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Numerical evaluation of the size distribution of particles obtained by suspension polymerization using data of the Coulter Counter TA II apparatus
P o w d e r T e c h n o l o g y . 25 (1980) 125 - 128
125
© Elsevier Sequoia S.A., Lausanne -- Printed in the Netherlands
N u m e r i c a l Evaluation o f the Size Distribution o f Particles O b t a i n e d b y Suspension Polymerization Using Data of the Coulter Counter TAII Apparatus
FRANTISEK
SVEC, DANIEL
HORAK
and M I I ~ D S L A V
KUBIN
I n s l i l u l e o f l~lacromolecular C h e m i s t r y . Czech-Jslot,ak A c a d e m y o f Sciences, 162 0 6 Prague 6 (Czechoslovatzia)
(Received June 9-6, 1{}79; in revised form Septamher 24, 1979)
SUMMARY T h e p a r t i c l e size d i s t r i b u t i o n d e t e r m i n e d by m e a n s of the Coulter C o u n t e r T A I I (CC T A I I ) a p p a r a t u s w a s c o m p a r e d w i t h t w o artificial d i s t r i b u t i o n s p r e p a r e d f r o m f r a c t i o n s o f p o l y m e r i c spherical particles. T h e d a t a were numerically treated using a new distribution f u n c t i o n , a n d t h e f i t w a s s a t i s f a c t o r y . T h e app l i c a b i l i t y o f CC T A I I a l o n g w i t h t h e n u m e r i cal a n d g r a p h i c e v a l u a t i o n is d o c u m e n t e d f o r a r e a l s a m p l e o f t h e p r o d u c t o f s u s p e n s i o n raciical p o l y m e r i z a t i o n .
INTRODUCTION T h e p a r t i c l e size d i s t r i b u t i o n o f p o l y m e r i c materials prepared by suspension 5olymerizat i o n is o n e o f t h e b a s i c c h a r a c S e r i s t i c s o f t h e p r o d u c t o b t a i n e d . T h e r e a t e meu~y m e t h o d s which allow us to obtain data needed for the determination of distribl,tion. These include, for example, sediment~tion measurements, sieve a n a l y s i s , m i c r o s c o p y e t a . A C o u l t e r C o u n t e r T A I I (CG T A .I) a p p a r a t u s t o g e t h e r with population count accessory finds universal a p p l i c a t i o n f o r p a r t i c l e s 0 . 6 - 8 0 0 p m in size, as i t g u a r a n t e e s a h i g h s p e e d o f a n a l y s i s , high p r o d u c t i v i t y , high statistical a c c u r a c y and low consumption of the sample. In most o f t h e a s p e c t s , t h i s a p p a r a t u s q u a l i t a t i v e l y surpasses all t h e m e t h o d s m e n t i o n e d a b o v e . A t t h e same time, the high degree of automation guarantees minimization of subjective experim e n t a l errors. T h e C o u l t e r p r i n c i p l e is b a s e d o n a n e l e c t r i c c u r r e n t p a t h o f s m a l l d i m e n s i o n s w h i c h is m o dulated b y m o m e n t a r y passage o f each particle o n e b y o n e . P a r t i c l e s s u s p e n d e d in a n elect r o l y t e are f o r c e d t h r o u g h a small aperture across which an electric current path has been
established. Each particle displaces electrolyte in t h e a p e r t u r e p r o d u c i n g a p u l s e e q u a l t o its displaced volume. Thus, three dimensions, or p a r t i c l e v o l u m e r e s p o n s e , is t h e basis f o r all measuring. T h e i n s t r u m e n t is c a p a b l e o f a n a l y s i n g a p a r t i c u l a t e s a m p l e a n d p r e s e n t i n g t h e d a t a in a n u m b e r o f d i f f e r e n t w a y s in o n e s i m p l e o p e r a t i o n . T h e c o m b i n a t i o n o f CC W A I I w i t h p o p u l a t i o n a c c e s s o r y gives the f a c i l i t y t o p r i n t o u t n u m b e r a n d size d i s t r i b u t i o n d a t a a n d w i t h a n X-Y r e c o r d e r t o r e c o r d t h e h i s t o g r a m s . The data obtained on the number or volume o f p a r t