Particle Size Distribution II - American Chemical Society

Chapter 2

Latex Particle Size Distribution from Turbidimetry Using Inversion Techniques Experimental Validation A. Brandolin , L. H. Garcia-Rubio , Theodore Provder , M . E. Koehler , and C. Kuo 1

1,3

2

2

Downloaded by UNIV OF MINNESOTA on October 3, 2013 | http://pubs.acs.org Publication Date: September 24, 1991 | doi: 10.1021/bk-1991-0472.ch002

2

1

Chemical Engineering Department, University of South Florida, Tampa, F L 33620 Dwight P. Joyce Research Center, The Glidden Company, Strongsville, OH 44136 2

A method is reported for the estimation of the size distribution of particle suspensions from spectral turbidity data. The proposed method is based on existing solutions to Fredholm integral equations of the first kind and the generalized cross validation technique. The capabilities of the proposed method are experimentally demonstrated through the recovery of the particle size distribution of polystyrene, poly(methyl methacrylate), and several copolymer latices. It is shown that the proposed method yields good recoveries of the shapes and the averages of the particle size distributions. The o p t i c a l s p e c t r a l e x t i n c t i o n ( t u r b i d i t y ) o f a l a t e x c o n t a i n s information that, i n p r i n c i p l e , c a n be used t o e s t i m a t e t h e s i z e d i s t r i b u t i o n (PSD) o f t h e s u s p e n d e d p a r t i c l e s . S e v e r a l a u t h o r s h a v e approached t h i s problem u s i n g d i f f e r e n t techniques (i-4). More recently (5.) , r e g u l a r i z a t i o n t e c h n i q u e s h a v e b e e n a p p l i e d t o e s t i m a t e t h e PSD o f p o l y s t y r e n e l a t i c e s . The r e g u l a r i z a t i o n techniques require t h a t t h e m o d e l r e l a t i n g t h e PSD a n d t h e t u r b i d i t y be f o r m u l a t e d i n a n i n t e g r a l form

(1)

E q . [ 1 ] c a n be r e c o g n i z e d a s a F r e d h o l m i n t e g r a l e q u a t i o n o f t h e f i r s t k i n d where: r ( A ) i s t h e t u r b i d i t y measured a t a wavelength i n vacuo A ; Q i s the extinction e f f i c i e n c y , D i s the diameter of t h e p a r t i c l e s ; a n d f ( D ) i s t h e number d e n s i t y o f p a r t i c l e s i n t h e sample s u c h t h a t f ( D ) d D i s t h e number o f p a r t i c l e s p e r u n i t v o l u m e w i t h d i a m e t e r s b e t w e e n D a n d D+dD. 0

0

3

Corresponding author 0097-6156/91/0472-0020S06.00/0 © 1991 American Chemical Society

In Particle Size Distribution II; Provder, T.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

2. B R A N D O L I N E T A L . The c o r r e s p o n d i n g form as L "

21

Latex Particle Size Distribution

discrete A f

+

model

for

Eq.[l]

c a n be w r i t t e n i n m a t r i x (2)

L

w h e r e : r i s a (mxl) v e c t o r c o n t a i n i n g the t u r b i d i t y measurements a t m d i f f e r e n t w a v e l e n g t h s ; A i s a (mxn) m a t r i x w h o s e e l e m e n t s a . , are given by ^

*

j-


a.. lj

4

2

Q . ( A . , D . ) D7 w . . ext i ' ] j l]

x

v

(3)

y

the w . s are weighting coefficients and they depend on the quadrature formula used i n the approximation to E q . [ 1 ] ; f i s a (nxl) vector w h o s e e l e m e n t s a r e t h e o r d i n a t e s o f t h e PSD a t e a c h D , d i a m e t e r ; and « i s a (mxl) v e c t o r t h a t accounts f o r t h e quadrature^ and m e a s u r e m e n t s e r r o r s a t e a c h w a v e l e n g t h . The r e g u l a r i z e d s o l u t i o n to Eq.[2] i s (5-6)

