Particle Size Distribution II - American Chemical Society

Chapter 20

Downloaded by NORTH CAROLINA STATE UNIV on August 2, 2012 | http://pubs.acs.org Publication Date: September 24, 1991 | doi: 10.1021/bk-1991-0472.ch020

Viscometry as a Detection Scheme for Particles in Separation Techniques for Size Distribution Analysis Grant Von Wald and Martin Langhorst Analytical Sciences Laboratory, The Dow Chemical Company, 1897 Building, Midland, MI 48667 Viscometry was investigated as a possible size and composition independent detector for hydrodynamic chromatography. The specific viscosity was found to be linear with latex concentration from 0.01 to 0.4% solids, did not depend on particle composition, and was independent of particle size above roughly 100 nm. However, the specific viscosity increased 30% as the diameter of the latex decreased from 100 nm to 30 nm. This size dependence was ascribed to the presence of a surface layer on the latex in solution. Although the size dependence would not preclude its application, the utility of the viscometer was limited by low sensitivity and long time response. A number o f t e c h n o l o g i e s , such as hydrodynamic chromatography (HDC) and t h e v a r i o u s t e c h n i q u e s o f f i e l d f l o w f r a c t i o n a t i o n ( F F F ) , c a n e f f i c i e n t l y s e p a r a t e p a r t i c l e s by s i z e i n o r d e r t o q u a n t i t a t e t h e d i s t r i b u t i o n o f s i z e s i n a sample. F o r any p a r t i c l e s e p a r a t i o n technique, i t i s necessary t o determine t h e c o n c e n t r a t i o n o f p a r t i c l e s e l u t i n g from t h e s e p a r a t i o n element. The i d e a l d e t e c t o r c o u l d d e t e r m i n e t h e c o n c e n t r a t i o n o f p a r t i c l e s w i t h o u t dependence on t h e p a r t i c l e d i a m e t e r o r c o m p o s i t i o n . A t t h e p r e s e n t time, t h e s p e c t r o p h o t o m e t r i c d e t e c t o r o p e r a t e d i n t h e u l t r a - v i o l e t wavelength range i s t h e most w i d e l y a p p l i e d d e t e c t o r f o r p a r t i c l e s e p a r a t i o n - d i s t r i b u t i o n analysis instruments. A l t h o u g h s p e c t r o p h o t o m e t r i c d e t e c t o r s have e x c e l l e n t s e n s i t i v i t y , t h e y s u f f e r from t h e d i s a d v a n t a g e t h a t t h e r e s p o n s e o f t h e d e t e c t o r i s a s t r o n g f u n c t i o n o f t h e p a r t i c l e c o m p o s i t i o n and o f t h e p a r t i c l e s i z e o v e r t h e c o l l o i d a l range o f 20 t o 2000 nm i n diameter. The a c c u r a c y 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 measurements by s e p a r a t i o n t e c h n i q u e s , such as HDC, would be g r e a t l y enhanced i f a s i z e and c o m p o s i t i o n independent d e t e c t o r c o u l d be d e v i s e d .

0097-6156/91/0472-0308$06.00/0 © 1991 American Chemical Society

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

20.

V O N WALD & LANGHORST

Viscometry

as a Detection

309

Scheme

One p o s s i b l e scheme f o r such a s i z e and c o m p o s i t i o n independent d e t e c t o r i s s u g g e s t e d by t h e E i n s t e i n v i s c o s i t y law which s t a t e s t h a t t h e s p e c i f i c v i s c o s i t y o f a p a r t i c l e s u s p e n s i o n , iy p, e q u a l s 2.5 t i m e s t h e f r a c t i o n o f t h e volume o f t h e s u s p e n s i o n o c c u p i e d by p a r t i c l e s , *, i . e . : S

^sp

=

2

- * * ^ s ~ *o »o 5

)/f

a

where i j i s t h e v i s c o s i t y o f t h e s u s p e n s i o n and i j i s t h e v i s c o s i t y without p a r t i c l e s p r e s e n t . I f the E i n s t e i n v i s c o s i t y law were r i g o r o u s l y t r u e f o r t h e p a r t i c l e s u s p e n s i o n s o f i n t e r e s t i n p a r t i c l e s e p a r a t i o n methods, a d e t e c t o r which measured t) p would be t h e i d e a l c o m p o s i t i o n and s i z e independent d e t e c t o r . D e v i a t i o n s o f t h i s s i m p l e r e l a t i o n s h i p between r j p and • a r e e x p e c t e d f o r p a r t i c l e volume f r a c t i o n s above a p p r o x i m a t e l y 0.01 (.1). An upper c o n c e n t r a t i o n l i m i t o f 0.01 volume f r a c t i o n i s not e x p e c t e d t o be a s i g n i f i c a n t l i m i t a t i o n i n t h i s work as p a r t i c l e c o n c e n t r a t i o n s i n HDC and FFF a r e a t l e a s t an o r d e r o f magnitude lower t h a n 0.01. A second c o m p l i c a t i o n i n t h e r e l a t i o n s h i p between i y and p a r t i c l e c o n c e n t r a t i o n a r i s e s from t h e s u r f a c e l a y e r o f bound s o l v e n t and s u r f a c e a c t i v e a g e n t s which i s p r e s e n t i n s t a b l e c o l l o i d a l s u s p e n s i o n s i n water (1) . The s u r f a c e l a y e r c o m p l i c a t e s t h e r e l a t i o n s h i p between t h e volume t h a t t h e p a r t i c l e s occupy i n a s u s p e n s i o n and t h e weight c o n c e n t r a t i o n o f p a r t i c l e s . F o r i n s t a n c e , i f t h e r e were no s u r f a c e l a y e r , t h e weight f r a c t i o n and t h e volume f r a c t i o n o f p a r t i c l e s i n a s u s p e n s i o n would be d i r e c t l y r e l a t e d by t h e d e n s i t i e s o f t h e p a r t i c l e s and t h e solvent. However, i f t h e r e i s a s u r f a c e l a y e r p r e s e n t , t h e e f f e c t i v e volume o f t h e p a r t i c l e s i n a s u s p e n s i o n w i l l be l a r g e r t h a n t h e " d r y " volume o f t h e p a r t i c l e s . In p a r t i c u l a r , as t h e d i a m e t e r o f t h e p a r t i c l e s d e c r e a s e s and t h e s u r f a c e a r e a p e r mass i n c r e a s e s , t h e c o n t r i b u t i o n o f a s u r f a c e l a y e r t o t h e volume o c c u p i e d by p a r t i c l e s w i l l i n c r e a s e . The s e n s i t i v i t y r e q u i r e m e n t s f o r a v i s c o s i t y d e t e c t o r s u i t a b l e f o r q u a n t i t a t i n g t h e p a r t i c l e c o n c e n t r a t i o n s e l u t i n g f r o m HDC o r FFF a r e s t r i n g e n t . The volume f r a c t i o n o f p a r t i c l e s would be e x p e c t e d t o be i n t h e 1x10"^ t o l x l O " range so t h a t v i s c o s i t y changes on t h e o r d e r o f 10"^ must be d e t e c t e d . Previous e x p e r i e n c e w i t h o t h e r v i s c o m e t e r d e s i g n s (2,3) i n d i c a t e s t h a t a s u i t a b l e viscometer design f o r d e t e c t i o n of s p e c i f i c v i s c o s i t i e s i n t h e range o f i n t e r e s t i n p a r t i c l e s e p a r a t i o n t e c h n o l o g i e s i s t h e d i f f e r e n t i a l v i s c o m e t e r p a t e n t e d by Max Haney (.4,5) . s


