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Studies on the electrokinetic behavior of monodisperse silver halide sols
JOTJ~NAL OF COLLOID SCIENCE 19, 606-620 (1964)
STUDIES ON THE ELECTROKINETIC BEHAVIOR OF MONODISPERSE SILVER HALIDE SOLS R. H. Ottewill~ and R. F. Woodbridge Department of Colloid Science, University of Cambridge, Cambridge Received August 19, 1963; revised April 13, 196~ 2~kBSTRACT Methods have been developed for the preparation of monodisperse sols of silver bromide and silver iodide. The electrokinetic properties of the sols were examined, using microeleetrophoresis, as a function of the pAg of the sol at virtually constant ionic strength. The results obtained showed some differences from those obtained with classical polydisperse silver bromide and silver iodide sols. The differences in the electrokinetic properties of the two types of dispersion were attributed to the difference in the crystal growth processes. In the case of the monodisperse sols the crystals appear to be more perfect and the space charge in the crystal possibly contributes to the surface potential, and hence to the electrokinetic potential.
INTRODUCTION In a previous communication methods have been described for the preparation of monodisperse sols of silver halides (i). In the case of silver bromide it was found that sols could be prepared in which the particles had a cubic form with (001) faces or an octahedral form with (iii) faces. In 1930 Frumkin (2) pointed out that because of the difference occurring in the work function for individual crystal faces, a difference in the behavior of the double layer would be expected to occur according to the crystal face exposed to the electrolyte solution. In support of this hypothesis Schmid and Hackerman (3) recently found differences in the differential capacity of a single crystal gold electrode according to whether an (001) or a (iii) face was exposed to the solution; Harvey, La Fleur, and Gatos (4) also found that the adsorption of iodide ions on to a germanium electrode differed a c c o r d i n g to w h e t h e r a n (001) or a (111) face was u s e d for t h e measurements. I t w a s t h e r e f o r e r e a s o n a b l e to s u p p o s e t h a t t h e a d s o r p t i o n e n e r g y of a silver or a b r o m i d e ion to a silver b r o m i d e c r y s t a l w o u l d v a r y a c c o r d i n g t o t h e n a t u r e of t h e a d s o r b i n g face. U n f o r t u n a t e l y t h e y i e l d of c r y s t a l s b y t h e m e t h o d used for t h e p r e p a r a t i o n of m o n o d i s p e r s e sols was n o t large e n o u g h to e n a b l e d i r e c t a d s o r p t i o n m e a s u r e m e n t s to b e a t t e m p t e d . A n a l t e r n a t i v e Present Address: Dept. of Physical Chemistry, University of Bristol, England. 6O6
MONODISPERSE SILVER HALIDE SOLS
607
method to detect differences in adsorption properties was therefore to measure the electrokinetie potential of the particles since, theoretically, adsorption of silver or bromide ions to the crystal would be expected to affect the surface charge and hence the zeta potential. Moreover, electrokinetic measurements on monodisperse silver halide sols were of direct interest since the results reported in the literature for this material, on polydisperse systems, showed several unexplained phenomena. Julien (5), using the streaming potential method and capillaries of fused silver bromide, was not able to obtain a positively charged surface even in silver concentrations of the order of 10-2 M. He found, however, that freshly prepared silver bromide exhibited a positive charge which disappeared on aging. A similar effect was observed by Jonker (6), who found that the zero point of charge of dilute silver bromide sols was initially at pAg 5.40 but moved to lower pAg values as the sol aged. Kolthoff, Reyerson, and Coad (7), who carried out streaming potential measurements on fused and recrystallized silver bromide, also found it difficult to obtain positively charged crystals. The variability of the electrokinetie potential of silver bromide was later investigated by Davies and tIolliday (8), who attributed the variation in results to the adsorption of silicate ions from the glass yessels in which storage and measurement were carried out. Treatment of all glassware with acid fluoride solutions enabled reproducible results to be obtained with a particular type of sol. Luvalle and Jackson (9), using a similar sol and washing technique, found substantially the same results. The effect of particle size and mode of preparation of the silver bromide crystals was investigated recently by Barr and Dickinson (10). It was found that the zero point of charge moved to lower pAg values as the size of the crystals increased and a correlation apparently existed between the two. EXPERIMENTAL
All inorganic chemicals used were of Analar quality. Dodecylpyridinium bromide, dodecylpyridinium iodide, and sodium dodecyl sulfate were from the same batch of material as that previously described (11, 12). Distilled water was twice redistilled from an all Pyrex apparatus just before use.
Preparation of Sols The following designation has been used for the sols prepared in this work: Sol A, silver bromide, prepared by dilution of the complex in excess ammonium bromide solution. Sol B, silver bromide, prepared by dilution of the complex in excess silver nitrate solution.
608
OTTEWILL AND WOODBRIDGE
Sol C, silver bromide, prepared by cooling a hot saturated solution of silver bromide. Sol D, silver bromide, prepared by a homogeneous precipitation reaction. Sol E, silver iodide, prepared by dilution of the complex in excess potassium iodide solution. Sol F, silver iodide, prepared by dilution of the complex in excess silver nitrate solution. The details of the preparative methods have been given elsewhere (1, 13). All operations involving the exposure of silver bromide to light were carried out in a darkroom illuminated by a red Kodak safelight, Wratten series 0. For every sol the size of the particles was determined by an electron microscope examination of carbon replicas.
Microelectrophoresis Measurements Electrophoretic measurements were carried out using an apparatus based on the design of van Gils and Kruyt (14) ; this has been described previously (11). The cell was immersed in a water bath to avoid refractive and convective effects. All measurements were carried out at a room temperature of 20 ° -~ I°C. A yellow filter was placed in front of the light source in order to minimize any small effect which might have occurred owing to exposure of silver bromide particles to the illuminating beam during electrophoresis. The electrophoresis cell was always treated by the procedure recommended by Davies and Holliday (8). In general, for each concentration, the mobility used for the calculation of zeta potential was the mean of at least 20 mobility determinations on different particles. Many of the sols, by virtue of the method of preparation, were initially in a high concentration of electrolyte. The particles were separated either by sedimentation under gravity or centrifugation. The supernatant was then poured off and replaced by 10-3 M hydrofluoric acid during storage. The sol was then recentrifuged, and the particles were washed several times with distilled water and then with the indifferent electrolyte to be used. Redispersion of the particles in the indifferent electrolyte was eventually achieved either by stirring with a high velocity iet or ultrasonically; the method employed for redispersion had no noticeable effect on the results obtained. The redispersed sol was then adiusted to the required pAg (pAg = --log [Ag+]) by addition of the appropriate amount of silver nitrate or potassium bromide solution. It was found that during electrophoresis coagula could easily be distinguished from single particles; measurements were confined to single particles. Zeta potentials were calculated from mobilities using the formula given by Overbeek (15). This formula, however, was derived for spherical particles and includes the radius of the sphere a and the Debye-Hfickel reciprocal length K. The monodisperse sol
