4892
Langmuir 1999, 15, 4892-4897
Comparison of Cationic Excesses in the Presence of Perchlorate and Chloride Anions G. Lo´pez-Pe´rez,* D. Gonza´lez-Arjona, M. Molero, and R. Andreu Department of Physical Chemistry, University of Seville, E-41012 Seville, Spain Received December 2, 1998. In Final Form: April 8, 1999 Cationic surface excesses of Li+, Na+, Mg2+, and Al3+ are obtained from electrocapillary curves corresponding to aqueous perchlorate solutions. They are compared with earlier reported data on chlorides, obtained under similar conditions. The influence of ionic sizes on the ion-free layer thickness is discussed in the framework of Gouy-Chapman and the generalized UDCA theory. Differences between the surface excesses of a given cation in the presence of perchlorate and chloride find a plausible explanation in terms of the anion distance of closest approach to the electrode.
1. Introduction The ionic surface excess is a well-established thermodynamic magnitude which plays a crucial role in the study of the structure of the electrified interphases.1 It has been commonly employed in the analysis of double-layer effects on electrode kinetics. Its behavior in concentrated solutions has been interpreted in terms of an ion-free layer thickness, whose value is readily obtained by comparison with theoretical values derived from the Gouy-Chapman (GC) theory.2,3 Only a few estimates of the ion-free layer thickness have been performed, and they seem to show some scatter for a given electrolyte. For instance, it is possible to find the following values for Li+: 1.9,4 2.5,5 and 1.24-2.5 Å6 derived from LiCl solutions. The range of ion-free layer thickness values reported by Segel’man et al.6 as well as by Parsons et al.7 for NaH2PO4 solutions, was explained due to the dependence of the ion-free layer thickness on the electrode charge. Moreover, for a given cation different values can be derived as the electrolyte anion is changed. In the case of Na+, the following values can be found: 1.7 Å from NaCl solutions,4 2.5 Å from NaClO4 solutions,5 and 2.5-3.5 Å from NaH2PO4 solutions.7 These values seem to indicate that anions play also an important role in the ion-free layer thickness, even when they are strongly repelled from the electrode surface, as was pointed out by M. Pe´rez et al.8 This influence of anions is not easily ascribed to either ion-pair formation or specific interactions with interfacial water structure, since the anions under comparison differ markedly in the strength of their interaction with water and in their ability to form ion-pairs. An alternative analysis of the ion-free layer thickness can be performed by accepting that cation and anion have different distances of closest approach to the electrode, as was pointed out by Joshi and Parsons9 for the first time. (1) Parsons, R. In Comprehensive Treatise of Electrochemistry; Bockris, J. O’M., Conway, B. E, Yeager, E., Eds.; Plenum Press: New York, 1980; Vol. 1. (2) Gouy, G. J. Phys. (Paris) 1910, 9, 457; Ann. Phys. 1917, 7, 129. (3) Chapman, D. L. Philos. Mag. 1913, 25, 475. (4) Andreu, R.; Molero, M. J. Electroanal. Chem. 1992, 322, 133. (5) Harrison, J. A.; Randles, J. E. B.; Schiffrin, D. J. J. Electroanal. Chem. 1970, 25, 197. (6) Segel’man, B. S.; Ivanov, V. F.; Damaskin, B. B. Elektrokhimiya 1976, 12, 451. (7) Parsons, R.; Zobel, F. G. R. J. Electroanal. Chem. 1965, 9, 333. (8) Pe´rez, M.; Barrera, M.; Andreu, R.; Molero, M. J. Electroanal. Chem. 1993, 361, 239. (9) Joshi, K. M.; Parsons, R. Electrochim. Acta 1961, 4, 129.
