Complexity in Polymer Phase Transitions

---from Materials Science to Life Sciences

Wenbing Hu ( 胡文兵 )

School of Chem. and Chem. Eng.

Nanjing University

CHINA 2008-05-20, Beijing

What are polymers?

• Chain-like macromolecules containing 1000 atoms or more.

---1953 Nobel Laureate H. Stäudinger

http://www.chemistryexplained.com/St-Te/Staudinger-Hermann.html

Age of polymer materials

• Plastics (include foam plastics, thin films)• Rubbers (tires, shoes, seals)• Fibers (clothes, textures)• Coatings (oil painting)• Adhesives• Water-absorbing and filtering resins• Artificial organs• ……

Two basic phase transitions in polymer materials

• Liquid-liquid phase separation

• Polymer crystallization

Liquid-liquid phase separation

• High-impact polystyrene (rubber-plastic blend)

Soft & tough+Hard & crispHard & toughAFM picture by Jiang Liu

Polymer crystallization

• Semi-crystalline contexture (solid+elastic)

Hard & tough

Hu, et al. Macromolecules 2003

Semi-crystalline

Plastics Fibers

Celluloses Starches Chitosan

Polymers belong to complex fluid

• Complexity: 32 definitions (Wikipedia)

“Integration larger than addition.”

Polymers belong to complex fluid

• Complexity: integration larger than addition.

“1+1>2”

Complexity in polymer phase transitions

L-L phase separation + Crystallization

Their interplay

Phase diagrams of polymer solutions

Interplay

Competitionand even more!

L-LL-S

L-S crystallization

Molecular driving forces

Mixing interactions B

Drive DriveNew energy parameter!Classic Flory-Huggins parameter

Flory J. Chem. Phys. 1942.Huggins Ann. N.Y. Acad. Sci. 1942.

Polymer concentration

T

L-L L-S

？

Why do we need new parameter?

• Phase diagrams in a single component

In a single componentGas Liquid Solid

Condensation Crystallization

In polymer solutions Dilute Concentrated CrystallineLiquid-Liquid demixing Crystallization

Molecular packing

Packing energy: first stage L-L demixing second stage L-S crystallization

Molecular driving forces

Mixing interactions B

Drive Drive

New energy parameter!

Classic Flory-Huggins parameterFlory J. Chem. Phys. 1942.Huggins Ann. N.Y. Acad. Sci. 1942.

Polymer concentration

T

L-L L-S

Hu J. Chem. Phys. 2000.

Parallel-packing interactions Ep

Partition function for polymer solutions

Coordination number q,volume n,solvent takes n1 sites,n2 polymer chains, each taking r sites.

Hu J. Chem. Phys. 113, 3901(2000); Hu et al. 118, 10343( 2003).

kT

E]

2/nq

n)1r(1[

2

2q

p

p2

ez

2222221 )1()1()2(

21

)2

()()( rnm

nrp

nrnrc

nnn zzezq

n

n

n

nZ

Verify mean-field theory with simulations

• 32-mers at T(Ep/Ec, B/Ec)

0.0 0.2 0.4 0.6 0.8 1.02

4

6

8

10

12

Tm (1, 0.1)

Td (1, 0.1)

Td (0, 0.25)

Td (1, 0.25)

T /E

c/k B

Polymer volume fraction0.0 0.2 0.4 0.6 0.8 1.0

2

4

6

8

10

12

Td (1, 0.1)

Tm (1, 0.1)

Td (0, 0.25)

Td (1, 0.25)

T /E

c/k B

Polymer volume fraction

Theoretical predictions Simulation verifications

Hu, W.-B.; Mathot, V.B.F; Frenkel, D. J. Chem. Phys. 118, 10343( 2003).

L-L

L-S

The first story---

Crystal nucleation enhanced by L-L demixing.

Crystallization influenced by L-L demixing

0.0 0.2 0.4 0.6 0.8 1.01

2

3

4

5

6

1st. Ep/E

c=1.0, B/E

c=0.092

2nd

3rd. Ep/E

c=1.14, B/E

c=0

3rd

2nd. Ep/E

c=1.064, B/E

c=0.05

1st

T /E

c/k B

Polymer volume fraction

L-S coexistence

L-L binodal

1st

3rd

2nd

Control the crystal morphology!

Hu, W.-B.; Frenkel, D. Macromolecules 37, 4336(2004)

Onset temperatures of crystal nucleation on cooling

128-mers in solutionsC1 ： B/Ec=0.076,Ep/Ec=1C2 ： B/Ec=0.03,Ep/Ec=1.072C3 ： B/Ec=-0.1,Ep/Ec=1.275Lines: crystal nucleationDashes: L-L binodalDots: L-L spinodal

Zha, L.-Y.; Hu, W.-B. J. Phys. Chem. B 111, 11373-11378(2007).

0.0 0.2 0.4 0.6 0.81.5

2.0

2.5

3.0

3.5

4.0

C3

C2

C1

Tem

pera

ture

/(E

c/k)

Polymer volume fraction

C2

C1

C1

C2

Crystal nucleation triggered by spinodal decomposition ！

Modulate morphology at low temperatures

Triggered by prior SD No prior SD

Zha, L.-Y.; Hu, W.-B. J. Phys. Chem. B 111, 11373-11378(2007).

Crystal nucleation enhanced at the interfaces of incompatible polymers

Ma, Y.; Zha, L.-Y.; Hu, W.-B.; Reiter G.; Han, C. C. Phys. Rev. E in press.