MONODISPERSE SILVER HALIDE SOLS
609
TABLE I Values of a used in the Calculation of Ka
Particle shape I r r e g u l a r or v e r y rounded Cube Octahedron Hexagonal b i p y r a m i d
Distance taken as equivalent to a Half the average of two directions measured a t r i g h t angles 0.70 X the l e n g t h of one side 0.55 X the l e n g t h of one side Half the average of the long and s h o r t axes
particles were not spherical, but since they possessed a high degree of symmetry they were assumed to behave as spheres during electrophoresis. It was necessary, however, to assign a value for the radius a. The values taken, which are listed in Table I, were based on simple geometric considerations. RESULTS
Classical sols. Microelectrophoresis measurements made on sols prepared in the manner described by Davies and Holliday (8) gave results in good agreement with those reported by these authors. The measurements were made in 10-~ 11I NaF solution on sols which contained particles having a mean diameter of 0.13 ~. The zero point of electrokinetie charge of these sols was found to be at pAg 5.1 ± 0.2. The results obtained were also in reasonable agreement with the microeleetrophoresis results of Jonker (6) and Luvalle and Jackson (9). Monodisperse sols. Extensive electrophoresis measurements were carried out on monodisperse silver bromide sols of type A, B, C, and D. The mobility against pAg curves for the various preparations are given in Fig. 1. Considerable variation was found from preparation to preparation, but each preparation gave a smooth curve which was consistent within itself. At high pAg values, the mobility appeared to reach a virtually constant value although in some cases a slight maximum appeared to be present in the curve. The spread in the results from preparation to preparation was greatest at the high p a t values, where the maximum mobility was found to vary between ca. - 2 . 2 and - 4 . 8 #/sec./volt/em. The results converged as the zero point of charge was approached. The zero points of charge of the various preparations were in the range pAg 1.3-3.0. The mean value was therefore considerably different from that obtained using classical preparations. The values of df/d pAg at the zero point of charge varied from --9 to --16 my. per p a t unit; these values are again considerably smaller than those obtained using classical sols. On taking an average value for each type of sol it was found that on the basis of the mobility against
610
OTTEWILL
AND WOODBRIDGE
Monodisperse silver betide sols -5
A A -4
--
•
&
•
=
°go C~
-3 -
A •
-~°
0
•
~t -2-
f,1 i~ r'] • r-] 1:3
0
o
0
~
O
[3
@ 0
°
0°[3
A o
•
0
@ ao
•
0
0
o
• o
8
O
x
0~
I
2
5
4
5
6
7
8
9
pAg
FIG. 1. Mobility against pAg curves for monodisperse silver bromide sols in 10-~ M sodium fluoride. --O--, sols, type A;--O--, sols, type B; --D--, sols, type C; --A--, sols, type D. pAg curves no significant difference was apparent among any of the three types oi" preparation. The effect of ionic strength on sol A was examined by determining the mobility against pAg curves in 10-~ M and 10-2 M sodium fluoride solutions. The results are presented in Fig. 2 in the form of zeta potential against pAg. The same sol preparation was used to obtain both curves in order to obtain internally consistent results. Sols prepared by the other methods exhibited similar behavior. The effects of using sodium nitrate, potassium bromate, and potassium chlorate were also investigated. The values obtained in sodium fluoride solution were slightly more negative than those in the other electrolytes
611
MONODISPEI~SE SILYER ttALIDE SOLS Monodisperse silver halide sols
-5
:~<
/
X
X
:::L >7,-2
3
I
l
4
5
.....
I
1
I
t
6
7
8
9
pAg
FIG. 2. M o b i l i t y against pAg curves for silver bromide sols of type A a t two differe n t c o n c e n t r a t i o n s of sodium fluoride. - - © - - , 10-8 M sodium fluoride; - - × - - , 10-* M sodium fluoride.
but there was no significant trend to indicate that any of the anions investigated, had any specific effect. The variation of mobility as a function of pH was investigated for a sol of type D in 10-8 M sodium fluoride at pAg 4. The results are shown in Fig. 3, and from the curve it is clear that the mobility is not influenced by pH in the region 4-9. Since all other measurements were carried out at pH 6.0 :t: 0.5 it appears unlikely that small variations in pH could explain the differences in mobility from preparation to preparation. The variation of mobility with time was investigated for sols of type A and type B. The results obtained are presented in Fig. 4. Unfortunately
612
OTTEWILL AND WOODBRIDGE Monodisperse silver haIide sols.
oe
-3
i/
~L-2 >: ~5
I
I
3
4
.........
I
I
5
6
,
I
I
7
8
I .......
9
I
I0
pH
FIG. 3. M o b i l i t y against p i t curve for a silver :bromide sol of t y p e D in 10-3 M sodium fluoride at pAg 4. silver halide sols
Monodisperse
g O-Q
=:L
-0.5
-I.0
°---
=-°
---
°-----
- - - - -
0
0"-0 I
I00 Time (minutes)
I
200
FIG. 4. V a r i a t i o n of mobility w i t h time for silver bromide sols. - - O - - , t y p e A; - - O - - , type B.
MONODISPERSE SILVER HALIDE SOLS
613
owing to the manipulation involved in centrifugation and decantation it was not possible to obtain results earlier than 12 minutes after mixing the complex with distilled water. Fifteen minutes after mixing and bringing to pAg 3, with silver nitrate, the particles of sols of type A exhibited a small positive mobility. This, however, gradually decreased with time and reached a constant negative value after several hours. The particles in sols of type B remained at a constant negative mobility throughout the whole period of examination. In view of the variation of mobility with time, found for sols of type A, all sols were allowed to age for at least 2 days before use. Silver Iodide Sols
Silver iodide sols prepared from excess potassium iodide and also sols prepared from excess silver nitrate were investigated. No significant difference, however, was observable between the two types of preparation. As in the case of the monodisperse silver bromide sols, the curve of mobility against pAg obtained for any given preparation was self consistent, but variation occurred from preparation to preparation, particularly at the higher pAg values. The variation, moreover, did not appear to be attributable to the difference in the methods of preparation of the sols. The results obtained in these experiments are summarized in Table II. For the majority of sols a zero point of charge was observed at pAg.2. The value of (d~/dpAg)~=o, however, varied from - 7 to - 2 3 i n v . per pAg unit, compared with a value of - 3 5 m y . per pAg unit found by Troelstra (16) for a classical sol. The values reported in the literature for the zero point of charge of classical sols vary from pAg 3.2 to pAg 5.4. The variation of mobility with time was investigated using sols E and F. Both TABLE II Mobility of Monodisperse Silver Iodide Sols in 10-s M Sodium Fluoride Solution
Type of sol preparation pAg 2 3 4 5 6 7 9 10 11 12 13
E I
F II
Mobility (~.cm./sec. volt) 0 --0.85 --1.05 --1.14 --1.14 --1.73 --1.76 --1.79 --1.95 --1.94 --2.00
0 --1.23 --2.16 --2.75 --3.05 --2.99 --3.38 --3.45 --3.43 --3.48 --3.41
I
II
Mobility (u.em./see. volt) --0.75 --1.36 --2.21 --2.47
--2.75 --2.62 --2.73 --2.97 --3.17 --3.11 --3.30
0 --0.45 --0.83 --1.57 --1.86 --1.99 --2.08 --2.54 --2.52 --2.53 --2.28
614
OTTEWILL
AND WOODBRIDGE
Monodisperse silver halide sols
-5
I
I
5
4
_1
I 5
6
phg or p(Dodecyl pryridinium)
FIG. 5. Mobility against -log molar concentration of dodecyl pyridinium bromide or pAg in 10-8 M sodium fluoride. --O--, sols of type A; --O--, sols of type B; ..... curves against pAg, • curve against p(dodecyl pyridinium ion). sols became slightly positive immediately after adjustment to pAg 3 but reached a constant negative mobility after approximately 24 hours.
