Colloids and Surfaces in Reprographic Technology - American

14 Physics of Nonaqueous Colloids

Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on June 23, 2016 | http://pubs.acs.org Publication Date: October 13, 1982 | doi: 10.1021/bk-1982-0200.ch014

V. J. NOVOTNY

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Xerox Research Centre of Canada, Mississauga, Ontario, Canada L5L1J9

Nonaqueous colloids differ considerably from aqueous dispersions because of their low electrical conductivity. This low conductivity leads to nonuniform, time varying electric fields in classical electrophoretic geometries and thus creates difficulties in determining colloidal properties. Characrerization methods, especially optical and electrical techniques, are reviewed and evaluated in terms of their utility in the study of nonaqueous colloids. Problems in the measurements of particle mobility, charge, particle-substrate forces, ionic concentrations and mobilities mainly due to space charge effects and electrohydrodynamics are also discussed. Based on colloid characterization, two classes of nonaqueous suspensions are distinguished. Colloids with intermediate conductivities correspond to physically adsorbed charge control agent (cca) which is in dynamic equilibrium with cca in solution. Low conductivity colloids have cca precipitated or chemically attached to the particle surfaces. The latter systems contain a few excess ions in solution and thus represent very nonclassical colloids. Despite low dissociation of cca in nonaqueous media, high particle mobilities and charges are attainable. Aforementioned colloidal properties are related to liquid development of latent images and important characteristics of liquid ink are outlined. Also, effect of space charge and turbulence are assessed in liquid development of electrostatic images.

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Current address: Exxon Enterprises, Sunnyvale, CA 94086.

0097-6156/82/0200-0281$06.00/0 © 1982 American Chemical Society Hair and Croucher; Colloids and Surfaces in Reprographic Technology ACS Symposium Series; American Chemical Society: Washington, DC, 1982.


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REPROGRAPHIC TECHNOLOGY

T h i s p a p e r i s i n t e n d e d t o r e v i e w c h a r a c t e r i z a t i o n methods o f nonaqueous c o l l o i d s , t h e i r p h y s i c a l p r o p e r t i e s and t e c h n o logical applications. The d e s c r i p t i o n o f a c o l l o i d s h o u l d i n c l u d e p a r t i c l e s i z e , m o b i l i t y , c h a r g e and t h e i r d i s t r i b u t i o n s , charge/mass r a t i o , e l e c t r i c a l c o n d u c t i v i t y o f t h e m e d i a , c o n c e n t r a t i o n and mob i l i t y of i o n i c s p e c i e s , t h e e x t e n t of a double l a y e r , p a r t i c l e - p a r t i c l e and p a r t i c l e - s u b s t r a t e i n t e r a c t i o n f o r c e s and complete i n t e r f a c i a l a n a l y s i s . The a p p l i c a t i o n o f c l a s s i c a l c h a r a c t e r i z a t i o n methods t o nonaqueous c o l l o i d s i s l i m i t e d and, f o r t h i s r e a s o n , the t e c h n i q u e s b e s t s u i t e d t o these s y s t e m s w i l l be r e v i e w e d . C h a r a c t e r i s t i c r e s u l t s obtained w i t h nonaqueous d i s p e r s i o n s w i l l be s u m m a r i z e d . Physical a s p e c t s , such as s p a c e c h a r g e e f f e c t s and e l e c t r o h y d r o d y n a m i e s , w i l l r e c e i v e s p e c i a l a t t e n t i o n w h i l e the r e l a t i o n s h i p s between c h e m i c a l and p h y s i c a l p r o p e r t i e s w i l l n o t be a d d r e s sed. An a p p l i c a t i o n o f nonaqueous c o l l o i d s , t h e e l e c t r o p h o r e t i c d e v e l o p m e n t o f l a t e n t i m a g e s , w i l l a l s o be d i s c u s s e d . Characterization

