Particle Size Distribution II - American Chemical Society

Chapter 13

Particle Separation and Size Characterization by Sedimentation Field-Flow Fractionation 1

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J. Calvin Giddings, Marcus N. Myers , Myeong Hee Moon , and Bhajendra N. Barman Downloaded by IMPERIAL COLLEGE LONDON on April 30, 2018 | https://pubs.acs.org Publication Date: September 24, 1991 | doi: 10.1021/bk-1991-0472.ch013

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Field-Flow Fractionation Research Center, Department of Chemistry, University of Utah, Salt Lake City, UT 84112 FFFractionation, Inc., P.O. Box 58718, Salt Lake City, UT 84158-0718

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This chapter provides, first, an overview of particle characterization by field-flow fractionation (FFF) and describes how FFF works, the applicable size range, the properties that can be characterized, and the underlying theory. Second, a number of applications of sedimentation FFF are shown to illustrate the applicability of this FFF technique to diverse particulate materials in both submicron and supramicron size ranges. The materials examined include uniform and broad latex populations, dense inorganic and metallic particles, elongated Teflon particles, and plate-like clay particles. It is shown that self-consistent particle size distributions can be obtained under different experimental conditions and that narrow fractions can be collected and further examined and characterized by microscopy or other means. The high speed of steric FFF is illustrated by a one minute run of 3-15 µm copper particles.

F i e l d - f l o w fractionation ( F F F ) is a family o f separation methods i n w h i c h p a r t i c l e s w i t h d i f f e r e n t p r o p e r t i e s are e l u t e d f r o m the t h i n F F F flow c h a n n e l at d i f f e r e n t t i m e s a n d t h e i r r e l a t i v e a m o u n t s r e c o r d e d ( 1 - 5 ) . T h e p r o p e r t i e s that c o n t r o l e l u t i o n t i m e s d e p e n d o n the F F F s u b t e c h n i q u e utilized: p a r t i c l e s i z e i n the case o f flow F F F , mass a n d d e n s i t y f o r sedimentation F F F , sedimentation coefficients for c y c l i c a l - f i e l d F F F , etc. In e a c h case the c o n c e n t r a t i o n v e r s u s e l u t i o n t i m e c u r v e c a n b e c o n verted into a property distribution curve: mass d i s t r i b u t i o n , size d i s t r i bution, sedimentation coefficient distribution, etc. Because F F F is capable o f y i e l d i n g so m a n y k i n d s o f i n f o r m a t i o n o n s o m a n y categories o f p a r t i c l e s a n d d o i n g these t a s k s b o t h flexibly and with high resolution, the F F F f a m i l y h a s e m e r g e d as t h e m o s t v e r s a t i l e a n d e f f e c t i v e s i n g l e m e t h o d ology available for detailed particle characterization. F o r highly complex c o l l o i d s , fractions c a n be collected and further characterized b y electron m i c r o s c o p y , elemental analysis, and other complementary techniques. 0097-6156/91/0472-0198$06.00/0 © 1991 American Chemical Society

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

13.

GIDDINGS ET AL.

Sedimentation

Field-Flow

199

Fractionation

F o r p e r s p e c t i v e , it is u s e f u l to d e s c r i b e the range o f a p p l i c a b i l i t y o f FFF. A t the s m a l l diameter end o f the s p e c t r u m , w e have a p p l i e d flow F F F to p a r t i c l e s (e.g., g l o b u l a r proteins) as s m a l l as 0.005 u m (5 n m ) and b e l o w . A t the l a r g e d i a m e t e r e x t r e m e , s e d i m e n t a t i o n F F F o p e r a t i n g i n the s t e r i c m o d e has been a p p l i e d i n o u r laboratories to p a r t i c l e s u p to 5 0 0 u m (0.5 m m ) i n diameter. T h e total mass range c o v e r e d is o v e r 1 0 . Applications h a v e been m a d e t h r o u g h o u t t h i s range. W h i l e m o s t w o r k has been d o n e w i t h aqueous s u s p e n s i o n s o f p a r t i c l e s , w e h a v e a p p l i e d s e d i m e n t a t i o n F F F to n o n a q u e o u s suspensions as w e l l (&). (Nonaqueous sedimentation F F F w o r k has also been reported by Y o n k e r et a l . (1).) M o r e r e c e n t l y , w e have d e m o n s t r a t e d that t h e r m a l F F F is a p p l i c a b l e to v a r i o u s c a t e g o r i e s of particles suspended i n organic l i q u i d s (&).

Downloaded by IMPERIAL COLLEGE LONDON on April 30, 2018 | https://pubs.acs.org Publication Date: September 24, 1991 | doi: 10.1021/bk-1991-0472.ch013

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T h e p a r t i c u l a t e m a t e r i a l s that h a v e been s u b j e c t e d to F F F a n a l y s i s h a v e n o w i n v o l v e d w o r k i n so m a n y l a b o r a t o r i e s , b o t h a c a d e m i c a n d i n d u s t r i a l , that they cannot be c o m p i l e d w i t h o u t s e r i o u s o m i s s i o n s . While m o s t o f the a n a l y z e d m a t e r i a l s are i n d u s t r i a l i n t e r m e d i a t e s o r p r o d u c t s , m a n y o f t h e m p r o p r i e t a r y , there have been m a n y a p p l i c a t i o n s o f F F F to b i o l o g i c a l and environmental materials. T h e p a r t i c l e s range f r o m h i g h d e n s i t y m e t a l a n d l o w d e n s i t y latex m i c r o s p h e r e s to v a r i o u s " s o f t " a n d h i g h l y d e f o r m a b l e p a r t i c l e s s u c h as those c o n s t i t u t i n g e m u l s i o n s , b i o l o g i cal cells, and liposomes. A l i s t i n g o f m a n y o f the p a r t i c u l a t e m a t e r i a l s s t u d i e d by F F F i n o u r l a b o r a t o r i e s , as s h o w n i n T a b l e I , is suggestive o f the b r o a d scope o f the m e t h o d o l o g y . (Polymers, analyzed by thermal and flow F F F , are not l i s t e d i n this table.)