The simplest theoretical tool that allows to estimate the influence of this type of effects was introduced by Valleau and Torrie,10 who developed a modified GC theory with unequal distances of closest approach (UDCA) to the electrode for the cation and the anion. This theory was generalized by Andreu et al.,11 who illustrated the influence of several parameters such as the ion-size asymmetry, electrolyte stoichiometry and dielectric constant on the expected ion-free layer thickness value. This straightforward extension of GC theory has been used successfully by Damaskin et al.12 to explain unusual double layer effects on electrode kinetics. Recently, MPB theory13,14 has been applied to the analysis of the ion-free layer thickness by Andreu et al.,15 providing a more sophisticated and exact theory for the electric double layer description.16 But unfortunately, the present formulation of this theory and its numerical implementation prevents their use within an extended range of surface charge densities, solution concentrations, ionic sizes and valences. Chloride and perchlorate are not strongly solvated in solution, and are expected to differ in their distances of closest approach to the electrode by an amount corresponding approximately to the diameter of an oxygen atom. Therefore, the analysis of the comparative behavior of chlorides and perchlorates should help (a) to assess the influence of unequal distances of closest approach on double layer properties and (b) to test the adequacy of UDCA theory to provide a coherent picture of such influence. 2. Experimental Section Differential capacities of the mercury-solution interphase were measured at 1020 Hz using a Solartron 1250 FRA and a Solartron 1286 potentiostat, employing the triggering and calibration procedures described by Andreu et al.17 The working electrode (10) Valleau, J. P.; Torrie, G. M. J. Chem. Phys. 1982, 76, 4623. (11) Andreu, R.; Molero, M.; Calvente, J. J.; Carbajo, J. J. Electroanal. Chem. 1993, 358, 49. (12) Damaskin, B. B.; Safonov, V. A.; Fedorovich, N. V. J. Electroanal. Chem. 1993, 349, 1. (13) Outhwaite, C. W.; Bhuiyan, L. B. J. Chem. Soc., Faraday Trans. 2 1983, 79, 707. (14) Outhwaite, C. W.; Bhuiyan, L. B. J. Chem. Phys. 1986, 84, 3461. (15) Andreu, R.; Molero, M.; Calvente, J. J.; Outhwaite, C. W.; Bhuiyan, L. B. Electrochim. Acta 1996, 41, 2125. (16) Carnie, S. L.; Torrie, G. M. Adv. Chem. Phys. 1984, 56, 141. (17) Andreu, R.; Gonza´lez-Arjona, D.; Domı´nguez, M.; Molero, M.; Rolda´n, E. Electroanalysis 1991, 3, 377.
10.1021/la981669a CCC: $18.00 © 1999 American Chemical Society Published on Web 06/05/1999
Cationic Excesses in the Presence of ClO4- and Cl- Anions
Langmuir, Vol. 15, No. 14, 1999 4893
Figure 1. Differential capacity curves for perchlorate salts. Perchlorate concentrations are: (b) 0.2, (O) 0.5, (1) 1.0, (3) 2.0, and (9) 3.0 M. was an SMDE EG&G model 303 A. The measuring system was controlled by a personal computer (PC 486 IBM-compatible) via a National Instruments GPIB. Mercury delivery was controlled with the same computer, and the time of measurement after drop birth was set to 2 s. A large mercury pool and a sodiumsaturated calomel electrode (SSCE) were used as auxiliary and reference electrodes, respectively. Potentials of zero charge were determined by the streaming electrode technique.18 The interfacial tension at the electrocapillary maximum (ecm) was measured by the maximum bubble pressure method.19 A perchlorate reversible electrode, Orion model 93-8101, was used to refer potentials to the anion reversible scale. Solution densities20,21 and mean ionic activity coefficients22,23 were interpolated from published data. In the case of the Al(ClO4)3 activity coefficients, a revised version of previous literature data was used.24 Mercury was purified by treatment with diluted nitric acid and mercurous nitrate during a week, and it was then distilled three times under vacuum. Solutions were made up with Merck p.a. salts and water purified using a Millipore Milli-Q water system. Before the measurements were made, oxygen was removed by bubbling nitrogen through the solutions, which had been presaturated with the cell solution. Experiments were carried out at 25 ( 0.1 °C using a Haake D8.G circulator thermostat. (18) Grahame, D. C.; Coffin, E. M.; Cummings, J. I.; Poth, M. A. J. Am. Chem. Soc. 1952, 74, 137. (19) Schiffrin, D. J. J. Electroanal. Chem. 1969, 23, 168. (20) So¨hnel, O.; Novotny, P. Densities of Aqueous Solutions of Inorganic Substances; Physical Sciences Data 22; Elsevier: Amsterdam, 1985. (21) Ho¨gna¨s, H. Ann. Acad. Sc. Fennicae 1969, 145, 1. (22) Hammer, W. J.; Wu, Y.-C. J. Phys. Chem. Ref. Data 1972, 1, 1047. (23) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions, 2nd ed, 5th revised impression; Butterworths: London, 1970. (24) Molero, M.; Gonza´lez-Arjona, D.; Calvente, J. J.; Lo´pez-Pe´rez, G. J. Electroanal. Chem. 1999, 460, 100.
