Recent Developments in the mechanism and modeling of emulsion polymerization

Recent Developments in the mechanism and modeling of emulsion polymerization - Presentation at Abrafati 2009 (Brazil)

1. Recent Developments in the Recent Developments in the
mechanism and modeling of mechanism and modeling of
emulsion polymerizationemulsion polymerization
Hugo HernándezHugo Hernández
1,21,2
and Klaus Tauer and Klaus Tauer
22
1
andercol S.A.
2
Max Planck Institute of Colloids and Interfaces
September, 2009

2. 2
ContentsContents
Motivation
Emulsion Polymerization
Understanding emulsion
polymerization
Particle nucleation
Mass transfer between phases
Multi-scale simulation
Applications
Conclusions

3. 3
MotivationMotivation
Polymer DispersionsPolymer Dispersions
World market:
 10 million metric tons/year
 €15 billion/year
 5% of polymer production

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!

5. 5
ContentsContents
Motivation
Emulsion Polymerization
Understanding emulsion
polymerization
Particle nucleation
Mass transfer between phases
Multi-scale simulation
Applications
Conclusions

6. 6
Emulsion PolymerizationEmulsion Polymerization
ji
k
ji PRR
t



Propagation
Termination
Initiator decomposition


02RI
dk




1i
k
i RMR
p
ji
k
ji PRR
t



Propagation
Termination
Initiator decomposition


02RI
dk




1i
k
i RMR
p
ji
k
ji PRR
t



Propagation
Termination
Initiator decomposition


02RI
dk




1i
k
i RMR
p
Phase Transfer
w
k
p
p
k
w
AA
AA
d
c


Micelle
( surfactant aggregate)
Monomer-swollen
micelle
Micelle
Surfactant-stabilized
Polymer particle
Surfactant-free
Polymer particle
Monomer
Free surfactant
I nitiator
Living polymer
Dead polymer
Free radical
Monomer
aggregate
Adsorbed
surfactant
Monomer droplet
Monomer droplet
Continuous phase: Water

7. 7
Macroscopic scale Mesoscopic scale Microscopic scale Colloidal scale
Molecular scale
O
-
S
O
O
HO
O
-
S
O
O
HO
O
S
O
O
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 processA multi-scale process
Macromolecular scaleAtomistic scale
Picometers - Femtoseconds
Liters, m
3
Meters - Hours
Milliliters
Centimeters - Minutes
Microliters
Millimeters - Seconds
Femtoliters, attoliters
Microns - Milliseconds
Nanometers - NanosecondsAngstroms –
Picoseconds

8. 8
ContentsContents
Motivation
Emulsion Polymerization
Understanding emulsion
polymerization
Particle nucleation
Mass transfer between phases
Multi-scale simulation
Applications
Conclusions

9. 9
Physical Chemical
Diffusion Initiator decomposition
Particle formation Radical propagation
Radical capture Radical termination
Radical desorption Chain transfer
Swelling
Coagulation

Kinetics of Emulsion PolymerizationKinetics of Emulsion Polymerization

A
pp
p
N
NnMk
r
Rate of polymerization
Monomer swelling
Radical absorption (capture)
and radical desorption
Particle formation, particle coagulation
Propagation

10. 1
0
ContentsContents
Motivation
Emulsion Polymerization
Understanding emulsion
polymerization
Particle nucleation
Mass transfer between phases
Multi-scale simulation
Applications
Conclusions

11. 1
1
Spontaneous emulsificationSpontaneous emulsification
10 m

12. 1
2
Precipitation nucleation Aggregative nucleation
Droplet nucleation Micellar nucleation
Particle FormationParticle Formation

13. 1
3
Particle FormationParticle Formation
Propagation-induced
desorption
Particle formation
H
polym
>>E
desorp
E
desorp
>>H
polym
Propagation
Nanodroplets formed by
spontaneous emulsification

14. 1
4
Particle FormationParticle Formation

15. 1
5
ContentsContents
Motivation
Emulsion Polymerization
Understanding emulsion
polymerization
Particle nucleation
Mass transfer between phases
Multi-scale simulation
Applications
Conclusions

