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PHYSICS OF SOLID POLYMERS
Professor Goran Ungar WCU C2E2, Department of Chemical
and Biological Engineering Seoul National University
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Course content
• Which polymers can crystallize and which can not?
• Conformation of polymer chains – why helices? why coils?
• Polymer crystal structure – the atomic scale
• Comparison between synthetic and biopolymers
• Polymer crystals and chain folding – the nanoscale
• Crystallinity in polymers – basics of wide and small-angle X-ray scattering
• Why chains fold? Polymer crystallization – a controversial topic. Case study: “self-poisoning effect in uniform model polymers – the “misled molecules”
• Spherulites and cylindrites – the microscale; basics of birefringence and polarized light microscopy
• Deformation of semicrystalline polymers – microfibrils, yielding, crazing;
Synthetic fibers
• Routes to high modulus and strength in flexible polymers: ultradrawing, solid-state extrusion, gel-spinning; the story of Spectra
• Routes to high modulus and strength in rigid polymers: thermotropic and lyotropic liquid crystal polymers; the story of Vectra and Kevlar
• Polymer blends: miscibility, bimodal and spinodal decomposition
• Viscoelasticity and glass transition – why it’s difficult to catch “silly putty”?
• Linear and nonlinear viscoelasticity, creep, stress-relaxation; Dynamic Mechanical Spectroscopy, dielectric spectroscopy
• Rubber elasticity; rubber band vs metal spring
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STRUCTURAL HYERARCHY IN SEMICRYSTALLINE POLYMERS
atomic scale - crystal unit cell
- several Angstroms (<1 nm to a few nm)
- detailed crystal structure, conformation of individual bonds - wide-angle XRD
scale of crystal thickness -100-500 Å (10 - 50 nm)
- electron microscopy, small-angle XRD scale of crystal aggregates (spherulites etc.)
-μm scale - optical microscopy
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Bragg equation relating diffraction angle θ to interplanar spacing d
θ
d θ
2dsinθ incident
diffracted
electron density
nλ = 2d sinθ Small d - large θ (wide angle XRD) when layers are layers of atoms
Large d - small θ (small-angle XRD) when layers are e.g.
thin crystals
5 WHICH POLYMERS CAN CRYSTALLIZE?
Linear
- thermoplastic (e.g. HDPE) - potentially crystallizable (can contain some long branches)
Branched (short and long branches) - thermoplastic (e.g. LDPE) - potentially crystallizable
(lightly) - vulcanized rubber - may crystallize at low T and under stress
Cross-linked (densely)
- cured thermoset resin - amorphous (glassy) Cross-linked
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C C
H
H H
H
C C
H
H H
H
C C
H
H H
H
C C
H
H H
H
C C
H
H H
H
C C
H
H H
H linear polyethylene
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Crystallizable polymers must also be:
• homopolymers
• stereoregular
• regioregular
Can crystallize?
Homopolymer AAAAAAAAAAAAA yes random copolymer AABABBABBBABA no block copolymer AAAAAAABBBBBB partially
AAAAAAAAAAAAA
graft copolymer partially
BBBBBBBBB
8 C
H
H C H X
[ ]
n vinyl polyomers:X = - Cl poly(vinyl cloride) (PVC - CH3 polypropylene (PP) - Phenyl polystyrene (PS)
- polyacrylonitrile (PAN) - COOCH3 poly(methyl acrylate)
poly(methyl methacryla (PMMA, Perspex)
C N
]
n[
CH
H C CH3 COOCH3 H
C
H CX
H H
C
H CX
H vinyl monomers
+
9 C C
H H
CH3 H
C C H H
CH3 H C C
H
H H
CH3 C C H
H CH3
H
C C H H
CH3 H
C C H H H CH3
C C H
H CH3
H C C H
H H
CH3 C C H
H CH3
H C C H
H H
CH3 C C
H H
CH3 H C C H H
CH3 H
C C H H
CH3 H C C H H H CH3 C C
H H
CH3 H
C C H H
CH3 H
C C H
H CH3
H C C H
H CH3
H isotactic polypropylene (i-PP)
syndiotactic polypropylene (s-PP)
atactic polypropylene
stereoregular
stereo-irregular
SEREOREGULARITY OF POLYMERS
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C C
H
H H
C C
H
H H
C C
H
H H
C C
H
H H
C C
H
H H
C C
H
H H
isotactic polystyrene (i-PS)
REGIOREGULARITY
= regularity in head-to-tail or head-to-tail orientation of monomers throughout the macromolecule.
