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Surface Force Measurements at a Copper Electrode/Electrolyte Interface C. Dedeloudis, J. Fransaer,* and J.-P. Celis Department of Metallurgy and Materials Engineering, Katholieke UniVersiteit LeuVen, 3001 LeuVen, Belgium ReceiVed: September 9, 1999; In Final Form: December 13, 1999

The surface force between a silica sphere and a copper electrode was measured in concentrated solutions of MgSO4 with an atomic force microscope as a function of the electrode potential. The interaction between the two surfaces was compared with the DLVO theory, and the surface potential of the copper electrode was determined as a function of the cathodic overpotential. The potential of zero charge of the copper electrode was identified in this way. This was found to correspond to the potential of zero charge obtained from the differential capacitance minimum. Moreover, the influence of the pH on the surface force between silica and copper was examined and the presence of a chemically adsorbed oxygen layer on copper was deduced from force measurements at high pH.

Introduction Surface forces play a very important role in many industrial processes where colloidal particles are employed. One such industrial process is composite plating, where particles are incorporated into a metal deposit during electrodeposition. Fransaer et al.1 have previously shown the importance of surface forces in the incorporation of such particles into a metal matrix. Moreover, they indicated the role of the potential of zero charge of the electrode in composite plating. The advent of the surface force apparatus (SFA)2 and atomic force microscope (AFM)3 allowed the direct measurement of surface forces with high precision. During the past decade, many direct measurements of DLVO forces have been carried out between mica surfaces,4 between surfactant monolayers5,6 or bilayers,7 between silica,8,9 and between alumina surfaces.10 More recently, force measurements have been performed in electrochemical systems. A dependence of the double layer force on the electrode potential was reported by Hillier et al.11 using an AFM. They measured the forces between a silica probe and gold electrodes in a series of aqueous alkali halide electrolyte solutions and found that the double layer forces were a strong function of the electrode potential. Similar results were obtained by Raiteri et al.12 on measuring the force between a Si3N4 tip and a gold or platinum electrode in 1 mM KCl solution at pH 9-10. Finally, Campbell et al.13 observed potential-dependent double layer adhesion and friction forces between a silica tip and a glassy carbon electrode or a thin film of sulfonatederivatized poly(aniline) in 1 mM KCl solution at pH 5.2. This dependence of the surface forces on the electrode potential was attributed to the variation of the surface charge of the electrode with the applied potential. The dependence of the surface charge of an electrode on the electrode potential has been known for a long time. Frumkin14 pointed out that the surface charge on an electrode depends on the electrode potential. That surface charge evolves from positive to negative and becomes zero at a certain electrode potential known as the potential of zero charge (Epzc). Many methods are used for the determination of the zero charge potential of * Corresponding author. E-mail: [email protected]. Fax: +32-16-32 19 91.

an electrode such as the electrocapillarity method,15 the crossed polarized metallic thread method,16 the immersion method,17 and the differential capacity minimum method.18 Up to now, force measurements in electrochemical systems were limited to dilute electrolytes (10-3 M or less) and noble metals. In industrial electrochemical processes, however, highly concentrated solutions are used and the electrode surfaces are usually less noble than gold or platinum. The aim of this work is the investigation of the surface force between a silica particle and copper by AFM and its dependence on the electrode potential in concentrated aqueous solutions relevant for the codeposition of particles in electrochemical systems.

Experimental Setup The surface force measurements were performed using the Nanoscope III (Digital Instruments, Santa Barbara, CA). Commercial AFM cantilevers (ThermoMicroscopes, Sunnyvale, CA) with a spring constant of 2.1 N/m were modified by gluing a single glass sphere to each. Cantilevers with a high spring constant were used in order to measure surface forces close to the electrode without interference of the cantilever instability. The glass spheres were obtained from Potters-Ballotini (Valley Forge, PA). The diameter of the glass spheres was between 20-30 µm and consisted of soda-lime glass (72.5% SiO2, 13.7% NaO, 9.8% CaO). Even though these glass spheres are not made of pure silica, their behavior with respect to the double layer force was found to be similar to that of pure silica particles.8 Henceforth, the glass will be referred to as silica. Such silica spheres were glued to the cantilevers with the epoxy resin Epikote 1004 (Shell) as described by Ducker et al.8 The cantilever was placed on a heating stage at a temperature above the melting point of the glue. A thin tungsten wire attached to a three-dimensional translation stage was used to position a drop of molten glue near the tip of the cantilever. With the help of another tungsten wire, a particle was positioned on the cantilever and the glue was solidified by lowering the temperature of the hot plate. After the surface force measurement experiments, the cantilevers were examined by scanning electron microscope (SEM) and the radius of the sphere was measured.

