
SMALL MOLECULES
What isundercooling ?
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CCCCrrrryyyyssssttttaaaalllllllliiiizzzzaaaattttiiiioooonnnn KKKKiiiinnnneeeettttiiiiccccssss GGGGeeeennnneeeerrrraaaallll FFFFeeeeaaaattttuuuurrrreeeessss
• Induction period - formation of primary nuclei
• Primary crystallization - a period of fast spherulitic growth
• Secondary crystallization - a period of slower crystallization that occurs once the spherulites have impinged on one another
Induction PeriodInduction Period(Nucleation Step)(Nucleation Step)
PrimaryPrimaryCrystallizationCrystallization
CrystallizationCrystallizationSecondarySecondary
Time
Degree of Crystallinity
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TTTThhhheeeerrrrmmmmooooddddyyyynnnnaaaammmmiiiicccc CCCCoooonnnnssssiiiiddddeeeerrrraaaattttiiiioooonnnnssssThe free energy of this primary nucleus is given by
∆∆∆∆Gcryst = (4xl)σσσσ + (2x 2 )σσσσ e- (x 2l)∆∆∆∆g
• The last term represents the free energy that we would obtain if all the segments were in the bulk.• The first two terms are the excess free energy that must be “added in” to account for those segments at the surface.
σσσσe
σσσσ
x
x
l
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EEEExxxxtttteeeennnnddddeeeedddd CCCChhhhaaaaiiiinnnn CCCCrrrryyyyssssttttaaaallllssssaaaannnndddd AAAAnnnnnnnneeeeaaaalllliiiinnnngggg
Courtesy of I.R. Harrison, Penn State
Thermodynamically most stable form
Crystals irreversibly thicken on annealing - so theywould like to get to the extended form
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CCCCrrrriiiittttiiiiccccaaaallll NNNNuuuucccclllleeeeuuuussss SSSSiiiizzzzeeee
So why don‛t polymers crystallize in theextended chain form to begin with?To answer this let‛s calculate the criticalnucleus size.
T = Tm0
m
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CCCCrrrriiiittttiiiiccccaaaallll NNNNuuuucccclllleeeeuuuussss SSSSiiiizzzzeeee
NucleationNucleation at temperature T at temperature T
The critical nucleus size is given bythe values of l and x that minimize∆Gcryst;
∂∆G∂l
= ∂∆G∂x
= 0
l∗ = 4σe
∆g
Solving the two simultaneousequations
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∆T = Tm0
− Tc
where ∆T is the undercooling;
Also, at the equilibrium melting temperature, Tc = Tm0, and only
lamellae with infinite fold periods could grow.
Note the inversedependence of fold periodon ∆T.
CCCCrrrriiiittttiiiiccccaaaallll NNNNuuuucccclllleeeeuuuussss SSSSiiiizzzzeeee
Critical Nucleus Size Critical Nucleus Size
Substituting for ∆g;
ll**l∗ =
4σeTm0
∆hf ∆T
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TTTThhhheeee RRRRaaaatttteeee ooooffff PPPPrrrriiiimmmmaaaarrrryyyy NNNNuuuucccclllleeeeaaaattttiiiioooonnnn
∆∆∆∆T∆∆∆∆T
l*l*
l∗ =
4σeTm0
∆hf Tm0 − T( ) =
4σeTm0
∆hf ∆T
For l* large,∆T has to be small
∆ f c ∆νnuc ~ exp− const.σ 2σ e Tm
0[ ]
2
h2kT T[ ] 2
vnucvnuc
At small ∆T Vnuc is small
An expression for the rateof nucleation can also beobtained:
Note that the rate ofnucleation is vanishingly smallat low undercoolings. Onlynuclei with relatively short foldperiods (compared to chainlength) form at an appreciablerate.
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PPPPrrrriiiimmmmaaaarrrryyyy CCCCrrrryyyyssssttttaaaalllllllliiiizzzzaaaattttiiiioooonnnn::::
CrystallizationCrystallization
• Once a nucleus has been formed growth is predominantly in the lateral direction.• There is a considerable increase in the fold period behind the lamellar front during crystallization from the melt
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TTTThhhheeee CCCCrrrryyyyssssttttaaaalllllllliiiinnnneeee MMMMeeeellllttttiiiinnnngggg TTTTeeeemmmmppppeeeerrrraaaattttuuuurrrreeee
MeltMelt
Semi-crystallineSemi-crystallineSolidSolid
HeatHeat
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CCCChhhhaaaarrrraaaacccctttteeeerrrriiiissssttttiiiiccccssss::::MMMMeeeellllttttiiiinnnngggg TTTTeeeemmmmppppeeeerrrraaaattttuuuurrrreeeessss
100-10-20-30-40-50-50-40
-20
0
20
40
Temperature of Crystallization
Tem
pera
ture
(0 C
)
Melting is Complete
Melting Starts
Crystallization
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TTTThhhheeee MMMMeeeellllttttiiiinnnngggg TTTTeeeemmmmppppeeeerrrraaaattttuuuurrrreeee ooooffff PPPPoooollllyyyymmmmeeeerrrr CCCCrrrryyyyssssttttaaaallllssss
TemperatureTemperature
ll
Tm = Tm0
1− 2σ e
l∆hf
TTmm00
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FFFFaaaaccccttttoooorrrrssss tttthhhhaaaatttt AAAAffffffffeeeecccctttt tttthhhheeee MMMMeeeellllttttiiiinnnnggggTTTTeeeemmmmppppeeeerrrraaaattttuuuurrrreeee ooooffff PPPPoooollllyyyymmmmeeeerrrr CCCCrrrryyyyssssttttaaaallllssss
- CC - =O
=O
--
- N N --
-
-
H
H
CH2 -- CH2- CH2 -- CH2
CH2 -- CH2
TTm m ~ 135 ~ 13500CC
TTm m ~ 370 ~ 37000CC
Why?
