Viscoelasticity of Copolymers andPolymer Blends with Bicontinuousand Other Structures
M. Takahashi
Kyoto Institute of Technology, Japan

Part I
Structure and Rheology ofBlock and Starblock Copolymers

Objectives
For SB block and starblock copolymers, to clarify
1. Structure-rheology relationships for lamellar-,cylinder- and gyroid-forming samples
2. Flow-induced orientations by large amplitude
oscillatory shear (LAOS) and steady flow (SF)LAOS
Lamella CylinderGyroidPoly-grainorientation

G′(ω) of SB Block Copolymers

chainmotion

defects andgrainboundary

motion of lamellar,cylinder, and gyroid
domainsGyroid-Forming
SB Diblock Copolymer

SB Diblock Copolymer
CodeMn(S)

Mn(B)

f(B)

Mw/Mn

1SB20

20.1K

10.8K

0.36

1.09

Anti-oxidant (2 wt%)
Kneader : 160oC
15min , 20rpm

Hot press : 160oC
15min , 2MPa

Temperature Sweep of G’ and G”
20K 10K
S
B
GyroidCylinderTime Sweep of G’ for 1SB20
C

20K 10K
SB

GyroidB
TOOT ~ 160oC

G’ becomes stable
after 74 hr at 150oC
after 25 hr at 160oC
after 40 min at 200oC

CylinderA

TEM Micrographs of 1SB20CylinderEnd○● FlowA

Flow

Initial State

RadialRadial

100nm

Edge

Edge
End

○● Radial

Flow

50nm

Quenched from T=160oC after Stabilization

B

Edge

○● Radial

Flow

Gyroid50nm

G’ and G” at T=160oC after Stabilization
B
Gcubic= 1.85×104 Pa

Quenched from T=200oC after Stabilization
Gyroid

C

Flow
Edge
RadialEnd

Edge○● Flow

50nm

End○● Radial

50nm

G’ and G” at T=200oC after stabilization

CGcubic= 2.61×104 Pa

G’ and G” at T=160oC after stabilized at T=200oC
200oC→160oC
Gcubic= 2.71×104 Pa

3D TEM Image of 1SB20(quenched from 160oC after stabilization at 200oC)

H. Jinnai et al.

S(interface)/V= 1.45×106 (cm-1)

220×220×74nm

Result of 3D Thinnig for 1SB20(quenched from 160oC after stabilization at 200oC)
H. Jinnai et al.

ν(network)=3.52×1017(cm-3)
3-branch: 75%

220×220×74nm

average length: 15.3nm

Gcubic= ν kT

ν : # of molecules per unit volume

ν(Gcubic) = 4.58×1018 (cm-3)
ν(network) = 3.52×1017 (cm-3)
S(interface) / Vν(interface) == 3.63×1018 (cm-3)
S(per chain)

PSPB

S(interface) / V = 1.45×106 (cm-1)
S(per chain) = π <S2>
1
2
<S > =[ (C∞Nl2)PS+ (C∞Nl2)PB ]6

Gcubic= ν kT

ν(Gcubic)(cm-3)

ν(network)(cm-3)

ν(interface)(cm-3)

ν : # of molecules per unit volume

160oC after
stabilized at 200oC

stabilized
at 200oC C

stabilized
at 160oC B

4.58×1018

4.00×1018

3.10×1018

3.52×1017

3.28×1017

2.20×1017

3.63×1018

2.78×1018

3.36×1018

Lamellar-Forming
SB Starblock Copolymer

(SB)n Star Block Copolymers
Armn234Code2SB10
3SB10
4SB10
n=2SBMn(PS)
9.31K
9.53K
9.51K

Mn(PB) fPB
11.6K 0.56
11.4K 0.55
11.4K 0.55
n=4n=3SB

2-3 wt% anti-oxidant was melt blended at T>TODTMelt pressed at T<TODT at 3MPa for 15 min.

LLLTEM Micrographs of Toluene Cast Films
10K 10K

Arm S

B

n=2

n=1

lamellarlamellar

n=4n=3lamellar

100nm

lamellar

Packing Effect
PSPB

n=4PS

n=3n=2

Freq. Despersion of G’ for Lamellar-forming 4SB10
10K
motion ofslope=1/2
lamellardomainconcentration
fluctuation

chainmotion

10K
Superposition ispossible in ordered
and disorderedstates

Poly-grain statesdisordered, one
phase

G’ ~ ω1/2at ω < ωCDecrease in G’ after LAOS for 4SB10
10K
10K

0.1ωC
slope=1/2

After LAOS

ωLAOS

G’

Evaluate
G’after/G’beforeat ω = 0.1 ωCDecrease in G’ after LAOS for 4SB10
10K
10K
A

B

C
At each T
G’after/G’before
D

ωLAOS

Observation of Lamellar Orientation
RadialFlow
EndEdgeTEM Micrographs of 4SB10 after LAOS (ωLAOS=0.1s-1, 160oC)