f 0 t h a t must be c h o s e n a p p r o p r i a t e l y t o o b t a i n s o l u t i o n s c l o s e t o t h e t r u e P S D ' s . The e f f e c t o f t h e p a r a m e t e r 7 on the s o l u t i o n i s v e r y i m p o r t a n t , i f 7 i s too s m a l l t h e s o l u t i o n w i l l be o s c i l l a t o r y , on the o t h e r hand i f 7 i s too l a r g e the f e a t u r e s o f the s o l u t i o n w i l l be l o s t . The s e l e c t i o n o f the parameter 7 is a c o m p l i s h e d u s i n g t h e g e n e r a l i z e d c r o s s v a l i d a t i o n t e c h n i q u e (GCV) ( 7 - 8 ) . The m e t h o d c o n s i s t i n m i n i m i z i n g t h e f o l l o w i n g o b j e c t i v e f u n c t i o n w i t h respect to 7 I

V(7)

»

m

[I

- A(A A + 7 H ) = T r a c e \[I - A(A A + T

_ 1

A ] T

r | r-zr-^ yU)' k ][ 2

L

(5)

L

T h r o u g h t h e a p p l i c a t i o n o f Eqs [ 4 ] and [ 5 ] , i t is possible to recover 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 d i r e c t l y from t u r b i d i t y m e a s u r e m e n t s . The p o t e n t i a l of t h i s t e c h n i q u e , i t s s e n s i t i v i t y and l i m i t a t i o n s have been demonstrated w i t h s i m u l a t i o n experiments u s i n g u n i m o d a l and bimodal p a r t i c l e s i z e d i s t r i b u t i o n s of v a r y i n g breadth a n d mean p a r t i c l e d i a m e t e r s ( 5 - 8 ) . I n t h i s p a p e r , t h e c a p a b i l i t i e s o f the p r o p o s e d method are experimentally demonstrated through the recovery of 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 of s y n t h e t i c polymer l a t i c e s h a v i n g a b r o a d r a n g e o f p a r t i c l e s i z e d i s t r i b u t i o n s and p o l y d i s p e r s i t i e s . The t y p e s o f p o l y m e r s h a v e b e e n s e l e c t e d t o test the performance of the proposed t u r b i d i m e t r i c technique w i t h a v a r i e t y of o p t i c a l p r o p e r t i e s . S t r o n g l y a b s o r b i n g p o l y m e r s s u c h as p o l y s t y r e n e (PS) and s y t r e n e - b u t a d i e n e copolymers (PSB) and p o l y m e r s c o n t a i n i n g weak chromophores s u c h as p o l y ( m e t h y l methacrylate) (PMMA) a n d v i n y l a c e t a t e - b u t y l a c r y l a t e c o p o l y m e r s ( P V A B A ) h a v e b e e n a n a l y z e d . The r e s u l t s f r o m t h e a p p l i c a t i o n o f t h e r e g u l a r i z e d


22

P A R T I C L E S I Z E D I S T R I B U T I O N II

s o l u t i o n to E q . [1] system.

are discussed within the context of each latex

Experimental:


Materials: Narrow PSD p o l y s t y r e n e standards were purchased from Polysciences (Warrington, PA); Poly(methyl methacrylate) l a t i c e s were o b t a i n e d from G l i d d e n C o r p o r a t i o n ( S t r o n g s v i l l e , Ohio); The v i n y l acetate copolymers were kindly provided by Dr. A. Rudin from the U n i v e r s i t y of Waterloo (Waterloo, O n t a r i o , Canada) and the styrene-butadiene l a t i c e s were p r o v i d e d by D r . G . P o e h l e i n from G e o r g i a T e c h . (Atlanta, Ga). Optical Properties: The o p t i c a l p r o p e r t i e s for polystyrene were obtained from the data of Inagaki et a l , (9); The values for poly-methyl methacrylate are from t h e d a t a r e p o r t e d by R i t s c o et a l , (10). The a b s o r p t i o n coefficients for the v i n y l acetate copolymers were estimated from t r a n s m i s s i o n measurements and the r e f r a c t i v e index values reported by Devon and Rudin (11). The r e f r a c t i v e indeces f o r the s t y r e n e b u t a d i e n e c o p o l y m e r s were estimated as a weighted sum o f the r e f r a c t i v e indexes of polystyrene and polybutadiene. The r e f r a c t i v e index v a l u e s f o r water were calculated from the equation given i n (11). Experimental Procedures: The UV/VIS t u r b i d i t y spectra were recorded i n a P e r k i n Elmer 3840 photodiode a r r a y UV/VIS spectrophotometer equipped w i t h a t h e r m o e l e c t r i c c e l l h o l d e r and a temperature c o n t r o l l e r w i t h temperature programming c a p a b i l i t i e s . A l l measurements were taken at 25 °C i n a 1-cm path length c e l l . The l a t i c e s were d i l u t e d i n d i s t i l l e d w a t e r u n t i l the l i n e a r range o f the instrument was reached. Several r e p l i c a t i o n s were taken under d i f f e r e n t sample p r e p a r a t i o n conditions to ensure r e p r o d u c i b i l i t y of the r e s u l t s . As a precaution, and i n order to avoid v a r i a b i l i t y i n the background, water s p e c t r a were always taken using d i s t i l l e d water from the same batch u t i l i z e d i n the d i l u t i o n s of the o r i g i n a l sample. Moreover, the background spectra were always taken shortly after or before the latex was measured i n order to compensate for any instrument d r i f t . The background corrected spectra were used for the analysis with the software developed i n house. The disc centrifuge photosedimentometer a n a l y s i s o f the poly(methyl methacrylate) l a t i c e s were conducted at Glidden with a Brookhaven DCP-1000 P a r t i c l e Size Analyzer (12). Effect of Small Molecules: A source of concern i n the t u r b i d i m e t r i c a n a l y s i s o f p o l y m e r l a t i c e s , p a r t i c u l a r l y at s h o r t wavelengths (200-300nm), i s the presence of chromophoric groups such as residual monomer, u n r e a c t e d i n i t i a t o r , s t a b i l i z e r s , e t c . In general, i f chromophores are present i n the water phase, t h e i r c o n t r i b u t i o n can be r e a d i l y i d e n t i f i e d because t h e i r extinction e f f i c i e n c y per unit mass i s high. In these cases i t i s p o s s i b l e to remove the small molecule c o n t r i b u t i o n s through d i l u t i o n and through the use of standard d e c o n v o l u t i o n techniques. I f the chromophores are d i s s o l v e d a n d / o r bound to the



2. B R A N D O L I N E T A L .


23

