Particle Size Distribution - American Chemical Society

Chapter 6

Using Quasi-Elastic Light Scattering To Study Particle Size Distributions in Submicrometer Emulsion Systems 1

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1

2

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Downloaded by UNIV OF CALIFORNIA SAN DIEGO on March 3, 2016 | http://pubs.acs.org Publication Date: February 12, 1987 | doi: 10.1021/bk-1987-0332.ch006

C. A. Herb , E. J. Berger , Κ. Chang , I. D. Morrison , and E. F. Grabowski 1

Technical Center, Owens-Corning Fiberglas Corporation, Granville, OH 43023 Webster Research Center, Xerox Corporation, Webster, NY 14580 2

Quasi-elastic light scattering is an excellent tech nique for studying the formation and stability of sub -micrometer emulsions. Improvements in the methods of quasi-elastic light scattering data acquisition and analysis that enable full particle-size distribution studies of sub-micrometer emulsion systems are dis cussed. Using several oil/water emulsion systems as examples, we demonstrate the ability of these tech niques to determine the effect of emulsifier concen tration on the particle-size distribution produced by an inversion method of emulsification. Some of the benefits of obtaining the full distribution are also discussed. In addition to affecting its own stability and rheology, an emul sion's particle-size distribution often influences the quality of the products in which the emulsion is incorporated. The full particle-size distribution is, therefore, of some concern to the researcher trying to improve or modify the product properties. Once the link between the properties and the particle-size distribution is known, the goal of creating an acceptable distribution through control of processing variables during the emulsification can be addressed. The mean diameter, the width of the distribution, or even the distribution shape may be affected by altering variables such as the surfactant concentration, agitation intensity, and temperature.Ο) Thus, the ability to monitor the full distribution, rather than just a mean diameter, allows better control of product quality and provides valuable additional information for product improvement and more fundamental emulsion studies. When the particle sizes in question are below about 1 micro meter, the techniques available for determining the distribution become limited. The use of quasi-elastic light scattering (QELS) for the measurement of these sub-micrometer particles is becoming increasingly popular with the availability of several commercial instruments capable of both gathering and analyzing data.(2) One of the major advantages of using QELS for emulsion studies is the 0097-6156/87/0332-0089$06.00/0 © 1987 American Chemical Society In Particle Size Distribution; Provder, Theodore; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.


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PARTICLE SIZE DISTRIBUTION

a b i l i t y t o w o r k i n a n y medium. T h u s , b o t h w a t e r / o i l and o i l / w a t e r emulsions are e a s i l y studied. I n a d d i t i o n , concentrated samples can be d i l u t e d w i t h t h e o r i g i n a l c o n t i n u o u s p h a s e , t h u s m a i n t a i n i n g t h e proper environment f o r the d r o p l e t s . L i k e w i s e , one c a n s y s t e m a t i c a l l y a l t e r t h e environment t o study t h e e f f e c t s o f such changes on the s t a b i l i t y o f t h e system. In addition, the preparation of the s c a t t e r i n g samples i s f a s t and s i m p l e . The a i m o f t h i s p a p e r i s t o d e s c r i b e t h e e x p e r i m e n t a l a n d n u m e r i c a l t e c h n i q u e s t h a t , when c o m b i n e d , p r o v i d e a p r o c e d u r e t h a t enables f u l l p a r t i c l e - s i z e d i s t r i b u t i o n s t u d i e s o f sub-micrometer emulsion systems. We t h e n p r e s e n t d i s t r i b u t i o n r e s u l t s f o r s e v e r a l o i l / w a t e r emulsions t o demonstrate the a b i l i t y o f these techniques to monitor t h e e f f e c t o f p r o c e s s i n g v a r i a b l e s (such as s u r f a c t a n t c o n c e n t r a t i o n ) on t h e f i n a l e m u l s i o n . F i n a l l y , we d i s c u s s some o f the problems o f c o n v e r t i n g t h e i n t e n s i t y weighted d i s t r i b u t i o n t o a mass w e i g h t e d d i s t r i b u t i o n and s u g g e s t methods f o r m i n i m i z i n g o r eliminating some o f t h e s e p r o b l e m s . Background Many e x c e l l e n t i n t r o d u c t i o n s t o q u a s i - e l a s t i c l i g h t s c a t t e r i n g c a n be f o u n d i n t h e l i t e r a t u r e d e s c r i b i n g t h e t h e o r y a n d e x p e r i m e n t a l t e c h n i q u e ( e . g . 3 - 6 ) . T h e u s e o f QELS t o d e t e r m i n e p a r t i c l e s i z e i s based on t h e measurement, v i a t h e a u t o c o r r e l a t i o n o f t h e time de pendence o f t h e s c a t t e r e d l i g h t , o f t h e d i f f u s i o n c o e f f i c i e n t s o f suspended p a r t i c l e s undergoing Brownian motion. The measured a u t o correlation function, G ( T ) , i s given by < 2 >

