Overview of Colloidal Aggregation by Sedimentation Field-Flow

Chapter 14

Overview of Colloidal Aggregation by Sedimentation Field-Flow Fractionation 1

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.ch014

Bhajendra N. Barman and J. Calvin Giddings Field-Flow Fractionation Research Center, Department of Chemistry, University of Utah, Salt Lake City, UT 84112

Sedimentation field-flow fractionation (SdFFF) is shown to have an extraordinary ability to probe aggregation phenomena and to track particle size distribution changes caused by aggregation in colloidal samples. This technique separates particles and particulate clusters based on particle mass and provides equal-mass fractions that can be further characterized by electron microscopy. The effects of experimental parameters such as flow rate and field strength on the resolution and speed of aggregate fractionation are examined here. Details are provided for the application of SdFFF to: (a) detection of both trace and large amounts of aggregated clusters, (b) monitoring of latex clusters broken up by sonication and formed by the addition of appropriate surfactant, and (c) tracking changes in the relative population of clusters due to aging. C o l l o i d a l or particulate aggregation is c o m m o n i n many industrial, biological, and environmental materials. T h e p h y s i c a l state o f a suspension o f i n d i v i d u a l particulate entities i s perturbed due to cluster f o r m a t i o n i n these m a t e r i a l s . A s a c o n s e q u e n c e o f t h i s , the apparent p a r t i c l e s i z e c h a n g e s a n d at the same t i m e b u l k p r o p e r t i e s that d e p e n d o n the p a r t i c l e s i z e d i s t r i b u t i o n are a l t e r e d , thus a f f e c t i n g t h e q u a l i t y a n d p e r f o r m a n c e o f the m a t e r i a l . T h e r e f o r e m e t h o d s that p r o v i d e b o t h a d e t a i l e d s i z e c h a r a c t e r i z a t i o n o f a g g r e g a t e d s a m p l e s a n d a u g m e n t the understanding o f aggregation phenomena h a v e great practical importance. The unique capability o f sedimentation field-flow fractionation ( S d F F F ) a p p l i e d to the p r o b l e m o f l o w o r d e r c o l l o i d a l a g g r e g a t i o n l i e s l a r g e l y i n i t s a b i l i t y t o p r o v i d e the h i g h - r e s o l u t i o n m a s s - b a s e d separation o f i n d i v i d u a l aggregated clusters according to w e l l - d e f i n e d principles.

L

Current address: FFFractionation, Inc., P . O . Box 58718, Salt Lake City, U T 84158-0718

0097-6156/91/0472-0217S06.00/0 © 1991 American Chemical Society

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


218

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

T h e S d F F F f r a c t o g r a m (plot o f detector s i g n a l v e r s u s t i m e ) o f monodisperse p o p u l a t i o n s that h a v e u n d e r g o n e a g g r e g a t i o n c o n s i s t s o f well-resolved p e a k s o f s i n g l e t , d o u b l e t , a n d h i g h e r o r d e r aggregates. S u c h a fractogram p r o v i d e s d i r e c t a n d d e t a i l e d i n f o r m a t i o n o n the p h y s i c a l state o f a g g r e gation. T h e r e l a t i v e peak areas, f o r e x a m p l e , reflect the amounts o f v a r i o u s aggregates i n the s a m p l e ; c h a n g e s i n peak areas s h o w h o w the populations o f different clusters change w i t h t i m e , w i t h altered c o n d i tions, or with processing. A n o t h e r advantage o f S d F F F i n the study o f a g g r e g a t i o n i s that it p r o v i d e s i s o l a t e d f r a c t i o n s o f constant p a r t i c l e m a s s (e.g., d o u b l e t s i n one f r a c t i o n , t r i p l e t s i n another) that c a n be s u b j e c t e d to a d d i t i o n a l c h a r a c terization by electron microscopy ( E M ) or other tools. B y combining S d F F F w i t h E M , it i s p o s s i b l e to correlate p a r t i c l e mass (obtained f r o m S d F F F retention) with morphology and dimensions (from E M ) , invaluable i n f o r mation in describing complex aggregates. I n recent p u b l i c a t i o n s w e h a v e d e m o n s t r a t e d that the p r e s e n c e of d i f f e r e n t s i z e d l a t e x aggregates c a n be e a s i l y e s t a b l i s h e d b y t h e i r s e p a r a t i o n i n an S d F F F system ( 1 - 3 ) . Aggregation is confirmed by retention c a l c u l a t i o n s that e s t a b l i s h a p p r o x i m a t e c l u s t e r mass a n d b y the E M e x a m i n a t i o n o f the f r a c t i o n s c o l l e c t e d f r o m each e l u t e d p e a k . A number of c o m m e r c i a l l y available polymethylmethacrylate ( P M M A ) latex samples w e r e f o u n d to h a v e c l u s t e r s c o m p o s e d o f m u l t i p l e s o f monodisperse primary particles. B o t h e x p e r i m e n t a l a n d t h e o r e t i c a l s t u d i e s r e l a t e d to the f o r m u l a t i o n o f r e s o l u t i o n c r i t e r i a ( 1 ) a n d aggregate p o l y d i s p e r s i t y ( 2 J w e r e c a r r i e d out w i t h these s a m p l e s . I n t h i s study w e report representative S d F F F results that s h o w the a b i l i t y o f F F F m e t h o d o l o g y to t r a c k changes i n c l u s t e r (apparent p a r t i c l e s i z e ) d i s t r i b u t i o n c a u s e d by v a r i a b l e l e v e l s o f a g g r e g a t i o n i n s o m e m o n o d i s p e r s e P M M A and p o l y s t y r e n e ( P S ) latex s a m p l e s . T h e scope and l i m i t a t i o n s o f t h i s m e t h o d f o r the c h a r a c t e r i z a t i o n o f aggregates f r o m p o l y disperse s a m p l e s are a l s o d i s c u s s e d . T h e application o f S d F F F for detecting trace l e v e l s as w e l l as l a r g e p o p u l a t i o n s o f aggregates i n c o l l o i d a l d i s p e r sions is e m p h a s i z e d . T h e m e t h o d i s demonstrated i n m o d e l studies i n v o l v i n g the m o n i t o r i n g o f l a t e x c l u s t e r s b r o k e n u p b y u l t r a s o n i c a t i o n a n d f o r m e d b y the a d d i t i o n o f s e l e c t i v e s u r f a c t a n t , a n d f o r t r a c k i n g c h a n g e s i n the r e l a t i v e p o p u l a t i o n o f c l u s t e r s due to a g i n g . The importance o f e x p e r i m e n t a l S d F F F parameters s u c h as c a r r i e r f l o w rate a n d f i e l d strength i n c a r r y i n g out these studies i s a l s o e s t a b l i s h e d . E x a m p l e s are p r o v i d e d s h o w i n g the effects o f a p p l i e d f i e l d and f l o w rate o n the r e s o l u t i o n a n d speed o f aggregate separation. Theory T h e t h e o r y o f s e d i m e n t a t i o n F F F d e s c r i b i n g the f r a c t i o n a t i o n a n d r e s o l u t i o n o f c o l l o i d a l aggregates c a n be f o u n d e l s e w h e r e ( 1 , 2 ) . H o w e v e r , a few e s s e n t i a l e l e m e n t s are a d d r e s s e d here f o r completeness. T h e basic retention equation i n F F F (applicable generally whether the f i e l d i s s e d i m e n t a t i o n , e l e c t r i c a l , c r o s s flow, etc.) relates r e t e n t i o n volume V to the t h e o r e t i c a l l y o b t a i n e d r e t e n t i o n p a r a m e t e r X as follows r