Principles of FFF F i e l d - f l o w fractionation is generally carried out i n a ribbon shaped c h a n n e l o n l y a f e w h u n d r e d u m t h i c k and 0.25-1 m i n l e n g t h . The channel contains no packing material. A c c o r d i n g l y , flow t h r o u g h the channel is even and predictable, assuming a parabolic flow profile b e t w e e n the t w o m a j o r c h a n n e l faces (see F i g u r e 1). The velocity of p a r a b o l i c flow approaches z e r o at both w a l l s and reaches a m a x i m u m at the m i d p o i n t b e t w e e n the w a l l s . T h e essence o f F F F is to apply a f i e l d o r gradient across the t h i n d i m e n s i o n o f the c h a n n e l p e r p e n d i c u l a r to flow s u c h that it w i l l d r i v e entrained particles into particular cross sectional positions or d i s t r i b u t i o n s w i t h i n the c h a n n e l . P a r t i c l e s d r i v e n c l o s e to a w a l l w i l l be d i s p l a c e d v e r y s l o w l y b y flow because o f the l o w flow v e l o c i t y n e a r the b o u n d i n g surfaces as s h o w n i n F i g u r e 1 (&). P a r t i c l e s p o s i t i o n e d f u r t h e r f r o m the w a l l are d i s p l a c e d m o r e r a p i d l y . B e c a u s e the a p p l i e d f i e l d causes d i f f e r e n t p a r t i c l e p o p u l a t i o n s to a c c u m u l a t e i n d i f f e r e n t d i s t r i b u t i o n s , t h e y are s w e p t a l o n g at d i f f e r e n t m e a n v e l o c i t i e s . W i t h u n e q u a l v e l o c i t i e s , the p o p u l a t i o n s m i g r a t e d i f f e r e n t i a l l y a n d are t h u s separated (2JDThe field most w i d e l y used for F F F particle characterization is sedimentation (hence sedimentation F F F ) . W h i l e g r a v i t y has h a d l i m i t e d use f o r p a r t i c l e s o v e r 1 u m i n d i a m e t e r ( 1 0 ) . the s e d i m e n t a t i o n f o r c e s are u s u a l l y generated i n a c e n t r i f u g e c u s t o m d e s i g n e d f o r F F F w o r k . H e r e the F F F c h a n n e l , rather t h a n h a v i n g a flat c o n f i g u r a t i o n as s u g g e s t e d i n F i g u r e 1, e n c i r c l e s the a x i s o f r o t a t i o n l i k e a r o t a t i n g b e l t , h e l d i n p l a c e i n a s p e c i a l l y d e s i g n e d basket. R o t a t i n g seals are used to b r i n g the l i q u i d stream i n t o a n d out o f the c h a n n e l . F o l l o w i n g s e p a r a t i o n , the p a r t i c l e s are



200

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

Table I.

Some Particles Characterized by F F F Methods i n F F F R C and F F F r a c t i o n a t i o n L a b o r a t o r i e s *

latex polystyrene (s,f) polyvinylchloride (s) polybutadiene (s) polyurethane (s) polymethylmethacrylate(PMMA) styrene-butadiene (s) grafted polybutadience - P M M A vinyltoluene t-butadiene (s) e p o x y - a c r y l i c latex (s) emulsions s o y b e a n o i l (s) s a f f l o w e r o i l (s) perfluorocarbon m i l k (s) liposomes (s)

(s) (s)

(s)

environmental fly ash (s) coal liquefaction residue ground coal (f) c o a l dust (s) w a t e r b o r n e c o l l o i d s (s) d i e s e l soot (s) p o l l e n g r a i n s (f)

(s)

• L e t t e r s s a n d f i n parentheses methods, respectively.

represent

inorganic g o l d (s) copper (s) silver (s) palladium (s) selenium (s) nickel (s) g l a s s beads (s,f) silica (s,f) hematite (s) T e f l o n (s) c l a y (s) limestone (0 zirconia (s) paint pigments (s,f) biological red b l o o d c e l l s (s,f) w h i t e b l o o d c e l l s (s,f) H e L a c e l l s (s) yeast c e l l s (s) h u m a n l e n s p a r t i c l e s (s) albumin microspheres (s) c a s e i n p a r t i c l e s (s) viruses ( T 2 , Q P , P B C V , T 4 D , P 2 2 ) (s,f) g y p s y m o t h N P v i r u s (s) mitochondria (s) lysosomes (s) sedimentation F F F and

flow


FFF


13.

GIDDINGS ETA L .

Sedimentation Field-Flow Fractionation

201

Figure 1. Structure of thin F F F channel (upper) and an enlarged edge view (lower) showing the different distributions of two particulate species A and B that are undergoing differential migration and separation in the channel. (Reproduced with permission from Ref. 9. Copyright 1989 John Wiley & Sons.)



