2006/2007 Macromolecules
Introduction to MacromoleculesIntroduction to MacromoleculesCHM5080 (CUHK) – CHEM588 (HKUST) – CHEM6108 (HKU)CHM5080 (CUHK) – CHEM588 (HKUST) – CHEM6108 (HKU)
Lecturers: Chi WU (CUHK) [email protected] Ben Zhong TANG (HKUST) [email protected] Wai Kin CHAN (HKU) [email protected]
Time/date: CUHK: L1 & L2 Science Centre Feb 10 & March 3 10:00-12:30 HKUST: Rm 2405 (Academic Building) March 17 & 3114:00-17:30 HKU: P3, Chong Yuet Ming Physics Building April 14 & 28
Final Exam: CUHK/HKUST/HKU May 12, 10:00-12:30 (Saturday)
Textbooks:
“Introduction to Macromolecular Science”By Petr Munk, 1989, John Wiley & Sons, QD381.M85
“Introduction to Polymers”, 2nd editionBy R. J. Young and P. A. Lovell, 1991, Chapman & Hall, QD381.Y68
TA: Ms Shi Feng, Room 226C, 2609-6266, [email protected]
2006/2007 Macromolecules
OutlinesCUHK 1. Concept of macromolecules 2. Structures of macromolecules 3. Characterization of macromolecules
HKUST 4. Classification of polymerization reactions 5. Step (or condensation) polymerization 6. Chain (or addition) polymerization 7. Copolymerization
HKU 8. Ionic polymerization 9. Coordination polymerization10. Controlled radical polymerization11. Synthesis of polymers with special properties
2006/2007 Macromolecules
Natural Macromolecules
Proteins, DNA, RNA Polysaccharides
(cellulose: plants & animals)
Synthetic Macromolecules
Polystyrene, polyethylene Poly(vinyl chloride)
Polyesters, polyurethane, ...
Small molecules Oligomers (M > 104 g/mol) Macromolecules
The difference between small molecules and macromolecules
* Homogeneous* No swelling in dissolution* Purification methods* Low viscosity* Simple structures
* Inhomogeneous (size & mass)
* Swelling in dissolution* Precipitation, GPC, …* High viscosity* Complicate structures.
The Basics of Macromolecules
2006/2007 Macromolecules
Structures of macromolecules
* Primary structures Composition: number & types of atoms
Configuration: how they are connectedHomopolymer & heteropolymers:block, seqential, graft, random, ...
* Secondary structures
linear, branching, star, grafting, ladder, ...
Comformation: folding, helix, sheet, ...
* Tertiary structures Special arrangements of larger segments(helix & sheet) to form a complicate structure
* Quaternary structures Spatial multi-chain aggregates, intra- andinter-chain interaction, e.g., triplethelix and enzyme
2006/2007 Macromolecules
Pri
mar
y st
ruct
ure
s * Backbone contains only carbon atoms
- Polymeric hydrocarbons: Polyethylene Polypropylene isotactic, syndiotactic & atactic
Polybutadiene 1,2 addition and 1,4 addition (cis & trans)
Polyisoprene -(CH2C(CH3)=CHCH2)n- natural rubber
Polystyrene
Low (H.P.) and high (L.P.) density PE
The most representative polymer
- Halogen-containing: Poly(vinyl chloride)Polytetrafluoroethylene
-(CH2CCl)n- common polymerTeflon, The king of plastic
Polytrifluorochloroethylene Tough and inert
- With polar side groups: Poly(methyl methacrylate) Organic glass
Poly(hydroxyethyl methacrylate) Gel contains 35% water
Polyacrylamide Typical water soluble polymer
Polyacrylic acid Washing power, useful polymers
Poly(vinyl alcohol), Poly(vinyl pyrrolidone), ….
- Polymers with heteroatoms in the backbone:
Polyether - PEO; Polyesters -(O-(CH2)a-CO)n-, PCL; Polycarbonates -(O-R-O-CO)n-;
Polyamides -(NH-(CH2)a-CO)n-; Polyurethanes -(NH-R1-NH-CO-O-R2-O)n-; Polyureas; ...
