Langmuir 1988,4, 565-569
565
Association of Counterions with Adsorbed Potential-Determining Ions at a Solid/Solution Interface. 2. Double-Layer Equilibria at a Metal Oxide Interface? Melanija Tomi8 and Nikola Kallay* Laboratory of Physical Chemistry, Faculty of Science, University of Zagreb, 41001 Zagreb, P. 0. Box 163, Yugoslavia Received June 25, 1987. I n Final Form: November 18,1987 The equilibria in the electrical double layer of metal oxide surfaces in water suspensions were analyzed by introducing a statisticaltreatment for the association of surface charged groups with counterions. Surface charge density and potential were calculated as a function of pH and ionic strength for a model system. The effects of the ionic size parameter (distance of closest approach), H+ and OH- adsorption affinities, and total number of active surface sites were examined. Results of calculations were qualitatively compared with experimental data published for some metal oxides.
Introduction The association of counterions with charged groups (e.g., adsorbed potential-determining ions; pdi) a t a solid/liquid interface was discussed in part 1 of this study.' The proposed model assumes that associated counterions are distributed according to Boltzmann statistics around the central surface charged groups. The difference with respect to the commonly adopted Bjerrum treatment24 (for the ionic association in the bulk of electrolyte solution) is in the assumption with regard to electrostatic potential affecting a counterion. In the bulk of an electrolyte solution, this Coulombic point charge potential is due to the influence of the central ion. At the solid/liquid interface, the double-layer potential was also taken into account. The proposed model explains why two ions, which are completely dissociated in the bulk of solution, may be strongly associated in the double layer. The aim of this article is to demonstrate some predictions of this model for the equilibria a t a metal oxide/ solution interface, to discuss the results, and to compare them with published experimental data. All calculations were performed by using the exact solution, described in the Appendix to part 1 of this study.l The model system was chosen to simulate the properties of ferric oxides, but the results can be applied to other metal oxides by taking into consideration the shift in the point of zero charge (PZC). Procedure The equilibria in the interfacial layer will be considered for a metal oxide immersed in an aqueous solution of a strong base (MOH) or a strong acid (HA) containing 1:l neutral electrolyte (MA). The model system was chosen to avoid introduction of extraneous ionic species by the addition of the salt. According t o site-binding or surface complexation the binding of potential-determining ions (H+ and OH-)to the amphoteric surface site S is described by
where K and Ptare total (apparent) and intrinsic equilibrium constants, respectively; #o is the electrostatic potential at the surface where adsorbed H+ and OH- ions are located, r is surface concentration, and a is the activity in the bulk of solution. The use of eq 1 and 2 assumes that Hf and OH-ions are bounded to the same kind of surface sites S and located in the same "zero" plane characterized by the potential #@ The association of counterions with oppositely charged surface groups is described by
where A- and M+ are monovalent counterions and K5H.A and KS0H.M are total (apparent) equilibrium constants for the association in the interfacial layer. In the triple-layer model?' the total association equilibrium constant is taken to be a product of intrinsic equilibrium constant and an exponential term including the electrostatic potential at the plane j3,where associated counterions are assumed to be located. Instead, we used expressions derived in part 1 of this study' to calculate total association constant as a function of permittivity e, temperature T, surface potential #o, ionic strength I , and the distance of closest approach (bSH.A in eq 3 or bSOH.M in eq 4). The surface charge density will be defined as U,
= Le(rsH+- FSOH-)
(5)
This treatment implies that ion pairs do not contribute to the surface charge density; i.e., the charge of associated surface groups is compensated by paired counterions. The (1)Kallay, N.; TomiE, M. Langmuir, preceding paper in this issue. (2)Bjerrum, N. Ergeb. Ezakten Naturwiss. 1926, 6, 125. (3) Fuoss, R. Tram. Faraday SOC. 1934,30,967. (4) Robinson, R.A.; Stokes,R. H. Electrolyte Solutions;Butterworths:
* Author to whom correspondence should be addressed. Supported by U.S.-YU Fund DOE P N 741. Present address: Water Chemistry Program, University of Wisconsin, Madison, WI 53706.
