Emulsion Polymerization

7 Kinetics and Mechanism of the Emulsion Polymerization of Vinyl Acetate M. NOMURA,**M. HARADA,* W. EGUCHI,* and S. NAGATA

Downloaded by UNIV OF PITTSBURGH on June 24, 2013 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/bk-1976-0024.ch007

Department of Chemical Engineering, Kyoto University, Kyoto, Japan To date i t has been a well-known fact that the Smith and Ewart theory does not apply to the emulsion polymerization of high ly water-soluble monomers such as vinyl acetate and vinyl chloride. Therefore, many experimental and theoretical investigations have been performed during the past decade to understand and explain the mechanism of the emulsion polymerization of such monomers. Recently, Ugelstad et al. (1) (2) have succeeded in explaining the kinetics of the emulsion polymerization of vinyl chloride introd ucing the mechanism of rapid radical desorption and reabsorption in the polymer particles, while the authors (3) (4) have developed a theoretical expression for the rate coefficient of radical esca pe process from the polymer particles assuming that the majority of escaping radicals is a monomeric one, and successfully explained the role of polymer particles in the emulsion polymerization of a wide variety of monomers including, of course, vinyl acetate and vinyl chloride. Recently, several investigations have been carr ied out to reexamine the kinetics and mechanism of the emulsion polymerization of vinyl acetate and vinyl chloride (5) (6), and clarified that the kinetics of the emulsion polymerization of these monomers are essentially identical. However, the mechanism of particle nucleation still remain equivocal and hence one cannot estimate the conversion-time relation in regard to monomer consu mption theoretically. The purpose of this paper is first to clarify the detailed characteristics of the emulsion polymerization of vinyl acetate using sodium lauryl sulfate as emulsifier and potassium persulfate as initiator, and second to propose a new reaction model, based on our theory relating to the role of polymer particles, which enable us to predict the number of polymer particles produced and consequently , the progress of vinyl acetate emulsion polymeriza tion. Experimental A schematic diagram of the experimental apparatus and the d i Present address *) Institute of Atomic Energy, Kyoto Univ. Uji, Japan **) Dept. of Industrial Chem., Fukui National Univ. Fukui, Japan 102

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

7.

NOMURA ET

Emulsion

AL.

Polymerization

of Vinyl

103

Acetate

mensions o f the r e a c t o r v e s s e l and the i m p e l l e r are shown i n F i g . l . The r e a c t o r i s a c y l i n d o r i c a l g l a s s v e s s e l w i t h a dished bottom, equipped with four-bladed paddle type i m p e l l e r and f o u r b a f f l e p l a t e s l o c a t e d on the v e s s e l w a l l a t 90° i n t e r v a l s . V i n y l acetate monomer was d i s t i l l e d twice under vacuum, s t o r e d a t -20°C and r e d i s t i l l e d before use. Sodium l a u r y l s u l f a t e and potassium p e r s u l f a t e o f e x t r a pure grade were used without f u r t h e r p u r i f i c a t i o n .


(3)

(SI

(6)

it) (1) (unit: mm) (2) Dimensions of reaction vessel and impeller (3) (4) (5) 1 Experimental apparatus and (6) (7)

(I)

N gas cylinder (8) Reaction vessel Pyrogallol solution (9) Sampling cock H SO« ί 10) Thermometer Voltage regulator (11) Impeller CaCl (12) Pressure regulator Electric furnace ( 13) Reflux condenser Feeder for aqueous initiator solution 2