2006/2007 Macromolecules
DNA
The living organisms (1-10 x 107)
Natural macromolecules: DNA, RNA, Proteins, Polysaccharides …
fundamentally similar inside
infinitely different outside
Heredity(1-10 x 1013 cells)
four nucleotides
Psugar
base Adenine ThymineGuanine Cytosinepurines pyrimidines
Replication DNA
RNA
Transcription
sugar
H
sugar
OH
Thymine UracilDNA / RNA
Proteins
Translation
catalytic function H2N-C-COOHH
R
3 basic ones2 acidic ones5 polar ones
10 non-polar ones
GenomesDNA chains
GenesSegments
regulatory sequences
exon (~1.5%) intron (~25%)
~30%
Procaryotes + eucaryotes
2006/2007 Macromolecules
Physical formsPhysical forms
Powders
Solutions
Hydrogels
Hydrocolloids
Fibres
Films
VariablesVariables
Monosaccharide substituents
Glycosidic linkages
Molecular size profile
Substitution patterns
Cross-linking
Polysaccharides: Physical Forms and Variables
2006/2007 Macromolecules
HO
CH2OH
OH
O
OOHO
OH
CH2OH
O
n4)--D-Glcp-(14)--D-Glcp-(1
Principal constituent of plant cell walls.Wood & Cotton are the major industrial sources
Cellulose
2006/2007 Macromolecules
Major industrial sources of starch are wheat, maize (yellow maize & waxy maize starches), potato, rice, tapioca and sago. The ratio of amylose to amylopectin is characteristic of botanical origin.
O
HOOH
CH2OH
O
OO
HOOH
CH2OH
OO
HOOH
CH2OH
O
4)--D-Glcp-(14)--D-Glcp-(1
amylose O
HOOH
CH2OH
O
OO
HOOH
CH2
OO
HOOH
CH2OH
O
O
HOOH
CH2OH
O
O
amylopectin
Starch ( Amylose & Amylopectin )
2006/2007 Macromolecules
Structures of macromolecules
* Primary structures Composition: number & typs of atoms
Configuration: how they are connectedHomopolymer & heteropolymers:block, seqential, graft, random, ...
* Secondary structures
linear, branching, star, grafting, laddle, ...
Conformation: folding, helix, sheet, ...
* Tertiary structures Special arrangements of larger segmentsto form a complicate structure, e.g., helix
* Quaternary structures Spatial multi-chain aggregates, intra- andinter-chain interaction, e.g., triplethelix and enzyme
2006/2007 Macromolecules
Structure of a protein chain: Primary: Secondary and Tertiary Structures
2006/2007 Macromolecules
Sec
onda
ry s
tru
ctu
res
- C
onfo
rmat
ion
*. Helical structure - Proteins, amylose and nucleic acids
Energy vs Entropy Random coil vs Ordered conformation
It requires two hydrogen bonds in the formation of the helix (not proline).
It contains 3.6 amino acid residues per turn; subsequent residues are rotated 100owith a pitch of 5.4 A; and the translation is 1.5 A per residue.
*. Chain folding of some regulated heteropolymer chains
O rd ere d co il
R an d o m co il
C o lla p sedco re -sh e ll
n an o p artic le
h ea t h ea t
Stickers moverandomly like a
“gas”Stickers move in
a more correlated fashion like a
“liquid” Stickers arerestricted
like a“solid”
2006/2007 Macromolecules
Sec
o nda
r y s
t ru
c tu
r es
T < ~32 oC
PNIPAM-g-PEO
Tincreases
dcreases
A single polymer chaincore-shell nanostructure
Chi Wu, Xingping Qiu, Physical Review Letters, 79, 620 (1998); Macromolecules, 30, 7921
Applications
One of the envisionedapplications is the smarttemperature-sensitivedrug delivery device. 0 10 20 30 40 50
1.2
1.4
1.6
1.8
t / min
0
20
40
60
I 1/I 3
T / oC
80pyrene: an imitated drug
Protein denaturation Heat denatured & chemical denatured
2006/2007 Macromolecules
Structures of macromolecules
* Primary structures Composition: number & typs of atoms
Configuration: how they are connectedHomopolymer & heteropolymers:block, seqential, graft, random, ...