202


e l u t e d f r o m the c h a n n e l , t h r o u g h the s e a l s , a n d i n t o a d e t e c t o r w h e r e relative concentrations c a n be recorded. B e c a u s e o f the r a p i d l y g r o w i n g i m p o r t a n c e o f s e d i m e n t a t i o n F F F i n p a r t i c l e c h a r a c t e r i z a t i o n , the a p p l i c a t i o n s s h o w n l a t e r i n t h i s c h a p t e r w i l l be b a s e d e n t i r e l y o n t h i s F F F t e c h n i q u e . W e note that flow F F F i s also b e i n g i n c r e a s i n g l y d e v e l o p e d f o r particle analysis. I n flow F F F , a cross f l o w o f fluid m o v i n g i n a d i r e c t i o n p e r p e n d i c u l a r to the c h a n n e l flow serves as the d r i v i n g f o r c e to d i s p l a c e p a r t i c l e s across the t h i n d i m e n s i o n o f the c h a n n e l . T h e flow F F F c h a n n e l s h a v e p e r m e a b l e w a l l s to f a c i l i t a t e the c r o s s flow. T h e apparatus a n d m e t h o d o l o g y f o r t h i s " u n i v e r s a l l y " a p p l i c a b l e F F F a p p r o a c h are d e s c r i b e d m o r e completely i n an a c c o m p a n y i n g report. W e h a v e v e r y r e c e n t l y d i s c o v e r e d that the F F F s u b t e c h n i q u e of t h e r m a l F F F i s a p p l i c a b l e to p a r t i c l e s suspended i n o r g a n i c l i q u i d s . This m e t h o d , i n w h i c h a temperature g r a d i e n t serves as a d r i v i n g f o r c e f o r t r a n s v e r s e d i s p l a c e m e n t , has b e e n a p p l i e d w i d e l y to p o l y m e r a n a l y s i s i n the past. T h e device consists of a thin channel sandwiched between s p e c i a l l y c o a t e d a n d p o l i s h e d c o p p e r b l o c k s , one heated a n d one c o o l e d so that a c o n t r o l l a b l e temperature g r a d i e n t c a n be a p p l i e d a c r o s s the channel (11). O t h e r variants o f F F F exist but have been less w e l l d e v e l o p e d . One these i s c y c l i c a l - f i e l d F F F , i n w h i c h the d i r e c t i o n o f the field is c y c l e d b a c k a n d forth d u r i n g the r u n ( 1 2 ) . Separation i n c y c l i c a l - f i e l d F F F is governed m a i n l y by differences i n a transport coefficient, which, d e p e n d i n g o n the field, m i g h t be the s e d i m e n t a t i o n c o e f f i c i e n t o r the electrophoretic mobility.

of

Theory of F F F T h e r e are a n u m b e r o f different o p e r a t i n g m o d e s o f F F F , e a c h associated w i t h its o w n t h e o r y . The principal operating modes for particle analysis are n o r m a l F F F , steric F F F , h y p e r l a y e r F F F , a n d c y c l i c a l - f i e l d F F F . (Any one o f these m o d e s c a n be used w i t h a s e d i m e n t a t i o n field.) It is not o u r purpose to d e t a i l a l l o f these theories here. Instead w e w i l l d e s c r i b e i n a g e n e r a l w a y h o w the t h e o r i e s are f o r m u l a t e d a n d w h a t t h e y a c c o m p l i s h . A f e w k e y equations f o r n o r m a l a n d steric F F F w i l l be g i v e n . P r o v i d i n g the f o r c e s a c t i n g o n p a r t i c l e s are k n o w n , t r a n s p o r t i n the F F F s y s t e m i s h i g h l y p r e d i c t a b l e because o f the u n i f o r m c h a n n e l g e o m e t r y , the e v e n a p p l i c a t i o n o f the field, and the w e l l u n d e r s t o o d flow profile. T h e first o b j e c t i v e o f theory is to d e s c r i b e the v e l o c i t y a n d thus the r e t e n t i o n t i m e o f d i f f e r e n t p o p u l a t i o n s o f p a r t i c l e s m a k i n g u p the particulate sample. F o r particles distributed over different streamlines, the v e l o c i t y o f d o w n s t r e a m t r a n s p o r t c a n be c a l c u l a t e d b y a v e r a g i n g the v e l o c i t y o f p a r t i c l e s o c c u p y i n g the d i f f e r e n t s t r e a m l a m i n a e (2-4). B y a somewhat more complicated procedure, band broadening, representing the a x i a l d i s p e r s i o n o f p a r t i c l e s a n d thus h a v i n g an i m p o r t a n t b e a r i n g o n r e s o l u t i o n , c a n a l s o be c a l c u l a t e d ( 1 3 ) . F F F has been w i d e l y a p p l i e d i n the n o r m a l m o d e o f o p e r a t i o n , g e n e r a l l y a p p l i c a b l e to p a r t i c l e s o f s u b m i c r o n s i z e . H e r e the d i s t r i b u t i o n o f p a r t i c l e s r e l a t i v e to d i e a c c u m u l a t i o n w a l l o f the c h a n n e l , fixed b y the b a l a n c e b e t w e e n f i e l d - d r i v e n t r a n s p o r t t o w a r d the a c c u m u l a t i o n w a l l a n d d i f f u s i v e transport i n the o p p o s i t e d i r e c t i o n , is e x p o n e n t i a l i n nature (2-5)


13. G I D D I N G S E T A L .

Sedimentation Field-Flow Fractionation c(x)