Methods

The k e y p a r a m e t e r s c h a r a c t e r i z i n g t h e c o l l o i d a r e p a r t i c l e m o b i l i t i e s and s i z e s . The most p o p u l a r t e c h n i q u e f o r m o b i l i t y measurement i s m i c r o e l e c t r o p h o r e s i s ( 1 _ , 2 ) i n w h i c h t h e c o l l o i d a l p a r t i c l e s a r e a l l o w e d t o move i n a u n i f o r m e l e c t r i c f i e l d and t h e i r v e l o c i t i e s a r e o b s e r v e d w i t h an o p t i c a l m i c r o s c o p e . Measurements a r e l i m i t e d t o c o l l o i d a l p a r t i c l e s o b s e r v a b l e m i c r o s c o p i c a l l y , w h i c h i s above~0.1 ym w i t h d a r k f i e l d i l l u mination. When t h i s t e c h n i q u e i s combined w i t h l i g h t s c a t t e r i n g d e t e c t i o n - q u a s i e l a s t i c ( 3 ^ 4 j o r crossbeam i n t e r f e r e n c e ^ ) , p a r t i c l e v e l o c i t i e s c a n be measured e a s i l y a n d t h e minimum d e t e c t a b l e s i z e i s s i g n i f i c a n t l y r e d u c e d t o - 20A. Application o f t h e s e methods t o aqueous c o l l o i d s i s s t r a i g h t f o r w a r d b e c a u s e t h e s u s p e n d i n g m e d i a g e n e r a l l y have h i g h e l e c t r i c a l c o n d u c t i v i t y (a* 10*2q- m- ; and t h e e l e c t r i c f i e l d between d i s tant electrodes is uniform. The same i s t r u e f o r h i g h c o n d u c t i v i t y nonaqueous c o l l o i d s . In r e l a t i v e l y n o n c o n d u c t i n g m e d i a (a y E/r where r i s the p a r t i c l e r a d i u s ) . The s e c o n d i m p o r t a n t phenomenon w h i c h c a n be s i g n i f i c a n t d u r i n g e l e c t r o p h o r e s i s i s EHD(27), shown in F i g u r e 3 . T h i s o c c u r s when i o n s m o v i n g i n t h e f l u i d d r a g a l o n g t h e f l u i d m o l e c u l e s and s e t up f l u i d m o t i o n , u s u a l l y i n t h e f o r m o f v o r t i c e s . As a r e s u l t o f EHD, t h e a p p a r e n t m o b i l i t i e s o f i o n s and c h a r g e d p a r t i c l e s can be s u b s t a n t i a l l y h i g h e r t h a n i n t h e s t a t i o n a r y fluid. In t h e c o l l o i d , EHD can be r e c o g n i z e d e a s i l y b e c a u s e p a r t i c l e s l a r g e l y f o l l o w the f l u i d f l o w . The m o t i o n o f c h a r g e d p a r t i c l e s i s n o t c o l i n e a r and many p a r t i c l e s may move i n d i f f e r e n t d i r e c t i o n s than expected from the p o l a r i t y of t h e i r c h a r g e and d i r e c t i o n o f t h e f i e l d . When t h e c h a r g e d p a r t i c l e s a r e a l l o w e d t o p l a t e - o u t o n t o t h e e l e c t r o d e i n t h e non-EHD regime, the d e p o s i t i s u n i f o r m . D u r i n g EHD, t h e p l a t e o u t d e p o s i t i s n o n u n i f o r m and u s u a l l y has f e a t u r e s and d i m e n s i o n s corresponding to the s i z e of the v o r t i c e s . Charged p a r t i c l e s t e n d t o c o l l e c t on t h e e l e c t r o d e s i n r e l a t i v e l y s t a t i o n a r y a r e a s where t h e r e i s minimum f l u i d f l o w . At low v o l t a g e s EHD i s not p r e s e n t ; at i n t e r m e d i a t e v o l t a g e s ( t y p i c a l l y tens of v o l t s ) EHD i s l a m i n a r w i t h v o r t i c e s o f t h e s i z e o f t h e c e l l t h i c k n e s s w h i l e a t h i g h e r v o l t a g e s EHD i s t u r b u l e n t and v o r t i c e s may be c o n s i d e r a b l y s m a l l e r . The o n s e t o f t u r b u l e n c e i s a f f e c t e d by many f a c t o r s i n c l u d i n g t h e c o n d u c t i o n m e c h a n i s m , space charge e f f e c t s , charge i n j e c t i o n , type of t r a n s i e n t , c o n d u c t i v i t i e s g e o m e t r y and p r o p e r t i e s o f t h e m e d i a . For u n i p o l a r c o n d u c t i o n the t h r e s h o l d v o l t a g e V from l a m i n a r i n t o the t u r b u l e n t r e g i m e i s r o u g h l y V = 30 n / ( p e e J / o r a b o u t 1 0 V o l t s f o r t y p i c a l values of v i s c o s i t y , n , and d e n s i t y , P . 0

c

c

0

1

2

Hair and Croucher; Colloids and Surfaces in Reprographic Technology ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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Physics of Nonaqueous Colloids

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NOVOTNY

Figure 2. Representation of space charge limited conditions in one dimension showing the profile of concentrations of positive (P) and negative (N) species and electricfieldvariations at time of thefieldapplication (t — 0) and at some later time (t > 0).