0 5 10 15 20 25 30 35 40 45 50 55 60 650

100

200

300

400

500

600

700

Pop

ulat

ions

of

clus

ters

Z positions of the largest clusters

0.0 0.1 0.3 0.5 0.7

16-mers 50:50 blends, EP/EC=1, variable B/EC, kT/EC=4.0.

Theoretical interpretation

Ma, Y.; Zha, L.-Y.; Hu, W.-B.; Reiter G.; Han, C. C. Phys. Rev. E in press.

0.0 0.2 0.4 0.6 0.8 1.0

4

5

6

7

8

9

10

-0.1

0

0.1

0.3

Me

ltin

g t

em

pe

ratu

res

/Ec/

k

Volume fractions of crystallizable polymers

0.5

L-S phase diagrams for variable B/Ec

L-S

Something different in polymer solutions

128-mers ， 50% ， Ep/Ec=1,variable B/Ec, kT/Ec=4.5

Manuscript under preparation.

0 5 10 15 20 25 30 35 40 45 50 55 60 650.00

0.01

0.02

0.03

0.04

0.05

Pro

babl

ity o

f th

e la

rges

t cl

uste

rsZ-positions for the largest clusters

0.5 0.4 0.3 0.2

Crystal nucleation enhanced at surfaces only with very poor solvent

0.5 0.6 0.7 0.8 0.9 1.04.5

4.6

4.7

4.8

4.9

5.0

5.1

5.2

5.3

5.4

5.5

5.6

5.7

0.5

0.4

0.3

0.2

0.5

0.40.30.2T

em

pe

ratu

res

(un

its o

f E

C/k

)

Volume fractions of polymers

L-S phase diagrams for variable B/Ec

Manuscript under preparation.

The second story---

L-L demixing enhanced by crystallizability.

L-L demixing among isotactic, atactic and syndiotactic polypropylenes

])1

1)(2

1()2[(lnln 2

2212

2

21

1

1

kT

E

rqkT

Bq

rrnkT

F pmix

Mixing free energy of polymer blends:

~0 for r1,r2>>1 ~0 for similar chemistry

Component-selective crystallizability drives L-L demixing!

Hu, W.-B.; Mathot, V.B.F. J. Chem. Phys. 119, 10953(2003).

>0

L-L demixing enhanced by fluctuations towards crystalline order

Tk

E

rqTk

Bq

rrTk

f

B

p

BB

mix

2

2122

11 1

12

12lnln

Mean-field treatment Fluctuations?

0.0 0.2 0.4 0.6 0.8 1.0

4

8

12

16

20

-0.02

-0.01

0

Tem

pera

ture

(un

its o

f E

c/k)

Volume fraction of the crystallizable component

0.01

Ma, Y.; Hu, W.-B.; Wang, H. Phys. Rev. E 76, 031801(2007).

32-mers in 323 latticeEp/Ec=1, variable B/Ec Data points: simulationsLines: L-L binodalsDashes: L-S coexistence

L-L

L-S

The third story---

Single-chain folding accelerated by collapse transition.

Classification of polymer solutions

Critical overlapping concentration C*

Dilute solutions C<C* ， Concentrated solutions C>C*

Phase diagrams in single-chain systems

Single 512-mer with variable B/Ep

Collapse transition Tcol

Crystallization Tcry

Hu, W.-B.; Frenkel, D. J. Phys. Chem. B 110, 3734-7(2006)

-0.1 0.0 0.1 0.2 0.30

5

10

15

Tcry

Tcol

T /E

p/k

B/Ep

Free energy calculation at equilibrium T

0 100 200 300 400 5000

10

20

30

40

50

60

70 B/E

p, T /E

p/k

-0.1, 2.198 0, 2.755 0.04, 2.976 0.1, 3.289 0.3, 3.683

F /(

kT)

Molten units

Height of free-energy

barrier

Crystal nucleation enhanced by prior collapse transition

-0.1 0.0 0.1 0.2 0.3

2

4

6

8

10

12

20

40

60

80

100

120

140

Tcry

Tcol

T /E

p/k

B/Ep

Height of F/kT

Height of free-energy barrier

Hu, W.-B.; Frenkel, D. J. Phys. Chem. B 110, 3734-7(2006)

Protein folding

Levinthal paradox:

It is formidable for protein folding to experience all possible conformation. The folding must have a fast path.

Beta folding is a crystal nucleation process!

1.Framework model via nucleation

2.Hydrophobic molten globule as intermediate

1+2=Nucleation-condensation model

Fast path of protein folding

-0.1 0.0 0.1 0.2 0.30

5

10

15

Tcry

Tcol

T /E

p/k

B/Ep

1. F

ram

ewor

k

Nuc

leat

ion

Con

dens

atio

n

2. H

ydro

ph

ob

ic C

olla

pse

Physics origin of life

• Life is a non-equilibrium phenomenon evolved in nature for dissipating energy more efficiently.

Physics origin of life

• Life emerges at the edge of phase transitions with their interplay. The interplay provides adaptability and efficiency to bio-functions, for instance, the fast path of protein folding.

• Chain-like macromolecules are favorable for performing interplay.

Summary

• Complexity in polymer phase transitions is rep

resented by their interplay ： 1 、 L-L demixing enhances crystal nucleation

and thus modulates crystal morphology ； 2 、 Sometimes crystallizability enhances L-L

demixing ；• Fast path of protein folding may be based on t

his kind of interplay.

Thanks for your attentions！

Discussions are welcome!