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Elastic Electrocapillary Properties of Polycrystalline Gold Gintaras Valincius Vilnius University, Naugarduko 24, Vilnius 2006, Lithuania Received April 17, 1998. In Final Form: July 10, 1998 To establish the applicability of the classical Lippmann electrocapillary equation to a polycrystalline gold electrode, the measurements of the derivative of the surface tension (stress) with respect to charge density (q-estance) have been performed. Measurements were carried out in the solutions of the surface inactive perchlorate anions. For all investigated systems, the estansograms revealed characteristic negative shift of the potential of electrocapillary maximum with respect to the potential of zero charge of the polycrystalline gold electrode found by measurements of the differential capacity. The shift suggests the modified (by A. Gokhshtein) electrocapillary equation - ∂γ/∂E ) q + ∂q/∂ should be used instead of the classical one. The second term in the modified equation appears due to the variation of the charge density of the solid electrode during the elastic stretching process. This term is positive and almost constant for gold electrode near the potential of zero charge and in the potential range E < Epzc. In this potential range, a positive term could be associated with the influence of the elastic stretching on the electronic dipole layer charge density of gold. At the potentials positive of Epzc, a second term strongly depends on both concentration of perchlorate anions and pH. This suggests that perchlorate anions appreciably influence structure of the double layer in this potential region.
elastic and purely plastic terms
Introduction A number of physical and physicochemical properties of liquids and solids are appreciably different. One of such property very important for the electrochemical field of research is energy of the formation of the new surface area. For liquids there is only one way of changing surface area. It is a process of extraction of atoms or molecules from the bulk of the liquid to the surface. An amount of energy per unit of the newly formed surface is called specific superficial energy. It could be measured by using well-known techniques.1 The situation for solids is different. The surface area of solids may be changed by means of elastic or/and plastic process. Breaking a solid may also produce the new surface. It is obvious that atomic level phenomena are very different in these processes. These processes may be written in the following sequence:
γ ) (p/tot)σ + (e/tot)f
(2)
equally as generalized surface intensive parameter γ are path-dependent quantities, which may obtain different values in different experiments. Couchman et al.,2-4 considering partially elastic and partially plastic processes, proposed to divide γ into purely
where tot denotes total surface strain p and e denote respectively plastic and elastic contributions to the total strain. The quantity σ is called the superficial work.5 The meaning of σ becomes clear if one assumes for a solid that (p/tot) f 1 in a hypothetical solely plastic process. In this case, γ ≡ σ. Following Linford,5 this is a process in which “the number of molecules in the surface region has changed but the area per surface molecule has not”. It is obvious that a solid in such a process would possess the properties of a liquid of very high viscosity. In the opposite extreme case, when (e/tot) f 1, “the number of molecules in the surface region ... remains constant but the area occupied by each molecule differs...”.5 In this case, γ ≡ f. The quantity f, now called surface stress, is the mechanical resistance of the surface of tension to the elastic stretching process.3,5 Both quantities, σ and f, are path independent, while γ becomes path dependent due to uncertain contributions of the plastic and elastic strains to the total strain in the particular experiment. It means that only results of the experiments, in which fully elastic conditions are maintained, could be unambiguously interpreted. The numerical value of γ, in this case, is equal to the force applied to the unit of the perimeter of the solid that should be applied to it in order to compensate all possible stresses of the surface. The tension of the surface is in equilibrium with this force and is measured by it.6 According to Gibbs, “... the tensions of the surface, thus determined, may evidently have different values in different directions, and are entirely different from the quantity which we denote by σ, which represents the work required to form a unit of the surface by any reversible process, and is not connected with any idea of direction”.6 Thus, in general, f is a tensorial property, but for the polycrystalline
(1) Adamson, A. W. Physical Chemistry of Surfaces, 3rd ed.; WileyInterscience: New York, 1976. (2) Couchman, P. R.; Jesser, W. E.; Kuhlmann-Wilsdorf, D.; Hirth, J. P. Surf. Sci. 1972, 33, 429. (3) Couchman, P. R.; Jesser, W. E. Surf. Sci. 1973, 34, 212.
