Computer Smui altoni of Self- Organization in Block Copolymers · The Physics of Block Copolymers, Ian W. Hamley, Oxford University Press, 1998 Block Copolymers: Past Successes and

Computer Simulation of Self-Organization in Block Copolymers

P BackgroundP MethodP Results

The Physics of Block Copolymers, Ian W.Hamley, Oxford University Press, 1998

Block Copolymers: Past Successes and FutureChallenges, Timothy P. Lodge, Macromol. Chem. Phys. 2003, 204, pp 265-273

[1] Computer simulation of structure and microphase separation in model A-B-A triblock copolymers, M. Banaszak, S. Woloszczuk, T. Pakula and S. Jurga, Phys. Rev. E, 66, 031804 (2002)

[2] Lamellar ordering in computer-simulated block copolymer melts by a variety of thermal treatments, M. Banaszak, S. Woloszczuk, S. Jurga and T. Pakula, J. Chem. Phys., 119, 11451-11457 (2003)

[3] Computer Simulation of Microphase Separation in IonicCopolymers ,M. Banaszak and J.H.R. Clarke, Phys. Rev. E, 60, 5753-5757(1999)

Monte Carlo

Molecular Dynamics

Monte Carlo

lattice model

triblock and diblockcopolymers

very short-rangepotential

more coarse-grained

Molecular Dynamics

off-lattice model

ionic diblock copolymers

long-range electrostaticpotential

less coarse-grained

Spheres of B in A

Cylinders of B in A

Layers

Cylinders of A in B

Spheres of A in B

Diblock copolymer phase diagam

Block copolymers are important self-assembling materials for the following

reasons:

PPrecise (and continuous) control over lengthscales - from 5 to 50 nm

PControl over morphology- L, C, G and S fordiblocks and over 30 for triblocks

PPossibility of selecting the polymer for each blockPQuantitative prediction of equilibrium structures -

SCMF

Applications of Block Copolymers

P“Old” - retain important features of theirconstituent homopolymers, do not take advantageof any particular nanostructure

P“New” - depend on long-range organization andorientation of the nanostructure

Challenges

P Synthesis and preparation of materialsP New nanostructures (theory and simulation)P

[ ]ABBBAA

BBABAA

BA

BABB

BA

A

Am

kT

z

NNf

εεεχ

εεεϕϕ

φχφϕφϕφ

22

,,

1

lnln

−+=

−−−=+

++=

Flory-HugginsTheory

A B

Macrophase and microphase separation

Reduced Temperature, T*/N

Pε - interaction energy between A and BPT* = kT/εPχ = (z -2)/T*PLeibler’s RPA theory (mean field)

< Flory interaction χ parameter< N - copolymer chain length (number of monomeric

units)< N χ = 10.5 - ODT for symmetric diblocks< T*/N - the copolymer reduced temperature

Triblock microarchitectures

1010 7 3

#10-10-10#7-16-7#3-24-3

# 30 x 30 x 30

# 60 x 30 x 30# 60 x 60 x 60

Simulation box, 60x30x30

T*/N=0.04 T*/N=0.10

T*/N=0.18 T*/N=0.24

Lamellar nanostructures

Bicontinuous nanostructure for the10-10-10 microarchitecture,

T*/N=0.04

7-16-7 Microarchitecture , T*/N=0.04

7-16-7 Microarchitecture, T*/N=0.04

3-24-3 Microarchitecture, T*/N=0.04

Phase diagram of the symmetric tribloccopolymer melt

00.050.1

0.150.2

0.250.3

0.350.4

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

T*/N

f

C B' L L' B C'

disordered

ordered

( )2*

2**

Tn

EEC

cv

−=

0

0.5

1

1.5

2

2.5

0.1 1

E/na a)

0

0.5

1

1.5

2

2.5

3

0.1 1

Cv

b)

70

80

90

100

110

120

130

0.1 1

R2

T*/N

c)

Quenching

Slow cooling

0

0.5

1

1.5

2

2.5

0.1 1

E/na a)

0

0.5

1

1.5

2

2.5

3

3.5

0.1 1

Cv

b)

70

80

90

100

110

120

130

0.1 1

R2

T*/N

c)

T*/N=0.04 T*/N=0.10

T*/N=0.18 T*/N=0.24

Lamellar nanostructures

( )

nrrM

rr

ii

M

i i

rr •=

−=Λ ∑ =1

2

00.20.40.60.8

11.21.4

0.04 0.06 0.08 0.1 0.12 0.14

Λ

T*/N

Λ parameter - low-temperature lamellarordering

Bridges and Loops

12

13

14

15

16

17

18

0.04 0.06 0.08 0.1

Φ

25

30

35

40

45

0.04 0.06 0.08 0.1

T*/N

D ~ Τ∗µ

Φ ~ Τ∗τ

D

µ = - 1/6

τ = 1/9

µ = - 0.21

τ = 0.24

Diblock melts

8-8microarchtekture

Box sizes

30x32x30 G

40x32x30 "

50x32x30 –

60x32x30 $

Monte Carlo steps

Lamellarreorientation

Ionic Block Copolymerφ WCA( rij) = 4ε((σ/ rij)

12-(σ/ rij)6) + ε rij < 21/6 σ

Cations

x 160

=

σεπεσ 4 E

2

Ro

jiijeqq

T* = kT/ Eσ

Conclusion

P MD simulation for triblock and diblockcopolymers

P Microphase separation as a function of pressureP Experimental search for low-temperature

ordering effects in block copolymer meltsP New efficient algorithms for copolymer

simulations