* Secondary structures
linear, branching, star, grafting, laddle, ...
Conformation: folding, helix, sheet, ...
* Tertiary structures Special arrangements of larger segmentsto form a complicate structure, e.g., helix
* Quaternary structures Spatial multi-chain aggregates, intra- andinter-chain interaction, e.g., triplethelix and enzyme
2006/2007 Macromolecules
Tertiary structures - Arrangement of larger segments
Secondary structure - helix
Heat
Chemical
Enzymatic Catalysis Specific & fast
Particular spatial arrangement
Energy - adenosine triphosphate (ATP)
Chymotrypsin - a “hydrophobic pocket - aromatic amino acids
Trypsin - an ionized carboxyl - interacted with the basic groups
2006/2007 Macromolecules
2006/2007 Macromolecules
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A zig-zag chain A thread chain A random coil
Let us start with a polymer chain in one dimensional space.It has N segments and each segment has a length of b.
ob-b
A random walk
After N steps and if n steps are positive, R = bn + (-b)(N-n) = b(2n-N)2/Nn
NIf
The chance (probability) to find n positive steps is a binomial distribution because Pn is related to (p + q)N when p = q = 1/2. !)(!
!
nNn
NP
N
n
2
1
The mean value of n can be calculated as
22
2
1
1
1
2
1
2
1 1
100
NN
nNn
NN
nNn
nNnPn N
N
n
NNN
n
NN
nn
!)(!)(
!)(
!)(!
!
NN
n
nNn qpnNn
Nqp )(
!)(!
!
0
<R> = 0
4
1
11
1
2
1
2
1
1 10
2
0
22 )(
!)(!)(
!
!)(!)(
!)(
!)(!
!
NN
nNn
N
nNn
Nn
nNn
NnPnn
N
n
N
n
NN
n
NN
nn
42 N
n
2
0
222 )]2([ NbPNnbRRRN
nn
Step motion: Rn = b or -b nmmn bRR 2 2
1
2
11
2 NbRRRRN
nn
N
mm
N
nn
22 NbR bNRRRMS2
1
2
12
2006/2007 Macromolecules
!)(!
!
nNn
N
2
1P
N
n
?
,
nP
NWhen
2006/2007 Macromolecules
2006/2007 Macromolecules
In a good solvent, a chain is in the random coil state.
Radius of gyrationHydrodynamic Radius (Rh)
51.h
g
R
R2
1212
0
2
12 bNR
N
iiRMS
/
rR
End-to-EndDistant
R = rN - ro
2
1
6
NbRg
2006/2007 Macromolecules
Let us imagine an increase in monomer size from 0.1 nm to 1 cm.
N ~ 102-1010 in poor solvent
R = bN cm m
Polymer size: Polymer size depends on solvent quality
N ~ 102-1010 in theta solvent
R = bN ~ 10 cm -1 km
N ~ 102-1010 in good solvent
R = bN~ 16 cm – 40 km R = bN ~ 100 cm - 105 km
N ~ 102-1010; A rigid chain
Earth
Moon
2006/2007 Macromolecules
Thin rod: Rg2 = L2/12
Thin disk: Rg2 = (1/2)R2
N
ii
N
ii
N
ii
N
ii
N
ii
i
g
m
m
m
m
m
mR
1
1
2Gi
1
1
2GjGi
1
2j
N
1ii
2
)rr(
2
)]rr()rr[(
2
)rr(
For an idea chain jibjiij 222 rrR
)(
)()()(
16
2
2
1
2
21
2
1 1
2
1
1
2
2
N
NNb
N
iib
N
jib
m
jibmR
N
i
N
i
N
jN
ii
N
ii
g
bNRRRMS21212 //
66
,2/12/1
2
12 bNN
bRRNAs gg
4526 .g
RSM
R
R
Short rangeConfiguration
1) IR: vibration and rotation; 2) NMR: chemical shift;3) chemical analysis, GC, UV and MS; and ….
