Colloids and Surfaces in Reprographic Technology - American

4 Silver Halide Precipitation and Colloid Formation Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on June 25, 2016 | http://pubs.acs.org Publication Date: October 13, 1982 | doi: 10.1021/bk-1982-0200.ch004

INGO H. LEUBNER Eastman Kodak Company, Research Laboratories, Rochester, NY 14650

Formation o f colloidal silver h a l i d e d i s p e r s i o n s (photographic emulsions) is one o f the principal steps in the p r e p a r a t i o n o f conventional photographic m a t e r i a l s . A t the same time it presents scientific c h a l l e n g e s , some o f which a r e common t o general colloid formation, such as c o n t r o l o f crystal s i z e , s i z e distrib u t i o n , and morphology. I n precipitation, two processes are o f s p e c i a l i n t e r e s t , i.e., formation o f s t a b l e c r y s t a l n u c l e i ( n u c l e a t i o n ) and subsequent growth. This s e q u e n t i a l process is specifically i n v o l v e d i n the double-jet precipitation o f silver bromide. F o r this case, a theoretical model o f n u c l e a t i o n was derived which is based on a dynamic mass balance and a growth mechanism which i n c l u d e s bulk diffusion and the Gibbs-Thomson effect. In qualitative agreement w i t h t h i s theory, experiments showed t h a t the number of s t a b l e n u c l e i increased w i t h i n c r e a s i n g reactant a d d i t i o n r a t e and decreased w i t h i n c r e a s i n g solubility and temperature. Subsequent growth o f the c r y s t a l s can be described by a simple mass-balance equation, as long as the growth r a t e is below a limiting maximum growth r a t e above which r e n u c l e a t i o n occurs. The growth r a t e was r e l a t e d t o a growth model based on bulk d i f f u s i o n and crystal number d e n s i t y . F o r AgBr, the morphology is dependent on the pAg o f the crystal suspension. In the formation o f c o l l o i d s , the c o n t r o l o f p a r t i c l e s i z e , s i z e d i s t r i b u t i o n , and p a r t i c l e morphology i s a great s c i e n t i f i c and t e c h n i c a l challenge. C o l l o i d a l s i l v e r h a l i d e d i s p e r s i o n s i n g e l a t i n e (photographic "emulsions") can be considered as model systems f o r c o l l o i d s which are formed by p r e c i p i t a t i o n o f spari n g l y s o l u b l e s a l t s . The formatiOn o f s i l v e r h a l i d e emulsions has been s t u d i e d i n great d e t a i l and i t i s l i k e l y that the r e s u l t s o f these s t u d i e s can be a p p l i e d t o other c o l l o i d a l systems. Three b a s i c methods have g e n e r a l l y been employed i n the p r e c i p i t a t i o n o f s i l v e r , , h a l i d e s : s i n g l e - j e t , d o u b l e - j e t , and continuous (Figure 1 ) . * * I n the s i n g l e - j e t method, the s i l v e r 0097-6156/82/0200-0081 $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.

Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on June 25, 2016 | http://pubs.acs.org Publication Date: October 13, 1982 | doi: 10.1021/bk-1982-0200.ch004