G

< 2 ,

(T)

= A[I + B | g

( 1 )

2

(T)| ]

(1)

A i s t h e base l i n e , which i s obtained e i t h e r from t h e long-time asymptote o f t h e measured a u t o c o r r e l a t i o n f u n c t i o n o r from t h e square o f t h e average photon f l u x . 3 i s an equipment-related con s t a n t , and g (τ) i s the normalized f i r s t - o r d e r autocorrelation f u n c t i o n , which i s e a s i l y o b t a i n e d from t h e measured function, G (x). F o r monodisperse systems g ( T ) i s a simple exponential decay w i t h t h e d e s i r e d i n f o r m a t i o n being contained i n the decay c o n s t a n t , Γ, w h i c h i s e q u a l t o q D , w h e r e q i s t h e m a g n i t u d e o f t h e s c a t t e r i n g v e c t o r ( q = ( 4 π η / λ ) s i n (Θ / 2 ) ) a n d D i s t h e t r a n s l a t i o n al diffusion coefficient. I f t h e sample i s d i l u t e enough t h a t t h e motion o f a p a r t i c l e i s n o t a f f e c t e d by t h e presence o f t h e other p a r t i c l e s i n t h e sample, o r i f Γ i s obtained as a f u n c t i o n of con c e n t r a t i o n and e x t r a p o l a t e d t o z e r o c o n c e n t r a t i o n , one o b t a i n s t h e single-particle diffusion coefficient. I f t h e medium i s a N e w t o n i a n f l u i d and one f u r t h e r assumes t h a t t h e p a r t i c l e s a r e s p h e r i c a l ( a n excellent assumption f o r emulsions), the Stokes-Einstein r e l a t i o n between t h e s i n g l e - p a r t i c l e d i f f u s i o n c o e f f i c i e n t and t h e h y d r o dynamic d i a m e t e r o f a p a r t i c l e c a n be used ( i . e . D = kT/(3irnd)), ( 1 )

C L )

c 2 >

2

Γ

=

2

2

2

(^kTn sin |-)/(3riX d)

(2)

where k i s t h e Boltzmann c o n s t a n t , Τ i s temperature, η i st h e r e f r a c t i v e index o f t h e f l u i d , θ i s t h e s c a t t e r i n g angle, η i st h e v i s c o s i t y , λ i s t h e wavelength o f t h e l i g h t , and d i s t h e p a r t i c l e diameter.

In Particle Size Distribution; Provder, Theodore; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

6.

HERB ET AL.

91

Quasi-Elastic Light Scattering ( 1 >

For p o l y d i s p e r s e samples, g ( x ) i s a f u n c t i o n not only of the d e l a y t i m e T, b u t a l s o o f t h e d i s t r i b u t i o n o f d e c a y c o n s t a n t s a s shown i n E q u a t i o n 3 i n i n t e g r a l f o r m and i n E q u a t i o n 4 i n a l g e b r a i c form.

g

( 1

(T)

=

M Σ i=l

θχρ(-Γ.τ)

(4)

1

( 1 )