i c l e s r e p r e s e n t e d in 1 6 t o 6 4 f r a c t i o n s , or the corresponding histograms, only allow one to describe the distribution graphically, a n d c o m p a r i s o n o f v a r i o u s s a m p l e s is d i f f i c u l t . I n a n u m b e r o f cases, i t is e x p e d i e n t t o c h a r a c t e r i z e t h e p a r t i c l e size d i s t r i b u t i o n o f v a r i o : s p r o d u c t s b y s t a t i s t i c s s u c h as m e a n , v a r i a n c e , s k e w n e s s , eta. T h e s e c a n be e v a l u a t e d u s i n g model distribution functions. Thus, for example, t h e R o s i n - R a m l e r - S p e r l i n g m o d e l f u n c t i o n h a s p r o v e d u s e f u l in d e s c r i b i n g t h e distribution o f particles o b t a i n e d by grinding, but in m a n y c a s e s it is n o t q u i t e a d e q u a t e f o r p a r ticles p r e p a r e d b y s u s p e n s i o n p o l y m e r i z a t i o n . F o r this r e a s o n , a n e w , v e r y f l e x t b l e m o d e l function has been suggested [1] : I ( x , a, b, a , ~ )
1
= -2
1
+ --arctg =
[e a t x - a ) - - e - B t x - b ) ]
(1)
w h e r e x is a r a n d o m variable, I is t h e c u m u l a tive d i s t r i b u t i o n a n d a, b, ~,/3 a r e a d j u s t a b l e parameters. Unlike many other distributions, this f u n c t i o n can be expressed analytically b o t h in t h e d i f f e r e n t i a l ( e q n . 2) a n d in t h e i n t e g r a l f o r m ( e q n . 1). dI w(x)
-- d x
1 ~r 1 +
orea t x - a )
+~e -B(x-b)
[ e a ( x - a } - - e - a ( x - b ) ] z (2)
126
T h e statistics o f the distribution are t h e n c a l c u l a t e d u s i n g i n t e g r a l s w h i c h d e f i n e statistical m o m e n t s w i t h r e s p e c t t o z e r o :
Pk =
kw(x) dx
(3)
and the central moments
uk = f (x --z'~)'~w(x) d x
(4)
However, these integrals c a n n o t be f o u n d a n a l y t i c a l l y f o r w ( x ) g i v e n b y e q n . (2) a n d have to be d e t e r m i n e d b y numerical integration. This procedure yields then the parameters m e a n U~, v a r i a n c e o 2 = ~2 a n d s k e w n e s s = Ua/U~/z. All t h e c a l c u l a t i o n s c a n b e e a s i l y carried out on a desk programmable computer (e.g. W a n g 2 2 0 0 ) . The validity of the function has been checked on a number of samples of the macroporous copolymer glycidylmethacrylate-ethylenedimethaczylate (GMA-EDMA), ~ct i o n e d b y memqs o f s t a n d a r d sieves. I r r e s p e c t i v e o f t h e f a c t t h a t t h e m e t h o d is v e r y t i m e - c o n s u m i n g , it is o b v i o u s t h a t t h e n u m b e r o f f r a c t i o n s is r e s t r i c t e d b y t h e n u m b e r o f available sieves. M o r e o v e r , f o r p a r t i c l e s s m a l l e r t h a n r o u g h l y 3 0 u m this p r o c e d u r e is v i r t u a l l y inapplicable. Attempts have therefore been m a d e t o f i n d o u t if t h e f u n c t i o n m a y also b e applied to data obtained by the Coulter Countex apparatus, which would allow us to extend considerably the investigated range to small-size p a r t i c l e s , w h i c h in r e c e n t y e a r s h a v e b e c o m e e x e x e m e l y i m p o r t a n t in c o n n e c t i o n vAth t h e i n t e n s i v e d e v e l o p m e n ~ o f m o d e r n c h r o m a t o g r a p h i c m e t h o d s , e.g. h i g h p e r f o r mance liquid chromatography. EXPERIMENTAL
Perfectly spherical, virtually n o n - p o r o u s and non-swelling particles of the copolymer glycidylmethacrylate-ethylenedimethacrylate h a v e b e e n u s e d as t h e t e s t i n g m a t e r i a l ( t h e i r preparation by suspension polymerization has b e e n d e s c r i b e d e l s e w h e r e [ 2 ] ). B y u s i n g a s e t o f U . S . A . s t a n d a r d t e s t i n g sieves w i t h sieve openings 90, 125, 150, 180, 250, 315 and 4 0 0 / ~ m , as q u o t e d b y t h e m a n u f a c t u r e r (W. S. Tyler, Inc., Mentor, Ohio, U.S.A.), fractions w e r e o b t a i n e d for p r e p a r i n g m i x t u r e s h a v i n g a