82

REPROGRAPHIC TECHNOLOGY

s o l u t i o n ( u s u a l l y s i l v e r n i t r a t e ) i s introduced i n t o an a g i t a t e d s o l u t i o n of excess h a l i d e and g e l a t i n . In the d o u b l e - j e t method, s i l v e r n i t r a t e and h a l i d e s o l u t i o n s are introduced simultaneously into a s t i r r e d gelatin solution. In the continuous process, s i l v e r n i t r a t e , h a l i d e , and g e l a t i n s o l u t i o n s are combined simultaneously and product i s removed continuously to achieve steady-state conditions. Of these methods, the d o u b l e - j e t method leads g e n e r a l l y to a r e l a t i v e uniform ("monodisperse") c r y s t a l p o p u l a t i o n w i t h uniform morphology when m a t e r i a l a d d i t i o n ^ r^ates, temperature, and pAg are c l o s e l y c o n t r o l l e d (Figure 2 ) . * For such systems, n u c l e a t i o n and subsequent growth have been s t u d i e d i n d e t a i l . The present review w i l l concentrate on some recent developments i n these areas. The course of p r e c i p i t a t i o n of most s p a r i n g l y s o l u b l e s a l t s i n d o u b l e - j e t p r e c i p i t a t i o n s can be i l l u s t r a t e d by the schematic p l o t of the s u p e r s a t u r a t i o n r a t i o S vs. time (Figure 3 ) . S i s defined as the r a t i o of the bulk s o l u t e c o n c e n t r a t i o n C to the e q u i l i b r i u m s o l u b i l i t y C . As soon as the reactants are i n t r o duced, S increases very r a p i d l y and exceeds the c r i t i c a l value S f o r spontaneous n u c l e a t i o n at t = t ^ . S w i l l now increase at a lower r a t e owing to solid-phase n u c l e a t i o n and subsequent growth u n t i l a maximum i s reached. T h e r e a f t e r , S w i l l decrease and drop below S at t = t ^ ; observable n u c l e a t i o n w i l l then stop. The region between t - and t ~ i s u s u a l l y r e f e r r e d to as the " n u c l e a t i o n r e g i o n . " Between and t ~ i s a " t r a n s i e n t r e g i o n " where S continues to decrease r a p i d l y . In t h i s region the number of n u c l e i may a c t u a l l y decrease owing to d i s s o l u t i o n of some of the s m a l l e r c r y s t a l s . At t > a quasi-steady s t a t e i s obtained where f u r t h e r decrease i s not a p p r e c i a b l e and the t o t a l number of c r y s t a l s remains p r a c t i c a l l y constant. This quasi-steady s t a t e region i s a l s o c h a r a c t e r i z e d as the "growth r e g i o n " of p r e c i p i t a t i o n . In k i n e t i c s t u d i e s of the formation of s i l v e r bromide, Meehan and M i l l e r found t h a t formation of c o l l o i d a l m a t e r i a l was complete w i t h i n 6 msec or l e s s . They f u r t h e r concluded t h a t f a s t f l o c c u l a t i o n , i n which every c o l l i s i o n of p a r t i c l e s r e s u l t s i n an agglomeration, occurs during the mixing process and f o r ^ a few seconds t h e r e a f t e r . Berry and S k i l l m a n and Berriman determined t h a t the t o t a l number of s i l v e r h a l i d e c r y s t a l s remained e s s e n t i a l l y unchanged a f t e r the f i r s t minute of doublejet precipitation. c

c

The N u c l e a t i o n Stage For the n u c l e a t i o n i n d o u b l e - j e t p r e c i p i t a t i o n of s i l v e r h a l i d e s , a dynamic model was d e r i v e d which r e l a t e s the £inal number of s t a b l e n u c l e i to v a r i o u s p r e c i p i t a t i o n v a r i a b l e s : R R

Z =

T S_ 87ivDV C ( r / r * - l ) m s

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

(i)

LEUBNER

Silver Halide

Precipitation

and Colloid


AgN0

Formation 3

Gelatin

Figure 1. Schematic of basic AgX precipitation methods. Key: single-jet, left; double-jet, middle; and continuous, right. (Reproduced, with permission, from Ref. 6. Copyright 1981, Marcel Dekker, Inc.)

Figure 2. Electron micrographs of AgBr crystals produced by the basic precipitation methods. Key: single-jet, upper left; double-jet, upper right; and continuous, lower. (Reproduced, with permission, from Ref. 6. Copyright 1981, Marcel Dekker, Inc.)