Thus, g i v e n g ( T ) , we n e e d t o d e t e r m i n e t h e p a r t i c l e s i z e distribution. For narrow s i z e d i s t r i b u t i o n s , 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 s s a t i s f a c t o r i l y a n a l y z e d by t h e method o f c u m u l a n t s t o g i v e t h e moments o f t h e p a r t i c l e s i z e d i s t r i b u t i o n . ( 7 ) However, the a n a l y s i s o f QELS d a t a f o r s a m p l e s w i t h p o l y d i s p e r s e o r m u l t i m o d a l d i s t r i b u t i o n s r e m a i n s an a r e a o f a c t i v e r e s e a r c h . ( 8 ) I n o r d e r t o o b t a i n t h e p a r t i c l e - s i z e d i s t r i b u t i o n , one must i n v e r t E q u a t i o n 3 o r 4 n u m e r i c a l l y . When t h e d a t a a r e a n a l y z e d v i a E q u a t i o n 4, o n e o b t a i n s a h i s t o g r a m d e s c r i b e d b y a p r o b a b i l i t y f o r each decay c o n s t a n t , expressed by the v e c t o r s e t (^,Γ^). A p a r t i c l e d i a m e t e r d i s t r i b u t i o n c a n t h e n be o b t a i n e d f r o m t h i s v i a E q u a t i o n 2. On f i r s t g l a n c e , i t w o u l d s e e m t h a t o n e c o u l d s i m p l y c h o o s e a l a r g e number o f p a r t i c l e s i z e s , c a l c u l a t e t h e c o r r e s p o n d i n g d e c a y c o n s t a n t s , a n d f i n d t h e b e s t s e t o f a^'s b y a l e a s t s q u a r e s f i t o f the g ( T ) d a t a t o E q u a t i o n 4 f o r t h e assumed p a r t i c l e s i z e s . The expectation i s t h a t only those s i z e s that are a c t u a l l y i n the d i s p e r s i o n w i l l appear i n the f i n a l d i s t r i b u t i o n . U n f o r t u n a t e l y , the i n v e r s i o n o f E q u a t i o n 4 i s known t o be i l l - c o n d i t i o n e d f o r t h e standard l e a s t squares technique. That i s , s m a l l changes i n the measured d a t a l e a d t o l a r g e v a r i a t i o n s i n the c a l c u l a t e d d i s t r i b u t i o n s . (9) A more d e t a i l e d d i s c u s s i o n o f t h e p r o b l e m has been g i v e n by P i k e ( 1 0 ) , i n w h i c h he s u g g e s t s t h a t t h e i l l - c o n d i t i o n e d n a t u r e o f t h e i n v e r s i o n w i l l be r e d u c e d by l i m i t i n g t h e r a n g e o f t h e s o l u t i o n s p a c e v i a a p r i o r i i n f o r m a t i o n a b o u t t h e d i s t r i b u t i o n , and by i n c r e a s i n g the range of delay times over which the a u t o c o r r e l a t i o n function i s obtained. The i n c r e a s e i n t h e r a n g e o f d e l a y t i m e s h a s been s u c c e s s f u l l y a d d r e s s e d by t h e m a n u f a c t u r e r s o f d i g i t a l a u t o c o r r e l a t o r s by p r o v i d i n g n o n - l i n e a r s p a c i n g o f t h e c o r r e l a t o r channels. The u s e o f r e a s o n a b l e a p r i o r i i n f o r m a t i o n t o l i m i t t h e r a n g e o f t h e s o l u t i o n s p a c e w i l l be d i s c u s s e d i n t h e n e x t s e c t i o n . ( 1 )

The

Inversion Algorithm

Requirements. A s u c c e s s f u l and y e t p r a c t i c a l n u m e r i c a l p r o c e d u r e f o r o b t a i n i n g p a r t i c l e - s i z e d i s t r i b u t i o n s f r o m QELS d a t a m u s t : 1) b e s t a b l e a g a i n s t r a n d o m e x p e r i m e n t a l e r r o r , 2) c l e a r l y d i f f e r e n t i a t e m u l t i m o d a l d i s t r i b u t i o n s from broad unimodal ones w i t h o u t a p r i o r i k n o w l e d g e o f t h e s h a p e o f t h e d i s t r i b u t i o n , 3) r e q u i r e o n l y m i n i m a l o p e r a t o r i n p u t , a n d 4) a p p l y t o b o t h n a r r o w a n d b r o a d particle size distributions. An a d d i t i o n a l d e s i d e r a t u m i s t h a t t h e c o m p u t e r r e q u i r e m e n t s be k e p t t o a r e a s o n a b l e l e v e l .


