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The ionic double layer at the ZnOsolution interface
The Ionic Double Layer at the ZnO/Solution InterFace III. Comparison of Calculated and Experimental Differential Capacities L. B L O K AND P. L. D E B R U Y N ~ Department of Metallurgy and Materials Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Received July 3, 1969; accepted October 21, 1969 Differential capacity curves on ZnO in different 1-1 electrolyte solutions are presented. The magnitude of the capacity agrees with similar measurements on Fe203 and TiO2 and is explained with a double-layer model which assumes specific adsorption of both cations and anions with an adsorption energy of a few kT. The specificity of adsorption of univalent anions on ZnO is in the order CIO~< NO~ < I- < Br- < CI-
and confirms previous observations on rutile. INTRODUCTION In a previous paper (1) in this series, it was shown that p H variations resulting from the addition of acid or base to a zinc oxide suspension proceed in two steps with widely different time constants. This observation is in accord with similar studies on Fe203 (2) and TIO2(3) suspensions which led to the conclusion that the fast step describes the true response of the interface to changes in composition of the solution phase. The slower step is generally believed to result from compositional changes involving the surface regions of the bulk solid phase. To obtain meaningful values for the characteristic properties of the ionic double layer, the effect of this slow process must, therefore, either be eliminated or at least be reduced in intensity. The error introduced b y the slow p H change in studies with ZnO was usually small compared to the corrections applied for the solubility of the oxide. The latter factor was mainly responsible for limiting experimental To whom requests for reprints should be directed.
tion to a narrow p H range in the vicinity of the pzc. EXPERIMENTAL D IFFEI~ENTIAL CAPACITY The differential capacity of the ionic double layer at 25°C and fixed ionic strength may be obtained from fast adsorption isotherms by utilizing the relation c
-
F dAFt* 0.059 d p H
li]
where AFt* is the net adsorption density due to all potential-determining species (4 (b)). Numerous investigators applied Eq. [1] to their experimental adsorption measurements. Parks and de Bruyn (5) and also Albrethsen (6) thus found large values for the differential capacity on Fe203. Subsequently, Onoda, and de Bruyn (2) showed that these high values are in part the result of the relatively slow potentiometric titrations performed by these investigators, but nevertheless noted that even fast adsorption measurements yielded differential capacities that are large by comparison with those observed on Journal o/Colloid and Interface Science, Vol. 32, No. 3, l~[aroh 1970
533
534
BLOK AND DE BRUYN I
(.)
I
(b) l
I
ZnOK 50 --
I
I I I
50
0.095--
40 o4 E u [L :q
I
Zn 0 Trr
40-
~
'
-
t
0.012
30
Q.QQ14
20-
20 10
o
~ 6 : o o o ~
10-- ~ 8.6
I
I 8.8
9.0 pH
I
9.2
o
9.4
t
I
I
88
90
(a)
I
pH
I
92
94
(b) 60 _ _ ( d ~ , , , , , , 1
60
50 -
50
-
10.32
~
] _
0.097 --
ZnO 40
E
40--
30 _
~
_
=L 20
~
0.014 u
0.005
8.6
0
1
3
30--
0.002 20--
10-0
.
U-
0.0005
_
0
E
10----
1 8.8
I 9.0
I 9.2
o
9.4
pH
- -
I
8.6
I
8.•
I
9.0 pH~
I
9.2
(c)
d4) Fie. 1. Differential capacity as a function on pH on different ZnO precipitates.
(e) ZnO II, (8) ZnO
III, (c) ZnO IV, (d) ZnO V. AgI and mercury systems. Recent studies on Ti02 by B@rub6 and de Bruyn (7) confirmed the high capacity values observed previously on Fe203. The experimental differential capacity curves on TiO2 were noted to parallel those calculated from simple diffuse layer theory. The capacities of the double layer on Ti02 in uni-univalent electrolytes of ionic strength 0.01 and 0.1 M were, for example, observed to be about 20 M/cm 2 and 60 ~f/cm 2, respectively. The experimental differential capacity curves for various ZnO precipitates (4 (a)) in NaNOa solutions are plotted in Fig. 1. The Journal of Colloid and Interface Science, Vol. 32, No. 3, MaIeh 1970
magnitude of the capacity is in general agreement with that observed on both Fe2 03 and Ti02. Although the pH range over which the measurements could be made was limited, we note also that the capacity appears to rise more steeply for a negatively (high pH) than for a positively (lower pH) charged surface. This effect is more strikingly shown on TiO~ (7).