16. 1
6
M
R*
I
T
T*
P
1*
M
P
n+1*
P
m*
D
n+m
P
n*
X
E<E
des
E>E
des
k
d
M +
k
iR
+
k
t
+
P
n*
+
k
p
k
fT
M
+
k
iT
T
R*
M
X
P
n*
D
m
M
I
E<E
abs
E>E
abs
Molecular picture of desorption Molecular picture of absorption
M
R*
I
T
T*
P
1*
M
P
n+1*
P
m*
D
n+m
P
n*
X
E<E
des
E>E
des
k
d
M +
k
iR
+
k
t
+
P
n*
+
k
p
k
fT
M
+
k
iT
T
R*
M
X
P
n*
D
m
M
I
E<E
abs
E>E
abs
Molecular picture of desorption Molecular picture of absorption
•Radical absorption/desorption
•Monomer swelling
•Surfactant/Polymer adsorption from solution
•Coagulation and heterocoagulation
RT
EE
p
pArc e
Nd
dNDk
3
)(4
*
6
2













Rate coefficient of irreversible
absorption of small molecules
*
:
BD simulation can be used to study the absorption/desorption
not only of radicals, but of any entity (molecule or particle)
subject to diffusion by Brownian motion.
Applicable to:
* Hernández and Tauer 2007, Macromol. Symp., 259, 274
Understanding Emulsion Polymerization Understanding Emulsion Polymerization
Molecular transfer between phasesMolecular transfer between phases

17. 1
7
ContentsContents
Motivation
Emulsion Polymerization
Understanding emulsion
polymerization
Particle nucleation
Mass transfer between phases
Multi-scale simulation
Applications
Conclusions

18. 1
8
Multi-scale simulationMulti-scale simulation
Macroscopic scale
Mesoscopic scale
Microscopic scaleMicroscopic scale
Colloidal scaleColloidal scale
Macromolecular scale
Molecular scale
Atomistic scale
Conservation equations, lumped kinetics
Computational Fluid Dynamics (CFD),
Finite Element Modeling (FEM)
Kinetic Monte Carlo Simulation (kMC) ,
Segregated kinetic models
Brownian Dynamics Simulation (BD) ,
Dissipative Particle Dynamics (DPD)
Coarse-grained Molecular Dynamics Simulation
Molecular Dynamics Simulation (MD)
Monte Carlo Simulation (MC)
Quantum mechanics, Mean Field methods

19. 1
9
Kinetic Monte Carlo simulationKinetic Monte Carlo simulation
Stochastic Simulation Algorithm (SSA)Stochastic Simulation Algorithm (SSA)
R

Aqueous-
phase radical
Capture by particles
Propagation
Termination
t=0
a
c
a
p
a
t

c

p

t
The fastest event
takes place!
i
i
a
)ln(
 Poisson distribution
Uniform random number
Gillespie, Annu. Rev. Phys. Chem. 58, 35 (2007)
Hernandez and Tauer, Macromol. Symp . 271, 64 (2008)
t=min(
i)

20. 2
0
Brownian Dynamics simulationBrownian Dynamics simulation
X
dt
dx
a
dt
xd
m 6
2
2
Langevin’s equation of Brownian motion
Dtx2
2

Einstein’s solution
Ddtdx
G2Monte Carlo Random Flight (MCRF) method:
Gaussian random numberBluett and Green, J. Phys. Chem. A 110, 6112 (2006)
Hernandez and Tauer, Ind. Eng. Chem. Res. 46, 4480 (2007)
 Multi-scale simulation methods: Colloidal scaleMulti-scale simulation methods: Colloidal scale
z
-
a
x
is
y
-
a
x
i
s
x-axisDtr6
2


21. 2
1
Simulating Brownian motionSimulating Brownian motion
Brownian Dynamics (BD) simulationBrownian Dynamics (BD) simulation
Monte Carlo Random Flight (MCRF) Algorithm of BD
simulation
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
 Multi-scale simulation methodsMulti-scale simulation methods

