(Polymer rheology Analyzer with Sliplink. Tatsuya Shoji JCII, Doi Project

Transcription

1 Rheology Simulator PASTA (Polymer rheology Analyzer with Sliplink model of entanglement) Tatsuya Shoji JCII, Doi Project

2 0 sec -3 msec -6 sec -9 nsec -12 psec -15 fsec GOURMET SUSHI PASTA COGNAC MUFFIN fm pm nm m mm m

3 Introduction Monomer Catalyst Polymerization Polymer Polymer Structure Molecule Weight Distribution Brainching Linear LCB Molecular weight Processing Processability Rheology viscosity, modulus, etc.. Products Mechanical property

4 Objectives Prediction of the rheological properties from the knowledge of the structure of polymer It is not feasible to simulate the rheological properties of polymer by MD simulations. coarse-grained model for polymer the Doi-Edwards theory(tube model) New stochastic simulation method (PASTA)

5 Classical tube model a Obstacle Tube Primitive path Assumption The length of primitive path is constant Obstacles are permanent Reptation is the only mechanism of the relaxation

6 Important Extensions of the tube model -1- Contour Length Fluctuation Constraint Release Convective Constraint Release (CCR)

7 Important Extensions of the tube model -2- Slip links (1) Each chain obeys the reptation dynamics. (2) Each slip link constrains a pair of chains, and disappears when eithe one of the chain moves away from the slip link.

8 Simulation method 1) Each polymer chain is modeled by a primitive path and slip links along it. r k r 1 r r n 1 2 s 2 s 1 1, r, L, r n Subchain vector 2 1 Length of the tube Length of the tail at each end r Lt = s 1, s 2 Length of the primitive path L = L t + s 1+ s 2 k r k

9 Simulation method 2) A collection of many chains (ex ) 3) The interaction among the chains is taken into account through the pairing of the slip links Pairing of the slip links (Each slip link has its partner, but only representative pairs are shown)

10 Simulation method 4 operations in each time step 1. Affine deformation of the tubes 2. Contour length fluctuation 3. Reptation 4. Constraint release / creation a a Unit of length a Unit of time τ e = τ M = M R ( e ) M e : Entanglement molecular weight

11 Operation-1 Affine deformation of the primitive path Each slip link is moved according the macroscopic flow of the sample. r ( t) r( t + t) x ( t + t) = x( t) + γ& t y( t) ( t + t) y( t) y =

12 Operation-2 L(t) L(t+dt) Contour length fluctuation dl dt 1 = & eq τ R ( L() t L ) + L + g() t affine Variation rate of L by the affine deformation Gaussian random force L eq = Za τ R = τ e Z Z M / 2 M e Equilibrium length Rouse relaxation time Average number of slip links

13 Operation-3 Reptation The center of mass of each primitive path is randomly moved by s along the path with diffusion constant D c 2 s = 2 D 1 D c Z c t

14 Operation-4 Constraint renewal If a end of a primitive path passes through the last slip link on the chain, the slip link and its partner are destroyed. partner

15 Operation-4 Constraint renewal If the length of a tail at the end of the primitive path becomes longer than a, a new slip link is created at the end and its partner is created on a randomly selected chain. randomly selected chain a

16 Simulation method Calculation of the Stress σ αβ = k F kα r k β r 1 r k r r n 1 2 F F k r = F r k k du = dl U ( L) 3kBT = a 3k T 2aL L L eq ( L) = B ( L L ) 2 eq eq σ αβ = 3k Tension Za T B 2 k L r Fk kα kβ r r k

17 Simulation method 4 operations in each time step 1. Affine deformation of the tubes 2. Contour length fluctuation 3. Reptation 4. Constraint release / creation a a Unit of length a Unit of time τ e = τ M = M R ( e ) M e : Entanglement molecular weight

18 Star Polymer branch point Z a Z a linear R = e Z 2 Z a Z a Z a star R = e (2Z a ) 2 Z a =1/2Z 3 operations in each time step 1. Affine deformation of the tubes 2. Contour length fluctuation 3. Reptation 3. Constraint release / creation

19 FUNCTION of PASTA Target Sample linear polymer monodisperse polydisperse star polymer monodisperse polydisperse linear/star mixture Flow type steady flow step strain noflow thermalization, stress relaxation Deformation type shear uniaxial elongation biaxial elongation planar elongation