—

-xAw

o>

e

w h e r e c ( x ) i s the c o n c e n t r a t i o n o f p a r t i c l e s at d i s t a n c e x a c c u m u l a t i o n w a l l , C Q is the c o n c e n t r a t i o n at the w a l l , w t h i c k n e s s , a n d X i s the retention parameter. parameter given by


203

The

a b o v e the i s the c h a n n e l

latter is a

dimensionless

w h e r e k T is t h e r m a l energy and F is the force exerted o n a s i n g l e p a r t i c l e b y the f i e l d . S e p a r a t i o n is based o n different l e v e l s o f f o r c e F , w h i c h l e a d to d i f f e r e n t d i s t r i b u t i o n s c ( x ) as expressed i n E q u a t i o n 1. T h e mean retention time t o f a population o f l i k e particles obtained r

by

the

above

mentioned 1 = t°

w h e r e t ° , the v o i d t i m e , m o v i n g w i t h the average s h o w n b y the a r r o w , is a F o r most fields, F p a r t i c u l a r l y p a r t i c l e mass

averaging

procedure

1 6X{coth(l/2X)-2X]

is

given

by

> J L (3)

is the t i m e needed to elute a tracer m a t e r i a l fluid velocity. T h e final part o f E q u a t i o n 3, s i m p l e f o r m approached b y t / t ° for X « 1. is a p r e d i c t a b l e f u n c t i o n o f p a r t i c l e p r o p e r t i e s , and s i z e . Thus for a sedimentation field r

Ap F =m ^ G or

( 4 )

equivalently

F =l*d ApG 3

where Ap

m

is the

particle mass, d

i s the p a r t i c l e density (p ) p

i s the e f f e c t i v e

( 5 )

spherical particle

less the c a r r i e r density (p),

diameter,

and G is the

acceleration. F o r flow F F F , F is g i v e n b y F = 370id U

(6)

s

w h e r e r\ is v i s c o s i t y , U is the v e l o c i t y o f cross f l o w , and d diameter.

s

i s the Stokes

T h e a b o v e force e q u a t i o n s , used i n c o n j u n c t i o n w i t h eqs 2 a n d 3, p r o v i d e a d i r e c t t h e o r e t i c a l l i n k b e t w e e n p a r t i c l e p r o p e r t i e s ( s u c h as m , d , d , and A p ) and retention t i m e t . T h u s m e a s u r e d r e t e n t i o n t i m e s c a n be u s e d to c a l c u l a t e r e l e v a n t p r o p e r t i e s . The observed distribution of r e t e n t i o n t i m e s , r e p r e s e n t e d by the r e c o r d e d e l u t i o n p r o f i l e o r f r a c t o g r a m , c a n then be u s e d to o b t a i n p r o p e r t y d i s t r i b u t i o n s , s u c h as the s

r


204


particle size distribution ( P S D ) . P a r t i c l e d e n s i t i e s c a n also b e o b t a i n e d b y sedimentation F F F . F o r steric a n d h y p e r l a y e r F F F , a p p l i c a b l e p r i m a r i l y t o p a r t i c l e s over 1 u m i n diameter, t is given by ( 1 4 ) r

l


w h e r e y i s the steric c o r r e c t i o n F F F , y > 2.

=

_w_

factor.

(7)

F o r steric F F F , y < 2 ; f o r h y p e r l a y e r

Experimental T h e e x p e r i m e n t s r e p o r t e d here w e r e c a r r i e d o u t o n s e v e r a l d i f f e r e n t ( b u t c l o s e l y related) s e d i m e n t a t i o n F F F d e v i c e s . T h e apparatus f o r s y s t e m s I and II i s the m o d e l S 1 0 1 c o l l o i d / p a r t i c l e f r a c t i o n a t o r f r o m 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 , U T ) . S y s t e m s I I I , I V , a n d V are research d e v i c e s used i n the F i e l d - F l o w Fractionation Research Center ( F F F R C ) laboratories. I m p o r t a n t features a n d e s s e n t i a l c o m p o n e n t s o f these s y s t e m s a r e provided i n Table II. F o r a l l runs, s m a l l (sub-milligram) samples i n s u s p e n s i o n w e r e i n j e c t e d i n t o a n a q u e o u s c a r r i e r stream that enters a n d f l o w s t h r o u g h the c h a n n e l . D e t e c t i o n i n a l l systems i s b a s e d o n l i g h t s c a t t e r i n g o f the e m e r g i n g c o m p o n e n t s w i t h i n t h e flow c e l l o f a U V detector designed for l i q u i d chromatography. Particle size distributions were obtained from F F F r a c t i o n a t i o n and F F F R C software. T h e runs s h o w n here w e r e m a d e e i t h e r at constant f i e l d strength o r u n d e r c o n d i t i o n s o f power programming, a unique form o f field programming yielding u n i f o r m f r a c t i o n a t i n g p o w e r ( I S ) . H e r e , t h e f i e l d strength G , after b e i n g h e l d constant f o r t i m e t i , decreases as the f o l l o w i n g p o w e r f u n c t i o n o f the e l a p s e d t i m e t f r o m the start o f the r u n

(8)

where

G o i s the i n i t i a l a c c e l e r a t i o n

Illustrative

and t

a

i s a constant.