Table 1. Salt Concentration, Coordinates of Electrocapillary Maximum, and Reversible Potentials for Li, Na, Mg, and Al Perchloratesa salt LiClO4
NaClO4
Mg(ClO4)2
Al(ClO4)3
csalt/M
Eecm/V
γecm/mN m-1
∆E-/V
0.20 0.50 1.00 2.00 3.00 0.20 0.50 1.00 2.00 3.00 0.10 0.25 0.50 1.00 1.50 0.07 0.17 0.35 0.67 1.00
-0.481 -0.494 -0.509 -0.532 -0.552 -0.488 -0.500 -0.513 -0.533 -0.548 -0.486 -0.499 -0.510 -0.527 -0.545 -0.490 -0.500 -0.512 -0.529 -0.551
424.9 423.8 422.5 420.8 420.0 424.9 423.9 422.7 420.9 420.1 424.8 423.7 422.3 420.6 419.1 424.6 423.5 422.0 420.0 418.4
+0.010 -0.015 -0.034 -0.054 -0.068 +0.011 -0.014 -0.031 -0.046 -0.054 +0.004 -0.018 -0.034 -0.051 -0.065 -0.004 -0.020 -0.034 -0.048 -0.060
a All potentials are referred to a sodium-saturated calomel electrode scale. Eecm and γecm values for NaClO4 have been taken from Andreu.25
3. Results Differential capacity curves of perchlorate solutions (see Figure 1) are typical of simple oxoanion electrolytes and they do not show important differences between them. Coordinates of ecm (γecm, Eecm) and potentials of the anion reversible electrode vs SSCE (∆E-) are listed in Table 1. Experimental measurements were performed at ca. 0.2, 0.5, 1.0, 2.0, and 3.0 M concentrations of the perchlorate anion in solution. These values are the same that those used previously for chlorides with the same cations,4
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Figure 2. Cationic surface excesses for the following perchlorate anion concentrations: (b) 0.2, (O) 0.5, (1) 1.0, (3) 2.0, and (9) 3.0 M. Symbols: experimental results. Solid lines: UDCA theory using the distances of closest approach listed in Table 3. Dotted lines: Gouy-Chapman theory.
allowing thus for a direct comparison between the two sets of data. Electrocapillary curves were obtained by integrating twice the differential capacity curves, using as integration constants the coordinates of the ecm. Cationic surface excesses were then computed from the derivative of Parsons’ function (ξ-):
ξ- ) γ + σME-
(1)
with respect to the salt chemical potential, where γ is the surface tension, σM is the charge density on the metal, and E- is the potential measured against a perchlorate reversible electrode. Some common trends in the behavior of the experimental cationic surface excesses of perchlorate solutions are evident from Figure 2. The values from GC theory, which provide a useful reference, are also included in the plots. Only at low concentrations and negative surface densities (e-10 µC cm-2), the experimental values agree with the GC prediction. At higher electrolyte concentrations and negative values of the surface charge excesses (e-4 µC cm-2) there is a continuous decrease of the experimental surface excesses, beyond the predictions of the GouyChapman theory, on increasing the electrolyte concentration. The magnitude of such decrease is characteristic of each electrolyte and is commonly attributed5,7,26 to the solvent contribution to the surface excesses. At more positive values of σM, the picture is more complex due to (25) Andreu, R. Thesis, University of Sevilla, 1982. (26) Damaskin, B. B.; Frumkin, A. N.; Ivanova, V. F.; Meleknova, N. I.; Khonina, V. F. Elektrokhimiya 1968, 4, 1336.