The effect of the nature of the electrolyte on the capacity of the ionic double layer near the pzc is illustrated in Table I, which compares the observed differential capacity in 0.1 ~ solutions.
IONIC DOUBLE LAYER AT ZRO/SOLUTION INTERFACE. III
TABLE I OBSERVED D I F F E R E N T I A L CAPACITIES MICRO FAR&D S / C E NTIMETER2 IN
0.1 M SOLUTIONS NaC104 NaNOa NaI
Precipitate V Precipitate II
-44
50 46
73 --
NaBr
NaC1
89 --
95 64
The large differences in the capacities in the pzc suggest a variation in adsorption specificity among the univalent anions. Assuming that the lowest capacity is connected with the least amount of specific adsorption these results indicate that the anions are more strongly adsorbed in the order CIO~- ~< NOs- < / - < Br- < C1This order for the halides is similar to that obtained previously from floceulation experiments on Fe203 (8) and from adsorption studies on TiO2 by B6rub6 and de Bruyn (7). Furthermore, this order in specificity for the halide ions, which suggests that Clis more strongly adsorbed than I - on Fe~O~, TiO2, and ZnO, is reversed from that observed at the mercury/electrolyte solution interface. B6rub6 and de Bruyn (7) also noted that on the negatively charged TiO2 surface the differential capacities of alkali cations increases in the order Cs+ < K + < Na+ < Li+ which is the reverse of the order observed on negative AgI surfaces (9). It is interesting to note that the activity coefficients of halide acids and alkali hydroxides in 0.1 M electrolyte solutions (10) increase in the order H I > HBr > HCl
and CsOH > KOH > N a O H > L/OH
Similarly, for sodium salts, the increased order is NaI > NaBr > NaCl > NaCl04 > NAN03 These observations suggest that there is an
535
interaction at the oxide surface which for some systems is comparable to the interactions which occur in concentrated electrolyte solutions. To relate these two phenomena, it must be assumed that an increase in the specificity in ionic adsorption at the oxide surface is analogous to a decrease in the activity coefficient of certain electrolytes in solution. This analogy led B~rub6 and de Bruyn to propose that specific adsorption of inorganic monovalent ions in the oxide/solution double layer may be related to their disrupting or promoting influence on the structural order in aqueous solutions. The limited capacity data on ZnO seem to support this postulate. A study of the effect of cesium halides on the adsorption behavior at the oxide interface should be of great interest because the observation that the activity coefficients of these salts increase in the order CsC1 > CsBr > CsI would suggest that the specific adsorption of halides from such solutions should increase in the order I->
Br->
C1-
which is the order normally observed on positively charged solid surfaces. C A L C U L A T E D P R O P E R T I E S OF T H E I O N I C DOUBLE LAYER
In view oI the experimental adsorption results discussed in the previous section, a theoretical study of the ionic double layer on oxide surfaces should consider the specific adsorption of both cations and anions in the inner region. A schematic picture of the inner region of the double layer is given in Fig. 2 with d +, d-, respectively, the distance separating the center of charge of positive and negative potential-determining ions from the outer Helmhol~z plane (OHP) and ~,+, ~,-, respectively, the distance separating the the center of charge of positive and negative specifically adsorbed ions from the OHP. This picture may be simplified by letting Journal of Colloid and Interface Science, ¥'o1. 32, No. 3, March 1970
536
BLOK AND DE BRUYN or Goiiy layer. From elementary electrostatic theory it follows that =
,
[3]
e7
where ev is the average dielectric constant between the IHP and the OHP; also
e~ -2
[41 t/) >O"
4~
0
--
_ _
O'i~
~a
where ~a is the average dielectric constant in the region separating the surface charge from the adsorbed charge ¢~. The quantities ev/4v-/ and e~/4~f~ can be regarded as the capacities of the regions ~/and fl separating the three planes. In general, for two sheets at a distance of x (£ngstroms) and with a dielectric constant e between the sheets, the capacity is expressed by FIG. 2. Schematic picture of the inner region of the ionic double layer. d+ = d- and 7 + = V-. We further neglect the influence of the discreteness of the adsorbed charges. With these assumptions the inner region of the double layer is reduced to a set of three planes, (1) the OHP with a potential of ¢~dwith respect to the bulk solution, (2) the inner Helmholtz plane (IHP) at a distance v from the OHP and which carries a charge density ~ and is at a potential ~ with respect to the bulk solution, and (3) the plane of adsorbed potential-determining ions separated from the I H P by the distance /~ = (d -- 7), carrying a charge density a~ and at a potential G with respect to the bulk solution. Electroneutrality in the double layer requires that ¢~+~i+~d
= O,
[2]
where cd is the charge density of the diffuse Journal of Colloid and Interface ~cienee, Vol. 32, No. 3, March 1970
c (x,~)
= 8.85 ~ / x ~ F / c m
2.