22. 2
2
ContentsContents
Motivation
Emulsion Polymerization
Understanding emulsion
polymerization
Particle nucleation
Mass transfer between phases
Multi-scale simulation
Applications
Conclusions

23. 2
3
Kinetic Monte Carlo simulationKinetic Monte Carlo simulation
Diffusion-limited reactions Diffusion-limited reactions
* Hernandez, H. F. and K. Tauer, 2008, “Hybrid stochastic simulation of imperfect mixing in free radical
polymerization”, Macromol. Symp., 271, 64.
Bulk radical polymerization of MMA up to high conversions
Application of the stochastic simulation algorithm for imperfect mixing
(SSA-IM)
*
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
SSA-IM
SSA
Experimental data
Cage effect
Gel effect
Glass effect
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
Experimental data
SSA-IM (adj. param.)

24. 2
4
Brownian Dynamics SimulationBrownian Dynamics Simulation
Radical captureRadical capture
Aprc
NdDk2
z
-
P
o
s
i
t
i
o
n

(
n
m
)
y
-P
o
s
itio
n
(n
m
)
x-Position (nm)
z
-
P
o
s
i
t
i
o
n

(
n
m
)
y
-P
o
s
itio
n
(n
m
)
x-Position (nm)
* Smoluchowski, M.v., 1906, Ann. Phys., 21, 756-780.
** Hernandez, H. F. and K. Tauer, 2007, Ind. Eng. Chem. Res., 46, 4480-4485.
Smoluchowski equation
*
:
Infinitely diluted particles
Apr
c
NdD
k
Sm
2

Smoluchowski number
**
:
Polymer particle
Radical
Polymer particles volume fraction, 
p
1e-7 1e-6 1e-5 1e-4 1e-3 1e-2 1e-1 1e+0
S
m
o
lu
c
h
o
w
s
k
i
n
u
m
b
e
r
,

S
m
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Simulation data points
Linear fit from simulation data
Smoluchowski equation
pSm1

25. 2
5
Radical captureRadical capture
•Collision model: k
c
 d
p
2
•Diffusion model: k
c
 d
p
•Colloidal model: k
c
 d
p
•Propagational model : k
c
 d
p
0
•BD simulation: k
c
 d
p
(1+
p
)


k
c
 d
p
+’Nd
p
4
~ d
p
a

Reference Data
Particle number
concentration
range (part/ m
3
)
Particle size
range (nm)
Polymer volume
fraction range
a (from
experim.)
a (BD
model)
Asua and de la Cal 9.810
18
– 4.9x10
19
94 – 154 4.2610
-3
– 9.3710
-2
0 – 1.75 1.43 – 2.34
López de Arbina 4.010
16
– 3.010
17
79 – 117 1.0310
-5
– 2.5210
-4
1 1.00
Liotta 2.010
18
– 2.010
19
93 – 215 8.4210
-4
– 1.0410
-1
2 1.17 - 2.08

1  a  4

26. 2
6
Particle diameter, d
p
(m)
1e-8 1e-7 1e-6 1e-5
k
c
/
D
w

(
m
/
m
o
l)
1e+16
1e+17
1e+18
1e+19
1e+20
1e+21
MCRF simulation data
Smoluchowski equation
1
0
2
1 p
a
r t/m
3
1
0
2
0 p
a
r t/m
3
1
0
1
9 p
a
r t/m
3
1
0
1
8 p
a
r t/m
3
1
0
1
7 p
a
r t/m
3
1
0
1
6 p
a
r t/m
3
Particle number concentration, N (part/m
3
)
1e+131e+141e+151e+161e+171e+181e+191e+201e+211e+221e+23
k
c
/
D
w

(
m
/
m
o
l)
1e+17
1e+18
1e+19
1e+20
1e+21
MCRF simulation data
Smoluchowski equation
5000 nm
2000 nm
1000 nm
500 nm
200 nm
100 nm
50 nm
Parameter Value (or Range)
Radical diameter
*
, d
r (nm) 0.5262
Radical mass, m
r (g) 1.59410
-22