)

Q

3

S

s p

7

The purpose o f t h i s r e p o r t was t o d e t e r m i n e i f measurements o f Tf p c o u l d p r o v i d e the d e s i r e d i d e a l p a r t i c l e c o n c e n t r a t i o n d e t e c t o r r e l a t i o n s h i p and t o e v a l u a t e t h e s u i t a b i l i t y o f t h e d i f f e r e n t i a l v i s c o m e t e r f o r use i n p a r t i c l e s e p a r a t i o n s . HDC was u s e d as t h e s e p a r a t i o n t o o l , a l t h o u g h t h e p r i n c i p l e o f t h e measurements c o u l d be a p p l i e d t o o t h e r s e p a r a t i o n t e c h n i q u e s . The Tj p o f l a t i c e s o f v a r y i n g c o m p o s i t i o n and d i a m e t e r s from 20 nm t o 1000 nm were s t u d i e d t o probe t h e g e n e r a l i t y o f t h e E i n s t e i n v i s c o s i t y law and t h e u t i l i t y o f t h e v i s c o m e t e r as a chromatographic d e t e c t o r . S

S


310

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

EXPERIMENTAL Apparatus. The HDC a p p a r a t u s t h a t was employed was s i m i l a r t o t h e one d e s c r i b e d p r e v i o u s l y (6.) . The sample l o o p volume was 100 11L which was t h e maximum l o o p volume p e r m i s s i b l e b e f o r e s i g n i f i c a n t peak b r o a d e n i n g o c c u r r e d due t o t h e i n j e c t i o n volume. The HDC e l u e n t c o n s i s t e d o f 0.2% B r i j 35 n o n - i o n i c s u r f a c t a n t ( p o l y o x y e t h y l e n e ( 2 3 ) l a u r y l e t h e r ) , 0.05% sodium l a u r y l s u l f a t e (SLS), and 2 mM N a H P 0 a d j u s t e d t o a pH o f 3-3.4.


2

4

The d i f f e r e n t i a l v i s c o m e t e r was a model number 100, V i s c o t e k , I n c . o f P o r t e r Texas. The h o l d - u p r e s e r v o i r i n t h i s v i s c o m e t e r was t h e o r i g i n a l d e s i g n , as opposed t o t h e r e s e r v o i r p r e s e n t l y u s e d i n t h i s model v i s c o m e t e r , i n o r d e r t o i n c r e a s e t h e s e n s i t i v i t y o f t h e viscometer s l i g h t l y . A spectrophotometry detector, Applied B i o s y s t e m s 773, was used i n s e r i e s a f t e r t h e d i f f e r e n t i a l viscometer t o a s s i s t i n the e v a l u a t i o n of the viscometer. The model 100 d i f f e r e n t i a l v i s c o m e t e r i s i n t e n d e d t o be u s e d as a d e t e c t o r f o r g e l p e r m e a t i o n chromatography. In o r d e r t o be a b l e t o d i r e c t l y measure i j p f o r l a t e x o f known c o n c e n t r a t i o n without the HDC column p r e s e n t , the HDC a p p a r a t u s was rearranged. The i n j e c t i o n l o p was i n c r e a s e d t o 1.4 mL u s i n g 310 cm o f 0.030" I.D. t u b i n g . The HDC column was removed and t h e i n j e c t i o n v a l v e was c o n n e c t e d t o t h e v i s c o m e t e r . I t was n e c e s s a r y t o put an a d d i t i o n a l p u l s e dampener between t h e v a l v e and t h e v i s c o m e t e r . T h i s p u l s e dampener c o n s i s t e d o f a "T" c o n n e c t o r (VALCO) w i t h one l e g of t h e "T" c o n n e c t e d t o a 35 cm l o n g l e n g t h o f 1/16" I.D. t u b i n g which was c l o s e d o f f t o t r a p a i r i n t h e end o f t h e t u b i n g . The t r a p p e d a i r , which was r e a d i l y compressed, a b s o r b e d t h e p r e s s u r e p u l s e when the v a l v e was s w i t c h e d . S

The d i a m e t e r o f f o u r p o l y s t y r e n e l a t i c e s were measured i n 5 mM N a C l and i n HDC e l u e n t u s i n g t h e C o u l t e r S c i e n t i f i c I n s t r u m e n t s N4M photon c o r r e l a t i o n s p e c t r o s c o p y i n s t r u m e n t . A measurement time o f 180 sec and a n g l e o f 90' were used. A v i s c o s i t y o f 0.890 cP was used f o r t h e NaCl s o l u t i o n . The r e l a t i v e v i s c o s i t y o f t h e HDC e l u e n t was measured t o be 1.021*0.005 ( S c h o t t - G e r a t e U b b e l h o l d e Automated V i s c o s i t y M e a s u r i n g System) a t 2 5 * C The i n d e x o f r e f r a c t i o n o f t h e HDC e l u e n t was measured t o be t h e same as water t o w i t h i n 0.002 u n i t s (Bausch and Lomb, Inc., ABBE-3L). The average d i a m e t e r r e p o r t e d i n T a b l e I was c a l c u l a t e d by f i t t i n g a s i n g l e e x p o n e n t i a l t o the a u t o c o r r e l a t i o n f u n c t i o n ( i . e . , t h e "unimodal" mean d i a m e t e r as d e s c r i b e d by C o u l t e r S c i e n t i f i c Instruments). Samples. The p o l y s t y r e n e and c a r b o x y l a t e d p o l y s t y r e n e l a t i c e s were p u r c h a s e d from Duke S c i e n t i f i c Corp. and Seradyn D i a g n o s t i c s . A d e n s i t y of 1.05 g/mL was u s e d f o r t h e p o l y s t y r e n e l a t e x (2*JL) • The a c r y l a t e copolymer, s t y r e n e - b u t a d i e n e copolymer, and p o l y b u t a d i e n e l a t i c e s were o b t a i n e d from i n t e r n a l Dow s o u r c e s .