2

2

# · · . . · J. « ., Schematic diagram of experimental apparatus

dimension of reaction vessel end im>el 1er •πα impener

The s t a r t - u p procedures are as f o l l o w s . The r e a c t i o n v e s s e l was charged with the d e s i r e d amounts of p u r i f i e d water, e m u l s i f i e r and monomer, and the d i s s o l v e d oxygen was removed by bubbling p u r i f i e d n i t r o g e n gas through the r e a c t i o n mixture f o r a t l e a s t h a l f an hour. The aqueous i n i t i a t o r s o l u t i o n p r e v i o u s l y deoxygenated with the n i t r o g e n gas was then f e d t o the r e a c t i o n v e s s e l and the p o l ymerization r e a c t i o n was s t a r t e d . In a l l cases the r e a c t i o n tem perature was maintained a t 50 0.5°C by means o f a thermostatted water bath and i m p e l l e r speed a t 400 r.p.m.. Monomer conversion was determined g r a v i m e t r i c a l l y and the degree of p o l y m e r i z a t i o n by the v i s c o s i t y i n benzen s o l u t i o n method employing Nakajima s equation given below( 1_) . 1

[η

1

= 5.36

χ ΙΟ"*

[ Μμ ]

0.62

( ι)

The number of polymer p a r t i c l e s was determined from the monomer conversion X and the volume average diameter o f the polymer p a r t i c l e s dp measured with an e l e c t r o n microscope. M

dp - W

âpi

/ Z n

i

(

2

)

Ν

= 6

Τ

Μ

ο

X

M

/

7

F

d

P

(

p p

3

)

where M = i n i t i a l monomer c o n c e n t r a t i o n ( g/cc-water ) , - the num ber of polymer p a r t i c l e s ( p a r t i c l e s / c c - w a t e r ) and p = d e n s i t y o f p o l y v i n y l acetate. The monomer concentration i n the monomer-swollen polymer p a r t i c l e s was determined by chemical a n a l y s i s a f t e r s e p a r a t i n g the remaining monomer d r o p l e t s i n the sample w i t h a c e n t r i f u g e . The d e t a i l s are given i n the previous p a p e r ( £ ) . q

p



104

EMULSION

POLYMERIZATION

Results and d i s c u s s i o n C h a r a c t e r i s t i c s o f v i n y l acetate emulsion p o l y m e r i z a t i o n . ( 1 ) R e l a t i o n s h i p between the v a r i a t i o n o f surface t e n s i o n o f aqu eous phase o f r e a c t i o n mixture and the number o f polymer p a r t i c l e s produced: Fig.2 shows a t y p i c a l r e p r e s e n t a t i o n o f the v a r i a t i o n i n the surface t e n s i o n of the r e a c t i o n mixture with r e a c t i o n time. Fig.3 g i v e s the r e l a t i o n s h i p between the number o f polymer p a r t i c l e s produced and the progress o f p o l y m e r i z a t i o n , corresponding t o F i g . 2 . When the i n i t i a l e m u l s i f i e r c o n c e n t r a t i o n i s very low, the s u r f a c e t e n s i o n i n c r e a s e s s h a r p l y from the very beginning and the number o f polymer p a r t i c l e s seems t o be constant from the s t a r t of p o l y m e r i z a t i o n . On the other hand, when the i n i t i a l e m u l s i f i e r c o n c e n t r a t i o n i s very h i g h , the s u r f a c e t e n s i o n remains almost co nstant r e g a r d l e s s o f progress o f p o l y m e r i z a t i o n and polymer p a r t i c l e s appears t o generate throughout the p o l y m e r i z a t i o n process. T h i s means t h a t e m u l s i f i e r m i c e l l e s e x i s t to the end of polymeri z a t i o n . When the i n i t i a l e m u l s i f i e r concentration i s i n between, the surface t e n s i o n s t a r t s t o i n c r e a s e abruptly i n the course o f polymerization. In t h i s case, the number of polymer p a r t i c l e s i n c r e a s e s g r a d u a l l y i n the r e a c t i o n i n t e r v a l where the s u r f a c e t e n s i o n remains u n a l t e r e d and a t t a i n s to a constant value a t a ce r t a i n conversion o f monomer where the surface t e n s i o n s t a r t s t o i n c r e a s e a b r u p t l y . Considering these c h a r a c t e r i s t i c s which are very c l o s e l y resemble t o those observed i n styrene emulsion p o l y m e r i z a t i o n ( 8_ ) , we may deduce t h a t polymer p a r t i c l e s generate from emulsifier micelles.