polymer p a r t i c l e s then, the o p t i c a l properties of the p a r t i c l e s w i l l be modified accordingly. For these cases i t i s necessary to r e s o l v e the s c a t t e r i n g and the deconvolution problems simultaneously. For the l a t i c e s analyzed here, the d i s t i n c t i v e absorption pattern due to the monomers, i n i t i a t o r s and/or emulsifiers could not be i d e n t i f i e d (see F i g s . 1,4 and 8 ) . On the other hand, the presence o f s m a l l q u a n t i t i e s o f r e s i d u a l monomer and i n i t i a t o r i n the polymer p a r t i c l e s cannot be ruled out at this point (see R e f s . 11-13.). The c o n t r i b u t i o n o f these chromophoric groups may be r e f l e c t e d on smaller than expected Dn values. However, the e x c e l l e n t r e c o v e r i e s of the measured s p e c t r a w i t h a s i n g l e s e t o f o p t i c a l parameters suggests that, although chromophores other than the polymer may be p r e s e n t , t h e i r c o n t r i b u t i o n to the o v e r a l l e x t i n c t i o n spectra i s small. Results and Discussion: In order to t e s t the p o t e n t i a l of the proposed r e g u l a r i z a t i o n technique (Eqs [4] and [ 5 ] ) f o r the deconvolution of the PSD from t u r b i d i t y mesurements, the analysis of the polymer l a t i c e s has been d i v i d e d i n t o t h r e e g r o u p s : The f i r s t group c o n s i s t o f w e l l characterized, commercially a v a i l a b l e , narrow polystyrene standards; the second group consists of poly(methyl methacrylate) l a t i c e s for which the PSD has been independently measured by d i s c c e n t r i f u g e photosedimentometry (DCP). These l a t i c e s have been p r e v i o u s l y u t i l i z e d i n comparative p a r t i c l e s i z e a n a l y s i s s t u d i e s (13.) . The t h i r d group, c o n s i s t o f s t y rene-butadiene and v i n y l acetate-butyl a c r y l a t e copolymer l a t i c e s . The v i n y l a c e t a t e - b u t y l a c r y l a t e copolymer l a t i c e s were analyzed as b l i n d samples. Narrow PSD Polystyrene Standards: From t h e p o i n t of view of s c a t t e r i n g mesurements, p o l y s t y r e n e l a t i c e s constitute an ideal o p t i c a l system. Polystyrene i s not only a s t r o n g chromophore but the r e f r a c t i v e index differences between the suspending medium and the polymer are s i g n i f i c a n t throughout the complete measurement range. Figure 1 shows t y p i c a l t u r b i d i t y spectra for the samples a n a l y z e d . The l a r g e d i f f e r e n c e s i n the s p e c t r a , observed as functions of the p a r t i c l e diameter, are a consequence of the o p t i c a l properties of polystyrene. From the point of view of the numerical inversion technique, narrow d i s t r i b u t i o n s are always d i f f i c u l t to recover ( 5 . - 8 . ) . The reason b e i n g t h a t the i d e n t i f i c a t i o n of sharp peaks requires the i n c l u s i o n of high frequencies ( i e ; s m a l l 7 ' s i n Eqs [4] and [ 5 ] ) making i t d i f f i c u l t to separate the d i s t r i b u t i o n s from the measurement noise. Nevertheless, as i t can be appreciated i n Figures 2-3 and i n Table I , the r e g u l a r i z a t i o n technique y i e l d s adequate r e s u l t s . F i r s t , there i s good agreement between the average p a r t i c l e diameters r e p o r t e d by the manufacturer and the v a l u e s c a l c u l a t e d from the r e c o v e r e d s i z e d i s t r i b u t i o n s . Second, a l t h o u g h t h e n u m e r i c a l d e c o n v o l u t i o n o f narrow d i s t r i b u t i o n s i s expected to be unstable, and therefore to show o s c i l l a t o r y behaviour ( 5 - 6 ) , the p a r t i c l e size d i s t r i b u t i o n s are recovered w i t h only m i l d o s c i l l a t i o n s a t the t a i l s . The smaller-than-expected o s c i l l a t i o n s are due to the f a c t t h a t the a c t u a l measurement noise ( F i g . 1) i s considerably smaller