k n o w n distribution by weighing. In addition, a sample o f small particles o f the same polymer was used without any treatment immediately after completion of the polymerization. T h e d i s t r i b u t i o n o f large p a r t i c l e s w a s m e a sured with the Coulter Counter TAII apparatus with population'accessory having an orifice t u b e with aperture 1 0 0 0 / ~ m ; f o r small particles a 1 4 0 / z m a p e r t u r e w a s u s e d . C a l i b r a t i o n was carried o u t b y m e a n s o f latexes p r o d u c e d b y C o u l t e r E l e c t r o n i c s L t d . A 1% NaC1 s o l u t i o n s e r v e d as t h e e l e c t r o l y t e . L a r g e p a r t i c l e s w e r e m e a s u r e d in t h e t i m e m o d e ( 3 0 s) w i t h Iaxge a p e r t u r e t e c h n i q u e [ 3 ] , a n d s m a l l o n e s w e r e m e a s u r e d in t h e m a n o m e t r i c m o d e w i t h s t a n d a r d g l a s s w a r e a s s e m b l y ( 2 ml).
RESULTS AND DISCUSSION Two polydisperse samples with different distributions (either mono or bimodal) were prepared by weighing from polymer fractions. The amount of the individual fractions present in t h e s a m p l e s c a n be s e e n in T a b l e 1. M e a s u r e m e n t s w i t h C C T A I I f o l l o w e d b y t h e assignTABLE I Participation of fractions of copolymer particles in measured samples Fraction (/~m)
Sample (wt.%)
A
Sample (wt.%)
90-125 125-150 150-180 180-250
15.24 20.01 23.03 19.43
6.99 22.93 6.17 32.71
250-315
11.65
21.20
315-400
10.58
I0_00
B
TABLE 2 Particle size distribution obtained b y m e s ~ u r e m e n f s o n samples f r o m Table 1 with C C T A I[
Fraction
Sample A
Sample B
(~m)
(wt.%)
(wt.~o)
95.4 120.2 151.4 190.7 240.3
3.74 16.35 19.13 19.12 16.41
2.51 13.94 24.37 8.73 17.25
240.3 - 302.8 302.8 - 381.5
12.61 12.64
26.18 7.02
75.7 95.4 120.2 151.4 190.7
-
127
TABLE 3 Characteristics of the particle size distribution Sample
Data from
Mean (/Im)
Variance ( / / m 2)
Std. dev. (/,/m)
Skewness
A
weight CO
193 170
6934 3983
83.3 63.1
1.28 0.95
B
weight CC
210 196
5915 5433
76.9 73.7
0.23 0.25
C
CC
24
87
m e n t o f v o l u m e p e r c e n t in t h e i n d i v i d u a l channels to calibrated values of the lower t h r e s h o l d o f t h e r e s p e c t i v e c h a n n e l gave d a t a a s s e m b l i e s s u m m a r i z e d in T a b l e 2. D a t a in Tables 1 a n d 2 are difficult to c o m p a r e because of the different fraction width. They were t h e r e f o r e u s e d in c a l c u l a t i o n s o f t h e i n t e g r a l v o l u m e d i s t r i b u t i o n c u r v e s ( e q n . 1), as well as o f o t h e r p a r a m e t e r s c h a r a c t e r i z i n g t h e distrib u t i o n ; t h e s e s t a t i s t i c s are s u m m a r i z e d in T a b l e 3 a n d in Figs. 1 a n d 2. The results o b t a i n e d d e m o n s t r a t e a g o o d fit b e t w e e n the t w o d a t a assemblies, which proves t h a t d a t a provided b y m e a s u r e m e n t s with CC T A I I are e n t i r e l y a d e q u a t e . A l s o , t h e f i t between the experimental data and the calculated c u r v e is p e r f e c t e v e n in t h e ease o f t h e b i m o d a l d i s t r i b u t i o n , s e l d o m e n c o u n t e r e d in p r a c t i c e . A small d i s p l a c e m e n t o f t h e c u r v e s ( w h i c h o t h e r w i s e are o f i d e n t i c a l s h a p e ) t o w a r d s s m a l ler p a r t i c l e sizes in t h e ease o f d a t a f r o m C C is due to the different character