14.

B A R M A N & GIDDINGS

219

Colloidal Aggregation by Sedimentation FFF

w h e r e V ° i s the c h a n n e l v o i d v o l u m e . E q u a t i o n 2 relates the parameter X to p a r t i c l e mass m o r p a r t i c l e d i a m e t e r d (for s p h e r i c a l p a r t i c l e s ) i n a f o r m that a p p l i e s s p e c i f i c a l l y to s e d i m e n t a t i o n F F F

X=

k

6kT

T

mwGlA l/p


P

s

w

w

G

|

A

p

l

d

3

(2)

w h e r e k is the B o l t z m a n n constant, T i s the absolute temperature, G i s the c e n t r i f u g a l a c c e l e r a t i o n , w i s the c h a n n e l t h i c k n e s s , p is the p a r t i c l e d e n s i t y , and A p is the d i f f e r e n c e i n d e n s i t y b e t w e e n the p a r t i c l e a n d carrier liquid. F o r n o n s p h e r i c a l p a r t i c l e s , d i s the e f f e c t i v e s p h e r i c a l diameter. F o r h i g h l e v e l s o f r e t e n t i o n , X is s m a l l and the f o l l o w i n g a p p r o x i m a t i o n to E q u a t i o n 1 is v a l i d s

F r o m E q u a t i o n s 2 a n d 3 w e f i n d that the r e t e n t i o n v o l u m e (therefore r e t e n t i o n t i m e ) i s a p p r o x i m a t e l y p r o p o r t i o n a l to p a r t i c l e m a s s . Since p a r t i c l e c l u s t e r s i n an aggregated s a m p l e w i l l d i f f e r f r o m one a n o t h e r b y one e l e m e n t a r y p a r t i c l e m a s s , S d F F F s h o u l d p r o v i d e a series o f p e a k s w i t h n e a r l y e q u a l s p a c i n g f o r the l o w o r d e r aggregates o f a m o n o d i s p e r s e latex population. S u c h r e g u l a r l y spaced peaks are i l l u s t r a t e d i n F i g u r e 1 f o r aggregated P M M A l a t e x . T h e s u c c e s s i v e p e a k s i n the S d F F F f r a c t o g r a m c o r r e s p o n d to s i n g l e t s , d o u b l e t s , t r i p l e t s , a n d so o n . T h e a b o v e e q u a t i o n s are f o r " n o r m a l " S d F F F o p e r a t i o n w h e r e the centrifugal Held is opposed by B r o w n i a n motion w h i c h drives particles a w a y f r o m the a c c u m u l a t i o n w a l l to y i e l d a steady state p a r t i c l e c l o u d o r layer (£). T h e l a y e r t h i c k n e s s , d i f f e r i n g f r o m c o m p o n e n t to c o m p o n e n t , d e p e n d s u p o n the i n t e r a c t i o n o f the c o l l o i d a l c o m p o n e n t w i t h the c e n t r i f u g a l f i e l d and u p o n the o p p o s i n g B r o w n i a n m o t i o n . I n the n o r m a l m o d e , s a m p l e p a r t i c l e s i z e d ( u s u a l l y s u b m i c r o n ) is less t h a n the m e a n l a y e r t h i c k n e s s I (often 2 - 2 0 um). Steric perturbations b e c o m e apparent w i t h i n c r e a s i n g p a r t i c l e d i a m e t e r as the i n c r e a s i n g d a p p r o a c h e s the d e c r e a s i n g I. I n t h i s s i t u a t i o n , the p o s i t i o n o f p a r t i c l e s i n the f l o w stream is determined both by their physical size and by their B r o w n i a n m o t i o n . A s a c o n s e q u e n c e o f t h i s d u a l i n f l u e n c e , p a r t i c l e s e l u t e e a r l i e r t h a n the " n o r m a l " mechanism w o u l d have allowed. A s has b e e n p o i n t e d out e l s e w h e r e , the s t e r i c e f f e c t i s p a r t i c u l a r l y s i g n i f i c a n t f o r a g g r e g a t e s w h i c h can have relatively large and extended configurations ( J J . The n o r m a l S d F F F r e t e n t i o n equations ( E q u a t i o n s 1 a n d 3) c a n be m o d i f i e d to i n c o r p o r a t e the s t e r i c m e c h a n i s m to y i e l d