20.

311

Viscometry as a Detection Scheme

VON WALD & LANGHORST

The d e n s i t y o f t h e copolymers was c a l c u l a t e d u s i n g l i t e r a t u r e v a l u e s f o r t h e d e n s i t y o f pure polymers o f each monomer (2) and assuming t h a t t h e d e n s i t y o f t h e copolymer was l i n e a r f u n c t i o n o f t h e c o m p o s i t i o n o f t h e polymer. A d e n s i t y o f 0.913 g/mL was u s e d f o r p o l y b u t a d i e n e (7). The d e n s i t i e s c a l c u l a t e d f o r t h e s t y r e n e b u t a d i e n e l a t i c e s a g r e e d w i t h p u b l i s h e d measurements (8) . The p o l y v i n y l t o l u e n e l a t e x was o b t a i n e d from Seradyn D i a g n o s t i c s and a l i t e r a t u r e v a l u e o f 1.03 g/mL was used f o r the polymer d e n s i t y

•

The d r y volume f r a c t i o n , * , o f l a t e x was c a l c u l a t e d from t h e f r a c t i o n o f s o l i d s i n the l a t e x , and t h e d e n s i t y o f t h e polymer i n t h e l a t e x , Pp, u s i n g t h e f o r m u l a :


d

•d = Si/Pp

where t h e d e n s i t y o f t h e e l u e n t was assumed t o be 1.00 g/mL. The p e r c e n t s o l i d s o f t h e l a t i c e s was measured b y w e i g h i n g l a t e x s u s p e n s i o n i n an A l pan, d r y i n g t h e l a t e x a t a p p r o x i m a t e l y 100 C f o r 20-40 minutes and then w e i g h i n g t h e d r i e d l a t e x . Repeat measurements were w i t h i n one p e r c e n t r e l a t i v e . The p e r c e n t s o l i d s o f t h e l a t e x s u s p e n s i o n a c t u a l l y s t u d i e d were c a l c u l a t e d from t h e d i l u t i o n r a t i o o f the o r i g i n a l l a t e x with eluent. The d i a m e t e r o f t h e l a t i c e s was e i t h e r g i v e n by t h e vendor from e l e c t r o n m i c r o s c o p y o r measured u s i n g HDC (6). Many o f t h e d i a m e t e r assignments from HDC o r e l e c t r o n m i c r o s c o p y were v e r i f i e d u s i n g photon c o r r e l a t i o n s p e c t r o s c o p y . 9

RESULTS F i g u r e s 1 t h r o u g h 6 summarize t h e measurements which were p e r f o r m e d t o c h a r a c t e r i z e t h e performance o f t h e d i f f e r e n t i a l v i s c o m e t e r and t o i n v e s t i g a t e t h e r e l a t i o n s h i p between ry p and p a r t i c l e concentration. An example d i r e c t measurement o f i j p w i t h o u t t h e column i s d i s p l a y e d i n F i g u r e 1 f o r a 0.412% s o l i d s 300 nm d i a m e t e r p o l y s t y r e n e l a t e x . F i g u r e l a p r e s e n t s t h e output o f t h e two p r e s s u r e t r a n s d u c e r s i n the d i f f e r e n t i a l v i s c o m e t e r v e r s u s t i m e . The sample was i n j e c t e d a t t h e f i v e minute p o i n t and was e x h a u s t e d a t r o u g h l y the 7 min p o i n t . The i? p was c a l c u l a t e d u s i n g t h e equation: S

S

g

''sp

4P /(P d

i

- 2P )

(3)

d

where P^ i s t h e change i n t h e d i f f e r e n t i a l t r a n s d u c e r r e a d i n g from t h e background l e v e l (1.2 min t o 5 min i n F i g u r e l a ) t o t h e p l a t e a u r e a c h e d a f t e r t h e sample i n j e c t i o n ( j u s t a f t e r 6 min t o 7 min) and P^ i s t h e i n l e t p r e s s u r e t r a n s d u c e r r e a d i n g (.4,5) . Figure l b presents the i7 c a l c u l a t e d u s i n g E q u a t i o n 3. The T j was a v e r a g e d o v e r t h e time p e r i o d from j u s t a f t e r 6 m i n u t e s t o 7 minutes where t h e d i f f e r e n t i a l p r e s s u r e was c o n s t a n t (between the s o l i d v e r t i c a l l i n e s i n F i g u r e l b ) . sp


s p


312


0.0025-r

5.0

6.0

7.0

Time (min) F i g u r e 1. iy Measurement f o r 0.412% s o l i d s 300 nm d i a m e t e r polystyrene latex. (a) D i f f e r e n t i a l and i n l e t p r e s s u r e t r a n s d u c e r o u t p u t v e r s u s time. Inlet pressure: D i f f e r e n t i a l pressure: (b) C a l c u l a t e d i j versus time. s p