of both methods used and has been observed by others [4]. W h e r e a s t h e sieving w a s d o n e in t h e d r y s t a t e , t h e u s e o f C C T A I I is p o s s i b l e o n l y w i t h t h e p a r t i c l e s d i s p e r s e d in a n e l e c t r o l y t e s o l u t i o n . T h e p o l y m e r i c b e a d s d o n o t n o t i c e a b l y swell in t h e e l e c t r o l y t e s o l u t i o n , b u t t h e i r s u r f a c e l a y e r is n o t p e r f e c t l y h o m o g e n e o u s a n d t h e r e fore a low range penetration of ions into the d o m a i n o f t h e p a r t i c l e is p o s s i b l e . T h e n t h e c h a n g e in e l e c t r i c c u r r e n t p a t h a t t h e p a s s a g e o f t h e p a r t i c l e t h r o u g h t h e a p e r t u r e is l o w e r t h a n it should be f o r a c o r r e s p o n d i n g m a c r o s c o p i c size. T h e r e s u l t i n g d a t a a r e t h e n s h i f t e d d o w n t o l o w e r v a l u e s c o m p a r e d w i t h sieve fractionation. The influence of porosity of p a r t i c l e s o n t h e d a t a r e s u l t i n g f r o m C~D T A I I is n o w u n d e r s t u d y . A s e c o n d s o u r c e f o r t h e s h i f t m a y also b e t h e d i f f e r e n t norm~li~.ation l i m i t s f o r b o t h dis-
9
0
I0
s
I(x) 05
I
100
200
300 I
f
~00
F i g . 1. C u m u l a t i v e w e i g h t d i s t r i b u t i o n f u n c t i o n o f s a m p l e A. E x p e r i m e n t a l d a t a a c c o r d i n g t o w e i g h e d amounts (o) and from CC TAII (o), curves calculated using eqn. (1)-
[Cx)/
/ / 100
1
!
200
300
l
/.00 X . ~.t En
F i g . 2. C u m u l a t i v e w e i g h t d i s t r i b u t i o n c u r v e s o f s a m p l e B. D e s i g n a t i o n a s i n F i g . ! .
t r i b u t i o n s ( f o r sieving 9 0 - 4 0 0 / ~ m , f o r C C T A I I 7 5 . 7 - 38~L.5 ~ m ) . E v e n so i t is o b v i o u s t h a t t h e u s e o f d a t a from CC TA II together with the distribution f u n c t i o n (1) is j u s t i f i e d . The procedure for numerical and graphic e v a l u a ~ o n o u t l i n e d h a s also b e e n e m p l o y e d in order to determine the true distribution of particles o b t a i n e d directly by suspension radic a l p o l y m e r i z a t i o n ( s a m p l e C). F i g u r e 3 a n d T a b l e 3 s u m m a r i z e t h e d a t a o b t a i n e d . A n imp o r t a n t f e a t u r e o f t h i s m e t h o d is t h a t d a t a
128 1o
I(x) 05
50
100
Fig. 3. Cumulative weight distribution curve of sample C. Experimental data, curve calculated using eQn. ( 2 ) .
the particles in question, because in contras~ to preparative methods it requires only an insignificant quantity of sample, often very hard to obtain. In conclusion it may be said that the use of CC TAII in, for example, optimizing the conditions of suspension radical polymerization considerably improves its productivity, reduces the research time, and combined with mathematical evaluation of the data makes possible an easy and objective comparison of the results obtained.
REFERENCES
describing the distribution may be obtained immediately after completion of the polymerization (or even during polymerization) and may be employed for control purposes without any need for a separation procedure, which is o f t e n v e r y t i m e - a n d l a b o u r - c o n s u m i n g . S u c h a p r o c e d u r e is p a r t i c u l a r l y a d v a n t a g e o u s f o r
I M. K u b i n , D. Horak a n d F. Svec, A n g e w . MakrotooL Chem.. 71 (1978) 51. 2 F. Svec, H. Hrudkova, D. Horak a n d J. Kalal, A n g e w . Makromol. Chem., 63 (1977) 23. 3 I n s t r u c t i o n m a n u a l for Coulter Couhter T~a. II, 0.81. 4 W. Reich, K o n t a k t e , E. Merck G m b H , ~ a r m s t a d t (1977), No. 3, p. 26.
