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 , Beijing

What are polymers? Chain-like macromolecules containing 1000 atoms or more Nobel Laureate H. Stäudinger

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 & crisp  Hard & tough AFM picture by Jiang Liu

Polymer crystallization Semi-crystalline contexture (solid+elastic) Hard & tough Hu, et al. Macromolecules 2003

Semi-crystalline Plastics Fibers CellulosesStarchesChitosan

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 Competition and even more! L-L L-S L-S crystallization

Molecular driving forces Mixing interactions B Drive New energy parameter! Classic Flory-Huggins parameter Flory J. Chem. Phys Huggins Ann. N.Y. Acad. Sci Polymer concentration T L-L L-S ？

Why do we need new parameter? Phase diagrams in a single component

In a single component Gas  Liquid  Solid Condensation Crystallization In polymer solutions Dilute  Concentrated  Crystalline Liquid-Liquid demixing Crystallization Molecular packing Packing energy: first stage L-L demixing second stage L-S crystallization

Molecular driving forces Mixing interactions B Drive New energy parameter! Classic Flory-Huggins parameter Flory J. Chem. Phys Huggins Ann. N.Y. Acad. Sci Polymer concentration T L-L L-S Hu J. Chem. Phys Parallel-packing interactions E p

Partition function for polymer solutions Coordination number q,volume n,solvent takes n 1 sites,n 2 polymer chains, each taking r sites. Hu J. Chem. Phys. 113, 3901(2000); Hu et al. 118, 10343( 2003).

Verify mean-field theory with simulations 32-mers at T(E p /E c, B/E c ) 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 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 solutions C1 ： B/E c =0.076,E p /E c =1 C2 ： B/E c =0.03,E p /E c =1.072 C3 ： B/E c =-0.1,E p /E c =1.275 Lines: crystal nucleation Dashes: L-L binodal Dots: L-L spinodal Zha, L.-Y.; Hu, W.-B. J. Phys. Chem. B 111, (2007). 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, (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. 16-mers 50:50 blends, E P /E C =1, variable B/E C, kT/E C =4.0.

Theoretical interpretation Ma, Y.; Zha, L.-Y.; Hu, W.-B.; Reiter G.; Han, C. C. Phys. Rev. E in press. L-S phase diagrams for variable B/E c L-S

Something different in polymer solutions 128-mers ， 50% ， E p /E c =1,variable B/E c, kT/E c =4.5 Manuscript under preparation.

Crystal nucleation enhanced at surfaces only with very poor solvent L-S phase diagrams for variable B/E c Manuscript under preparation.

The second story--- L-L demixing enhanced by crystallizability.

L-L demixing among isotactic, atactic and syndiotactic polypropylenes Mixing free energy of polymer blends: ~0 for r 1,r 2 >>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 Mean-field treatment Fluctuations? Ma, Y.; Hu, W.-B.; Wang, H. Phys. Rev. E 76, (2007). 32-mers in 32 3 lattice E p /E c =1, variable B/E c Data points: simulations Lines: L-L binodals Dashes: 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*

Phase diagrams in single-chain systems Single 512-mer with variable B/E p Collapse transition T col Crystallization T cry Hu, W.-B.; Frenkel, D. J. Phys. Chem. B 110, (2006)

Free energy calculation at equilibrium T Height of free-energy barrier

Crystal nucleation enhanced by prior collapse transition Hu, W.-B.; Frenkel, D. J. Phys. Chem. B 110, (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

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 represented 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 this kind of interplay.

Thanks for your attentions ！ Discussions are welcome!