92



Proposal. We h a v e r e c e n t l y d e s c r i b e d a p r o c e d u r e t h a t we b e l i e v e m e e t s t h e r e q u i r e m e n t s l i s t e d a b o v e . ( 1 1 ) M o r e s p e c i f i c a l l y , we h a v e s h o w n tha.t t h e 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 n b e e x t r a c t e d f r o m t h e QELS d a t a b y a c o m b i n a t i o n o f a ) a c o n v e r g e n t n u m e r i c a l a l g o r i t h m t h a t makes use o f t h e f a c t t h a t t h e d i s t r i b u t i o n o f s i z e s must be n o n - n e g a t i v e ( 1 2 ) , b) a n a l y s i s o f e a c h d a t a s e t w i t h m u l t i p l e b u t e q u i v a l e n t b a s i s s e t s o f p a r t i c l e s i z e s ( 1 3 ) , and c) t h e a v e r a g i n g of d i s t r i b u t i o n s o b t a i n e d from r e p e a t e d , independent measurements f o r each sample analyzed.(11) Only a b r i e f d i s c u s s i o n of the proce d u r e w i l l be g i v e n h e r e . More complete d i s c u s s i o n s are g i v e n e l s e w h e r e . (Π.,12) The N o n - N e g a t i v e C o n s t r a i n t . A s d i s c u s s e d a b o v e , t h e i n v e r s i o n o f Equation 4 i s i l l - c o n d i t i o n e d . T h i s m a n i f e s t s i t s e l f most c l e a r l y by p r o v i d i n g d i s t r i b u t i o n s w i t h n e g a t i v e components when o r d i n a r y l e a s t squares algorithms are used. The t e n d e n c y t o p r o d u c e t h e s e p h y s i c a l l y i m p o s s i b l e s o l u t i o n s c a n b e r e d u c e d b y l i m i t i n g t h e num b e r o f assumed p a r t i c l e s i z e s u s e d i n t h e i n v e r s i o n . T h i s d e c r e a s e s the range of the s o l u t i o n space, thus reducing the i l l - c o n d i t i o n e d n a t u r e o f t h e p r o b l e m as d i s c u s s e d i n t h e l a s t s e c t i o n . Unfortu n a t e l y , i t has b e e n f o u n d t h a t t h e number o f s i z e s t h a t can be u s e d s u c c e s s f u l l y i s s o f e w (5 o r 6 a t b e s t ) t h a t t h e s i z e r e s o l u t i o n i s poor. A n o t h e r way t o s i g n i f i c a n t l y d e c r e a s e t h e r a n g e o f t h e s o l u t i o n s p a c e i s t o d i s a l l o w a l l s o l u t i o n s t h a t c o n t a i n n e g a t i v e compo nents. The u s e o f t h i s n o n - n e g a t i v e c o n s t r a i n t d u r i n g t h e c a l c u l a t i o n s s u b s t a n t i a l l y reduces the i l l - c o n d i t i o n e d nature of the inversion. The i n c r e a s e i n t h e s t a b i l i t y o f t h e i n v e r s i o n a l l o w s a l a r g e r number o f unknowns t o be u s e d , t h u s i n c r e a s i n g t h e p o t e n t i a l resolution. To i m p l e m e n t t h e m e t h o d o f n o n - n e g a t i v e l y constrained l e a s t s q u a r e s , we c h o o s e t h e m e t h o d o f L a w s o n a n d H a n s o n ( 1 4 ) c a l l e d NNLS ( f o r n o n - n e g a t i v e l e a s t s q u a r e s ) . The u s e o f t h i s a p r i o r i i n f o r m a t i o n has not l i m i t e d the g e n e r a l n a t u r e of the d i s t r i b u t i o n i n a n y way. The d e t a i l s o f u s i n g NNLS f o r t h e QELS p r o b l e m h a v e been presented elsewhere.(12) M u l t i p l e P a s s A n a l y s i s . P i k e and c o w o r k e r s (13) h a v e p r o v i d e d a method t o i n c r e a s e the r e s o l u t i o n of the o r d i n a r y l e a s t s q u a r e s a l g o r i t h m somewhat. I t was n o t e d t h a t a n y r e a s o n a b l e s e t o f a s s u m e d p a r t i c l e s i z e s c o n s t i t u t e s a b a s i s set f o r the i n v e r s i o n ( w i t h i n experimental error). T h u s , t h e d a t a c a n be a n a l y z e d a number o f t i m e s w i t h a d i f f e r e n t b a s i s s e t e a c h t i m e , and t h e r e s u l t s c o m b i n e d . A s t a t i s t i c a l l y m o r e - p r o b a b l e s o l u t i o n r e s u l t s f r o m an a v e r a g e o f the s e v e r a l e q u a l l y - l i k e l y s o l u t i o n s . Although t h i s " m u l t i p l e pass a n a l y s i s " helps l o c a t e the peaks of the d i s t r i b u t i o n w i t h b e t t e r r e s o l u t i o n and p r o v i d e s a s m o o t h e r p r e s e n t a t i o n o f t h e r e s u l t , i t can s t i l l o n l y p r o v i d e l i m i t e d r e s o l u t i o n w i t h o u t t h e use of a nonn e g a t i v e l y constrained l e a s t squares technique. We h a v e s h o w n , however, t h a t the combination of both the n o n - n e g a t i v e l y constrained c a l c u l a t i o n and t h e m u l t i p l e p a s s a n a l y s i s g i v e s t h e a d v a n t a g e s o f both. We i m p l e m e n t m u l t i p l e p a s s a n a l y s i s f o r a n a r b i t r a r y s p a c i n g o f assumed s i z e s as f o l l o w s . L e t t h e r e be M assumed p a r t i c l e s i z e s s u b m i t t e d t o t h e NNLS i n v e r s i o n r o u t i n e f o r e a c h o f Ρ p a s s e s . Thus, t h e f i n a l h i s t o g r a m w i l l c o n t a i n MP d i f f e r e n t p a r t i c l e s i z e s s p a c e d i n some f a s h i o n ( e . g . l o g a r i t h m i c a l l y , q u a d r a t i c a l l y , o r l i n e a r l y )


6.