125
© Elsevier Sequoia S.A., Lausanne -- Printed in the Netherlands
N u m e r i c a l Evaluation o f the Size Distribution o f Particles O b t a i n e d b y Suspension Polymerization Using Data of the Coulter Counter TAII Apparatus
FRANTISEK
SVEC, DANIEL
HORAK
and M I I ~ D S L A V
KUBIN
I n s l i l u l e o f l~lacromolecular C h e m i s t r y . Czech-Jslot,ak A c a d e m y o f Sciences, 162 0 6 Prague 6 (Czechoslovatzia)
(Received June 9-6, 1{}79; in revised form Septamher 24, 1979)
SUMMARY T h e p a r t i c l e size d i s t r i b u t i o n d e t e r m i n e d by m e a n s of the Coulter C o u n t e r T A I I (CC T A I I ) a p p a r a t u s w a s c o m p a r e d w i t h t w o artificial d i s t r i b u t i o n s p r e p a r e d f r o m f r a c t i o n s o f p o l y m e r i c spherical particles. T h e d a t a were numerically treated using a new distribution f u n c t i o n , a n d t h e f i t w a s s a t i s f a c t o r y . T h e app l i c a b i l i t y o f CC T A I I a l o n g w i t h t h e n u m e r i cal a n d g r a p h i c e v a l u a t i o n is d o c u m e n t e d f o r a r e a l s a m p l e o f t h e p r o d u c t o f s u s p e n s i o n raciical p o l y m e r i z a t i o n .
INTRODUCTION T h e p a r t i c l e size d i s t r i b u t i o n o f p o l y m e r i c materials prepared by suspension 5olymerizat i o n is o n e o f t h e b a s i c c h a r a c S e r i s t i c s o f t h e p r o d u c t o b t a i n e d . T h e r e a t e meu~y m e t h o d s which allow us to obtain data needed for the determination of distribl,tion. These include, for example, sediment~tion measurements, sieve a n a l y s i s , m i c r o s c o p y e t a . A C o u l t e r C o u n t e r T A I I (CG T A .I) a p p a r a t u s t o g e t h e r with population count accessory finds universal a p p l i c a t i o n f o r p a r t i c l e s 0 . 6 - 8 0 0 p m in size, as i t g u a r a n t e e s a h i g h s p e e d o f a n a l y s i s , high p r o d u c t i v i t y , high statistical a c c u r a c y and low consumption of the sample. In most o f t h e a s p e c t s , t h i s a p p a r a t u s q u a l i t a t i v e l y surpasses all t h e m e t h o d s m e n t i o n e d a b o v e . A t t h e same time, the high degree of automation guarantees minimization of subjective experim e n t a l errors. T h e C o u l t e r p r i n c i p l e is b a s e d o n a n e l e c t r i c c u r r e n t p a t h o f s m a l l d i m e n s i o n s w h i c h is m o dulated b y m o m e n t a r y passage o f each particle o n e b y o n e . P a r t i c l e s s u s p e n d e d in a n elect r o l y t e are f o r c e d t h r o u g h a small aperture across which an electric current path has been
established. Each particle displaces electrolyte in t h e a p e r t u r e p r o d u c i n g a p u l s e e q u a l t o its displaced volume. Thus, three dimensions, or p a r t i c l e v o l u m e r e s p o n s e , is t h e basis f o r all measuring. T h e i n s t r u m e n t is c a p a b l e o f a n a l y s i n g a p a r t i c u l a t e s a m p l e a n d p r e s e n t i n g t h e d a t a in a n u m b e r o f d i f f e r e n t w a y s in o n e s i m p l e o p e r a t i o n . T h e c o m b i n a t i o n o f CC W A I I w i t h p o p u l a t i o n a c c e s s o r y gives the f a c i l i t y t o p r i n t o u t n u m b e r a n d size d i s t r i b u t i o n d a t a a n d w i t h a n X-Y r e c o r d e r t o r e c o r d t h e h i s t o g r a m s . The data obtained on the number or volume o f p a r t i c l e s r e p r e s e n t e d in 1 6 t o 6 4 f r a c t i o n s , or the corresponding histograms, only allow one to describe the distribution graphically, a n d c o m p a r i s o n o f v a r i o u s s a m p l e s is d i f f i c u l t . I n a n u m b e r o f cases, i t is e x p e d i e n t t o c h a r a c t e r i z e t h e p a r t i c l e size d i s t r i b u t i o n o f v a r i o : s p r o d u c t s b y s t a t i s t i c s s u c h as m e a n , v a r i a n c e , s k e w n e s s , eta. T h e s e c a n be e v a l u a t e d u s i n g model distribution functions. Thus, for example, t h e R o s i n - R a m l e r - S p e r l i n g m o d e l f u n c t i o n h a s p r o v e d u s e f u l in d e s c r i b i n g t h e distribution o f particles o b t a i n e d by grinding, but in m a n y c a s e s it is n o t q u i t e a d e q u a t e f o r p a r ticles p r e p a r e d b y s u s p e n s i o n p o l y m e r i z a t i o n . F o r this r e a s o n , a n e w , v e r y f l e x t b l e m o d e l function has been suggested [1] : I ( x , a, b, a , ~ )