Long rangeConformation
1) viscometry: ~ Vh or Rh; 2) laser light scattering: Rg and Rh; 3) fluorescence: NRET; 4) x-ray and neutron scattering & diffraction; 5) relaxation: mechanical, electrial, optical, ...
Experimental Methods
2006/2007 Macromolecules
Structures of macromolecules
* Primary structures Composition: number & typs of atoms
Configuration: how they are connectedHomopolymer & heteropolymers:block, seqential, graft, random, ...
* Secondary structures
linear, branching, star, grafting, laddle, ...
Conformation: folding, helix, sheet, ...
* Tertiary structures Special arrangements of larger segmentsto form a complicate structure, e.g., helix
* Quaternary structures Spatial multi-chain aggregates, intra- andinter-chain interaction, e.g., triplethelix & enzyme
2006/2007 Macromolecules
Small molecules Conventional colloidsassembly Physical methods
Chemical methods
Macromolecules Polymeric colloids (supramolecules)assembly
P o l y ( p h e n y l v i n y l s u l f o x id e ) ( P V S O ) P o ly a c e ty le n e (PA )P o ly (p -m e th y l s ty re n e )
n P h S O H
2006/2007 Macromolecules
Qu
ater
nar
y st
ruc t
ure
s
Rc
RR
More Chains
Assembled
Self-assembly of rod-coil diblockcopolymers in dilute solution
2006/2007 Macromolecules
DNA
--OOCOOC
NHNH22
PPPP
Lipid Lipid bilayerbilayer
CytosolCytosolSingle-pass Single-pass multi-pass multi-pass
Non-cytosolNon-cytosol
Cell Membrane Proteins
2006/2007 Macromolecules
Molar mass distributons Mn , Mw , Mz, M
Absolute methods The end-group, colligative properties MS, light scattering, ultracentrifuge.
Relative methods viscosity, chromatography, FFFelectrophoresis, flow birefrigence
fn(M); fw(M); fz(M)
M
f M Mf Mw n( ) ( ) f Mf M M f Mz w n ( ) ( )2
The n-average molar mass
MMf M dM
f M dMn
no
no
( )
( )M
M N
Nn
ii
i
ii
1
1
The w-average molar mass MM f M dM
Mf M dM
Mf M dM
f M dMw
no
no
wo
wo
2 ( )
( )
( )
( )M
M W
W
M N
M Nw
ii
i
ii
ii
i
i ii
1
1
2
1
1
The z-average molar mass MM f M dM
Mf M dM
M f M dM
M f M dMz
wo
wo
no
no
2 3
2
( )
( )
( )
( )M
M W
M W
M N
M Nz
ii
i
i ii
ii
i
i ii
2
1
1
3
1
2
1
fM
Mf Mw
nn ( )
Schulz-Zimm Distribution
f Mb
zM ew
zz bM( )
( )
1
1
Poisson Distribution
f MM
w ( ) ( ) exp[( )
]/ 2
21 2
2
Logarithmic normal distribution
f M Az
nM
PwM
( ) exp[ ( ( )] 1
iii nMW 2iiiii nMnWZ
?n
w
M
M
2006/2007 Macromolecules
Review MacromoleculesNatural: DNA, protein, Polysaccharides ...
Synthetic: different polymers ...
Difference between small and macro-moleculesHigh-order structures
Polydispersity, solubility, ...
The statistic nature of chain conformations
R = <R2>1/2 = N2b
Rg = <Rg2>1/2 = N2b/6
Rh ~ Rhard with the same D
Different distributions of molar mass : Number- MN , weight- MW and Z- MZ ...
Different scaling relationships between the size and mass of linear flexible coiled chains
5
3
3
1 withM~Rg
5
4
2
1 withM~
2006/2007 Macromolecules
Experimental Methods
For polymer chains,molar mass distribution, conformation chain size distribution are important because “M and R” are directly related to properties and performance.