Quasi-Elastic Light Scattering

HERB ET AL.

93


over the a p p r o p r i a t e range. The u p p e r and l o w e r l i m i t s o f t h e r a n g e c a n be c h o s e n by t h e o p e r a t o r i f r e a s o n a b l e v a l u e s a r e known, o r t h e y can be c h o s e n by t h e p r o g r a m f r o m t h e shape o f t h e f i r s t a u t o correlation function. O n c e t h e r a n g e i s s e l e c t e d , a l l MP s i z e s a r e c a l c u l a t e d a c c o r d i n g t o t h e c h o s e n s p a c i n g scheme. We a c t u a l l y s u b m i t M+l s i z e s t o NNLS o n e a c h p a s s , t h e e x t r a size corresponding to a "dust" signal ( i . e . i n f i n i t e p a r t i c l e s i z e o r a z e r o d e c a y c o n s t a n t ) . T h u s , o n t h e f i r s t p a s s , we f i n d t h e best f i t to the c o r r e l a t i o n f u n c t i o n using only the M f l p a r t i c l e sizes: d

In

d

d

l ' P + l ' 2P+l»

g e n e r a l , on

V

t h e j t h p a s s , we d

P+j> 2P+j d

a

"W-P+l' use

t h e M+l

n

d

d

dust

particle

"W-P+j'

a

n

d

d

sizes:

dust

The a n a l y s i s f r o m t h e Ρ p a s s e s a r e c o m b i n e d t o g i v e a n o v e r a l l m u l t i p l e pass a n a l y s i s of the data. The r e s u l t i s a n MP b i n h i s t o g r a m and a m e a s u r e o f t h e amount o f t h e s i g n a l t h a t i s due t o " d u s t " . D i s t r i b u t i o n Averaging. Although the r e s o l u t i o n i s s i g n i f i c a n t l y improved by t h e use o f a n o n - n e g a t i v e l y c o n s t r a i n e d l e a s t s q u a r e s a l g o r i t h m , i t h a s two s h o r t c o m i n g s : 1) C o r r e l a t e d e x p e r i m e n t a l e r r o r i s o f t e n i n t e r p r e t e d a s s m a l l s p u r i o u s p e a k s ; a n d 2) B r o a d unimodal d i s t r i b u t i o n s t e n d t o be r e p r e s e n t e d by a s e t o f s e p a r a t e d p e a k s . Although m u l t i p l e pass a n a l y s i s improves the p r e s e n t a t i o n of m u l t i m o d a l d i s t r i b u t i o n s and u n i m o d a l d i s t r i b u t i o n s t h a t a r e n o t t o o w i d e , i t f a i l s t o c o r r e c t t h e s e two shortcomings. We h a v e f o u n d t h a t b o t h t h e s e s h o r t c o m i n g s c a n b e r e d u c e d o r e l i m i n a t e d b y t a k i n g m u l t i p l e d a t a s e t s o n t h e same s a m p l e , a n a l y z i n g e a c h d a t a s e t i n d e p e n d e n t l y , and a v e r a g i n g a l l o f t h e r e s u l t i n g size distributions. The c o r r e c t p e a k s a r e r e i n f o r c e d w h i l e s p u r i o u s p e a k s a r e d i m i n i s h e d . A gap w i l l r e m a i n b e t w e e n t h e p e a k s o f a t r u e bimodal sample. I f , however, the sample a c t u a l l y has a w i d e u n i modal d i s t r i b u t i o n , the p o s i t i o n s of the separated peaks w i l l v a r y f r o m one d a t a s e t t o a n o t h e r , t h u s f i l l i n g i n t o a s m o o t h u n i m o d a l peak. Once a g a i n , a s t a t i s t i c a l l y m o r e - p r o b a b l e s o l u t i o n r e s u l t s f r o m an a v e r a g e o f t h e s e v e r a l e q u a l l y - l i k e l y s o l u t i o n s . (The number o f i n d e p e n d e n t d a t a s e t s u s e d s h o u l d b e g r e a t e r t h a n t w i c e t h e num b e r o f p a r t i c l e s i z e s i n t h e b r o a d e s t p e a k d i v i d e d b y P, t h e n u m b e r of passes.) What 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 i s t h a t t h e QELS a n a l y s i s i s enhanced by t h e c o m b i n a t i o n o f the t h r e e t e c h n i q u e s p r e s e n t e d h e r e w i t h o u t i n t r o d u c i n g a n y new a s s u m p t i o n s o r r e q u i r i n g a n y unreasona b l e a p r i o r i i n f o r m a t i o n , n o t even t h a t t h e d i s t r i b u t i o n must be smooth. Peak Broadening. The p e a k s o b t a i n e d b y t h e p r o c e d u r e o u t l i n e d a b o v e c a n b e b r o a d e n e d b e y o n d t h e t r u e d i s t r i b u t i o n b y two t h i n g s . First, t h e use o f t o o few assumed p a r t i c l e s i z e s f o r t h e i n v e r s i o n w i l l o b v i o u s l y c a u s e t h e r e p o r t e d d i s t r i b u t i o n t o be b r o a d e r t h a n i t s h o u l d be. T h i s p r o b l e m i s r e s o l v e d by c h o o s i n g a l a r g e r number o f assumed s i z e s . (We t y p i c a l l y c h o o s e t w e n t y p a r t i c l e d i a m e t e r s f o r e a c h i n v e r s i o n . ) The s e c o n d p r o b l e m i s t h a t t h e r e p o r t e d d i s t r i b u t i o n w i l l be a r t i f i c i a l l y b r o a d e n e d by e x c e s s i v e n o i s e i n t h e a u t o -