[5]
It may be pointed out that for Eq. [5] to apply it is not necessary that e be a constant in the region between the charged sheets. In the inner region of the double layer adsorbed ions experience short-range interactions in addition to the long-range electrostatic forces. At the interface between an ionic crystal and an aqueous solution the assumption of discrete adsorption sites available for specific adsorption is reasonable and, as first suggested by Stern (11), we may describe ¢i for small values of O, the fraction of the total available sites (N,) occupied by specifically adsorbed ions of type j, by the following relation: a~ = z~ eN~O -
zj eN~ n j ° M NAy p
(-zj F~ + ,j~/ exp \~
[6] ,
IONIC DOUBLE LAYER AT ZnO/SOLUTION INTEP~FACE. I I I Surface
Charge
/
( ) z C / c m 2)
537
0.1 M
.
O01M
+100 ;
+80 I
+60 I
+40 I~
+20
i
r.---D,,,.~, /
.+~
I -80
-40 Surface
I
Potentiol
I (rnv)
FIG. 3. Calculated adsorption isotherms for 10-3, 10-2 and 10-~ M, 1 -- 1 electrolyte solutions at 25°C.
where ns° = n u m b e r of ions j per cubic centimeter in bulk of solution; NA~ = Avogadro's number; M = molecular weight of solvent; p = density of solvent; and @ = Stern adsorption potential, as a first approximation assumed independent of surface charge density. When both cations and anions of a 1-1 electrolyte are specifically adsorbed, Eq. [6] must be modified to give Gi =
Gi + -~- G l -
Are.
p
proper values are chosen for the quantities ¢+, q$-, e~/47rT, e~/47r/7, and N~. The result of such a calculation is shown in Fig. 3 for the following values of these parameters;
~+ = 2kT,
Na~ p
(_e~;+ O-_)
exp \
kT
and N~+ = N~- = 1015 per cm 2. The calculation was done as follows. For ~d = 10 m v and for a 10 -8 M solution of a 1-1 electrolyte at 25°C, Eq. [8] gives ¢d = --0.072 t~C/em2. Substitution of this result lOO
"
~
-sinh \2~/
I
I
I
I
I
I
80-E
% 60-5
Is]
with e the dielectric constant of the bulk solution phase. Equations [3], [4], [7], and [8] can now be used to calculate a theoretical adsorption isotherm (z~ versus ¢J,) provided
40--
<
u
=
I
0.1. M
F r o m diffuse double-layer theory, we obtain a relation between ze and the potential at the O H P , 7Jd. For a 1-1 electrolyte with a bulk solution concentration no molecules per cubic centimeter this relation becomes ~
e~ 4~
eo _ 100~F/em 2 4v~
_
[7]
N,-en-°M
¢- = 4kT,
20
o
I
I
I
I
120
80
40
0
SURFACE
I -40
I -80
I -120
POTENTIAL Ts ( m y )
Fie. 4. Calculated differential capacity curves (C in microfarads per square centimeter versus ¢~ in millivolts). Journal of Colloid and Interface Science, VoL 32, No. 3, March 1970
538
BLOK AND DE BRUYN
into Eq. [3] gives ¢~ = 10.7 my. This value of ¢~ when introduced into Eq. [7] then yields z~ = --0.23 ~C/cm 2, and with the aid of Eq. [4] we find ~ = 13.7'mv. z~ values are then obtained using Eq. [2]. One point is thus obtained on the adsorption isotherm for a 10-3 M electrolyte solution. Choosing other values for ~e and repeating the procedure for the same and different ionic strengths yield the adsorption isotherms shown in Fig. 3. The capacity curves resulting from the differentiation of the calculated adsorption isotherms are shown in Fig. 4. The theory predicts minima in the differential capacity of about 11 ~ F / c m ~ for 10-3 M, 40 # F / c m ~ for 10-2 M, and 85 # F / c m ~ for 10-1 M electrolyte solutions. At high ionic strengths, these values