y'

where

d ' i s an e f f e c t i v e

factor o f

v°

6X+ 3yd'/w

p a r t i c l e d i a m e t e r and y

w

is the

steric

correction

order unity


220


Combining Equations 2

and 4,

v —


r

we

obtain

AmG 1 + BTd'mG

5

w h e r e A a n d B are constants. T h e s e c o n d t e r m i n the d e n o m i n a t o r results f r o m the i n c o r p o r a t i o n o f steric p e r t u r b a t i o n s . I f steric effects were n e g l i g i b l e , this term, for a l l practical purposes, w o u l d v a n i s h . I n t h i s case one w o u l d e x p e c t the retention v o l u m e o r t i m e to be p r o p o r t i o n a l e i t h e r to p a r t i c l e mass m at constant f i e l d strength G , o r to G f o r a p a r t i c u l a r c l u s t e r s i z e o f a f i x e d mass. W e note that f i e l d p r o g r a m m i n g i s not used i n t h i s study. Field p r o g r a m m i n g i s e s s e n t i a l to f r a c t i o n a t e b r o a d p a r t i c l e p o p u l a t i o n s ( w h e r e p a r t i c l e d i a m e t e r s v a r y w i d e l y ) to m i n i m i z e r u n t i m e ( 6 - 9 ) . However, resolution is generally sacrificied i n a field-programmed run (£). For c o l l o i d a l a g g r e g a t e s , the e f f e c t i v e s p h e r i c a l d i a m e t e r s o f d o u b l e t s , t r i p l e t s , q u a d r u p l e t s , and q u i n t u p l e t s are 1.26, 1.44, 1.59, a n d 1.71 t i m e s the diameter of singlets, respectively. S i n c e the e f f e c t i v e s p h e r i c a l d i a m e t e r s o f the s u c c e s s i v e h i g h e r o r d e r c l u s t e r s d i f f e r o n l y s l i g h t l y , h i g h r e s o l u t i o n r u n c o n d i t i o n s u s i n g a c o n s t a n t f i e l d s t r e n g t h are p r e f e r a b l e f o r r e s o l v i n g these aggregates. Experimental T h r e e S d F F F systems were used i n this study. S y s t e m I is a m o d e l S 1 0 1 sedimentation F F F instrument from F F F r a c t i o n a t i o n , Inc. (Salt L a k e C i t y , UT). I n this apparatus a c h a n n e l 0 . 0 2 5 4 c m t h i c k , 89.4 c m l o n g , and 1.90 c m i n breadth i s u s e d . T h e distance between the c h a n n e l a n d a x i s o f r o t a t i o n i s 15.1 c m . T h e c h a n n e l v o i d v o l u m e m e a s u r e d as the e l u t i o n v o l u m e o f a nonretained s o d i u m benzoate peak is 4.25 m L . T h e sample a c c u m u l a t i o n w a l l is a h i g h l y p o l i s h e d stainless steel s u r f a c e . T h i s system w a s c o u p l e d w i t h a M o d e l 8815 I s o C h r o m i s o c r a t i c p u m p f r o m S p e c t r a p h y s i c s ( S a n Jose, C A ) and a M o d e l 153 U V detector f r o m B e c k m a n Instruments ( B e r k e l e y , C A ) . T h e detector response w a s r e c o r d e d and c o l l e c t e d b y b u i l t - i n S d F F F data c o l l e c t i o n a n d a n a l y s i s s o f t w a r e (FFFractionation, Inc.). S y s t e m II i s an apparatus s i m i l a r i n m o s t t e c h n i c a l respects to the s y s t e m I i n s t r u m e n t and w a s d e s c r i b e d e l s e w h e r e ( 1 , 1 Q ) . T h e apparatus c o n s i s t s o f a s i n g l e i n l e t a n d t w o o u t l e t s , the latter c a p a b l e o f p r o v i d i n g s t r e a m - s p l i t t i n g at the o u t l e t e n d o f the c h a n n e l to e n h a n c e d e t e c t o r signal ( U J . T h e system II c h a n n e l has a l e n g t h o f 90.5 c m , t h i c k n e s s 0 . 0 2 5 4 c m , breadth 2.0 c m , radius o f rotation 15.3 c m , and a v o i d v o l u m e o f 4.50 m L . T h e sample accumulation w a l l i n this channel consists o f a h i g h l y p o l i s h e d H a s t e l l o y C surface. In t h i s s y s t e m , a B e c k m a n U V d e t e c t o r w o r k i n g at 2 5 4 n m was u s e d ; the d e t e c t o r response w a s t r a n scribed onto a Houston Instrument ( A u s t i n , T X ) strip chart recorder. T h e t h i r d S d F F F system (III) consists o f a l l the c o m p o n e n t s o f the s y s t e m I apparatus e x c e p t f o r the c h a n n e l , w h i c h w a s r e p l a c e d b y a n e w c h a n n e l w i t h the same n o m i n a l d i m e n s i o n s as the s y s t e m I c h a n n e l but w i t h a measured v o i d v o l u m e o f 4.52 m L . T h r e e P M M A samples w e r e a n a l y z e d i n this w o r k . A n o m i n a l 0.230 U m latex sample was obtained from Seradyn (Indianapolis, I N ) . Another s a m p l e , a n o m i n a l 0.207 \im P M M A latex, w a s a gift f r o m D r . T . P r o v d e r o f