Applications

F i g u r e 2 i l l u s t r a t e s the r e s o l u t i o n o f s i x p o l y s t y r e n e l a t e x p a r t i c l e s i n the d i a m e t e r range 0 . 2 0 to 0 . 8 6 u m u s i n g s y s t e m I a n d a p o w e r p r o g r a m m e d r u n w i t h parameters G o = 3 8 0 . 2 g r a v i t i e s ( 1 5 0 0 r p m ) , t i = 13 m i n , t = - 1 0 4 a

m i n , flow rate V = 6.37 m L / m i n , a n d s t o p - f l o w t i m e t f = 12 m i n . T h e aqueous carrier solution contained 0 . 0 5 % ( w / v ) sodium d o d e c y l sulfate ( S D S ) and 0 . 0 1 % ( w / v ) sodium azide. W h i l e m i x t u r e s o f n a r r o w latex standards, as r e s o l v e d i n F i g u r e 2 , are i n n o sense t y p i c a l o f i n d u s t r i a l s a m p l e s , a n attempt t o r e s o l v e s u c h standards p r o v i d e s an i m p o r t a n t r e s o l u t i o n test. E v e n for broad distributions, h i g h resolution is necessary f o r distinguishing subtle population changes, discerning bimodal and trimodal distributions, a c c u r a t e l y m e a s u r i n g the t a i l s o f a d i s t r i b u t i o n , a n d g e n e r a l l y o b t a i n i n g s


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

standard

SdFFF

type

dual

outlet

Minipuls 2 Gilson, (Middleton, WI)

Isochrom L C Spectra-Physics (San Jose, C A )

Isochrom L C Spectra-Physics, (San Jose, C A )

Data

recording

U V at 254 n m

Detectors

Pump

15.3

strip chart recorder

15.1

FFFractionation software

15.1

FFFractionation software

(cm) U V at 2 5 4 n m

radius

4.50

90.5 2.0 0.0254

III

Systems

Devices

U V at 254 n m

Channel

(mL)

4.52

volume

4.25

Void

89.4 2.0 0.0254

89.4 1.9 0.0254

tip),

C h a n n e l length (tip breadth, thickness (cm)

to

II

SdFFF

Description of S d F F F

Features/Components

T a b l e II.

standard

M o d e l L C 414 Kontron Electrolab (London, U K )


U V at 254 n m

15.75

4.20

90.0 2.0 0.0254

IV


slow-flow injection

Model QD-1 Fluid Metering (Oyster B a y , N Y )


U V at 350 n m

15.1

1.40

0.0127

90.0 1.0


206


Figure 2. High resolution separation of polystyrene latex standards of indicated diameters by sedimentation FFF.



207


o t h e r d e t a i l s o f the s i z e d i s t r i b u t i o n c u r v e that m a y h a v e an i m p o r t a n t bearing on product quality. A n y m e t h o d o r i n s t r u m e n t that c a n n o t r e s o l v e c l o s e l y i n g latex standards is l i k e l y to g l o s s o v e r s i g n i f i c a n t d e t a i l s c h a r a c t e r i z i n g the p a r t i c u l a t e m a t e r i a l . T h e a b i l i t y to r e s o l v e m o n o d i s p e r s e latex s a m p l e s is r e c o m m e n d e d as a standard test f o r a l l m e t h o d o l o g i e s d e s i g n e d to p r o v i d e accurate a n d d e t a i l e d p a r t i c l e s i z e distributions. M o r e t y p i c a l o f an i n d u s t r i a l latex s a m p l e is the a c r y l i c b a s e d latex m a t e r i a l w h o s e f r a c t o g r a m is s h o w n i n F i g u r e 3 a . T h i s run was obtained w i t h system I u s i n g G o = 169.0 gravities, t i = 10 m i n , t = -80 m i n , V = 1.25 m L / m i n , and t f = 2 0 m i n . A 0 . 0 5 % ( w / v ) S D S s o l u t i o n w i t h 0.01 ( w / v ) s o d i u m azide w a s used as c a r r i e r l i q u i d . U s i n g a p a r t i c l e density o f 1.1 g / m L , eqs 2, 3, and 5 can be c o m b i n e d to p r o v i d e a u n i q u e v a l u e o f the p a r t i c l e d i a m e t e r d f o r p a r t i c l e s e l u t i n g at any s p e c i f i e d r e t e n t i o n t i m e t . T h i s e x e r c i s e m a k e s it p o s s i b l e to a f f i x a d i a m e t e r scale ( a l o n g w i t h the o b s e r v e d t i m e s c a l e ) to the f r a c t o g r a m o f F i g u r e 3 a , m a k i n g it easy to v i s u a l i z e the e m e r g i n g p a r t i c l e peak i n t e r m s o f c o n s t i t u e n t d i a m e t e r s . H o w e v e r , i n o r d e r to a r r i v e at a p a r t i c l e s i z e d i s t r i b u t i o n ( P S D ) f o r the s a m p l e , a standard scale c o r r e c t i o n p r o c e d u r e must be e m p l o y e d (16). W h e n t h i s p r o c e d u r e , i m p l e m e n t e d t h r o u g h the S 1 0 1 software ( F F F r a c t i o n a t i o n , I n c . ) , i s a p p l i e d to the f r a c t o g r a m o f F i g u r e 3 a , the P S D s h o w n i n F i g u r e 3b e m e r g e s .