ιο'η

0.625 1.88 6.25 12.5 Δ3.75 • 2.50 •7750 A2.50 Gl.25 • 1.25 «0 Δ1.25 Φ0.63 dO.63 Δ0.625 ... 0Λ mo.31 .. B0. J 6 * g/Z-water 1 I I L "0 0.2 0. Ί 0.6 0.8 1.0 MOnomer conversion X I - ] F i g . 3 Relationship between the number of polymer particles and monomer conversion i i

0.8& 0.6 -

0

Fig* 2

10

20

30

Reaction

tlm

V a r i a t i o n of surface tension of aqueous phase of

r e a c t i o n mixture with progress of

polymerization.

M

( 2) E f f e c t of e m u l s i f i e r c o n c e n t r a t i o n upon the number of polymer p a r t i c l e s and the progress o f p o l y m e r i z a t i o n : F i g . 4 shows the e f f e c t of i n i t i a l e m u l s i f i e r c o n c e n t r a t i o n on the number o f polymer p a r t i c l e s produced. From the l o g - l o g


7.

NOMURA ET

Emulsion

AL.

of Vinyl

Acetate

105

p l o t of N versus s , i t can be seen t h a t a t lower range o f emuls i f i e r c o n c e n t r a t i o n the e m u l s i f i e r dependence exponent f o r p a r t i c l e number i s 2, but a t higher range o f e m u l s i f i e r c o n c e n t r a t i o n , t h i s exponent changes t o the 0.92 power. T h i s w i l l be a c l e a r evidence t h a t the mechanism of p a r t i c l e n u c l e a t i o n i n a lower ran ge o f the i n i t i a l e m u l s i f i e r c o n c e n t r a t i o n must be d i f f e r e n t from t h a t i n a h i g h e r range. Therefore, i t can be deduced t h a t i n the lower range of e m u l s i f i e r concentration the n u c l e a t i o n o f polymer p a r t i c l e s occurs p o s s i b l y by p r e c i p i t a t i o n o f polymer formed by homogeneous p o l y m e r i z a t i o n i n the water phase and i n the higher range of e m u l s i f i e r c o n c e n t r a t i o n p a r t i c l e n u c l e a t i o n from m i c e l l e s w i l l become dominant, though the change of p a r t i c l e n u c l e a t i o n mechanism occurs at the e m u l s i f i e r c o n c e n t r a t i o n somewhat lower than CMC of sodium l a u r y l s u l f a t e i n pure water. F i g . 5 sh ows monomer conversion versus time p l o t s a t d i f f e r e n t e m u l s i f i e r concentrations with i n i t i a t o r and monomer concentrations f i x e d , corresponding t o F i g . 4 . I t i s seen t h a t p o l y m e r i z a t i o n r a t e i s almost l i n e a r from 15 t o over 80 % o f monomer conversion, i n c r e a T


Polymerization

Q

O M - 0 . 2 g/cc-water • « o - 0 . 5 g/cc-water o

l "1.25g/Zweter 0

Eo

10 20 "30 Reaction time t [ m i n ] 0.1 utsifler

1 concentration

10

S

[g/Z-water]

0

5 E f f e c t of i n i t i a l

Fig.

t r a t i o n on the course of

e m u l s i f i e r concen polymerization.

. 4 E f f e c t of i n i t i a l e m u l s i f i e r concentration on the number of polymer p a r t i c l e s produced.