(4) Couchman, P. R.; Everett, D. E. J. Electroanal. Chem. 1976, 67, 382. (5) Linford, R. G. Chem. Rev. 1978, 78, 81. (6) Gibbs, J. W. The Collected Works of J.Willard Gibbs, Vol.1, Thermodynamics; Longmans, Green and Co: New York, 1928.
elastic limit
elastic stretching 98 breaking point
plastic stretching 98 cleavage All right-side processes could not be performed without left-side processes. However, left-side processes could be performed without right-side processes. In many cases, one cannot accurately define what kind of stretching is dominant and what the contributions of the elastic and plastic strains are in a particular experiment. For this reason, the total reversible surface work dW required to affect an infinitesimal area change dΩ
dW ) γ dΩ
(1)
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surfaces, it could be regarded as scalar. Nevertheless, this scalar “... quantity depends on the work spent in stretching the surface, while the quantity σ depends on the work spent in forming the surface”.6 The property f depends on strain e. Under elastic conditions:2-4
γ ≡ f ) σ + (∂σ/∂e)P,T,n
(3)
where T is temperature, P is pressure, and n is the number of particles on the surface. An equation of the form of eq 3 first was derived by Shuttleworth7 for a general case. Equation 3 is the most important one because it reveals a major difference between the properties of the solid and liquid surface. All solids should possess nonzero values of the second term in eq 3. On the contrary, for liquids (ideally plastic material) the identity γ ≡ σ is always valid5 (except for very high strain rates and a very small radius of the liquid droplet8). Introducing the Lippmann equation1,5
-∂σ/∂E ) q
(4)
where E is the potential and q is the surface charge density of the solid, into eq 3, one obtains an electrocapillary equation of the ideally elastic solid surface
-(∂γ/∂E)e ) -∂σ/∂E - ∂/∂E(∂σ/∂e)E,P,T,n ) q + (∂q/∂e)E,P,T,n (5) Equation 5 first was derived by Gokhshtein.9 An explicit derivation of eq 5 is presented in the Appendix. It was shown9-11 by him that an additional relationship related to eq 5 is valid for an ideally elastic surface:
(∂γ/∂q)e ) (∂E/∂e)q
(6)
Gokhshtein proposed9,10,12,13 an original experimental technique that allows one to measure derivatives ∂γ/∂E and ∂γ/∂q under elastic conditions. Quantities ∂γ/∂E and ∂γ/∂q are related by the simple relationship
∂γ/∂E ) ∂γ/∂q × dq/dE ) ∂γ/∂q × Cd
(7)
where Cd is the differential capacity of the solid/liquid electrolyte interface. He called these derivatives respectively E-estance and q-estance. As noted by Parsons,14 these terms were derived from “elasticity” by analogy with “impedance”. Another method proposed by Gokhshtein9-11 allows one to measure periodic oscillations of the potential of periodically stretched solid electrode under elastic conditions, i.e., derivative ∂E/∂e of eq 6. Despite different experimental techniques, curves ∂γ/∂q vs E and ∂E/∂e vs E are identical in an electrochemical system Pt/H+ in which the second term of eq 5 is dominant.9,10 Essentially, these (7) Shuttleworth, R. G. Proc. Phys. Soc. (London) 1950, A63, 444. (8) Vermaak, J. S.; Mays, C. W.; Kuhlmann-Wilsdorf, D. Surf. Sci. 1968, 12, 134. (9) Gokhshtein, A. Ya. Surface tension of Solids and Adsorption; Nauka: Moscow, 1976. (10) Gokhshtein, A. Ya. Russ. Chem. Rev. 1975, 44, 921. (11) Gokhshtein, A. Ya. Dokl. Akad. Nauk SSSR 1969, 187, 601; 1971, 200, 620. (12) Gokhshtein, A. Ya. Elektrokhimiya 1966, 2, 1318. (13) Gokhshtein, A. Ya. Electrochim. Acta 1970, 15, 219. (14) Parsons, R. In Comprehensive Treatise of Electrochemistry; Bockris, J. O’M., Conway, B. E., Yeager, E., Eds.; Plenum Press: New York and London, 1981; Vol. 1, p 1.