Temperature, T (K) 353
Particle diameter, d
p (m) 2.010
-8
– 5.010
-6

Number concentration, N (part/m
3
) 1.4410
14
- 7.2110
21

Diffusion coefficient, D
r (m
2
/s) 1.010
-11
– 1.010
-7

Polymer volume fraction
**
, 
p 6.54510
-7
– 5.23610
-1


Radical captureRadical capture

27. 2
7
Radical size (nm)
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
k
c

(
m
3
/
m
o
l.
s
)
1e+9
2e+9
3e+9
4e+9
5e+9
MCRF simulation data
Best fit
Distance to particle surface, r (nm)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
k
c

(
m
3
/
m
o
l.
s
)
1e+8
1e+9
1e+10
1e+11
1e+12
1e+13
1e+14
1e+15
1e+16
MCRF simulation data
Best fit
Uniformly distributed radicals
Smoluchowski equation
E/RT
0 5 10 15 20
C
a
p
t
u
r
e

E
f
f
ic
ie
n
c
y
,

f
0.0
0.2
0.4
0.6
0.8
1.0
MCRF simulation data
Exponential decay best fit
E/RT
0 5 10 15 20
k
c

(
m
3
/
m
o
l.
s
)
1e+6
1e+7
1e+8
1e+9
1e+10
293 K
333 K
353 K
Almost constant collision rate
Exponential decay
T
h
r
e
s
h
o
ld

e
n
e
r
g
y

E
*
A general picture of AbsorptionA general picture of Absorption

28. 2
8
Brownian Dynamics SimulationBrownian Dynamics Simulation
Radical desorptionRadical desorption
20
p
p
d
D
k


* Hernandez, H. F. and K. Tauer, 2008, “Radical desorption kinetics in emulsion polymerization 1. Theory and
Simulation”, Ind. Eng. Chem. Res., In press.
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

29. 2
9
Desorption in complex systemsDesorption in complex systems
Core-shell particlesCore-shell particles
Shell
Core
d
c

s
D
c
D
s
Volume fraction of the soft polymer, 
soft
0.0 0.2 0.4 0.6 0.8 1.0
S
im
p
le

d
e
s
o
r
p
t
io
n

r
a
t
e

c
o
e
f
f
ic
ie
n
t
,

k
0

(
s
-
1
)
1e+3
1e+4
1e+5
1e+6
1e+7
Hard polymer core / soft polymer shell
Soft polymer core / hard polymer shell
Soft polymer limit
Hard polymer limit
Hernandez, H. F. and K. Tauer, 2008, “Radical desorption kinetics in emulsion polymerization 2. Application of
Brownian Dynamics Simulation”, Submitted to Ind. Eng. Chem. Res.
Soft core/Hard shell  Hard core/Soft shell

30. 3
0
Temperature, T (K)
300 320 340 360
S
im
p
le

d
e
s
o
r
p
t
io
n

r
a
t
e

c
o
e
f
f
ic
ie
n
t
,

k
0

(
s
-
1
)
1e+6
1e+7
1e+8
1e+9
E
des
= 0 kJ/mol
E
des
= 13.25 kJ/mol
Energy barrier for desorption, E
des
/k
B
T
0 2 4 6 8
E
q
u
ilib
r
iu
m

d
e
s
o
r
p
t
io
n

r
a
t
e

c
o
e
f
f
ic
ie
n
t
,

k
0
(
*
)
(
s
-
1
)
0.0
5.0e+7
1.0e+8
1.5e+8
2.0e+8
BD simulation data points
Exponential decay best fit
Desorption in complex systemsDesorption in complex systems
Core-shell particlesCore-shell particles
Shell volume fraction, 
s
0.0 0.2 0.4 0.6 0.8 1.0
S
im
p
le

