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.

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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

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

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, 10018.

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.

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.

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

NAPLES: a spatial-temporal slip-link model

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

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

Case 3: Star polymer Masubuchi, Y.; Yaoita, T.; Matsumiya, Y.; Watanabe, H. The Journal of Chemical Physics 2011, 134, 194905.

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

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

Future outlook and challenge ?

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)= 0.204 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, 154901.

Entangled PS melt - Frequency scan Mw= 2.0×105 g/mole Me= 7200 g/mole Entangled number (Z0= Mw/Me)= 28 Plateau modulus (G0)= 0.204 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, 154901.

- Relaxation Modulus for various strain rates Entangled PS Solution - Relaxation Modulus for various strain rates Mw= 6.7×105 g/mole Me= 29700 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, 174902

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

Comparison of Experimental and Simulation Result - Frequency Sweep