Figure 3. Schematic of electrohydrodynamic conditions in unipolar and bipolar conduction.



14.

291


NOVOTNY

I t i s p r e f e r a b l e t o p e r f o r m e l e c t r o p h o r e t i c measurements w i t h o u t s p a c e c h a r g e and EHD e f f e c t s , w h i c h i s o f t e n d i f f i c u l t because high v o l t a g e s (hundreds of v o l t s ) are r e q u i r e d to avoid space charge c o n d i t i o n s w h i l e lower o p e r a t i n g v o l t a g e s ( t e n s o f v o l t s ) a r e needed t o p r e v e n t EHD. I t s h o u l d be e m p h a s i z e d t h a t i t t a k e s t i m e t o e s t a b l i s h EHD. It is a n t i c i p a t e d that times l o n g e r t h a n i o n i c t r a n s i t t i m e s i n t h e c e l l a r e needed t o s e t up EHD m o t i o n . Space c h a r g e c o n d i t i o n s can be d e s c r i b e d w i t h n u m e r i c a l m o d e l l i n g and a r e more e a s i l y t r e a t e d a n a l y t i c a l l y than problems a s s o c i a t e d w i t h t u r b u l e n c e . In some t e c h n o l o g i c a l a p p l i c a t i o n s w h i c h a r e a f f e c t e d by s p a c e c h a r g e and t u r b u l e n c e , the apparent p a r t i c l e m o b i l i t i e s are r e l e v a n t . The r e l a t i o n s h i p between p a r t i c l e c h a r g e , q , and m o b i l i t y , y , depends on t h e e x t e n t o f t h e e l e c t r i c a l d o u b l e l a y e r w h i c h i s g i v e n by

K

-1

/

1/2

ee kT n

e

2

s ,z, n

i

\ (3)

2

where n-j i s t h e c o n c e n t r a t i o n o f i o n s and z-j t h e i r v a l e n c y , e i s t h e e l e c t r o n i c c h a r g e , k i s t h e B o l t z m a n n ' s c o n s t a n t and T i s the a b s o l u t e temperature. The i o n i c c o n c e n t r a t i o n s and m o b i l i t i e s can be d e t e r m i n e d f r o m t h e a n a l y s i s o f e l e c t r i c a l transients. When t h e d o u b l e l a y e r s a r e e x t e n d e d ( x » r ) r e l a x a t i o n and r e t a r d a t i o n e f f e c t s ( 2 8 ) can be n e g l e c t e d . A p a r t i c l e w i t h c h a r g e q moves w i t h a u n i f o r m v e l o c i t y v w h i c h i s d e t e r m i n e d by t h e e q u a l i t y between t h e e l e c t r i c f o r c e qE and t h e S t o k e s f r i c t i o n f o r c e f v (where f i s a f r i c t i o n c o e f f i c i e n t e q u a l t o 6Trnvr f o r a s p h e r i c a l p a r t i c l e of r a d i u s , r , suspended i n t h e media w i t h v i s c o s i t y , n ). Thus, f o r a s p h e r i c a l p a r t i c l e i n t h e LC c o l l o i d q=

The c o r r e s p o n d i n g and m o b i l i t y i s

relationship

y = 2 ee £ / 3 Q

6frnyr

(4)

between

the z e t a p o t e n t i a l , c

,

(5)

n

Results The t y p i c a l r e s u l t s w i l l be i l l u s t r a t e d by one LC and one IC colloid. An example o f an LC s y s t e m ( 2 9 ) w i t h b a c k g r o u n d c o n d u c t i v i t i e s below 1 0 " n r ' w i l l be c a r b o n b l a c k d i s p e r s e d i n a l i p h a t i c h y d r o c a r b o n w i t h p o l y m e r i c m a t e r i a l s and charged with a metal s a l t of s t e a r i c a c i d . Electron microscopy r e v e a l e d t h a t the p a r t i c l e s are agglomerates in the 1 1