S D


8.0

20. V O N W A L D & L A N G H O R S T

313


F i g u r e 2 p r e s e n t s d a t a which d e m o n s t r a t e s t h e s e n s i t i v i t y o f t h e d i f f e r e n t i a l v i s c o m e t e r when i t was u s e d as a d e t e c t o r f o r HDC. R e s u l t s c o l l e c t e d w i t h two c o n c e n t r a t i o n s o f a 2 9 nm p o l y s t y r e n e l a t e x , 0 . 0 9 9 % s o l i d s and 0 . 0 0 9 9 % s o l i d s , a r e displayed. B o t h t h e d i f f e r e n t i a l p r e s s u r e t r a n s d u c e r o u t p u t i n Pa from t h e v i s c o m e t e r and t h e a b s o r b a n c e measured b y t h e s p e c t r o p h o t o m e t r i c d e t e c t o r were c o l l e c t e d and a r e d i s p l a y e d i n F i g u r e 2 . F o r a l l t h e s u s p e n s i o n s s t u d i e d , t h e change i n t h e d i f f e r e n t i a l p r e s s u r e was i n s i g n i f i c a n t compared t o t h e i n l e t p r e s s u r e so t h a t i y was d i r e c t l y p r o p o r t i o n a l t o t h e d i f f e r e n t i a l p r e s s u r e (See E q u a t i o n 3 ) . Repeat measurements o f t h e peak h e i g h t of t h e d i f f e r e n t i a l p r e s s u r e r e a d i n g o v e r a s e v e r a l d a y t i m e p e r i o d were w i t h i n a 1 0 % range. The r e p r o d u c i b i l i t y c o u l d have been improved b y c o l l e c t i n g t h e i n l e t p r e s s u r e a l s o i n o r d e r t o n o r m a l i z e o u t f l u c t u a t i o n s i n t h e pumping r a t e . The e f f e c t o f l a t e x s i z e on t h e v i s c o m e t e r r e s p o n s e was s t u d i e d by i n j e c t i n g a s e r i e s o f 0 . 4 1 2 % s o l i d s p o l y s t y r e n e l a t i c e s onto t h e HDC column. The r e s u l t s a r e summarized i n F i g u r e 3 where t h e peak d i f f e r e n t i a l p r e s s u r e change i s p l o t t e d v e r s u s t h e l a t e x diameter. F i g u r e 4 d i s p l a y s t h e peak d i f f e r e n t i a l p r e s s u r e change i n Pa v e r s u s t h e l a t e x d i a m e t e r f o r d i f f e r e n t t y p e s o f l a t e x . F i g u r e s 5 a n d 6 p r e s e n t t h e r e s u l t s f r o m d i r e c t measurements of Tj p. The l i n e a r i t y o f t h e r e l a t i o n s h i p between i | p a n d l a t e x c o n c e n t r a t i o n was e v a l u a t e d . The measured ty p i s p l o t t e d a g a i n s t t h e d r y volume f r a c t i o n o f 3 8 nm, 1 0 6 nm, a n d 3 0 0 nm d i a m e t e r p o l y s t y r e n e l a t i c e s i n F i g u r e 5 . The l e a s t s q u a r e s f i t o f t h e d a t a t o a s t r a i g h t l i n e a r e r e p o r t e d i n F i g u r e 5 where " X 1 0 6 nm" s t a n d s f o r t h e d r y volume f r a c t i o n o f l a t e x . The dependence o f Tj p on t h e l a t e x d i a m e t e r was a l s o i n v e s t i g a t e d i n 0 . 0 0 2 % B r i j 3 5 ,


s p

g

S

g

S

0.0005%

SLS w i t h

2 mM

NaH P0 2

4

and i n 0 . 1 % SLS w i t h

2 mM

NaH P0 . 2

4

r e s u l t s are presented i n Figure 6 . The e f f e c t o f t h e s u r f a c t a n t s i n HDC e l u e n t on t h e e f f e c t i v e d i a m e t e r o f f o u r p o l y s t y r e n e l a t i c e s was measured u s i n g p h o t o n c o r r e l a t i o n spectroscopy f o l l o w i n g a s i m i l a r study o f t h e i n t e r a c t i o n o f polyethylene oxide with the surface o f polystyrene l a t e x (9) • The r e s u l t s a r e summarized i n T a b l e I where t h e mean d i a m e t e r i s g i v e n f o r measurements w i t h p o l y s t y r e n e l a t i c e s i n 5 mM N a C l w i t h o u t any s u r f a c t a n t added, b e s i d e s t h e s u r f a c t a n t i n t h e s t o c k l a t e x s u s p e n s i o n s , and i n s t a n d a r d HDC e l u e n t . The

TABLE I . Photon C o r r e l a t i o n S p e c t r o s c o p y Measurements o f t h e D i a m e t e r o f F o u r P o l y s t y r e n e L a t i c e s i n 5 mM N a C l and HDC E l u e n t Latex Identification

Latex Diameter From Vendor

Duke

5003

29

Duke

3030

30

Duke 5 0 1 0

106

Seradvn 1 B 5 8

204

nm ** nm nm nm

* *

Latex Diameter 5 mM N a C l

Latex

Diameter

HDC E l u e n t

27.7,

27,.3

nm

30.6,

30, .4

nm

30.7,

30, .5

nm

35.8,

35, .0

nm

121,

122

nm

120,

122

nm

209,

210

nm

211,

202

nm

*Determined from e l e c t r o n m i c r o s c o p y . D e t e r m i n e d by photon c o r r e l a t i o n s p e c t r o s c o p y .



314


Time (min)

+0.15

Time (min)

Figure 2. Responses of the d i f f e r e n t i a l pressure transducer and the spectrophotometry detector at a wavelength of 254 nm to injections of 29 nm diameter polystyrene latex, (a) 0.0099% solids i n j e c t i o n . (b) 0.099% solids i n j e c t i o n . D i f f e r e n t i a l pressure: Absorbance:


fj O


30--

Latex Diameter

400

(nm)

600

800

F i g u r e 3. Dependence o f t h e v i s c o m e t r i c r e s p o n s e t o l a t e x d i a m e t e r f o r a s e r i e s o f p o l y s t y r e n e l a t i c e s i n j e c t e d a t 0.412% s o l i d s w i t h HDC e l u e n t measured as t h e change i n d i f f e r e n t i a l pressure. • Polystyrene l a t i c e s A Carboxylated polystyrene l a t i c e s

200

B


1000


0)

a

§

< D 0)

0

2(H

30--

40--

50+

60--

70-r

•

1

1

100

A

•

•

1

AA

A

1

1

Diameter

200

(nm)

1 300

1

1 400

F i g u r e 4. Response o f t h e v i s c o m e t e r t o i n j e c t i o n s o f 0.0040 d r y volume f r a c t i o n o f l a t i c e s o f d i f f e r e n t c o m p o s i t i o n s measured as t h e change i n d i f f e r e n t i a l p r e s s u r e . 0 Carboxylated polystyrene o Polyvinyltoluene A S/B copolymer V B u t a d i e n e A Acrylate Q Polystyrene

o B

1


1 500

g C d 25

H

©

M

GO

w

2

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

5

5

5

F i g u r e 5. i j p v e r s u s c o n c e n t r a t i o n f o r t h r e e p o l y s t y r e n e l a t i c e s i n l o w e r s u r f a c t a n t c o n c e n t r a t i o n HDC e l u e n t . • Duke 5010 106 nm A Duke C004 38 nm O Duke 5030 300 nm 3.156MX 106 nm) - 1 . 0 4 x l 0 " 3BBBSSS 3.398x(X 38 nm) - 7 . 0 8 x l 0 ~ — 2 . 6 6 9 * ( X 300 nm) - 6 . 1 1 x l 0 "



