SLIDE 1 Can single particle models describe the rheology of complex polymer liquids?
- J. Sprakel, J.T. Padding, E. van Ruymbeke and D, Vlassopoulos, J.K.G. Dhont
W.J. Briels
SLIDE 2 Contents
- 1. Coarse chains
- wormlike micelles
- 2. Coarse graining
- 3. Single particle models
- star polymers
- linear polymers
- telechelic polymers
SLIDE 4 Potential of mean force
Calculated using Boltzmann inversion Simple Brownian dynamics with forces from
SLIDE 5
Entanglements
SLIDE 6
Viscosities PE
SLIDE 7 Viscosities PEP
No fitting !!
SLIDE 8 I.a. Wormlike micelles
+ + + + + + + +
+salt wormlike micelle viscoelastic network surfactant
SLIDE 9
The coarse model
Join rods to form breakable chains
SLIDE 10
Parameters
Persistence length Scission energy Activation energy Diameter Elastic modulus
SLIDE 11
Atomistic simulation
calculate persistence length, diameter and elastic modulus
SLIDE 12
Thou shall not cross
bead-bead interactions are short-ranged and soft, and cannot prevent bond crossing
SLIDE 13 Viscosities
10
10
1 10 2 10 3 10 4 10
shear rate [s
10
10
10
10 10
1
10
2
10
3
viscosity [Pa s]
308 K - 348 K, cone-plate 300 K, simulation 8% EHAC, 2% KCl
SLIDE 14 Viscosities
10
10
1 10 2 10 3 10 4 10
shear rate [s
10
10
10
10 10
1
10
2
10
3
viscosity [Pa s]
308 K - 348 K, cone-plate 298 K, plate-plate 300 K, simulation 8% EHAC, 2% KCl
slope -2/3 slope -1
SLIDE 15 No branching?
Twisted PBC: M.P. Allen and A.J. Masters, Mol. Phys. 79, 277 (1993)
SLIDE 16
Fusing
SLIDE 17
Relaxing
SLIDE 18 No branching !
- Branches cost a lot of free energy
- Branches easily slide off one end
- Sliding branches are difficult to simulate
SLIDE 19
As coarse as coarse can be
SLIDE 20 Coarse graining
As coarse as coarse can be; a bit more resolution
SLIDE 21 Coarse graining
Transient forces after a compression
SLIDE 22 Coarse graining
A bit less coarse
SLIDE 23 Two ingredients
- Friction/memory is due to non equilibrium of the bath
- Potential of mean force
W.J. Briels, Soft Matter 5 (2009), 4401
SLIDE 24 Memory
Introduce variables describing the state of the bath: and write i.e. W.J. Briels, Soft Matter 5 (2009), 4401
SLIDE 25 Dynamics
Brownian dynamics in a slow bath W.J. Briels, Soft Matter 5 (2009), 4401
SLIDE 26
III.a. Star polymers
SLIDE 27
Potentials and overlap
SLIDE 28
Transient forces
SLIDE 29
Linear rheology
SLIDE 30 Theory for stars
(with Jan Dhont)
Assuming affine displacements, the stress tensor contains a shear thinning viscous term, a shear curvature term and coupling of diffusion and flow
SLIDE 31
III.b. Linear polymers
SLIDE 32 Potentials and overlap
- Three body potential
- Overlap functions: Gaussians
SLIDE 33 Polymer melts: C800H1602
Structure factor reproduces right compressibility. ‘Ideal gas’
SLIDE 34 Potential of mean force
Taylor expansion Three body interactions suffice !!
SLIDE 35 Polymer solution ‘Worm-like micelles’
Polymer solutions
Free energy from Flory-Huggins
SLIDE 36
Chaining
SLIDE 37
Chaining again
SLIDE 38
III.c. Telechelic polymers
Low density High density Flowers Flowers and bridges
SLIDE 39 Potential of mean force
from SCF calculations from plateau modulus
SLIDE 40 Parameters
This will lead to intelligible values of
SLIDE 41
Linear rheology
Viscosities used to fix
SLIDE 42 Predicted non linear rheology
From upper left to lower right, increasing concentration
SLIDE 43 Shear banding
1 1 2 2 3 3
SLIDE 44 Shear banding 20 g/l
Open symbols from experiments, everything else from simulations
SLIDE 45
Banding to fracture
SLIDE 46 1 2 1 2
Melt fracture
SLIDE 47
Melt fracture
SLIDE 48
Structure formation
SLIDE 49
Non-equilibrium phase diagram
SLIDE 50 Contents
- 1. Coarse chains
- wormlike micelles
- 2. Coarse graining
- 3. Single particle models
- star polymers
- linear polymers
- telechelic polymers
SLIDE 51 I am done
- 1. Coarse chains
- wormlike micelles
- 2. Coarse graining
- 3. Single particle models
- star polymers
- linear polymers
- telechelic polymers
SLIDE 52 Thank You
Brrrrrrrrrrrrrrrrrrrrrrrrrrriels
SLIDE 53
Simplified theory (1)
Langevin equation
SLIDE 54
Simplified theory (2)
Potential of mean force
SLIDE 55
Coarse model from atomistic simulation
Friction Potential of mean force
SLIDE 56 Scaling with N
1) Characteristic time 3) Friction 2) Equilibrium
SLIDE 57
Diffusion coefficients of polymer melts
SLIDE 58
- tubes conserve (to a large extent) prevalent configuration
- f 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.
Discussion
SLIDE 59 Model and Dynamics
Brownian dynamics in a slow bath number of bridges between and
SLIDE 60 Model and Dynamics
Brownian dynamics in a slow bath number of bridges between and
SLIDE 61 Coarse graining (dynamics)
Eliminate variables: Only useful in case is much faster than , i.e. when no memory occurs
SLIDE 62
Entanglement free energy
SLIDE 63 Experiments
Open symbols 60 g/l, filled symbols 20 g/l