1



292


r a n g e o f 0 . 1 - 0 . 8 urn, e a c h composed o f c a r b o n b l a c k p i g m e n t as s m a l l as 0 . 0 3 ym. Due t o t h e p o s s i b i l i t y o f a g g l o m e r a t i o n in t h e p r e p a r a t i o n of m i c r o s c o p y s a m p l e s , the p a r t i c l e s i z e was d e t e r m i n e d by 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 . The a u t o c o r r e l a t i o n f u n c t i o n C ( T ) i s shown i n F i g u r e 4 t o g e t h e r w i t h an e x p o n e n t i a l f i t g i v i n g t h e a v e r a g e d i a m e t e r o f 0 . 3 ± 0 . 0 6 y m . The method o f c u m u l a n t s ( 3 0 ) y i e l d e d a s i m i l a r r e s u l t . N o n s p h e r i c i t y o f p a r t i c l e s was n e g l e c t e d . C a r e was t a k e n i n t h e s e measurements n o t t o i n d u c e t h e r m o p h o r e s i s . I t demons t r a t e s i t s e l f as e x c e s s m o t i o n o f p a r t i c l e s above t h e i r n o r mal B r o w n i a n m o t i o n c a u s e d by t h e a b s o r p t i o n o f l i g h t by p a r t i c l e s and t h e s u b s e q u e n t h e a t i n g o f p a r t i c l e s and t h e i r s u r rounding f l u i d . E l e c t r i c a l p l a t e o u t gave a charge/mass r a t i o o f 0 . 8 8 ± 0.05 C k g and showed t h a t t h e p a r t i c l e s were u n i p o l a r and p o s i t i v e l y charged. P a r t i c l e m o b i l i t i e s were d e t e r m i n e d by o p t i c a l sweepout t r a n s i e n t s . F o r t h i s c o l l o i d , a M a x w e l l , one parameter d i s t r i b u t i o n p r o v i d e d a b e t t e r f i t of t r a n s i e n t s than G a u s s , Gamma or L o g - N o r m a l d i s t r i b u t i o n s but no p h y s i c a l s i g n i f i c a n c e i s assigned to i t . The r e s u l t i n F i g u r e 5 was o b t a i n e d a t an e l e c t r i c f i e l d o f 0.8V/ym, a c e l l t h i c k n e s s o f 125 ym and a p a r t i c l e c o n c e n t r a t i o n o f 15 ppm by v o l u m e . The c o r r e s p o n d i n g s p a c e c h a r g e f a c t o r was s = 0 . 1 5 . The a v e r a g e p a r t i c l e m o b i l i t y o b t a i n e d f r o m t h e a n a l y s i s was 0 . 3 0 5 x 1 0 - ° 2 v - 1 s ~ l . A l t h o u g h t h e i n v e s t i g a t i o n was l i m i t e d a t low v o l t a g e s by s p a c e c h a r g e e f f e c t s and by e l e c t r i c a l d i s c h a r g e a c r o s s t h e c e l l a t h i g h e r v o l t a g e s , t h e m o b i l i t y was s t u d i e d as a f u n c t i o n o f f i e l d s t r e n g t h and was f o u n d t o be i n d e p e n dent of f i e l d . Most e x p e r i m e n t s a t h i g h e r p a r t i c l e c o n c e n t r a t i o n s , l o w e r a p p l i e d v o l t a g e s , and t h i c k e r c e l l s t h a n g i v e n above were i n s p a c e c h a r g e l i m i t e d c o n d i t i o n s . The d i s t r i b u t i o n o f p l a t e d - o u t p a r t i c l e s on t h e e l e c t r o d e was u n i f o r m i n t h i n ( - 100 ym) c e l l s , i n d i c a t i n g t h a t t u r b u l e n c e was n o t i m portant in these experiments. 1

m

The p a r t i c l e s i z e was a l s o c a l c u l a t e d f r o m ( 4 ) and c h a r g e / mass and was f o u n d t o be 0 . 1 9 + 0 . 0 5 ym. D i f f e r e n c e s between t h i s e s t i m a t e and t h e 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 v a l u e were p r o b a b l y due t o n o n s p h e r i c i t y o f t h e p a r t i c l e s . Using t h i s s i z e and a p p l y i n g ( 4 ) and ( 5 ) t o t h i s LC c o l l o i d g i v e s q = 56 x 10'^C = 35 p o s i t i v e u n i t c h a r g e s and c = 250mV. Ionic chara c t e r i s t i c s a r e e v a l u a t e d f r o m t h e e l e c t r i c a l sweepout t r a n s i e n t in Figure 6. The c u r r e n t d e n s i t y c a n be a c c o u n t e d f o r a c c o r d i n g t o ( 1 ) by c o n t r i b u t i o n s f r o m p a r t i c l e s w i t h t h e a bove m o b i l i t i e s and c h a r g e s and w i t h a c o u n t e r i o n m o b i l i t y yj = 0 . 4 x l 0 " m V" s " and c o n c e n t r a t i o n n i = 1 . 3 x l 0 m" . The d o u b l e l a y e r o f LC c o l l o i d c o n t a i n s i o n s o f m o s t l y one p o l a r i t y and t h e Debye l e n g t h f r o m ( 3 ) i s i n d e e d e x t e n s i v e A* 5 y m . 8

2

1

1

1 7

3


NOVOTNY



14.