Fig

— xlO « 3.0, «

2.0L

to

f

r

Ή ' l -1.25 g/Z-water 0

Stop*

8,.01 ™ 0.61-

0.20 g/cc0.1 0.2 O.k 0.81.0 2 6 8 10 20 Initial emulsifier concentration S [g/Z-water] Fig.6 Effect of Initial emulsifier concentration on the rate of polymerization. .eo.d0.0k

c


ιοβ

EMULSION

POLYMERIZATION


s i n g s l i g h t l y with i n c r e a s i n g e m u l s i f i e r c o n c e n t r a t i o n s . The slope o f a l i n e a r p o r t i o n o f conversion-time curve v a r i e s approx imately i n p r o p o r t i o n t o the 0.15 power o f the i n i t i a l e m u l s i f i e r c o n c e n t r a t i o n , as shown i n F i g . 6 . From the r e l a t i o n s h i p between e m u l s i f i e r concentration and the number o f polymer p a r t i c l e s and p o l y m e r i z a t i o n r a t e , r e s p e c t i v e l y , i t can be found t h a t the r a t e of p o l y m e r i z a t i o n i s p r o p o r t i o n a l to the 0.16 power o f the number of polymer p a r t i c l e s . ( 3) E f f e c t o f i n i t i a t o r c o n c e n t r a t i o n upon the number o f polymer p a r t i c l e s and progress of polymedization: F i g s . 7 and 8 r e s p e c t i v e l y show the e f f e c t of i n i t i a l i n i t i a t o r concentration on the number of polymer p a r t i c l e s and the progress of p o l y m e r i z a t i o n at f i x e d i n i t i a l e m u l s i f i e r and monomer concen t r a t i o n s . I t can be concluded t h a t the number o f polymer p a r t i c l e s i s independent of i n i t i a l i n i t i a t o r c o n c e n t r a t i o n , as shown i n F i g . 7 . Fig.9 shows l o g - l o g p l o t s of p o l y m e r i z a t i o n r a t e r ( g / cc-H 0*sec) versus i n i t i a t o r c o n c e n t r a t i o n . r i s c a l c u l a t e d from the slope of the l i n e a r p o r t i o n o f the monomer conversion versus time p l o t shown i n F i g . 8 . The order of r e a c t i o n with r e s p e c t t o the i n i t i a t o r concentration i s found t o be approximately 0.5 from F i g . 9 . The same r e s u l t was obtained by recent i n v estigation of F r i i s et a l . (5). p

a

p

g/Z-water| -

! Δ Ο

5

.

I

3

B

2

S «0.7 g/Z-water o

M o

•

5.0 1.25 0.625 0.313

! 1

ft

-J

-0.20 g/cc-water

J

L

50 To 70 60 Reaction time t [ min ] F i g . 8 Effect of I n i t i a t o r concentration on the course of polymeri zation. OA 0.8 1 2.0 k.O 8.0 xlO" * I n i t i a t o r concentration l [g/Z-water ] —« Τ h S »0.70 g/Z-water υ M «0.20 g/cc-water F i g . /Effect of i n i t i a l i n i t i a t o r concentr* ation on the number of polymer p a r t i c l e s prI oduced. £ 10

20

30

k0

S »0.70 g/Z-water MQ»0.20 g/cc-water o

1

0

o

o

I 0. (4) E f f e c t of monomer concent- i 0. r a t i o n upon the number o f polymer Σ 0.4 p a r t i c l e s and progress o f polym- e 0.1 0.2 0.i» 0.7 1 2 1» 6 810 erization: I n i t i a t o r concentration l [g/Z-water] -log plots o f N Fig.10 versus shows i n i t i allo gmonomer F i g . 9 Effect of i n i t i a l i n i t i a t o r concentration on the rate of polymerization. c o n c e n t r a t i o n M (g/cc-water). No e f f e c t of monomer concentration i s observed on the number of polymer p a r t i c l e s , though the data p o i n t s shows some s c a t t e r . Fig.11 g i v e s the r e l a t i o n s h i p between monomer conversion and r e a c t i o n time, corresponding t o Fig.10. Fig.12 shows the r e l a t i o n s h i p u

0

T

Q


7.

NOMURA E T A L .

