Consistent mechanism of emulsion polymerization - A multi-scale stochastic approach

Consistent mechanism of emulsion polymerization: A multiscale stochastic approach

1. Consistent mechanism of emulsion Consistent mechanism of emulsion
polymerization: A multiscale stochastic polymerization: A multiscale stochastic
approachapproach
Hugo Hernandez
Polymer Dispersions Group
Colloid Chemistry Department
Max Planck Institute of Colloids and Interfaces
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2. 2
OutlineOutline
•Motivation
•Colloidal scale
•Macromolecular scale
•Molecular scale
•Microscopic scale
•Multi-scale integration
•Outlook
•Acknowledgments

3. 3
Comprehensive modelingComprehensive modeling
•Design of polymer particles:
–Morphology
–Particle size distribution
–Molecular weight distribution
–Mechanical properties
–Stability
–Performance
•Industrial production:
–Process optimization
–Quality control
 MotivationMotivation

4. 4
Some unresolved issuesSome unresolved issues
A complete consistent picture of emulsion
polymerization is not available.
Some controversial topics:
–Particle nucleation
–Radical capture
–Radical desorption
–Monomer swelling
Limitations:
–Lack of adequate experimental methods
–Models developed for very specific conditions
–Unreliable model discrimination
Better models and more accurate validation data are
needed!
 MotivationMotivation

5. 5
Macroscopic scale Mesoscopic scale Microscopic scale Colloidal scale
Molecular scale
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HO
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HO
H
2O
H
2O
H
2O
H
2O
H
2O
H
2O
H
2O
H
2O
H
2O
H
2O
Emulsion Polymerization Emulsion Polymerization
A multi-scale stochastic processA multi-scale stochastic process
Macromolecular scaleAtomistic scale
Different length scales
 MotivationMotivation
Heterogeneous-multicomponent
Different time scales Random events

6. 6
Diffusion by Brownian motionDiffusion by Brownian motion
Dtnx
d2
2

 Colloidal scaleColloidal scale
Einstein’s equation of Brownian motion:
Langevin description:
n
d=1,2 or 3 number of dimensions
Fick’s second law:
D: Diffusion coefficient
cD
t
c
2



d
t
mD
kT
nCeD
dt
xd








2
2

7. 7
Simulating Brownian motionSimulating Brownian motion
Brownian Dynamics (BD) simulationBrownian Dynamics (BD) simulation
Monte Carlo Random Flight (MCRF) Algorithm
of BD simulation
 Colloidal scaleColloidal scale
Time (ns)
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
<
x
2
>

(
n
m
2
)
0
1
2
3
4
5
6
MCRF Simulation
Einstein's equation

8. 8
BD simulation of radical captureBD simulation of radical capture
Aprc NdDk2
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x-Position (nm)
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(n
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x-Position (nm)
 Colloidal scaleColloidal scale
* Smoluchowski, M.v., 1906, “Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen”.
Ann. Phys., 21, 756-780.
** Hernandez, H. F. and K. Tauer, 2007, “Brownian Dynamics Simulation of the capture of primary radicals in
dispersions of colloidal polymer particles”, Ind. Eng. Chem. Res., 46, 4480-4485.
Volume fraction of particles, 
p
1e-7 1e-6 1e-5 1e-4 1e-3 1e-2 1e-1 1e+0
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S
m
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2
4
6
8
10
12
BD simulation
Smoluchowski equation
Smoluchowski equation
*
:
Infinitely diluted particles
Apr
c
NdD
k
Sm
2

Smoluchowski number
**
:

9. 9
Models of radical captureModels of radical capture
 Colloidal scaleColloidal scale
•Collision model: (Gardon, 1968; Fitch and Tsai, 1971)
k
c  d
p
2
•Diffusion model: (Ugelstad and Hansen, 1976)
k
c
 d
p
•Colloidal model: (Penboss et al., 1983)
k
c  d
p
•Propagational model: (Maxwell et al., 1991)
k
c
 d
p
0
•BD simulation: (Hernandez and Tauer, 2007)
k
c  d
p(1+
p)
k
c  d
p+’Nd
p
4

10. 10
Models of radical desorptionModels of radical desorption
20
p
p
d
D
k


 Macromolecular scaleMacromolecular scale
* Hernandez, H. F. and K. Tauer, 2008, “Radical desorption kinetics in emulsion polymerization - Theory and
Simulation”, Submitted to Ind. Eng. Chem. Res.
Theoretical model based on the 3-dimensional Einstein‘s equation
*
:
Model 
Ugelstad et al. (1969) 1.542
Harada et al. (1971) 12
Friis and Nyhagen (1973) 8
Ugelstad and Hansen (1976) 12
Nomura and Harada (1981) 2
Chang, Litt and Nomura (1982) 5
Nomura (1982) 2 – 5
Asua et al. (1989) 6
Grady and Matheson (1996) 20/3
Present theoretical model 60
BD simulation results 57.14

D
p
/d
p
2
(s
-1
)
1e-1 1e+0 1e+1 1e+2 1e+3 1e+4 1e+5 1e+6 1e+7
k
0
(
s
-
1
)
1e+1
1e+2
1e+3
1e+4
1e+5
1e+6
1e+7
1e+8
1e+9
2
14.57
p
p
desorp
d
D
k
=60