*
London, 1955. (5)Yates, D. E.;Levine, S.; Healy, T. W. J. Chem. SOC.,Faraday Tram. 1 1974, 70, 1807. (6) Davis, J. A.; James, R. 0.; Leckie, J. 0. J. Colloid Interface Sci. 1978,63,480. (7) Davis, J. A.; Leckie, J. 0. J. Colloid Interface Sci. 1978, 67, 90. (8) Bowden, J. W.; Poener, A. M.; Qukk, J. P. Aus. J. Soil Res. 1977, 15, 121.
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566 Langmuir, Vol. 4, No. 3, 1988
TomiE and Kallay
potentiometric titration of suspensions yields the surface charge u, , which is due to the total amount of adsorbed H+ and Oh-ions. The data do not distinguish between the associated and free surface charged groups. Accordingly Uexp
= Lerexp = Le(rSH+
+ r S H e A - FSOH- - rS0H.M)
L.-
\\
440
IF2\
\ \ \
(6)
I
N
When the triple-layer model6,' is used, this charge density is taken to equal up The relation between surface charge density and surface potential is given by the Gouy-Chapman t h e ~ r y : ~ J ~
e
+o = 2kT In
[
(8ekTLI)' 1 2
+
(L + 8fkTLI 1)'/2]
(7)
Furthermore, in calculations it was taken that H2O + H+ logy = -
+ OH-;
K, = a H + a O H - - 10-14
A (I/mol dm-3)1/2 1 + (I/mol dm-3)1/2' *
(8)
for monovalent ions (9)
where y is the activity coefficient, I is the ionic strength in the bulk of solution, and the constant A = 0.507 for water a t 25 OC. For total surface concentration of surface sites, rtot, the following relationship holds: r ~ = t
rs + rSH+ + IISH.A +
I(SOH-
+ r S 0 H . M (10)
Equations 1-10, together with expressions for KSH.A and (part 1of this study'), were solved by an iterative procedure for given values of distances of closest approach (bSH.A and bSOH.M), the intrinsic constant, eh+,total surface concentration of surface sites, rbt, and point.of zero charge, pH(pzc). The value of F{&H- is related to @A+ and pH(pzc) through 1 PH(Pzc) = 2 log ( @ & + / ( ~ H + K ~ ) ) (11)
PH
Figure 1. Surface concentration, rm,and surface charge density, u,, , as a function of pH at different ionic strengths, calculated wit%the parameters presented in eq 12. The distance of closest and (rex approach, b = bsH.A = bS0H.M = 3.6 A. Quantities reXp correspond to those obtained by potentiometric titration o! suspensions and are defined by eq 6.
-
l l ~ ~ . ~ \
KS0H.M
The values of parameters used in calculations were chosen close to those exhibited by colloidal hematite particles (a-Fe203)" in aqueous suspension a t 25 OC: e = 6.954 X
rtot=
F m-';
t,
= 78.54;
T = 298.15 K; pH(pzc) = 7.3; mol m-2 (corresponding to 96.5 pC cm-2); = 7 x 105 (12)
a+
In order to examine the effects of these parameters, their values were varied within reasonable limits. The ionic size parameter b (distance of closest approach of the center of a counterion to the center of the charged surface group) influences the extent of ion pairing within the interfacial layer. The value of b was also varied, being always larger than 3.5 A. For b < 3.5 A the association of ions in the bulk should be also taken into account, as shown in part 1 of this study.
Results and Discussion The results presented in Figures 1-8 were obtained by numerical integration of eq A18 which, together with eq 32 in part 1 of the study,' provides total (apparent) equilibrium constants KSH.A and KS0H.M and by iteration (9) Gouy, G. J. Phys. 1910, 9, 457. (10) Chapman, D. L. Phil.Mag. 1913,25,475. (11) Hesleitner, P.; BabiE, D.; KaUay, N.; MatijeviC, E. Langmuir 1987, 3, 815.
