Micellar Size Effect in Emulsion Polymerization - ACS Symposium

3 M i c e l l a r Size Effect in Emulsion Polymerization IRJA PIIRMA and PAO-CHI W A N G *

Downloaded by CORNELL UNIV on December 18, 2014 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/bk-1976-0024.ch003

Institute of Polymer Science, The University of Akron, Akron, Ohio 44325

One of the methods for preparing monodispersed latices, i . e . latices of uniform particle size d i s t r i bution, is to use mixed surfactants as the emulsifier in the emulsion polymerization process. The term mixed surfactants, in general, refers to mixtures of ionic and nonionic surfactants. Besides giving latices of narrow particle size distribution, mixed surfactant systems have shown several other interesting characteristics which lighten some aspects concerning the mechanism of par t i c l e nucleation in emulsion polymerization process. Woods, Dodge, Krieger, and Piece (1) obtained monodispersed polystyrene latices at about 50 percent conversion from a series of polymerization recipes with mixed surfactants of different ionic to nonionic ratios. They found that the size of the polystyrene particles in these latices decreased with increasing amount of the ionic component in the surfactant mixtures. To interpret their observations, they adopted the theory of mixed micelle formation by mixed surfactant in aqueous solutions. This concept had been previously confirmed by Nakagawa and Inoue (2) with electro phoresis experiments. Later, Kuriyama, Inoue and Nakagawa (3), showed that the size of the mixed micelles decreased with increasing amounts of ionic component in a mixed surfactant system. Thus, Woods, Dodge, Krieger and Piece recognized the important relationship between the size of the latex-particles *Presentaddress: Lucidol Division, Pennwalt Corp., Buffalo, Ν. Y. 34

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


3.

PIIRMA AND W A N G

Micelhr

Size

Effect

35

and the s i z e of the mixed micelles i n t h e i r polymeri z a t i o n experiments and proposed that the larger polystyrene p a r t i c l e s were associated with the larger micelles. In the polymerization of styrene, using AIBN as i n i t i a t o r , Medvedev and co-workers (4) found that rates of polymerization showed a maximum and, the p a r t i c l e s i z e , a minimum value as the concentrations of the i o n i c component i n the mixed surfactant increased. In the polymerization of styrene, using potassium per s u l f a t e as i n i t i a t o r , Roe (5_) observed that the t o t a l number of p a r t i c l e s i n l a t i c e s depended on the composition of the mixed surfactants and not on the t o t a l number of m i c e l l e s . Therefore, he devaluated the m i c e l l a r nucleation mechanism for emulsion polymeri z a t i o n as proposed by Harkins (6.) -Smith-Ewart (j) . In a p e r s u l f a t e i n i t i a t e d styrene polymerization, using sodium l a u r y l s u l f a t e , (SLS), and Emulphogene BC-840, as the mixed surfactants, Kamath(8) and Wang(9.) found that the rate of polymerization increased r a p i d l y with small increases i n the i o n i c component, SLS. Their recipe o f polymerization i s reproduced i n Table I, and Figure 1 shows the rate o f polymerization, Rp, p l o t t e d against SLS concentration i n the mixed s u r f a c tants. In that p l o t , the concentration of SLS was expressed i n parts of SLS/5-parts BC-840/100 parts styrene. Based on t h i s study, Kamath (8) proposed that p a r t i e l e - n u c l e a t i o n i n h i s system was c o n t r o l l e d by m i c e l l a r nucleation mechanism following Harkins and Smith-Ewart s theory. The above c i t e d information showed unanimously that, i n a mixed-surfactant system of emulsion polymerization, the composition of the mixed surfactant a f f e c t s the r a t e of polymerization. Since by HarkinsSmith-Ewart theory, rate of polymerization i s prop o r t i o n a l to the t o t a l number of p a r t i c l e s i n the system, composition of mixed surfactants seems to a f f e c t the e f f i c i e n c y of nucleation. The k i n e t i c studies of Kamath (8) i s of p a r t i c u l a r i n t e r e s t . In emulsion polymerization of styrene, again according to Smith-Ewart s theory, a logarithmic p l o t of the number of p a r t i c l e s formed, and, therefore, the rate of polymerization, Rp, against t o t a l surfactant concentrations, C , should generate a s t r a i g h t l i n e . 1

1

1

s


36

EMULSION

POLYMERIZATION

Table I


Polymerization Recipe (Ref. 8,9,15) Ingredient

PHM

SLS Κ-persulfate KOH

180 100 5 Variable 0.18 0.075

BC-840:

Emulphogene BC-840 Tr idecyloxypoly(ethyleneoxy)-ethano1 Donated by GAF Company

SLS:

Sodium l a u r y l s u l f a t e

However, by neglecting the v a r i a t i o n s i n the composi t i o n of the mixed-surfactants, Kamath's data and the preliminary experimental r e s u l t s of the present study d i d not generate a s t r a i g h t l i n e by such a p l o t , but a curve instead as i l l u s t r a t e d by Figure 2. Therefore, i t seemed that some other factor or factors was (were) a f f e c t i n g the rate of polymerization, or more p r e c i s e l y , the e f f i c i e n c y of nucleation. Since t h i s system of polymerization was using mixed surfactant as e m u l s i f i e r , mixed-micelles should have been formed, and, based on the findings of Kuriyana, Inoue and Nakagawa (3_) , the sizes of such mixed m i c e l l e s should vary with varying composition of the mixed-surfactants. This v a r i a t i o n was confirmed by l i g h t s c a t t e r i n g measurements, applying a method used by other i n v e s t i g a t o r s (3,10.11. 12) for the same purpose. The r e s u l t s obtained are summarized i n Figure 3, where i t can be seen that the m i c e l l a r weight of the mixed m i c e l l e s dropped r a p i d l y with increasing value o f surfactant r a t i o , r , of the mixed-surfactants. Surfactant r a t i o , r , i s defined as r = moles SLS/mole BC-840. Since i t i s reasonable to assume that the s i z e of the mixed m i c e l l e i s pro p o r t i o n a l to i t s weight, Figure 3 implies that each s p e c i f i c value r stands for a s p e c i f i c value of m i c e l l a r s i z e i n t h i s surfactant system.