results may be considered as the first experimental verification of eqs 3, 5, and 6 for elastically stretched solid surfaces. A very important conclusion emerges from eq 5. Contrary to liquids, the potential of zero charge, Epzc, of solid electrodes does not necessarily coincide with a potential of electrocapillary maximum Eecm (potential of estance zero). The magnitude and the sign of Eecm shift vs Epzc should depend on the magnitude and sign of the second term in eq 5. From the great variety of the experimental techniques proposed to measure the generalized surface intensive parameter γ, only several may be considered as measurements performed under purely or, at least, partially elastic conditions. (It is obvious that all methods based on cleavage, scratching, scrape methods, etc.15-18 cannot be assigned to this group.) Besides the already mentioned Gokhshtein estance method, one should mention an extensometer method proposed by Beck,19,20 a method proposed by Bockris and co-workers,21,22 and a method used by Bard and co-workers23 and Seo and co-workers.24,25 The last methods are modified versions of the Gokhshtein method. Recently developed by Lang and Huesler,26-28 an interferometric technique equally as a scanning tunneling microscopy (STM) technique used by Ibach and co-workers29 and Haiss and Sass30,31 also could be assigned to this group of methods. However, even results of this group of the experimental techniques are greatly inconsistent. For example, the potential of electrocapillary curve maximum of polycrystalline gold was found to be not coinciding with a potential of zero charge when using the estance method9 and extensometer method.19,20,32 Methods in which measurements have been performed using thin sputtered gold films21,22,26-28 show that Epzc ≈ Eecm. It is worth noting that evidently nonelastic measurements often demonstrate closeness of Epzc to Eecm.15-18 The results obtained by use of the STM technique29 show no extremums of the surface stress curves in the potential range where the Epzc should be expected. A very flat region of the dependency ∆γ,E has been observed for the Au(100) surface in the potential interval between -0.14 and 0.10 V. The STM measurements in refs 30 and 31 have been performed in a quite complex electrochemical system, which involves an underpotential deposition process and coadsorption of halide ions. Nevertheless, in these papers,29-31 the authors reported the apparent thermodynamic inconsistencies between the Lippmann equation and their experimental results. (15) Noninski, Kh. I.; Lazarova, E. M. Elektrokhimiya 1975, 11, 1103. (16) Perkins, R. S.; Livingstone, R. C.; Anderson, T. N.; Eyring, H. J. Phys. Chem. 1965, 69, 3329. (17) Bode´, D. D.; Andersen, T. N.; Eyring, H. J. Phys. Chem. 1967, 71, 792. (18) Frumkin, A. Potentials of Zero Charge; Nauka: Moscow, 1979. (19) Beck, T. R. J. Phys. Chem. 1969, 73, 466. (20) Lin, K. F.; Beck, T. R. J. Electrochem. Soc. 1976, 123, 1146. (21) Fredlein, R. A.; Damjanovic, A.; Bockris, J. O’M. Surf. Sci. 1971, 25, 261. (22) Fredlein, R. A.; Bockris, J. O’M. Surf. Sci. 1974, 46, 441. (23) Malpas, R. E.; Fredlein, R. A.; Bard, A. J. J. Electroanal. Chem. 1979, 98, 171; 1979, 98, 339. (24) Seo, M.; Aomi, M.; Yoshida, K. Electrochim. Acta 1994, 39, 1039. (25) Seo, M.; Ueno, K. J. Electrochem. Soc. 1996, 143, 899. (26) Jaeckel, L.; Lang, G.; Heusler, K. E. Electrochim. Acta 1994, 39, 1081. (27) Lang, G.; Heusler, K. E. Elektrokhimiya 1995, 31, 826. (28) Lang, G.; Heusler, K. E. J. Electroanal. Chem. 1995, 391, 169. (29) Ibach, H.; Bach, C. E.; Giesen, M.; Grossmann, A. Surf. Sci.1997, 375, 107. (30) Haiss, W.; Sass, J. K. J. Electroanal. Chem. 1995, 386, 267; 1996, 410, 119. (31) Haiss, W.; Sass, J. K. Langmuir 1996, 12, 4311. (32) Lin, K. F. J. Electrochem. Soc. 1978, 125, 1077.