20 Simulation results

21 Steady shear flow (z=60 monodisperse) Z=60 N σ, N 1, -N σ -N 2 η /τ R shear rate z

22 Steady shear viscosity Monodisperse Polystyrene Vertical shift: (15/4) G N0 e Horizontal shift: e -1 M e =14400 G N 0 = dyn/cm 2 η (poise) PS 183 N e e simulation z3.3 simulation z12.4 simulation z16.8 experiment Mw48500 experimant Mw experiment Mw R. A. Stratton, J. Colloid Interfac. Sci., 22, 517 (1966) shear rate (sec -1 )

23 Self diffusion coefficient T.P. Lodge, Phys. Rev. Lett. 83, 3218 (1999)

24 Self diffusion coefficient (monodisperse) ( R ( t) R (0)) = D t ( t ) G G 6 G 10-2 Ð < Z < 80 D Z G 3.5 ( c. f. η Z ) 0 6D G Ð Z

25 Elongational viscosity Polydisperse Polystyrene Mw = Mw/Mn = V shifted by 5.3e5 H shifted by 4.9e dw/dlogm G', G'' (Pa) experiment simulation M ω a T (sec -1 )

26 Elongational viscosity Polydisperse PS Mw = Mw/Mn = PS686 dw/dlogm η e (t) (Pas) experiments dε/dt=0.564 dε/dt=0.123 dε/dt= dε/dt= M 3η (t) t (s)

27 Elongational viscosity Polydisperse PS 10 8 PS686(98.5)+W320(1.5) Mw = Mw/Mn = HMW-PS Mw = % η e (t) (Pas) experiments dε/dt=0.572 dε/dt=0.097 dε/dt=0.047 dε/dt= η (t) t (s)

28 Shear viscosity of star polymer η Z=30 2Z a =20 Z=20 2Z a =10 Z=60 2Z =30 Branch point a Z=10 Z= shear rate zero-shear viscosity η Star Linear Z linear or 2Z arm

29 PASTA on GOURMET Usage Step1. Creating inputudf of PASTA Step2. Running PASTA Step3. Analysis of outputudf

30 Editing InputUDF of PASTA on GOURMET Sample: Chain type: Linear or Arm Zi (=Mi/Me :Average number of slip links) Ni (Number of the i-th Chain) max (Max Stretch Ratio) Z max Ni Monodisperse Polydisperse Z max Ni

31 Editing InputUDF of PASTA on GOURMET select function Simulation: Flowtype: flow / noflow / step Deformation type: shear/ uniaxial/ biaxial/ planar Strain: (in the case of step) Strain rate: dt: time step per 1 e MaxTimeStep: Number of iteration IntervalStep: output every IntarvalStep steps

32 FORK (a support tools for PASTA) FORK is a tool to generate inputudf for PASTA. properties of polymer Me, M0, GN0, e...etc MWD Mw, Mw/Mn, distribution function, GPC data simulation condition deformation type shear, =0.01, 10000step FORK inputudf for PASTA i Zi Ni

33 Running PASTA on GOURMET Monitor Engine Run Window Run

34 Analyze output by GOURMET By Action, Python script and the other tools - shear viscosity, elongational viscosity, relaxation modulus G'( ), G''( ), etc... Example of Action (plot_stress) instant plot by Gnuplot

35 PASTA: Linking to other layers Linear Non-linear Viscoelastic Response MUFFIN Friction constant, Me SUSHI PASTA COGNAC Non-equilibrium structure Strain Strain rate Deformation type

36 Summary PASTA New stochastic simulation method tube model + contour length fluctuation + constraint renewal Successfully calculates most of the linear/nonlinear rheology of monodisperse/polydisperse linear/star polymer Easy and convenient manipulation on GOURMET

37 Developer of PASTA Theory & Program Verification Prof. Jun-ichi Takimoto (Nagoya Univ.) Hiroyasu Tasaki (JCII, Doi Project) Connection with GOURMET & FORK Tatsuya Shoji (JCII, Doi Project)

38 Acknowledgements This work is supported by the national project, which has been entrusted to the Japan Chemical Innovation Institute (JCII) by the New Energy and Industrial Technology Development Organization (NEDO) under MITI's Program for the Scientific Technology Development for Industries that Creates New Industries.