mesoscopic simulations of entangled polymers, blends, copolymers, and branched structures

Mesoscopic simulations of entangled polymers, blends, copolymers, and branched structures F. Greco, G. Ianniruberto, and G. Marrucci Naples, ITALY

Y. MasubuchiTokyo, JAPAN

Network of entangled polymersActual chains have slackPrimitive chains are shortest path

Microscopic simulations:

Atomistic molecular dynamics (Theodorou, Mavrantzas, etc.) Coarse-grained molecular dynamics (Kremer, Grest, Everaers et al.; Briels et al.) Lattice Monte Carlo methods (Evans-Edwards, Binder, Shaffer, Larson et al.)

Mesoscopic simulations:

Brownian dynamics of primitive chains (Takimoto and Doi, Schieber et al.) Brownian dynamics of the primitive chain network (NAPLES)

Brownian dynamics of primitive chains along their contourSliplinks move affinelySliplinks are renewed at chain endsEach sliplink couples the test chain to a virtual companion

3D sliplink modelSimulation box typically contains ca. 2 x 104 chain segments

Nodes of the rubberlike network are sliplinks (entanglements) instead of crosslinksCrucial difference: Monomers can slide through the sliplink

Primitive Chain Network ModelJ. Chem. Phys. 2001+3D motion of nodes1D monomer sliding along primitive pathDynamic variables: node positions R monomer number in each segment n number of segments in each chain Z

Node motionBrownian forceRelative velocity of node

Monomer sliding

Network topological rearrangementni monomers at the endEndifUnhooking (constraint release)else ifHooking (constraint creation)n0: average equilibrium value of n

Chemical potential of chain segment from free energy EThe numerical parameter e was fixed at 0.5, which appears sufficient to avoid unphysical clustering. The average segment density is not a relevant parameter. We adopted a value of 10 chain segments in the volume a3, where a is the entanglement distance.

Non-dimensional equations(units: length = a=bno , time = a2z/6kT = , energy= kT)n=n/no Relevant parameters:

Nondimensional simulation: equilibrium value of (slightly different from initial value Z0)Comparison with dimensional data: modulus G = kT = RT/Me elementary time

LVE prediction of linear polymer melts

Polybutadiene melt at 313K from Wang et al., Macromolecules 2003

Polyisoprene melt at 313K from Matsumiya et al., Macromolecules 2000

Polymethylmethacrylate melts at 463K from Fuchs et al., Macromolecules 1996

G = kT = RT/Me = M/Me

PolymersG (MPa)Me (kDa)Me literature Me (s)PS (453K) 0.33111.70.002PB (313K) 1.81.61.67x10-6PI (313K) 0.633.51.45x10-5PMMA (463K)1.253.91.60.6

Polystyrene solution by Inoue et al., Macromolecules 2002

Simulations by Yaoita with the NAPLES code

Step strain relaxation modulus G(t,g)

Viscosity growth. Shear rates (s-1) are: 0.0113, 0.049, 0.129, 0.392, 0.97, 4.9

Primary normal stress coefficient. Shear rates as before.

Polystyrene solution fitting parameters:

Vertical shift, G = 210 Pa

Horizontal shift, t = 0.55 s

= 18.4 implying Me = 296

Blends and block copolymers

Phase separation kinetics in blendst=02.5 = 10 (td ~ 40), f=0.5, c=4.05.010.020.040.0

Block ratio = 0.5

= 0.5

= 40BLOCKCOPOLYMERS

Block ratio 0.1Block ratio 0.3 = 40 = 2

Branched polymers

Backbone-backbone entanglements cannot be renewedtwo entangled H-moleculesBackbone chains have no chain ends

SliplinkBranch pointEndA star polymer with q=5 arms

Free armIf one of the arms happens to have no entanglements, it has the chance to change topology

Possible topological changes1/q1/q1/q1/q1/qThe free arm has q options, all equally probable (under equilbrium conditions)

Double-entanglementIt can penetrate a sliplink of another arm, thus forming a

If later another arm becomes entanglement-free,

the topological options are Enhanced probability for the double entanglement because the coherent pull of the 2 chains makes the branch point closer to double entanglement2/q1/q1/q1/q

If the multiple entanglement is chosen, the branch point is sucked through the multiple entanglemet

The multiple entanglement has now the chance to be destroyed by arm fluctuationsSimilar topological changes would allow backbone-backbone entanglements in H polymers to be renewed

H-polymer simulationsClick to play

Relaxation modulus for H-polymersWith the topological change (liquid behavior)without (solid behavior)

Stress auto-correlation

Effect on diffusion of 3-arm star polymers

Diffusion coefficientFor 3-arm starsFor Hs having arms with Za= 5

Arm molecular weight, Za

5

10

20

Topological change

w/o

w

w/o

w

w/o

w

Diffusion Coefficient

4.8 e-3

6.0 e-3

4.3 e-4

4.3 e-4

2 e-6

2 e-6

Acceleration Ratio

1.2

1.0

1.0

Code

H05

H10

H20

Topological change

w/o

w

w/o

w

w/o

w

Diffusion Coefficient

1.6e-3

2.4e-3

4e-5

1.3e-3

1e-8

6e-4

Acceleration Ratio

1.5

~33

>1000

Backbone-backbone entanglement (BBE) clusterThe largest BBE cluster for H05 including 58 molecules

Size distribution of BBE clusterH05H10H20

ConclusionsMesoscopic simulations based on the entangled network of primitive chains describe many different aspects of the slow polymer dynamicsFor linear polymers, quantitative agreement is obtained with 2 (or at most 3) chemistry-and-temperature-dependent fitting parameters.More complex situations are being developed, and appear promising.A word of caution: Recent data by several authors (McKenna, Martinoty, Noirez) on thin films (nano or even micro) show that supramolecular structures can exist. These can hardly be captured by simulations.

Conclusion (social)http://masubuchi.jp to get the code & docs.NAPLESNew Algorithm for Polymeric Liquids Entangled and Strained

Diffusion of H-polymersWith the topological changeConventional (some still diffuse in the network)