Properties of Polycrystalline Gold
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The results of Beck19 and Lin20,32 are extremely interesting because they found that the value of Eecm of gold is always more negative compared to the value of Epzc obtained by using a differential capacitance method.33 This trend was observed independently of the nature of electrolyte (SO42-, ClO4-, NO3-, or halide anions).20,32 Unfortunately, the authors assigned the value of Eecm found in their experiments to the value of Epzc. Therefore, this “discrepancy” was not explained until now.20,27,28 This has prompted us to perform the investigations reported here. The main objective of the present study was to determine the applicability of a modified Lippmann eq 5 to elastically stretched solid electrodes. We have performed simultaneous measurements of differential capacitance and electrocapillary curves under elastic conditions and under the same all other experimental conditions. The comparison of the data of two different experiments for the same electrochemical system allowed us to evaluate the magnitude of the second term in eq 5 equally as applicability of eq 5 to the particular system. Gokhshtein’s method was chosen to measure surface tension because infinitesimal strains (lower than 10-8) are ensured in this technique. On the other hand, an electrochemical system for which most reliable experimental values of Epzc are known should be chosen. One of such system is Au(polycrystalline)/perchlorate solution.33 Additionally, we will try to explain possible reasons that may cause nonzero values of the second term (∂q/∂e) in eq 5. As will be shown, the nonzero values of this derivative should be a rule rather than exception for solid surfaces if experimental conditions are close to purely elastic. Further in the text of the paper we shall use shorter notations of these quantities: γE for (∂γ/∂E)e, γq for (∂γ/ ∂q)e, and q for (∂q/∂e)E,P,T,n. Experimental Section The device that converts the surface tension force to ac voltage is shown in Figure 1. It consists of a piezoelectric plate holder, a bipolar piezoelectric plate, and a working electrode with its holder. The bipolar piezoelectric plate (BPP) was made from two identical lead zirconate titanate plates (Gzhel, Russia) covered with silver foil which served as the electrodes. The plates were glued together (with epoxy) in a +-/+- configuration. The outer electrodes of BPP were shorted with each other and connected to ground. One of the upper corners of the BPP was inserted into the gap of its holder and glued with epoxy, the inner electrode was connected through a screw in the holder to the input of a narrow-band amplifier U2-9 (Russia). An output of the narrow-band amplifier was connected to the linear detector and phase-shift meter F2-16 (Russia). Output signals from these devices were directed to either an X-Y recorder N307 (Russia) or analog-digital converter FP4434 (Vikama Co, Lithuania). Thus the potential dependencies of |γq| or arg γq could be recorded in the form of an X-Y diagram or stored in a digital form. A major concern is the minimization of cross talk between the BPP and the electrochemical cell, which has an appreciable ac voltage between auxiliary and working electrodes during experiments. The outer electrodes of the BPP acted as electric shields which minimized spurious electromagnetic pick up of the modulating potential (cross-talk signal). In addition, the bottom portion of the BPP was glued into the gap of a circular grounded metallic (nonmagnetic) plate, which provided additional electromagnetic shielding of the BPP. The working electrode was made from a 0.25 mm thick gold plate (99.99%) with dimensions 25 × 5 mm. The dimensions of the lower part of the L-shaped electrode were 5 × 5 mm. Only this part of the electrode was in contact with electrolyte solution. The contact was through a meniscus, which extended 1-2 mm (33) Clavilier, J.; Van Houng, N. J. Electroanal. Chem. 1973, 41, 193; 1977, 80, 101.