14.



221


The Glidden Company (Strongsville, O H ) . A third P M M A sample obtained f r o m P o l y s c i e n c e s ( W a r r i n g t o n , P A ) w a s r e p o r t e d to h a v e p a r t i c l e d i a m e t e r o f 0 . 3 2 5 am. T h e p o l y s t y r e n e sample used i n t h i s study is a b l e n d e d m i x t u r e o f f o u r d i s t i n c t p o p u l a t i o n s ( 0 . 2 2 5 , 0 . 5 5 1 , 1.003, a n d 1.347 u m ) , and w a s s u p p l i e d b y S e r a d y n as a p o l y d i s p e r s e P S s a m p l e w i t h n o m i n a l d i a m e t e r o f 0.478 ±. 0.215 u m . T h e c a r r i e r u s e d f o r the latex a n a l y s i s w a s d o u b l y d i s t i l l e d w a t e r c o n t a i n i n g 0 . 0 5 % ( w / v ) s o d i u m d o d e c y l sulfate ( S D S ) a n d 0 . 0 1 % (w/v) sodium azide. Results

and

Discussion

O p t i m i z a t i o n o f F i e l d Strength and F l o w rate. A c c o r d i n g to E q u a t i o n s 2 and 3, w e p r e d i c t that the r e t e n t i o n v o l u m e (and c o n s e q u e n t l y the r e t e n t i o n t i m e ) o f a p a r t i c u l a r c l u s t e r w i l l i n c r e a s e p r o p o r t i o n a t e l y w i t h an increase i n centrifugal f i e l d strength. N o r m a l F F F theory also predicts that the r e s o l u t i o n b e t w e e n s u c c e s s i v e c l u s t e r p e a k s w i l l be h i g h e r i n the f r a c t o g r a m o b t a i n e d w i t h a h i g h e r c e n t r i f u g a l f i e l d ( h i g h e r r p m ) ( £ , 123. T h e effect o f f i e l d strength o n the f r a c t i o n a t i o n and r e s o l u t i o n o f 0 . 2 0 7 [ i m P M M A aggregates i n system I is i l l u s t r a t e d i n F i g u r e 1. T h e three r e p r e sentative fractograms i n this figure were obtained w i t h different field strengths at a constant f l o w rate o f 1.10 m L / m i n . W e o b s e r v e that the a b o v e p r e d i c t i o n s are a p p a r e n t l y v a l i d f o r the e a r l i e r e l u t i n g a g g r e g a t e s . H o w e v e r , m a j o r d e p a r t u r e s , i n c l u d i n g the l o s s o f r e s o l u t i o n f o r l a r g e r s i z e aggregates, are o b s e r v e d that c a n be attributed to steric effects (1,11). P r e v i o u s l y w e s t u d i e d the d e p e n d e n c e o f r e t e n t i o n v o l u m e o n the f l o w rate at constant f i e l d (1). F o r this w e plotted e x p e r i m e n t a l data o f V / V ° against a g g r e g a t i o n n u m b e r n , p r o p o r t i o n a l to c l u s t e r m a s s . We o b s e r v e d s i g n i f i c a n t d e v i a t i o n s f r o m the e q u a t i o n s o f n o r m a l S d F F F , w h i c h p r e d i c t that V is independent o f f l o w rate (see E q u a t i o n s 1-3). The d e v i a t i o n s w e r e a t t r i b u t e d to the v e l o c i t y d e p e n d e n c e o f the s t e r i c c o r r e c t i o n f a c t o r y w h i c h reflects h y d r o d y n a m i c l i f t f o r c e e f f e c t s . F o r an i n t e r p r e t a t i o n o f the a n o m a l o u s b e h a v i o r , a n e q u a t i o n v a l i d f o r c o n s t a n t field o p e r a t i o n s i m i l a r to E q u a t i o n 5 w a s u s e d . r