10.1021/jp9931814 CCC: $19.00 © 2000 American Chemical Society Published on Web 02/11/2000

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Flat silica surfaces were prepared by oxidizing silicon wafers at 900 °C in air for 10 min. The mean roughness Ra of the silica surface thus obtained was 0.4 nm, measured by AFM on a 3 × 3 µm area. Silicon wafers, coated with a sputtered titanium layer of 30 nm and 130 nm of copper, were used as flat copper electrodes. From AFM images, the mean roughness Ra of the copper electrode was found to be 0.8 nm over a 3 × 3.5 µm area. Before each experiment, the wafers were ultrasonically cleaned in ethanol in order to remove possible organic contaminants and carbon residues from the surface. The surface force measurements were done at 23 °C ( 2 in 0.01 or 0.1 M solutions of MgSO4 at pH 3.4 and 5.8. The pH was adjusted using 0.2 M H2SO4. All chemicals used were pro analysis reagents supplied by ACROS. Milli-Q water from Millipore was used in the preparation of the solutions. The force measurements were performed in a liquid cell made of glass (Digital Instruments) with silicone tubes as input and output leads. Prior to experiments, the liquid cell was thoroughly rinsed in purified water and ethanol. For the electrochemical experiments, a three electrode cell was used consisting of a copper electrode as the working electrode and two platinum wires as the counter and pseudo-reference electrode. The potential of the working electrode was controlled with a Nanoscope bipotentiostat (Digital Instruments). The open circuit potential of that copper working electrode in 0.01 M MgSO4 solutions is -370 mV vs Pt or +297 mV vs NHE. All potentials of the working electrode cited in this work are overpotentials, measured with respect to this open circuit potential. The force between the flat surface (wafer) and the silica particle is measured as a function of the displacement of the wafer which is mounted on a piezoelectric crystal, toward and away from the sphere. The relative linear velocity of the surface to the sphere was 10 nm/s. In view of the relatively large size of the silica sphere (20- 30 µm), a low velocity was chosen in order to minimize the hydrodynamic forces between sphere and flat surface.19 In this investigation, only the force curves obtained during the approach of the two surfaces were taken into account. The retraction curves, which give information on sphereelectrode adhesion, show the same trend as the approach curves, e.g., if an attraction was observed during the approach, high adhesion could be seen in the retraction curves. The conversion of the photodiode voltage into surface force data and the conversion of the piezo displacement into a surface separation were done from the slope of the linear change of the cantilever deflection with respect to the piezo displacement when both are in contact (constant compliance region). This also defines the point of zero distance. The zero force corresponds to the deflection data when the two surfaces are far apart from each other. Force measurements were done at different sites on the surface of the flat electrode, yielding consistent results. The reported surface force curves are the average of 10 curves and they were scaled by dividing the force by the radius, ap, of the silica sphere. In this way, the force between a sphere and a plane equals the interaction energy per unit area between parallel plates. The AFM results were analyzed using the DLVO theory which states that the surface force between a sphere and a flat surface, Ftotal, consists of a London-van der Waals part, FLvdW, and a double layer interaction part, Fψ1-ψ2. However, at the high electrolyte concentrations used in this work, a hydration force, Fhydr, has to be taken into account. Hence, the surface force can be expressed as:

Ftotal ) FLvdW + Fψ1-ψ2 + Fhydr

(1)

The London-van der Waals force between a sphere of radius ap and a flat surface, is equal to

FLvdW ) -

Aap 6h2

(2)

with A the Hamaker constant, and h the separation between the two surfaces. Although eq 2 is not exact since it assumes that the dispersion forces are linearly additive, it was found to give excellent results, e.g., in the case of the dispersion force between two spheres.20 The Hamaker constants were obtained from optical data of copper and silica using the DLP theory.21 For the silica/water/silica system we used a Hamaker constant of 8 × 10-21 J and for the silica/water/copper system the Hamaker constant had a value of 2 × 10-20 J. The double layer force, Fψ1-ψ2, between a sphere of radius ap and a flat surface is given by:22