Emulsion

Polymerization

of Vinyl

107

Acetate

between p o l y m e r i z a t i o n r a t e r (g/cc-water·sec)calculated from the slope o f the l i n e a r p o r t i o n o f monomer conversion versus time p l o t s and monomer c o n c e n t r a t i o n M . I t i s found t h a t the r a t e o f p o l y m e r i z a t i o n i s p r o p o r t i o n a l t o the 0.38 power o f monomer conce n t r a t i o n . T h i s r e s u l t i s q u i t e d i f f e r e n t from styrene emulsion p o l y m e r i z a t i o n where monomer c o n c e n t r a t i o n does not a f f e c t the rate of polymerization. p

0

S -0.70 g/î-water

S -0.70 g/Z-water

l - l . 2 5 g/Z-water

Io-1-25 g/Z-water

o


o

0

A

key

+25* 0.*

—tV-

0.05 0.10 0.20 0.30 0.50

Ο Δ •

0Λ

F i g . 10 Effect of I n i t i a l monomer con centration on the number of polymer p a r t i c l e s produced.

0

• Ο

"-"25* 0.5 0.1 0.2 M© { g/cc-water ]

M g/cc-water

10

20

30

k0

50

60

70

Reaction time t [ min ] F i g . l l t f f e c t of i n i t i a l monomer concentration on the course of polymerization.

10 8 6

I - 1.25 g/Z-water S - 0.70 g/Z-water 0

0

~

2

ta.

key So Ο '2.5 θ 6.25 Φ 6.25 • 0.63

Ιο «ο 1.25 0.5 0.63 0.5 0.31 0.5

2.50 0.5 9 Ο.70 5.0 0.2 Δ 0.70 1.25 0.1

«4

ιοί οΤ2

Monomer concentration M

0

[g/cc-water]

F i g . 12 Effect of i n i t i a l monomer concentr atlon on the rate of polymerization.

675

ο

Monomer conversion

' Χ

Μ

[- J

F i g . 13 Effects of e m u l s i f i e r , i n i t i a t o r and monomer concentration on the viscosityaverage degree of polymerization.

( 5 ) E f f e c t o f i n i t i a t o r , e m u l s i f i e r and monomer concentrations on molecular weight development: Fig.13 shows the e f f e c t o f i n i t i a t o r , e m u l s i f i e r and monomer concentrations on the v i s c o s i t y - a v e r a g e degree o f p o l y m e r i z a t i o n , the v a r i a t i o n i s i d e n t i c a l with each other independently o f i n i t i a t o r , e m u l s i f i e r and monomer c o n c e n t r a t i o n s . T h i s leads t o the c o n c l u s i o n , as a matter o f course, t h a t p a r t i c l e number and i t s volume do not a f f e c t the molecular weight development i n v i n y l acetate emulsion p o l y m e r i z a t i o n . The constant value o f Ρy i n the lower range o f monomer conversion can be reasonably explained by assuming t h a t c h a i n t r a n s f e r r e a c t i o n t o monomer molecules i s a dominant f a c t o r determining the degree o f p o l y m e r i z a t i o n . Based on t h i s s u p p o s i t i o n , the v i s c o s i t y - a v e r a g e degree o f p o l y m e r i z a t ion can be c a l c u l a t e d by the f o l l o w i n g simple equations as long as the mathematical form o f molecular weight d i s t r i b u t i o n c o i n c i d e s


108

EMULSION

with t h a t o f the"most probable" 5

N

= k

k

(

p/ mf

4

)

POLYMERIZATION

distribution. 1

P = {r0|

• 0.8

* /// 0.6

>

Ύ/γ/

0 M «0.2 g/cc-water o

Ό - 1.25 g/Z-water key S g/Z-water

Ο.ί»

D

00

ι 10

Ο Δ

2.0 1.0

•

o.u

• Calculât on I 20 30

Reaction time

0.J ι

1 : 50

l min ]

t

0

0.2

0.1*

0.6

0.8

MOnomer conversion X

F i g . 2 2 Comparison between calculated and observed conversion vs. time curve at various i n i t i a l emulsifier concentrations.