1
= -2
1
+ --arctg =
[e a t x - a ) - - e - B t x - b ) ]
(1)
w h e r e x is a r a n d o m variable, I is t h e c u m u l a tive d i s t r i b u t i o n a n d a, b, ~,/3 a r e a d j u s t a b l e parameters. Unlike many other distributions, this f u n c t i o n can be expressed analytically b o t h in t h e d i f f e r e n t i a l ( e q n . 2) a n d in t h e i n t e g r a l f o r m ( e q n . 1). dI w(x)
-- d x
1 ~r 1 +
orea t x - a )
+~e -B(x-b)
[ e a ( x - a } - - e - a ( x - b ) ] z (2)
126
T h e statistics o f the distribution are t h e n c a l c u l a t e d u s i n g i n t e g r a l s w h i c h d e f i n e statistical m o m e n t s w i t h r e s p e c t t o z e r o :
Pk =
kw(x) dx
(3)
and the central moments
uk = f (x --z'~)'~w(x) d x
(4)
However, these integrals c a n n o t be f o u n d a n a l y t i c a l l y f o r w ( x ) g i v e n b y e q n . (2) a n d have to be d e t e r m i n e d b y numerical integration. This procedure yields then the parameters m e a n U~, v a r i a n c e o 2 = ~2 a n d s k e w n e s s = Ua/U~/z. All t h e c a l c u l a t i o n s c a n b e e a s i l y carried out on a desk programmable computer (e.g. W a n g 2 2 0 0 ) . The validity of the function has been checked on a number of samples of the macroporous copolymer glycidylmethacrylate-ethylenedimethaczylate (GMA-EDMA), ~ct i o n e d b y memqs o f s t a n d a r d sieves. I r r e s p e c t i v e o f t h e f a c t t h a t t h e m e t h o d is v e r y t i m e - c o n s u m i n g , it is o b v i o u s t h a t t h e n u m b e r o f f r a c t i o n s is r e s t r i c t e d b y t h e n u m b e r o f available sieves. M o r e o v e r , f o r p a r t i c l e s s m a l l e r t h a n r o u g h l y 3 0 u m this p r o c e d u r e is v i r t u a l l y inapplicable. Attempts have therefore been m a d e t o f i n d o u t if t h e f u n c t i o n m a y also b e applied to data obtained by the Coulter Countex apparatus, which would allow us to extend considerably the investigated range to small-size p a r t i c l e s , w h i c h in r e c e n t y e a r s h a v e b e c o m e e x e x e m e l y i m p o r t a n t in c o n n e c t i o n vAth t h e i n t e n s i v e d e v e l o p m e n ~ o f m o d e r n c h r o m a t o g r a p h i c m e t h o d s , e.g. h i g h p e r f o r mance liquid chromatography. EXPERIMENTAL
Perfectly spherical, virtually n o n - p o r o u s and non-swelling particles of the copolymer glycidylmethacrylate-ethylenedimethacrylate h a v e b e e n u s e d as t h e t e s t i n g m a t e r i a l ( t h e i r preparation by suspension polymerization has b e e n d e s c r i b e d e l s e w h e r e [ 2 ] ). B y u s i n g a s e t o f U . S . A . s t a n d a r d t e s t i n g sieves w i t h sieve openings 90, 125, 150, 180, 250, 315 and 4 0 0 / ~ m , as q u o t e d b y t h e m a n u f a c t u r e r (W. S. Tyler, Inc., Mentor, Ohio, U.S.A.), fractions w e r e o b t a i n e d for p r e p a r i n g m i x t u r e s h a v i n g a
k n o w n distribution by weighing. In addition, a sample o f small particles o f the same polymer was used without any treatment immediately after completion of the polymerization. T h e d i s t r i b u t i o n o f large p a r t i c l e s w a s m e a sured with the Coulter Counter TAII apparatus with population'accessory having an orifice t u b e with aperture 1 0 0 0 / ~ m ; f o r small particles a 1 4 0 / z m a p e r t u r e w a s u s e d . C a l i b r a t i o n was carried o u t b y m e a n s o f latexes p r o d u c e d b y C o u l t e r E l e c t r o n i c s L t d . A 1% NaC1 s o l u t i o n s e r v e d as t h e e l e c t r o l y t e . L a r g e p a r t i c l e s w e r e m e a s u r e d in t h e t i m e m o d e ( 3 0 s) w i t h Iaxge a p e r t u r e t e c h n i q u e [ 3 ] , a n d s m a l l o n e s w e r e m e a s u r e d in t h e m a n o m e t r i c m o d e w i t h s t a n d a r d g l a s s w a r e a s s e m b l y ( 2 ml).