293

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gs:

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5s g»

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294


0.0

100.

200.

TIME (msec) Figure 5. Optical transient from LC colloid and the mobility distribution used to provide a fit (solid line) to the experimental data. (Reproduced, with permission, from Ref. 29.)

TIME (msec) Figure 6. Electrical transient from LC colloid corresponding to the optical transient in Figure 5. Solid line is based on calculations using an estimate of ionic mobility and the particle mobilities determined by optical transients. (Reproduced, with permission, from Ref. 29.)



14.

NOVOTNY

295


I t a p p e a r s t h a t many o f t h e r e s u l t s f r o m s i m i l a r LC s y s t e m s r e p o r t e d i n t h e l i t e r a t u r e (3T_,32,33) were u n k n o w i n g l y o b t a i n e d under space charge l i m i t e d c o n d i t i o n s . F o r a d i s c u s s i o n o f IC c o l l o i d p r o p e r t i e s a d i s p e r s i o n o f inorganic oxide in aromatic hydrocarbon i s s e l e c t e d . It i s s t a b i l i z e d and c h a r g e d w i t h a c c a , m e t a l s u l f o n a t e , w h i c h i s p h y s i c a l l y a d s o r b e d on t h e o x i d e s u r f a c e s and i s i n e q u i l i b r i u m w i t h some c c a i n s o l u t i o n . The c o n c e n t r a t i o n o f c c a i n s o l u t i o n c o n t r o l s t h e b a c k g r o u n d c o n d u c t i v i t i e s w h i c h a r e around 5x10"^ Q -lm~l. The a d s o r p t i o n i s o t h e r m o f c c a was d e t e r mined by f o u r t e c h n i q u e s as shown i n F i g u r e 7 . The " p a r k i n g " a r e a o f t h e c c a m o l e c u l e as d e t e r m i n e d f r o m a m o n o l a y e r c o v e r age i s - 7 0 A . The a v e r a g e p a r t i c l e s i z e p l o t t e d i n F i g u r e 8 as a f u n c t i o n o f c c a c o n c e n t r a t i o n d e c r e a s e s i n i t i a l l y w i t h i n c r e a s i n g c c a c o n c e n t r a t i o n and s t a b i l i z e s a t h i g h c o n c e n trations. I n t e r e s t i n g l y , t h e p a r t i c l e s i z e dependence p a r a l l e l s the adsorption isotherm very w e l l ; i . e . , the p a r t i c l e s i z e becomes i n d e p e n d e n t o f t h e c c a c o n c e n t r a t i o n at a p p r o x i m a t e l y a m o n o l a y e r c o v e r a g e i m p l y i n g t h a t c c a a c t s as s t e r i c and/or e l e c t r o s t a t i c s t a b i l i z e r . The c h a n g e s o f p a r t i c l e mob i l i t y w i t h c c a c o n c e n t r a t i o n a r e shown i n F i g u r e 9 f o r t h i s s y s t e m t o g e t h e r w i t h a n o t h e r t y p i c a l nonaqueous s y s t e m . The c o n c e n t r a t i o n a t w h i c h m o b i l i t y r e a c h e s a maximum o r s a t u r a t e s g e n e r a l l y c o i n c i d e s w i t h a monolayer coverage of c c a . Surprisi n g r e s u l t s a r e o b t a i n e d when t h e m o b i l i t y a t a g i v e n c c a c o n c e n t r a t i o n i s examined as a f u n c t i o n o f t h e e l e c t r i c f i e l d . The m o b i l i t y i n c r e a s e s w i t h i n c r e a s i n g f i e l d a t l e a s t w i t h i n t h e r a n g e o f 0 . 1 t o 4.0V/ym. S i m i l a r r e s u l t s were f o u n d i n v e r y d i f f e r e n t IC d i s p e r s i o n s . 0