3. PIIRMA AND W A N G

— J

ai

Micellar

.

Size

Effect

1

1

0.2

Part

SLS/5

37

I

0.3

part

BC-840 per

0.4

100 p a r t »

L .

0.5

monomer

Figure I. Effect of mixed surfactant composition on polymerization rate (SLS-BC 840 system; Ref. 8)

c

1 3.5

IM Ο,χΙΟ

1 3.6 3

aoL.A-aqiMotM

1 3J

pha

I M

Figure 2. Effect of total surfactant concentra tion with varying surfactant ratio on polymeriza tion rate


38

EMULSION

POLYMERIZATION

For a given t o t a l concentration of mixed s u r f a c tants, C , with known compositions, the value of sur factant r a t i o , r , can be c a l c u l a t e d . Thus, data on Figures 2 and 3 can be combined to generate Figure 4 which shows a possible r e l a t i o n s h i p between the s i z e of the micelles and the rate of polymerization. Then, other things being equal, the rate of polymerization, Rp, of an emulsion polymerization process should be a function o f two v a r i a b l e s , namely, the t o t a l concen t r a t i o n of mixed surfactants, C , expressed i n moles per l i t e r aqueous phase, and the m i c e l l a r weight, M , i n grams per mole, which a l s o can be expressed i n terms of surfactant r a t i o , r , or by m i c e l l a r s i z e . Thus, s


s

m

R

(c

M

( 1 )

P = f s> m> which implies that, at a given concentration of i n i t i a t o r and under a s p e c i f i e d temperature, the k i n e t i c s of emulsion polymerization should be expressed by a three parameter model, (R , C , M ) , rather than by the c l a s s i c a l two parameter one, (Rp, C ) . This i s i l l u s t r a t e d schematically i n Figure 5. For a s i n g l e surfactant system of emulsion polymerization with rather narrow range of v a r i a t i o n s i n surfactant con centration, the size and shape of the micelles should be constant, and thus the three parameter model of polymerization k i n e t i c s reduces i t s e l f to the c l a s s i c a l two parameter one, and the logarithmic p l o t of rate against concentration y i e l d s a s t r a i g h t l i n e with slope,χ , to f i t the r e l a t i o n s h i p of n

p

g

m

s

Rp

«

c

s

x

(2)

and χ = 0.6 i s one of the e s s e n t i a l s of Smith-Ewart theory. Therefore, the nonlinear r e l a t i o n s h i p between rate of polymerization and the t o t a l surfactant concentra t i o n , as shown i n Figure 2, was believed to be caused by a change i n m i c e l l a r s i z e . Thus, the purpose of the present study was to v e r i f y the v a l i d i t y of the concept of m i c e l l a r s i z e e f f e c t i n emulsion polymer i z a t i o n k i n e t i c s . Furthermore, although the HarkinsSmith-Ewart theory of m i c e l l a r nucleation was proposed i n 1948, and has found widespread a p p l i c a t i o n ever since, i t s v a l i d i t y i s s t i l l challenged even for the case of polymerization of styrene (5_) . I f m i c e l l a r




Micellar

0.1

Size

0.2

Effect

03

0.4

39

0.5

0.6

r · a o l « » SLSL^aol* BC-840

Figure 3. Effect of surfactant ration on micelhr weight of mixed surfactant (SLS BC-840 system)

35

ST

S* In

3

CjtlO

Figure 4. Effect of surfactant concentration with varying surfactant ratio on size of micelles and on polymerization rate


40

EMULSION

POLYMERIZATION

s i z e should be proven to a f f e c t the e f f i c i e n c y of nucleation, then, a t l e a s t i n the case o f styrene polymerization, the m i c e l l a r s i z e should be considered as an a d d i t i o n a l and important v a r i a b l e i n the aqueous phase i n i t i a t i o n as proposed by some investigators (5,13* W-


Experimental Procedures I. M i c e l l a r Size Measurements. T u r b i d i t y measurements for m i c e l l a r weight c a l culations were c a r r i e d out using the Price-Phoenix l i g h t s c a t t e r i n g apparatus with green l i g h t of mercury as the l i g h t source. Refractive index increments o f the BC-840 and o f the SLS were determined by B r i c e Phoenix d i f f e r e n t i a l refractometer , while that o f the mixed surfactants were calculated using the following equation C ( n / a ) + C ( n/ôc) s ° « k b C + α s b a

(cm/dc) = m

c

a

(3)

where (^n/dc) denotes the r e f r a c t i v e index increment, c the concentration i n g./mole. with sub m, s, and b r e f e r r i n g to mixed surfactant, sodium l a u r y l s u l f a t e and BC-840 r e s p e c t i v e l y . This equation has been used by other investigators i n several mixed surfactant systems (3) . For t u r b i d i t y measurements, a stock solution o f desired mole r a t i o o f sodium l a u r y l s u l f a t e to BC-840 was prepared on a weight b a s i s . The stock s o l u t i o n was d i l u t e d volumetrically to a series of d i f f e r e n t concentrations. These d i l u t e d solutions were allowed to stand overnight for e q u i l i b r a t i o n of m i c e l l e s . Solutions were f i l t e r e d four times under pressure through HAWP 0.25 f i l t e r d i r e c t l y into scattering c e l l s for measurements.