Figure 2. Surface concentration of adsorbed species, r, as a function of pH calculated for I = mol dm-3. The values of other parameters are the same as in Figure 1.
of eq 5 and 14-23 for the model system at different values of pH and ionic strength. The results for high ionic strengths, such as 1 mol dm-3, are not expected to be realistic, because some of the initial assumptions are not satisfied (e.g., low surface charge density, applicability of Debye-Huckel and Gouy-Chapman theories). Figure 1displays the calculated values of ufW(as defined by eq 6) as a function of pH for four different ionic strengths. The quantity uexpis commonly evaluated from the results of potentiometric titrations and it includes both associated and free H+ and OH- ions adsorbed on the surface. The values of parameters used in calculations are given in eq 12, and the distance of closest approach was chosen to be b = 3.6 i\ for both anion and cation association. The low value of b corresponds to a high degree of counterion association. As expected, an increase in ionic strength promotes adsorption. A common intersection point was obtained a t the pzc, indicating the absence of specific adsorption, as postulated. Adsorbed Species. According to eq 6 the quantity, ,a is related to the surface concentrations of SH+, SH'A, SOH-, and SOH'M. Figure 2 illustrates the surface concentration of these components a t a moderate ionic strength of mol dm-3. Two points are noteworthy: (i) No association was found in the vicinity of the pzc. The explanation is simple; surface potential in this region is too low to produce a critical distance larger then the distance of closest approach (see eq 27 in part 1 of this
Langmuir, Vol. 4, No. 3, 1988 567
Counterion Association at Solid/Solution Interface
root I
i
I
-2+*
6
8
lo
12
'
Figure 3. Surface potential, q0,as a function of pH for different ionic strengths calculated by using the same values of parameters as in Figure 1. The dotted line represents the values satisfying the Nernst equation. study1). The criterion for association is not satisfied in the region when surface potentials are lower than the critical value (see Figures 4 and 5 in part 1)due to the absence of association space. Although the behavior of SH'A and SOHM pairs (described by different distances of closest approach) may differ, no discrepancy between the pzc, the isoelectric point (iep), and the common intersection point will result. The opposite finding may be obtained by applying the approach based on intrinsic association constants. The unequal values of R{A.* and R$jH.M will produce a shift in the pzc with respect to iep and intersection point. (ii) There is a broad pH region over which both H+ and OH- ions are adsorbed. This observation depends on the values of @&+ (and K'{& and points to the significance of the assumption that there is only one kind of amphoteric surface active site S. The overlap of the H+and OHadsorption regions indicates the sensitivity of the results on the above assumption. Different results would be obtained if different sites for adsorption of H+ and OH- ions were assumed; these ions would not compete for the same sites. Surface Potential. The described treatment made it possible to calculate the surface potential, +,,. Figure 3 shows that this potential depends significantly on the ionic strength. While no direct measurements of surface potential are available, the results (Figure 3) are comparable to the electrode potentials of a-Fe203electrodes measured by Penners.12 Platinum coated with a-Fe2O3particles (and sintered) gave a potential close to the Nernst potential but gave a somewhat lower value a t high acidity. These measurements were performed at 5 X mol dm-3 KCl. It would be of interest to obtain data at higher ionic strength where significant deviations from the Nernst potential are expected (Figure 3). Ionic Size Parameter. The effect of the ionic size parameter b on ueIpand q0 was examined for moderate ionic strength mol dm-3). The upper part of Figure 4 gives ueIpvalues as a function of pH. It is interesting to note that in an increase in the value of b from 3.6 to 6 A did not produce a significant change in uew For strong electrolytes (consisting of ions as H+, Na+, Cs+, K+,NO3-, C1-, C104-)the distance of closest approach is4in the range 4-6 A. Consequently, no pronounced sensitivity of the (12)Penners, N.G.H. Ph.D. Thesis, Agricultural University, Wageningen, The Netherlands, 1985.