M

1.0

{ - ]

F i g . 24 Compa rison of the average num ber of radicals per p a r t i c l e between exa ct c a l c u l a t i o n and experiment

(4) E f f e c t o f i n i t i a t o r c o n c e n t r a t i o n upon number o f polymer par t i c l e s and progress of p o l y m e r i z a t i o n : According to our r e a c t i o n model, i t i s found t h a t the number of polymer p a r t i c l e s does not i n c r e a s e with an i n c r e a s e i n the i n i t i a l i n i t i a t o r c o n c e n t r a t i o n , but may be considered t o be r a t h e r constant, as shown i n Fig.25. S o l i d l i n e i n Fig.25 g i v e s the value c a l c u l a t e d with an assumption t h a t CMC i s very low, and rep r e s e n t s w e l l the tendency o f the observed data p o i n t s . From the s t r a i g h t l i n e the i n i t i a t o r dependence exponent i s c a l c u l a t e d to be 0.04: N « I °-°* (40) T

o

Fig.26 shows a comparison between the observed and c a l c u l a t e d con v e r s i o n versus time curves, corresponding t o Fig.25. I t i s seen t h a t the c a l c u l a t e d l i n e s agree with the experimental data to over 90 % conversion. (5) E f f e c t o f monomer c o n c e n t r a t i o n upon number o f polymer p a r t i c l e s and progress o f p o l y m e r i z a t i o n : In Fig.27 i s shown a l o g - l o g p l o t o f the number o f polymer p a r t i c l e s versus i n i t i a l monomer c o n c e n t r a t i o n . The s o l i d l i n e i n Fig.27 represents the c a l c u l a t e d v a l u e . I t i s concluded t h a t the r e a c t i o n model proposed here can express the tendency o f the experimental data p o i n t s and the absolute value o f Ν . From the φ


7.

NOMURA

ET

Emulsion

AL.

Polymerization

s t r a i g h t l i n e i n Fig.27, we Ν

«

Τ

χ!0»

f υ

3!

^

2

ι ι ι ι 111

ι

ι

0.0

(41)

ο

» ι

Calculated

0.8 •stove:

0.04

jt_

• 0..8*n °-.6-

1

I

M

I

1 11

o

M»0.2 g/cc-water o

t t

-L.

S -0.7 g/Z-water -

0.6

S »0.70 g/ >water · MQ-0.20 g/cc-water o


119

Acetate

find:

M

Τ

of Vinyl

key

O.i»

Δ Ο

*

0Γ2 o.ito.6 1.0 2T0 075" i n i t i a t o r concentration I© [9/Z-water] " F i g . 2 5 Comparison of experimental results § with exact c a l c u l a t i o n c

5.0 1.25 0.625 o.2i?

•

0.2

•Calculation

20

30

^0

Reaction time t

•ο g/Z-water

50

80

60

[ min 3

1

«xlO

F i g . 2 6 Comparison between the calculated and observed conv ersion vs. time curve at various i n i t i a t o r concentrations.

|- S -0.70 g/Z-water o

l - l -25 g/Z-water 0

jx

ζ

0.8P O.k

•. ·t ·t

- Calculated love : 0.0

0.6

0.1

Ο

O.k

0.6

M [g/cc-water] F i g . 2 7 Comparison of experimental results with c a l c u l a t i o n . 0

(6) Summary: The r e s u l t s o f c a l c u l a t i o n f o r the number of polymer p a r t i c l e s produced are summarized as f o l l o w s :

Ν

«

s

R e a c t i o n time t [min] F i g . 2 8 C o m p a r i s o n between t h e c a l c u l a t e d and o b s e r v e d c o n v e r s i o n v s . t i m e c u r v e a t v a r i o u s monomer c o n c e n t r ations .

