Structural Framework for Modelling Emulsion Polymerization Reactors

23 Structural Framework for Modelling Emulsion Polymerization Reactors

Downloaded by NANYANG TECHNOLOGICAL UNIV on August 21, 2015 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/bk-1976-0024.ch023

K. W. MIN and W. H. RAY Department of Chemical Engineering, State University of New York at Buffalo, Buffalo, Ν. Y. 14214

Although emulsion polymerization has been carried out for at least 50 years and has enormous economic importance, the detailed quantitative behavior of these reactors i s still not well understood. For example, there are many more mechanisms and phenomena reported experimentally than have been incorporated i n the existing theories. Considerations such as non -micellar particle formation, non-uniform p a r t i c l e morphologies, polymer chain end s t a b i l i z a t i o n of latex p a r t i c l e s , particle coalescence, etc. have been discussed q u a l i t a t i v e l y , but not quantitatively included i n existing reactor models. Our purpose i n this paper is to present a general modelling framework capable of including these and other possible mechanisms and testing their effect on the model predictions. We s h a l l i l l u s t r a t e the application of this framework through the modelling of a polymethylmethacrylate emulsion polymerization reactor. The Mathematical Model As a means of beginning our discussion, l e t us choose to i l l u s t r a t e the model with a rather standard free radical k i n e t i c mechanism: Initiation: I τ* d R+M τ * k.

2R

k

P1

359

In Emulsion Polymerization; Piirma, I., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1976.

EMULSION

360 Propagation: Ρ +M τ * n k Chain

Ρ Transfer: Ρ +M τ * η kc fm Ρ +Tr η


Ρ

rk , -

., n+1

n^l

Ρ,+Μ i n

η;>1

P i "HI

n*l

1

ft

POLYMERIZATION

η

Termination: k Ρ +P -+ M . n m n+m Ρ +P τ* Μ +M n m k , n m c c

n,m*l n,m^l

tu

We s h o u l d e m p h a s i z e t h a t w e c h o o s e t h i s m e c h a n i s m o n l y as an example; o t h e r mechanisms c a n be t r e a t e d i n a s i m i l a r way. The s t r u c t u r e o f the m a t h e m a t i c a l model i s shown i n F i g u r e 1 w h e r e we h a v e d i v i d e d t h e m o d e l u p i n t o g e n e r a l b a l a n c e s , aqueous phase b a l a n c e s , i n d i v i d u a l p a r t i c l e b a l a n c e s , and p a r t i c l e s i z e d i s t r i b u t i o n balances - a l l o f w h i c h exchange i n f o r m a t i o n w i t h each other. To g i v e a n e x a m p l e o f t h e f o r m o f t h e p a r t i c l e s i z e d i s t r i b u t i o n balances l e t us c o n s i d e r the total particle size distribution, F(V,t). For a g i v e n set o f mechanisms the p a r t i c l e size d i s t r i b u t i o n takes the form:

+

φ

(&(ϊ)μ)

rchange o f t o t a l number,rrate o f change by volume , of p a r t i c l e s w i t h time increase of growing p a r t i c l e s ν » - J * k ( V - ν , ν , σ ) F ( V - v ) F ( v ) d v - F ( V ) J" k o ο rate of formation of particlesj frate of o f volume V to V + d V b y c o I 1particl alescence \ V + dV

[ +

c

p

(ν,ν,σ

c

)F(v)

dv

p

d i s a p p e a r a n c e of" e s of volume V to by coalescence

k

(V-V V σ )mF(V-V ) - k (V,V σ )mF(V) c m m p m c m p C r a t e of change of p o p u l a t i o n by coalescence ^micelles

and polymer

between Τ

particles


J

M I N A N D RAY

23.

+

i

k

0 1 11 ==1

n ( [

Emulsion

V

W

) 6 ( V

Polymerization

-V

+

Reactors

r ^r^ ' ^ l f e e d "

361

F ( V

'

t ) }


r a t e o f new p a r t i c l e f o r - l f r a t e o f p o p u l a t i o n c h a n g e matlon of volume Vg by l\by i n f l o w and o u t f l o w oligomer p r e c i p i t a t i o n i n ' aqueous phase

+

k

A ([R] + [P] )6(V-V ) mm m w w' m r a t e o f new p a r t i c l e f o r m a t i o n of volume V by r a d i c a l entry into micelles

(1)

m

[

Similar partial-differential-integral c a n be w r i t t e n down f o r the f^(V,t)

-

equations

r a d i c a l number d i s t r i b u t i o n

£ (i,V,t)

-

growing

G (i,V,t)

-

dead

n

n

p o l y m e r MWD

polymer

MWD

etc. These r e p r e s e n t the most g e n e r a l (and most complex) form of the modelling framework. A very detailed d e s c r i p t i o n of the m o d e l l i n g equations and mechanisms c a n b e f o u n d i n (1^). A n i l l u s t r a t i o n o f some o f the d e t a i l e d i n f o r m a t i o n made p o s s i b l e b y t h i s m o d e l i s given i n Figure 2. V e r y o f t e n one does n o t r e q u i r e as much d e t a i l as p r e s e n t e d i n F i g u r e 2 and the model c a n be s i m p l i f i e d considerably. F o r e x a m p l e , o n e may o n l y b e i n t e r e s t e d i n t h e f i r s t few moments o f t h e l a t e x p a r t i c l e s i z e d i s t r i b u t i o n , F ( V , t ) so as t o g e t a mean and v a r i a n c e of the d i s t r i b u t i o n . T h i s c a n be r e a d i l y c a l c u l a t e d f r o m t h e d e f i n i t i o n o f t h e j t h moment:

F

v

f

j

l

( t )

=

J ο

(V)

j

F(V,t)

w h i c h when combined w i t h E q ' n

dV

(1),

(2)

leads

to


EMULSION

362

POLYMERIZATION

General Balances Emulsifier Monomer Droplets

Total MWD Energy Balance


Total Conversion

Aqueous Phase Balances

P a r t i c l e Size D i s t r i b u t i o n Balances

Individual Particle Balances

Total p a r t i c l e size

[M] , p

[Trl

^ | r a d i c a l number distribution growing polymer

or MWD

M(r,t),I(r,t), Tr(r,t),P(r,t)|

dead polymer

MWD

Figure 1. Structure of the mathematical model


M I N A N D RAY

23.

Structural Framework for Modelling Emulsion Polymerization Reactors

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