MiceUar

Size

41

Effect

I I . Polymerization Recipe. Ingredients

Parts by Weight (grams)


Styrene 100.0 D i s t i l l e d water 180.0 Potassium p e r s u l f a t e 0.3 Mixed s u r f a c t a n t * v a r i a b l e

Moles/liter agueous phase 5.342 0.0062 variable

Nonionic component: Emulphogene BC-840, ave. mol. wt. 860, i s a t r i d e c y l o x y p o l y 4-ethyleneoxy Methanol was donated by GAF Ionic component: Sodium l a u r y l s u l f a t e , mol. wt. 288 The composition of mixed surfactant i s designated by r , the surfactant r a t i o and expressed i n moles SLS per mole of BC-840. This r a t i o can be adjusted as desired. In the case where a series of polymerizations with i d e n t i c a l r-values of mixed surfactant were needed, a stock s o l u t i o n with the desired r-value was made. This s o l u t i o n was then aged for 4 hours to have the s u r f a c tants dissolved completely before being used to prepare the polymerization emulsions. These polymerizations were then run i n random order to minimize p o s s i b l e error caused by h y d r o l y s i s . III.

Polymerization.

Polymerizations were c a r r i e d out i n 8-ounce glass b o t t l e s with metal caps containing s e l f - s e a l i n g b u t y l rubber gaskets. The capped b o t t l e s with t h e i r contents were rotated end-over-end at 45 rpm at 50°C. i n a thermostatted water-bath. Samples for conversion and for p a r t i c l e s i z e measurements were withdrawn at regular time i n t e r v a l s using hypodermic needle and syringe. Hydroquinone was used as a shortstop. IV.

P a r t i c l e Size A n a l y s i s .

A JEM 120U electron microscope (japan Electron Optics Co.) was used to obtain the photographic images of the p a r t i c l e s . The f i n a l photographs were prepared using a photographic enlarger. The electron photographs were analyzed on a Carl-Zeiss TGZ-3 p a r t i c l e s i z e


42

EMULSION

POLYMERIZATION

analyzer. Three thousand p a r t i c l e s were counted for each sample. Data from the analyzer were treated by a computer program to obtain the following q u a n t i t i e s : •Number average diameter of p a r t i c l e s D

= S n.d./Σ η.

n

i

l

ι

with η. p a r t i c l e s o f diameter d. ι ι e


•Weight average diameter o f p a r t i c l e s D = Σ n.d. / . w ι ι Σ n.d. ι ι 4

3

•Volume average diameter of p a r t i c l e s = [ Σ n.d. /E n . ] 3

D

1 / / s

•Number o f partieles/ml-aqueous phase N

m

=

x

% conversion/V.ρ 3

where V = volume of p a r t i c l e s = ~ π D^

ρ = density of polystyrene = 1.05

g/ml.

• P a r t i c l e s i z e d i s t r i b u t i o n , PSD, expressed by i) D /D w η i i ) Standard deviation of diameter S.D.

2

= [(D.-D ) / ( f - l ) ] * ~ i n

where f = Number of p a r t i c l e s counted. Results and Discussion I. Rates of Polymerization with Recipes of I d e n t i c a l Size of M i c e l l e s . The basic concept of the present study was to show, other things being equal, that the rate of polymeriza t i o n i s affected by the s i z e of the micelles and not by the t o t a l surfactant concentration as expressed by Equation ( l ) . This m i c e l l a r s i z e e f f e c t was believed to be the reason why a nonlinear, i . e . , a convex curve, r e l a t i o n s h i p between In Rp and In C was obtained with emulsion polymerization systems of changing surfactant s



3.

PIIRMA AND W A N G

Micellar

Size

Effect

43

compositions as i l l u s t r a t e d by Figure 2. To check the v a l i d i t y of t h i s concept, the simp l e s t and most straight-forward approach seemed to be to carry out rate studies of emulsion polymerizations with recipes of i d e n t i c a l m i c e l l a r s i z e s . Since, as mentioned previously, each s p e c i f i c value of surfactant r a t i o , r , of the mixed surfactant stands for a s p e c i f i c s i z e of the mixed m i c e l l e s , the experimental approach b o i l s down to run several s e r i e s of k i n e t i c studies with d i f f e r e n t surfactant r a t i o s between s e r i e s , but with varying surfactant concentrations within each s e r i e s . The standard recipe for such experiments was described i n the Experimental Section. This standard recipe i s e s s e n t i a l l y i d e n t i c a l with the one used by Kamath (8) , Wang (9.) and Letchford (15) with the exception of eliminating KOH. The purpose of adding KOH to recipes of emulsion polymerization i s mainly to c o n t r o l the pH-value of the r e a c t i o n medium. However, being an e l e c t r o l y t e , KOH a f f e c t s the s i z e of the changed micelles (12.16-18). For mixed surfactant systems, t h i s e f f e c t may be d i f ferent for d i f f e r e n t values of surfactant r a t i o s of the mixed surfactants. Furthermore, i t was observed, during the e a r l i e r period of the present study, that the d i l u t e solutions of sodium l a u r y l s u l f a t e became t u r b i d i n the presence of KOH, presumably due to a l k a l i n e h y d r o l y s i s . Therefore, KOH was not used i n t h i s study. Using the standard recipe mentioned above, eight d i f f e r e n t m i c e l l a r s i z e s , i . e . , d i f f e r e n t r-values were used, and for each r-value s i x concentrations, thus r e s u l t i n g i n 48 rate curves. The conversion-time p l o t for r = 0.051 i s shown i n Figure 6 where i t can be seen that there i s a l i n e a r portion i n every curve of such p l o t s i n t h i s s e r i e s of experiments. This agrees with the t y p i c a l behavior of the s o - c a l l e d constant-rate period of emulsion polymerization systems as proposed by Harkins i n 1948 and has been confirmed by many other investigators ever since. The slopes of the l i n e a r portions of these curves were taken as the rate of polymerization at corresponding surfactant concentration. The logarithmic p l o t of these rates and corresponding surfactant concentrations are shown i n Figure 7. A perfect s t r a i g h t l i n e i s obtained which


