NAPLES New Algorism for Polymeric Liquids Entangled and Strained. Yuichi Masubuchi ICR, Kyoto University

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1 NAPLES New Algorism for Polymeric Liquids Entangled and Strained Yuichi Masubuchi ICR, Kyoto University

2 The ul:mate goal of polymer rheology Predict viscoelas:c behaviors from Mw Mw/Mn LCB Blends Copolymers Fillers. Shorter relax. :me Less elas:c Longer relax. :me More elas:c Mol. Arch. Rheology Processability Sugimoto, Koyama (2000)

3 May MD aoack this problem? NO! Transi:onal Glassy region Rubbery region Terminal flow region Domain for atomic MD Domain for CG- MD Data by Osaki & Inoue Problem of interest Molecular weight dependent, Chemistry weakly dependent Molecular weight independent, Chemistry dependent

equilibrium, i.e., below the bead size, Assume local ergodicity Use

4 So we introduce: Coarse- graining For reduc:on of calcula:on cost, bundle several atoms into one calcula:on unit (bead) In the bead, assume local equilibrium, i.e., below the bead size, Assume local ergodicity Use equilibrium conforma:onal distribu:on Use local free- energy and its deriva:ves

D and CGMD is ideal for grass- rubber region, but quite tough for rubber- flow region 10 10 10 9 Atomistic MD Kremer-Grest MD Rouse-fitted Rouse-fitted 10 8 G(t) /

5 D and CGMD is ideal for grass- rubber region, but quite tough for rubber- flow region Atomistic MD Kremer-Grest MD Rouse-fitted Rouse-fitted 10 8 G(t) / Pa PE melt with C1000 Rela:vely low accuracy log t / ps log t / ps Collabora:on with Prof Yasuoka

(and :me), To use equilibrium conforma:onal distribu:on To use local free- energy and its deriva:ves NOT

6 Two different coarse- graining ideas Op1: Assume the local equilibrium & ergodicity i.e., below a certain length (and :me), To use equilibrium conforma:onal distribu:on To use local free- energy and its deriva:ves NOT USEFUL for FLOW REGION Op2: Extract a certain mode domina:ng the slowest dynamics To perform long :me simula:ons To get more reduc:on in degree of freedom (by a hypothe:cal setup in case of polymers)

surrounding chains Big reduc:on in degree of freedom by a hypothe:cal model No

7 A hypothe:cal setup of polymer mo:on :The tube model de Gennes- Edwards- Doi Mul;- body dynamics is represented by single chain mo;on in a tube Constraints by surrounding chains Big reduc:on in degree of freedom by a hypothe:cal model No microscopic basis for the model; what is the tube? But if we accept the model we can make rheology

8 Problems in the tube modeling Single chain modeling Diﬃcult to take account the dynamics of surrounding chains (CR & CCR) Hard to extend to blends and copolymers Branch point dynamics/ﬂuctua:on S:ll challenging for branch polymers

Primi:ve Chain Network Model; Mixing up the coarse-

µ " # # $ % & & ' ( " = ) * + + + + + + + 0 1 1 2 0 3!

1 2 0 1 1 2 0 β β α α β β α α β α µ µ ζ ζ n n n n a n

= Tension + Osmotic f. + Random f. JCP2001 CG Op.

9 Primi:ve Chain Network Model; Mixing up the coarse- graining op1 & op 2 f n n r n r a ktn n i i i i +!µ " # # $ % & & ' ( " = ) * ! f r r r r R k R = ) ( 3 ) )( ( β β α α β β α α β α µ µ ζ ζ n n n n a n n n a n kt j j j j i i i i Drag f. = Tension + Osmotic f. + Random f. JCP2001 CG Op.2: assume constraints due to entanglement CG Op.1: assume local equilibrium +!

10 Network reconstruction; procedure for Z evolution Check monomer number at chain ends, n e, and - if (n e /n 0 > 1.5) make a new entanglement by hooking - elif (n e /n 0 < 0.5) delete the neighboring entanglement

11 code: Z=10 (corresponds to PS of M~100,000 Number of molecules 512 Unit cell 8x8x8

12 Basic scaling behaviors 2 P η 0 D 2 P ~M 1 ~M 3.5 ~M -2.2

13 Model parameters 2 parameters in the equa:ons; fric:on coefficient, ζ, and network mesh size a (or strand MW, M 0 ) For prac:cal usage, we choose characteris:c :me, τ = ζa 2 /6kT, and characteris:c modulus, G 0 =ρkt/m 0 as the basic parameters 13 / 41

14 Viscoelas:city for various polymers System M 0 τ 0 (sec) PS(453K) 1.1x10 4 2x10-3 PI(313K) 3.5x10 3 5x10-5 PB(313K) 1.6x x10-5 J- Non Newtonian Fluid Mech 2008