are in good agreement with the observed values, especially in the case of ZnO precipitate V. In 10-3 M solutions, the calculated capacities are still smaller than those derived from the experimental adsorption measurements. The increasing error introduced in the experimental measurements at low ionic strength when the adsorption density is low may account for this discrepancy. It is interesting to compare these calculated results with those calculated in the absence of specific adsorption, but with the same geometry for the inner region. Such a calculation gives capacity minima of 6, 15, and 30 ~ F / c m s for ionic strengths of 10-3, 10-3, and 10-1 M, respectively. By choosing different numerical values for the physical parameters characterizing the proposed model, the calculated differential capacities may be made to agree even better with the observed values, especially in NaNO3 solutions, for which most experimental data are available. It is also interesting to point out that the calculations predict a small shift in the pzc with increasing ionic strength. Such a shift was also observed experimentally, about --20 mv for 10-I M solutions. Since at high ionic strength or high potentials ~ is much larger than ze, a limiting capacity equal to e~/4~r¢~ must be reached eventually. This implies that at high
potentials the adsorption isotherms at different ionic strengths should be parallel. Such observations have been made with Fe203 suspensions (12) but could not be tested with ZnO suspensions because of experimental limitations. The crude model of specific adsorption outlined above accounts semiquantitatively for the high capacity values on oxides compared with those values commonly observed on mercury and silver iodide. The experimental data on ZnO are not accurate enough, however, to make meaningful statements about the values of the specific adsorption potential (~) of different univalent ions or about the magnitude of the integral capacity of the inner region of the double layer. I t also is not clear to what extent the neglect of the discreteness of charge effect will modify this relatively simple model. ACKNOWLEDGMENTS The authors wish to acknowledge the interest shown by Professor J.Th.G. Overbeek in this investigation. Financial support for this study was made available by the U.S. Army Research Office, Durham, North Carolina. REFERENCES 1. BLOK, L., AND DE BRUYN, P. L., J. Colloid Interfac. Sci. 32, 527 (1970). 2. ONODA, JR., G. Y., AND DE •RUYN, P. L., Surface Sci. 4, 48 (1966). 3. BI~RUB~,Y. G., AND DE BRUYN, P. L., J. Colloid Interfac. Sci. 27,305 (1968). 4. (a) BLox, L., AND DE BRU]rN, P. L., Paper I in
5. 6.
7. 8. 9. 10. 11.
this series submitted for publication to J. Colloid Interfac. Sci., (b) ibid., Eq. [15]. PARXS,G. A., AND DE BRUrN, P. L., J. Phys. Chem. 66,967 (1962). ALBRETHSEN, A. E., Doctoral Dissertation, Massachusetts Institute of Technology, Cambridge, Massachusetts, (1963). B~RUB]~,Y. G., AND DE BRUYN, P. L., J. Colloid Interfac. Sci. 28, 92 (1968). KRUYT,H. R., ed., "Colloid Science," Vol. I, p. 309. Elsevier, Amsterdam, 1952. LYKLEMA, J., Discussions Faraday Soc., 42, 81 (1966). ROBINSON,R. A., AND STOXES,R. H., "Electrolyte Solutions." Butterworths, London, 1959. STERN,0., Z. Ele]~trochem. 30,508 (1924).
12.. ' A ~ s o N , R. J., POSNER, A. M., AND Q~IRK, • J . P . , J. Phys. Chem. 71,550 (1967).