The Effects of Surface-Active Agents on Monodisperse Silver Bromide and Silver Iodide Sols. In Fig. 5 curves are given of mobility against log molar concentration of dodecylpyridinium bromide for silver bromide sols of type A and B in 10-3 M sodium fluoride solution at pBr 4. With sols of type A reversal of charge was observed at ca. 10-3 M dodecylpyridinium bromide, whereas with sols of type B it was not reached experimentally; extrapolation indicated a value in the region of ca. 10-~ M. Luvalle and Jackson (9) using a classical silver bromide sol at p H 9 and pAg 8 found a reversal of charge at 6 X 10-5 M dodecylpyridinium bromide. The effects of sodium dodecyl sulfate were investigated on a sol of type B. Over the concentration range 10-6 M to 10-4 M the mobility of the particles increased fl'om - 2 . 7 to --3.0 p/sec./volt/cm, at pAg 6.3. The trend of the results was towards slightly more negative mobilities but the total variation was only of the order of the experimental error. The effect of dodecylpyridinium iodide on silver iodide sols at pI 4 was examined using sols of type E and F. The results of these experiments are given in Fig. 6. The concentrations required to reverse the charge on the particles were 5.7 X 10-4 M and 2.5 X 10-4 M for E and F, respectively. In earlier work (11) with classical silver iodide sob reversal of charge was found to occur with 3.6 X 10-8 M dodecylpyridinium iodide at pI 4.
615
MONODISPERSE SILVER HALIDE SOLS
Monodisperse silver holide sols
..-" /
>~::L-'1
;'
j/
~-
I I
js
,,.sO
"/.-'7
,..,.~ s4
S
" -
/
[ /
~3__//_ ,.-
o
//
.
I
2
/ (|
o/
.
.
l
.
.
.
I
.
.
.
I
3 4 5 6 pAg or p(Dodecyl pryridinium)
FIG. 6. M o b i l i t y against --log molar c o n c e n t r a t i o n of dodecl p y r i d i n i u m iodide or pAg in 10.8 M sodium fluoride. - - O - - , sols of type E ; - - O - - , sols of t y p e F ; . . . . . curve against pAg, - curve against p (dodeeyl p y r i d i n i u m ion).
Thus both monodisperse silver bromide and monodisperse silver iodide sols exhibited a behavior towards organic cations which differed from that observed with classical dispersions. DISCUSSION
The results obtained in the present studies on the eleetrophoretic properties of monodisperse silver bromide and silver iodide sols differed in many features from the results reported in the literature for measurements on classical sols. The main differences may be summarized as follows: The zero point of charge of monodisperse silver bromide and silver iodide sols occurred at very low pAg values, compared to those observed with classical sols, and it was found extremely difficult to give the particles a positive charge. The slope of the zeta potential against pAg curves for the monodisperse sols, at the zero point of charge, was smaller than that obtained with classical sols. The results obtained for classical sols appear to be reasonably reproducible from preparation to preparation and from author to author. With monodisperse sols, although each preparation gave a consistent mobility
616
OTTEWILL
AND WOODBRIDGE
against pAg curve, considerable variation was experienced from preparation to preparation in the magnitude of the mobility observed. The average behavior of a large nmnber of preparations did not reveal any significant difference among the properties of cubic, octahedral, or irregular cubic particles; the spread of results would, however, have obscured such an effect. Classical sols became positively charged in the presence of very low concentrations of cationic surface-active agents; for example, negative silver iodide sols reversed their charge in the presence of ca. 10-6 M dodecylpyridininm iodide (11). The monodisperse sols, however, required concentrations two orders of magnitude larger, i.e., ca. 10-6 M. A shift of the zero point of charge, both with age and with the mode of preparation of silver halide crystals, has been observed by several authors (5, 6, 17). In most cases the shift of the zero point of charge was ascribed to the increase in size of the crystal; this, however, although a valid point, may not be the most important one. In the present work a zero point of charge of ca. pAg 2 was obtained using crystals with a side length of 0.3 to 0.8 t~, whereas Barr and Dickinson (10) had to use crystals several millimeters in length, to obtain a similar value of the zero point of charge. Davies and Holliday (8) have suggested that the difficulty of obtaining positive silver bromide particles was associated with adsorption of impurities, in particular, silicate ions, from the glass electrophoresis cell and storage vessels. These authors suggested treatment of all vessels with hydrofluoric acid to prevent contamination with silicate ions. This procedure has been scrupulously adhered to in the present work. In view of the relatively large concentration of a cationic surface-active agent required to reverse the charge, it would seem unlikely that small traces of organic impurities could have caused the effects. Also, since sols of type A and B were formed from high concentrations of salts, if contamination had been present these sols would have exhibited a different behavior to those prepared at very low concentrations, namely, sols C and D. The cause of the differences between the classical sols and monodisperse sols would appear more likely to be connected with the mode of growth of the crystals. In the preparation of classical sols mixing usually occurs at a high supersaturation of silver halide. Growth therefore occurs very rapidly producing a very imperfect crystal the surface of which is covered with imperfections; also multivalent cation in]purities, e.g., Pb 2+, may be incorporated into the crystals. The particles in the monodisperse sols, on the other hand, are produced by a slow growth process; nucleation occurs at low supersaturation levels and is followed by slow diffusional growth. Thus it seems probable a more perfect crystal is obtained with fewer imperfections per unit area of surface. I t is of interest to observe that in the work
MONODISPERSE SILVER HALIDE SOLS
617
of Barr and Dickinson (10) there also appears to be some correlation between the rate of growth of the crystal and the shift of the zero point of charge. In general, the electrokinetic properties of the monodisperse sols auggested that the behavior was in some way connected with the properties of the solid. In particular the wide spread of results obtained for different preparations resembles the behavior of bulk samples of silver bromide in the structure-sensitive region (18). For example, differences from sample to sample have been reported for the potentials of electrodes made using solid silver bromide by Matejec (19) and by Kolthoff and Sanders (20).
Mechanism of Charge Determination The classical basis of charge determination at a silver halide surface is that due to Lange (21) and ¥erwey and Kruyt (22). This has proved satisfactory for explaining many of the properties of classical silver iodide sols and suspensions (23, 24). However, it does not appear, in its simple form, to provide an adequate explanation for the electrophoresis results obtained on the monodisperse sols examined in the present work. In the case of heteroionic crystals it has been pointed out by Griraley (25) that if lattice defects are present in the crystal a balancing charge may reside inside the crystal in the form of a space charge of lattice defects whose structure is similar to that existing in electrolyte solutions. The charge density due to the defects would be highest near the solid-liquid interface and fall exponentially to zero inside the crystal. At the zero point of charge, where the two phases are uncharged, the concentration of defects is uniform throughout the crystal. To facilitate theoretical treatment Grimley assumed that the defects were of the Schottky type, so that the charge arose through the presence of vacant cation and anion sites in unequal concentrations. However, as pointed out by Grimley, the treatment is not altered in its essential details if the defect structure is of the Frenkel type. Thus it would seem reasonable to conclude that for silver halide sols two charge-determining mechanisms have to be taken into consideration; (a). that arising from adsorption of an excess of one species of lattice ion (21, 22); (b). that arising from the space charge set up in the solid owing to its defect structure (25). In the case of classical sols, with a high degree of surface imperfection, mechanism (a) is probably predominant. In the case of monodisperse sol particles, however, where more perfect crystals are obtained, mechanism (b) may become the predominant one.