d
e
s
o
r
p
t
io
n

r
a
t
e

c
o
e
f
f
ic
ie
n
t
,

k
0

(
s
-
1
)
1e+3
1e+4
1e+5
BD simulation results
Best fit
Core without the shell
Shell volume fraction, 
s
0.0 0.2 0.4 0.6 0.8 1.0
S
im
p
le

d
e
s
o
r
p
t
io
n

r
a
t
e

c
o
e
f
f
ic
ie
n
t
,

k
0

(
s
-
1
)
1e+4
1e+5
1e+6
1e+7
BD simulation data
Best fit

31. 3
1
Desorption in complex systems Desorption in complex systems Monomer Monomer
concentration gradientconcentration gradient
Temperature, T (K)
300 320 340 360
D
if
f
u
s
io
n

c
o
e
f
f
ic
ie
n
t
,

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

32. 3
2
Desorption in complex systems Desorption in complex systems Non-Non-
spherical particlesspherical particles
Experimental details:
Ab-initio batch styrene emulsion polymerization
at 40°C and 300 rpm. Stabilizer: Sodium dodecyl
sulfate (1.1 phm). Initiator system:
PEGA-200/Sodium metabisulfite/Ferrous sulfate
(0.20/1/0.03). Total solids: 5.15%.
Champion et al. (2007) Proc Natl Acad Sci USA 104:11901

33. 3
3
Desorption in complex systems Desorption in complex systems Non-Non-
spherical particlesspherical particles
1e+6
1e+7
1e+8
1e+9
1
10
1
10
S
im
p
le

d
e
s
o
r
p
t
io
n

r
a
t
e

c
o
e
f
f
ic
ie
n
t
,

k
0

(
s
-
1
)

z

y
Sphere
Needle
Thin disc
O
b
la
te
s p
h
e
r o
id
s
P
r
o
la
te
s
p
h
e
r
o
id
s
1e+6
1e+7
1e+8
1e+9
1
10
1
10
S
im
p
le

d
e
s
o
r
p
t
io
n

r
a
t
e

c
o
e
f
f
ic
ie
n
t
,

k
0

(
s
-
1
)

z

y
Sphere
Needle
Thin disc
O
b
la
te
s p
h
e
r o
id
s
P
r
o
la
te
s
p
h
e
r
o
id
s
Surface-to-volume ratio
0.05 0.10 0.15 0.20 0.25
S
im
p
le

d
e
s
o
r
p
t
io
n

r
a
t
e

c
o
e
f
f
ic
ie
n
t

k
0

(
s
-
1
)
0.0
2.0e+7
4.0e+7
6.0e+7
8.0e+7
1.0e+8
1.2e+8
2
0 






V
S
Dk
p
Particular example: Ellipsoidal particles

34. 3
4
Energy BarriersEnergy Barriers
•The difference in energy barriers E=E
abs-E
des determines the
steady state distribution
K  exp(-E/RT)
•The sum of energy barriers E=E
abs
+E
des
determines the
dynamics of the process
  exp(E/RT)
Absorption
E
abs
Desorption
E
des

35. 3
5
Macroscopic picture of swellingMacroscopic picture of swelling

36. 3
6
Molecular picture of swellingMolecular picture of swelling

37. 3
7
Molecular uptake by particlesMolecular uptake by particles
Simultaneous absorption and desorptionSimultaneous absorption and desorption
0.001
0.01
0.1
1
10
100
1000
1e-3
1e-2
1e-1
0.1
1
10
100
K
s
s

p
D w
/D p
Parameter Value
Temperature 45°C
Unswollen particle diameter 50 nm
Initial particle volume fraction
of the dispersion
12.5%
Monomer molecular weight 100.12 g/mol
Monomer molecular diameter 0.7063 nm
Diffusion coefficient of
monomer in water
310
-9
m
2
/s
Monomer molar volume 0.111 L/mol
Amount of monomer added to
the dispersions
0.08 – 2.40 L
monomer/L particles