83


84

where 00


r = f

oo

nrdr/ f

ndr

(2)

Here, Z i s the f i n a l number of s t a b l e n u c l e i , R represents the reactant a d d i t i o n r a t e , R i s the gas constant, T i s the absolute temperature, Y i s the surface energy, D i s the d i f f u s i o n c o e f f i c i e n t , V i s the molar volume, and C i s the s o l u b i l i t y of the m — s p r e c i p i t a t e , r represents a number average c r y s t a l r a d i u s and i s g r e a t e r than the c r i t i c a l radius r * . The c r i t i c a l s i z e r * i s d e f i n e d as the s i z e at which a c r y s t a l has an equal p r o b a b i l i t y of d i s s o l u t i o n by Ostwald r i p e n i n g vs. growth to s t a b l e s i z e s . Equation (1) i s based on a model where c r y s t a l growth i s dominated by bulk d i f f u s i o n and the Gibbs-Thomson e f f e c t (e.g., A g C ^ a ^ AgBr systems). JThis equation d i f f e r s from previous models ' by the f a c t o r ( r / r * - 1) which r e s u l t s from c o n s i d e r a t i o n s of the dynamic mass balance and the i n f l u e n c e of s u p e r s a t u r a t i o n . I t s importance w i l l become apparent during the d i s c u s s i o n of experimental r e s u l t s . The v a l i d i t y of eq (1) was e x p e r i m e n t a l l y t e s t e d by d o u b l e - j e t p r e c i p i t a t i o n of AgBr where reactant a d d i t i o n r a t e R, pAg and s o l u b i l i t y , and temperature were c l o s e l y c o n t r o l l e d . In these experiments, i n i t i a l r e a c t o r volume and g e l a t i n concent r a t i o n (2-8% ,range) d i d not s i g n i f i c a n t l y a f f e c t the number of stable nuclei. E f f e c t of Reactant A d d i t i o n Rate - According to eq ( 1 ) , the number of s t a b l e n u c l e i should increase w i t h i n c r e a s i n g a d d i t i o n r a t e . For the slope of the c o r r e l a t i o n of In Z vs. In R, the f o l l o w i n g e x p r e s s i o n i s obtained:

d In R

/ r/r"

i - 1

dR

^

The f i r s t term jof the product on the r i g h t s i d e of eq (3) i s p o s i t i v e s i n c e r / r * > 1.0. I t can be shown t h a t the second term ( d ( r / r * ) / d R ) i s a l s o p o s i t i v e . Therefore, a p l o t of In Z vs. In R (or l o g Z vs. l o g R) should have a slope l e s s than one. This i s c o n s i s t e n t w i t h experimental r e s u l t s f o r AgBr shown i n F i g u r e 4. The slopes f o r the ascending P ^ t of the data by K l e i n and Moisar and Loginov and Deniso^a are 0.8 and 0.5, r e s p e c t i v e l y . Leubner, Jagannathan, and Wey d i d not observe the bend-over observed by the other authors, and the slope of t h e i r c o r r e l a t i o n was 0.84. D i f f e r e n t experimental techniques by these authors may account f o r the observed d i f f e r e n c e s i n the experimental results.



LEUBNER

Silver Halide Precipitation

and Colloid

Formation

Time Figure 3.

Supersaturation ratio, S, vs. precipitation time, t. (Reproduced, with permission, from Ref. 2. Copyright J980, J. Photogr. Sci. Eng.)

I0

1 4

1

1

1

Klein & Moisor I0

J*

1 3

£ /

/

Loginov & Denisova

_

' Leubner, Jagannathan & Wey

icr

9

i icr

8

i iO

-7

R (mol/sec-ml)

i i 0

-

6

icr

5

Figure 4. Number of stable AgBr crystals, Z, as a function of reactant addition rate, R. (Reproduced, with permission, from Ref. 2. Copyright 1980, J. Photogr. Sci. Eng.)