Fψ1-ψ2 )

κap

[2ψ1ψ2 exp(-κh) 2[1 - exp(-2κh)] (ψ21 + ψ22) exp(-2κh)] (3)

with κ the inverse Debye length,  the dielectric constant of the solution and ψ1 and ψ2 the surface potentials of the interacting surfaces. This expression is valid at low surface potentials ( 10. Both conditions are satisfied due to the high ionic concentrations of the solutions used in our experiments. Equation 3 is valid for interactions between bodies at a constant surface potential. The constant surface potential model was preferred to the constant surface charge model because it was found earlier that a better fit to the AFM force curves is obtained using the constant surface potential model.8 However, other researchers found that the constant surface charge model describes better the double layer interaction.11 Metal electrodes, though, have an appreciable exchange current density, so that it can be assumed that the surface potential of the copper electrode remains constant on approach.1 The hydration force, Fhydr, was approximated by a sum of two exponentials, decaying with separation h according to:

Fhydr ) apA1 exp(-h/λ1) + apA2 exp(-h/λ2)

(4)

From SFA experiments between two mica surfaces in a Mg2+ electrolyte, A1 and A2 were found to be equal to 25 mN/m and 600 mN/m and, and the decay lengths λ1 and λ2, were found to be equal to 1.8 and 0.3 nm respectively.23,24 The preexponential terms A1 and A2 depend on the nature of the two surfaces, but the decay lengths were found to depend mostly on the valency of the ions in solution and are nearly independent of solution concentration. Equation 1 was fitted to the experimental surface force vs separation curves using a Levenberg-Marquardt method. In the fitting procedure for silica/silica interactions, the Debye length κ-1, the Hamaker constant A, and the decay lengths of the hydration force were kept constant while the surface potential ψ1 ) ψ2 ) ψ and the preexponential terms A1 and A2 were fitted to the experimental force curve. For the copper/silica interactions, only the surface potential of the copper electrode was fitted while all other parameters were kept constant. It was assumed that the hydration forces between silica and silica and copper and silica are equal. This assumption is not fully correct since the magnesium ions adsorb differently on copper than on

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Figure 1. Force vs separation curves (approach only) measured by AFM between a silica sphere and a copper electrode at open circuit potential and at different cathodic overpotentials in a 0.01 M MgSO4 solution of pH 3.4 and 23 °C.

silica. However, the lack of information on the hydration forces between copper surfaces in the presence of Mg2+ ions makes this assumption necessary. The surface potential of silica was derived from the force measured between silica spheres and SiO2 wafers immersed in 0.01 M MgSO4 at pH 3.4. The surface force is repulsive and by fitting our results with the DLVO theory, the surface potential of silica was found equal to -19 ( 2 mV. This surface potential is half the value reported by Ducker et al.8 for a 0.01 M 1:1

electrolyte. It is known that the surface potential of silica reduces in absolute values by decreasing the thickness of the double layer.8,9 In this respect and taking into account that there is a difference in the pH between the two experiments, the surface potential of -19 mV for silica determined in the 0.01 M MgSO4 solution is very close to the surface potential of silica (-21 mV) in 0.1 M NaCl, which has a comparable Debye length.8 For a 0.1 M MgSO4 solution of pH 3.4, the surface potential of silica is -12 ( 4 mV.

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The preexponential terms A1 and A2 of the hydration force between silica surfaces were found to be 60 and 1.8 mN/m, respectively. These values are about 10 times smaller than the values reported for mica surfaces.23,24 According to the literature, the hydration force depends on the energy balance for the processes involved in the replacement of hydrogen cations on the surface of mica or silica by hydrated magnesium cations.25 On the other hand, the surface charge or potential of mica in aqueous solutions is almost double that of silica,8,9,26 which is the result of a larger number of sites available to exchange hydrogen. It can be assumed, therefore, that a higher number of magnesium cations replace hydrogen cations on mica than on silica and hence the hydration force is expected to be larger for mica-mica interactions than for silica-silica interactions. The potential of zero charge of the copper electrode was determined from differential capacity measurements. The differential capacitance of the double layer of the copper electrode in 0.01 M MgSO4 at pH 3.4 was measured by a coulostatic pulse method. A very short current pulse was applied to the cell, and the variation of the electrode potential with time after the pulse was recorded. If the current pulse length, ∆t, is substantially shorter than τ, where τ ) RpCdl and Rp is the polarization resistance, the capacity of the double layer is given by:

Cdl )

∆Q ∆E

Figure 2. Surface potential of a copper electrode as a function of the cathodic overpotential calculated by fitting the experimental force vs separation data of Figure 1 with the DLVO theory plus a hydration force according to eq 1.

(5)

with ∆Q the charge injected in the cell and ∆E the difference between the potential at the end of the charge step and the potential of the electrode at time t ) 0. In our experiments, a current step of 1 mA was applied for 10 µs (∆Q ) 10-8 C) using an EG&G Princeton Applied Research 263A potentiostat and an HP 3314A function generator. The potential response was recorded with a digital oscilloscope (Nicolet 2090, sample frequency 1 MHz). The cell consisted of a copper electrode, identical to the one used for the AFM experiments, a platinum grid as counter electrode and a Hg/HgSO4 reference electrode. A platinum wire in series with a 2.2 nF capacitor was connected in parallel with the reference electrode to improve its highfrequency behavior. The differential capacity of the Cu electrode was measured as a function of the applied potential. Results and Discussion Force-separation curves between a silica sphere and a copper electrode held at different potentials in 0.01 M MgSO4 at pH 3.4 are shown in Figure 1. At the open circuit potential (Figure 1a), the force between a silica sphere and the copper electrode is attractive and the attraction force on the sphere becomes measurable at a distance of 4.5 nm. By polarizing the copper electrode cathodically, the attraction force and interaction distance become smaller. At 35 mV cathodic overpotential the interaction distance is 2 nm (Figure 1b), 1.5 nm at 65 mV (Figure 1c) and 1 nm at 115 mV (Figure 1d). When the cathodic overpotential is higher than 165 mV, the force between copper and silica sphere becomes repulsive (Figure 1e-f). The variation of the surface force with potential and the shift from repulsion to attraction at the point of zero charge of the copper electrode show that the electrostatic component dominates the interaction even in these electrolytes of high concentration where the van der Waals attractive force is expected to be dominant. This can be explained if a strong hydration force between silica and copper counteracts the van der Waals

Figure 3. Double layer capacitance of a copper electrode as a function of the cathodic overpotential in 0.01 M MgSO4 at pH 3.4 and 23 °C.

attraction. In concentrated divalent electrolytes the hydration force is significant at distances where the van der Waals attraction becomes measurable. The surface potential of the copper electrode deduced by fitting the experimental results of Figure 1 with the DLVO theory assuming a constant surface potential of silica equal to -19 mV is shown in Figure 2. The standard deviation of the fitted surface potential was calculated from the different surface potentials obtained by fitting eq 1 to the 10 force curves recorded at each overpotential value. The surface potential of the copper electrode at open circuit is +6 mV. This implies that the copper surface bears a positive charge under open circuit conditions. When the electrode is polarized cathodically, the positive surface potential of copper reduces to +3 mV and +2 mV for cathodic overpotentials of 35 and 65 mV, respectively. At a cathodic overpotential of 115 mV, the surface potential changes sign and becomes negative and equal to -1 mV. Beyond this overpotential, the double layer force between the negatively charged silica and copper becomes repulsive and the repulsive force increases with increasing cathodic overpotential. The surface potential of the copper electrode decreases to -9 mV and -13 mV for cathodic overpotentials of 165 mV and 215 mV, respectively. The surface potential of the copper electrode varies

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Figure 4. Force vs separation curves (approach only) measured between a silica sphere and a copper electrode at open circuit potential and at different cathodic overpotentials in 0.1 M MgSO4 solution of pH 3.4 and 23 °C.