44

EMULSION


In R

R

f

p • n

POLYMERIZATION

p

^)

R ; Rate of polymerisation. p

G ; Tétai concentration of surfactant. e

H^; weight or size of micelles. Figure 5. Three dimensional model of micellar nucleation for emulsion polymerization process at given initiator concentrations


3.

PIIRMA AND W A N G

Micellar

Size

45

Effect

i s usually the case with s i n g l e e m u l s i f i e r , i . e . , with emulsifiers of constant m i c e l l a r s i z e . By following i d e n t i c a l experimental approach, seven other s t r a i g h t l i n e s of such logarithmic p l o t s were obtained with d i f f e r e n t surfactant r a t i o s . Regres sion equation of the form Υ = xZ + Β

(4)

of these s t r a i g h t l i n e s were obtained by repressional analysis and are l i s t e d i n Table I I . In the above regression equation Y corresponds to In Rp χ ΙΟ , Ζ to In C χ 10 , and χ i s the slope of the l i n e . Since each of these 8 s t r a i g h t l i n e s of the logarithmic p l o t of Rp vs C were obtained from a constant value of surfactant r a t i o , r , and thus a con stant value of the s i z e of the m i c e l l e s , t h i s series of experiments indicates that:


3

3

s

s

1. m i c e l l a r s i z e does play a r o l e i n a f f e c t i n g the rate of polymerization, and 2. the nonlinear r e l a t i o n s h i p between Rp and C i n a logarithmic p l o t , as shown i n Figure 2, was caused by the v a r i a t i o n of s i z e of micelles as the concentration of the t o t a l surfactant varied. s

I t i s i n t e r e s t i n g and important to note from Table II that the eight s t r a i g h t l i n e s are of d i f f e r e n t slopes. This indicates that the x-value i n the r e l a t i o n s h i p of Equation (2) κ Rp

oc

c

s

should also be dependent on s i z e of the mixed m i c e l l e s . In the p a r t i c u l a r system of the present study, the r e l a t i o n s h i p between x-value and m i c e l l a r s i z e , as expressed i n surfactant r a t i o , r , i s χ

> 0.6 when r

This i s shown g r a p h i c a l l y i n Figure 8. S t r i c t l y speaking, i f the s i z e of the micelle, i s to play a r o l e i n emulsion polymerization, i t should be the s i z e of the monomer-swollen surfactant micelle , and not the monomer free one . However, these two sets of " s i z e s " should be proportional i n the present case



46

EMULSION

POLYMERIZATION

3

in CgXiO , •ol«./Uaqu*ou« phase

Figure 7. Logarithmic plot of polymerization rate against concentration of mixed surfactants at r== 0.051

0.1

02

03

0.4

0.5

0.6

0.7

r * aoLes SLS/aole BC-840 Figure 8.

Effect of r-values on the value of χ IN R œ C/ p


α»


3.

PIIRMA AND W A N G

Micellar

Size

Effect

47

of study. The argument i s that a t low values o f surfactant r a t i o , r , the monomer free micelles are large i n s i z e but low i n charge density. Therefore, they can be considered low i n p o l a r i t y . This type of mixed micelles should have higher s o l u b i l i z i n g power towards hydrophobic monomers such as styrene. Thus, the r e s u l t i n g monomer-swollen micelles are also large i n s i z e . Similar argument leads to the conception that smaller mixed micelles generate monomer-swollen m i c e l les o f smaller s i z e . Accordingly, either set o f these mixed micelles can be used for the purpose o f i n t e r p r e t a t i o n o f the polymerization behaviors i n t h i s mixed surfactant system. Since the x-value i n the r e l a t i o n s h i p o f Rp « Cg * depends on the s i z e o f monomer-swollen m i c e l les and the l a t t e r i s , i n turn, r e l a t e d to the solubi l i z i n g power o f the monomer-free micelles and the hydrophobic properties o f the monomers, the "micellar s i z e e f f e c t " should p r e d i c t the following: 3

