1. 工研院 講稿
11/9/2017
NAPLES: a practical pathway toward computer simulation of complex molten materials
Complex Fluids & Molecular Rheology Lab., Department of Chemical Engineering

2. The Reputation Theory and Tube Model
Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics; Oxford, 1988.

4. Governing equations for the kinetic (reputation) tube model
1. Langevin equations of motion for the confined chain
2. Affined deformation for the confining tube
3. Stress tensor expression
Hua, C. C.; Schieber, J. D. The Journal of Chemical Physics 1998, 109,

5. Entangled polymers of complex architecture
Polybutadiene
Polyisoprene
Star Polymer
Linear Polymer
Pom-Pom Polymer
Shie, S. C.; Wu, C. T.; Hua, C. C. Macromolecules 2003, 36, 2141.
Hua, C. C.; Kuo, H. Y. Journal of Polymer Science Part B: Polymer Physics 2000, 38, 248.

6. the slip-link model and the tube model
Modeling of Entangled Polymer: Pioneer Researches
Reptation model
(de Gennes)
Tube model
(Doi and Edwards)
Pearl necklace model
(Kremer and Grest)
Bond-fluctuation model
(Carmesin and Kremer, Shaffer)
Slip-link model
(Hua and Schieber)
1980
1990
Primitive path fluctuation
(depend on the chain length)
Entanglement due to binary interaction (core assumption in the slip link model)
Spatial distribution of “links”
Assumptions:
Primitive path potential
Tube confinement
With increasing level of coarse graining: the pearl necklace model, the bond-fluctuation model,
the slip-link model and the tube model
Larson, R. G.; Zhou, Q.; Shanbhag, S.; Park, S. J. AIChE Journal 2007, 53, 542.

7. Masubuchi, Y. ; Watanabe, H. ; Ianniruberto, G. ; Greco, F
Masubuchi, Y.; Watanabe, H.; Ianniruberto, G.; Greco, F.; Marrucci, G. Macromolecules 2008, 41, 8275.

8. NAPLES: a spatial-temporal slip-link model

9. Case 1: Linear polymer
Yaoita, T.; Isaki, T.; Masubuchi, Y.; Watanabe, H.; Ianniruberto, G.; Marrucci, G. Macromolecules 2011, 44, 9675.

10. Case 2: Polymer blends
Masubuchi, Y.; Amamoto, Y. Macromolecules 2016, 49, 9258.

11. Case 3: Star polymer
Masubuchi, Y.; Yaoita, T.; Matsumiya, Y.; Watanabe, H. The Journal of Chemical Physics 2011, 134,

12. Case 4: Pom-Pom polymer
Masubuchi, Y.; Matsumiya, Y.; Watanabe, H.; Marrucci, G.; Ianniruberto, G. Macromolecules 2014, 47, 3511.

13. Case 5: Block copolymer
Masubuchi, Y.; Ianniruberto, G.; Greco, F.; Marrucci, G. Journal of Non-Crystalline Solids 2006, 352, 5001.

14. Future outlook and challenge ?

15. Entangled PS melt - Start-up shear flow
Mw= 2.0×105 g/mole
Me= 7200 g/mole
Entangled number (Z0= Mw/Me)= 28
Plateau modulus (G0)= MPa
Unit stress= 1.6*G0
Unit time [Maximum Relaxation Time/ (0.0025*(maximum Z-value^3.6))] = 1.2*10-3 s
0.1
0.3
1.0
3.0
10.0
30.0
Yaoita T.; Isaki T.; Masubuchi Y.; Watanabe H.; Ianniruberto G.; Greco F. and Marrucci G. The Journal of Chemical Physics 2008, 128,

16. Entangled PS melt - Frequency scan
Mw= 2.0×105 g/mole
Me= 7200 g/mole
Entangled number (Z0= Mw/Me)= 28
Plateau modulus (G0)= MPa
Unit stress= 1.6*G0
Unit time [Maximum Relaxation Time/ (0.0025*(maximum Z-value^3.6))] = 1.2*10-3 s
Yaoita T.; Isaki T.; Masubuchi Y.; Watanabe H.; Ianniruberto G.; Greco F. and Marrucci G. The Journal of Chemical Physics 2008, 128,

17. - Relaxation Modulus for various strain rates
Entangled PS Solution
- Relaxation Modulus for various strain rates
Mw= 6.7×105 g/mole
Me= g/mole
Entangled number (Z0= Mw/Me)= 23
Plateau modulus (G0)= 0.34 MPa
Unit stress= 1.6*G0
Unit time= 0.9 s
Furuichi et al., The Journal of Chemical Physics 2010, 133,

18. - Relaxation Modulus for various strain rates
Entangled PS Solution
- Relaxation Modulus for various strain rates
NAPLES
NAPLES

19. Comparison of Experimental and Simulation Result - Frequency Sweep