2
4
6
8 PH
1012
Figure 4. Surface concentration, (upper part); surface charge density, u?slp(upper part); and surface potential, $0 (lower part) mol dm-3 for different values of as a function of pH for I = the distance of closest approach b, means that b > d (6) for all pH (rexp) values, i.e., association does not occur. The values of parameters used in calculationsare presented in eq 12. The dotted line represents the values satisfying the Nernst equation. QD
2
4
6
81012 PH
Figure 5. Surface concentration, rexp (A, upper part); surface charge density, ,a (A, upper part); and surface potential, q0 (B, lower part) as a function of pH at I = mol dm-3 for different values of rtot.The distance of closest approach was taken as b = 3.6 A, while the values of other parameters used in calculations which was varied. The dotted are presented in eq 12,except rtot, line represents the values satisfying the Nernst equation. counterion size on adsorption is expected, as supported by experiments.13 If b > d , ions cannot approach each other close enough to exceed the critical distance d(0) (see eq 27 in part 1). The association cannot occur, yielding Iuexplvalues lower than calculated for b = 3.6 or 6 A. Such a condition may exist in reality, such as when surface groups are surrounded by a thick layer of water molecules, or if the center of charge is somehow located inside the solid bulk. The lower part of Figure 4 illustrates the calculated values of +o as a function of pH for three different values of b. For b > d (nonassociative systems), the value of is much less affected by the value of b than ueIpwhile when near linearity of +o (pH) was obtained over a relatively broad range of pH the slope is less than 59 mV, in agreement with the analysis16 of experimental data on TiOB Density of Surface Sites. Figure 5 shows the effect of the total number of surface sites. Both ueexp (part A) and b,to (part B) become smaller when rtotis lowered. This result indicates the importance of rtot, which is usually (13)Sprycha, R. J. Colloid Interface Sci. 1984,102, 173. (14)Sprycha, R.;Szczypa, J. J. Colloid Interface Sci. 1984,102,288. (15)Kallay, N.;BabiE, D.; MatijeviE, E. Colloids Surf. 1986,19, 375.
TomiE and Kallay
568 Langmuir, Vol. 4, No. 3, 1988 I
I
I
"L
2
4
I 6
81012 PH
Figue 6. Surface concentration, (upper part);surface charge density, uFp (upper part); and surface potential, J.o (lower part) mol dm" and different values of as a function of pH at I = ak+ The . distance of closest approach was b = 3.6 A, while the values of other parameters used in calculations are presented in eq 12, except IC&+, which was varied; (1) 7 X 10'; (2) 7 X los; also varied, since pzc (3) 7 X lo6; (4)7 X lo4. Note that was kept constant (see eq 11). The dotted line represents the values satisfying the Nernst equation.
.
0 1 VI
"
-1 0 " log(l/mol dm-3)
-3 -2
+,,
Figure 7. Surface potential, (upper part); surface concentrations, r (lower part); and charge density, u (lower part) as a function of ionic strength at pH 4 for the distance of closest approach b = 3.6 A. The values of parameters used in calculations are presented in eq 12. The dotted line in the upper part represents the values satisfying the Nernst equation. In the lower (and ueXp),while dotted lines corpart solid lines represent rexp respond to net surface charge densities uB(see eq 5 and 6).
