Polymer Synthesis
CHEM 421
Block Copolymers
Block Copolymer Basics
Polymer Synthesis
CHEM 421
• MOST polymers DO NOT mix
(like oil and water).
Polymer A
Polymer B
Let’s consider the fundamentals of mixing…
Mixing Thermodynamics
Polymer Synthesis
CHEM 421
Consider a binary mixture :
mixing
VA
VB
Volume occupied
by species A
Volume occupied
by species B
VTOT = VA + VB
Rubinstein, M. and Colby, R. H. Polymer Physics, Oxford University Press, 2003.
Mixing Thermodynamics
Volume Fractions:
VA
A 
VA  VB
Polymer Synthesis
CHEM 421
B  1   A
NA = Number of lattice sites occupied by
each molecule of species A
NB = Number of sites occupied by B molecules
v0 = lattice site volume
Lattice
Volume
molecularvolumeof species A   A   0 N A
molecularvolumeof species B   B   0 N B
Regular solutionsare mixturesof low molar mass species with NA  NB  1
Polymer solutions are mixtures of macromolecules ( NA  N  1) with
low molar mass species ( NB  1)
Rubinstein, M. and Colby, R. H. Polymer Physics, Oxford University Press, 2003.
Polymer Synthesis
CHEM 421
Rubinstein, M. and Colby, R. H. Polymer Physics, Oxford University Press, 2003.
Mixing Thermodynamics
Polymer Synthesis
CHEM 421
Three cases of interest:
NA
Small Molecule Solutions 1
Polymer Solutions
N
Polymer Blends
NA
NB
1
1
NB
• VTOT = VA + VB occupy n sites: n  VA  VB
0
• All molecules of A occupy:
VA  n
A
0
Rubinstein, M. and Colby, R. H. Polymer Physics, Oxford University Press, 2003.
Mixing Thermodynamics
Polymer Synthesis
CHEM 421
Consider a solution of polymer A
(species B is the solvent)
T heentropyS is theproduct of the Boltsmanconstantk
and thenaturallogarithmof thenumber of ways (ln )
to arrange moleculeson thelattice
S  k ln 
 A  nA
 AB  n
For a homogeneous mixture of A and B, each molecule
has ΩAB possible states where n is the total # of lattice sites
 
S A  k ln  AB  k ln  A  k ln AB 
 A 
S A  k ln A
Rubinstein, M. and Colby, R. H. Polymer Physics, Oxford University Press, 2003.
Mixing Thermodynamics
Polymer Synthesis
CHEM 421
• To calculate the total entropy of mixing, sum entropy
contributions from each molecule:
Smix  nA SA  nB SB  k nA ln  A  nB ln B 
• The number of molecules of A and B are:
nA 
n A
NA
nB 
nB
NB
Rubinstein, M. and Colby, R. H. Polymer Physics, Oxford University Press, 2003.
Mixing Thermodynamics
Polymer Synthesis
CHEM 421
• Entropy of mixing:
Smix
B
 A

 k  ln A 
ln B 
NB
 NA

• For a regular solution, NA = NB = 1
Smix  k A ln A  B ln B 
A large entropy of mixing for small
molecule solutions!
Rubinstein, M. and Colby, R. H. Polymer Physics, Oxford University Press, 2003.
Mixing Thermodynamics
Polymer Synthesis
CHEM 421
• Entropy of mixing for polymer solutions,
NA = N and NB = 1
Smix
 A

 k  ln A  B ln B 
 NA

• Enormous differences in the entropy of
mixing for polymer solutions versus
regular solutions versus polymer blends!
ΔSmix, polymer < ΔSmix, small molecule
Rubinstein, M. and Colby, R. H. Polymer Physics, Oxford University Press, 2003.
Mixing Thermodynamics
Polymer Synthesis
CHEM 421
• Entropy of mixing for polymers,
NA = N and NB = N
Smix
B
 A