Figure 1. Scheme of the device that converts surface tension force to the ac voltage. over the surface of the liquid. The variation of the height of the meniscus in the interval 0-2 mm caused variation of the sensitivity of the converter by some 10-20%. The height of the meniscus did not appreciably influence the position of the mechanical resonance frequency. The working electrode was fixed into the gap of its holder with a small screw. A contact wire was inserted between the inner wall of the gap of the holder and the electrode. The electrode’s holder was mounted on a metallic rod (approximate diameter 1 mm). This rod was mechanically (not electrically) connected to the lower part of the circular plate of the BPP. The radial position of the working electrode’s holder with respect to the symmetry plane of the BPP appreciably affected both the sensitivity and the position of the resonance frequency of the device. Optimal position was found empirically. The conversion of the surface tension at the electrode surface (meniscus contact) into a voltage of the piezoelectric plate takes place in the following manner. The elastic surface tension force is a function of the potential of the working electrode; thus, an alternating potential applied to the working electrode induces an oscillatory variation of the surface tension force. The surface tension force leads to mechanical deformations of the electrode which in turn lead to minute deformations of the BPP. The amplitude of the mechanical deformations is very small and usually cannot be detected by BPP. However, the whole mechanical system shown in Figure 1 exhibits several (usually three to five) mechanical resonances in the frequency range 0.520 kHz. At these frequencies, the mechanical system is in resonance with an applied periodic force and the amplitude of oscillation of BPP becomes very large compared to nonresonance oscillations. The output amplitude and phase of BPP are proportional to the amplitude and the phase of the surface tension force. In practice, we have performed measurements at the resonances where the BPP output signal was not less than 10
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µV, when the modulated surface charge amplitude was 10 µC/ cm2 and the γq value was 1 V. In all our experiments, the electromagnetic cross-talk signals were lower than 0.5 µV, as measured at frequencies some 10% below and above the resonance frequency. Though the amplitude of the oscillation of the whole mechanical system is large, the amplitude of periodic strain of the working electrode is very small. The amplitude of the periodic strain of the working electrode, which is in contact with a solution of electrolyte, can be estimated as follows. The dimensions of the L-shaped portion of the working electrode are 5 × 5 × 0.25 mm. Assuming 1 V for the magnitude of γq (this corresponds to γE value of 50 µC/cm2, if the double layer capacity CD is 50 µF/ cm2) and 10 µC/cm2 for the modulation charge density, the amplitude of the surface tension force is estimated as 0.001 N/cm. The unidirectional longitudinal strain, ∆, of the plate can be calculated in accordance with Hook’s law:
∆ ) (1/EY)F/A where EY is Young’s modulus (EY(Au) ) 8.06 × 1010 N/m2 34), A is the cross-sectional area of the plate (A ) 0.005 × 0.00025 ) 1.25 × 10-6 m2 ), and F is the force normal to the cross-sectional plane of the plate (F ) 0.1 × 0.005 ) 5 × 10-4 N). The sideways contraction may be ignored in an approximate calculation. Substituting these values into the equation, one find an approximate value of the strain ∆ ) 5 × 10-9. This value is far below the elastic limit of real metals. This means that the conditions Ω ) const, tot f 0, and tot ) e are fulfilled in an estance experiment. As seen from Figure 1, the mechanical system, which converts surface tension force to electrical signal, is quite complex. To obtain absolute values of γq or γE an additional calibration of the sensitivity of the device has to be carried out. Gokhshtein9,10 proposed several ex situ calibration methods, which were used by other investigators.23 He also emphasized that properties of the electrochemical system themselves could be used to find calibration coefficients KE and Kq for quantities γE and γq:
KE ) UE/γE
(8)
Kq ) Uq/γq
(9)
where UE and Uq are correspondingly the E- or q-modulated response of the BPP. It was shown9 that in an electrochemical system where the potential of estance zero Eecm coincides with the potential of zero charge Epzc, and when q ) 0, the slope of γq, E curve converges to value -1 as the concentration of 1,1-valent electrolyte decreases to 0. This fact could be used to calculate coefficient Kq. In this paper, we shall describe a more general, in situ method of calibration, which is not associated with condition q ) 0. This method will be discussed further in the discussion section as it is related to the topic of our investigation. In our experiments, we measured q-estance, i.e., the derivative γq. The quantity γE was obtained by multiplying γq by the differential capacity CD (eq 7) at the corresponding potential of the working electrode. The values of CD were calculated from the electrochemical impedance data in the frequency range 2035 Hz. However, estance measurements in this work were carried out in the frequency range 800-15000 Hz. The parameter CD in essence is a physical property of the interface and it does not depend on frequency (in the case of an ideally polarized electrode). Nevertheless, the actual value of CD calculated from impedance data at different frequencies may exhibit some frequency dispersion due to the roughness (inhomogeneity) of the electrode. This possible influence of the CD dispersion is encountered in the calibration of coefficients Kq and KE. Two auxiliary Pt electrodes were used in the experimental set. One electrode was connected to the output of the custombuilt potentiostat, which maintained a constant or linearly changing value of the working electrode’s potential. Another auxiliary electrode was connected via a 1 µF capacitance to the output of sinusoidal ac generator G6-28 (Russia). ac and dc (34) Tables of Physical Quantities. A handbook; Kikoin, I. K., Ed.; Atomizdat: Moscow, 1976.