a

s

r

S e d i m e n t a t i o n F F F c a n be a p p l i e d w i t h e q u a l f a c i l i t y to dense inorganic and metallic particles. Figure 4a, for example, shows a fractogram obtained from system I V for a finely d i v i d e d z i r c o n i a p o w d e r h a v i n g a p a r t i c l e density o f 6.0 g / m L . T h e carrier was 0 . 1 % (v/v) F L - 7 0 solution with 0 . 0 1 % (w/v) sodium azide. T h e s i z e d i s t r i b u t i o n c a l c u l a t e d (as a b o v e ) f o r this m a t e r i a l is s h o w n i n F i g u r e 4 b . T h e r u n w a s c a r r i e d out u s i n g p o w e r p r o g r a m m i n g ( i n w h i c h the v a r i a t i o n o f r p m w i t h t i m e i s s h o w n b y the b r o k e n l i n e ) w i t h G o = 7.05 g r a v i t i e s , t i = 5 m i n , and t = - 4 0 a

m i n , and w i t h V = 9.5 m L / m i n and t f = 10 m i n . T h e v a l i d i t y o f the s i z e - b a s e d f r a c t i o n a t i o n a n d o f the r e s u l t i n g s i z e d i s t r i b u t i o n c u r v e s o b t a i n e d f r o m s e d i m e n t a t i o n F F F c a n be v e r i f i e d i n several ways. O n e o f these is to c o l l e c t fractions and e x a m i n e t h e m b y electron microscopy. A s e c o n d means o f v a l i d a t i o n is to c o m p a r e s i z e distribution results obtained under different conditions, perhaps even by u s i n g different F F F systems. B o t h o f these approaches are i l l u s t r a t e d i n F i g u r e 5 where a T e f l o n sample is e x a m i n e d . A 0 . 1 % (v/v) A e r o s o l - O T s o l u t i o n w i t h 0 . 0 1 % ( w / v ) s o d i u m a z i d e w a s used as c a r r i e r l i q u i d f o r the analysis o f T e f l o n particles. T h e u p p e r f r a c t o g r a m (a) w a s o b t a i n e d f r o m s

s y s t e m III u s i n g a constant f i e l d strength o f 10.7 g r a v i t i e s w i t h V = 1.33 m L / m i n and t f = 19 m i n . F r a c t i o n s ( c o r r e s p o n d i n g to the shaded areas) w e r e c o l l e c t e d f r o m t h i s r u n a n d subjected to e l e c t r o n m i c r o s c o p y . The r e s u l t i n g m i c r o g r a p h s are s h o w n at the top o f F i g u r e 5. The mean d i a m e t e r s f o r the p a r t i c l e s eluted i n these c u t s are c a l c u l a t e d f r o m eqs 2 , 3, and 5 ( w i t h a T e f l o n density o f 2.20 g / m L ) to be 0 . 2 1 , 0.27, and 0.32 u m , respectively. T h e s e s i z e s s h o w g o o d c o r r e s p o n d e n c e w i t h those o b t a i n e d f r o m the e l e c t r o n m i c r o g r a p h s . ( T h i s c o m p a r i s o n i s s i m p l e to q u a n t i f y w i t h s p h e r i c a l p a r t i c l e s but less s i m p l e f o r the s o m e w h a t e l o n g a t e d T e f l o n particles.) s

T h e l o w e r fractogram a constant

f i e l d strength o f

(b) 15.2

of

Figure 5 was obtained

gravities and with V =

from

1.68

system

II at

m L / m i n and t f


s


208


b

DIAMETER (/xm) Figure 3. Fractionation of a broad acrylic based latex dispersion by sedimentation FFF. (a) Fractogram with diameter scale. The diameter scale is based on a particle density of 1.1 g/mL. (b) Particle size distribution of acrylic latex dispersion derived from the fractogram in (a).



GIDDINGS ET AL.


b

0

0.2

0.4

0.6

0.8

1.0

(a)

Fractogram;

DIAMETER (/xm) Figure 4 . Sedimentation size distribution.

F F F of zirconia.

(b)

Particle




210

F i g u r e 5. F r a c t o g r a m s o f T e f l o n p a r t i c l e s o b t a i n e d f r o m (a) s y s t e m III a n d (b) s y s t e m II u n d e r d i f f e r e n t e x p e r i m e n t a l c o n d i t i o n s (see t e x t ) . T h e e l e c t r o n m i c r o g r a p h s (top) o f p a r t i c l e s c o l l e c t e d i n the i n d i c a t e d s h a d e d areas o f f r a c t o g r a m (a) v e r i f y f r a c t i o n a t i o n a n d s i z e s c a l i n g .




211


= 15 m i n . T h e t w o fractograms are o b v i o u s l y s i m i l a r despite the use o f different systems and conditions. H o w e v e r the r e s u l t s b e c o m e m e a n i n g f u l o n l y w h e n the t w o 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 u r v e s are c o m p a r e d . Such a c o m p a r i s o n i s p r o v i d e d i n F i g u r e 6. T h e agreement b e t w e e n the t w o curves is quite satisfactory. F F F , o f c o u r s e , does not r e q u i r e s p h e r i c a l p a r t i c l e s f o r a n a l y s i s . S e p a r a t i o n i n the n o r m a l m o d e o f s e d i m e n t a t i o n F F F is based s t r i c t l y u p o n e f f e c t i v e p a r t i c l e m a s s , m ' = m A p / p p , as is apparent f r o m E q u a t i o n 4. For s p h e r i c a l p a r t i c l e s , m ' relates d i r e c t l y to sphere d i a m e t e r d . For n o n s p h e r i c a l p a r t i c l e s , one c a n e i t h e r o b t a i n a p a r t i c l e m a s s ( o r volume) d i s t r i b u t i o n f r o m the f r a c t o g r a m o r ( m o r e c o m m o n l y ) p r o c e e d w i t h the c a l c u l a t i o n o f a p a r t i c l e s i z e d i s t r i b u t i o n w i t h the u n d e r s t a n d i n g that the " d i a m e t e r " s c a l e refers to 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 o f e m e r g i n g particles. T h i s a p p r o a c h w a s u s e d f o r the n o n s p h e r i c a l T e f l o n p a r t i c l e s i n F i g u r e 6. A m o r e extreme e x a m p l e is p r o v i d e d b y c l a y . F i g u r e 7 s h o w s three fractograms o f a s a m p l e o f k a o l i n c l a y o b t a i n e d f r o m system I. B e c a u s e o f the h i g h aspect r a t i o o f the c l a y p a r t i c l e s a n d the c o n s e q u e n t e n h a n c e d r i s k o f s t e r i c p e r t u r b a t i o n s , the three r u n s w e r e m a d e u n d e r q u i t e d i f f e r e n t e x p e r i m e n t a l c o n d i t i o n s to c h e c k the s e l f - c o n s i s t e n c y o f the r e s u l t s . T h e c o n d i t i o n s f o r the three r u n s , a l l u t i l i z i n g p o w e r p r o g r a m m i n g , were as f o l l o w s : (a) Go = 6.7 g r a v i t i e s , t i = 5 m i n , t = -40 m i n ; (b) Go = 15.2 gravities, t i = 5 m i n , t = -40 m i n ; (c) Go = 2 7 gravities, t i = 10 m i n , and t = -80 m i n . F o r a l l three runs a a