the likely presence of perchlorate specific adsorption, and it will not be analyzed in this paper. W Experimental or Gibbs cationic surfaces excesses, ΓM z+, are defined as
ΓW Mz+ ) ΓMz+ -
( ) 0 cM z+
c0W
ΓW
(2)
where Γi represents the absolute surface excess of either the solvent (W) or the cation (Mz+), and c0i is their bulk concentration. The second term on the right-hand side of eq 2 appears to be negligible in diluted solutions, but as the bulk concentration increases (g1/z+ M) its contribution W 27 to ΓM z+ becomes significant. In the absence of specific adsorption, it is usually accepted that ΓW originates from a layer of solvent molecules, which retain their bulk density, interposed between the electrode and the ions. It then follows that5 0 ΓW Mz+ ) ΓMz+ - λcMz+
(3)
where the ion-free layer-thickness (λ) is the distance between the cationic outer Helmholtz plane (OHP) and the plane through the centers of the water molecules immediately adjacent to the electrode.7 At high negative charges on the electrode (σM e -15 µC cm-2) specific adsorption of the anion is absent and the Gouy-Chapman theory can be used to evaluate the W absolute surface excesses, so that ΓM z+ ≈ ΓGC and λ can W 0 easily be obtained by plotting z+F(ΓGC - ΓM z+) vs z+cMz+. (27) Mohilner, D. M. In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, 1966; Vol. 1.
Cationic Excesses in the Presence of ClO4- and Cl- Anions
Figure 3. Differences between GC calculated and experimental W 0 surface excesses z+F(ΓGC - ΓM z+) vs z+cMz+. Straight lines correspond to least-squares fitting passing through the origin. Symbols correspond to Na+ (b), Li+ (O), Mg2+ (1), and Al3+ (3). Table 2. Ion-Free Layer Thickness (λ) Values Obtained According to Eq 3 and GC Theorya cation
Li+
Na+
Mg2+
Al3+
λ(Cl-)b/Å
1.9 2.8
1.7 2.4
2.5 3.5
3.0 3.7
λ(ClO4)c/Å
a Chloridesb are taken from Table 1 of Andreu et al.4 and values for perchloratesc were derived in this work.
Figure 3 shows a typical plot for σM ) -18 µC cm-2, experimental data were fitted to straight lines passing through the origin, and the slopes of the straight lines gave the λ values listed in Table 2. No significant (e5%) dependence of λ on σM was found in the range -15 e σM e -20 µC cm-2. Previous results for the same cationic chlorides4 are also included in Table 2. The differences between λ values obtained from different electrolytes with a common cation suggest a systematic influence of the anion. Within the context of the GC theory, this influence can only be indirect, i.e., via ion-pairing or via modification of the interfacial water structure as indicated before. However, this type of explanation does not seem to be entirely satisfactory since anions are strongly repelled from the interphase at the very negative σM values at which λ values are obtained. 4. Discussion A detailed explanation on UDCA theory application to the analysis of the ion-free layer thickness can be found in a previous work.11 Figure 4 shows a schematic diagram of the interfacial structure within the UDCA context. The interphase is divided into three regions: (I) 0 e x e ai. No ions are present in this region, so the electric field is constant and it is directly related to the charge density on the electrode. (II) ai e x e aj. Only the smaller i ions can enter into this region. (III) aj e x e ∞. Ions j move up to the x ) aj plane, and both anion and cation are able to populate this zone. The UDCA theory shows that cationic surface excesses, which are defined with respect to the plane defined by the centers of the water molecules adjacent to the electrode, at a given σM are dependent on the thickness (aj - ai) of region II. This thickness is expected to be different for a given cation in the presence of either chloride or perchlorate.