618
OTTEWILL
AND WOODBRIDG]E
Correlation of the Experimental Data with Grimley's Theory On the basis of Grimley's theory the potential at the crystal-solution interface, ¢~, is given, for constant x potential, by the expression, ¢*=
-e-, In(1+-//~)
--
In
1+
,
[1]
where ~ = V/~/noe., No = ionic concentration per milliliter in the solution, no = the number of defects per milliliter of solid, and e~ and e = the dielectric constants of the solid and liquid, respectively. Also ~, = ~/~/C°Ag, where C O Ag = the concentration of silver ions in solution at the zero point of charge. Although the equation was derived, strictly, for an infinitely thick crystal, it was found that provided that the diameter of the crystal was greater than 10-6 cm. it could be assumed to be infinite for the purposes of calculation. On differentiation Eq. [1] yields
e L(~ + ~ ( ~
d~
# ~)J"
[2]
At the zero point of charge Cxg = C°g, and hence 7 = 1. Therefore taking ¢~ -- i" and putting pAg = --log Cx~, Eq. [2] becomes: (dd~)~0
=
2"303 ( kT l ~ ) e
"
[3]
Equation [3] was used by Davies and ttolliday (8) in their work on the electrophoresis of classical silver bromide sols. T h e y found the zero point of charge to be at pAg 5.4 and using Eq. [3] calculated a value for ~ which gave no = 4.3 X 10 ~7 defects per milliliter. The upper and lower limits of the values obtained in the present work, using this procedure, are tabulated in Table III. In order to obtain direct evidence that the electrokinetic results are influenced by the defects in the crystal a direct comparison of the results from electrophoresis with those from solid-state work is required. Such a comparison, however, raises some difficulties since the results of solidTABLE III
no for Silver Bromide and Silver Iodide Sols Obtained by Electrophoresis Material
AgBr AgBr AgI AgI
Zero point of charge
pAg pAg pAg pAg
= = = =
3 1.3 2 2
d~/d pAgunit mv per pAg
--9 --16 --8 --25
n0
1.2 2.6 1.1 2.6
× X X X
1017 10t9 1018 10'9
MONODISPERSE SILVER HALIDE SOLS
619
state work on silver bromide given in the literature vary over several orders of magnitude. Grimley (25), assuming the defects were of the Schottky type, obtained a value for no of 1.7 X 1017from the data of Koch and Wagner (26). An extrapolation of the defect concentration against temperature data of Christy (27) down to 75 °, gives 1.2 X 1017. However, Klein and Matejee (28) quote 4 X 1014, and .Mitchell (29), assuming the defects are of the Frenkel type, obtains 1.4 X 10~2. The values obtained from eleetrophoresis experiments lie in the upper range of the results obtained from solid-state measurements. However, the latter values are based on the assumption that the defects are uniformly spread throughout the crystal, whereas a greater concentration would be expected in the surface region (30). In a qualitative way the concept of a space charge in the solid phase leads to a possible explanation of several of the phenomena observed in the present work and in the literature. During the growth of ionic crystals a number of point defects are trapped (31). However, since the equilibrium concentration of bromide ion vacancies is much smaller than the equilibrium concentration of silver ion vacancies the former would tend to migrate out of the crystal leaving a negative space charge within it (32). Under these conditions the charge density due to the defects would be highest near the crystal-liquid interface (30), and as a consequence of the migration the zero point of charge would move to lower pAg values. It would appear a reasonable conclusion that the eleetrokinetie properties of silver halide sols are influenced by the solid-state properties of the crystals. In order to establish more directly, however, the correlation between the two sets of properties it would seem desirable to pursue a course of experiments in which silver bromide specimens can be prepared by a method which allows their solid-state properties to be characterized before electrokinetie experiments are performed. ACKNOWLEDGMENTS We wish to thank Messrs Ilford Ltd., for a maintenance grant to one of us (1%. F. W.). I t is also a pleasure to record our thanks to Mr. g . O. Dickinson for many stimulating discussions on the subject matter of this paper. I~EFERENCES 1. 2. 3. 4. 5. 6.
7. 8.
OTTEWtJ-L, R. It., AND WOOI)~RIDGE, R. F., J. Colloid Sci. 16, 581 (1961). FRUM]~IN, A. N., Colloid Symposium Annual 7, 89 (1930). SCI-IMID,C-. M., AND HACKERMAN, 1~., J. Electrochem. Soc. 109, 243 (1962). HARVEY, W. W., LA FI~EUR, W. J., AND GATOS, ~-~/[.C., J . Electrochem. Soc. 109, 155 (1962). JULIEN, P. F. J. A., Doctoral Thesis, Utrecht, 1933. JONKE:a, G. IX., Doctoral Thesis, Utrecht, 1943. KOLTHOFF, I. M., REYERSON, L. I-I., AND COAD, I~., J. Phys. Chem. 51, 321 (1947). DAVIES, K. N., AND HOLLIDAY, A. l~., Trans. Faraday Soc. 48, 1061, 1066 (1952).
620
OTTEWILL AND WOODBRIDG]~
9. LUVALLE, J. H., AND JACKSON, J. M., J. Phys. Chem. 61, 1216 (1957). 10. BAI%R,J., AND DICKINSON,t~. O., J. Phot. Sci. 9, 222 (1961). 11. OTTEWILI~,R. H., AND RASTOGI,M. C., Trans Faraday Soc. 56, 866 (1960). 12. OTTEWlLL,R. H., AND WATANABE, A., Kolloid-Z. 170, 38 (1960). 13. OTTEWlLL,1%. It., AND WOODBmDGE,R. F., J. Phot. Sci., to be published. 14. VAN GILS, G. E., AND KRUYT, H. R., Kolloid-Beih. 45, 60 (1937). 15. OVERBEEK, J. Th. G., Kolloid-Beih. 54, 287 (1943). 16. TROELSTRA, S. A., Doctoral Thesis, Utrecht, 1941. 17. 1V~IRNIK,M., FLAJSMAN, F., AND TE~AK, B., Croat. Chem. Acta 28, 167 (1956). 18. MAamJEC, R., Z. Physik. 148, 454 (1957). 19. MATEJEC, R., Z. Elektrochem. 62, 400 (1958). 20. I~OLTHOFF,I. M., AND SANDERS,H. L., J. Am. Chem. Soc. 59,416 (1937). 21. LANGE, E., "Handbuch der Experimental Physik," 12th ed., p. 265. 1933. 22. VERWEY, E. J. W., AND I4~RUYT, H. I~., Z. physik. Chem. (Leipzig) A167, 137 (1933). 23. MACKOR,E. L., Rec. Tray. Chim. 70, 663, 747, 763 (1951). 24. LYKLEMA, J., Doctoral Thesis, Utrecht, 1957. 25. GRI~ImY, T. B., Proc. Roy. Soc. (London) A201, 40 (1950). 26. KOCH, E., AND WAGNER, C., Z. physilc. Chem. (Leipzig) BSS, 295 (1937). 27. CHmSTY, R. W., J. Chem. Phys. 31, 1148 (1961). 28. KLEIN, E., AND MATEJEC, 1%., Z. Elelctrochem. 61, 1127 (1957). 29. MITCHELl,, J. W., J. Phot. Sci. 66, 57 (1958). 30. LEROVEC,K., J. Chem. Phys. 21, 1123 (1953). 31. WEnB, W. W. J. Appl. Phys. 33, 1961 (1962). 32. KOLTHOFF,I. M., AND BOWERS, R. C., J. Phys. Chem. 76, ]503, 1510 (1954).