24


wavelength(nm)

Figure 1: Normalized Measured T u r b i d i t y S p e c t r a of Commercial P o l y s t y r e n e L a t i c e s : a ) . Dn- 50nm; b ) . Dn- 120nm; c ) . Dn- 530nm; d). Dn- 1050 and e). Dn- 2790.

F i g u r e 2: P a r t i c l e S i z e D i s t r i b u t i o n s estimated from Turbidity Measurements and Eqs. [4] and [5]: Narrow Polystyrene Latices PS01 and PS-02.



PS-03

I

0.9-

25



0.8PS-04

0.70.6>»

c

&

PS-05

0.5 -

1

0.4-

\

0.30.2-

1

0.1 0-

0.5

1.5

2

2.5

3.5 xlO^

CKcm)

Figure 3: P a r t i c l e Size D i s t r i b u t i o n s estimated from T u r b i d i t y Measurements and Eqs. [4] and [5]: Polystyrene Latices PS-03, PS04 and PS-05.

Table I: P a r t i c l e Size Averages i n nm for Commercial Polystyrene Standards Turbidimetry

PS-01 PS-02 PS-03 PS-04 PS-05

Dn

Dw

47 98 524 937 2730

55 103 570 1028 2744

Manufacturer

Dr Dw/Dn 57 104 586 1059 2757

1.17 1.05 1.09 1.10 1.01

D(nominal) 50 120 530 1050 2790

S.D (nm) 9 6 5 70 60


26



than the v a l u e s u s e d f o r the s i m u l a t i o n s t u d i e s (5.) . I t i s i n t e r e s t i n g to notice that not a l l the d i s t r i b u t i o n s are narrow and that some of them show bimodal c h a r a c t e r , where the s m a l l e r peaks a r e c l e a r l y d i s t i n g u i s h a b l e from the o s c i l l a t i o n s due to the numerical technique. PolvOfethvl Methacrylate Latices^: In t h i s group, a series of seven latex samples were a n a l y z e d . F i v e of the samples were p r e v i o u s l y c h a r a c t e r i z e d i n a comparative study of p a r t i c l e s i z e a n a l y s i s techniques (10). Two a d d i t i o n a l r e p l i c a t e samples (68ar and 68br) have been included i n the s e r i e s . In p r i n c i p l e , the only d i f f e r e n c e between o r i g i n a l and r e p l i c a t e samples i s t h a t the r e p l i c a t e samples were f i l t e r e d p r i o r to shipping. The measured t u r b i d i t y s p e c t r a f o r t y p i c a l PMMA l a t i c e s are shown i n F i g 4 and the recovered p a r t i c l e size d i s t r i b u t i o n s are shown i n Figs 5-7 and i n Table I I . In c o n t r a s t w i t h p o l y s t y r e n e , the o p t i c a l properties of PMMA make the problem of p a r t i c l e size determination, by scattering techniques and by turbidimetry i n p a r t i c u l a r , a d i f f i c u l t one. PMMA has rather weak chromophores with small refractive index d i f f e r e n c e s r e l a t i v e to water (11, 13). In addition, the PMMA l a t i c e s analysed appear to aggregate upon d i l u t i o n with d i s t i l l e d water. The extent to which PMMA l a t i c e s aggregate can be appreciated i n F i g 5, where the weight based PSDs f o r samples 68a and 68ar are shown. N o t i c e that the e x t e n t of a g g r e g a t i o n i s different i n each case, and that the main p o p u l a t i o n from each d i s t r i b u t i o n spans approximately the same diameter range and yields s i m i l a r p a r t i c l e size averages (Table I I ) . The aggregation observed could explain discrepancies reported i n the l i t e r a t u r e between t u r b i d i m e t r y and other techniques and why t u r b i d i t y and l i g h t scattering average diameters are c o n s i s t e n t l y h i g h e r than the averages obtained w i t h techniques l i k e DCP (13). I n s p i t e of these d i f f i c u l t i e s , Eqs [4] and [5] y i e l d a d e q u a t e r e s u l t s . The average diameters, c a l c u l a t e d from the r e c o v e r e d d i s t r i b u t i o n s are c e r t a i n l y within two standard d e v i a t i o n s of a l l the v a l u e s p r e v i o u s l y reported for the same samples (see reference (13) and Table I I ) . Figures 6 and 7 show the PSD f o r a l l the PMMA samples a n a l y s e d . Comparison of turbidimetry and DCP results (13), indicate that the PSDs estimated from turbidimetry are broader and b i a s e d towards smaller p a r t i c l e diameters. Differences i n the shape of the PSDs estimated t u r b i d i m e t r y and other t e c h n i q u e s , can be e x p l a i n e d on the b a s i s of the biases p a r t i c u l a r to each technique. Standard l i g h t s c a t t e r i n g methods, i n which a b s o r p t i o n i s n o t c o n s i d e r e d , w i l l tend to emphasize large p a r t i c l e s . However, i f the absorbing portion of the spectrum i s c o n s i d e r e d , s m a l l p a r t i c l e s h a v i n g l a r g e s u r f a c e to volume r a t i o s w i l l dominate the spectrum, r e s u l t i n g i n s m a l l e r Dn v a l u e s and l a r g e r v a r i a n c e s . O t h e r measurement techniques, l i k e DCP, r e l y on the effectiveness of the f r a c t i o n a t i o n mechanism, the r e s o l u t i o n o f w h i c h , g e n e r a l l y decreases as a function of the p a r t i c l e diameter. As a r e s u l t , the PSDs estimated from DCP w i l l tend to have s m a l l e r v a r i a n c e s . Although f r a c t i o n a t i o n techniques have l i m i t e d resolution for small p a r t i c l e s , multimodal d i s t r i b u t i o n s are b e t t e r r e s o l v e d through f r a c t i o n a t i o n because d i s c r e t e elements of the o v e r a l l population are s e l e c t i v e l y sampled. On the o t h e r h a n d , s c a t t e r i n g and



2.

BRANDOLIN ET AL.

27


wavelength(nm)

F i g u r e 4: Turbidity Spectra Typical of Poly(Methyl Methacrylate) L a t i c e s : a ) . PMMA68a; b ) . PMMA68b; c ) . PMMA93a; d) . PMMA8a and e ) . PMMA8c.