Journal of Colloidand Interface Science, Vol. 32, No. 3, March 1970
Received July 3, 1969; accepted October 21, 1969 Differential capacity curves on ZnO in different 1-1 electrolyte solutions are presented. The magnitude of the capacity agrees with similar measurements on Fe203 and TiO2 and is explained with a double-layer model which assumes specific adsorption of both cations and anions with an adsorption energy of a few kT. The specificity of adsorption of univalent anions on ZnO is in the order CIO~< NO~ < I- < Br- < CI-
and confirms previous observations on rutile. INTRODUCTION In a previous paper (1) in this series, it was shown that p H variations resulting from the addition of acid or base to a zinc oxide suspension proceed in two steps with widely different time constants. This observation is in accord with similar studies on Fe203 (2) and TIO2(3) suspensions which led to the conclusion that the fast step describes the true response of the interface to changes in composition of the solution phase. The slower step is generally believed to result from compositional changes involving the surface regions of the bulk solid phase. To obtain meaningful values for the characteristic properties of the ionic double layer, the effect of this slow process must, therefore, either be eliminated or at least be reduced in intensity. The error introduced b y the slow p H change in studies with ZnO was usually small compared to the corrections applied for the solubility of the oxide. The latter factor was mainly responsible for limiting experimental To whom requests for reprints should be directed.
tion to a narrow p H range in the vicinity of the pzc. EXPERIMENTAL D IFFEI~ENTIAL CAPACITY The differential capacity of the ionic double layer at 25°C and fixed ionic strength may be obtained from fast adsorption isotherms by utilizing the relation c
-
F dAFt* 0.059 d p H
li]
where AFt* is the net adsorption density due to all potential-determining species (4 (b)). Numerous investigators applied Eq. [1] to their experimental adsorption measurements. Parks and de Bruyn (5) and also Albrethsen (6) thus found large values for the differential capacity on Fe203. Subsequently, Onoda, and de Bruyn (2) showed that these high values are in part the result of the relatively slow potentiometric titrations performed by these investigators, but nevertheless noted that even fast adsorption measurements yielded differential capacities that are large by comparison with those observed on Journal o/Colloid and Interface Science, Vol. 32, No. 3, l~[aroh 1970
533
534
BLOK AND DE BRUYN I
(.)
I
(b) l
I
ZnOK 50 --
I
I I I
50
0.095--
40 o4 E u [L :q
I
Zn 0 Trr
40-
~
'
-
t
0.012
30
Q.QQ14
20-
20 10
o
~ 6 : o o o ~
10-- ~ 8.6
I
I 8.8
9.0 pH
I
9.2
o
9.4
t
I
I
88
90
(a)
I
pH
I
92
94
(b) 60 _ _ ( d ~ , , , , , , 1
60
50 -
50
-
10.32
~
] _
0.097 --
ZnO 40
E
40--
30 _
~
_
=L 20
~
0.014 u
0.005
8.6
0
1
3
30--
0.002 20--
10-0
.
U-
0.0005
_
0
E
10----
1 8.8
I 9.0
I 9.2
o
9.4
pH
- -
I
8.6
I
8.•
I
9.0 pH~
I
9.2
(c)
d4) Fie. 1. Differential capacity as a function on pH on different ZnO precipitates.
(e) ZnO II, (8) ZnO
III, (c) ZnO IV, (d) ZnO V. AgI and mercury systems. Recent studies on Ti02 by B@rub6 and de Bruyn (7) confirmed the high capacity values observed previously on Fe203. The experimental differential capacity curves on TiO2 were noted to parallel those calculated from simple diffuse layer theory. The capacities of the double layer on Ti02 in uni-univalent electrolytes of ionic strength 0.01 and 0.1 M were, for example, observed to be about 20 M/cm 2 and 60 ~f/cm 2, respectively. The experimental differential capacity curves for various ZnO precipitates (4 (a)) in NaNOa solutions are plotted in Fig. 1. The Journal of Colloid and Interface Science, Vol. 32, No. 3, MaIeh 1970
magnitude of the capacity is in general agreement with that observed on both Fe2 03 and Ti02. Although the pH range over which the measurements could be made was limited, we note also that the capacity appears to rise more steeply for a negatively (high pH) than for a positively (lower pH) charged surface. This effect is more strikingly shown on TiO~ (7).