thus with the electrode potential and shifts from positive to negative values around a cathodic overpotential of 96 mV. This implies that the point of zero charge of the copper electrode is near a cathodic overpotential of 96 mV. It is clear from Figure 2 that the change in the surface potential of the copper electrode is much smaller than the change in the applied overpotential. The surface potential varies 19 mV for an overpotential change of 215 mV. This can be explained as follows. Thermodynamically, the electrode potential is the difference between the Galvani potential of the metal, φm, and

the aqueous phase, φs:

E ) φ m - φs

(6)

The difference, ∆φ, between the Galvani potential of the metal electrode and the electrolyte phase can be separated into two parts: the work done in bringing an ion from the bulk solution to a point in the double layer, ∆ψ, and the contribution, ∆χ′, due to the orientation of the dipolar molecules and the specifically adsorbed ions which lie between the electrode and

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Figure 5. Force vs separation curves (approach only) measured between a silica sphere and a copper electrode at open circuit potential in a 0.1 M MgSO4 solution at pH 3.4 and 5.8 and 23 °C.

Figure 6. Force vs separation curves measured in a 0.1 M MgSO4 solution of pH 5.8 and 23 °C between a silica sphere and a copper electrode polarized at a cathodic overpotential of 50 mV for 3 different durations of polarization.

the outer Helmholtz plane. With this definition,

E ) ψo + ∆χ′

(7)

with ψo the surface potential of the metal electrode.27 Since, according to the results of Figure 2, only a small part of the applied overpotential contributes to a change in the surface potential, most of the applied overpotential is lost between the metal surface and the outer Helmoltz plane. The potential of zero charge of the copper electrode in a 0.01 M MgSO4 solution of pH 3.4 was also determined from differential capacitance measurements (Figure 3). The capacitance of the double layer of the copper electrode decreases with increasing cathodic overpotential until it reaches a minimum. That minimum corresponds to the potential of zero charge.29 The potential of zero charge of the copper electrode determined in that way was found at a cathodic overpotential of 79 mV. This value is quite close to the potential of zero charge found in our AFM experiment, especially in view of the fact that, according to the literature, values of the potential of zero charge for the same electrolyte measured with different methods can differ up to 100 mV.30 A potential-dependent force was measured even if the concentration of the electrolyte was increased to 0.1 M MgSO4 at pH 3.4 (Figure 4). The force is attractive at open circuit potential and cathodic overpotentials of 50 and 100 mV, but repulsive at cathodic overpotentials of 150 and 250 mV. However, the change of the force vs separation curve from attraction to repulsion due to the overpotential is less pronounced in a 0.1 M MgSO4 (Figure 4) than in a 0.01 M MgSO4 (Figure 1). This is due to the reduced thickness of the double layer, which reduces the contribution of the double layer force (cf. eq 3). Nevertheless, as before we can clearly see from Figure 4 that the interaction changes from attraction to repulsion between 100 and 150 mV cathodic overpotential. At pH 5.8, the force between the SiO2 sphere and copper at the open circuit potential is repulsive, while it is attractive at pH 3.4 (Figure 5). This is not due to a change in the surface charge of the silica particle since the charge is negative at both pHs. If anything, the surface charge of silica becomes more negative as the pH increases.8,9 Therefore, we have to conclude that at pH 5.8, the copper electrode is negatively charged at the open circuit potential. Indeed, several researchers found that most metals are negatively charged at higher pHs.31,32 This