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TTTThhhheeee EEEEffffffffeeeecccctttt ooooffff CCCChhhheeeemmmmiiiiccccaaaallll SSSSttttrrrruuuuccccttttuuuurrrreeee
∆∆∆∆Gf = ∆∆∆∆Hf - T∆∆∆∆Sf
ΤΤΤΤm = ∆∆∆∆Hf /∆∆∆∆Sf
∆∆∆∆Gf = 0000
EquilibriumEquilibrium at temperature T at temperature Tmm
ΤΤΤΤm = ∆∆∆∆Hf /∆∆∆∆Sf
And at Equilibrium
Hence
The subscript “f” stands for fusion
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CH2 -- CH2- CH2 -- CH2
CH2 -- CH2
TTm m ~ 135 ~ 13500CC
TTm m ~ 265 ~ 26500CC
IIIInnnntttteeeerrrrmmmmoooolllleeeeccccuuuullllaaaarrrr IIIInnnntttteeeerrrraaaaccccttttiiiioooonnnnssss
CH2 -- CH2- CH2 -- CH2 N
--C
O
=
-H
CH2
-
Is this Is this nylon 6nylon 6or or nylon 66nylon 66 ? ?
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OK, now it‛s your turn !Supposing you could synthesize such beasts, wouldyou expect syndiotactic poly(propylene) orsyndiotactic PVC to have the higher melting point?
- CH2 - CH - Cl
-
- CH2 - CH - CH3
-
TTTThhhheeee EEEEffffffffeeeecccctttt ooooffff IIIInnnntttteeeerrrrmmmmoooolllleeeeccccuuuullllaaaarrrr IIIInnnntttteeeerrrraaaaccccttttiiiioooonnnnssss
A.
B.
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EEEEnnnnttttrrrrooooppppyyyy aaaannnndddd CCCChhhhaaaaiiiinnnn FFFFlllleeeexxxxiiiibbbbiiiilllliiiittttyyyy
FlexibleFlexible
StiffStiff
ΤΤΤΤm = ∆∆∆∆Hf /∆∆∆∆Sf
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EEEEnnnnttttrrrrooooppppyyyy aaaannnndddd CCCChhhhaaaaiiiinnnn FFFFlllleeeexxxxiiiibbbbiiiilllliiiittttyyyy
∆∆∆∆∆∆∆∆SSff
∆Sf = k (lnΩmelt - lnΩcrystal ) = Large
S = k lnΩ
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CCCCoooonnnnffffoooorrrrmmmmaaaattttiiiioooonnnnaaaallll EEEEnnnnttttrrrrooooppppyyyy aaaannnndddd tttthhhheeee MMMMeeeellllttttiiiinnnngggg PPPPooooiiiinnnntttt
∆∆∆∆∆∆∆∆SSff = k ( = k (lnlnΩΩΩΩΩΩΩΩmeltmelt - - lnlnΩΩΩΩΩΩΩΩcrystalcrystal))
= Small= Small
TTmm = = ∆∆HHff / / ∆∆SSff
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- CH2 - CH2 -
- CH2 - CH2 - O -
- CH2 - CH2 - -
TTm m ~ 135 ~ 13500CC
TTm m ~ 65 ~ 6500CC
TTm m ~ 400 ~ 40000CC
PolyethylenePolyethylene
Poly (ethylene oxide)Poly (ethylene oxide)
Poly (p-Poly (p-xylenexylene))
EEEEnnnnttttrrrrooooppppyyyy aaaannnndddd tttthhhheeee MMMMeeeellllttttiiiinnnngggg PPPPooooiiiinnnntttt
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- CH2 - CH2 -
-
TTm m ~ 135 ~ 13500CC
TTm m ~ ? ~ ?
TTm m ~ ? ~ ?
PolyethylenePolyethylene
IsotacticIsotactic Polystyrene Polystyrene
EEEEnnnnttttrrrrooooppppyyyy aaaannnndddd tttthhhheeee MMMMeeeellllttttiiiinnnngggg PPPPooooiiiinnnntttt
- CH2 - CH - CH3 -
- CH2 - CH -
IsotacticIsotactic Polypropylene Polypropylene
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TTTThhhheeee EEEEffffffffeeeecccctttt ooooffff DDDDiiiilllluuuueeeennnnttttssss
∆∆∆∆∆∆∆∆SS11
∆∆∆∆∆∆∆∆SS22
∆∆∆∆∆∆∆∆SS2 2 > > ∆∆∆∆∆∆∆∆SS11
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TTTThhhheeee EEEEffffffffeeeecccctttt ooooffff CCCCooooppppoooollllyyyymmmmeeeerrrriiiizzzzaaaattttiiiioooonnnnaaaannnndddd MMMMoooolllleeeeccccuuuullllaaaarrrr WWWWeeeeiiiigggghhhhtttt