0.0100H

0.0110"

0.0120--

0.0130"

0.0140T

S

Diameter

400

(nm)

600

2

4

—h— 800

2

4

F i g u r e 6. i j p v e r s u s d i a m e t e r measured f o r p o l y s t y r e n e latices. • 0.002% B r i j 35, 0.005% S L S , 2 mM N a H P 0 A 0.1% S L S , 2 mM N a H P 0

200

6

•

A


1000

o

I

n

00

20. V O N

WALD & LANGHORST

319


DISCUSSION L i n e a r i t y and S e n s i t i v i t y . In o r d e r t o p e r m i t e v a l u a t i o n o f t h e r e l a t i o n s h i p between p a r t i c l e c o n c e n t r a t i o n and i j , t h e r e q u i s i t e s e n s i t i v i t y and l i n e a r i t y o f t h e d i f f e r e n t i a l v i s c o m e t e r had t o be verified. The s e n s i t i v i t y o f t h e v i s c o m e t e r can be e s t i m a t e d t o be a p p r o x i m a t e l y 0 . 0 0 1 % s o l i d s i n j e c t e d from t h e measurements o f t h e d i f f e r e n t i a l v i s c o m e t e r response t o i n j e c t i o n s o f 0 . 0 9 9 and 0 . 0 9 9 % s o l i d s o f a 29 nm p o l y s t y r e n e l a t e x ( F i g u r e 2 ) . The d i f f e r e n t i a l v i s c o m e t e r was f o u n d t o g i v e a l i n e a r r e s p o n s e t o l a t e x c o n c e n t r a t i o n o v e r t h e range from 0 . 0 1 - 0 . 4 % s o l i d s i n j e c t e d onto t h e column. A l s o ij was f o u n d t o be l i n e a r w i t h l a t e x c o n c e n t r a t i o n o v e r t h e range o f 0 . 0 1 - 0 . 4 % s o l i d s w i t h o u t t h e HDC column p r e s e n t (See F i g u r e 5 ) .


s p

f

s p

Dependence on Diameter and C o m p o s i t i o n . Given acceptable s e n s i t i v i t y and l i n e a r i t y , t h e dependence o f t h e v i s c o m e t e r s i g n a l on l a t e x d i a m e t e r and c o m p o s i t i o n was i n v e s t i g a t e d . The r e s u l t s for c o n s t a n t c o n c e n t r a t i o n o f p o l y s t y r e n e l a t e x i n j e c t e d onto t h e HDC column a r e summarized i n F i g u r e 3 . The peak d i f f e r e n t i a l p r e s s u r e r e s u l t i n g from i n j e c t i o n s o f 0 . 4 1 2 % s o l i d s p o l y s t y r e n e l a t i c e s was o b s e r v e d t o i n c r e a s e from 4 5 . 3 Pa f o r a 106 nm d i a m e t e r l a t e x t o 5 6 . 1 Pa f o r a 29 nm d i a m e t e r l a t e x . The r e s p o n s e a l s o d e c r e a s e d t o 2 9 . 3 Pa a t 913 as e x p e c t e d because o f the t r a p p i n g of p a r t i c l e s with diameters g r e a t e r than roughly 500 nm by t h e HDC column (6,10,) . On t h e o t h e r hand, when l a t i c e s of v a r y i n g c o m p o s i t i o n s were i n j e c t e d onto t h e column a t 0 . 0 0 4 0 dry volume f r a c t i o n (See E q u a t i o n 2 ) , no dependence on t h e l a t e x c o m p o s i t i o n , w i t h i n e x p e r i m e n t a l e r r o r , c o u l d be d i s c e r n e d f o r t h e l a t e x t y p e s s t u d i e d (See F i g u r e 4 ) . One p o s s i b l e h y p o t h e s i s t o e x p l a i n t h e s i z e dependence o f t h e v i s c o m e t e r measurements c o u l d have been a n o n - l i n e a r r e l a t i o n s h i p between i j and p a r t i c l e c o n c e n t r a t i o n as has been o b s e r v e d f o r higher p a r t i c l e concentrations ( l j . However, as d i s c u s s e d above and d i s p l a y e d i n F i g u r e 5 , measurements o f T f from 0 . 0 1 t o 0 . 4 percent s o l i d s with t h r e e d i f f e r e n t l a t i c e s , demonstrated the l i n e a r i t y of i y with concentration. Another component o f t h e s i z e dependence o f t h e v i s c o m e t e r r e s u l t s c o l l e c t e d w i t h t h e HDC column can be a c c o u n t e d f o r by t h e measurements o f i j as a f u n c t i o n o f d i a m e t e r . Figure 6 displays the T j f o r a s e r i e s of p o l y s t y r e n e l a t i c e s at 0.412% s o l i d s . Above r o u g h l y 200 nm t h e i j o f l a t i c e s measured w i t h o u t t h e column i s c o n s t a n t ( F i g u r e 6) w h i l e a s i g n i f i c a n t d e c r e a s e was o b s e r v e d w i t h t h e column p r e s e n t ( F i g u r e 3 ) . The d i f f e r e n c e between t h e two s e t s o f r e s u l t s i n F i g u r e s 3 and 6 i l l u s t r a t e s t h e i n f l u e n c e o f t r a p p i n g by t h e HDC column as e x p e c t e d from p r e v i o u s work (6,10). However, t h e most s i g n i f i c a n t f e a t u r e o f t h e d i r e c t r j measurements d i s p l a y e d i n F i g u r e 6 i s t h e i n c r e a s e i n i y for l a t e x d i a m e t e r l e s s t h a n 100 nm. The dependence o f i j on d i a m e t e r f o r t h e s u s p e n s i o n s w i t h B r i j 35 and SLS s u r f a c t a n t s ( F i g u r e 6) i s n e a r l y i d e n t i c a l t o t h a t o b s e r v e d w i t h t h e HDC column ( F i g u r e 3 ) . Thus, t h e dependence o f v i s c o m e t e r r e s p o n s e on l a t e x d i a m e t e r i s not t h e consequence o f a HDC c o l u m n - p a r t i c l e interaction. s p