Absolute methods
which does not require atleast two or more narrowlydistributed standards withknown molar masses
for low molar mass chains :
end-group; vapor pressure osmometry; NMR;colligative properties; and MALDI-TOF-MS
for high molar mass chains :
membrane osmometry; ultracentrifugation; and static laser light scattering,
Relative methods which requires calibration
fractionation; translational diffusion; viscocity; chromatographic methods;dynamic laser light scattering; and …
2006/2007 Macromolecules
Macromolecules In solution
In bulk (solid)
thermodynamicshydrodynamicsamorphouscrystallinegels - hydrogels
In solution:In solution: dissolution process G G n Gmix ii
N
i
1
o
G
nii
*The Flory-Huggins Theory Simple & Effective: ~1940’s developed on the basis of a “pseudo lattice” model.
G H T Smix mix mix 2)( pspsmix VH
m
i ip V
F
The Hildebrand’s solubility equation
Condition : no volume change in the mixing
= e1/2 and e is the cohesive energydensity, i.e., the vaporization energy of unit volume liquid under zero pressure.
F is the attractionforce per molar
chemical groups.
G = H - TS when T = constant
2006/2007 Macromolecules
The end-group analysis Mn < 10,000 g/mol
e.g., Nylon-6 H2N(CH2)5CO-(-NH(CH2)5CO-)n-NH(CH2)5COOH
We can titrate the number of ends H2N- and -COOHFor a monodisperse sample : M = W/n ; For a polydispersed sample, W = niMi ; n = ni , and Mn = W/n
Colligative properties The boiling or freezing point change
limC
b or f
v or f n
T
C
RT
H M
0
2 1
why Mn ?
Membrane osmometry
solution solvent
popo+ /C = RT/Mfor small molecules
/C = RT/Mn
for macromolecules C
RTM
A C A Cn
( )1
2 32
MALDI-TOF-MS and NMRThere will be special courses to cover them.Here we only ontline their basic principles.
2006/2007 Macromolecules
RTPVornRTPVornT
PVR m
TkPvTkN
VP BB
A
m
R = kBNA
v
TkP B
particle one
VWhen one particle agitated by the
thermal energy (kBT) undergoes
a Brownian motion. It produces
a pressure (in solution, it is often
called osmotic pressure).
2006/2007 Macromolecules
The diameter decreases
D
rb = Rg
rb ~ D
D
D > Rg
D < Rg
The concept of “blob” in polymer science
2006/2007 Macromolecules
Nv
TkBosmotic
N
2NV
TkBosmotic
N’
V V
2'B'osmotic V
TkN
'osmoticosmotic
'NN
N”
V
'" NNN
"osmoticosmotic 'osmotic
"osmotic
2006/2007 Macromolecules
Laser Light ScatteringLaser Light Scattering
2006/2007 Macromolecules
Laser light scattering (LLS)
E = Eosin(2vt - )Es = k (d2P/dt2)
= E = 4’P = p +
H = ocE i = <EsHs> = oc<Es2>
ir
c Er
Io
o oo
o 16 164 2
4 22
4 2
4 2
' '
( )i ~
-4 i ~ r --2
i ~ ‘2 ~ V 2
For N particles
I = Ni
Rayleigh ratio : Rvv(q) = Ir2/Io = KCM Kn
dndC
N
o
AV o
4 2 2 2
4
( )Rvv(q) = KCMw
For a large particle :
i
j
Rqr
qro
i j
ijj
N
i
N
16 4
42
sin( ), KC
R q M P qA C
vv w( ) ( )
12 2
qn
o
4
2
sin p q
R q q
R qq Rvv
vvg( )
( )
( )
0
11
32 2
KC
R q Mq R A C
vv wg Z( )
( ) 1
11
322 2
2
why <Rg2>Z ? The z-average ?