]~DITOR'S ~OTE The only other investigation of the differences in mobility between monodispersed and classically prepared sols is that of R. H. Smellie, Jr., and V. K. La Mer, in the Journal of Physical Chemistry 58, 583 (1954), on Sulfur Hydrosols. Monodispersed sulfur hydrosols are prepared from dilute (0.003 M) HC1 and (0.001 M) Na2S20~, whereas the classical sols are prepared using much more concentrated reagents. In the latter case, polythionates are formed in appreciable amounts as side reactions. The monodispersed sulfur is stabilized by adsorbed H + ion. This positive charge becomes negative on addition of NaOH and aging, and particularly when 10-5 M pentathionate is added. The latter replaces the H + by preferential adsorption. The sulfur particle is a latex droplet of supercooled k sulfur, presumably consisting of a linear polymer of sulfur. It would seem that lattice defects are not a complicating factor in the sulfur colloids. VICTOR K . LA MER
STUDIES ON THE ELECTROKINETIC BEHAVIOR OF MONODISPERSE SILVER HALIDE SOLS R. H. Ottewill~ and R. F. Woodbridge Department of Colloid Science, University of Cambridge, Cambridge Received August 19, 1963; revised April 13, 196~ 2~kBSTRACT Methods have been developed for the preparation of monodisperse sols of silver bromide and silver iodide. The electrokinetic properties of the sols were examined, using microeleetrophoresis, as a function of the pAg of the sol at virtually constant ionic strength. The results obtained showed some differences from those obtained with classical polydisperse silver bromide and silver iodide sols. The differences in the electrokinetic properties of the two types of dispersion were attributed to the difference in the crystal growth processes. In the case of the monodisperse sols the crystals appear to be more perfect and the space charge in the crystal possibly contributes to the surface potential, and hence to the electrokinetic potential.
INTRODUCTION In a previous communication methods have been described for the preparation of monodisperse sols of silver halides (i). In the case of silver bromide it was found that sols could be prepared in which the particles had a cubic form with (001) faces or an octahedral form with (iii) faces. In 1930 Frumkin (2) pointed out that because of the difference occurring in the work function for individual crystal faces, a difference in the behavior of the double layer would be expected to occur according to the crystal face exposed to the electrolyte solution. In support of this hypothesis Schmid and Hackerman (3) recently found differences in the differential capacity of a single crystal gold electrode according to whether an (001) or a (iii) face was exposed to the solution; Harvey, La Fleur, and Gatos (4) also found that the adsorption of iodide ions on to a germanium electrode differed a c c o r d i n g to w h e t h e r a n (001) or a (111) face was u s e d for t h e measurements. I t w a s t h e r e f o r e r e a s o n a b l e to s u p p o s e t h a t t h e a d s o r p t i o n e n e r g y of a silver or a b r o m i d e ion to a silver b r o m i d e c r y s t a l w o u l d v a r y a c c o r d i n g t o t h e n a t u r e of t h e a d s o r b i n g face. U n f o r t u n a t e l y t h e y i e l d of c r y s t a l s b y t h e m e t h o d used for t h e p r e p a r a t i o n of m o n o d i s p e r s e sols was n o t large e n o u g h to e n a b l e d i r e c t a d s o r p t i o n m e a s u r e m e n t s to b e a t t e m p t e d . A n a l t e r n a t i v e Present Address: Dept. of Physical Chemistry, University of Bristol, England. 6O6
MONODISPERSE SILVER HALIDE SOLS
607
method to detect differences in adsorption properties was therefore to measure the electrokinetie potential of the particles since, theoretically, adsorption of silver or bromide ions to the crystal would be expected to affect the surface charge and hence the zeta potential. Moreover, electrokinetic measurements on monodisperse silver halide sols were of direct interest since the results reported in the literature for this material, on polydisperse systems, showed several unexplained phenomena. Julien (5), using the streaming potential method and capillaries of fused silver bromide, was not able to obtain a positively charged surface even in silver concentrations of the order of 10-2 M. He found, however, that freshly prepared silver bromide exhibited a positive charge which disappeared on aging. A similar effect was observed by Jonker (6), who found that the zero point of charge of dilute silver bromide sols was initially at pAg 5.40 but moved to lower pAg values as the sol aged. Kolthoff, Reyerson, and Coad (7), who carried out streaming potential measurements on fused and recrystallized silver bromide, also found it difficult to obtain positively charged crystals. The variability of the electrokinetie potential of silver bromide was later investigated by Davies and tIolliday (8), who attributed the variation in results to the adsorption of silicate ions from the glass yessels in which storage and measurement were carried out. Treatment of all glassware with acid fluoride solutions enabled reproducible results to be obtained with a particular type of sol. Luvalle and Jackson (9), using a similar sol and washing technique, found substantially the same results. The effect of particle size and mode of preparation of the silver bromide crystals was investigated recently by Barr and Dickinson (10). It was found that the zero point of charge moved to lower pAg values as the size of the crystals increased and a correlation apparently existed between the two. EXPERIMENTAL
All inorganic chemicals used were of Analar quality. Dodecylpyridinium bromide, dodecylpyridinium iodide, and sodium dodecyl sulfate were from the same batch of material as that previously described (11, 12). Distilled water was twice redistilled from an all Pyrex apparatus just before use.
Preparation of Sols The following designation has been used for the sols prepared in this work: Sol A, silver bromide, prepared by dilution of the complex in excess ammonium bromide solution. Sol B, silver bromide, prepared by dilution of the complex in excess silver nitrate solution.
608
OTTEWILL AND WOODBRIDGE
Sol C, silver bromide, prepared by cooling a hot saturated solution of silver bromide. Sol D, silver bromide, prepared by a homogeneous precipitation reaction. Sol E, silver iodide, prepared by dilution of the complex in excess potassium iodide solution. Sol F, silver iodide, prepared by dilution of the complex in excess silver nitrate solution. The details of the preparative methods have been given elsewhere (1, 13). All operations involving the exposure of silver bromide to light were carried out in a darkroom illuminated by a red Kodak safelight, Wratten series 0. For every sol the size of the particles was determined by an electron microscope examination of carbon replicas.
Microelectrophoresis Measurements Electrophoretic measurements were carried out using an apparatus based on the design of van Gils and Kruyt (14) ; this has been described previously (11). The cell was immersed in a water bath to avoid refractive and convective effects. All measurements were carried out at a room temperature of 20 ° -~ I°C. A yellow filter was placed in front of the light source in order to minimize any small effect which might have occurred owing to exposure of silver bromide particles to the illuminating beam during electrophoresis. The electrophoresis cell was always treated by the procedure recommended by Davies and Holliday (8). In general, for each concentration, the mobility used for the calculation of zeta potential was the mean of at least 20 mobility determinations on different particles. Many of the sols, by virtue of the method of preparation, were initially in a high concentration of electrolyte. The particles were separated either by sedimentation under gravity or centrifugation. The supernatant was then poured off and replaced by 10-3 M hydrofluoric acid during storage. The sol was then recentrifuged, and the particles were washed several times with distilled water and then with the indifferent electrolyte to be used. Redispersion of the particles in the indifferent electrolyte was eventually achieved either by stirring with a high velocity iet or ultrasonically; the method employed for redispersion had no noticeable effect on the results obtained. The redispersed sol was then adiusted to the required pAg (pAg = --log [Ag+]) by addition of the appropriate amount of silver nitrate or potassium bromide solution. It was found that during electrophoresis coagula could easily be distinguished from single particles; measurements were confined to single particles. Zeta potentials were calculated from mobilities using the formula given by Overbeek (15). This formula, however, was derived for spherical particles and includes the radius of the sphere a and the Debye-Hfickel reciprocal length K. The monodisperse sol