15 Predic:on for PS melts: monodisperse 380K 200K 100K

16 Bidisperse melts (short & long chain blends) Macromol, 2008 Exp. Data for PS Mw 294 kda/83kda, 100, 60, 40, 20, 10, 0 wt %, Watanabe 1985

17 Comparison on rheology for entangled λ- DNA solu:ons *only two parameters for data fitting; unit of time and length Linear viscoelas:city Viscosity growth curve under start- up shear JCP2009

18 Direct comparison of chain conforma:on under shear for entangled λ- DNAs Fluorescent microscopy In the simula:on! = 0.3 s s s C* Distribution C* C* x (µm) JCP2009

19 Asymmetric Star PI Solu:ons Linear! (simulation) N250K60 exp sim G'G" (Pa) arm star S101K60 exp sim Asymmetric star A2B73K60 exp sim ! (experiment) [1/s] Data by Lee et al 2006

H- Branch PS Melt G' G" (Pa) 10 5 10 3 10 5 10

Mb=100k 10 4 10 2 10-4 10-2 10 0 10 2 10 4 275k

20 H- Branch PS Melt G' G" (Pa) Ma=19k Mb=19k Ma=44k Mb=46k Ma=103k Mb=100k k ωa T (sec -1 ) Exp. Data by Roovers 1984, PS melt

Comb PI Melt 10 6 10 6 G' G" (Pa) 10 5 10 4 10 3 G(t, γ) (Pa) 10 5 4 2 4 2 10 2 10 4 10-5 10-3

21 Comb PI Melt G' G" (Pa) G(t, γ) (Pa) ω (rad/sec) Time (sec) Ma=10.2k, Mb=85.1, #b=5 Exp. Data by Kirkwood et al 2009

PCN simula:on with the fric:on reduc:on 10 10 without ζ-

22 PCN simula:on with the fric:on reduc:on without ζ- reduc:on [Pa s] E with ζ-reduction [s -1 ]

Pom- Pom PS Melt with ζ- reduc:on G* [Pa]

9 10 8 10 7 0.1 0.01 0.03 0.001 0.003 0.

0001 10 1 10-6 10-4 10-2 10 0 10 2 10 6 10

23 Pom- Pom PS Melt with ζ- reduc:on G* [Pa] η+ [Pa s] w [sec-1] Time [sec] Ma=25k, Mb=170k, q=3 Exp. Data by Nielsen et al, 2009

24 Kine:cs of microscopic phase separa:on of block co- polymers t /τ d = 0 t /τ d = 0.2 Symmetric block t /τ d = 2.0 t /τ d = 20 J. Non- crystal. Solid. 2006

25 Limita:ons Expression of total free- energy is unknown Fare for blend & copolymers? Further considera:on is needed for the systems including Crystalline Solid fillers Solid surfaces

26 Mul:- scale simula:ons Integra:on of material design and process design Coarse- graining parameters for fric:on and interac:ons Entanglement extrac:on Fiung to a phenomenological cons:tu:ve eq. Parameter Structure Rheology Atomis:c MD CGMD This model Con:nuum calc. Parameter Stress & Deforma:ons Obtaining entanglement parameters via the packing length argument Direct embedding into con:nuum calcula:ons

27 Link to CGMD by the Primi:ve Path Extrac:on (by Prof. Uneyama) 10 4 scale difference in :me scale between two methods Very wide :me span can be calculated (10 8 ) by the linkage Kremer- Grest MD PP- extrac:on (Kroger s Z1 code) Our model

28 Rheology- based linkage with process simula:ons Flow curve Flow analysis Small Mw Residual stress Warpage Large Mw Relaxa:on spectrum Warpage predic:on from molecular weight Saito et al, JSPP Autumn Symp. 2006

29 Direct embedding of the polymer- sims into par:cle CFD The polymer- sims are u:lized to calculate stress in each :me step Parallel comp. by GPU JST- CREST collabora:ng Prof. Taniguchi & Prof. Murashima

30 Contents & Summary Coarse- graining ideas for entangled polymers Op1: Structural - > robust & general, but slow Op2: Dynamical - > fast, but specific Primi:ve chain network (PCN) model Op1 (structural) +Op2 (Dynamical) Fast and general (and quan:ta:ve) Mul:- scale simula:ons MD+PCN - > wide range dynamics of polymers PCN+CFD - > complex flows in polymer processing

31 Collaborators

32 Acknowledgement Funding NEDO JST- PRESTO & CREST JSPS Kakenhi B,C, Wakate B Mitsui- Chem Sumitomo- Chem TOSO Bridgestone Sumitomo- Rubber Japan- Polyethylene JSOL Plamedia Toray Research Center

Part III. Polymer Dynamics molecular models

Part III. Polymer Dynamics molecular models I. Unentangled polymer dynamics I.1 Diffusion of a small colloidal particle I.2 Diffusion of an unentangled polymer chain II. Entangled polymer dynamics II.1.