The effect of the nature of the electrolyte on the capacity of the ionic double layer near the pzc is illustrated in Table I, which compares the observed differential capacity in 0.1 ~ solutions.
IONIC DOUBLE LAYER AT ZRO/SOLUTION INTERFACE. III
TABLE I OBSERVED D I F F E R E N T I A L CAPACITIES MICRO FAR&D S / C E NTIMETER2 IN
0.1 M SOLUTIONS NaC104 NaNOa NaI
Precipitate V Precipitate II
-44
50 46
73 --
NaBr
NaC1
89 --
95 64
The large differences in the capacities in the pzc suggest a variation in adsorption specificity among the univalent anions. Assuming that the lowest capacity is connected with the least amount of specific adsorption these results indicate that the anions are more strongly adsorbed in the order CIO~- ~< NOs- < / - < Br- < C1This order for the halides is similar to that obtained previously from floceulation experiments on Fe203 (8) and from adsorption studies on TiO2 by B6rub6 and de Bruyn (7). Furthermore, this order in specificity for the halide ions, which suggests that Clis more strongly adsorbed than I - on Fe~O~, TiO2, and ZnO, is reversed from that observed at the mercury/electrolyte solution interface. B6rub6 and de Bruyn (7) also noted that on the negatively charged TiO2 surface the differential capacities of alkali cations increases in the order Cs+ < K + < Na+ < Li+ which is the reverse of the order observed on negative AgI surfaces (9). It is interesting to note that the activity coefficients of halide acids and alkali hydroxides in 0.1 M electrolyte solutions (10) increase in the order H I > HBr > HCl
and CsOH > KOH > N a O H > L/OH
Similarly, for sodium salts, the increased order is NaI > NaBr > NaCl > NaCl04 > NAN03 These observations suggest that there is an
535
interaction at the oxide surface which for some systems is comparable to the interactions which occur in concentrated electrolyte solutions. To relate these two phenomena, it must be assumed that an increase in the specificity in ionic adsorption at the oxide surface is analogous to a decrease in the activity coefficient of certain electrolytes in solution. This analogy led B~rub6 and de Bruyn to propose that specific adsorption of inorganic monovalent ions in the oxide/solution double layer may be related to their disrupting or promoting influence on the structural order in aqueous solutions. The limited capacity data on ZnO seem to support this postulate. A study of the effect of cesium halides on the adsorption behavior at the oxide interface should be of great interest because the observation that the activity coefficients of these salts increase in the order CsC1 > CsBr > CsI would suggest that the specific adsorption of halides from such solutions should increase in the order I->
Br->
C1-
which is the order normally observed on positively charged solid surfaces. C A L C U L A T E D P R O P E R T I E S OF T H E I O N I C DOUBLE LAYER
In view oI the experimental adsorption results discussed in the previous section, a theoretical study of the ionic double layer on oxide surfaces should consider the specific adsorption of both cations and anions in the inner region. A schematic picture of the inner region of the double layer is given in Fig. 2 with d +, d-, respectively, the distance separating the center of charge of positive and negative potential-determining ions from the outer Helmhol~z plane (OHP) and ~,+, ~,-, respectively, the distance separating the the center of charge of positive and negative specifically adsorbed ions from the OHP. This picture may be simplified by letting Journal of Colloid and Interface Science, ¥'o1. 32, No. 3, March 1970
536
BLOK AND DE BRUYN or Goiiy layer. From elementary electrostatic theory it follows that =
,
[3]
e7
where ev is the average dielectric constant between the IHP and the OHP; also
e~ -2
[41 t/) >O"
4~
0
--
_ _
O'i~
~a
where ~a is the average dielectric constant in the region separating the surface charge from the adsorbed charge ¢~. The quantities ev/4v-/ and e~/4~f~ can be regarded as the capacities of the regions ~/and fl separating the three planes. In general, for two sheets at a distance of x (£ngstroms) and with a dielectric constant e between the sheets, the capacity is expressed by FIG. 2. Schematic picture of the inner region of the ionic double layer. d+ = d- and 7 + = V-. We further neglect the influence of the discreteness of the adsorbed charges. With these assumptions the inner region of the double layer is reduced to a set of three planes, (1) the OHP with a potential of ¢~dwith respect to the bulk solution, (2) the inner Helmholtz plane (IHP) at a distance v from the OHP and which carries a charge density ~ and is at a potential ~ with respect to the bulk solution, and (3) the plane of adsorbed potential-determining ions separated from the I H P by the distance /~ = (d -- 7), carrying a charge density a~ and at a potential G with respect to the bulk solution. Electroneutrality in the double layer requires that ¢~+~i+~d
= O,
[2]
where cd is the charge density of the diffuse Journal of Colloid and Interface ~cienee, Vol. 32, No. 3, March 1970
c (x,~)
= 8.85 ~ / x ~ F / c m
2.