sp

s p

s p

s p

s p

g p

s p

3 p


320


P r o p o s e d Cause f o r S i z e Dependence. The i n c r e a s e i n i j as t h e p a r t i c l e d i a m e t e r d e c r e a s e d from 100 nm t o 30 nm s u g g e s t s a more complex r e l a t i o n s h i p between t j p and p a r t i c l e c o n c e n t r a t i o n i n t h e c o l l o i d a l regime t h a n t h e E i n s t e i n v i s c o s i t y law i n d i c a t e s . A l t h o u g h a l i n e a r r e l a t i o n s h i p e x i s t s between i j p and l a t e x c o n c e n t r a t i o n , t h e p r o p o r t i o n a l i t y c o n s t a n t between i j p and t h e " d r y " volume f r a c t i o n o f l a t e x c a l c u l a t e d from weight c o n c e n t r a t i o n i s l a r g e r t h a n t h e v a l u e o f 2.5 p r e d i c t e d by E i n s t e i n f o r e v e r y l a t e x s t u d i e d and i n c r e a s e d f r o m 2.67 f o r t h e 300 nm l a t e x t o 3.40 f o r t h e 29 nm l a t e x . The dependence o f t h e p r o p o r t i o n a l i t y c o n s t a n t between T j and p a r t i c l e c o n c e n t r a t i o n on p a r t i c l e d i a m e t e r i s h y p o t h e s i z e d t o be t h e consequence o f the s o l v a t i o n l a y e r on t h e s u r f a c e o f t h e p a r t i c l e (11). I t has been w e l l e s t a b l i s h e d t h a t t h e s u r f a c e o f a l y o p h o b i c c o l l o i d i n an aqueous d i s p e r s i o n , such as l a t e x , w i l l have a s s o c i a t e d w i t h i t a v a r i e t y o f s p e c i e s t h a t w i l l i n c r e a s e the e f f e c t i v e d i a m e t e r o f t h e c o l l o i d (11) . I f t h e s u r f a c e l a y e r o f a p o l y s t y r e n e l a t e x p a r t i c l e i n an aqueous s o l u t i o n were 1.5 nm t h i c k , the volume o f a 300 nm d i a m e t e r p a r t i c l e would i n c r e a s e o v e r the " d r y " volume by 2.8%. The same t h i c k n e s s o f s o l v a t i o n l a y e r would change the volume o f a 29 nm p a r t i c l e by 34%. A s u r f a c e l a y e r s l i g h t l y g r e a t e r t h a n 1.5 nm i n t h i c k n e s s would a c c o u n t f o r the o b s e r v e d i n c r e a s e o f Ty f o r l a t e x d i a m e t e r s below 100 nm and t h e r e l a t i v e l y s m a l l dependence o f i j p on l a t e x d i a m e t e r f o r s i z e s g r e a t e r t h a n 300 nm (e.g., See F i g u r e 3 o r 6) . s p

S

S


S

s p

sp

S

C o n f i r m a t i o n o f P r o p o s e d Cause o f S i z e Dependence. I f the o b s e r v e d dependence o f Ty on p a r t i c l e d i a m e t e r i s t h e consequence o f a s u r f a c e l a y e r , t h e n i t would not be c o r r e c t t o s t a t e t h a t i j p i s a f u n c t i o n of diameter. Rather, i t would be more a c c u r a t e t o s t a t e t h a t the e f f e c t i v e d i a m e t e r o f a c o l l o i d i s dependent on t h e s u s p e n s i o n c o n d i t i o n s which i s an a s s e r t i o n a l r e a d y w e l l e s t a b l i s h e d i n the l i t e r a t u r e . F u r t h e r m o r e , i t s h o u l d be emphasized t h a t the o b s e r v e d i n c r e a s e i n T j as t h e p a r t i c l e d i a m e t e r d e c r e a s e s i s h y p o t h e s i z e d t o be the consequence o f a d i f f e r e n c e i n the e f f e c t i v e d i a m e t e r between the measurement c o n d i t i o n s where t h e T j measurements were made and t h e c o n d i t i o n s under which the d i a m e t e r was a s s i g n e d by t h e vendor f o r t h e s e polystyrene l a t i c e s . F o r t h e l a t i c e s l a r g e r t h a n 100 nm i n d i a m e t e r , the e x p e r i m e n t a l c o n d i t i o n s o f TEM measurements and HDC measurements a r e much d i f f e r e n t . However, f o r t h e s e l a r g e r l a t i c e s the c o n t r i b u t i o n o f s u r f a c e l a y e r s t o t h e e f f e c t i v e p a r t i c l e d i a m e t e r i s not e x p e c t e d t o be l a r g e . Some o f t h e s m a l l e r l a t i c e s were a s s i g n e d d i a m e t e r s u s i n g TEM. For these l a t i c e s i t would be e x p e c t e d t h a t s o l u t i o n measurements might g i v e d i f f e r e n t diameters than e l e c t r o n microscopy. On t h e o t h e r hand, some o f the o t h e r l a t i c e s w i t h d i a m e t e r s l e s s t h a n 100 nm were s i z e d u s i n g photon c o r r e l a t i o n s p e c t r o s c o p y . For these l a t i c e s the change i n e f f e c t i v e d i a m e t e r would be between t h e s o l u t i o n c o n d i t i o n s f o r t h e photon c o r r e l a t i o n s p e c t r o s c o p y measurements and the c o n d i t i o n s i n t h e HDC eluent. sp

S

s p

s p


20.