circuits were separated by using a custom-built low-frequency second-order filter (time constant 0.08 s). In this work, the working electrode was grounded in all experiments. The electrochemical cell was made from Pyrex glass. It was washed with a hot mixture of concentrated H2SO4 and H2O2 solutions (1:3). The working electrode was successively boiled in a 20% KOH solution (5 min) and then heated in a 96% H2SO4 at temperature 150-160° C (5 min). No polishing of the working part of the electrode was carried out in experiments. All solutions were prepared by using triply distilled water. The second distillation was carried out from acidic (≈1% H2SO4) solution of KMnO4 (≈1%). The third distillation was done in all-quartz equipment. Water was stored in quartz vessel no longer than 12 h before the start of each experiment. Specific conductance of the water was Epzc, variation of term q with the electrode potential is more pronounced as well as more complex. Possible Reasons of Nonzero Values of Term qE. Figure 8 shows that term q is almost independent of potential in the range E < Epzc. It is not surprising because in this potential range no contact adsorbed ions are present on the surface of the electrode. We suppose there are only two reasons that may cause nonzero values of term q in this potential range. The first reason is related to the presence of the electronic double layer at the metal surface. The latter arises due to the electronic spillover at the surface.48 The electronic double layer is fully elastic by nature. This is because positive ion cores of the metal belong to the metallic phase and the total number of them does not vary during elastic stretching. The following equation may be written for the electronic double layer contribution to the term q
q ) ∂q/∂e ) ∂(qe + qion)/∂e ) ∂χM/∂e × ∂qe/∂χM ) ∂χM/∂e × CM (16) where qe is the charge density of the electronic dipole layer, qion is the ionic charge density of the electrode, χM is the surface potential of the metal in contact with electrolyte solution caused by an inhomogeneous charge distribution at the surface, and CM is the metal contribution to the Helmholtz capacity, which also contains the effect of the metal solvent coupling through the distance of the closest approach of the solvent molecules to the surface and its variation with the charge density.49 Ionic charge density qion turns to zero at the Epzc in the solutions of surface inactive electrolytes, but electronic charge density qe never turns to zero. Also, the partial derivative ∂qion/∂e ) 0 because ionic countercharge is located in an ideally plastic media: liquid solution. Equation 16 allows one to evaluate the sign of the electronic dipole layer contribution to the term q of electrocapillary eq 5. The moment of the electronic dipole layer is always directed with its positive end toward the bulk of the metal. This means that the partial derivative ∂χM/∂e should be always negative. On the other hand, metal contribution to the Helmholtz capacity (CM) of the electrode is always negative.48 That is why the electronic contribution qe to the term q as well as to the eq 5 should be always positive. In other words, one can always expect a nonzero and positive value of the term q of the electrocapillary eq 5 if electronic contribution qe to the term q is the only one. Additionally, in such a case the potential of electrocapillary maximum of all solid metals should not coincide with the potential of zero charge. The former should be shifted negatively with respect to the latter as was observed in present work for the polycrystalline gold electrode. It is worth to consider the possible magnitude of the contribution qe and to compare these values with ones obtained in present experiments. As seen from eq 16, quantity qe is a product of two multipliers. Theoretical treatment using the jellium model and its extensions yields absolute values of metal capacity CM and describes variation of this quantity with the charge density of the electrode.48,49 The theoretical calculations predict the appearance of the maximum of the absolute value of CM (48) Schmickler, W. Chem. Rev. 1996, 96, 3177. (49) Amokrane, S.; Badiali, J. P. J. Electroanal. Chem. 1989, 266, 21.