[5]
It may be pointed out that for Eq. [5] to apply it is not necessary that e be a constant in the region between the charged sheets. In the inner region of the double layer adsorbed ions experience short-range interactions in addition to the long-range electrostatic forces. At the interface between an ionic crystal and an aqueous solution the assumption of discrete adsorption sites available for specific adsorption is reasonable and, as first suggested by Stern (11), we may describe ¢i for small values of O, the fraction of the total available sites (N,) occupied by specifically adsorbed ions of type j, by the following relation: a~ = z~ eN~O -
zj eN~ n j ° M NAy p
(-zj F~ + ,j~/ exp \~
[6] ,
IONIC DOUBLE LAYER AT ZnO/SOLUTION INTEP~FACE. I I I Surface
Charge
/
( ) z C / c m 2)
537
0.1 M
.
O01M
+100 ;
+80 I
+60 I
+40 I~
+20
i
r.---D,,,.~, /
.+~
I -80
-40 Surface
I
Potentiol
I (rnv)
FIG. 3. Calculated adsorption isotherms for 10-3, 10-2 and 10-~ M, 1 -- 1 electrolyte solutions at 25°C.
where ns° = n u m b e r of ions j per cubic centimeter in bulk of solution; NA~ = Avogadro's number; M = molecular weight of solvent; p = density of solvent; and @ = Stern adsorption potential, as a first approximation assumed independent of surface charge density. When both cations and anions of a 1-1 electrolyte are specifically adsorbed, Eq. [6] must be modified to give Gi =
Gi + -~- G l -
Are.
p
proper values are chosen for the quantities ¢+, q$-, e~/47rT, e~/47r/7, and N~. The result of such a calculation is shown in Fig. 3 for the following values of these parameters;
~+ = 2kT,
Na~ p
(_e~;+ O-_)
exp \
kT
and N~+ = N~- = 1015 per cm 2. The calculation was done as follows. For ~d = 10 m v and for a 10 -8 M solution of a 1-1 electrolyte at 25°C, Eq. [8] gives ¢d = --0.072 t~C/em2. Substitution of this result lOO
"
~
-sinh \2~/
I
I
I
I
I
I
80-E
% 60-5
Is]
with e the dielectric constant of the bulk solution phase. Equations [3], [4], [7], and [8] can now be used to calculate a theoretical adsorption isotherm (z~ versus ¢J,) provided
40--
<
u
=
I
0.1. M
F r o m diffuse double-layer theory, we obtain a relation between ze and the potential at the O H P , 7Jd. For a 1-1 electrolyte with a bulk solution concentration no molecules per cubic centimeter this relation becomes ~
e~ 4~
eo _ 100~F/em 2 4v~
_
[7]
N,-en-°M
¢- = 4kT,
20
o
I
I
I
I
120
80
40
0
SURFACE
I -40
I -80
I -120
POTENTIAL Ts ( m y )
Fie. 4. Calculated differential capacity curves (C in microfarads per square centimeter versus ¢~ in millivolts). Journal of Colloid and Interface Science, VoL 32, No. 3, March 1970
538
BLOK AND DE BRUYN
into Eq. [3] gives ¢~ = 10.7 my. This value of ¢~ when introduced into Eq. [7] then yields z~ = --0.23 ~C/cm 2, and with the aid of Eq. [4] we find ~ = 13.7'mv. z~ values are then obtained using Eq. [2]. One point is thus obtained on the adsorption isotherm for a 10-3 M electrolyte solution. Choosing other values for ~e and repeating the procedure for the same and different ionic strengths yield the adsorption isotherms shown in Fig. 3. The capacity curves resulting from the differentiation of the calculated adsorption isotherms are shown in Fig. 4. The theory predicts minima in the differential capacity of about 11 ~ F / c m ~ for 10-3 M, 40 # F / c m ~ for 10-2 M, and 85 # F / c m ~ for 10-1 M electrolyte solutions. At high ionic strengths, these values are in good agreement with the