321


In o r d e r t o t e s t t h i s h y p o t h e s i s , t h e d i a m e t e r o f f o u r l a t i c e s were d e t e r m i n e d u s i n g photon c o r r e l a t i o n s p e c t r o s c o p y i n 5 mM N a C l s u s p e n s i o n which had no s u r f a c t a n t i n i t , b e s i d e s t h e s u r f a c t a n t which was i n t h e l a t e x s t o c k s u s p e n s i o n s s u p p l i e d by t h e vendor, and i n HDC e l u e n t . The r e s u l t s a r e summarized i n T a b l e I . F o r the 29 nm and 30 nm l a t i c e s , a c l e a r i n c r e a s e i n t h e e f f e c t i v e d i a m e t e r i n HDC e l u e n t v e r s u s 5 mM NaCl was o b s e r v e d . The o b s e r v e d change i n d i a m e t e r between HDC e l u e n t and 5 mM NaCl, a p p r o x i m a t e l y 3 nm, a g r e e d w i t h t h e 3 nm i n c r e a s e i n d i a m e t e r p r e d i c t e d from t h e i y measurements. No d i f f e r e n c e was o b s e r v e d f o r t h e 204 nm and 10b nm d i a m e t e r l a t i c e s . T h i s i s presumably t h e consequence o f t h e r e l a t i v e l y s m a l l e f f e c t a s u r f a c e l a y e r would have on t h e d i a m e t e r o f t h e s e l a t i c e s .


sp

Dependence o f i ? . S i z e R e l a t i o n s h i p on S o l u t i o n C o n d i t i o n s . G i v e n t h e s t r o n g dependence o f t h e e f f e c t i v e p a r t i c l e volume on l a t e x d i a m e t e r below 100 nm, i t would be important t o u n d e r s t a n d the dependence o f t h e s o l v a t i o n l a y e r t h i c k n e s s on t h e s o l v e n t conditions i n order t o apply viscometry t o p a r t i c l e d e t e c t i o n f o r s e p a r a t i o n methods. In a d d i t i o n t o t h e s o l u t i o n c o n d i t i o n s , t h e n a t u r e o f t h e s u r f a c e o f t h e p a r t i c l e would be e x p e c t e d t o a f f e c t the l a y e r w i t h which i t i s i n c o n t a c t . However, measurements o f 3 p

^sp f o r a v a r i e t y o f l a t e x t y p e s , summarized i n F i g u r e 4, d i d n o t depend on t h e l a t e x c o m p o s i t i o n . Also, t h e composition independence o f p a r t i c l e e l u t i o n i n HDC i n d i c a t e s t h a t a t l e a s t a t low i o n i c s t r e n g t h s , t h e e f f e c t i v e p a r t i c l e d i a m e t e r i s n o t a strong f u n c t i o n o f p a r t i c l e composition (10). The s o l u t i o n c o n d i t i o n s which would be e x p e c t e d t o a f f e c t s i z e and s t r u c t u r e o f t h e s u r f a c e l a y e r on a l a t e x i n c l u d e a t l e a s t t h e i o n i c s t r e n g t h , s u r f a c t a n t t y p e and s u r f a c t a n t c o n c e n t r a t i o n (.11) . When t h e s u r f a c t a n t c o n c e n t r a t i o n was r e d u c e d 100 f o l d a t c o n s t a n t phosphate b u f f e r c o n c e n t r a t i o n , t h e s i z e dependence o f t h e d i f f e r e n t i a l viscometer response t o i n j e c t i o n s o f p o l y s t y r e n e l a t e x from 29 nm t o 913 nm was unchanged. These r e s u l t s i n d i c a t e t h a t s i z e o f t h e s u r f a c e l a y e r does n o t depend s t r o n g l y on surfactant concentration. The Tf p o f 300 nm and 913 nm d i a m e t e r p o l y s t y r e n e l a t e x was the same i n 0.002% B r i j 35 and 0.0005% SLS w i t h 2 mM NaH P0 and i n 0.1% SLS w i t h 2 mM NaH P0 ( F i g u r e 6). However, below 100 nm i n d i a m e t e r t h e i n c r e a s e i n Tf as a f u n c t i o n o f n o m i n a l d i a m e t e r was s l i g h t l y g r e a t e r i n t h e s o l u t i o n w i t h B r i j 35. These r e s u l t s ( F i g u r e 6) suggest t h a t SLS may have a s l i g h t l y s m a l l e r s u r f a c e layer thickness. The i o n i c s t r e n g t h i s a l s o known t o a f f e c t t h e s t r u c t u r e and t h i c k n e s s o f t h e s u r f a c e l a y e r on a c o l l o i d . However, f o r t h e a p p l i c a t i o n o f v i s c o m e t r y t o HDC, t h i s dependence would n o t be important because o f t h e r e q u i r e m e n t t h a t t h e i o n i c s t r e n g t h be kept c o n s t a n t t o m a i n t a i n t h e c a l i b r a t i o n o f HDC columns. I t would be p o s s i b l e t o c a l i b r a t e t h e v i s c o m e t e r so t h a t v i s c o m e t e r response was c o r r e c t e d from t h e e f f e c t i v e volume t h e p a r t i c l e s occupy i n HDC e l u e n t t o a volume more r e f l e c t i v e o f t h e d i a m e t e r a s s i g n e d u s i n g TEM o r photon c o r r e l a t i o n s p e c t r o s c o p y i n s o l u t i o n s w i t h o u t SLS o r B r i j 35 p r e s e n t . S