94


c o r r e l a t i o n f u n c t i o n s o b t a i n e d . T h i s can o n l y be s o l v e d by i n c r e a s ing the q u a l i t y of the data c o l l e c t e d , which implies longer data c o l l e c t i o n times o r an i n c r e a s e i n t h e photon count r a t e , i f p o s s i ble. We h a v e p r e v i o u s l y d e m o n s t r a t e d t h i s n o i s e r e l a t e d b r o a d e n i n g w i t h a mixture of l a t e x standards (11,15). P r a c t i c a l l y , we h a v e found that t h i s broadening i s n o t a s e r i o u s problem i f t h e t o t a l p h o t o n c o u n t f o r e a c h a u t o c o r r e l a t i o n f u n c t i o n i s k e p t a b o v e 15 o r 20 m i l l i o n ( e . g . 10 m i l l i o n s a m p l e s w i t h a c o u n t r a t e o f 1.5 t o 2 photons p e r sample t i m e ) .


Emulsion

Studies

As d i s c u s s e d e a r l i e r , i t i s known t h a t 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 present d u r i n g e m u l s i f i c a t i o n can a f f e c t the p a r t i c l e s i z e o f an emulsion. I t h a s a l s o b e e n shown t h a t t h e s t a b i l i t y o f a n e m u l s i o n c a n be a f f e c t e d i n r a t h e r u n e x p e c t e d ways by c h a n g i n g t h e c o n c e n t r a t i o n o f t h e s u r f a c t a n t ( 1 6 ) . The t e c h n i q u e s p r e s e n t e d i n t h e l a s t section allow the researcher to follow the f u l l particle-size dis t r i b u t i o n o f t h e emulsion system r a t h e r than j u s t an average diame ter. U s i n g s e v e r a l o i l / w a t e r e m u l s i o n s y s t e m s a s e x a m p l e s , we dem onstrate t h e a b i l i t y o f these techniques t o determine the e f f e c t of e m u l s i f i e r c o n c e n t r a t i o n on t h e p a r t i c l e - s i z e d i s t r i b u t i o n produced by a n i n v e r s i o n method o f e m u l s i f i c a t i o n . Some o f t h e b e n e f i t s o f o b t a i n i n g t h e f u l l d i s t r i b u t i o n w i l l a l s o be d i s c u s s e d . Experimental. P a r t i c l e - s i z e d i s t r i b u t i o n r e s u l t s were o b t a i n e d f o r three emulsion systems, r e f e r r e d t o a s s y s t e m s A , B, a n d C. T h e o i l phase o f e m u l s i o n systems A and C c o n s i s t s o f 70% by weight o f a thermoset r e s i n i n an o r g a n i c s o l v e n t . The o i l phase o f e m u l s i o n s y s t e m Β i s a d i f f e r e n t t h e r m o s e t r e s i n w i t h no s o l v e n t p r e s e n t . A d i f f e r e n t n o n i o n i c e m u l s i f i e r was u s e d f o r e a c h o f t h e t h r e e e m u l s i o n systems. The e m u l s i o n s were p r e p a r e d by s l o w l y a d d i n g w a t e r t o the m i x t u r e o f o i l phase and s u r f a c t a n t i n a h i g h shear m i x e r . Fol lowing i n v e r s i o n from the w a t e r / o i l t o o i l / w a t e r emulsion, a d d i t i o n a l w a t e r was added t o b r i n g t h e f i n a l i n t e r n a l p h a s e t o 5 0 % b y weight. The l i g h t s c a t t e r i n g s a m p l e s w e r e p r e p a r e d b y d i l u t i n g a s m a l l p o r t i o n o f t h e e m u l s i o n t o 20 mg/L o i l p h a s e w i t h a d u s t f r e e , 10 mg/L s o l u t i o n o f t h e e m u l s i f i e r . The s a m p l e was t h e n f i l t e r e d t h r o u g h a 5 m i c r o m e t e r membrane f i l t e r d i r e c t l y i n t o t h e s c a t t e r i n g cell. Equipment. A l l s c a t t e r i n g e x p e r i m e n t s were done on a BI240 l i g h t s c a t t e r i n g goniometer from Brookhaven Instruments C o r p o r a t i o n . T h i s i n c l u d e s a l l t h e n e c e s s a r y o p t i c s , sample c e l l assembly, p h o t o m u l t i p l i e r tube, a m p l i f i e r / d i s c r i m i n a t o r , and t h e goniometer base i t s e l f . The t e m p e r a t u r e o f t h e s a m p l e c e l l a n d i n d e x m a t c h i n g l i q u i d s u r r o u n d i n g t h e c e l l w a s h e l d a t 25°C w i t h a N e s l a b RTE-5DD c i r c u l a t i n g bath. T h e l i g h t s o u r c e i s a S p e c t r a - P h y s i c s , M o d e l 1 2 4 B , 15 mW, l i n e a r l y p o l a r i z e d , HeNe l a s e r . The l a s e r a n d o p t i c a l components a r e mounted on a Newport R e s e a r c h C o r p o r a t i o n v i b r a t i o n i s o l a t i o n table. A BI2020 d i g i t a l c o r r e l a t o r , a l s o from Brookhaven Instruments, r e c e i v e s t h e s i g n a l from t h e a m p l i f i e r / d i s c r i m i n a t o r . The c o r r e l a t o r h a s 136 c h a n n e l s f o l l o w e d b y 4 b a s e l i n e c h a n n e l s s t a r t i n g a t 1024 s a m p l e t i m e s . I n our laboratory, the correlator i s controlled


6.

HERB ET AL.