r

A c c o r d i n g to E q u a t i o n 5, w e e x p e c t a s i g n i f i c a n t d e v i a t i o n f r o m a l i n e a r d e p e n d e n c e o f Y o n G as G is increased. T h i s is p a r t i c u l a r l y true f o r l a r g e s i z e c l u s t e r s f o r w h i c h s e r i o u s s t e r i c p e r t u r b a t i o n s are e x p e c t e d to result i n a negative curvature i n the plot o f V versus G . T h e plots for the singlets and s i x clusters o f 0.207 \im P M M A beads are s h o w n i n F i g u r e 2. R e p r e s e n t a t i v e f r a c t o g r a m s i l l u s t r a t i n g the e f f e c t o f c a r r i e r f l o w rate o n c l u s t e r r e s o l u t i o n f o r the 0 . 2 3 0 \im P M M A latex are p r o v i d e d i n F i g u r e 3. F r a c t o g r a m s a, b , and c were obtained f r o m s y s t e m II at a constant field o f 4 2 . 8 g r a v i t i e s but w i t h c a r r i e r f l o w rates o f 1.73, 1.23, and 0.44 m L / m i n , r e s p e c t i v e l y . A considerable loss o f resolution w i t h i n c r e a s i n g f l o w rate is o b s e r v e d i n these f r a c t o g r a m s . T h e s e results are c o n s i s t e n t w i t h the r e s o l u t i o n c r i t e r i a d e v e l o p e d i n e a r l i e r w o r k w h e r e w e p r e d i c t e d that s h a r p e r peaks a n d better r e s o l u t i o n c a n be a c h i e v e d b y d e c r e a s i n g the c a r r i e r l i q u i d flow rates (1). T h e loss o f r e s o l u t i o n at h i g h e r flow c o n d i t i o n s c a n be a t t r i b u t e d to n o n e q u i l i b r i u m b a n d broadening (1_, 23. to a s t e r i c m e c h a n i s m p a r t i c u l a r l y f o r l a r g e r c l u s t e r s i z e s (1), a n d to the peak b r o a d e n i n g effects o f the f i n i t e p o l y d i s p e r s i t y o f the p r i m a r y latex p a r t i c l e s a n d thus o f the clusters (2). r

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F i g u r e 1. F r a c t o g r a m s o f p a r t i a l l y aggregated n o m i n a l 0 . 2 0 7 | i m P M M A latex spheres o b t a i n e d w i t h S d F F F s y s t e m I at d i f f e r e n t field strengths ( e x p r e s s e d as n u m b e r o f g r a v i t i e s g) w i t h a c o n s t a n t f l o w rate o f 1.10 + 0.02 m L / m i n . T h e n u m b e r o f spheres p e r c l u s t e r i s s h o w n as n . S a m p l e v o l u m e s : (a) 4 0 | i L , (b) 45 u L , and (c) 4 0 u . L .

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50

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FIELD STRENGTH F i g u r e 2. Plots of gravities) for seven identified by their w i t h S d F F F system I

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r e t e n t i o n v o l u m e v e r s u s f i e l d strength ( i n d i f f e r e n t c l u s t e r s o f 0 . 2 0 7 n m P M M A l a t e x spheres aggregation number n . Fractograms were obtained at a c a r r i e r flow rate o f 1.10 + 0.03 m L / m i n .



14.


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F i g u r e 3. F r a c t o g r a m s o f n o m i n a l 0.230 u.m P M M A l a t e x aggregates o b t a i n e d w i t h S d F F F s y s t e m II w i t h d i f f e r e n t f l o w c o n d i t i o n s . Field strength was kept constant at 42.8 g. Sample volumes: (a) 20 u . L , (b) u.L, and (c) 14 j i L .