taken as an adjustable parameter in the interpretation of adsorption data according to any surface complexation model. As the value of rtotincreases, the value of the surface potential approaches Nernst's value, confirming the limited applicability of the Nernst equation.16 Intrinsic Equilibrium Constant for Adsorption of Potential-Determining Ions. The effect of the variation of the adsorption intrinsic equilibrium constant, psi+, on ueXpand rl0 is shown in Figure 6. A change in p;h+ produces an effect similar to the effect observed with rtot (see cannot be determined by an indeFigure 5). Since pendent method, and it is interrelated with Fbt,one should estimate rtotfrom surface structure or tritium-exchange measurements. Then K'&+ remains as the only adjustable parameter. Ionic Strength. Surface potential a t constant pH significantly decreases with an increase in the ionic strength. This decrease is more pronounced with "smaller" ions, i.e., ions characterized by a smaller distance of closest approach (Figure 7). Accordingly, constant-potential considerations should not be employed in the interpretation of the electrolyte effect on the stability of colloidal (16) Blesa, M. A.; Kallay, N. Adu. Colloid Interface Sci., in press.
I
I
1
2
4
6
8
1 0 1 2
PH Figure 8. Potential in the diffuse layer at a plane separated by 20 8, from the surface, $(Z = 20&, as a function of pH. Calculations were performed by means of eq 13, using parameters given in eq 12. The curves for b = 3.6-6 8, are indistinguishable.
metal oxides. The presence of electrolytes will produce both a decrease in rl0 and a "compressionn of the double layer. Smaller counterions (lower b) are found to be more effective in coagulation (lyotropic effect), which may be explained by this model. Small coagulating ions reduce J/o more effectively (especially a t higher concentrations) as shown in the upper part of Figure 7. As the ionic strength increases, values of both u, and a,, also increase (lower part of Figure 7). Despite the abrupt increase in the total density of the adsorbed potential-determining ions (uex ), the net charge of surface (a,) does not change much. $his effect can be understood by recognizing that the association is negligible a t I < mol but plays mol dm-3. The effect of the ionic a major role a t I > size parameter on u and u, is reversed. The total amount of adsorbed pdi's isyigher for shorter distances of closest approach, because the higher value of K,, results in stronger association and, consequently, lowers the density of free surface sites and charged groups (SH' and SOH-). Accordingly, the net charge (a,) is lower for smaller b (Figure 7, lower part). Electrokinetic Properties. The electrokinetic potential ({-potential) may be taken as the potential at the shear plane in the diffuse layer. According to the Gouy-Chapman theory?1° the electrostatic potential a t distance 2 from the planar solid surface and for a 1:l electrolyte is
It was suggested17that the shear plane is located a t a distance Z 2 20 A. Figure 8 shows that {-potentials calculated according to eq 26 a t Z = 20 do not differ for b = 3.6 and 6 A, indicating the absence of any specific effects of counterions. The calculated functions exhibit the same general dependence of {-potential on pH as experimentally demonstrated. At higher electrolyte concentration, the calculated {-potentials are lowered somewhat more than expected from experiments.l' With the triple-layer model the {-potential was often equated with the potential a t the d plane, defined as the onset of the diffuse layer that is separated from the surface
a
(17) Hading, T. H.; Healy, T. W. J. Colloid Interface Sci. 1985,107, 382.
Langmuir 1988,4, 569-572 by several ionic diameter^.'^
Conclusions The analysis of the electrical double-layer equilibria, as presented in this study (the theoretical part is published separately'), introduced the evaluation of the equilibrium constant for association of surface charged groups with counterions. The surface association equilibrium constant was obtained on the basis of a statistical distribution of counterions in the vicinity of central charged groups on the surface. This procedure is limited to 1:l electrolytes and systems of relatively low surface charge density. The specificity of counterions in adsorption and coag-
569
ulation phenomena is described by means of the ionic size parameter, i.e., the distance of closest approach between surface charged groups and associated counterion. In the pH region around pzc, the low value of $+, does not permit association. Consequently,no specific effect of counterions in this region is expected. The presented results indicate possible applications; the interpretation of adsorption equilibria, colloid stability, and electrokinetic properties.
Acknowledgment. We are indebted to Mr. Darko BabiE for useful discussions and his help with computations.