2006/2007 Macromolecules
Encoder
Photomultiplier tube
Preamplifier/Discriminator
Stepping motor
Monitor diode
Focus Lens
Diode Laser Pumped Nd:YAG Laser532nm Wavelength
400 祄 pin-hole
Cell housing and index matching vat
Position-sensitive Detector
Cuvette
PhotonCounter
Static, Classic LLS(time average intensity)
Dynamic, Modern LLS(digital time correlator)
Polymer : 5x103 - 107 g/molParticles : 2 - 2000 nm
Dilute solution / suspension C = 10-3 - 10-6 g/ml
Rotating Arm
Spectra-Physics Helium Neon Laser632.8 nm Wavelength
Laser Light Scattering Spectrometer incorporated with differential refractometer
Laser
Laser
2006/2007 Macromolecules
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Static LLS Angular and Concentration dependence of <I>
CAqR
MqR
KC g
WVV2
22
2)3
1(1
)(
4
222 )/(4
oAN
dCdnnK
)2/sin(4
o
nq
)()()(o
r
o
r
S
roVVVV n
n
II
II
II
qRqR
A plot ofKC
R qvs C A
VVq"[
( )] " 0 2
A plot ofKC
R qvs q R
VVC g"[
( )] " 0
2 2
The extroplation ofKC
R qM
VVC q W[
( )] ., 0 0
<Rg2>
z1/2
A2
1/Mw
1 < < 2
2006/2007 Macromolecules
Dynamic laser light scattering
* Intensity fluctuation :
I
slow
* Doppler frequency shift :
~ 1015 Hz ; Hz It is rather difficult to detect .
* Time correlation function:
deGg
)()0(0)E(E
)(0)E(E)(
0*
*
)1(
c1
20
2 )(
2)(
S
deSEE i
)()()0( *
deEES i
)()0(
2
1)( *
+
-
fast
]|),q(|1[)0,q(
),q()0,q(),q(
2)1(2
|)2(
gI
IIG
The Siegert relation
Dynamic LLS
It
The fast the movements, the fast the fluctuation
2006/2007 Macromolecules
A typical time correlation function of the chains in solution
0.0 20.0 40.0 60.0 80.0 100.00.00
0.20
0.40
0.60
0.80[g
(2)(t
,q)-
A]/
A
t / ms
0.00
4.00
8.00
12.00
-2
10-1
10
G(
)
/ ms -1
)1)(1( 222 qRfCkDq gd
Dq
Cq
00
2
2006/2007 Macromolecules
temperature
size
Physical Review Letters 83, 4105 (1999)
The transition on surfacePhysical Review Letters
86, 822 (2001)
JACS, 123, 1376 The transition in mixed solvents
Physical Review Letters79, 4092 (1998)
Physical Review Letters77, 3053 (1996)
The folding of a single homopolymer chain
Macromolecules, 28, 5225 (1995);
28, 5388 (1995); 28, 8381 (1995);
29, 4998 (1996); 30, 0204 (1997);
30, 7921 (1997); 31, 2972 (1998).
No additional knotting
The molten globular state
2006/2007 Macromolecules
The collapsing of a single homopolymer chain
2.00 4.00 6.00 8.000.50
1.00
1.50
2.00
0
35.9 oC, Globule, R
g = 17.9 nm, R
g/R
h = 0.72
30.1 oC, Coil
Rg = 127 nm
Rg/R
h = 1.5
(Chi Wu) Figure1
[KC
/Rv
v(q
)] /
10-7
(m
ol/
g)
q2 / 10
10 cm
-2
Mw-1
101 1020.00
0.40
0.80
1.2035.9 oC 30.1 oC
f(Rh)
Rh / nm
2006/2007 Macromolecules
Ultra-fast infrared laser heating pulse induced conformation change
= 1.54 mWidth ~ 20 ns
2006/2007 Macromolecules
0 1 2 3 4
0.00
0.01
0.02
0 1 210-2
10-1
100
1-f
t / ms
I F(t
)-I F
(0)
(a.u
.)
t / ms
Kinetics of the coil-to-globule transition of single polymer chains
2006/2007 Macromolecules
0 1 2 3 40.00
0.25
0.50
0 1 2 3 40.0
0.2
0.4
[Is(t
)-I s(0
)]/I
s(0)
(%)
t / ms
I scat
teri
ng (
a.u.
)
t / ms
Time dependent scattering intensity after the laser heating pulse
2006/2007 Macromolecules
Nucleation and initial growthof pearls
Merging and coarseningof pearls
Nucleation and initial growthof pearls
Merging and coarseningof pearls
2006/2007 Macromolecules
Size exclusion chromatorgraphy
V = V0 + Vifor small M : Ve = V0 + Vi
for large M : Ve = V0
In general : Ve = V0 + Vi
Ve = A + B log (M) Ve = A’ + B’ log ([]M)standards A’ and B’
In practice , one can obtain Ve and calculate []M . If knowing [], one can find M.