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Figure 4. Schematic diagram of the double-layer structure as described by the UDCA theory. Table 3. UDCA Distances of Closest Approach for Cation and Anion (ai - as)a ion Li+ Na+ Mg2+ Al3+ ClClO4-
(ai - as)/Å
aion/Å
rH /Å
2.2 1.7 2.5 3.0
3.6 3.1 3.9 4.4
3.82 3.58 4.28 4.75
e1.7 4.5
e3.1 5.9
3.32 3.38
a a ion ) (ai - as) + 1.4 Å. rH values are hydrated radii, taken from Nightingale.29
Thus, theoretical cationic excesses have been computed using the generalized UDCA theory, with I ) II ) 33, and III ) 78.5. The choice of a relatively low value for the average permittivity in the first two regions is intended to account, up to some point, for the expected dielectric saturation in the close vicinity to the electrode. In any case, this choice involves changes of only ca. 0.5 Å in the estimation of the ion free layer thickness when they are compared with the results obtained by assuming I ) II ) III ) 78.5. The use of a lower II value would result in a further decrease of the estimated ion-free layer thickness, W but it would also lead to nonlinear z+F(ΓGC - ΓM z+) vs 0 11 z+cMz+ plots, which are not observed. This situation would imply an unrealistic dielectric profile in the vicinity of the electrode.28 To obtain individual distances of closest approach a further hypothesis is required, therefore we assumed that (aCl- - as) e (aMz+ - as), so that λMClz+ ) aMz+ - as.11 In this way, we could assign the (aMz+ - as) values listed in Table 3. Figure 5 shows a comparison between the experimental and UDCA surface excesses computed from that set of distances of closest approach. The distance (aClO4- - as) was chosen to reproduce the experimental results obtained for the Li+, Na+, Mg2+, and Al3+ perchlorates (see Figure 2). The distances of closest approach of the ions (in Å) up to the metal surface, namely the ion-electrode contact distance (aion), can be readily obtained by adding the radius of one water molecule (as ) 1.4 Å) to those values given by the UDCA, and are also listed in Table 3. Such distances show a good correlation with ionic hydrated radii taken from Nightingale29 in the case of cations, as can be seen in Figure 6. The straight line acation ) rH - 0.3 Å indicates that electrode and cations share their solvation shell, though the cations seem to lose some (28) Levine, S.; Fawcett, W. R. J. Electroanal. Chem. 1979, 99, 265. (29) Nightingale, E. R. J. Phys. Chem. 1959, 63, 1382.
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Figure 5. Cationic surface excesses for the following chloride concentrations: (b) 0.2, (O) 0.5, (1) 1.0, (3) 2.0, and (9) 3.0 M. Symbols: experimental results taken from Andreu et al.4 Solid lines: UDCA theory using the distances of closest approach listed in Table 3.
Figure 6. Correlation between distances of closest approach obtained using UDCA theory for Li+ (b), Na+ (9), Mg2+ (2), and Al3+ (1) and their hydrated radii, taken from Nightingale.29
of this solvation along a direction perpendicular to the electrode surface, probably due to the strong action of the electric field in this region. Chloride anion can be included in this correlation without making any other assumption, but ion-electrode contact distance for the perchlorate anion is much larger than its hydrated radius. This difference between aClO4- and rH is ca. the diameter of one water molecule (2.8 Å). This behavior suggests that one water molecule remains interposed between the electrode and the perchlorate anion. Adding the diameter of one water molecule to the perchlorate crystallographic radius (2.92 Å)29 gives a distance of closest approach of 5.7 Å, in good agreement with the UDCA value of 5.9 Å.
The cationic distances of closest approach to the electrode can be estimated using the generalized UDCA theory by assuming that chloride may approach to the electrode closer than its counterions. A consistent set of distances of closest approach for anions and cations can be obtained in this way, accounting for the behavior of the four chlorides and the four perchlorates examined in this work. Though the physical picture at negative charge densities is considerably clarified, some questions can be raised concerning the nature of perchlorate “specific adsorption” at more positive charge densities on the electrode. Given the relatively large value of the perchlorate distance of closest approach found at negative charge densities, it seems likely that extensive changes of the interfacial water structure will be required to allow superequivalent adsorption of perchlorate. At this point, it is unclear whether these changes may lead to a field-assisted contact adsorption, or to a hydrophobically driven adsorption. In any case, it should be noted that “specific adsorption” of perchlorate is greatly reduced in the presence of the more hydrophilic gold electrode surface.30 5. Conclusion The ion-free layer thicknesses of a series of perchlorates have been shown to be systematically larger than those previously reported for chlorides with the same cations. This result supports the hypothesis that nonspecifically adsorbed anions determine to some extent the value of the cationic surface excesses, and it does not seem to find (30) Clavilier, J.; Van Huong, C. N. J. Electroanal. Chem. 1977, 80, 101.
Cationic Excesses in the Presence of ClO4- and Cl- Anions
a satisfactory explanation within the framework of GC theory. Application of UDCA theory in a wide range of electrolyte concentrations provides a quantitative explanation for the observed cationic surface excesses in the presence of a negatively charged electrode. A coherent set of distances of closest approach for cations, which are independent of the accompanying anion, has been obtained. Moreover, such distances of closest approach are
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shown to correlate with Nightingale hydrated radii for individual ions in solution. Acknowledgment. This work has been partially supported by the Direccio´n General de Investigacio´n Cientı´fica y Tecnolo´gica (CAICYT) under Grant PB0950537. LA981669A