86



E f f e c t of pAg and S o l u b i l i t y . S o l u b i l i t y and pAg are i n t r i c a t e l y ^ r e l a t e d f o r a given temperature as shown i n F i g u r e 5. ' ' I t was expected from eq (1) t h a t the number of s t a b l e n u c l e i would be i n v e r s e l y r e l a t e d t o the s o l u b i l i t y . The c o r r e l a t i o n of l o g Z v s . pAg f o r AgBr i s indeed i n v e r s e t o that of the l o g s o l u b i l i t y / pAg c o r r e l a t i o n (Figure 6 ) . From eq ( 1 ) , the slope of the c o r r e l a t i o n of In Z v s . In C can be d e r i v e d as:

d In Z

(A)

s

L

r/r- - 1

The f i r s t term of the product on the r i g h t s i d e i s p o s i t i v e s i n c e r / r * > 1.0. I t can be shown that the second term i s negative and t h a t t h e r e f o r e the slope o f a p l o t of l n Z v s . l n C £or l o g Z v s . l o g C ) should be greater (more p o s i t i v e ) than This i s c o n s i s t e n t w i t h a p l o t o f l o g Z v s . l o g C where slopes of -0.76 and -0.40 were obtained f o r cubic and octahedral c r y s t a l s , r e s p e c t i v e l y (Figure 7 ) . For the AgBr system, the c r y s t a l morphology i s determined by the pAg and temperature of the c r y s t a l suspension. As i n d i c a t e d i n F i g . 6, a t 70°C the octahedral morphology i s s t a b l e at pAg's g r e a t e r than about 8, whereas the cubic morphology i s s t a b l e a t lower pAg's. There i s a continuous t r a n s i t i o n from cubic t o o c t a h e d r a l morphology v i a cuboctahedral shapes. At pAg's higher than about 9.5, c r y s t a l morphologies based on twinned c r y s t a l s t r u c t u r e s are a l s o obtained. E f f e c t of Temperature. The e f f e c t of temperature was s t u d i e d f o r constant a d d i t i o n rate R and constant s o l u b i l i t y C (1.6 x 10 mole/L). At each temperature, two pAg's were chosen which correspond t o t h i s s o l u b i l i t y value (see F i g . 5 ) . The higher and lower pAg's u s u a l l y lead to o c t a h e d r a l and cubic c r y s t a l h a b i t s , r e s p e c t i v e l y . From eq ( 1 ) , the slope of the l n Z/ln T (or l o g Z/log T) c o r r e l a t i o n can be given as: g

0 and t h a t t h e r e f o r e d In Z r

nn

< 0


(6)

M

LEUBNER


and Colloid

Formation


4.

Figure 6. Number of stable AgBr crystals as a function of pAg. Conditions: temperature, 70 C; and R, 3.56 X 10 mol/s mL. Key: • , cubes; and O, octahedra. (Reproduced, with permission, from Ref. 2. Copyright 1980, J. Photogr. Sci. Eng.) 7


87

88


A p l o t of l o g Z v s . l o g T (Figure 8) indeed has a negative s l o p e , which agrees w i t h the t h e o r e t i c a l p r e d i c t i o n . The experimental r e s u l t s obtained from balanced double-jet p r e c i p i t a t i o n s of AgBr c r y s t a l s can thus be q u a l i t a t i v e l y explained reasonably w e l l by the dynamic model of n u c l e a t i o n which includes both d i f f u s i o n and the Gibbs-Thomson e f f e c t .


The Growth Stage Once the number of s t a b l e n u c l e i has been e s t a b l i s h e d i n the n u c l e a t i o n stage, t h e i r growth rate ^ f o r constant a d d i t i o n r a t e can be given by a simple mass-balance dr

V o

R m

, _. >.