RESULTS AND DISCUSSION Two polydisperse samples with different distributions (either mono or bimodal) were prepared by weighing from polymer fractions. The amount of the individual fractions present in t h e s a m p l e s c a n be s e e n in T a b l e 1. M e a s u r e m e n t s w i t h C C T A I I f o l l o w e d b y t h e assignTABLE I Participation of fractions of copolymer particles in measured samples Fraction (/~m)
Sample (wt.%)
A
Sample (wt.%)
90-125 125-150 150-180 180-250
15.24 20.01 23.03 19.43
6.99 22.93 6.17 32.71
250-315
11.65
21.20
315-400
10.58
I0_00
B
TABLE 2 Particle size distribution obtained b y m e s ~ u r e m e n f s o n samples f r o m Table 1 with C C T A I[
Fraction
Sample A
Sample B
(~m)
(wt.%)
(wt.~o)
95.4 120.2 151.4 190.7 240.3
3.74 16.35 19.13 19.12 16.41
2.51 13.94 24.37 8.73 17.25
240.3 - 302.8 302.8 - 381.5
12.61 12.64
26.18 7.02
75.7 95.4 120.2 151.4 190.7
-
127
TABLE 3 Characteristics of the particle size distribution Sample
Data from
Mean (/Im)
Variance ( / / m 2)
Std. dev. (/,/m)
Skewness
A
weight CO
193 170
6934 3983
83.3 63.1
1.28 0.95
B
weight CC
210 196
5915 5433
76.9 73.7
0.23 0.25
C
CC
24
87
m e n t o f v o l u m e p e r c e n t in t h e i n d i v i d u a l channels to calibrated values of the lower t h r e s h o l d o f t h e r e s p e c t i v e c h a n n e l gave d a t a a s s e m b l i e s s u m m a r i z e d in T a b l e 2. D a t a in Tables 1 a n d 2 are difficult to c o m p a r e because of the different fraction width. They were t h e r e f o r e u s e d in c a l c u l a t i o n s o f t h e i n t e g r a l v o l u m e d i s t r i b u t i o n c u r v e s ( e q n . 1), as well as o f o t h e r p a r a m e t e r s c h a r a c t e r i z i n g t h e distrib u t i o n ; t h e s e s t a t i s t i c s are s u m m a r i z e d in T a b l e 3 a n d in Figs. 1 a n d 2. The results o b t a i n e d d e m o n s t r a t e a g o o d fit b e t w e e n the t w o d a t a assemblies, which proves t h a t d a t a provided b y m e a s u r e m e n t s with CC T A I I are e n t i r e l y a d e q u a t e . A l s o , t h e f i t between the experimental data and the calculated c u r v e is p e r f e c t e v e n in t h e ease o f t h e b i m o d a l d i s t r i b u t i o n , s e l d o m e n c o u n t e r e d in p r a c t i c e . A small d i s p l a c e m e n t o f t h e c u r v e s ( w h i c h o t h e r w i s e are o f i d e n t i c a l s h a p e ) t o w a r d s s m a l ler p a r t i c l e sizes in t h e ease o f d a t a f r o m C C is due to the different character of both methods used and has been observed by others [4]. W h e r e a s t h e sieving w a s d o n e in t h e d r y s t a t e , t h e u s e o f C C T A I I is p o s s i b l e o n l y w i t h t h e p a r t i c l e s d i s p e r s e d in a n e l e c t r o l y t e s o l u t i o n . T h e p o l y m e r i c b e a d s d o n o t n o t i c e a b l y swell in t h e e l e c t r o l y t e s o l u t i o n , b u t t h e i r s u r f a c e l a y e r is n o t p e r f e c t l y h o m o g e n e o u s a n d t h e r e fore a low range penetration of ions into the d o m a i n o f t h e p a r t i c l e is p o s s