0.9i* 0.0tf I

0.00

M

(

4

2

)

Τ ο ο ο From the slope o f a l i n e a r p o r t i o n of the c a l c u l a t e d conversion versus time curves, the f o l l o w i n g r e l a t i o n s h i p can be obtained f o r the r a t e of the p o l y m e r i z a t i o n : oc

r

ρ

S

0 J 5

ο

j0.5 0 0.38 M

ο

(43)

ο

I t i s concluded t h a t these equations represent w e l l the cha r a c t e r i s t i c s o f the emulsion p o l y m e r i z a t i o n of v i n y l acetate with sodium l a u r y l s u l f a t e as an e m u l s i f i e r and potassium p e r s u l f a t e as an i n i t i a t o r . To conclude In c o n c l u s i o n , we may

say t h a t our r e a c t i o n model developed


120

EMULSION

POLYMERIZATION


by assuming t h a t the polymer p a r t i c l e s form from the e m u l s i f i e r mi c e l l e s expresses w e l l the c h a r a c t e r i s t i c s o f the emulsion polyme r i z a t i o n o f v i n y l a c e t a t e . I t must be emphasized here t h a t desor p t i o n from the polymer p a r t i c l e s and the m i c e l l e s i s the most imp o r t a n t and e s s e n t i a l mechanism on which our r e a c t i o n model i s based. T h i s r e a c t i o n model may be a p p l i c a b l e t o the s i m i l a r sys tems such as v i n y l c h l o r i d e and a c r y l o n i t r i l e emulsion polymeriza t i o n because d e s o r p t i o n mechanism i s dominant i n these systems. The authors wish t o express t h e i r g r a t i t u d e t o Mr. K. Nakagawara, Mr. K. F u j i t a and Mr. S. Sasaki f o r e a r r i n g out the exp eriments . Appendix I D e r i v a t i o n o f k f the r a t e c o e f f i c i e n t f o r escape o f monomer r a d i c a l s : The f o l l o w i n g assumptions are made; (1) a p a r t i c l e contains not more than 1 r a d i c a l . (2) a r a d i c a l o f c h a i n - l e n g t h not longer than s can escape and r e e n t e r the p a r t i c l e with the same r a t e . (3) Instantaneous t e r m i n a t i o n takes p l a c e when another r a d i c a l en t e r the p a r t i c l e which c o n t a i n a r a d i c a l . (4) we do not make d i s t i n c t i o n between r a d i c a l s with o r without an i n i t i a t o r fragment. Taking m a t e r i a l balance f o r the p a r t i c l e s N* and N£ c o n t a i n i n g an i n i t i a t o r r a d i c a l I * and a r a d i c a l o f c h a i n - l e n g t h i , r e s p e c t i v e l y , and assuming steady s t a t e , we have: dN* / d t I dN* / dt 1 dN* / d t ι dN* / d t s

= k Ν I * - (k R*+k M + k.M + k )N* = 0 (A 1) e ο e mt ρ ι ρ oi I = k N M* + k.M N* +k _M N*-(k R* + k M + k M +k )N* (A 2) e o l i p l mfp e mfp pp ο 1_ = k N M* +k M N* - (k R* + k J i +k M + k )N* « 0 (A3) e ο ι ρ p î-l e mf ρ ρ ρ ο ι = k N M* + k M N* , - (k R* + k J4 + k M + k )N* « 0 (A4) e o s pps-1 e mf ρ ρ ρ ~ Q

where N «particle number c o n t a i n i n g no r a d i c a l , M =monomer conce n t r a t i o n i n the p a r t i c l e s , k ^ t r a n s f e r r a t e constant t o monomer, k . = i n i t i a t i o n r a t e c o n s t a n t , k - r a t e constant o f r a d i c a l absorp t i o n , k = r a t e constant o f r a d i c a l d e s o r p t i o n from the p a r t i c l e s , k = r a t e constant o f i n i t i a t o r r a d i c a l d e s o r p t i o n from the p a r t i c l e , N*«number o f p a r t i c l e s c o n t a i n i n g a r a d i c a l Mj, N*=total nu mber o f a c t i v e p a r t i c l e s and R* i s R* = I * M*. (A 5) i=0 Taking m a t e r i a l balance f o r r a d i c a l s i n the water phase and assuming steady a t a t e , we g e t : m

Q

Q l

1

dl*/dt - r + k jN*. - k ^ I * = 0 ±

Adding

0

dM*/dt = k N* - k Ν J * ι ο ι e Τ ι dM*/dt = k N* - k Ν M* s os e T s (A 6) t o (A 8) leads t o :

(A 6)

• 0

(A 7)

=0

(A 8)


7.