2

The summary o f c o l l o i d a l p r o p e r t i e s at a m o n o l a y e r c o v e r age o f c c a i s as f o l l o w s : At h i g h f i e l d s , (3V/ym), where e q u a t i o n s ( 4 ) and ( 5 ) a r e a p p l i c a b l e , t h e c h a r g e i s 4 . 3 x 1 0 " c. The m o b i l i t y does n o t v a r y w i t h p a r t i c l e s i z e . Electrical transi e n t s a r e d o m i n a t e d by c c a i n s o l u t i o n e x c e p t at h i g h p a r t i c l e c o n c e n t r a t i o n s a n d , t h e r e f o r e , c a n n o t be used t o e s t i m a t e mob i l i t i e s and s i z e s o f p a r t i c l e s . The c o n c e n t r a t i o n o f i o n s i s 2xl0 p a i r s / m , and t h e m o b i l i t y o f t h e p o s i t i v e and n e g a t i v e i o n s i s about 0 . 9 and 0 . 7 x 1 0 * 8 2 y - 1 - l respectively, and t h e Debye l e n g t h i s x = 1 . 3 ym. The a v e r a g e e l e c t r i c f i e l d n e c e s s a r y f o r the removal of a charged p a r t i c l e from the e l e c t r o d e i s 0.6V/ym , and t h e c o r r e s p o n d i n g t o t a l p a r t i c l e - w a l l i n t e r a c t i o n f o r c e (34) i s 0 . 7 x l 0 " N . In IC c o l l o i d s , s p a c e c h a r g e c o n d i t i o n s c a n n o t be s i m p l y d e t e r m i n e d f r o m an e x p r e s s i o n ( 2 ) and n u m e r i c a l m o d e l l i n g i s r e q u i r e d . Modelling i n d i cates that the presence of i o n i c d i s s o c i a t i o n in the bulk s o l u t i o n r e l a x e s t h e s p a c e c h a r g e e f f e c t s b u t t h a t t h e y do become i m p o r t a n t a t f i e l d s b e l o w 0.1V/ym even a t low p a r t i c l e c o n c e n trations. The o n s e t o f t u r b u l e n c e i s d i r e c t l y o b s e r v a b l e above 1 7

1 8

3

m

s

1 0


Hair and Croucher; Colloids and Surfaces in Reprographic Technology ACS Symposium Series; American Chemical Society: Washington, DC, 1982. I

I

Figure 7. Typical adsorption isotherm of charge control agent on oxide particles in nonaqueous media. Key: • and O, atomic absorption; | , electrical conductivity; A, IR absorption; and • , ESCA.

1.0 2.0 3.0 CCA CONCENTRATION IN SOLUTION (mM)

1


NOVOTNY

297


B U H


< u H

< a.

a < >

0.0 Figure 8.

2 3 C C A CONCENTRATION

4

23

(mM)

Dependence of average particle size on the concentration of charge control agent in nonaqueous media.

> 6 ao b X PQ O 2 to s >

2

3

C C A CONCENTRATION Figure 9.

(mM)

Two typical dependencies of mobility on the concentration of charge control agent in nonaqueous media.



298


50V i n d i s p e r s i o n s w i t h h i g h p a r t i c l e c o n c e n t r a t i o n s (above 1% by v o l u m e ) . D e t e c t a b i 1 i t y i s more d i f f i c u l t at low p a r t i c l e c o n c e n t r a t i o n s (

0.1

I

I

1.0

1—I—I I I |

ELECTRIC FIELD (V/jum)

ony-"

SWEEPOUT EXP. o TRANSIT EXP. • *

1

-i T

Figure 10. Dependence of particle mobility on the applied electric field. (Reproduced, with permission, from Ref. 12.)

0.

3.

o

CO

T—I—I 1 I |


300


W i t h h i g h p a r t i c l e c h a r g e s and low i o n i c c o n c e n t r a t i o n s , e l e c t r o s t a t i c r e p u l s i o n ( 3 9 , 40) a l o n e s h o u l d be c a p a b l e o f s t a b i l izing, the c o l l o i d . T h i s T y p i c a l l y o c c u r s when s u r f a c e p o t e n t i a l s a r e a r o u n d lOOmV. S t e r i c s t a b i l i z a t i o n (41,42) i n nonaqueous m e d i a i s i m p o r t a n t t o a c h i e v e s t a b i l i t y i n w e a k l y c h a r g e d systems. D i r e c t e x p e r i m e n t a l measurements o f p a r t i c l e - p a r t i c l e f o r c e s o r p o t e n t i a l s i n nonaqueous m e d i a a r e n o t y e t a v a i l a b l e .