4/lZr o if g < g

c

( c r i t i c a l growth r a t e )

(8)

Here, V , R, and Z have the same meaning as i n the previous d i s c u s s i o n , t i s time and r i s the c r y s t a l diameter a t time t . Here, s p h e r i c a l morphology i s assumed f o r s i m p l i c i t y . The c o r r e l a t i o n i s e s s e n t i a l l y the same f o r cubic and octahedral c r y s t a l s except f o r d i f f e r e n t p r o p o r t i o n a l i t y constants, g i s the c r i t i c a l growth r a t e above which r e n u c l e a t i o n occurs, ft i s equal t o the maximum growth r a t e that a system can s u s t a i n without going i n t o r e n u c l e a t i o n . I t s value i s dependent on the temperature, pAg, average^cr^ys^ta^size, and p a r t i c l e d e n s i t y of the s i l v e r h a l i d e system. * * ' Fox^ a d i s p e r s i o n of AgCl i n g e l a t i n , a pH e f f e c t was a l s o observed. Another approach f o r determining the growth rate g i s based on c o n s i d e r a t i o n s of s u p e r s a t u r a t i o n , growth k i n e t i c s , and c r y s t a l number d e n s i t y . For d i f f u s i o n - c o n t r o l l e d growth systems, l i k e AgBr, eq (9) was d e r i v e d , which r e l a t e s the growth r a t ^ to the s u p e r s a t u r a t i o n r a t i o , S, and c r y s t a l number d e n s i t y , p.

g =

= n g„

(9)

where DC (S - 1) s pr

(1 +

1/6)


(10)


4.

LEUBNER

Silver Halide

Precipitation

and Colloid

Formation

Figure 7. Number of stable AgBr crystals as a junction of solubility. Conditions: temperature, 70 C; and R, 3.56 χ 10 mol/s mL. Key: Φ, cubes; and O, octahedra. (Reproduced, with permission, from Ref. 2. Copyright 1980, J. Photogr. Sci. Eng.) 7

Figure 8. Number of stable AgBr crystals as a function of temperature. Condi tions: C , 1.6 χ 10 mol/L; and R, 3.56 X 10 mol/'s mL. Key: Φ, cubes; and O, octahedra. (Reproduced, with permission, from Ref. 2. Copyright 1980, J. Photogr. Sci. Eng.) K

7

s


89

90


2

zg> C*i

- i)

0

(11) (r

a

- 0)(2r V 1

- 't

x

- 0)

(1 + 1/6)

r1

(12)

6

(13)


0 i s defined as f o l l o w s :

0 = 1 for r

1

< 1 + 6

0 = r - ( l + 6) f o r r . > 1 + 5

(14) (15)

Here, g i s the growth r a t e f o r a crowded system, r| i s the crowding f a c t o r , and g^ i s the growth rate f o r a noncrowded system. A crowded system i s obtained when the p a r t i c l e suspension d e n s i t y i s so high that the d i f f u s i o n l a y e r s of adjacent p a r t i c l e s o v e r l a p , i . e . , ^ < r + 6 as sketched i n F i g u r e 9. Here, r i s the p a r t i c l e r a d i u s , r ^ i s the i n t e r p a r t i c l e d i s t a n c e , and 6 i s the d i f f u s i o n l a y e r t h i c k n e s s . The other symbols i n eqs (9-15) are the same as defined p r e v i o u s l y . The numerical e v a l u a t i o n of t h i s growth model (eqs 9-15) i s g e n e r a l l y d i f f i c u l t f o r s p a r i n g l y s o l u b l e p r e c i p i t a t e s s i n c e the determination of the s u p e r s a t u r a t i o n r a t i o S presents s i g n i f i c a n t experimental d i f f i c u l t i e s . However, when g i s equal t o the c r i t i c a l growth r a t e g , the s u p e r s a t u r a t i o n becomes constant and equal to the c r i t i c a l s u p e r s a t u r a t i o n ( F i g . 1 ) . Determination of the c r i t i c a l growth r a t e o f a system thus allows v e r i f i c a t i o n of the proposed growth model and determina t i o n of S and 6. Q