1. For a given surfactant, the x-value should depend on w a t e r - s o l u b i l i t y o f the monomer Monomers with s o l u b i l i t y less than that o f styrene should give x-values which are greater than 0.6. 2. For a given monomer, the x-values should be d i f f e r e n t with d i f f e r e n t surfactants i f these surfactants give micelles o f d i f f e r e n t s i z e s under s i m i l a r r e a c t i o n conditions. Therefore, the "micellar s i z e e f f e c t " o f f e r s , at l e a s t , an explanation for the v a r i a t i o n s observed i n the x-values i n emulsion polymerization with various monomer-surfactant combinations. V e r i f i c a t i o n of t h i s argument i n d e t a i l i s under i n v e s t i g a t i o n , however, and discussion o f these r e s u l t s i s beyond the scope o f the present paper. I I . Rates o f Polymerization with Recipes o f Constant Surfactant Concentrations but Varying M i c e l l a r Size. What w i l l happen to rates o f polymerization in a s e r i e s o f polymerizations where t o t a l surfactant concentrations are constant, but the s i z e o f the m i c e l l e s , as expressed by surfactant r a t i o , r , are varying from

American Chemical Society Library 1155 16th St. N. W.

In Emulsion Polymerization; Piirma, I., et al.; ACS Symposium Series; Washington, American Chemical D. C. Society: 20036 Washington, DC, 1976.

48

EMULSION

POLYMERIZATION

t e s t to t e s t ? This information can be derived from the linear regression equations shown i n Table I I . Since these equations are of the form In R

10

p

3

= χ In C

· 10

s

3

+ Β

(4b)

where χ and Β are constants but d i f f e r e n t for d i f f e r e n t r-values. The rate of polymerization can be c a l c u l a t e d i f both the values of r and C are known. Thus, the values of rate of polymerization, expressed as In R^ 10 , so obtained are p l o t t e d against the corresponding r-values at fixed values of t o t a l surfactant concen tration, C . These p l o t s are summarized i n Figure 9. The curves show c l e a r l y that, at any given value of t o t a l surfactant concentration, the rate of polymer i z a t i o n increases r a p i d l y with increasing values of surfactant r a t i o i n region where r-values are small, however, i t l e v e l s o f f when r-values become larger. These curves have a great resemblance with the one shown i n Figure 2, where both the t o t a l surfactantconcentration and the surfactant r a t i o were changing. I f the nucleation process i n t h i s polymerization system i s c o n t r o l l e d p r i m a r i l y by the Harkins-SmithEwart mechanism, the following equation should apply. s


3

s

Rp = k

[M]Np/2

p

(5)

or, simply Rp « N

(5b)

p

and, since not every one of the o r i g i n a l micelles i n an emulsion polymerization system becomes a polymer p a r t i c l e (6., 7 ) , the following equation should be true Rp

oc

N

p

= P(N) N

m

(6)

where, i n the above equations: Np = Number of polymer p a r t i c l e s per u n i t volume of aqueous phase N = Number of s t a r t i n g mixed micelles per u n i t volume of aqueous phase P(N) Percentage of the t o t a l micelles to become polymer p a r t i c l e s , or, the p r o b a b i l i t y of a monomer-swollen m i c e l l e to become a polymer p a r t i c l e , or, the p r o b a b i l i t y of nucleation, and m



3.

PIIRMA AND W A N G

Micellar

Size

Effect

49

Rp, kp, [M] are r a t e , rate constant and monomer concentration i n p a r t i c l e r e s p e c t i v e l y . Equation (5) or (5b) i s the highly important deduction of Harkins-Smith-Ewart theory. I t s v a l i d i t y has been f u l l y confirmed for many cases of polymeri z a t i o n (19). Furthermore, although i t i s d i f f i c u l t to determine the number of p a r t i c l e s , Np, accurately (19) t h i s simple r e l a t i o n s h i p has been used to determine the absolute value of the rate constant, kp, s a t i s f a c t o r i l y for the polymerization of butadiene and isoprene by Smith (20) and by Morton et a l . ( 2 1 ) . Conditions where the r a t e of polymerization i s not proportional to the number of p a r t i c l e s are where Trommsdorff s e f f e c t (22-24) or Gordon's unsteady state (25) p r i n c i p l e s apply. However, the existence of l i n e a r portions of the conversion-time p l o t s proves the absence of these p r i n c i p l e s i n t h i s system. Accepting that the simple r e l a t i o n s h i p of Equation (5) and (5b) are v a l i d i n the present case of polymeri z a t i o n , Equation (6) shows some c h a r a c t e r i s t i c s of the p r o b a b i l i t y of nucleation, P ( N ) , of the present system of polymerization. Since the sizes of the mixed micelles i n the present mixed surfactant system are known to decrease with increasing surfactant r a t i o , r , the t o t a l number of mixed micelles must increase i n a s e r i e s of recipes with the same amount of mixed surfactant but of increasing surfactant r a t i o s . Therefore, the curves i n Figure 9 indicate that: 1

1. both P ( N ) and N were increasing with increasing r-values i n region of r < 0.2. This i s shown by the rapid increase i n the t o t a l number of polymer p a r t i c l e s , Np, i n that region as represented by the r a p i d increase i n rates of polymerization, Rp, however, m

2. the t o t a l number of p a r t i c l e s , Np, becomes constant and independent at surfactant r a t i o s i n the region of r > 0.2. Since the t o t a l number of mixed m i c e l l e s , N , i s s t i l l increasing with increasing r-values i n that region, the p r o b a b i l i t y of nucleation, P ( N ) , must decrease correspondingly to keep the product P ( N ) * N = N constant. m

m

p


50

EMULSION

POLYMERIZATION

Since d i f f e r e n t surfactant r a t i o s stand f o r d i f ferent values of the s i z e of the mixed m i c e l l e s , the above reasoning leads to the following p o s s i b i l i t i e s . 1. The p r o b a b i l i t y , P(N), of a monomer-swollen surfactant m i c e l l e to become a polymer p a r t i c l e i s a function o f i t s s i z e .


