Langmuir 1985,1,195-201 Unfortunately, there are at present no computer simulation results for n(r,w) and for n '"(z), so that direct test of these calculations is not possikle. According to the suggestion of Street and Tddesley17(cf. also 18),the determination of the coefficients n,"(z) from computer simulation can be performed by evaluating n,"(z)
= 41/2~no00(z) ( Ylm(w)cos [27r(slg1 + s2g2)I ) (34)
where the T position on the unit lattice cell is expressed in terms of the vectors a1 and a2,T = slal + s2a2,and ( ) denotes the average value in the layer between z and z + dz. The leading coefficient nom(%)is the average center distribution of the molecules and is calculated in the usual way. As is commonly the case, neither the Percus-Yevick integral equation nor the perturbation calculation converge satisfactorily at low temperatures (kT/u,,
W
5 . O
3> 0 0.ea
5
0
0
V
z s cn
HEMATITE-OXALIC ACID 25 O C O X A L I C ACID: 4X10-' mol dm-' NaNO,: I XIO-'mol dm-'
I 0'
I
I
2
4
;
HEMATITE-CITRIC ACID
I
0
1 0:
I
I
I
II
I 10
5
7
9
I1
1
I 3
I
E
4
9 I-
2
E -50 0
n
6
8
PH Figure 5. Plota of adsorption potentials, $, as a function of pH calculated from adsorption data of citric acid on hematitelBassuming different combinations of adsorbed species. Circles and squares give the values of the {-potential of hematite particles in the presence of citric acid (2 X mol dm-3) and NaN03 (1 X mol dm-3); different symbols represent duplicate runs. I
3
9
7
5
II
PH
Figure 4. Lower: Species distribution in 4 X mol dm-3oxalic acid aqueous solution as calculated by using Kl = 5.62 X and Kz= 5.19 X in the presence of 1 X 10" mol dm-3 NaN03. Upper: Critical surface concentration, r (or coverage,e), above
which there is no change in the adsorption potential (circles). Dashed line represents the surface concentration of X2-species calculated from the corresponding potentials by means of eq 16 for oxalic acid concentrationof 4 X mol d d ,using K, = 9800.
between the concentration of X2- anions in bulk and on the surface can be understood if the effecta of the potential are taken into consideration. Above pH 6 the solution content in X2- is constant, yet the surface excess decreases due to the influence of surface OH- groups. Between pH 6 and 2 the solution concentration of X2-decreases while the surface concentration increases, which is caused by gradual rise in the positive value of the potential on hematite particles in the absence of oxalic acid. Over the same pH range the limiting surface potential (Figure 3) becomes gradually less negative. At pH 2.7 the content of X2- ions in bulk is rather small. The adsorbed amount at equilibrium just suffices to neutralize the charge of the original hematite particles (iep).
Hematite/Citric Acid System Equation 16 derived for a dibasic acid adsorbate can be extended to a tribasic acid case, by introducing an additional term:
+ KlsKl exp(FWRT) aH+
+
KzsK1K2 exp(2FWRT) aH+2
+
]
K3'KlK2& ~XP(~FIC/~/RT) (19) QH+3
In the interpretation of the adsorption of citric acid on hematite the following constants were used in the calcu-
lation of the corresponding equilibria:" K1 = 1.2 X K2 = 5.0 X and K3 = 2.5 X lo4. The isoelectric point of hematite in the presence of a sufficient amount of citric acid mol dm-3) is at pH 3.3. The adsorption data reported earlier16are treated in the same manner as the oxalic acid/hematite system. From eq 17 and 19, which are applicable to citric acid, the obtained value of rmax = 5 X lo4 mol m-2 corresponds to a saturation surface coverage of 33 A2/molecule, and K" = 5 X lo2dm3mol-'. It is noteworthy that a surface area of 32 A2 per molecule was obtained for the adsorption of citrate ion on colloidal silver, using the radioactive tracer technique.la With these values 16 different combinations of adsorbate species were tested in order to select those that could be responsible for the observed adsorption effects. Figure 5 illustrates the calculated potentials as a function of pH for several combinations of adsorbed citric acid species, along with the [-potentials as obtained from mobility measurements of hematite in the presence of 2 X mol dm-3 citric acid. Only anions X3- and the combination X3- + HX2- give potentials that show more negative)I values than the [-potential. The other plotted combinations and those not shown in this figure can be eliminated from further consideration. It is quite obvious that of the two possibilities the pair X3- HX2- (with Ks = 7800) approximates much more closely the {-potential curve and is favored over the single X3- anion for the configurational reason. It is quite likely that the citrate ions are bound to the surface by two peripheral carboxyl groups. Both HX2-and X" species allow for such bonding, which is analogous to what was found with oxalic acid. A triple bond to the surface sites, characterizing the X3- ion as the only adsorbate, would require an area per molecule significantly larger than calculated from the adsorption data. Figure 6 compares the experimental with calculated adsorption densities of citric acid on hematite. The computation (solid line) was based on the potentials given in Figure 5 for the combination HX2- + X3- using eq 17 and 19. The corresponding adsorbed amounts of the individual ions are given by dashed lines. The latter curves explain the irregular shape of the adsorption envelope; the max-
+
~~~
~
(18)Siiman, 0.; Blumm, L. A.; Callaghan, R.; Blatchford, C. G.; Kerker, M. J . Phys. Chem. 1983,87, 1014.