 k  ln A 
ln B 
NB
 NA

• Is even worse!!
Rubinstein, M. and Colby, R. H. Polymer Physics, Oxford University Press, 2003.
Polymer Synthesis
CHEM 421
Rubinstein, M. and Colby, R. H. Polymer Physics, Oxford University Press, 2003.
Block Copolymer Basics
Polymer Synthesis
CHEM 421
• MOST polymers DO NOT mix
(like oil and water).
Polymer A
Polymer B
Let’s consider the fundamentals of mixing…
Microphase Separation
• Most polymers are immiscible
Polymer Synthesis
CHEM 421
Block Copolymer Basics
Polymer Synthesis
CHEM 421
The chemically different segments of a block
copolymer cannot completely phase
separate, because they are covalently
bound (“frustrated” separation).
The propensity of two different polymers to
phase separate can lead to interesting
solid-state and solution morphologies.
Let’s consider the parameters affecting
phase separation in diblock copolymers …
Polymer Synthesis
CHEM 421
Diblock Morphologies (TEM)
Polymer Synthesis
CHEM 421
• Spheres
PS-b-PI
fPS = 0.16
100 nm
Han, C. D.; Vaidya, N. Y.; Kim, D.; Shin, G.; Yamaguchi, D.; Hashimoto, T.;
Macromolecules 2000, 33(10), 3767-3780.
Polymer Synthesis
CHEM 421
Diblock Morphologies (TEM)
Cylinders
(Dendritic Benzyl Ether)-b-PS
Stained w/ RuO4
Pochan, D. J.; Pakstis, L.; Huang, E.; Hawker, C.; Vestberg, R.;
Pople, J.; Macromolecules 2002, 35(24), 9239-9242.
200 nm
Polymer Synthesis
CHEM 421
Diblock Morphologies (TEM)
Polymer Synthesis
CHEM 421
Lamellae
PS-b-PI fPS = fPI
Stained with OsO4
Bailey, T.S.; Pham, H. D.; Bates, F. S.
Macromolecules 2001, 34, 6994-7008.
50 nm
PS-b-PI
Same magnification
Same volume fraction…
Left: MW = 104
Right: MW = 105
Polymer Synthesis
CHEM 421
Polymer Synthesis
CHEM 421
• PS-b-PI
• 45% PS
• Differences in TEMs?
discrete block copolymer
tapered block copolymer
Copolymerization Kinetics
Polymer Synthesis
CHEM 421
Homo-propagation
Cross-propagation
Cross-propagation
Homo-propagation
Styrene = M1
Bd = M2
r1 = k11 / k12 = 0.04
r2 = k22 / k21 = 26
For free radical r2 >>1 and r1 < 1 gives….?
For living polymerization r2 >>1 and r1 < 1 gives….?
Mixing Thermodynamics
• Free Energy of mixing for polymers,
ΔG = ΔH - T ΔS
Smix
B
 A

 k  ln A 
ln B 
NB
 NA

• ln of a fraction is negative!
Polymer Synthesis
CHEM 421
Block Copolymer Uses
• Unique properties of triblocks
Polymer Synthesis
CHEM 421
Polymer Synthesis
CHEM 421
Triblock Morphologies
Polymer Synthesis
CHEM 421
Bates, F.S., 1999 MSRI Lecture notes: http://www.msri.org/publications/ln/msri/1999/materials/fbates/1/banner/03.htm,
accessed 9/2003.
Polymer Synthesis
CHEM 421
TEM of PI-b-PS-b-PDMS
Polymer Synthesis
CHEM 421
Bates, F.S., 1999 MSRI Lecture notes: http://www.msri.org/publications/ln/msri/1999/materials/fbates/1/banner/03.htm,
accessed 9/2003.
Phase Separation in
PS-b-(PE-co-PB)-b-PMMA
0.5μm
Breiner, U.; Krappe, U.; Thomas, E. L.; Stadler, R. Macromolecules 1998, 31, 134-141.
Polymer Synthesis
CHEM 421