Q

The v a l i d i t y o f t h i s model was t e s t e d by the ^ c r i t i c a l growth r a t e method on the AgBr system (Figure 10). 6 was a r b i t r a r i l y chosen as 10 f o r a l l c r y s t a l s i z e s . The data c o r r e l a t e reasonably w i t h a s t r a i g h t l i n e ; however, the l i n e does not i n t e r c e p t the o r i g i n . P o s s i b l y , a more d e t a i l e d knowledge of the value o f the d i f f u s i o n l a y e r t h i c k n e s s 6 w i l l improve t h i s c o r r e l a t i o n . The i n c l u s i o n of the crowding f a c t o r r| s i g n i f i c a n t l y improved the c o r r e l a t i o n v s . a previous model where t h i s f a c t o r had not been i n c l u d e d . Summary The formation of c o l l o i d a l s i l v e r h a l i d e d i s p e r s i o n s (photographic emulsions) was reviewed as a model system o f c o l l o i d s which are formed by p r e c i p i t a t i o n of s p a r i n g l y s o l u b l e s a l t s . F o r such systems, models f o r c r y s t a l n u c l e a t i o n and growth were d e r i v e d which were v e r i f i e d f o r the AgBr system. These models can probably be extended t o the study of n u c l e a t i o n and growth o f other h i g h l y i n s o l u b l e c o l l o i d a l systems.



4.

LEUBNER

Figure 9.


and Colloid

Formation

Schematic of a two-particle crowded system. Key: r„, particle radius; 8, diffusion layer thickness; and 2 , interparticle distance. t±

(M/8)T?AO

1

(/^m- )

Figure 10. AgBr growth rates vs. (1 -f 1 /$)r)/r„. (Reproduced, with permission, from Ref. 3. Copyright 1981, North-Holland Publishing Company.)


91


92


Literature Cited (1) B e r r y , C. R. I n "The Theory o f the Photographic P r o c e s s " , 4th e d . ; James, T. H., Ed.; M a c m i l l a n : New Y o r k , 1977. (2) Leubner, I . H.; Jagannathan, R . ; Wey, J. S. Photogr. Sci. Eng. 1980, 24, 268. (3) Jagannathan, R.; Wey, J. S. J. C r y s t . Growth 1981, 5 1 , 601. (4) Wey, J. S . ; S t r o n g , R. W. Photogr. Sci. Eng. 1977, 2 1 , 14; ibid. 1977, 2 1 , 248. (5) Wey, J. S.; Terwilliger, J. P.; G i n g e l l o , A. D. AIChE Symposium S e r i e s 1980, 76, 34. (6) Wey, J. S. I n " P r e p a r a t i o n and P r o p e r t i e s o f S o l i d S t a t e M a t e r i a l s " , Vol. 6,Wilcox, W. R., Ed.; M a r c e l Dekker: New Y o r k , 1981. (7) Meehan, E . J.; Miller, J. K . Phys. Chem. 1968, 72, 2168. (8) B e r r y , C. R.; S k i l l m a n , D. C. J. Phys. Chem. 1964, 68, 1138. (9) Berriman, R. W. J. Photogr. Sci. 1964, 12, 12. (10) K l e i n , E.; M o i s a r , E . B e r . Bunsenges. Phys. Chem. 1963, 67, 348. (11) K h a r i t o n o v a , A . I.; S h a p i r o , B . I.; Bogomolov, K . S . ; Zh. Nauchn. Prikl. F o t o g r . Kinematogr. 1979, 24, 34. (12) Loginov, V . G.; Denisova, N . B . Ibid. 1975, 20, 231. (13) H a r d i n g , M. J. J. Photogr. Sci. 1979, 27, 1. (14) P e r r y , R. H.; C h i l t o n , C. H . Chemical E n g i n e e r s ' Handbook, 5 t h ed., M c G r a w - H i l l : New Y o r k , 1973; pp 3-235. (15) S t r o n g , R. W.; Wey, J. S. Photogr. Sci. Eng. 1979, 23, 344. (16) Matsuzaka, S . ; Yamamichi, E.; K o i t a b a s h i , T. presented at the SPSE 34th Annual Conference, New York, 1981. RECEIVED April 30,

1982


Colloids and Surfaces in Reprographic Technology - American

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