negative charge was attributed to a layer of chemically adsorbed oxygen. Within this chemisorbed oxygen layer, the electrons of the metal-oxygen bond are displaced to the oxygen. This gives rise to a dipole layer causing a negative surface charge. Hence, an adsorbed oxygen layer probably exists on the surface of copper at pH 5.8 which results in a negative surface charge. At pH 3.4, this oxide layer is thermodynamically unstable according to Pourbaix’s diagram for copper.34 If a layer of adsorbed oxygen is present on the surface of copper at pH 5.8, it should be possible to remove this layer by polarizing the copper electrode cathodically. The effect of cathodic polarization on the force vs separation curves at pH 5.8 is shown in Figure 6. The copper electrode was polarized at a cathodic overpotential of 50 mV and the surface force between copper and silica was measured at this potential as a function of time. It was found that the force between copper and silica gradually shifts from a repulsion to an attraction. After 30 min of cathodic polarization, the force is attractive and no longer changes with time. Hence, we assume that the oxygen layer is removed after polarizing the copper electrode cathodically at 50 mV for 30 min. It is surprising to see that the chemisorbed oxide layer persists for such a long time. However, comparable time periods of 1 to 20 min were reported by other researchers for the removal of oxide layers from platinum electrodes.33 The time needed for the removal of the oxide layer becomes shorter by increasing the cathodic overpotential of the copper electrode. For example, if the electrode is polarized cathodically at 300 mV, the oxygen layer is removed in 3 min. This was concluded by measuring the force between silica and copper at open circuit potential before and immediately after the polarization (Figure 7). After the oxygen layer is removed by cathodic polarization, the force vs separation curves at pH 5.8 are identical to the ones measured at pH 3.4, i.e., the force between copper and silica is attractive for overpotentials between the open circuit potential and the potential of zero charge and repulsive at still higher overpotentials. However, after stopping the cathodic polarization of the copper electrode, the force between silica and copper at the open circuit potential gradually shifts with time from an attraction back to a repulsion. Specifically, after 5 min at the open circuit potential, the force between the two surfaces becomes repulsive again and is equal to the force measured at the open circuit

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Dedeloudis et al. the variation of the codeposition with applied potential is due to the variation of the hydration force with potential. This assumption could not be verified in this work in view of the limited resolution of the AFM. However, our results do demonstrate that the surface forces vary considerably with applied potential, even in highly concentrated electrolytes. Hence, it is very likely that the surface immobilization of particles in codeposition is a function of applied overpotential. Acknowledgment. C. Dedeloudis thanks the European Commission for a Marie-Curie Fellowship (Contract No. ERBFMBICT961034). J. Fransaer wishes to thank FWO Vlaanderen for their financial support. Part of this research was done within the IUAP P4/33 contract funded by the Belgian government and the G.0337.98 contract funded by FWO Vlaanderen.

Figure 7. Force vs separation curves measured at open circuit potential in a 0.1 M MgSO4 solution of pH 5.8 and 23 °C, between a silica sphere and a copper electrode 9-before polarization, b-immediately after polarizing cathodically for 3 min at 300 mV, and 2-5 min after polarizing the copper electrode cathodically for 3 min at 300 mV.

potential before any cathodic overpotential was applied (Figure 7). On polarizing the copper electrode slightly anodically (anodic overpotential of 50 mV), the transition in the force curve from attraction to repulsion is instantaneous. This means that under anodic conditions, the oxygen layer forms immediately on the surface of copper.35 Therefore, the formation and removal of the oxygen layer on copper in MgSO4 solutions is reversible, but the kinetics of both processes are very different. Conclusions The surface force between copper and silica in concentrated 0.01 and 0.1 M MgSO4 solutions at pH 3.4 depends on the electrode potentials. Specifically, the surface force between silica and copper is attractive at potentials between the open circuit potential and the potential of zero charge of the copper electrode, and repulsive at lower overpotentials. This indicates that, despite the high ionic strength of the MgSO4 solutions, the interaction between silica and copper is dominated by the electrostatic double layer interaction and not by the van der Waals force. Similar effects were observed previously in diluted electrolytes for noble metals such as gold and platinum. At pH 5.8, the surface force between silica and copper is repulsive at the open circuit potential. The reason for this phenomenon is the formation of a chemically adsorbed oxygen layer on the surface of copper, which results in a negative surface charge. This oxygen layer can be removed by a cathodic polarization or by lowering the pH. After the removal of that oxygen layer, the surface force between copper and silica becomes attractive and is identical to the one measured at pH 3.4. Our results demonstrate the suitability of the AFM for the characterization of electrode/electrolyte interfaces, even in highly concentrated electrolytes. This makes this technique useful in processes involving short distance interactions between particles and metal electrodes immersed in concentrated electrolytes as occurs, e.g., in the composite plating process. The codeposition of alumina and polystyrene particles with copper was reported in the literature to reach a maximum at the point of zero charge of the electrode.1,35 These results cannot be explained by the variation of the double layer force with potential that we have observed in this work. Therefore it was assumed in ref 1 that