Quasi-Elastic Light Scattering

95


by a H e w l e t t - P a c k a r d 236 m i c r o c o m p u t e r ( f o r m e r l y d e s i g n a t e d t h e H P 9 8 3 6 ) , w h i c h a l s o p e r f o r m s t h e d i s t r i b u t i o n a n a l y s i s . The p r o g r a m c o n t r o l s t h e BI2020 c o r r e l a t o r w h i l e c a l c u l a t i n g t h e d i s t r i b u t i o n f r o m t h e l a t e s t a u t o c o r r e l a t i o n f u n c t i o n . I n t h i s way d a t a c a n be collected while the i n d i v i d u a l d i s t r i b u t i o n s are being calculated and a v e r a g e d . The s y s t e m r e q u i r e s no o p e r a t o r i n p u t once t h e r u n has b e e n s t a r t e d . The f i n a l d i s t r i b u t i o n s a r e c o n v e r t e d f r o m l i g h t i n t e n s i t i e s t o mass f r a c t i o n s u s i n g t h e M i e c o r r e c t i o n f a c t o r s a s i s discussed i n a later section. Results. F i g u r e 1 shows t h e d i s t r i b u t i o n s f o r e m u l s i o n s y s t e m A f o r t o t a l e m u l s i f i e r c o n c e n t r a t i o n s r a n g i n g f r o m 3.5 t o 2 0 g / 1 0 0 g o i l phase. I t c a n b e s e e n t h a t b o t h t h e mean d i a m e t e r a n d t h e w i d t h o f the d i s t r i b u t i o n decrease w i t h i n c r e a s i n g s u r f a c t a n t l e v e l . The same t r e n d w a s s e e n f o r s y s t e m Β o v e r t h e r a n g e o f 8 t o 21 g / 1 0 0 g o i l phase. System Β c o u l d n o t be e m u l s i f i e d by t h e i n v e r s i o n t e c h nique below t h i s range. F i g u r e 2 s h o w s t h e mean d i a m e t e r a n d s t a n d ard d e v i a t i o n s o f both systems as a f u n c t i o n o f e m u l s i f i e r concen tration. ( I t i s interesting, but only a coincidence, that both s y s t e m s g i v e t h e same r e s u l t s o v e r t h e 8 t o 2 0 g / 1 0 0 g r a n g e . ) Thus, f o r t h e s e s y s t e m s o n e c a n now p r e d i c t t h e mean d i a m e t e r a n d t h e w i d t h o f t h e d i s t r i b u t i o n once 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 i s known. Conversely, i f t h e d i s t r i b u t i o n o f a sample were measured f o r q u a l i t y c o n t r o l purposes and t h e d i a m e t e r and w i d t h were t o o h i g h , an i n c o r r e c t s u r f a c t a n t c o n c e n t r a t i o n d u r i n g e m u l s i f i c a t i o n would be i n d i c a t e d as a p o s s i b l e cause. A m o r e i n t e r e s t i n g way t o l o o k a t t h e d a t a i s t o p l o t t h e s p e c i f i c surface area of the emulsion droplets as a f u n c t i o n of the s u r f a c t a n t c o n c e n t r a t i o n a s s h o w n i n F i g u r e 3. ( T h e s u r f a c e a r e a w a s c a l c u l a