Detectors * differential refractometer ; * viscometer ; * UV ; and * small angle light scattering from Ve to M
Field flow fractionation (FFF)Field
wflow
C(x) = C0 exp(-x/l) where l = D/u = kT/f
If d << l < 400 nm, it will be a normal FFF - Smaller ones come out first.If d >> l > 2 m, it will be a steric FFF - Larger ones come out first.
f
TkD
fuF
B
2006/2007 Macromolecules
Viscoelastic Properties of Bulk Polymers
Small molecules (liquid) Crystals and glass
Macromolecules (melts) Crystalline and amorphous
Temperature glassy melts viscoelastic
Several conceptsStress : F/A = Strain : L/L =
GG : the shear modulus Rigidity
J = 1/G (Compliance)
EE : the Young’s modulus Elasticity
E = 2G (1 + )
= -(d/d)/(L/L)
The tensile strength : The elongation at break
Viscosity ()
Shear stress F
L L
F
L
L
Normal stress
dt
d
2006/2007 Macromolecules
The Maxwell Model The stress relaxation T = constant
Elastic
Viscous
viselT
011
dt
d
Gdtdtdt
d viselT )exp(0 t
where
G
elGvisd/dt) since
)cos()sin()cos(0 tG
CBt
G
BCt
)sin()1(
)cos()1(
)(2222
22
0 ttt
For a dynamic experiment
G’() G’’()
GG )("
lim0
0
Storage modulus Loss modulus
0 0
G
CBand
G
BC
1
)('
)("tan
G
G
)sin()cos(assuming&)sin(If 0 tCtBtT
2006/2007 Macromolecules
The Voigt Model The creep experiment T = constant
viselT
dt
dGT
)exp(1)(
t
Gt T
where
G
)sin()()cos()()cos(0 tBGCtCGBt CGB 0
BGC 0
)sin()1(
)cos()1(
1)(
22220 ttt
For a dynamic experiment
G’() G’’()
GG )("
lim0
0
Storage modulus Loss modulus
)('
)("tan
G
G
elGvisd/dt) since
Ela
stic
Vis
cous
)sin()cos(assuming&)cos(If 0 tCtBtT
2006/2007 Macromolecules
Example Polycarbonate withtwo molar masses.
The time domain can be divided into four regions, I, II, III and IV.
I : t << 10 -1 s & G ~ 1010 dynes/cm2
The glassy state : hard, stiff, brittleThe backbone chain cannot movebecause t is too short or T is too low.
II : 1 < t < 10 2 s & 108 < G < 1010
The glass-to-rubber transition andthe polymer becomes leathery
III : 102 < t < 10 6 s & G ~ 108
The rubbery plateau : tough, elasticThe chains are entangled, but theirsegments start to move at a relatively long t or a relatively higher T.
IV : t > 10 6 s & G < ~106
The viscous state : viscous liquid,no elasticity, no shape and flowingThe chains can move & entanglementsare overcome at a long t or a higher T.
The backbone chain has t or T to jostle into a more relaxed conformation.
2006/2007 Macromolecules
logG
log t
log t1 log t3 log t2 log t4
log a1
log a2
logG
log t
log t1 log t2
log t2 - log a1
log t3 - log a1
log t3 - log a2
log t4 - log a2
The Time-Temperature Equivalency
G(t’, T’) = G(t’’, T’’) G(t2 , T1) = G(t1 , T2)
G(t3 , T1) = G(t2 , T2)G(t4 , T1) = G(t2 , T3)
log t1 + log a = log t2
…
The Williams-Landel-Ferry (WLF) equation
)(
)(
2
1
o
o
TTC
TTCaog
t1 = t2 / a
If Tg is taken as T0 ,
11
2
C
TT
C
C
aog
TT gg
The “universal” values of C1 and C2
C1 = 17.4
C2 = 51.6 T
VSP
Tg, true
Tg,2
Tg,1
a
e
bc
The glass transition temperature (Tg)