Absorption/Desorption Equilibrium


w
p
ss
M
M
K

38. 3
8
Time (ns)
0 500 1000 1500 2000
V
o
lu
m
e

f
r
a
c
t
io
n

o
f

m
o
n
o
m
e
r

in

t
h
e

p
a
r
t
ic
le
s
0.0
0.2
0.4
0.6
0.8
1.0
Monomer volume fraction at equilibrium according to MKA eq.: 0.7557
Monomer to unswollen particles volume ratio: 2.40
2.00
1.60
1.20
0.96
0.80
0.64
0.40
0.24
0.08
Molecular uptake by particlesMolecular uptake by particles
Dynamic and equilibrium swellingDynamic and equilibrium swelling
Steady-state
Example: MMA in PMMA
Monomer to unswollen particles volume ratio
0.0 0.5 1.0 1.5 2.0 2.5
M
o
n
o
m
e
r

c
o
n
c
e
n
t
r
a
t
io
n

[
M
]
0
2
4
6
8
Steady-state monomer concentration in aqueous phase
Steady-state monomer concentration inside the particles
Overall monomer concentration
Limit concentration

39. 3
9
Example: MMA/PMMA Example: MMA/PMMA
(Zero energy barriers)(Zero energy barriers)
Monomer to unswollen particles volume ratio
0.0 0.5 1.0 1.5 2.0 2.5 3.0M
o
n
o
m
e
r m
o
la
r c
o
n
c
e
n
tra
tio
n
in
s
id
e
th
e
p
a
rtic
le
s
, [M
]
p
0
2
4
6
8
D
iffu
s
io
n
c
o
e
ffic
ie
n
t in
s
id
e
th
e
p
a
rtic
le
s
, D
p
(
m
2
/s
)
1e-16
1e-15
1e-14
1e-13
1e-12
1e-11
1e-10
1e-9
1e-8
Monomer concentration, [M]
p
Diffusion coefficient, D
p

40. 4
0
Example: MMA/PMMAExample: MMA/PMMA
Monomer to unswollen particles volume ratio
0.0 0.5 1.0 1.5 2.0 2.5 3.0
M
o
n
o
m
e
r
m
o
la
r
c
o
n
c
e
n
tr
a
tio
n
0.0
0.5
1.0
1.5
2.0
2.5
Equilibrium concentration in water
Overall concentration

41. 4
1
Example: MMA/PMMAExample: MMA/PMMA
Monomer to unswollen particles volume ratio
0.0 0.5 1.0 1.5 2.0 2.5 3.0
E
q
u
ilib
r
iu
m

d
e
g
r
e
e

o
f

s
w
e
llin
g
,

Q
e
q
1.0
1.5
2.0
2.5
3.0
3.5
E
q
u
ilib
r
iu
m

m
o
n
o
m
e
r

p
a
r
t
it
io
n

c
o
e
f
f
ic
ie
n
t
,

K
e
q
1
10
100
1000
10000
Equilibrium swelling
Equilibrium partition coefficient

42. 4
2
Swelling DynamicsSwelling Dynamics
Time (ns)
0 500 1000 1500 2000
R
a
te
o
f s
w
e
llin
g
(n
m
3
/n
s
)
-100
0
100
200
300
400
Monomer/particles volume ratio = 0.10
Monomer/particles volume ratio = 0.05
Monomer/particles volume ratio = 0.01

43. 4
3
Time (ns)
0.02.0e+54.0e+56.0e+58.0e+51.0e+61.2e+61.4e+61.6e+61.8e+6
N
/
N
0
0.0
0.2
0.4
0.6
0.8
1.0
BD simulation - Fast aggregation results
BD simulation - Slow aggregation results
Smoluchowski's fast aggregation rate
Slow aggregation - Best fit
Particle Aggregation: CoagulationParticle Aggregation: Coagulation
Parameter Value
Temperature 80°C
Initial particle diameter 50 nm
Initial particle number
concentration
10
20
part/m
3

Particle density 1.06 g/cm
3

Water viscosity 3.5510
-4
Pa·s
Surface potential of the
particles
10 mV
Average valence at the surface 3
Ionic concentration 0.01 M
Hamaker constant 0.5810
-21
J