A

Flow

Flow

Edge

Radial200nm

Radial100nm

End200nm

100nm

Parallel > Perpendicular >> Transverse

TEM micrographs of 4SB10 after LAOS (ωLAOS=10s-1, 160oC)

C

Flow

FlowEdge

Radial

100nm

Radial

60nm

End

100nm

Parallel orientation is prevailing

60nm

Effect of n (=2,4) on G’ Reduction
LAOS at γ = 0.5

slope=1/2

n=2
n=4

ωLAOS/ωC ≅ 0.80 T/TODT ≅ 0.90
Data of 2SB10
are superposed
onto those of
4SB10 at ω ≥ ωC
When n , G’due to stronger
orientation oflamellae

Cylinder-Forming
SB Starblock Copolymers

(SB)n Star Block Copolymers
Armn234Code2SB203SB20
4SB20
n=2S
B

Mn(PS)
20.0K
19.9K
19.9K

Mn(PB) fPB
10.5K 0.34
10.8K 0.35
10.2K 0.34

n=3n=4SB

2-3 wt% anti-oxidant was melt blended at T>TODTMelt pressed at T<TODT at 3MPa for 15 min.

CCC

TEM Micrographs of Toluene Cast Films
Arm

20K 10K

100nm

n=1n=2SB

cylindercylindern=3cylinder

n=4
DisorderedcylinderFreq. Despersion of G’,G” for Cylinder-forming 2SB20
２０K １０K

ωCIn poly-grain stateG’ ~ ω1/3at ω < ωC

Freq. Despersion of G’,G” for Cylinder-forming 3SB20

ωCIn poly-grain stateG’ ~ ω1/4at ω < ωC

Freq. Despersion of G’,G” for Cylinder-forming 4SB20

ωCIn poly-grain stateG’ ~ ω1/5at ω < ωCDecrease in G’ after LAOS and SF for 4SB20
20K
10K

After LAOS
G’ showsminimum at

ωLAOS = 0.5s-1.

ωLAOS = γSF = 0.5s-1
SF is more effective
for cylinder orientation

Decrease in G’ due to LAOS
20K
10K

At 160oC, 180oC
ωLAOS
G’For SF
G’after / G’before=0.10

Orientation of Hexagonal Cylinders
RadialEdgeFlowEnd。

30d100d100
d110d110

Parallel

Perpendicular4SB20・.

at ωLAOS = γSF = 0.5s-1 (160oC)

After LAOS

After SF

60nm

60nm

End

○●Flow Radial

End○●Flow Radial

SF is more effective for Parallel Orientation

4SB20 after LAOS (ωLAOS = 100s-1, 160oC)
End○● Flow

Radial

100nm

Edge

○● Radial

Flow

100nm

Cylinders are perpendicular to the disc surface!!

Orientations of Lamellae and Cylinders
RadialFlowParallel

Perpendicular Transverse

Conclusions
For lamellar-forming samples
1) In ordered state, G’ ~ ω1/2.
2) After LAOS, G’ decreases with increasing ωLAOS
due to parallel orientation.
3) Perpendicular orientation is also observed for lowωLAOS.

For cylinder-forming samples
1) In ordered state, G’ ~ ω1/(n+1).
2) After LAOS, G’ decreases with decreasing ωLAOS(showing minimum) due to parallel orientation.
3) SF is more effective for parallel orientation.
4) For ωLAOS > ωC, cylinders orient perpendicular to disc.

Time sweep of G’, G” for 1SB20
G20K 10K
SBG

CG’C
C → G is fast
G → C is slowG”.

2SB20at ωLAOS = γSF = 0.5s-1 (160oC)

After LAOS

End

○●

After SF

60nm

Flow Radial

Perpendicular orientation

End○●60nm

Flow Radial

Parallel orientation

Theories for Slow Relaxation behavior
Lamellar-forming，Poly-grains (randomly oriented )Kawasaki-Onuki (1990)

Rubinstein-Obukhov (1993)

Hydrodynamic mode of lamellar motion Collective diffusion of copolymer
chains along the interface
Overdamped second-sound mode
controlled by defects
G’(ω) G”(ω)(Bη0)1/2ω1/2
G’(ω) G” (ω) ~ ω1/2
B : bending modulus of lamella
η0 : viscosity in the disordered phaserandomlyorientedMechanisms of lamellar orientation
1. Selective rotation of grains
2. Selective melting and reformation of lamellae
3. Defect migration
4. Reduction of mechanical resistance
5. Tube orientation (for entangled chains)
6. Coupling of the lamella motion and the shear
field (shear-induced lamella formation)
H.Watanabe in “Structure and Properties of Multiphase PolymericMaterials”, pp. 317-360, Marcel Dekker, New York (1998)