Valincius
as well as the maximum of the distance of closest approach of the solvent molecules to the jellium edge at more negative potentials with respect to Epzc, when interactions between metal and solvent molecules are taken into account.49 The point of the maximum of |CM| and the distance of closest approach lie in the vicinity of electrode charge density ca. -5 µC/cm2. As already noted, the not strongly pronounced maximum of q also is observed in this range of charge density (Figure 8A-C, curves 2). Unfortunately, the second multiplier in eq 16 that expresses variation of the surface potential with elastic strain was not considered in the literature yet. Still, there is a possibility to calculate the approximate values (at least order of magnitude) of the surface potential drop by using present experimental data and to compare them with the theoretical calculations of the surface potential of metals. As the electronic dipole layer is fully elastic by nature, the following equation should be valid
Qe ) qeΩ where Qe is total charge of the electronic dipole layer and Ω is an area of the metal surface. The differential form of the equation is
dQe ) qe dΩ + Ω dqe
(17)
During the elastic stretching process, the total number of the positive ion cores and free electrons maintains constant in the surface region. That is why dQe ) 0. Then, from eq 17 follows:
qe ) Ω dqe/dΩ ) ∂qe/∂ ) - qe
(18)
Equation 18 means that electronic contribution to the term q numerically is equal to the charge density of the electronic dipole layer. Here we must take notice of the sign of the quantity qe. It should be negative despite the fact that the positive end of the surface dipole is located at the bulk side of the metal. It may seem somehow confusing from the classical electrochemical point of view. This is because from the classical point of view the negative charge at the solution side (outside metal) means a positively charged metal. But, in accordance to the classical model of the charged interface two kinds of charge carriers take place in the formation of double layer: electrons inside the metal and ions outside the metal. Variation of the concentration of electrons inside the metal always leads to variation of the concentration of ions outside the metal and to variation of the corresponding parameters of the classical double layer, while only one kind of charge carrier takes place in the formation of the metal surface double layer: free electrons. In addition, the variation of only their surface density changes the parameters of the electronic double layer. The same reason causes also the negative values of the metal capacitance CM. If the electronic surface dipole layer is the only reason that causes nonzero values of q in the potential range E < Epzc, one may evaluate the magnitude of the electrostatic potential drop across the electronic double layer. It could be done by using classical electrostatics
χM ) - l qe/0 ) l q/0
(19)
where 0 is vacuum permittivity and l is the dipole charge separation distance. The latter parameter is not known for gold. Nevertheless, it is known from the jellium theory
Properties of Polycrystalline Gold
that decay of the electronic density at the metal surface occurs over a distance of 1-2 Å in the case of a metalvacuum interface. According to Schmickler, the presence of the dielectric media near metal leads to a significant decrease of the effective image plane.48 The latter in its turn should diminish dipole charge separation distance. That is why a realistic value of 1 Å for parameter l could be chosen for the approximate calculation of the surface potential χM. Substituting q ) 11 ( 1 µC/cm2 (the most precisely known value of q at the potential of estance zero Eecm), 0 ) 8.85 × 10-12 F/m, and l ) 10-10 m into eq 19, one may find a value of χM ) 1.2 ( 0.1 V. The value of χM at Epzc is a little bit lower 1.1 ( 0.1 V (Figure 8). It is evident that the obtained order of magnitude of χM is correct despite the fact that the value of l was chosen rather arbitrarily.50 The second reason, which may cause the nonzero value of the term q, is the presence of the elastic layer of adsorbate on the surface of metal. The elastic layer should be a layer of adsorbate in which the number of adsorbed particles does not vary in an elastic stretching process but the area per particle does vary. It is obvious that such layer could be formed when the chemical bond between adsorbate and adsorbent is established. On the contrary, when formation of the adsorbate layer is due to weak physisorptive interactions, the properties of the layer should be plastic. A number of recent experimental results show that formation of the chemical bond between water molecules and the gold surface is unlikely in the potential range E < Epzc. For example, no electrode mass variation with potential was observed in this region using the electrochemical quartz microbalance technique.51,52 Results of the potential-dependent infrared spectroscopy method show that water molecules at the surface of gold easily reorient when the potential is changed within the doublelayer region.53 Moreover, potential-induced reorientation was observed only in acidic solutions while no reorientation was observed