2. In a series o f polymerizations, the value o f P(N) seems t o pass through a maximum with increasing s i z e of the surfactant m i c e l l e s . I I I . Rates o f Polymerization with Recipes o f Constant Number o f M i c e l l e s but Varying M i c e l l a r Size. Since i t seemed to be true that the p r o b a b i l i t y of nucleation, P ( N ) , i s maximum with micelles o f a c e r t a i n s u i t a b l e s i z e , i t would be i n t e r e s t i n g and necessary to f i n d j u s t at what surfactant r a t i o , i . e . , m i c e l l a r s i z e , t h i s maximum P(N) i s located i n the present sys tem o f polymerization. This information can again be obtained from those l i n e a r regression equations i n Table I I . Since for a given surfactant r a t i o , r , the m i c e l l a r s i z e or m i c e l l a r weight, i s known from the r e s u l t s of l i g h t s c a t t e r i n g studies (Figure 3), the t o t a l surfactant concentration, expressed i n In C χ 10 , can be c a l c u l a t e d t o give the desired number of mixed m i c e l l e s . From these c a l c u l a t e d values of In C χ 10 , the rate o f polymerization i s then obtained from the proper regression equation with s p e c i f i e d surfactant r a t i o , r . This c a l c u l a t i o n i s i l l u s t r a t e d for r = 0.207 as an example below. Let: Mj^ = weight o f mixed m i c e l l e s , g ./mol. 3

s

3

s

= c a l c u l a t e d molecular weight of the mixed surfactant with surfactant ratio, r. m

w

Where: N

m

C

s

A

= (288 r + 860)/(l + r) 288 = molecular wt. o f SLS 860 == ave. mol. wt. o f BC-840.

= number of mixed micelles/l-aqueous

phase

= moles o f mixed surfactants/l-aqueous phase = Avogadro s number. 1



y = bx + a

r

0.9995 0.9986

0.0077 0.0132

Y = 0.582X + 1.674 Y = 0.573X + 1.571

0.3015

0.8205

0.9987 0.9954

0.0154 0.0297

Y = 0.589x + 1.734

aqueous phase.

y = In R xlO , moles monomer converted/min./l-

0.9960

0.0249

Y = 0.558x + 1.802 Y = 0.587x + 1.707

χ = In C xlO , mol./l-aqueous;

0.6642

0.5041

3

0.9985

0.0146

Y = 0.609x + 1.502

0.2073

0.4274

0.9996

0.0083

Y = 0.669x + 1.094

0.1032

c

0.9997

r 0.0083

b

C o r r e l a t i o n Coeff.

y = 0.759x + 0.480

Slope, S

Standard Deviation Of

0.0509

3

Regression Equation

Surfactant Ratio

REGRESSION EQUATIONS OF RATE OF POLYMERIZATION ON CONCENTRATION OF MIXED SURFACTANT AT GIVEN VALUES OF SURFACTANT RATIOS

Table II


52

EMULSION

POLYMERIZATION

Then C

for

s

= N /m / A/M m

w

= N

m

m

M /A

^

m

21

r = 0.207 and Ν = 4.5 χ ΙΟ /l-aqueous , m phase

m = (288 χ 0.207 + 860)/(l + 0.207) = 761.9 w m = 6.0 χ 10 g./mol. w C = 4.5 χ 1 0 χ 6.0 χ 10 /6.02 χ 1 0 χ 762 s ' = 5.884 χ 10*" mol./l-aqueous phase InC χ 10 = 4.074 s From the regression equation f o r r = 0.207, we obtain 3


21

3

23

2

3

lnR

n

χ 10

3

= 0.609 x 4.074 + 1.502 = 3.983

Using t h i s i l l u s t r a t e d procedure,values for rates of polymerization were obtained at several l e v e l s of t o t a l number o f s t a r t i n g mixed m i c e l l e s , N , with varying surfactant r a t i o s . Figure 10 shows a graph o f the c a l c u l a t e d InRp values p l o t t e d against r-values, at several l e v e l s of t o t a l number of s t a r t i n g m i c e l l e s . These curves show that the rate o f polymerization gives a maximum with increasing values o f surfactant r a t i o , r . This maximum value i s located at approximately r = 0.2. A maximum i n rate was also observed by Medvedev and co-workers (4) with increasing i o n i c com ponent i n surfactant-mixture without f i x i n g the t o t a l number of micelles i n each i n d i v i d u a l t e s t of the polymerization. To explain the shape and t o explore the meaning of the curves shown i n Figure 10, Equation (6), has again to be considered. In the present case of d i s cussion, the t o t a l number o f mixed m i c e l l e s , N , i s a constant f o r a l l surfactant r a t i o s . Therefore, the t o t a l number o f polymer p a r t i c l e s , Np, i n t h i s system i s r e l a t e d t o P ( N ) only. The fact that the value o f Np, as represented by rate o f polymerization Rp, goes through a maximum with increasing value o f surfactant r a t i o , indicates that the p r o b a b i l i t y o f nucleation, P(N), must correspondingly also have a maximum value. This argument leads d i r e c t l y t o the conelusion that: The maximum value of the p r o b a b i l i t y o f nuclea t i o n , P(N) i s associated with a s u i t a b l e s i z e m

M


PIIRMA A N D W A N G

3.