MONODISPERSE SILVER HALIDE SOLS
609
TABLE I Values of a used in the Calculation of Ka
Particle shape I r r e g u l a r or v e r y rounded Cube Octahedron Hexagonal b i p y r a m i d
Distance taken as equivalent to a Half the average of two directions measured a t r i g h t angles 0.70 X the l e n g t h of one side 0.55 X the l e n g t h of one side Half the average of the long and s h o r t axes
particles were not spherical, but since they possessed a high degree of symmetry they were assumed to behave as spheres during electrophoresis. It was necessary, however, to assign a value for the radius a. The values taken, which are listed in Table I, were based on simple geometric considerations. RESULTS
Classical sols. Microelectrophoresis measurements made on sols prepared in the manner described by Davies and Holliday (8) gave results in good agreement with those reported by these authors. The measurements were made in 10-~ 11I NaF solution on sols which contained particles having a mean diameter of 0.13 ~. The zero point of electrokinetie charge of these sols was found to be at pAg 5.1 ± 0.2. The results obtained were also in reasonable agreement with the microeleetrophoresis results of Jonker (6) and Luvalle and Jackson (9). Monodisperse sols. Extensive electrophoresis measurements were carried out on monodisperse silver bromide sols of type A, B, C, and D. The mobility against pAg curves for the various preparations are given in Fig. 1. Considerable variation was found from preparation to preparation, but each preparation gave a smooth curve which was consistent within itself. At high pAg values, the mobility appeared to reach a virtually constant value although in some cases a slight maximum appeared to be present in the curve. The spread in the results from preparation to preparation was greatest at the high p a t values, where the maximum mobility was found to vary between ca. - 2 . 2 and - 4 . 8 #/sec./volt/em. The results converged as the zero point of charge was approached. The zero points of charge of the various preparations were in the range pAg 1.3-3.0. The mean value was therefore considerably different from that obtained using classical preparations. The values of df/d pAg at the zero point of charge varied from --9 to --16 my. per p a t unit; these values are again considerably smaller than those obtained using classical sols. On taking an average value for each type of sol it was found that on the basis of the mobility against
610
OTTEWILL
AND WOODBRIDGE
Monodisperse silver betide sols -5
A A -4
--
•
&
•
=
°go C~
-3 -
A •
-~°
0
•
~t -2-
f,1 i~ r'] • r-] 1:3
0
o
0
~
O
[3
@ 0
°
0°[3
A o
•
0
@ ao
•
0
0
o
• o
8
O
x
0~
I
2
5
4
5
6
7
8
9
pAg
FIG. 1. Mobility against pAg curves for monodisperse silver bromide sols in 10-~ M sodium fluoride. --O--, sols, type A;--O--, sols, type B; --D--, sols, type C; --A--, sols, type D. pAg curves no significant difference was apparent among any of the three types oi" preparation. The effect of ionic strength on sol A was examined by determining the mobility against pAg curves in 10-~ M and 10-2 M sodium fluoride solutions. The results are presented in Fig. 2 in the form of zeta potential against pAg. The same sol preparation was used to obtain both curves in order to obtain internally consistent results. Sols prepared by the other methods exhibited similar behavior. The effects of using sodium nitrate, potassium bromate, and potassium chlorate were also investigated. The values obtained in sodium fluoride solution were slightly more negative than those in the other electrolytes
611
MONODISPEI~SE SILYER ttALIDE SOLS Monodisperse silver halide sols
-5
:~<
/
X
X
:::L >7,-2
3
I
l
4
5
.....
I
1
I
t
6
7
8
9
pAg
FIG. 2. M o b i l i t y against pAg curves for silver bromide sols of type A a t two differe n t c o n c e n t r a t i o n s of sodium fluoride. - - © - - , 10-8 M sodium fluoride; - - × - - , 10-* M sodium fluoride.
but there was no significant trend to indicate that any of the anions investigated, had any specific effect. The variation of mobility as a function of pH was investigated for a sol of type D in 10-8 M sodium fluoride at pAg 4. The results are shown in Fig. 3, and from the curve it is clear that the mobility is not influenced by pH in the region 4-9. Since all other measurements were carried out at pH 6.0 :t: 0.5 it appears unlikely that small variations in pH could explain the differences in mobility from preparation to preparation. The variation of mobility with time was investigated for sols of type A and type B. The results obtained are presented in Fig. 4. Unfortunately
612
OTTEWILL AND WOODBRIDGE Monodisperse silver haIide sols.
oe
-3
i/
~L-2 >: ~5
I
I
3
4
.........
I
I
5
6
,
I
I
7
8
I .......
9
I
I0
pH
FIG. 3. M o b i l i t y against p i t curve for a silver :bromide sol of t y p e D in 10-3 M sodium fluoride at pAg 4. silver halide sols
Monodisperse
g O-Q
=:L
-0.5
-I.0
°---
=-°
---
°-----
- - - - -
0
0"-0 I
I00 Time (minutes)
I
200
FIG. 4. V a r i a t i o n of mobility w i t h time for silver bromide sols. - - O - - , t y p e A; - - O - - , type B.
MONODISPERSE SILVER HALIDE SOLS
613
owing to the manipulation involved in centrifugation and decantation it was not possible to obtain results earlier than 12 minutes after mixing the complex with distilled water. Fifteen minutes after mixing and bringing to pAg 3, with silver nitrate, the particles of sols of type A exhibited a small positive mobility. This, however, gradually decreased with time and reached a constant negative value after several hours. The particles in sols of type B remained at a constant negative mobility throughout the whole period of examination. In view of the variation of mobility with time, found for sols of type A, all sols were allowed to age for at least 2 days before use. Silver Iodide Sols
Silver iodide sols prepared from excess potassium iodide and also sols prepared from excess silver nitrate were investigated. No significant difference, however, was observable between the two types of preparation. As in the case of the monodisperse silver bromide sols, the curve of mobility against pAg obtained for any given preparation was self consistent, but variation occurred from preparation to preparation, particularly at the higher pAg values. The variation, moreover, did not appear to be attributable to the difference in the methods of preparation of the sols. The results obtained in these experiments are summarized in Table II. For the majority of sols a zero point of charge was observed at pAg.2. The value of (d~/dpAg)~=o, however, varied from - 7 to - 2 3 i n v . per pAg unit, compared with a value of - 3 5 m y . per pAg unit found by Troelstra (16) for a classical sol. The values reported in the literature for the zero point of charge of classical sols vary from pAg 3.2 to pAg 5.4. The variation of mobility with time was investigated using sols E and F. Both TABLE II Mobility of Monodisperse Silver Iodide Sols in 10-s M Sodium Fluoride Solution
Type of sol preparation pAg 2 3 4 5 6 7 9 10 11 12 13
E I
F II
Mobility (~.cm./sec. volt) 0 --0.85 --1.05 --1.14 --1.14 --1.73 --1.76 --1.79 --1.95 --1.94 --2.00
0 --1.23 --2.16 --2.75 --3.05 --2.99 --3.38 --3.45 --3.43 --3.48 --3.41
I
II
Mobility (u.em./see. volt) --0.75 --1.36 --2.21 --2.47
--2.75 --2.62 --2.73 --2.97 --3.17 --3.11 --3.30
0 --0.45 --0.83 --1.57 --1.86 --1.99 --2.08 --2.54 --2.52 --2.53 --2.28
614
OTTEWILL
AND WOODBRIDGE
Monodisperse silver halide sols
-5
I
I
5
4
_1
I 5
6
phg or p(Dodecyl pryridinium)
FIG. 5. Mobility against -log molar concentration of dodecyl pyridinium bromide or pAg in 10-8 M sodium fluoride. --O--, sols of type A; --O--, sols of type B; ..... curves against pAg, • curve against p(dodecyl pyridinium ion). sols became slightly positive immediately after adjustment to pAg 3 but reached a constant negative mobility after approximately 24 hours.