Table I I : P a r t i c l e Size Averages i n nm for Poly-Methyl Methacrylate Latices Turbidimetry Dn PMMA68a PMMA68ar PMMA68b PMMA68br PMMA08a PMMA08c PMMA93a

120 121 109 108 463 590 341

Dw 256 262 189 187 554 741 434

Dr 300 307 215 212 594 788 468

DCP Dw/Dn 2 2 1 1 1 1 1

13 16 73 73 20 26 27

Dn

Dw

Dr

Dw/Dn

233

247

275

1.06

182

192

237

1.05

550 658 418

566 686 432

667 817 459

1.03 1.04 1.03




28




29


t u r b i d i m e t r y techniques, sample the whole population simultaneously r e s u l t i n g i n the absorption and s c a t t e r i n g e f f e c t s b e i n g averaged o v e r t h e whole p o p u l a t i o n . How much the s m a l l p a r t i c l e s are emphasized i n t u r b i d i m e t r y depends on t h e m a g n i t u d e o f t h e a b s o r p t i o n c o e f f i c i e n t s . Therefore, the importance of having good estimates o f the o p t i c a l p r o p e r t i e s cannot be u n d e r s t a t e d . The averages reported i n Table II were obtained using l i t e r a t u r e values f o r the r e f r a c t i v e indexes (10.) and a b s o r p t i o n c o e f f i c i e n t s estimated from solution data. Stvrene-Butadiene L a t i c e s : Styrene butadiene l a t i c e s have been extensively used i n the past for the evaluation of l i g h t s c a t t e r i n g methods ( 1 4 ) . T h e r e f o r e , they p r o v i d e a reasonable basis to asess potential applications for the proposed turbidimetry technique. In this p a r t i c u l a r case, changes i n the PSD f o r g r a f t i n g r e a c t i o n s have been analyzed as function of conversion for two sets of grafting conditions (15). From the p a r t i c l e s i z e a n a l y s i s p o i n t o f view, styrene-butadiene l a t i c e s r e p r e s e n t an i n t e r m e d i a t e c a s e between p o l y ( m e t h y l m e t h a c r y l a t e ) and p o l y s t y r e n e . U n f o r t u n a t e l y i n our c a s e , the styrene-butadiene copolymer contained a s i g n i f i c a n t f r a c t i o n of g e l and t h e r e f o r e the determination of the absorption c o e f f i c i e n t s v i a transmission measurements was not p o s s i b l e . The r e f r a c t i v e index, h o w e v e r , c o u l d be r e a d i l y estimated as a weighted sum of the r e f r a c t i v e indexes of p o l y s t y r e n e and polybutadiene (Table I I I ) . Because the a b s o r p t i o n c o e f f i c i e n t of polybutadiene could not be adequately measured, the PSD was determined u s i n g only the nonabsorbing portion of the spectrum (280-900 nm). The results obtained are shown i n Table I I I . Notice the good agreement between the v a l u e p r o v i d e d f o r the seed l a t e x and the value c a l c u l a t e d from the recovered PSD. The PSD's showed no special features r e t a i n i n g t h e i r shape through the r e a c t i o n . Thus suggesting t h a t no s i g n i f i c a n t p a r t i c l e nucleation has taken place as a r e s u l t from the g r a f t i n g conditions. V i n v l Acetate-Butvl Acrylate L a t i c e s : A series of four v i n y l acetate-butyl acrylate copolymer l a t i c e s were analyzed as b l i n d samples. At the time of the a n a l y s i s only the polymer composition was known (85:15). As i n the case o f s t y r e n e - b u t a d i e n e copolymers, the a b s o r p t i o n c o e f f i c i e n t f o r the v i n y l a c e t a t e - b u t y l a c r y l a t e copolymers i s unknown over the measurement range (200-900nm). I n i t i a l l y , the r e f r a c t i v e indexes of the copolymer were approximated as a weighted sum of the r e f r a c t i v e indexes of p o l y v i n y l a c e t a t e and p o l y b u t y l a c r y l a t e (19.) . Subsequently, the refractive indexes were estimated from solution measurements. In terms of o p t i c a l p r o p e r t i e s , PVABA polymers are s i m i l a r to PMMA l a t i c e s ( F i g 8 ) . The chromophores p r e s e n t i n PVABA copolymers are weak, however, the r e f r a c t i v e indexes r e l a t i v e to water are larger than PMMA. As a consequence, the balance of o p t i c a l properties allows e a s i e r r e c o v e r i e s o f the PSDs. The r e s u l t s from the application of Eqs [4] and [5] together with the solution estimates of the refractive indexes, are shown i n Table IV and i n F i g 9. A number of interesting features are c l e a r l y