«

Micellar

Size

Effect

4.4

! 1 u «

4.0

> e 8

3.8


u «

i 3.4 ο

X

30

0!

02

03

0.4

0.5

0.6

r - «οι·, SLS^.. . Κ

S i

0.7

Figure 9. Effect of r on polymeriza tion rate at given concentrations of mixed surfactant

06

Β 4 0

«β.

of e t c « l U « / l -

aq. pha««,

xio"

2 1

i ·ο| 4

! 1 *·*

3.8

s

η* e

> f-l

3.7

"51

θ2

ÔS

54

r» mol— SLS/ M U t€-a*0

ÔS"

Figure 10. Effect of r-value on polymerization rate at given number of mixed micelles


54

EMULSION

POLYMERIZATION

of the mixed m i c e l l e s . In the present system of polymerization, t h i s optimum occurs at a s i z e of the mixed micelles which corres ponds to a surfactant r a t i o of about 0.2.


IV. Hypothesis of M i c e l l a r Size E f f e c t on Confirmation of the Hypothesis.

Nucleation.

Experimental r e s u l t s and i n t e r p r e t a t i o n s so far presented lead to the j u s t i f i c a t i o n of proposing a hypothesis concerning the m i c e l l a r s i z e e f f e c t on p a r t i c l e nucleation i n mixed surfactant systems of emulsion polymerization. E s s e n t i a l s of t h i s hypothesis are as follows: 1. The p r o b a b i l i t y , P ( N ) , of a monomer-swollen surfactant m i c e l l e to become a nucleus for p a r t i c l e growth i s a function of i t s s i z e . 2. High P(N) associates with a s u i t a b l e s i z e of micelle. 3. For a given number of m i c e l l e s , N , the number of p a r t i c u l e s being nucleated should be Np = P(N) -N . m

m

4. High P(N) r e s u l t s i n •fast rate of polymerization due to larger number of p a r t i c l e s , Np, being nucleated, and •narrow p a r t i c l e s i z e d i s t r i b u t i o n , due shorter time period of nucleation.

to

5. The x-value i n the Smith-Ewart r e l a t i o n s h i p of Rp oc C i s also being a f f e c t e d by P(N) . x

s

Therefore, t h i s hypothesis claims that the s i z e of surfactant micelles plays an important r o l e i n an emulsion polymerization process. Since, i n the present system of study, the maximum value o f P(N) happened at a surfactant r a t i o of about 0.2, a l l the above p r e d i c t i o n s should be true with polymerization recipe at that s p e c i f i e d value of surfactant r a t i o . To confirm these p r e d i c t i o n s , however, three polymerization experiments were c a r r i e d out with recipes of surfactant r a t i o s of 0.051, 0.207 and 0.427. These three recipes were made to have the same t o t a l s t a r t i n g number of mixed micelles which was 4.0 χ 10 21



Micellar

Size

Effect

55


m i c e l l e s per l i t e r o f aqueous phase. From these three polymerizations, latex samples were taken a t conversions f a l l i n g i n the beginning o f the region o f constant r a t e period of polymerization. These samples were used for the p a r t i c l e number and the p a r t i c l e s i z e d i s t r i b u t i o n , PSD, determinations. The experimental programs for the above three confirmation t e s t s were made on the basis o f the f o l lowing concepts : 1. From mixed surfactant systems of emulsion polymerization, monodispersed l a t i c e s were u s u a l l y obtained a t f a i r l y low conversions with rather wide v a r i a t i o n s i n emulsifier compositions (l). Therefore, samples for the determination o f the p a r t i c l e s i z e d i s t r i b u t i o n i n t h i s system should be taken a t r e l a t i v e l y low conversions, otherwise, monodispersed l a t i c e s w i l l be obtained due t o competitive growth from a l l samples regardless o f the surfactant r a t i o s i n the recipe o f polymerization. These p a r t i c l e s w i l l be d i f f e r e n t i n s i z e , but not i n s i z e d i s t r i b u t i o n . 2. To obtain s i g n i f i c a n t l y d i f f e r e n t values i n the p a r t i c l e s i z e d i s t r i b u t i o n and i n the number of p a r t i c l e s formed, comparative t e s t s should be c a r r i e d out with r-values considerably d i f f e r e n t one from another. Otherwise, s i g n i f i c a n t l y d i f f e r e n t r e s u l t s might not be obtainable due t o the inherently high error i n the determination o f t o t a l number o f p a r t i c l e s , Np (19). Since the m i c e l l a r weight determinations i n t h i s s e r i e s o f experiments were l i m i t e d t o the range o f r = 0.05 to r = 0.5, which was also the range o f r-values w i t h i n which the maximum P(N) happened, the selected three values o f surfactant r a t i o s for the confirmation t e s t s were considered proper and sufficient. From these three polymerizations, the conversion-time p l o t s are shown i n Figure 11. Obviously, the rates o f polymerization i n these three t e s t runs were not the same, the one at r = 0.20 7 i s higher than