i b l e . T h e n t h e c h a n g e in e l e c t r i c c u r r e n t p a t h a t t h e p a s s a g e o f t h e p a r t i c l e t h r o u g h t h e a p e r t u r e is l o w e r t h a n it should be f o r a c o r r e s p o n d i n g m a c r o s c o p i c size. T h e r e s u l t i n g d a t a a r e t h e n s h i f t e d d o w n t o l o w e r v a l u e s c o m p a r e d w i t h sieve fractionation. The influence of porosity of p a r t i c l e s o n t h e d a t a r e s u l t i n g f r o m C~D T A I I is n o w u n d e r s t u d y . A s e c o n d s o u r c e f o r t h e s h i f t m a y also b e t h e d i f f e r e n t norm~li~.ation l i m i t s f o r b o t h dis-
9
0
I0
s
I(x) 05
I
100
200
300 I
f
~00
F i g . 1. C u m u l a t i v e w e i g h t d i s t r i b u t i o n f u n c t i o n o f s a m p l e A. E x p e r i m e n t a l d a t a a c c o r d i n g t o w e i g h e d amounts (o) and from CC TAII (o), curves calculated using eqn. (1)-
[Cx)/
/ / 100
1
!
200
300
l
/.00 X . ~.t En
F i g . 2. C u m u l a t i v e w e i g h t d i s t r i b u t i o n c u r v e s o f s a m p l e B. D e s i g n a t i o n a s i n F i g . ! .
t r i b u t i o n s ( f o r sieving 9 0 - 4 0 0 / ~ m , f o r C C T A I I 7 5 . 7 - 38~L.5 ~ m ) . E v e n so i t is o b v i o u s t h a t t h e u s e o f d a t a from CC TA II together with the distribution f u n c t i o n (1) is j u s t i f i e d . The procedure for numerical and graphic e v a l u a ~ o n o u t l i n e d h a s also b e e n e m p l o y e d in order to determine the true distribution of particles o b t a i n e d directly by suspension radic a l p o l y m e r i z a t i o n ( s a m p l e C). F i g u r e 3 a n d T a b l e 3 s u m m a r i z e t h e d a t a o b t a i n e d . A n imp o r t a n t f e a t u r e o f t h i s m e t h o d is t h a t d a t a
128 1o
I(x) 05
50
100
Fig. 3. Cumulative weight distribution curve of sample C. Experimental data, curve calculated using eQn. ( 2 ) .
the particles in question, because in contras~ to preparative methods it requires only an insignificant quantity of sample, often very hard to obtain. In conclusion it may be said that the use of CC TAII in, for example, optimizing the conditions of suspension radical polymerization considerably improves its productivity, reduces the research time, and combined with mathematical evaluation of the data makes possible an easy and objective comparison of the results obtained.
REFERENCES
describing the distribution may be obtained immediately after completion of the polymerization (or even during polymerization) and may be employed for control purposes without any need for a separation procedure, which is o f t e n v e r y t i m e - a n d l a b o u r - c o n s u m i n g . S u c h a p r o c e d u r e is p a r t i c u l a r l y a d v a n t a g e o u s f o r
I M. K u b i n , D. Horak a n d F. Svec, A n g e w . MakrotooL Chem.. 71 (1978) 51. 2 F. Svec, H. Hrudkova, D. Horak a n d J. Kalal, A n g e w . Makromol. Chem., 63 (1977) 23. 3 I n s t r u c t i o n m a n u a l for Coulter Couhter T~a. II, 0.81. 4 W. Reich, K o n t a k t e , E. Merck G m b H , ~ a r m s t a d t (1977), No. 3, p. 26.