30



Table I I I :

P a r t i c l e Size Averages i n nm for StyreneButadiene Copolymer Latices

Turbidimetry Dn PSB-01 PSB-02 PSB-03 PSB-04 PSB-05

62 67 70 67

Data

Dw

Dr

Dw/Dn

101 121 118 114

111 133 129 125 160

1.63 1.79 1.69 1.71

Ref(15)

D

Cw

Pw

122

0.0 42.2 98.3 49.3 98.2

7.0 31.4 49.2 52.6 65.9

Cw: % Conversion of Styrene i n the Grafting Process Pw: Weight percent of Styrene i n the Latex


Run Seed 3 3 5 5

2.

BRANDOLIN ET AL.



1.2

wavelength(nm)

Figure 8: Normalized Measured T u r b i d i t y S p e c t r a of P o l y - V i n y l A c e t a t e - B u t y l A c r y l a t e L a t i c e s : a) PVABA-01; b) PVABA-02; c) PVABA-03 and d) PVABA-04.

Figure 9: P a r t i c l e Size Distributions of P o l y - V i n y l Acetate-Butyl Acrylate Copolymer Latices estimated from Turbidity Measurements and Eqs. [4] and [5].


31

32


Table IV: P a r t i c l e Size Averages for V i n y l Acetate-Butyl Acrylate Copolymer Latices Turbidimetry Dn


PVABA-01 PVABA-02 PVABA-03 PVABA-04

38 137 199 342

Dw 46 164 238 410

Manufacturer

Dr

Dw/Dn

Dn

Dw

49 172 250 430

1. 21 1. .20 1. .20 1. .20

54 148 233 390

158 239 405

Dr

Dw/Dn

162 242 411

1.07 1.03 1.04

d i s t i n g u i s h i b l e : In agreement with DCP r e s u l t s , the PVABA l a t i c e s appear to be unimodal. The bimodal character reported before (12) was due to the i n i t i a l approximation used f o r the r e f r a c t i v e indexes. The r e f r a c t i v e index values reported i n the l i t e r a t u r e (18) include only a small f r a c t i o n of the wavelength range used, whereas, the r e f r a c t i v e indexes obtained from solution data cover the same wavelength range u s e d f o r the t u r b i d i t y m e a s u r e m e n t s . As a consequence, the agreement between DCP and turbidimetry improved considerably (Table IV). The results from Eq. [1] also indicate that the PSD's obtained form turbidimetry span a broad range of p a r t i c l e diameters and p o l y d i s p e r s i t i e s . As i n the case of PMMA l a t i c e s , the d i s t r i b u t i o n s appear to be b i a s e d to smaller p a r t i c l e diameters. Nevertheless, as i t can be a p p r e c i a t e d i n Table IV, the averages o b t a i n e d from t u r b i d i m e t r y are reasonably close to the DCP values (16). The agreement for this set of samples i s s u r p r i s i n g when i t i s considered that no information on the PSD was available and that the o p t i c a l properties were roughly approximated. Summary and Conclusions: From the r e s u l t s o b t a i n e d , i t i s e v i d e n t that the r e g u l a r i z e d s o l u t i o n to E q . [1], i s capable of y i e l d i n g both, the moments and the shape of the p a r t i c l e size d i s t r i b u t i o n of a v a r i e t y of l a t i c e s . The l a t i c e s analyzed contain polymers that cover a s i g n i f i c a n t range of o p t i c a l properties that t e s t the c a p a b i l i t i e s of the proposed method; from small r e f r a c t i v e index differences and weakly absorbing chromophores, where s c a t t e r i n g techniques are known to have low r e s o l u t i o n ; to l a r g e r e f r a c t i v e index d i f f e r e n c e s and s t r o n g l y absorbing m a t e r i a l s , where the use of s c a t t e r i n g techniques i s optimal. It i s highly s i g n i f i c a t i v e that the moments calculated from the r e g u l a r i z e d s o l u t i o n are i n reasonable agreement w i t h the results obtained using other techniques (13). The differences i n shape observed between some DCP and t u r b i d i m e t r y measurements can be explained on the basis of the biases p a r t i c u l a r to each measurement technique and the u n c e r t a i n t y a s s o c i a t e d w i t h the o p t i c a l p r o p e r t i e s of the l a t i c e s a n a l y z e d . One i n t e r e s t i n g aspect of the turbidimetry technique i s i t s apparent s e n s i t i v i t y to s m a l l p a r t i c l e s . I n s p i t e of the d i f f e r e n c e s i n shape observed between the turbidimetry and the results from other t e c h n i q u e s , i t i s e v i d e n t that the l e a d i n g moments of the PSD are adequately recovered. T h i s , added to the s i m p l i c i t y and robustness of t u r b i d i t y measurements, makes t u r b i d i m e t r i c techniques coupled with t h e i r