2006/2007 Macromolecules
The Glass Trenasition Temperature (Tg)Tg > Troom Plastic materials
Tg < Troom Rubbery materials
Glassy RubberyG decreases 3-4 ordersThe factors affect Tg
1. The flexibility of the chain backbone Tg PE : -80 oC; PP : -20 oC; PMA : 3 oC
2. The size of the side groups Tg (Two exceptions: symmetric or too long)
3. The interaction between chains Tg
The methods to change Tg
1. The addition of small molecules with a high boiling point .
2. The copolymerization of A and B so that Tg,A < Tg < Tg,B or Tg > or < Tg,A and Tg,B
3. The chain length Tg
4. The crosslinking of the chains. 5. The mixing of different polymers.
How to change a plastic material to a rubbery one?
2006/2007 Macromolecules
The Kinetics of Crystallization
The Avrami equation )exp(1 mKtis the crystallized fraction and can be determined by any property,such as volume, diffraction intensity, …. M depends on geometry, crystallization rate, & nucleation mode so that m is in the range 0.5-4.
0 1Pa
P Pc
P = Pa + (Pc - Pa)0
0
VV
VVt
e.g.,
In practice, plot “ ln [ ln [1/(1-)] ] versus ln t “
The glassy polymers
Non-equilibrium
The specific volume depends on how fast a sample was cooled down and how long it remains at a particular temperature.
V = V0 + VfreeV0 : the core and vibration & Vfree : the translation Vfree ~ 2.5%V
The elastic networks PTL
STF
,
)32
(2
2
vkS B
)1
(2
0
L
TvkF B
)1
(2
V
Tvk
A
F B
L
dL
V
Tvkd B
)
2(
2 )
2(
2
CM
RTE
CM
RTE
3
CM
RTG
2006/2007 Macromolecules
The Crystalline Polymers f
fm S
HT
STHG
Folding chains and Spherulites G is continuous at Tm , but not S or V.
G = H - ST; H = U + PV; U = Q - PdV;
Q = TdS dG = VdP - SdT S
T
G
P
dTT
GdP
P
GdG
PT
VP
G
T
T
G
eT
?
?T
V or S
eT
In general, there are three regions:T < Tg ; Tg < T < Tm ; and T > Tm
In reality, the process of “Crystal < > Melts” is a kinetic process. For example,Tm decreases with Tcry; Tm is higher than Tcry, the crytal size decreases as thecooling rate increases; and Tm < Te (infinite size), ….
Tg is related to the cooling rate, but not Tm.
Glassy stateAmorphous - it can be viewed as a supercooled liquid
Crystalline (0-100%) - it can be viewed as “crosslinking points”
2006/2007 Macromolecules
Morphology of crystalline polymers
The chain folding: 10-20 nm thicknessSpherulites in a concentrated solution.
Mechanical properties of crystalline polymers
0.5 < Tg/Tm < 0.8 Below Tg => Glassy and above Tm => Melts
Drawn in fibers
If Tg < T < Tm, the crystalline regions act as crosslinking points, so that the materials will be hard and tough. Such a structure can also be achieved by copolymering some hard segments into flexible chain backbone.
2006/2007 Macromolecules
Multicomponent and multiphase materials
Plasticization of polymers
Addint small molecules to decrease Tg .
Blending of different polymers
To obtain different Tg and toughness.
Heterophase polymers
Block and other structure copolymers
2221 VnVn
G
V
GG mixmixV
mix
222,122
21
1
1 lnln B
VVRTGV
mix
1
2,12,1 V
RTB
where
2006/2007 Macromolecules
SEM micrograph of pH-sensitive copolymer P(DEAM-co-MAA) hydrogels obtained at different pH values.
MD2 MD3 MD4
MD5 MD6 MD7pH = 7.0
MD2 MD3 MD4
MD5 MD6 MD7pH = 9.5
A polymer gel is a three-dimensional network swollen by a large amount of solvent. It has some properties between solutions and solids.
2006/2007 Macromolecules
mixing
Protein network microgels25 oC 37 oC
swelling state shrinking state
2006/2007 Macromolecules
Have a good term and Please do not forget chain conformations, different sizes, and so on