NOMURA

Emulsion

E T AL.

Polymerization

of Vinyl

121

Acetate

k Ν (I*+M* + .··+ Μ* + · · · +M* ) = r . +k N * +k N * +... + k N * + eT 1 ι s ι oi I ο 1 o i ...+ k N * ) (A 9) I n s e r t i n g Eq. (A5) i n t o Eq. (A9) g e t s : k N R* = r . + k Ν * (A10) e Τ i f k N * = k N * + k N * +---+k N * (All) f o I ο 1 o s Eq.(All) defines k . Considering t h a t polymers with high degree o f p o l y m e r i z a t i o n can be obtained i n the emulsion p o l y m e r i z a t i o n , we could assume k R*, k M < £ k Μ , k.M e mf p ^ ρ ρ ι ρ . From Eq. (A 1) , (A 2) and N*=nN^, we gets approximately f o r N * , T

x


t

h

a

t

:

N* = r . ( l - n ) / ( k n + k.M ) I i oi ιρ By s i m i l a r treatment we g e t f o r N* and N* ? 1 ι N* = [k M A% M +k ri) }N* + [k.M /(k M +k ή) ]N* 1 m f p p p o ι ρ' ρ ρ ο I kM k M . k . k. N* = ( —) N*=( ) > Γ( • ) N * + f - i ) N * l i k M +k r ^1 \ M +k ÏÏ k V P p o P p o ρ ρ From Eq. ( A l l ) , (Al4) and Ν* = ΠΝ^,, we get:

(A12)

T

P

P

v

U

j

(A13)

(A14^ k

1

}

n

k

k

.

f

= k

oI .

( N

î

/ N

T

)

+ k

o

[ ( k

mf

/ k

p

)

* < 1

W

W

^

f

e P P Q

1(

A

1

5

)

Literature Cited (1) J. Ugelstad, P.C. Mork, P. Dahl and P. Rangnes, J. Polymer Sci. part c, 27, 49 (1969) (2) J. Ugelstad and P.C. Mork, Brit. polymer J.,2,31 (1971) (3) M. Harada, M. Nomura, W. Eguchi and S. Nagata, J.Chem. Eng. Japan, 4, 54 (1971) (4) M. Nomura, M. Harada, K. Nakagawara, W. Eguchi and S. Nagata, J. Chem. Eng. Japan, 4, 160 (1971) (5) N. Friis and L. Nyhagen, J. Appl. Polymer Sci.,17,2311(1973) (6) Ν. Friis and A. E. Hamielec, J. Polymer Sci., 19, 97 (1975) (7) Nakaj ma, Α., Kobunshi Kagaku, 11, 142 (1954) (8) M. Harada, M.Nomura, H. Kojima, W. Eguchi and S. Nagata, J. Polymer SCi, 16, 811 (1972) (9) Sakurada, I., ed.,"vinyl acetate resin", p77 Kobunshi Kagaku Pub., Kyoto (1964) (10) C.R. Wilke and P. Chang, Α. I. Ch. Ε. Journal, 1,264 (1955) (11) D.H. Napper and A.G. Parts, J. Polymer Sci.,61,113 (1962) (12) I.M. Kolthoff and I.K. Miller, J.Am. Chem. Soc., 73,3055 (1951) (13) Morris,C.,and A.G. Parts, Makromol. Chem., 119,212 (1968) (14) Matheson,M.S.,Ε.Α. Auer, E.B. Bevilaqua and E.J. Hart, J. Am. Chem. Soc., 71, 173 (1949) (15) Dixson-Lewis, G., Proc. Royal Soc., (London) A198 ,510 (1949) (16) Burnett, G.M., L. Valentine and H.W. Melville, Trans. Faraday Soc., 45, 960 (1949)


Emulsion Polymerization

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