2

2

4

g


4



322

L i m i t a t i o n s i n t h e Performance o f t h e V i s c o m e t e r . However, f u r t h e r i n v e s t i g a t i o n o f the p r a c t i c a l u t i l i t y o f viscometry f o r p a r t i c l e d e t e c t i o n was not u n d e r t a k e n because o f o t h e r l i m i t a t i o n s i n t h e performance o f t h e V i s c o t e k d i f f e r e n t i a l v i s c o m e t e r . The s h o r t term s i g n a l t o n o i s e r a t i o and l o n g term s t a b i l i t y o f t h e viscometer s u f f i c e d t o permit p r e l i m i n a r y e v a l u a t i o n o f the u t i l i t y of viscometry. I t i s not c e r t a i n t h a t t h e d i f f e r e n t i a l v i s c o m e t e r s i g n a l t o n o i s e a n d s t a b i l i t y would p e r m i t a c c u r a t e size distribution calculation. Another l i m i t a t i o n i n t h e p e r f o r m a n c e o f t h e V i s c o t e k d i f f e r e n t i a l v i s c o m e t e r f o r c h r o m a t o g r a p h i c a n a l y s e s was t h e b r o a d e n i n g o f peaks by t h e v i s c o m e t e r . The b r o a d e n i n g due t o t h e v i s c o m e t e r i t s e l f was s t u d i e d by i n j e c t i n g a s o l u t i o n o f 0.2% B r i j 35 and 0.05% SLS s u r f a c t a n t when 0.002% B r i j 35, 0.005% SLS w i t h 2 mM NaH P0 e l u e n t was b e i n g pumped t h r o u g h t h e HDC column. R e s u l t s were c o l l e c t e d w i t h b o t h t h e v i s c o m e t e r a n d t h e s p e c t r o p h o t o m e t r i c d e t e c t o r l o c a t e d a f t e r t h e v i s c o m e t e r . The f u l l w i d t h a t h a l f maximum (FWHM) o f t h e peak from t h e s u r f a c t a n t s was measured t o be 20 s e c w i t h an e l u t i o n time o f 614 seconds a s d e t e c t e d a t 210 nm w i t h a f l o w r a t e o f 1 mL/min. The FWHM f o r t h e same peak was 23 s e c as measured b y t h e v i s c o m e t e r . At a flow r a t e o f 0.5 mL/min, t h e FWHM o f t h e absorbance peak was 40 s e c a t an e l u t i o n t i m e o f 1248 s e c w h i l e t h e FWHM was 44 s e c a s d e t e c t e d by t h e v i s c o m e t e r . C l e a r l y the a d d i t i o n a l broadening by the v i s c o m e t e r cannot be due t o t h e dead volume o f t h e v i s c o m e t e r because t h e peak w i d t h was narrower f o r t h e s p e c t r o p h o t o m e t r i c d e t e c t o r which was l o c a t e d a f t e r t h e v i s c o m e t e r . A l s o , t h e r e was a s l i g h t r e d u c t i o n i n t h e r e l a t i v e d i f f e r e n c e i n t h e peak w i d t h s f o r t h e two d e t e c t o r s when t h e f l o w r a t e was d e c r e a s e d . This suggests t h a t the broadening observed with the V i s c o t e k d i f f e r e n t i a l v i s c o m e t e r i s t h e consequence o f t h e response t i m e o f t h e d i f f e r e n t i a l p r e s s u r e t r a n s d u c e r . F o r HDC where t h e f r a c t i o n a t i o n power o f t h e column j u s t s u f f i c e s t o p e r m i t a u s e f u l s i z e s e p a r a t i o n , b r o a d e n i n g by t h e d e t e c t o r as was o b s e r v e d w i t h t h e V i s c o t e k v i s c o m e t e r c a u s e s an u n a c c e p t a b l e l o s s o f r e s o l u t i o n . D e c o n v o l u t i o n o f t h e d e t e c t o r b r o a d e n i n g , which i s commonly p r a c t i c e d when t h i s d e t e c t o r i s used i n g e l p e r m e a t i o n chromatography, cannot remedy t h i s d e f i c i e n c y . The chromatograms a r e a l r e a d y d e c o n v o l v e d t o remove as much b r o a d e n i n g as i s f e a s i b l e (6.) . F o r o t h e r t e c h n i q u e s , such as F F F and g e l p e r m e a t i o n chromatography which have g r e a t e r r e s o l v i n g power, t h i s b r o a d e n i n g may not be s i g n i f i c a n t , b u t s h o u l d be c o n s i d e r e d when using the V i s c o t e k d e t e c t o r . 2

4

CONCLUSION The a p p l i c a t i o n o f v i s c o m e t r i c d e t e c t i o n t o c o l l o i d a l p a r t i c l e s e p a r a t i o n t e c h n i q u e s has been f o u n d t o be more complex t h a n t h e E i n s t e i n v i s c o s i t y law s u g g e s t s . Although v i s c o m e t r i c d e t e c t i o n was found t o meet one o f t h e two c r i t e r i a o f t h e i d e a l p a r t i c l e q u a n t i t a t i o n d e t e c t o r , independence from p a r t i c l e composition, an i n c r e a s e i n tj p o f 30% as t h e d i a m e t e r o f t h e l a t e x d e c r e a s e d from 100 nm t o 30 nm was o b s e r v e d . E v i d e n c e from photon c o r r e l a t i o n S


20.



323

s p e c t r o s c o p y and v i s c o m e t r y s u g g e s t s t h i s s i z e dependence i s t h e consequence o f a 1.5 nm t h i c k s u r f a c e l a y e r i n HDC e l u e n t . This s i z e dependence does n o t p r e c l u d e t h e a p p l i c a t i o n o f v i s c o m e t r y for p a r t i c l e q u a n t i t a t i o n , p a r t i c u l a r l y f o r p a r t i c l e s with d i a m e t e r g r e a t e r t h a n 100 nm where t h e i j was o b s e r v e d t o be c o n s t a n t w i t h i n 10% o u t t o p a r t i c l e d i a m e t e r s o f 913 nm. However, t h e m i n i m a l s e n s i t i v i t y and l o n g time response o f c u r r e n t p r e s s u r e t r a n s d u c e r technology l i m i t t h e u t i l i t y o f viscometer f o r use with HDC. I f more s e n s i t i v e t r a n s d u c e r s were d e v e l o p e d , v i s c o m e t r y s h o u l d be r e c o n s i d e r e d as t h i s d e t e c t i o n scheme c o u l d g r e a t l y enhance t h e a c c u r a c y o f s i z e d e t e r m i n a t i o n s u s i n g p a r t i c l e s i z e s e p a r a t i o n methods by p r o v i d i n g c o m p o s i t i o n , and a t l e a s t above 100 nm i n d i a m e t e r , s i z e independent d e t e c t i o n .


s p

Literature Cited 1. Vold, R. D.; Vold, M. J. Colloid and Interface Chemistry; Addison-Wesley: Reading 1983; p. 347. 2. Abbott, S. D.; Yau, W. W. U.S. Patent 4 578 990, 1986. 3. Chamberlin, A.; Tuinstra, H. E. J. Applied Polymer Sci. 1988, 35, 1667-82. 4. Haney, M. A. U.S. Patent 4 463 598, 1984. 5. Haney, M. A. J. Applied Polymer Sci. 1985, 30, 3023-36. 6. McGowan, G. R.; Langhorst, M. A. J. of Colloid and Interface Sci. 1982, 89, 94-106. 7. Brandrup, J . ; Immergut, E. H. Polymer Handbook, 2nd ed.; Wiley: New York, 1975. 8. Nagy, D. J. Anal. Chem. 1989, 61, 1934-37. 9. Kato, T.; Nakamura, K.; Kawaguchi, M.; Takahashi, A. Polymer J . , 1981, 13, 1037-1043. 10. McHugh, A. J. CRC Critical Rev. in Anal. Chem. 1984, 15, 63-117. 11. Hiemenz, P. C. Principles of Colloid and Surface Chemistry; Marcel Dekker: New York, 1977; pp. 62-75. RECEIVED

M a r c h 5, 1991


Particle Size Distribution II - American Chemical Society

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