The Effects of Surface-Active Agents on Monodisperse Silver Bromide and Silver Iodide Sols. In Fig. 5 curves are given of mobility against log molar concentration of dodecylpyridinium bromide for silver bromide sols of type A and B in 10-3 M sodium fluoride solution at pBr 4. With sols of type A reversal of charge was observed at ca. 10-3 M dodecylpyridinium bromide, whereas with sols of type B it was not reached experimentally; extrapolation indicated a value in the region of ca. 10-~ M. Luvalle and Jackson (9) using a classical silver bromide sol at p H 9 and pAg 8 found a reversal of charge at 6 X 10-5 M dodecylpyridinium bromide. The effects of sodium dodecyl sulfate were investigated on a sol of type B. Over the concentration range 10-6 M to 10-4 M the mobility of the particles increased fl'om - 2 . 7 to --3.0 p/sec./volt/cm, at pAg 6.3. The trend of the results was towards slightly more negative mobilities but the total variation was only of the order of the experimental error. The effect of dodecylpyridinium iodide on silver iodide sols at pI 4 was examined using sols of type E and F. The results of these experiments are given in Fig. 6. The concentrations required to reverse the charge on the particles were 5.7 X 10-4 M and 2.5 X 10-4 M for E and F, respectively. In earlier work (11) with classical silver iodide sob reversal of charge was found to occur with 3.6 X 10-8 M dodecylpyridinium iodide at pI 4.
615
MONODISPERSE SILVER HALIDE SOLS
Monodisperse silver holide sols
..-" /
>~::L-'1
;'
j/
~-
I I
js
,,.sO
"/.-'7
,..,.~ s4
S
" -
/
[ /
~3__//_ ,.-
o
//
.
I
2
/ (|
o/
.
.
l
.
.
.
I
.
.
.
I
3 4 5 6 pAg or p(Dodecyl pryridinium)
FIG. 6. M o b i l i t y against --log molar c o n c e n t r a t i o n of dodecl p y r i d i n i u m iodide or pAg in 10.8 M sodium fluoride. - - O - - , sols of type E ; - - O - - , sols of t y p e F ; . . . . . curve against pAg, - curve against p (dodeeyl p y r i d i n i u m ion).
Thus both monodisperse silver bromide and monodisperse silver iodide sols exhibited a behavior towards organic cations which differed from that observed with classical dispersions. DISCUSSION
The results obtained in the present studies on the eleetrophoretic properties of monodisperse silver bromide and silver iodide sols differed in many features from the results reported in the literature for measurements on classical sols. The main differences may be summarized as follows: The zero point of charge of monodisperse silver bromide and silver iodide sols occurred at very low pAg values, compared to those observed with classical sols, and it was found extremely difficult to give the particles a positive charge. The slope of the zeta potential against pAg curves for the monodisperse sols, at the zero point of charge, was smaller than that obtained with classical sols. The results obtained for classical sols appear to be reasonably reproducible from preparation to preparation and from author to author. With monodisperse sols, although each preparation gave a consistent mobility
616
OTTEWILL
AND WOODBRIDGE
against pAg curve, considerable variation was experienced from preparation to preparation in the magnitude of the mobility observed. The average behavior of a large nmnber of preparations did not reveal any significant difference among the properties of cubic, octahedral, or irregular cubic particles; the spread of results would, however, have obscured such an effect. Classical sols became positively charged in the presence of very low concentrations of cationic surface-active agents; for example, negative silver iodide sols reversed their charge in the presence of ca. 10-6 M dodecylpyridininm iodide (11). The monodisperse sols, however, required concentrations two orders of magnitude larger, i.e., ca. 10-6 M. A shift of the zero point of charge, both with age and with the mode of preparation of silver halide crystals, has been observed by several authors (5, 6, 17). In most cases the shift of the zero point of charge was ascribed to the increase in size of the crystal; this, however, although a valid point, may not be the most important one. In the present work a zero point of charge of ca. pAg 2 was obtained using crystals with a side length of 0.3 to 0.8 t~, whereas Barr and Dickinson (10) had to use crystals several millimeters in length, to obtain a similar value of the zero point of charge. Davies and Holliday (8) have suggested that the difficulty of obtaining positive silver bromide particles was associated with adsorption of impurities, in particular, silicate ions, from the glass electrophoresis cell and storage vessels. These authors suggested treatment of all vessels with hydrofluoric acid to prevent contamination with silicate ions. This procedure has been scrupulously adhered to in the present work. In view of the relatively large concentration of a cationic surface-active agent required to reverse the charge, it would seem unlikely that small traces of organic impurities could have caused the effects. Also, since sols of type A and B were formed from high concentrations of salts, if contamination had been present these sols would have exhibited a different behavior to those prepared at very low concentrations, namely, sols C and D. The cause of the differences between the classical sols and monodisperse sols would appear more likely to be connected with the mode of growth of the crystals. In the preparation of classical sols mixing usually occurs at a high supersaturation of silver halide. Growth therefore occurs very rapidly producing a very imperfect crystal the surface of which is covered with imperfections; also multivalent cation in]purities, e.g., Pb 2+, may be incorporated into the crystals. The particles in the monodisperse sols, on the other hand, are produced by a slow growth process; nucleation occurs at low supersaturation levels and is followed by slow diffusional growth. Thus it seems probable a more perfect crystal is obtained with fewer imperfections per unit area of surface. I t is of interest to observe that in the work
MONODISPERSE SILVER HALIDE SOLS
617
of Barr and Dickinson (10) there also appears to be some correlation between the rate of growth of the crystal and the shift of the zero point of charge. In general, the electrokinetic properties of the monodisperse sols auggested that the behavior was in some way connected with the properties of the solid. In particular the wide spread of results obtained for different preparations resembles the behavior of bulk samples of silver bromide in the structure-sensitive region (18). For example, differences from sample to sample have been reported for the potentials of electrodes made using solid silver bromide by Matejec (19) and by Kolthoff and Sanders (20).
Mechanism of Charge Determination The classical basis of charge determination at a silver halide surface is that due to Lange (21) and ¥erwey and Kruyt (22). This has proved satisfactory for explaining many of the properties of classical silver iodide sols and suspensions (23, 24). However, it does not appear, in its simple form, to provide an adequate explanation for the electrophoresis results obtained on the monodisperse sols examined in the present work. In the case of heteroionic crystals it has been pointed out by Griraley (25) that if lattice defects are present in the crystal a balancing charge may reside inside the crystal in the form of a space charge of lattice defects whose structure is similar to that existing in electrolyte solutions. The charge density due to the defects would be highest near the solid-liquid interface and fall exponentially to zero inside the crystal. At the zero point of charge, where the two phases are uncharged, the concentration of defects is uniform throughout the crystal. To facilitate theoretical treatment Grimley assumed that the defects were of the Schottky type, so that the charge arose through the presence of vacant cation and anion sites in unequal concentrations. However, as pointed out by Grimley, the treatment is not altered in its essential details if the defect structure is of the Frenkel type. Thus it would seem reasonable to conclude that for silver halide sols two charge-determining mechanisms have to be taken into consideration; (a). that arising from adsorption of an excess of one species of lattice ion (21, 22); (b). that arising from the space charge set up in the solid owing to its defect structure (25). In the case of classical sols, with a high degree of surface imperfection, mechanism (a) is probably predominant. In the case of monodisperse sol particles, however, where more perfect crystals are obtained, mechanism (b) may become the predominant one.