15

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F r o m b o t h F i g u r e s 1 a n d 3 , w e f i n d that the shorter r u n t i m e i n s e d i m e n t a t i o n F F F is c o m p r o m i s e d w i t h a l o w e r r e s o l u t i o n l e v e l . However, it i s e x p e c t e d that g o o d r e s o l u t i o n o f the l o w - o r d e r aggregates c a n b e o b t a i n e d at h i g h speed b y m o d e r a t e increases i n G a n d l a r g e i n c r e a s e s i n f l o w rate. S c o n e o f the A n a l y s i s o f A g g r e g a t e d S a m p l e s b v S d F F F . Aggregates from b o t h m o n o d i s p e r s e and p o l y d i s p e r s e samples c a n be a n a l y z e d b y S d F F F . So f a r , o u r a t t e n t i o n has been f o c u s s e d p r i m a r i l y o n l a t e x aggregates formed f r o m m o n o d i s p e r s e latex beads f o r s i m p l i c i t y . L a t e x aggregates h a v e f i x e d c o m p o s i t i o n a n d d e n s i t y and therefore t h e i r s e p a r a t i o n b y S d F F F is b a s e d a p p r o x i m a t e l y o n p a r t i c l e mass a c c o r d i n g to E q u a t i o n s 2 and 3. Moreover, the l o w p o l y d i s p e r s i t y o f the p r i m a r y l a t e x p a r t i c l e s m i n i m i z e s b a n d broadening and provides better resolution between successive cluster p e a k s (2J. T h e areas o f w e l l separated c l u s t e r peaks p r o v i d e a c l e a r p i c t u r e o f the extent o f a g g r e g a t i o n i n s u c h s a m p l e s . T h e S d F F F a n a l y s i s o f aggregates r e s u l t i n g f r o m p o l y d i s p e r s e samples i s m o r e d i f f i c u l t . C l u s t e r s o f a g i v e n mass e l u t i n g at a s p e c i f i e d t i m e w i l l a c c o m p a n y c l u s t e r s o f the same m a s s w i t h d i f f e r e n t a g g r e g a t i o n numbers and elementary particle size. ( M i x e d clusters made up o f different s i z e d e l e m e n t a r y p a r t i c l e s are l i k e l y to be f o u n d as w e l l . ) As a r e s u l t o f the a g g r e g a t i o n , the e l u t i o n p r o f i l e a n d p a r t i c l e s i z e d i s t r i b u t i o n o f the aggregated p o p u l a t i o n w i l l be d i f f e r e n t f r o m those o f the o r i g i n a l polydisperse nonaggregated sample. H o w e v e r , a c l e a r p i c t u r e o f the d e t a i l s o f a g g r e g a t i o n w i l l not e m e r g e u n l e s s f r a c t i o n s are c o l l e c t e d f o r e x a m i n a t i o n b y o t h e r m e a n s s u c h as e l e c t r o n m i c r o s c o p y . A s noted e a r l i e r , S d F F F p r o v i d e s f r a c t i o n s o f e q u a l m a s s that c a n t h e n be c h a r a c terized structurally and d i m e n s i o n a l l y by E M . T h e f r a c t o g r a m s s h o w n i n F i g u r e s 1 a n d 3 i n d i c a t e d that the 0 . 2 0 7 and 0.230 u m P M M A s a m p l e s are e x t e n s i v e l y aggregated. H o w e v e r it i s p o s s i b l e to o b s e r v e v e r y s m a l l a m o u n t s o f aggregated c l u s t e r s b y s e d i m e n t a t i o n F F F i f the p r i m a r y p a r t i c l e s are m o n o d i s p e r s e and thus p r o v i d e separate c l u s t e r p e a k s . F i g u r e 4 p r o v i d e s an e x a m p l e w h e r e the d o u b l e t s o f the m a j o r c o m p o n e n t o f a b l e n d e d s a m p l e o f f o u r P S beads elute as a separate peak. T h e s a m p l e is reported to be p o l y d i s p e r s e w i t h a m e a n diameter o f 0.478 + 0.215 \im. T h e sample i s s h o w n b y S d F F F ( F i g u r e 4) to consist o f four distinct populations. T h e i r d i a m e t e r s w e r e r e p o r t e d as 0 . 2 2 5 ± 0.004, 0.551 ± 0.011, 1.003 ± 0.017, and 1.347 ± 0.014 n m w i t h n u m b e r fractions o f 0 . 3 1 8 , 0 . 6 2 5 , 0 . 0 4 3 , and 0.014, r e s p e c t i v e l y ( B a n g s , L . B . , Seradyn Inc., Indianapolis, I N , private c o m m u n i c a t i o n , M a r c h 17, 1988). W e note that the r e s o l u t i o n b e t w e e n peaks a c h i e v e d b y S d F F F i s v e r y h i g h . T h e e x p e r i m e n t a l c o n d i t i o n s c h o s e n f o r the f r a c t i o n a t i o n are s u c h that w e c o u l d separate 1.00 and 1.35 \im P S beads b y a v o i d i n g the s t e r i c t r a n s i t i o n n o r m a l l y f o u n d i n that r e g i o n . U s i n g E q u a t i o n s 1 a n d 2 f o r the first f r a c t i o n a n d E q u a t i o n s 2 a n d 4 f o r the rest, w e d e t e r m i n e m e a n d i a m e t e r s o f p a r t i c l e s e l u t i n g at the p o s i t i o n s w h e r e cuts w e r e t a k e n (see F i g u r e 4 ) . T h e f i v e m e a n diameters are as f o l l o w s : 0.20, 0 . 5 2 , 0.64 (for the doublets), 0.89, and 1.2 n m . T h e s e v a l u e s are consistent w i t h but s o m e w h a t s m a l l e r than the r e p o r t e d v a l u e s . F o r a r i g o r o u s c o m p a r i s o n , p a r t i c u l a r l y i n the v i c i n i t y o f 1.0 \im p a r t i c l e s i z e , it m a y be necessary to use y v a l u e s o t h e r than unity.



14.



F i g u r e 4. F r a c t o g r a m s h o w i n g c o m p o n e n t s o f n o m i n a l 0.478 +. 0.215 u.m P S s a m p l e . T h i s b l e n d e d s a m p l e c o n t a i n s trace amounts o f a g g r e g a t e d d o u b l e t s f o r m e d f r o m its m a j o r c o m p o n e n t . Experimental conditions: S d F F F system II was used w i t h a f i e l d strength o f 4 2 . 8 g and a f l o w rate o f 0.97 m L / m i n .