EMULSION


56

POLYMERIZATION

the other two. This agrees with the p r e d i c t i o n s (points represented by hexagonals i n Figure 10). Three thousand p a r t i c l e s were counted f o r each sample. The frequency o f occurrence o f p a r t i c l e s o f various sizes i s expressed g r a p h i c a l l y i n Figure 12 as frequency polygons. These polygons showed these three latex samples to have p a r t i c l e s o f d i f f e r e n t average sizes even though they had been grown t o almost equal l e v e l of conversions. I t i s i n t e r e s t i n g to note that the p a r t i c l e sizes obtained from recipes with s u r f a c tant r a t i o s o f r = 0.051 and r = 0.427 were both larger than theories obtained from r = 0.207. Since the s i z e of the mixed micelles at r = 0.207 i s i n between the other two, the s i z e o f polymer p a r t i c l e s does not corr e l a t e l i n e a r l y with the s i z e o f mixed m i c e l l e s , but was c o n t r o l l e d by the p r o b a b i l i t y of nucleation, P ( N ) . From the observed values o f the p a r t i c l e s i z e analysis o f each o f the latex samples, the number and weight average diameters o f the p a r t i c l e s , the s i z e d i s t r i b u t i o n s , and the standard deviations, S.D., o f the average diameters were c a l c u l a t e d . Knowing the rate o f polymerization and the t o t a l number of p a r t i c l e s i n a system, the rate o f polymerization per p a r t i c l e , Rpp, can also be c a l c u l a t e d . The values are l i s t e d on Table I I I , where i t can be seen that, i n comparison with the other two recipes, the one with surfactant r a t i o of r = 0.20 7 has the following features. 1. Highest R^. i . e . , faster r a t e than the other two although the t o t a l number o f the m i c e l l e s was the same for a l l three. 2. largest value o f Np. i . e . , more p a r t i c l e s formed from the same number o f m i c e l l e s . 3. Narrowest PSD i . e . , D /D other two.

value o f 1.02 vs 1.04 f o r the

The s i g n i f i c a n t differences i n N and i n PSD, i n terms of S.D., were confirmed by the student t- Test and the F-test, using the procedures described by L i (27). p




Micellar

Size

Effect

Tine,

Figure 11.

«in.

Effect of r on polymerization rate

Diameter of

Figure 12.

57

Particle,

9 A

Frequency polygon of particle size distribution



D

;

574.38

521.94

617.89

D η

1.037

1.024

1.038

D /D w η

68.48

47.42

72.79

S.D.

582.12

526.17

626.14

D ν 1 5

1.14

1.51

0.93

N_ ρ xlO-

0.0438

0.0489

0.0400

f = Number of p a r t i c l e s counted,

- 1) Ύ

3000 f o r r=0.051 3001 f o r r=0.207 3003 f o r r=0.427

/(£

z

Rate per p a r t i c l e .

R ; Rate of polymerization, moles monomer converted/min./l-aqueous phase. Ρ

R^i

R_ ρ

Weight, Number, and Volume average of diameters of the p a r t i c l e s .

600.67

538.08

647.61

D w

S.D.j Standard Deviation p a r t i c l e diameter = l(O^-D^)

n*

22.3

0.427

D

21.7

0.207

w*

22.5

0.051

v

Conversion

Ratio, r

D

Percent

Surfactant

20

3.84

3.24

4.32

R pp xlO

EFFECT OF SURFACTANT RATIO ON NUMBER AND SIZE DISTRIBUTION OF LATEX PARTICLES

Table I I I


3.

PIIRMA AND W A N G

Micellar

59

Size Effect

Since the probablity of nucleation f o r a given m i c e l l e can be c a l c u l a t e d by P

(

N

)

=

N

/

N

the values of P(N) f o r the t h r e i confirmation t e s t s are as follows: surfactant r a t i o r P(N) χ 10 0.051 2.33 0.207 3.78 0.427 2.85 Downloaded by CORNELL UNIV on December 18, 2014 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/bk-1976-0024.ch003

4

Thus the r e s u l t s of our c a l c u l a t i o n s do confirm our predictions. Conclusions We havm shown that with the use of a mixed sur factant system i n styrene emulsion polymerization, the composition of the mixed surfactant has an e f f e c t on the rate of polymerization, the number of p a r t i c l e s formed and the p a r t i c l e size d i s t r i b u t i o n . We have a l s o shown that a change i n the r a t i o , r of the two surfactants i n the mixture r e s u l t s i n a considerable change i n the m i c e l l a r weight of the r e s u l t a n t mixed m i c e l l e s . We have thus proposed and proven that the e f f i c i e n c y of nucleation of p a r t i c l e s (even when the same number of micelles i s used i n the experiment) i s dependent on the s i z e of the mixed m i c e l l e , and that there i s an optimum s i z e a t which the polymerization rate i s the f a s t e s t and the p a r t i c l e s i z e d i s t r i b u t i o n i s the narrowest. The l i n e a r r e l a t i o n s h i p between the r a t e of poly merization, Rp# and the t o t a l surfactant concentration, C # i n a logarithmic p l o t i s v a l i d only f o r systems where the m i c e l l a r s i z e , i s constant. For systems where m i c e l l a r size i s a v a r i a b l e , other things being equal, the k i n e t i c s of emulsion polymerization should be expressed by a three parameter model, i n v o l v i n g Rp, Mi*' s' than by the c l a s s i c a l two parameter model which involves the rate dependence on the t o t a l emulsifier concentration only. The two parameter model gives a nonlinear r e l a t i o n s h i p between lnR^ and InCs i f M i s a v a r i a b l e . This v a r i a t i o n i n the m i c e l l a r weignt can be brought about a l s o by the addition of e l e c t r o l y t e s to the emulsion system, and, of course, by the change i n the chain length of the surfactant (18). The x-value i n the r e l a t i o n s h i p of Rp

Micellar Size Effect in Emulsion Polymerization - ACS Symposium

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