observed values, especially in the case of ZnO precipitate V. In 10-3 M solutions, the calculated capacities are still smaller than those derived from the experimental adsorption measurements. The increasing error introduced in the experimental measurements at low ionic strength when the adsorption density is low may account for this discrepancy. It is interesting to compare these calculated results with those calculated in the absence of specific adsorption, but with the same geometry for the inner region. Such a calculation gives capacity minima of 6, 15, and 30 ~ F / c m s for ionic strengths of 10-3, 10-3, and 10-1 M, respectively. By choosing different numerical values for the physical parameters characterizing the proposed model, the calculated differential capacities may be made to agree even better with the observed values, especially in NaNO3 solutions, for which most experimental data are available. It is also interesting to point out that the calculations predict a small shift in the pzc with increasing ionic strength. Such a shift was also observed experimentally, about --20 mv for 10-I M solutions. Since at high ionic strength or high potentials ~ is much larger than ze, a limiting capacity equal to e~/4~r¢~ must be reached eventually. This implies that at high
potentials the adsorption isotherms at different ionic strengths should be parallel. Such observations have been made with Fe203 suspensions (12) but could not be tested with ZnO suspensions because of experimental limitations. The crude model of specific adsorption outlined above accounts semiquantitatively for the high capacity values on oxides compared with those values commonly observed on mercury and silver iodide. The experimental data on ZnO are not accurate enough, however, to make meaningful statements about the values of the specific adsorption potential (~) of different univalent ions or about the magnitude of the integral capacity of the inner region of the double layer. I t also is not clear to what extent the neglect of the discreteness of charge effect will modify this relatively simple model. ACKNOWLEDGMENTS The authors wish to acknowledge the interest shown by Professor J.Th.G. Overbeek in this investigation. Financial support for this study was made available by the U.S. Army Research Office, Durham, North Carolina. REFERENCES 1. BLOK, L., AND DE BRUYN, P. L., J. Colloid Interfac. Sci. 32, 527 (1970). 2. ONODA, JR., G. Y., AND DE •RUYN, P. L., Surface Sci. 4, 48 (1966). 3. BI~RUB~,Y. G., AND DE BRUYN, P. L., J. Colloid Interfac. Sci. 27,305 (1968). 4. (a) BLox, L., AND DE BRU]rN, P. L., Paper I in
5. 6.
7. 8. 9. 10. 11.
this series submitted for publication to J. Colloid Interfac. Sci., (b) ibid., Eq. [15]. PARXS,G. A., AND DE BRUrN, P. L., J. Phys. Chem. 66,967 (1962). ALBRETHSEN, A. E., Doctoral Dissertation, Massachusetts Institute of Technology, Cambridge, Massachusetts, (1963). B~RUB]~,Y. G., AND DE BRUYN, P. L., J. Colloid Interfac. Sci. 28, 92 (1968). KRUYT,H. R., ed., "Colloid Science," Vol. I, p. 309. Elsevier, Amsterdam, 1952. LYKLEMA, J., Discussions Faraday Soc., 42, 81 (1966). ROBINSON,R. A., AND STOXES,R. H., "Electrolyte Solutions." Butterworths, London, 1959. STERN,0., Z. Ele]~trochem. 30,508 (1924).
12.. ' A ~ s o N , R. J., POSNER, A. M., AND Q~IRK, • J . P . , J. Phys. Chem. 71,550 (1967).
Journal of Colloidand Interface Science, Vol. 32, No. 3, March 1970