Characterization of Vacuum-Deposited Perfluorocarboxylic Acid Monomolecular Film by Penning Ionization Electron Spectroscopy Munehisa Mitsuya* Advanced Research Laboratory, Hitachi Ltd., Kokubunji, Tokyo 185, Japan
Hiroyuki Ozaki and Yoshiya Harada Department of Chemistry, College of Arts and Sciences, The University of Tokyo, Meguro, Komaba, Tokyo 153, Japan
Kazuhiko Sekif and Hiroo Inokuchi Institute for Molecular Science, Myodaiji, Okazaki 444, Japan Received June 12, 1987. In Final Form: November 16, 1987 The molecular arrangement of perfluorocarboxylic acid monomolecular film, vacuum-deposited on a dehydrated SiOzsubstrate, is studied through cyclic thermal treatment using Penning ionization electron spectroscopy. The film was ascertained to cover the substrate surface up to 60 O C . Reversible spectral change due to the thermal fluctuation of fluorocarbon tails is observed in the temperature range 80-100 "C,while irreversible disordering of the molecules occurs above 150 "C. The film prepared on an undehydrated substrate easily desorbs in ultrahigh vacuum even at room temperature. These results suggest that the chemical bond between the molecules and the substrate dominates the stability of the ordered film.
Introduction There has been considerable interest in the use of molecular orient6d films where designed molecules are artificially arranged in a preferable direction. Such film is known to be traditionally prepared by the LangmuirBlodgett (LB) method.' Another method for preparing oriented films is vacuum deposition, which has been developed mainly from the viewpoint of epitaxial In a sequence of studies of molecular arrangements and the related properties of such films, much attention has begun to be devoted to the structure studied in more detail from a microscopic point of view. Tredgold and Winter postulated that the electrical conduction in monolayers is via defects and presented experimental evidence to support the view.' Peterson et al. showed that molecules are reorganized both on the subphase and on the substrateas Matsuzaki e t al. investigated the growth mechanism of stearic acid films from the vapor phase and determined
the optimum condition for preparing homogenous films.g Such studies on the packing of constituent molecules will become more important in both scientific and practical fields. This paper reports on the Penning ionization electron spectroscopy (PIES)of perfluorocarboxylic acid monomolecular film prepared by vacuum deposition. Because of the small polarizability of constituent fluorine atoms, the first layer deposited on a hydrophilic surface with its polar groups is supposed to hinder further deposition, and
Present address: Department of Materials Science, Faculty of Science, Hiroshima University, Higashisenda-machi, Hiroshima 730,
1983,109, 371. (9) Matsuzaki, F.; Inaoka, K.; Okada, M.; Sato, K. J. Cryst. Growth 1984, 69, 231.
f
Japan.
0743-7463/88/2404-0569$01.50/0
(1) Blodgett, K. B. J. Am. Chem. Soc. 1935, 57, 1007. (2) Buchholz, J. C.; Somorjai, G. A. J. Chem. Phys. 1977, 66, 573. Firment, L. E.; Somorjai, G. A. J. Chem. Phys. 1978, 69, 3940. (3) Ueda, Y.;Ashida, M. J. Electron Microsc. 1980,29, 38. (4) Kobayashi, T.; Fujiyoshi, Y.;Iwatau, F.; Uyeda, N. Acta Crystallogr., Sect. A Found. Crystallogr. 1981,37,692. Kobayashi, T.; Fijiyoshi, Y.;Uyeda, N. Acta Crystallogr., Sect. A: Found. Crystallogr. 1982,38, 3.M.
(5)Debe, M. K. J. Vac. Sci. Technol. 1982,21, 74. ( 6 ) Harada, Y.;Ozaki, H.; Ohno, K. Phys. Rev. Lett. 1984,52, 2269. (7)Tredgold, R. H.; Winter, C. S. J.Phys. D 1981,14, L185. ( 8 ) Peterson, I. R.; Russell, G. J.; Roberta, G. G. Thin Solid Films
0 1988 American Chemical Society