a

a

0 . 1 % (v/v) was 1.50

D i s p e x A 4 0 s o l u t i o n was used as c a r r i e r l i q u i d .

+. 0.02 m L / m i n and the

field,

The

once it reached a l e v e l o f

flow

rate

V

0.95

g r a v i t i e s , w a s h e l d constant f o r the r e m a i n d e r o f the r u n . T h e f r a c t o g r a m s o f F i g u r e 7 s h o w l i t t l e r e s e m b l a n c e to o n e a n o t h e r except for a slight hint of bimodality. H o w e v e r w h e n the s i z e d i s t r i b u t i o n c u r v e s ( w h e r e one m u s t k e e p i n m i n d that s i z e i s m e a s u r e d i n terms o f 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 ) are c o m p a r e d f o r the three r u n s , v e r y s i m i l a r d i s t r i b u t i o n s are o b t a i n e d as s h o w n i n F i g u r e 8. A density v a l u e o f 2.55 g / m L w a s used f o r the c l a y s a m p l e . W h i l e there are a f e w s p e c i f i c d i f f e r e n c e s i n the three c u r v e s o f F i g u r e 8, 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 the first m o d e , the o v e r a l l agreement i s q u i t e s a t i s f a c t o r y c o n s i d e r i n g the c o m p l e x i t y o f the s a m p l e and the d i v e r s i t y o f e x p e r i m e n t a l c o n d i t i o n s . We note that the m o d a l i t y features o f the a b o v e d i s t r i b u t i o n w o u l d not be clearly represented by any method p r o v i d i n g s i g n i f i c a n t l y less resolution than F F F . E l e c t r o n m i c r o g r a p h s o b t a i n e d f r o m another r u n o n k a o l i n c l a y (not s h o w n here) demonstrate a c l e a r s i z e f r a c t i o n a t i o n . W e c o n c l u d e that s e d i m e n t a t i o n F F F is g e n e r a l l y a s u i t a b l e m e t h o d f o r the s i z e c h a r a c t e r i z a t i o n o f c l a y but c a u t i o n that the d i a m e t e r s c a l e m u s t be c a r e f u l l y i n t e r p r e t e d as d e s c r i b e d above. F o r completeness, we show i n Figure 9 a fractogram o f metallic c o p p e r p a r t i c l e s ( m a i n l y spheres) w i t h d i a m e t e r s g r e a t e r t h a n 1 u m obtained from system V . T h e o r i g i n a l p o w d e r s a m p l e w a s first d i s p e r s e d i n an a q u e o u s s o l u t i o n c o n t a i n i n g 0 . 0 7 % ( w / v ) s o d i u m salt o f n a p h t h a l e n e sulfonic acid-formaldehyde. T h e resulting dispersion was then analyzed i n 0 . 1 % (v/v) F L - 7 0 solution with 0.02% (w/v) sodium azide. A constant f i e l d o f 2 9 . 9 g r a v i t i e s and a flow rate o f 29.4 m L / m i n were u s e d . F o r these l a r g e r p a r t i c l e s the steric m o d e o f o p e r a t i o n i s u t i l i z e d ( w i t h o u t s t o p - f l o w ) a n d the r e t e n t i o n t i m e o f i n d i v i d u a l s u b p o p u l a t i o n s i s d e t e r m i n e d b y E q u a t i o n 7. F o r steric F F F , the f l o w rates c a n be v e r y h i g h and the runs c o r r e s p o n d i n g l y short w i t h o u t a s i g n i f i c a n t l o s s o f r e s o l u t i o n . T h u s the




F i g u r e 7. different

Fractograms of a kaolin clay experimental conditions.

sample

obtained

under





213

DIAMETER (/im) Figure 8. Particle size distributions of a kaolin clay sample derived from the three fractograms shown in Figure 7.



214


b

DIAMETER

(/im)

Figure 9. Sedimentation steric FFF of copper particles, (a) Fractogram; (b) Particle size distribution. The inserted micrographs obtained from cuts 3, 8, and 11 verify steric mechanism and size scaling.