t e d f r o m t h e f u l l d i s t r i b u t i o n r a t h e r t h a n f r o m a mean d i a m e ter.) Thus, i t c a n be seen t h a t , o v e r t h e r a n g e s t u d i e d , a n i n c r e a s e i n t h e amount o f s u r f a c t a n t p r e s e n t c a u s e s a p r o p o r t i o n a l i n crease i n the surface area created. Because a l l o f these d i s t r i b u t i o n s a r e unimodal and have r e l a t i v e s t a n d a r d d e v i a t i o n s l e s s t h a n 3 5 % , t h e method o f c u m u l a n t s c o u l d h a v e b e e n u s e d t o o b t a i n t h e d a t a o f F i g u r e 2. H o w e v e r , t h e d i s t r i b u t i o n t e c h n i q u e used h e r e c a n d i s t i n g u i s h between b i m o d a l and b r o a d u n i m o d a l d i s t r i b u t i o n s w i t h no o p e r a t o r i n t e r v e n t i o n o r a p r i o r i knowledge about t h e sample. The i m p o r t a n c e o f t h i s a b i l i t y i s d e m o n s t r a t e d b y t h e d i s t r i b u t i o n o f e m u l s i o n s y s t e m C shown i n F i g u r e 4. T h i s s y s t e m w a s p r e p a r e d i n a n i d e n t i c a l f a s h i o n t o s y s t e m s A a n d B, b u t w i t h a l o w c o n c e n t r a t i o n o f a d i f f e r e n t n o n i o n i c emulsifier. The r e s u l t i n g b i m o d a l d i s t r i b u t i o n was c e r t a i n l y n o t an expected r e s u l t . Note t h a t t h e broad unimodal o f F i g u r e l a and t h e b i m o d a l o f F i g u r e 4 h a v e s i m i l a r mean d i a m e t e r s a n d s t a n d a r d d e v i a tions. The a b i l i t y t o d i s t i n g u i s h b e t w e e n t h e two c a n b e o f s i g n i f i c a n t a s s i s t a n c e i n t h e i n v e s t i g a t i o n o f emulsion systems. Indeed, t h e d i s t r i b u t i o n shown i n F i g u r e 4 i s i n d i c a t i v e o f n o n - u n i f o r m shear conditions during the e m u l s i f i c a t i o n rather than a s u r f a c t a n t concentration problem. F l o c c u l a t i o n versus Coalescence. The b r e a k i n g o f a n e m u l s i o n i s a two s t e p p r o c e s s r e q u i r i n g t h e c o a l e s c e n c e o f t h e d r o p l e t s a f t e r they a r e i n contact.(17) I f t h e system f l o c c u l a t e s b u t i s r e s i s t a n t to coalescence, t h e system w i l l n o t phase separate. Over a p e r i o d


96


(a) d = 754 nm σ = 212 nm (excluding 5 bins of n o i s e a g a i n s t upper bound)

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(c) d = 286 σ = 98

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d = 202 σ = 65

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Particle Size Distribution - American Chemical Society

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