225


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M o d e l Studies I n v o l v i n g Cluster B r e a k u p and F o r m a t i o n . T h e disruption of aggregated species i n the 0.299 \im P M M A s a m p l e b y u l t r a s o n i c a t i o n w a s monitored by S d F F F (14). F o r t h i s , the s a m p l e w a s agitated f o r a s p e c i f i c p e r i o d a n d then a n a l y z e d b y S d F F F . T h e same s a m p l e w a s s o n i c a t e d a g a i n f o r o t h e r s p e c i f i e d p e r i o d s to repeat the a n a l y s i s . T h e effects o f s o n i c a t i o n t i m e o n the b r e a k u p o f aggregated c l u s t e r s are r e f l e c t e d i n the c h a n g i n g e l u t i o n patterns w i t h s o n i c a t i o n t i m e . W i t h these e x p e r i m e n t s w e c o u l d f o l l o w a g r a d u a l d e s t r u c t i o n o f h i g h e r o r d e r aggregates to p r o d u c e a singlet population. W e note that due to the r e m a r k a b l e r e s o l v i n g p o w e r o f S d F F F , i n d i v i d u a l c l u s t e r s w e r e r e s o l v e d a n d the b r e a k u p k i n e t i c s o f these clusters c o u l d be f o l l o w e d i n d e t a i l ( B a r m a n , B . N . ; G i d d i n g s , J . C . L a n g m u i r . to be s u b m i t t e d ) . S e d i m e n t a t i o n F F F w a s a l s o a p p l i e d to t r a c k the f o r m a t i o n o f aggregated species i n P S a n d P M M A p o p u l a t i o n s ( 1 4 . B a r m a n , B . N . ; G i d d i n g s , J . C . L a n g m u i r . to be s u b m i t t e d ) . F o r this purpose, tetra-hexyl a m m o n i u m b r o m i d e ( T H A B ) w a s u s e d as a c a t i o n i c surfactant to i n d u c e the a g g r e g a t i o n o f these n e g a t i v e l y c h a r g e d latex spheres. A n original 0.327 n m P S latex d i s p e r s i o n w a s p r e p a r e d i n s o d i u m d o d e c y l sulfate ( S D S ) s o l u t i o n (0.05% w/v). D i f f e r e n t amounts o f c a t i o n i c surfactant w e r e a d d e d to v i a l s c o n t a i n i n g the o r i g i n a l d i s p e r s i o n a n d m i x e d w e l l . The resulting dispersions w i t h 0 . 1 2 , 0 . 4 5 , a n d 1.03 m M T H A B were f o u n d to be stable ( w i t h o u t observable precipitates or flocculates). T h e sample from each v i a l of stable s u s p e n s i o n w a s subjected to a n a l y s i s b y S d F F F . T h e fractograms o f the o r i g i n a l a n d the three s a m p l e s c o n t a i n i n g d i f f e r e n t a m o u n t s o f T H A B p r o v i d e d d a t a o n the r e l a t i v e i n c r e a s e i n the p o p u l a t i o n o f d o u b l e t s a n d h i g h e r o r d e r aggregates w i t h i n c r e a s i n g a m o u n t o f T H A B i n the c o l l o i d a l dispersion. S i m i l a r results were obtained w h e n different amounts o f T H A B were added i n a m o n o d i s p e r s e 0 . 2 9 9 n m P M M A d i s p e r s i o n c o n t a i n i n g 0 . 0 5 % (w/v) S D S . C h a n g e i n A g g r e g a t e P o p u l a t i o n D u e to A g i n g . T h e d e t e r i o r a t i o n o f latex s a m p l e s u p o n a g i n g was studied b y S d F F F . B y way o f example, two fractograms o f the 0.325 n m P M M A beads o b t a i n e d at t w o d i f f e r e n t t i m e s are s h o w n i n F i g u r e 5. F r a c t o g r a m a w a s o b t a i n e d m o r e t h a n 2.5 years b e f o r e f r a c t o g r a m b. ( W e note that peak p o s i t i o n s d o not c o i n c i d e e x a c t l y because e x p e r i m e n t a l c o n d i t i o n s are s l i g h t l y d i f f e r e n t i n the t w o c a s e s ) . In both f r a c t o g r a m s , p e a k s f o r the s i n g l e t t h r o u g h q u a d r u p l e t c l u s t e r s are o b s e r v e d , f o l l o w e d b y a t a i l i n g e n d f o r the u n r e s o l v e d h i g h e r o r d e r aggregates. A c u r s o r y e x a m i n a t i o n suggests that the p e a k areas o f d o u b l e t s t h r o u g h q u a d r u p l e t s are n e a r l y the s a m e i n these f r a c t o g r a m s . H o w e v e r , the d i f f e r e n c e i n the s i n g l e t peak areas i s q u i t e s i g n i f i c a n t , i n d i c a t i n g a l o s s o f s i n g l e t p o p u l a t i o n due to s a m p l e a g i n g . A m o r e q u a n t i t a t i v e c o m p a r i s o n i s p r o v i d e d b y the n o r m a l i z e d ( w i t h respect to u n i t area) s i z e d i s t r i b u t i o n s o b t a i n e d f r o m the f r a c t o g r a m s o f F i g u r e 5 a n d s h o w n i n F i g u r e 6. The overlaid size distributions of the o r i g i n a l a n d aged s a m p l e s i n d i c a t e that the s i n g l e t t h r o u g h q u a d r u p l e t p e a k p o s i t i o n s are b r o u g h t i n t o r e g i s t r y w h e n c o n v e r t e d to a d i a m e t e r s c a l e , s h o w i n g that n o n e o f the c l u s t e r s has c h a n g e d i n s i z e . The observed c h a n g e s are due i n s t e a d to a g g r e g a t i o n . T h u s the l o s s o f the s i n g l e t p o p u l a t i o n i n the o r i g i n a l s a m p l e ( s h o w n b y the r e d u c e d area o f the s i n g l e t peak i n F i g u r e 6) is r e f l e c t e d i n the i n c r e a s e i n the p o p u l a t i o n s o f d o u b l e t s , t r i p l e t s , a n d h i g h e r o r d e r aggregates. W e n o t e that there are s o m e u n c e r t a i n t i e s (due to s t e r i c effects) i n the c a l c u l a t i o n o f e f f e c t i v e