215


r u n s h o w n i n F i g u r e 9 a i s c o m p l e t e d w i t h i n about one m i n u t e o f s a m p l e injection. T h e resulting size distribution for this material, obtained by a s p e c i a l l y m o d i f i e d software p a c k a g e , i s s h o w n i n F i g u r e 9 b . The density of c o p p e r p a r t i c l e s w a s a s s u m e d to be 8.92 g / m L . T h e steric m o d e s e p a r a t i o n o f c o p p e r p a r t i c l e s i s v e r i f i e d b y s u b j e c t i n g f r a c t i o n s c o l l e c t e d at d i f f e r e n t p o s i t i o n s o f the f r a c t o g r a m to o p t i c a l m i c r o s c o p y (see F i g . 9 a ) . Inserted m i c r o g r a p h s o b t a i n e d f r o m cuts 3, 8, and 11 p r o v i d e d p a r t i c l e diameters o f 11.6 + 0.6 u m , 7.0 ± 0.7 J i m , and 5.3 ± . 0.4 u m , r e s p e c t i v e l y , i n g o o d agreement w i t h the d i a m e t e r scale (see figure) obtained by calibration. T h e steric F F F a n a l y s i s o f l a r g e r p a r t i c l e s ( s u c h as those o f c o p p e r s h o w n a b o v e ) i s a p p l i c a b l e to p r a c t i c a l l y a n y p a r t i c u l a t e m a t e r i a l f o r w h i c h d i a m e t e r s e x c e e d 1 \im and f o r w h i c h p a r t i c l e d e n s i t y is k n o w n . A p p l i c a t i o n s i n our laboratories have i n c l u d e d latex spheres, glass beads, f l y a s h , a n d o t h e r m e t a l l i c p a r t i c l e s i n c l u d i n g those o f p a l l a d i u m , s i l v e r , and g o l d . F o r the P S D c u r v e s s h o w n i n the v a r i o u s f i g u r e s , the c u r v e h e i g h t is w e i g h t e d b y l i g h t scattering since the detector f o r the s y s t e m i s a U V d e t e c t o r o f the t y p e u s e d i n l i q u i d c h r o m a t o g r a p h y , w h i c h f o r c o l l o i d s a n d p a r t i c l e s p r o d u c e s its p r i m a r y s i g n a l as a c o n s e q u e n c e o f l i g h t s c a t t e r i n g . L i g h t s c a t t e r i n g c o r r e c t i o n s h a v e been d e s c r i b e d i n the l i t e r a t u r e (12., ID but w e r e not u t i l i z e d f o r the P S D c u r v e s o f t h i s s t u d y . (Such corrections are e s s e n t i a l w h e n w a v e l e n g t h X » d , but less s i g n i f i c a n t w h e n X ~ d o r X « d as f o u n d g e n e r a l l y here.) It is l i k e l y that e f f e c t i v e detectors w i l l e v e n t u a l l y be d e v e l o p e d that r e s p o n d m o r e d i r e c t l y to s a m p l e m a s s o r volume. S u c h detectors m i g h t i n c l u d e the e v a p o r a t i v e l i g h t s c a t t e r i n g mass detector first tested w i t h F F F i n 1984 (12). It c o u l d also i n c l u d e d e n s i t y detectors, a v e r s i o n o f w h i c h w a s p r o p o s e d f o r c o u p l i n g w i t h F F F i n d i s c u s s i o n s w i t h D r . B e r n d T r a t h n i g g i n 1987 ( T r a t h n i g g , B . , p e r s o n a l c o r r e s p o n d e n c e , J u l y 2 0 , 1987). Other possibilities exist.

Conclusions T h e e x a m p l e s d e s c r i b e d h e r e i l l u s t r a t e the a p p l i c a t i o n o f s e d i m e n t a t i o n F F F to a v a r i e t y o f particulate m a t e r i a l s . H o w e v e r , the true scope o f F F F is m u c h b r o a d e r t h a n suggested b y these e x a m p l e s ; F F F has been a p p l i e d to p a r t i c l e s m u c h s m a l l e r and m u c h l a r g e r t h a n those d e s c r i b e d here a n d it has been a p p l i e d to nonaqueous suspensions o f p a r t i c l e s as w e l l . F o r most o f these a p p l i c a t i o n s , F F F has the advantage o f h i g h r e s o l u t i o n a n d a degree o f f l e x i b i l i t y that m a k e s s i m p l e s e l f - c o n s i s t e n c y tests p o s s i b l e . The a b i l i t y to c o l l e c t f r a c t i o n s and e x a m i n e t h e m b y e l e c t r o n m i c r o s c o p y a n d other t o o l s , b o t h to c o n f i r m the results c a l c u l a t e d f r o m F F F and to e x t e n d the a n a l y s i s t o i n c l u d e o t h e r p r o p e r t y d i s t r i b u t i o n s ( e . g . , s h a p e , e l e m e n t a l c o n t e n t , e t c . ) , s i g n i f i c a n t l y broadens the c a p a b i l i t y o f F F F . The flexibility o f o p e r a t i o n c a n also be u t i l i z e d i n t r a d i n g speed f o r r e s o l u t i o n ; i f less r e s o l u t i o n is needed i n the s u b m i c r o n s i z e range, the speed o f the r u n c a n be c o r r e s p o n d i n g l y i n c r e a s e d . F o r the l a r g e r p a r t i c l e s subject to s t e r i c F F F , the runs are a l r e a d y e x t r a o r d i n a r y fast as i l l u s t r a t e d i n F i g u r e 9. Acknowledgment This work 8800675.

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RECEIVED January 14,

1991


Particle Size Distribution II - American Chemical Society

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