regioregular:
head-to-tail
head-to-head
regioirregular:
C C H H
CH3 H C C H H
CH3 H
C C H H
CH3 H
C C H H
CH3 H
C C H
H CH3
H C C H
H CH3
H
C C CH3
H H
H C C CH3
H H
H C C H
H CH3
H C C CH3
H H
H C C H
H CH3
H C C H
H CH3
H
C C CH3
H H
H C C H
H CH3
H C C CH3
H H
H C C H
H CH3
H C C H
H CH3
H C C CH3
H H
H head-to-tail
head-to-head
regioirregular
Trans (anti) and gauche conformations - hindered rotation about single C-C bond
Æ polymers flexible
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Conformation = shape of a molecule having a degree of flexibility
also conformation of a bond Å Potential energy as a function of torsion angle around C-C bond
Minima:1 “trans” (deepest) 2 “gauche” C
C H
H H
H
C
H C
H H
H
trans anti( ) gauche
Newman projection – view along C-C bond ΔEg
ΔE*
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Rotational Isomeric State Model Rotational Isomeric State Model
• fraction of gauche increases with T
• - factor 2 because 2 gauche states (g+, g-), only 1 trans
ΔEg≈ 1-2 kJ/mol –Æat r.t. fg≈ 0.5
) / exp(
2 1
) / exp(
2
kT E
kT f E
g g
g
+ − Δ
Δ
= −
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Rotational Isomeric State Model
• RIS model – an approximation
• neglects all dihedral (torsion) angles other than 180
oand ±60
o(Flory)
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Random Coil
• Polymer chain in solution, melt, or amorphous glass
segment root-mean-square
(monomer) end-end distance:
“random walk”:
distance ∝ no. of steps (strictly true only for “ideal chains”)
• End-to-end distance:
R a1,2
a2,3
∑
− −= N
i i i 1
,
a 1
R
2 / 2 1 / 2 1
0
R aN
R ≡ =
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Gaussian Coil
• “ideal chain” = freely-jointed non-self-avoiding chain – freely jointed: any angle between aiand ai+1equally
probable
– non-self-avoiding: chain can overlap with itself
• Distribution of end-to-end distances
– e.g. for one chain over time – Gaussian distribution – probability of finding a monomer at the end of vector R
starting from centre of gravity:
p
R
2 2 2 / 3
2 2
exp 3 2
) 3 (
G
G R
R R
p −
⎟⎟
⎟
⎠
⎞
⎜⎜
⎜
⎝
=⎛ R
π
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Radius of Gyration
• Radius of gyration RG2tells us about the expanse of the random coil
• (N = number of monomers, rivector from centre of gravity (mean momomer position) to monomer i)
• RGof polymer in solution can be found by light scattering or SAXS
• RGof polymer in melt can be found by small-angle neutron scattering (SANS) of polymer doped with labeled (deuterated) chains
∑
==
Ni i
G
N
R
1 2
2
1
r
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Radius of Gyration
• For an ideal chain in melt or in a theta-solvent:
– (random walk in 3d – remember end-to-end distance
N a R
0=
6 a N R
G=
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Persistence Length
• Theory of worm-like chains (Kratky and Porod)
• Persistence length is the distance along the chain at which orientational correlation with the starting segment drops to 1/e.
• Persistence length is a measure of the rigidity of a polymer chain
e = 2.72
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Crystal Structure of Polyethylene
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Crystal Structure of Polyethylene
i-PP – What conformation in crystal?
all-trans conformation relaxed
(energy minimized) helix
i-PP – What conformation in crystal?
helix
25 The three-fold helix of isotactic polypropylene in front of
the Giulio Natta Research Center in Ferrara, Italy
Photo of the right-handed helix courtesy of Pr. Galli t(he left-handed one is courtesy of Powerpoint)
QuickTime™ et un décompresseur Graphique sont requis pour visionner cette image.
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Synthetic polymers form regular helices.
- To fit into crystal lattice chains must be:
- straight - periodic
- Helix: avoids close contact between side groups.
• Notation of single-strand helices
m/n or mn
m: number of chemical repeat units (monomers) in a full crystallographic period (unit cell length)
n: number of turns of the (continuous) helix per full crystallographic period
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Example 1: 3/1 (or 31) helix of i-PP:
3 monomers per full repeat 1 turn of a helix per full repeat
0,3 1
2
projection
of helix +120o
3/1 right
0,3 2
1 -120o 3/1
left Unit operation of a 31axis: translation by 1/3 repeat period
+ rotation by 1/3 of a circle (120 deg)
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0,4 2 1
90o
4/1 3
4/1 helix: i-poly(1-butene)
(Form III)
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7-fold helices
0,7 1 2
51.4o
7/1 3 4
5
6 0
4 1
7/2 2
3
102.80
5
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,7 , Poly(ethylene oxide), PEO
[-CH2-CH2-O-]n
Per crystallographic repeat:
•7 monomer repeats,
•2 helical turns
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Problem:
Describe the all-trans planar zig-zag conformation of polyethylene in terms of helical notation.
Rotation between successive repeat units:
360*(n/m) Translation along helical axis:
c/m
(c = crystal unit cell length)
31 History of the three crystal phases of isotactic polypropylene.
α phase. Discovered and Solved by Natta and Corradini, 1954 β phase. Discovered 1959 (Padden & Keith), Solved 1994 (by Meille, Brückner, Ferro, Lovinger, Padden and by Lotz, Kopp, Dorset). It is a frustrated structure.
γ phase. Discovered 1959 (Addink& Beintema), Solved 1989 (Brückner & Meille). Non-parallel chains.
Packing of helical chains in crystals i-PP
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i-PP, a-Form α
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i-PP, a-Form
X-ray fibre diffraction pattern (fibre axis vertical)
•1stmeridional reflection on 3rdlayer line
α
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Poly(ethylene oxide) Crystal packing of 7
2helices
Poly(ethylene oxide) Crystal packing of 7
2helices
1stmeridional reflection on 7thlayer line
8 6 4 2 0