11. 11
Desorption in complex systemsDesorption in complex systems
Core-shell particlesCore-shell particles
Shell
Core
d
c

s
D
c
D
s
 Macromolecular scaleMacromolecular scale
Shell thickness (nm)
0 20 40 60 80 100 120
D
e
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e

c
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f
f
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(
s
-
1
)
1e+3
1e+4
1e+5
Radicals generated in the core
Radicals generated in the shell
Radicals generated in both phases

12. 12
Desorption in complex systems Desorption in complex systems
Monomer concentration gradientMonomer concentration gradient
 Macromolecular scaleMacromolecular scale
Temperature, T (K)
300 320 340 360
D
if
f
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n

c
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f
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,

D

(
m
2
/
s
)
1e-13
1e-12
1e-11
1e-10
1e-9
1e-8
BD simulation
Particle surface
Particle center
d
p
w
p
0.8
0
d
p
/2r
D
p
10
-9
10
-12

13. 13
Desorption in complex systems Desorption in complex systems
Non-spherical particlesNon-spherical particles
 Macromolecular scaleMacromolecular scale

y
=1, 
z
=1
(Sphere)

y
=1, 
z
>1
(Oblate spheroid)

y
=
z
>1
(Prolatespheroid)

y
=1, 
z
>>1
(Thin disc)

y
=
z
>>1
(Needle)
1e+6
1e+7
1e+8
1
10
1
10I
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k
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Sphere
Needle
Thin disc
O
blate spheroids
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14. 14
Intermolecular forcesIntermolecular forces
 Molecular scaleMolecular scale
The effect of intermolecular forces:
–Electrical double layer
–Interfacial tension, Laplace pressure
–Chemical potential, energy and entropy of mixing
–Flory-Huggins interaction parameters
–Maxwell-Stefan diffusion coefficients
–Non-conservative forces: Friction
–Spontaneous emulsification
*
Molecular Dynamics
Monte Carlo
* Tauer, K., H. Hernandez, S. Kozempel, O. Lazareva and P. Nazaran, 2007, “Towards a consistent mechanism
of emulsion polymerization – new experimental details”, Colloid Polym. Sci., In press.
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2O
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H
2O
H
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2O
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2O
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2O
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2O
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H
2O
H
2O
H
2O
H
2O
H
2O
H
2O
H
2O
H
2O
H
2O
H
2O

15. 15
Diffusion-limited reactions Diffusion-limited reactions
Cage, gel and glass effectsCage, gel and glass effects
 Microscopic scaleMicroscopic scale
Time (s)
0 5000 10000 15000 20000 25000 30000
C
o
n
v
e
r
s
io
n
0.0
0.2
0.4
0.6
0.8
1.0
HSSA-IM
HSSA
Experimental data
Cage effect
Gel effect
Glass effect
* Hernandez, H. F. and K. Tauer, 2008, “Hybrid stochastic simulation of imperfect mixing in free radical
polymerization”, Submitted to Macromol. Symp.
Bulk radical polymerization of MMA up to high conversions
Application of the hybrid stochastic simulation algorithm for imperfect
mixing (HSSA-IM)
*

16. 16
Hybrid BD-kMC simulationHybrid BD-kMC simulation
**
Time, t (s)
0 2000 4000 6000 8000 10000
C
a
p
t
u
r
e

r
a
t
e

c
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f
f
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,

k
c

(
l
w
a
t
e
r
/
p
a
r
t
.
s
)
1e-12
1e-11
1e-10
BD simulation updates
 Multi-scale integrationMulti-scale integration
Aqueous phase propagation vs. capture by particles
Particle diameter, d
p
(nm)
0 100 200 300 400 500 600
L
n
,

L
w
,

P
D
I
1
2
3
4
5
L
m
a
x
0.1
1
10
100
Weight average chain length, Lw
Polydispersity index, PDI
Number average chain length, Ln
Max. chain length, Lmax
Seed volume fraction: 1%
* Hernandez, H. F. and K. Tauer, 2007, “Brownian Dynamics and Kinetic Monte Carlo Simulation in Emulsion
Polymerization”, Accepted in 18th European Symposium on Computer Aided Process Engineering

17. 17
Further developmentsFurther developments
•Aggregation dynamics:
–Particle nucleation
–Micellization
•Energy barriers:
–Phase transfer
–Phase transition
•Diffusion in polymer media
•Multiscale integration:
–Secondary particle nucleation
–Particle morphology
–Swelling equilibrium and dynamics
–…
 OutlookOutlook

18. 18
Concluding remarksConcluding remarks
•Emulsion polymerization is a complex multiscale
stochastic process.
•A consistent mechanism of emulsion polymerization
can only be formulated within this framework.
•The modeling, simulation and integration of the
different scales is a powerful tool for the investigation
and understanding of emulsion polymerization.
•Some of these results can be generalized to other
types of heterogeneous and homogeneous
polymerization processes.
 OutlookOutlook