33

interpretation by means of the r e g u l a r i z e d s o l u t i o n o f E q . [ 1 ] , a viable alternative for the characterization of polymer l a t i c e s .


Acknowledgments: T h i s r e s e a r c h was supported by NSF Grants RII 8507956 and INT8602578. A. Brandolin i s with a Fellowship from Consejo N a c i o n a l de I n v e s t i g a c i o n e s C i e n t i f i c a s y Tecnicas de l a Republica Argentina. The Authors wish to acknowledge Dr. D. Peramunage for the t u r b i d i t y measurements of the polystyrene standards and Dr. F . K. Hansen from the University of Oslo, Norway for h i s useful suggestions r e g a r d i n g possible aggregation of the poly(methyl methacrylate) l a t i c e s .

Literature Cited: 1.

Wallach, M. L., Heller, W. and Stevenson, A. F., J. Chem. Phys. 34, 1796 (1961). 2. Wallach, M. L. and Heller, W., J. Phys. Chem. 68, 924 (1964). 3. Zollars, R. L., J. Coll. Interface Sci. 74, 163 (1980). 4. Melik, D. H. and Fogler, H. S., J. Coll. Interface Sci. 92, 161 (1983). 5. Elicabe, G. E. and Garcia-Rubio, L. H., J. Coll. Interface Sci. 129(1), 192 (1989). 6. Twomey, S., "Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements". Elsevier, New york, (1979). 7. Golub, G. H., Heath, M. and Wahba, G., Technometrics 21, 215 (1979). 8. Elicabe, G. E. and Garcia-Rubio, L. H., To be published in: ACS Symposium Series on Polymer Characterization by Interdisciplinary Methods.(1989). 9. Inagaki, T., Arakawa, E. T., Hamm, R. N. and Williams, M. W., Physical Review B 15, 3243 (1977). 10. Ritsco J. L; Brillson L. J; Bigelow R. L and Fabish, T. J., J. Chem. Phys. 69(9), 3931 (1978). 11. Devon M. J . and Rudin A.,J. Appl. Polym. Sci. 34, 469 (1987). 12 Koheler M. E . , Zander R. A., Gill T. and Provder T., ACS Symposium Series No 332, Particle Size Distribution Assesment and Characterization. Chapter 12., T. Provder Ed., (1987). 13. Koheler M. E., and Provder T., ACS Symposium Series No 332 Particle Size Distribution Assesment and Characterization. Chapter 16, T. Provder Ed., (1987). 14. Maron, S. H., Pierce, P. E. and Ulevitch, I. N., J. Colloid Sci. 18, 470 (1963). 15. Xizhen Qian and Poehlein G., 'An Approach for Reliable Determination of Grafting Efficiency of Styrene onto Butadiene Seed". Report, School of Chemical Engineering, Georgia Institute of Technology, (1990). 16. Rudin A., Private Communication., University of Waterloo, Canada (1990). 17. Brandolin A., Garcia-Rubio L. H., Provder T., Koehler M. E and Kuo C., "Latex Particle Size Distribution from Turbidimetery Using Inversion Techniques: Experimental Validation", Presented at the ACS Symposium on Particle Size Analysis. ACS NAtional Meeting, Boston, Massachussetts, April 23-27, 1990. 18 Huglin M. B., Ed., "Light Scattering From Polymer Solutions". Academic Press, NY, (1972). RECEIVED January 14, 1991 In Particle Size Distribution II; Provder, T.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

Particle Size Distribution II - American Chemical Society

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