References and Notes (1) Fransaer, J.; Celis, J. P.; Roos, J. R. J. Electrochem. Soc 1992, 139, 413. (2) Israelachvili, J. N.; Adams, G. E. J. Chem. Soc., Faraday Trans. 1 1992, 74, 975. (3) Binnig, G.; Quate, C. F.; Gerber, C. Phys. ReV. Lett. 1986, 56, 930. (4) Pashley, R. M. J. Colloid Interface Sci. 1981, 83, 531. (5) Pashley, R. M.; Israelachvili, J. N. Colloids Surf. 1981, 2, 169. (6) Claesson, P. M.; Herder, P. C.; Rutland, M. W.; Waltermo, Å.; Anhede, B. Prog. Colloid Polym. Sci. 1992, 88, 64. (7) Pashley, R. M.; Ninham, B. W. J. Phys. Chem. 1987, 91, 2902. (8) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Langmuir 1992, 8, 1831. (9) Hartley, P. G.; Larson, I.; Scales, P. J. Langmuir 1997, 13, 2207. (10) Ducker, W. A.; Xu, Z.; Clarke, D. R.; Israelachvili, J. N. J. Am. Ceram. Soc. 1994, 77, 437. (11) Hillier, A. C.; Kim, S.; Bard, A. J. J. Phys. Chem. 1996, 100, 18 808. (12) Raiteri, R.; Grattarola, M.; Butt, H.-J. J. Phys. Chem. 1996, 100, 16 700. (13) Campbell, S. D.; Hillier, A. C. Langmuir 1999, 15, 891. (14) Frumkin, A. Phys. Z. Sowjetunion 1933, 4, 239. (15) Guy, G. Ann. Phys., Paris 1916, 6, 3. (16) Voropoeva, T. N.; Deryaguin, B. V.; Kabanov, B. N. Dokl. Acad. Nauk. USSR 1963, 133, 257. (17) Jakuszewski, B.; Koslowski, Z. Roczn. Chem. 1962, 36, 1873. (18) Vorsina, M.; Frumkin, A. N. Dokl. Akad. Nauk. USSR 1939, 24, 918. (19) Brenner, H. Chem. Eng. Sci. 1961, 16, 242. (20) Pailthorpe, B. A.; Russel, W. B. J. Colloid Interface Sci. 1982, 89, 563. (21) Dzyaloshinskii, I. E.; Lifshitz, E. M.; Pitaevskii, L. P. AdV. Phys. 1961, 10, 165. (22) Hogg, R.; Healy, T. W.; Fuerstenau, D. W. Trans. Faraday Soc. 1966, 62, 1638. (23) Pashley, R. M.; Israelachvili, J. N. J. Colloid Interface Sci. 1984, 97, 446. (24) Pashley, R. M.; Quirk, J. P. Colloids Surf. 1984, 9, 1. (25) Pashley, R. M. AdV. Colloid Interface Sci. 1982, 16, 57. (26) Shubin, V. E.; Ke`kichef, P. J. Colloid Interface Sci. 1993, 155, 108. (27) Hunter, R. J. Foundations of Colloid Science, 1st ed.; Clarendon Press: London, 1995; Vol. 1, p 326. (28) Bockris, J. O’M.; Khan, S. U. M. Surface Electrochemistry: a Molecular LeVel Approach, 1st ed.; Plenum Press: New York, 1993; p 69. (29) Sugenova, M. I.; Alekseeva, R. A.; Kuznetsov, V. A. Russian J. Electrochem. 1980, 16, 924. (30) Gileadi, E.; Argade, S.; Bockris, J. O’M. J. Phys. Chem. 1966, 70, 2044. (31) De Boer, J. H.; Verwey, E. J. Rec. TraV. Chim. 1936, 55, 675. (32) Hurd, R. M.; Hackerman, N. J. Electrochem. Soc. 1956, 103, 316. (33) Knapen, W. Kinetics of Electrochemical Nucleation. Ph.D. Thesis, Universiteit Utrecht, Utrecht, 1998; p 30. (34) Pourbaix, M. Atlas of Electrochemical Equilibria in Aqueous Solutions, 2nd ed.; NACE Cebelcor: New York, 1974; p 385. (35) Celis, J.-P.; Roos, J. R.; Buelens, C. J. Electrochem. Soc. 1987, 134, 1402.