Applications Nonaqueous d i s p e r s i o n s have been used i n a number o f i n t e r e s t i n g t e c h n o l o g i c a l a p p l i c a t i o n s , s u c h as t h e e l e c t r o p h o r e t i c development o f l a t e n t images, e l e c t r o p h o r e t i c d i s p l a y s , the d e p o s i t i o n o f s p e c i a l c o a t i n g s and p a r t i c l e c o n t a m i n a n t r e m o v a l f r o m nonaqueous m e d i a . Only l i q u i d development of l a t e n t e l e c t r o s t a t i c images w i l l be d i s c u s s e d h e r e . These images can be f o r m e d by a number o f p r o c e s s e s . These i n c l u d e t h e s t a n d a r d l i g h t o r x - r a y e x p o s u r e o f a c h a r g e d p h o t o c o n d u c t o r and e l e c trographic processes. In e l e c t r o g r a p h y , breakdown due t o t h e a p p l i c a t i o n o f a h i g h v o l t a g e between a s t y l u s and a c o n d u c t o r c o v e r e d w i t h a d i e l e c t r i c d e p o s i t s a c h a r g e on t h e d i e l e c t r i c . L i q u i d d e v e l o p e r s f i r s t d e m o n s t r a t e d by M e t c a l f e ( 4 3 ) have s a t i s f y a number o f r e q u i r e m e n t s . The c o n c e n t r a t i o n o f e x c e s s i o n s has t o be v e r y l o w , o t h e r w i s e i o n s o f t h e same p o l a r i t y as p a r t i c l e s w i l l be e f f e c t i v e l y c o m p e t i n g w i t h p a r t i c l e s f o r t h e development o f the e l e c t r o s t a t i c image. This implies that l i q u i d d e v e l o p e r s s h o u l d be LC c o l l o i d s . For f a s t d e v e l o p m e n t o f images w i t h h i g h l a t e n t c h a r g e d e n s i t y , t h e c o l l o i d s h o u l d have h i g h c h a r g e / m a s s and m o b i l i t y . F o r d e v e l o p m e n t o f low c h a r g e d e n s i t i e s ( e . g . , x - r a y g e n e r a t e d ) where s l o w d e v e l o p ment i s a c c e p t a b l e , t h e c o l l o i d s s h o u l d have low charge/mass and m o b i l i t y . In o r d e r t o a c h i e v e h i g h s p a t i a l r e s o l u t i o n , t h e p a r t i c l e s i z e s h o u l d be s u b m i c r o n . The c o l l o i d s h o u l d a d h e r e w e l l t o t h e s u b s t r a t e i n b o t h t h e l i q u i d and d r y s t a t e s and s h o u l d be s e l f - f i x i n g . S t a b i l i t y o f s i z e and c h a r g e i s also very important.

to

The t y p i c a l c o n f i g u r a t i o n f o r l i q u i d d e v e l o p m e n t i s shown i n F i g u r e 1 1 . A l i q u i d d e v e l o p e r i s c o n t a i n e d between a c h a r g e d d i e l e c t r i c p l a t e and a d e v e l o p m e n t e l e c t r o d e . Normal e l e c t r o s t a t i c a t t r a c t i o n between c h a r g e d p a r t i c l e s and t h e image i s aided w i t h development f i e l d s d r i v i n g p a r t i c l e s towards the image. I f t h e s p a c e c h a r g e e f f e c t s a r e i g n o r e d and t h e main p a r a m e t e r s q i v e n i n t h e r e s u l t s e c t i o n a r e known, a s i m p l e model (_44) c a n p r e d i c t t h e d i s c h a r g e o r d e v e l o p m e n t o f t h e image. The model c o n s i s t s o f t h e e x p r e s s i o n f o r t h e e l e c t r i c f i e l d i n t h e d i s p e r s i o n and t h e d i s c h a r g e o f t h e s u r f a c e by a c u r r e n t of charged p a r t i c l e s . The s u r f a c e v o l t a g e V ( t ) i s V(t)

= V

b

+ (V

0

- V ) b

e-t/x

(6)



Figure 11.

ELECTROSTATIC LATENT IMAGE

DEVELOPED IMAGE

DIELECTRIC

CONDUCTING SUBSTRATE

Typical configuration of liquid development of latent electrostatic images.

LIQUID INK (CHARGED TONER & COUNTERIONS IN DIELECTRIC LIQUID

DEVELOPMENT ELECTRODE


302


where V

0

and V

b

are i n i t i a l

T

and b i a s v o l t a g e s .

The

time constant

(7)

