Can single particle models describe therheology of complex polymer liquids?

W.J. Briels

J. Sprakel, J.T. Padding, E. van Ruymbeke and D, Vlassopoulos, J.K.G. Dhont

Contents
1. Coarse chains- wormlike micelles
2. Coarse graining
3. Single particle models- star polymers- linear polymers- telechelic polymers

I. Coarse chains

Potential of mean force
Simple Brownian dynamics with forces from

Calculated using
Boltzmann inversion

Entanglements

Viscosities PE

Viscosities PEP

No fitting !!

I.a. Wormlike micelles

+salt
++

+ +

++ +

surfactant

wormlike micelleviscoelastic network

The coarse model

Join rods to form breakable chains

Parameters
Persistence length
Diameter
Elastic modulus
Scission energy
Activation energy

Atomistic simulation

calculate persistence length, diameter andelastic modulus

Thou shall not crossbead-bead interactions are short-ranged and soft,and cannot prevent bond crossing

Viscosities

4

10

308 K - 348 K, cone-plate
3

10

300 K, simulation

viscosity [Pa s]

2

10

1

10

0

10

-1

10

-2

10

8% EHAC, 2% KCl
-3

10

-3

10

-2

10

-1

10

0

10

1

10

2

10

-1

shear rate [s ]

3

10

4

10

5

10

Viscosities

4

10

308 K - 348 K, cone-plate
310

298 K, plate-plate
300 K, simulation

viscosity [Pa s]

2

10

1

10

slope -1

0

10

-1

10

slope -2/3

-2

108% EHAC, 2% KCl
-3

10

-3

10

-2

10

-1

10

0

10

1

10

2

10

-1

shear rate [s ]

3

10

4

10

5

10

No branching?

Twisted PBC:
M.P. Allen and A.J. Masters, Mol. Phys. 79, 277 (1993)

FusingRelaxingNo branching !
• Branches cost a lot of free energy• Branches easily slide off one end• Sliding branches are difficult to simulateII. Coarse graining
As coarse as coarse can beCoarse graining
As coarse as coarse can be; a bit more resolution

Coarse graining
Transient forces after a compression

Coarse graining
A bit less coarse

Two ingredients•Potential of mean force•Friction/memory is due to non equilibrium of the bath

W.J. Briels, Soft Matter 5 (2009), 4401

Memory
Introduce variables describing the state of the bath:and write
i.e.

W.J. Briels, Soft Matter 5 (2009), 4401

Dynamics
Brownian dynamics in a slow bath

W.J. Briels, Soft Matter 5 (2009), 4401

III.a. Star polymers

Potentials and overlap

Transient forcesLinear rheology

Theory for stars(with Jan Dhont)
Assuming affine displacements, thestress tensor contains a shear thinningviscous term, a shear curvature term
and coupling of diffusion and flow

III.b. Linear polymers

Potentials and overlap• Three body potential• Overlap functions: Gaussians

Polymer melts: C800H1602

Structure factor reproduces rightcompressibility.

‘Ideal gas’Potential of mean force

Taylor expansion

Three body interactions suffice !!

Polymer solutions

Polymer solution
Free energy from Flory-Huggins‘Worm-like micelles’ChainingChaining again

III.c. Telechelic polymers
Low density

Flowers

High density

Flowers and bridges

Potential of mean force

from SCF calculations

from plateau modulus

Parameters

This will lead to intelligible
values ofLinear rheology

Viscosities used to fix

Predicted
non linear
rheology

From upper left to lower
right,
increasing concentration

Shear banding
1

2

3
1

2

3

Shear banding 20 g/l

Open symbols from experiments,
everything else from simulations

Banding to fracture

Melt fracture
1

2
1

2

Melt fractureStructure formation

Non-equilibrium phase diagram

Contents
1. Coarse chains- wormlike micelles
2. Coarse graining
3. Single particle models- star polymers- linear polymers- telechelic polymers

I am done
1. Coarse chains- wormlike micelles
2. Coarse graining
3. Single particle models- star polymers- linear polymers- telechelic polymers

Thank You
Brrrrrrrrrrrrrrrrrrrrrrrrrrriels

Simplified theory (1)Langevin equation

Simplified theory (2)Potential of mean force

Coarse model from atomistic
simulation

Friction

Potential of mean
force

Scaling with N
1) Characteristic time2) Equilibrium

3) FrictionDiffusion coefficients ofpolymer melts

Discussion• tubes conserve (to a large extent) prevalent configurationof centres of mass, as do the transient forces• probabilities of entanglement
survival-times decay exponentially;
do we need tubes at long times?
• to describe elongational flow use dumbbells• types of entanglements, and therefore their relaxation
times depend on the distance between polymers.

Model and Dynamics
Brownian dynamics in a slow bathnumber of bridges between andModel and Dynamics
Brownian dynamics in a slow bathnumber of bridges between andCoarse graining (dynamics)
Eliminate variables:

Only useful in casethanis much faster, i.e. when no memory occurs

Entanglement free energy

Experiments

Open symbols 60 g/l, filled symbols 20 g/l