618
OTTEWILL
AND WOODBRIDG]E
Correlation of the Experimental Data with Grimley's Theory On the basis of Grimley's theory the potential at the crystal-solution interface, ¢~, is given, for constant x potential, by the expression, ¢*=
-e-, In(1+-//~)
--
In
1+
,
[1]
where ~ = V/~/noe., No = ionic concentration per milliliter in the solution, no = the number of defects per milliliter of solid, and e~ and e = the dielectric constants of the solid and liquid, respectively. Also ~, = ~/~/C°Ag, where C O Ag = the concentration of silver ions in solution at the zero point of charge. Although the equation was derived, strictly, for an infinitely thick crystal, it was found that provided that the diameter of the crystal was greater than 10-6 cm. it could be assumed to be infinite for the purposes of calculation. On differentiation Eq. [1] yields
e L(~ + ~ ( ~
d~
# ~)J"
[2]
At the zero point of charge Cxg = C°g, and hence 7 = 1. Therefore taking ¢~ -- i" and putting pAg = --log Cx~, Eq. [2] becomes: (dd~)~0
=
2"303 ( kT l ~ ) e
"
[3]
Equation [3] was used by Davies and ttolliday (8) in their work on the electrophoresis of classical silver bromide sols. T h e y found the zero point of charge to be at pAg 5.4 and using Eq. [3] calculated a value for ~ which gave no = 4.3 X 10 ~7 defects per milliliter. The upper and lower limits of the values obtained in the present work, using this procedure, are tabulated in Table III. In order to obtain direct evidence that the electrokinetic results are influenced by the defects in the crystal a direct comparison of the results from electrophoresis with those from solid-state work is required. Such a comparison, however, raises some difficulties since the results of solidTABLE III
no for Silver Bromide and Silver Iodide Sols Obtained by Electrophoresis Material
AgBr AgBr AgI AgI
Zero point of charge
pAg pAg pAg pAg
= = = =
3 1.3 2 2
d~/d pAgunit mv per pAg
--9 --16 --8 --25
n0
1.2 2.6 1.1 2.6
× X X X
1017 10t9 1018 10'9
MONODISPERSE SILVER HALIDE SOLS
619
state work on silver bromide given in the literature vary over several orders of magnitude. Grimley (25), assuming the defects were of the Schottky type, obtained a value for no of 1.7 X 1017from the data of Koch and Wagner (26). An extrapolation of the defect concentration against temperature data of Christy (27) down to 75 °, gives 1.2 X 1017. However, Klein and Matejee (28) quote 4 X 1014, and .Mitchell (29), assuming the defects are of the Frenkel type, obtains 1.4 X 10~2. The values obtained from eleetrophoresis experiments lie in the upper range of the results obtained from solid-state measurements. However, the latter values are based on the assumption that the defects are uniformly spread throughout the crystal, whereas a greater concentration would be expected in the surface region (30). In a qualitative way the concept of a space charge in the solid phase leads to a possible explanation of several of the phenomena observed in the present work and in the literature. During the growth of ionic crystals a number of point defects are trapped (31). However, since the equilibrium concentration of bromide ion vacancies is much smaller than the equilibrium concentration of silver ion vacancies the former would tend to migrate out of the crystal leaving a negative space charge within it (32). Under these conditions the charge density due to the defects would be highest near the crystal-liquid interface (30), and as a consequence of the migration the zero point of charge would move to lower pAg values. It would appear a reasonable conclusion that the eleetrokinetie properties of silver halide sols are influenced by the solid-state properties of the crystals. In order to establish more directly, however, the correlation between the two sets of properties it would seem desirable to pursue a course of experiments in which silver bromide specimens can be prepared by a method which allows their solid-state properties to be characterized before electrokinetie experiments are performed. ACKNOWLEDGMENTS We wish to thank Messrs Ilford Ltd., for a maintenance grant to one of us (1%. F. W.). I t is also a pleasure to record our thanks to Mr. g . O. Dickinson for many stimulating discussions on the subject matter of this paper. I~EFERENCES 1. 2. 3. 4. 5. 6.
7. 8.
OTTEWtJ-L, R. It., AND WOOI)~RIDGE, R. F., J. Colloid Sci. 16, 581 (1961). FRUM]~IN, A. N., Colloid Symposium Annual 7, 89 (1930). SCI-IMID,C-. M., AND HACKERMAN, 1~., J. Electrochem. Soc. 109, 243 (1962). HARVEY, W. W., LA FI~EUR, W. J., AND GATOS, ~-~/[.C., J . Electrochem. Soc. 109, 155 (1962). JULIEN, P. F. J. A., Doctoral Thesis, Utrecht, 1933. JONKE:a, G. IX., Doctoral Thesis, Utrecht, 1943. KOLTHOFF, I. M., REYERSON, L. I-I., AND COAD, I~., J. Phys. Chem. 51, 321 (1947). DAVIES, K. N., AND HOLLIDAY, A. l~., Trans. Faraday Soc. 48, 1061, 1066 (1952).
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9. LUVALLE, J. H., AND JACKSON, J. M., J. Phys. Chem. 61, 1216 (1957). 10. BAI%R,J., AND DICKINSON,t~. O., J. Phot. Sci. 9, 222 (1961). 11. OTTEWILI~,R. H., AND RASTOGI,M. C., Trans Faraday Soc. 56, 866 (1960). 12. OTTEWlLL,R. H., AND WATANABE, A., Kolloid-Z. 170, 38 (1960). 13. OTTEWlLL,1%. It., AND WOODBmDGE,R. F., J. Phot. Sci., to be published. 14. VAN GILS, G. E., AND KRUYT, H. R., Kolloid-Beih. 45, 60 (1937). 15. OVERBEEK, J. Th. G., Kolloid-Beih. 54, 287 (1943). 16. TROELSTRA, S. A., Doctoral Thesis, Utrecht, 1941. 17. 1V~IRNIK,M., FLAJSMAN, F., AND TE~AK, B., Croat. Chem. Acta 28, 167 (1956). 18. MAamJEC, R., Z. Physik. 148, 454 (1957). 19. MATEJEC, R., Z. Elektrochem. 62, 400 (1958). 20. I~OLTHOFF,I. M., AND SANDERS,H. L., J. Am. Chem. Soc. 59,416 (1937). 21. LANGE, E., "Handbuch der Experimental Physik," 12th ed., p. 265. 1933. 22. VERWEY, E. J. W., AND I4~RUYT, H. I~., Z. physik. Chem. (Leipzig) A167, 137 (1933). 23. MACKOR,E. L., Rec. Tray. Chim. 70, 663, 747, 763 (1951). 24. LYKLEMA, J., Doctoral Thesis, Utrecht, 1957. 25. GRI~ImY, T. B., Proc. Roy. Soc. (London) A201, 40 (1950). 26. KOCH, E., AND WAGNER, C., Z. physilc. Chem. (Leipzig) BSS, 295 (1937). 27. CHmSTY, R. W., J. Chem. Phys. 31, 1148 (1961). 28. KLEIN, E., AND MATEJEC, 1%., Z. Elelctrochem. 61, 1127 (1957). 29. MITCHELl,, J. W., J. Phot. Sci. 66, 57 (1958). 30. LEROVEC,K., J. Chem. Phys. 21, 1123 (1953). 31. WEnB, W. W. J. Appl. Phys. 33, 1961 (1962). 32. KOLTHOFF,I. M., AND BOWERS, R. C., J. Phys. Chem. 76, ]503, 1510 (1954).
]~DITOR'S ~OTE The only other investigation of the differences in mobility between monodispersed and classically prepared sols is that of R. H. Smellie, Jr., and V. K. La Mer, in the Journal of Physical Chemistry 58, 583 (1954), on Sulfur Hydrosols. Monodispersed sulfur hydrosols are prepared from dilute (0.003 M) HC1 and (0.001 M) Na2S20~, whereas the classical sols are prepared using much more concentrated reagents. In the latter case, polythionates are formed in appreciable amounts as side reactions. The monodispersed sulfur is stabilized by adsorbed H + ion. This positive charge becomes negative on addition of NaOH and aging, and particularly when 10-5 M pentathionate is added. The latter replaces the H + by preferential adsorption. The sulfur particle is a latex droplet of supercooled k sulfur, presumably consisting of a linear polymer of sulfur. It would seem that lattice defects are not a complicating factor in the sulfur colloids. VICTOR K . LA MER