i s d e p e n d e n t upon d i e l e c t r i c c o n s t a n t s o f t h e s u b s t r a t e , e p and t h e d i s p e r s i o n , e , t h i c k n e s s o f t h e d i e l e c t r i c , L p , d i s t a n c e between c h a r g e d s u r f a c e and d e v e l o p m e n t e l e c t r o d e , L|_, and i n v e r s e l y p r o p o r t i o n a l t o t h e number d e n s i t y , n , c h a r g e , q , and m o b i l i t y , y o f t h e i n k p a r t i c l e s . The s p a c e c h a r g e f a c t o r s f r o m ( 2 ) e x c e e d s 0 . 3 a t n o r m a l d e v e l o p m e n t d e n s i t i e s 0 . 1 - 1 . 0 g/m? and w i d e r a n g e o f c h a r g e / m a s s , 0 . 0 1 - 5 C / k g , even at h i g h d e v e l o p m e n t f i e l d s p r o v i d e d by ( o * b ) z 200V a c r o s s a gap o f Li = 1mm. C h a r g e d p a r t i c l e s w i l l m i g r a t e i n a n o n u n i f o r m f i e l d and c o n c e n t r a t i o n g r a d i e n t s w i l l be s e t u p , c a u s i n g back d i f f u s i o n . The e l e c t r i c a l l y d r i v e n m o t i o n w i l l d o m i n a t e when t h e f i e l d E » D/uL, where D i s t h e d i f f u s i o n c o e f f i c i e n t . For t y p i c a l v a l u e s o f r and y t h e i n e q u a l i t y i s s a t i s f i e d by s e v e r a l o r d e r s o f m a g n i t u d e even when t h e f i e l d i s s e v e r e l y r e d u c e d due t o s p a c e charge. T h i s shows t h a t d i f f u s i o n can be n e g l e c t e d w h i l e s p a c e c h a r g e e f f e c t s have t o be i n c l u d e d i n a m e a n i n g f u l m o d e l . A m a t h e m a t i c a l model ( 4 5 ) , c o n s i s t i n g o f e q u a t i o n s o f m o t i o n f o r c h a r g e d p a r t i c l e s and c o u n t e r i o n s , P o i s s o n ' s e q u a t i o n and Gauss* l a w , has been d e v e l o p e d . The model can p r e d i c t t h e d e v e l o p m e n t o f t h e image as shown i n F i g u r e 1 2 . The main p a r a m e t e r s i n t h e model a r e p a r t i c l e c h a r g e and t h e r a t i o o f p a r t i c l e t o i o n i c mobilities. The g r a p h compares t h e z e r o s p a c e c h a r g e p r e d i c t i o n with a complete model. The r e a l i s t i c model p r e d i c t s more complete development f o r s h o r t e r development t i m e s than the s i m p l i f i e d model. For l o n g e r d e v e l o p m e n t t i m e s , t h e same o c c u r s at low d e v e l o p m e n t v o l t a g e s b u t t h e r e v e r s e i s t r u e at high v o l t a g e s . A c o m p l e t e s t u d y o f optimum d e v e l o p m e n t c o n d i t i o n s can be p e r f o r m e d w i t h t h e r e a l i s t i c model w h i c h c o n s i d e r s the e f f e c t s of input v o l t a g e , i n i t i a l charge d e n s i t i e s , d e v e l o p m e n t t i m e , e l e c t r o d e s p a c i n g s and d i s p e r s i o n p a r a m e t e r s . I t s h o u l d a l s o be n o t e d t h a t t u r b u l e n c e i s o f t e n p r e s e n t i n l i q u i d d e v e l o p m e n t and t h a t t h i s may a f f e c t o r c o n t r o l d e v e l opment c h a r a c t e r i s t i c s .


L

v

v

The d e v e l o p m e n t o f e l e c t r o s t a t i c images can be a c h i e v e d w i t h e i t h e r l i q u i d or d r y p r o c e s s e s . L i q u i d developer u s u a l l y p r o v i d e s h i g h e r r e s o l u t i o n due t o i t s s m a l l e r p a r t i c l e s i z e . Images w i t h low e l e c t r o s t a t i c d e n s i t i e s c a n be d e v e l o p e d w i t h l i q u i d i n k s w h i c h can have charge/mass much l o w e r t h a n d r y powders. L i q u i d t o n e r s a r e o f t e n s e l f - f i x i n g and a l l o w a s i m p l e r development system. Color p r i n t i n g w i t h s u c c e s s i v e imaging and d e v e l o p m e n t s i s a l s o f e a s i b l e . Disadvantages of l i q u i d d e v e l o p m e n t compared w i t h d r y d e v e l o p m e n t i n c l u d e s o l v e n t c a r r y - o v e r , h i g h e r o p t i c a l b a c k g r o u n d and l o w e r imaged o p t i cal d e n s i t i e s . A p p l i c a t i o n t r a d e o f f s u s u a l l y determine the d e s i r a b l e method o f image d e v e l o p m e n t .



303


NOVOTNY

Figure 12. Development of electrostatic images as a function of the applied initial voltage with development time as a parameter. Key: , space charge included; and , space charge not included. (Reproduced, with permission, from Ref. 45 J


304


Acknowledgments Thanks are due to Dr. J . Becker and Dr. D. Zwemer for h e l p f u l discussions.


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