44. 4
4
Particle Aggregation: CoagulationParticle Aggregation: Coagulation
Cluster formation

45. 4
5
Thermodynamic Factors Kinetic Factors
Sequence and amount of
monomer fed into the system
Method of addition of
monomer
Hydrophilicity of monomers
(and polymers)
Molecular weight of polymers
Surface and interfacial
tensions
Viscosity of polymers
Compatibility between
polymers
Crosslinking
Polymerization temperature

Application Example: Application Example:
Multicomponent colloidal polymer particlesMulticomponent colloidal polymer particles
Core/Shell
Inverted core/shell
Polymer 1
Polymer 2
Multilayered (onion-like)
Raspberry structure
Cross sectionMorphology
Acorn
Cross section Morphology
Occluded
Core/Shell
Inverted core/shell
Polymer 1
Polymer 2
Multilayered (onion-like)
Raspberry structure
Cross sectionMorphology
Acorn
Cross section Morphology
Occluded

46. 4
6
Application Example: Application Example:
Multicomponent colloidal polymer particlesMulticomponent colloidal polymer particles
Seed latex Seed latex Structured polymer particlesStructured polymer particles
Seeded emulsion
polymerization
Experimental details:
150 nm polystyrene seed particles prepared by emulsion polymerization at 80°C. Surfactant: Sodium
dodecylsulfate. Initiator: Potassium persulfate
Second stage polymerization of n-butyl methacrylate at 80°C. Initiator: Potassium persulfate
Shell
Core

47. 4
7
Application Example: Application Example:
Multicomponent colloidal polymer particlesMulticomponent colloidal polymer particles

Seed latex Seed latex Structured polymer particlesStructured polymer particles
Seeded emulsion
polymerization
Experimental details:
600 nm seed particles prepared by dispersion polymerization in methanol of styrene and divinyl
benzene at 55°C. Initiator: AIBN. Stabilizer: Polyvinyl pyrrolidone. Dispersion transferred to poly vinyl
alcohol aqueous solution.
Second stage semi-batch emulsion polymerization of methyl methacrylate at 80°C. Initiator: KPS.

48. 4
8
Application Example: Application Example:
Multicomponent colloidal polymer particlesMulticomponent colloidal polymer particles
Experimental details:
1.4 m seed particles prepared by dispersion polymerization in methanol of styrene and divinyl
benzene at 55°C. Initiator: AIBN. Stabilizer: Polyvinyl pyrrolidone. Dispersion transferred to water.
Second stage emulsion polymerization of vinyl acetate at 80°C. Initiator: AIBN.
Seed latex Seed latex Structured polymer particlesStructured polymer particles
Seeded emulsion
polymerization

49. 4
9
Application Example: Application Example:
Multicomponent colloidal polymer particlesMulticomponent colloidal polymer particles
Seed particle
Monomer
Initiator
Structured particles
Radical and oligomer
capture by seed particles
Secondary
particle
nucleation
Secondary
particles
Particle shell
Particle core
Unstable
secondary
particles
Heterocoagulation
Stable secondary
particles
Bimodal distribution
No structured particles
Particle core
Particle shell

50. 5
0
Multiscale integrationMultiscale integration
System and conditionsSystem and conditions
Vinyl Acetate
Polystyrene seed latex
Parameter Value Parameter Value
Temperature (°C) 80
Simulation volume
(l)
1x10
-14
Seed volume
fraction (%)
0.01 - 10
Seed particle
diameter (nm)
10-500
Seed polymer
density (g/ml)
1.044 Water density (g/ml) 0.972
Poly(vinyl
acetate) density
(g/ml)
1.15
Aqueous monomer
concentration
(mol/l)
0.3
Monomer feed
rate (mol/ls)
3x10
-4
Initiator efficiency 0.9
Initial initiator
concentration
(mol/l)
1x10
-3