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ELUTION VOLUME (mL) F i g u r e 5. E f f e c t s o f s a m p l e a g i n g are r e f l e c t e d b y the t w o f r a c t o g r a m s o f n o m i n a l 0.325 u.m d i a m e t e r P M M A latex s a m p l e . T h e sample was run i n (a) A u g u s t , 1 9 8 7 , a n d (b) M a r c h , 1 9 9 0 . E x p e r i m e n t a l c o n d i t i o n s : (a) S d F F F system II w a s used w i t h a f l o w rate o f 0.59 m L / m i n a n d a f i e l d strength o f 19.8 g ; (b) S d F F F system III w a s used w i t h a f l o w rate o f 0.56 m L / m i n a n d a field strength o f 15.2 g.

n=l

EFFECTIVE PARTICLE DIAMETER (/xm) F i g u r e 6. Particle size distributions derived from fractograms o f F i g u r e 5. A portion o f each size distribution curve indicated b y a d a s h e d l i n e h a s c o n s i d e r a b l e u n c e r t a i n t y d u e to t h e i n t e r p l a y o f s t e r i c exclusion and inversion mechanisms.


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particle diameter i n the tailing e n d o f the size indicated b y the broken lines.

d i s t r i b u t i o n c u r v e s as


Conclusions Because o f its high intrinsic resolution, S d F F F is capable o f resolving aggregated c o l l o i d a l clusters f r o m one another based o n differences i n their mass. T h e a b i l i t y t o c o l l e c t f r a c t i o n s o f constant ( a n d k n o w n ) p a r t i c l e m a s s a n d t o subject t h e m t o e l e c t r o n m i c r o s c o p y adds a n o t h e r d i m e n s i o n to the characterization o f aggregates. T h e flexibility o f S d F F F makes it possible to achieve different r e s o l u t i o n l e v e l s b y c o n t r o l l i n g b o t h c a r r i e r f l o w rate a n d c e n t r i f u g a l field strength. U s i n g optimized conditions, one c a n achieve desired level o f separation o f i n d i v i d u a l clusters i n an aggregated sample. T h e S d F F F t e c h n i q u e i s e f f e c t i v e f o r m o n i t o r i n g f r o m trace u p t o extensive levels o f aggregation occurring i n c o l l o i d a l samples. Some demonstrated applications o f this method include the f o l l o w i n g : (a) f i n d i n g a n d m e a s u r i n g the relative content o f aggregates i n different monodisperse latex samples, (b) studying the b r e a k d o w n o f aggregated s p e c i e s t o s i n g l e t s a n d l o w e r o r d e r aggregates b y s o n i c a t i o n , ( c ) t r a c k i n g the c o n t r o l l e d a g g r e g a t i o n f r o m m o n o d i s p e r s e l a t e x p o p u l a t i o n s i n d u c e d by t h e a d d i t i o n o f a c a t i o n i c s u r f a c t a n t , a n d ( d ) o b s e r v i n g c h a n g e s o f t h e p o p u l a t i o n o f d i f f e r e n t l a t e x aggregates c a u s e d b y a g i n g .

Acknowledgment T h i s work w a s supported by U . S . P u b l i c Health Service Grant G M 1 0 8 5 1 - 3 3 f r o m t h e N a t i o n a l Institutes o f H e a l t h .

Literature Cited 1. Jones, H. K.; Barman, B. N.; Giddings, J. C. J. Chromatogr. 1989, 455, 115. 2. Giddings, J. C.; Barman, B. N.; Li, H. J. Colloid Interface Sci. 1989, 132, 554-565. 3. Schure, M. R.; Barman, B. N.; Giddings, J. C. Anal. Chem. 1989, 61, 27352743. 4. Giddings, J. C.; Yang, F. J. F.; Myers, M. N. Anal. Chem. 1974,46,19171924. 5. Lee, S.; Giddings, J. C. Anal. Chem. 1988,60,2328-2333. 6. Yang, F. J. F.; Myers, M. N.; Giddings, J. C. Anal. Chem. 1974, 46, 19241930. 7. Williams, P. S.; Giddings, J. C. Anal. Chem. 1987, 59, 2038-2044. 8. Yau, W. W.; Kirkland, J. J. Sep. Sci. Technol. 1981,16,577-605. 9. Giddings, J. C.; Williams, P. S.; Beckett, R. Anal. Chem. 1987, 59, 28-37. 10. Jones, H. K.; Phelan, K.; Myers, M. N.; Giddings, J. C. J. Colloid Interface Sci. 1987, 120, 140-152. 11. Giddings, J. C. Anal. Chem. 1985, 57, 945-947. 12. Giddings, J. C.Sep.Sci. 1973, 8, 567-575. 13. Myers, M. N.; Giddings, J. C. Anal. Chem. 1982, 54, 2284-2289. 14. Barman, B. N.; Giddings, J. C. Polym Mater. Sci. Eng. 1990,62,186-190. RECEIVED January 14, 1991


Overview of Colloidal Aggregation by Sedimentation Field-Flow

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