Kallay and MatijeviE
200 Langmuir, Vol. 1, No. 2, 1985 E a
I
I
HEMATITE- CITRIC ACID
8 0.250
w'
a W > 0 0
0.125 0
ia 0
solutions on charged surfaces is that no assumptions are necessary with respect to the double-layer equilibria. The procedure yields information on the specific species that adsorb and on the surface area they occupy. The corresponding intrinsic equilibrium constants can also be evaluated. Since no specific double-layer model was required, the above information was generated in a rather accurate manner. However, in doing so the predictability was sacrificed. For example, it is not possible to estimate a priori the isoelectric point of the solids in the presence of a given adsorbate. The applied analysis of the adsorption data of oxalic and citric acids on hematite resulted in the identification of solute species that interact with the hematite surface, i.e., X2-in the case of oxalic acid and HX2- X3- in the case of citric acid. The calculated areas clearly indicate that these ions are vertically oriented with two carboxyl groups attached to the surface bonding sites. This conclusion is supported by the finding that adgorbed species must carry at least a 2- charge. I t is noteworthy that the K* values for the two adsorbates are rather similar (9800 vs. 7800). While both acids use two bonds in adsorbed state the areas they occupy differ appreciably, which is understandable in view of their different ionic size and shape. The area covered by the oxalate ion corresponds to two iron sites on the hematite surface; in contrast, citric acid covers approximately eight surface sites. The calculated adsorption potential, IF/, is characteristic of the plane of the adsorbed ions, while {-potential corresponds to the slipping plane. Consequently, $ must be the same or larger in magnitude than the {-potential of like sign. The difference between IF/ and {-potentials at a given pH is larger for oxalic than citric acid. This effect may be again due to the difference in the size of adsorbed species; the larger citrate ion should be closer to the slipping plane. The employed procedure in the evaluation of adsorption data makes it possible to draw conclusions with respect to the nature, charge, and orientation of the adsorbate species at the interface. It also yields information on the potentials in the interfacial layer. The treatment explains the shapes of the adsorption envelopes as affected by the electrostatic phenomena. Adsorption effects of organic species at solid/solution interface were interpreted either in terms of ligand exchange or site bonding reactions.' It was shown that ligand-exchange mechanisms alone cannot fully explain the uptake of organic ions on metal oxides.14 This work further indicates that the ligand exchange does not play a role in the adsorption of oxalic and citric acids on hematite; such a mechanism could not account for the charge reversal that was observed below the iep of pure hematite. It was shown by infrared spectro~copy'~ that the adsorption of oxalate ions on goethite is caused by bonding the carboxylate oxygen to iron. Although the effect was ascribed to ligand exchange, there was no evidence of simple stoichiometry to subatantiate such a mechanism; only a limited release of OH- accompanied the adsorption of oxalate ions on gibbsite.20,21It would seem that a more appropriate explanation could be made by considering the mutual dependence of the adsorption equilibria of OH- and oxalate ions with hematite.
+
PH
Figure 6. Lower: Species distribution in 2 X mol dm-3citric acid solution as calculated by using K 1= 1.2 X K2= 4.9 X mol dm-3 and K3 = 2.5 X lo* in the presence of 1 X NaNO,. Upper: Surface concentration (or coverage, e) of citric acid on hematite as a function of pH calculated by means of eq 17 and 19, using ICI = 7800 and the potentials shown in Figure 5 for the combination HX2- + X" (solid line). The circles represent the experimental data taken from ref 16. Dashed lines give the calculated contributions of individual ions to the total adsorption density.
imum at pH -5.5 is caused by the uptake of the Xs ion, which becomes more abundant in solution due to a rise in pH. The increase in the amount of adsorbed HX" ions as the pH is lowered to -5 is due to the enrichment of this species in solution and to the lowering of the negative potential of the hematite surface. The isoelectric point is again consistent with the pH at which the concentration of the doubly negatively charged species approaches zero, which is analogous to the behavior of the hematite/oxalate system.
Discussion The analysis applied to experimental data on the adsorption from solution is based on the consideration of various bonding mechanisms of organic species on oxide surfaces. The limitation of the treatment is in the neglect of directly accounting for the uptake of H+and/or OHions, which contribute to the surface charge and, consequently, determine the surface potential as well as the surface equilibrium of the organic adsorbates. Instead, the potential is calculated from the experimental adsorption densities and compared with the electrokinetic potentials measured under identical conditions (ionic strength, solution composition, etc.). This procedure allows for the selection of the reaction mechanism that best fits the adsorption results. The assumptions that all reactions take place at the same surface site and that they are characterized by the same intrinsic equilibrium constant K Eare reasonable for oxalic acid, in which case the only adsorbate is the X2- ion. The same approach certainly represents just the first approximation for the hematite/citric acid system. The major advantage of the described method for the interpretation of the adsorption of solutes from aqueous
(19) Parfitt. R. L.:. Farmer, V. C.: Russell, J. D. J. Soil Sci. 1977, 28, . 29. (20) Parfitt. Parfitt, R. L.: L.; Fraser. Fraser, A. R.: R.; Russell, J. D.: D.; Farmer, V. C. J. Soil Sci. 1977, 28,40. Sci: B , 40. ' (21) Cornell, R. M.; Schindler, P. W. Colloid Polym. Sci. 1980, 258,