Initiator
decomposition rate
coefficient (s-1)
8.6x10
-5

Propagation rate
coefficient
(l/mols)
1.29x10
4

Termination rate
coefficient (l/mols)
1.13x10
10

Primary radical
molar volume
(l/mol)
0.046
Primary radical
molar mass (g/mol)
96.16
Monomer unit
molar volume
(l/mol)
0.075
Monomer unit molar
mass (g/mol)
86.09
Water viscosity
(cP)
0.355
Particle size
tolerance for BD
simulation
triggering
5%

51. 5
1
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
o
e
f
f
ic
ie
n
t
,

k
c

(
l
w
a
t
e
r
/
p
a
r
t
.
s
)
1e-12
1e-11
1e-10
BD simulation updates
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%
Aqueous phase propagation vs. capture by particles
Hernandez, H. F. and K. Tauer, 2008, Comp.-Aided Chem. Eng., 25, 769.
Secondary particle suppression

52. 5
2
Influence of the Locus of radical Influence of the Locus of radical
generationgeneration
Thermal Initiation
Radicals
Initiator
molecules
Particle
Interfacial Redox Initiation
Radicals
Reducing
molecules
Particle
Oxidizing
molecules
Inisurf Initiation
Radicals
Particle
Inisurf
molecules
+

53. 5
3
Influence of the Locus of radical Influence of the Locus of radical
generationgeneration
Seed volume fraction
0.0 0.1 0.2 0.3 0.4 0.5
N
u
m
b
e
r

o
f

n
e
w

p
a
r
t
ic
le
s
/
1
0
0

r
a
d
ic
a
ls

g
e
n
e
r
a
t
e
d
0
5
10
15
20
25
Thermal initiation
Interfacial redox initiation
Inisurf initiation

Seed particle size (nm)
0 200 400 600 800 1000 1200
N
u
m
b
e
r

o
f

n
e
w

p
a
r
t
ic
le
s
/
1
0
0

r
a
d
ic
a
ls

g
e
n
e
r
a
t
e
d
0
2
4
6
8
10
12
14
Thermal initiation
Interfacial redox initiation
Inisurf initiation
Negligible secondary particle formation
Inisurf results evidenced experimentally!*
*Soltan-Dehghan et al., 2006, J.Appl.Polym.Sci., 100, 2409.

54. 5
4
Potential ApplicationsPotential Applications

55. 5
5
ContentsContents
Motivation
Emulsion Polymerization
Understanding emulsion
polymerization
Particle nucleation
Mass transfer between phases
Multi-scale simulation
Applications
Conclusions

56. 5
6
ConclusionsConclusions
•Heterophase polymerization is a complex multi-scale stochastic
process.
•Adequate integration of all relevant scales is required: Multiscale
dynamic simulation methods.
•Multiscale dynamic simulation methods were used to investigate the
optimal conditions for the suppression of secondary nucleation in
semi-batch seeded emulsion polymerization.
•Controlling the locus of radical generation at the surface of the
particles greatly reduces the probability of secondary particle
formation.
•Enormous possibilities for the investigation and exploration of multi-
scale integration in heterogeneous polymerization systems.

57. 5
7
ConclusionsConclusions
•Heterophase polymerization: A complex multiscale stochastic process.
•Multi-scale modeling and simulation: Powerful tool for investigating and
understanding heterophase polymerization
•Significant results obtained in the kinetic description of emulsion
polymerization, e.g.
–Radical capture
–Radical desorption
–Monomer swelling
–Secondary particle formation
–Kinetics of emulsion polymerization in complex systems
•Example: Suppression of secondary nucleation in semi-batch seeded
emulsion polymerization by kMC-BD multi-scale simulation.
 ConclusionsConclusions

58. Thank you!Thank you!
Andercol s.a.:
Alvaro Aguirre, Jorge Zapata
Max Planck Institute of Colloids and Interfaces:
Klaus Tauer and Markus Antonietti
Technical support: Ursula Lubahn, Sylvia Pirok, Irina
Shekova, Rona Pitschke, Heike Runge, Marlies
Gräwert
Polymer Dispersions Group: Pantea Nazaran, Nancy
Weber, Farnoosh Roohi, Olga Lazareva

59. 5
9
Selected ReferencesSelected References