in neutral solutions. According to authors, protonation of the surface water molecules would result in a reorientation from the oxygen-down to oxygen-up position.53 This means that interaction energy between water molecules and the gold surface is of the same order as energy of hydrogen bonding. Therefore, one can rule out possible direct contribution of the solvent layer to the term q at least in the potential range E < Epzc. Of course, concrete orientation of water molecules may influence both the magnitude and dependence of electronic contribution on potential. A rather more complex variation of the term q is observed in the range E > Epzc. As seen from Figure 8A (curve 2), in acidic solution a small initial increase is followed by a decrease some 0.25 V positive of Epzc and subsequent change of the sign of q. This suggests that negative contribution in q appears and starts growing. Negative q means that on the gold surface an elastic layer of adsorbate oriented with its negative dipoles end toward solution appears. Such a layer could be formed by chemisorbed water molecules. Indeed, it was revealed recently54 by using the surface-enhanced Raman spec(50) Desjonqueres, M. C.; Spanjaard, D. Concepts in Surface Physics; Springer-Verlag: Berlin, Heidelberg, 1993. (51) Gordon, J. S.; Johnson, D. C. J. Electroanal. Chem. 1994, 365, 267. (52) Kautek, W.; Sahre, M.; Soares, D. M. Ber. Bunsen-Ges. Phys. Chem. 1995, 99, 667. (53) Parry, D. B.; Samant, M. G.; Seki, H.; Philpott, M. R. Ashley, K. Langmuir 1993, 9, 1878. (54) Ataka, K.; Yotsuyanagi, T.; Osawa, M. J. Phys. Chem. 1996, 100, 10664.
Langmuir, Vol. 14, No. 21, 1998 6317
troscopy (SERS) technique that a layer of water molecules partially hydrogen bonded to the water molecules from the adjacent solvent layer is present on the gold surface in this potential range in the solution of 0.5 M HClO4. Variation of pH value and composition of the solutions strongly influences q, E dependency at E > Epzc (parts A, B, and D of Figure 8). At higher pH, q starts growing instead of decreasing. It means that net dipole moment of the chemisorbed layer becomes positively oriented toward solution. The concentration of the perchlorate ions is another factor that influences q, E dependencies. As seen from parts B and C of Figure 8, despite lower pH, term q grows more strongly as concentration of ClO4- is decreased. This suggests that perchlorate ion traditionally accepted as weakly specifically adsorbing ion noticeably influences the structure of double layer at E > Epzc. Again, this fact is in agreement with SERS observations,54 according to which perchlorate is present on the gold surface in the form of a surface complex of C3v or C2v symmetry. The measurements of estance also agree well with the results of the quartz microbalance technique, which indicated appreciable increase of the gold electrode mass in this potential region.51,52 Therefore, one may conclude that, despite of relatively small charging current flow observed in voltammograms (Figure 2, region VI), chemisorption processes take place at E > Epzc in the solutions of perchlorates. As seen from Figure 8, at most positive potentials term q becomes (or tends to become) negative in all solutions. It seems that the negative value of q is a general property of oxidized surfaces of all metals. This is because all oxide layers on the metallic surfaces exhibit a negatively outward oriented dipole layer. Comparison with Other Systems. On the surface of every metal, there exists an electronic double layer. This prompts the supposition that the Eecm value of every metal should be more or less shifted negatively with respect to its Epzc. However, there are a number of low melting point metals for which no shift (type I estansogram) was experimentally observed. First, it should be noted that for these metals both values of Eecm and values of Epzc strongly depend on electrode pretreatment. For example, if the surface of the Pb electrode was oxidized prior to surface tension measurements, type I estansogram turns into type III estansogram.9 In addition, even type I estansograms of Bi and Tl are unnaturally asymmetric. The cathodic branch of the estansograms rapidly grows as the potential becomes more negative while the growth of the anodic branch ceased within some 0.1 V positive of Eecm and the modulus of the estansogram starts to decrease. The situation is quite different in the case of gold. One can see that growth of the gold estansogram proceeds up to approximately +0.7 V in acidic solution (Figures 4A-C and 5). In addition, the potential of the estansogram maximum depends on the pH value of the solution (Figure 4D). This leads to the conclusion that, as in the case of gold, the cease of the growth of estansogram of the low melting point metals is due to the early stage of oxidation of the surface, which in the latter case starts near the potential of zero charge. This means that the second term of the electrocapillary equation could possess appreciable negative contribution from the oxidation of the surface of low melting point metals even at the Epzc. The latter negative contribution may to some extent compensate positive electronic double layer contribution, and consequently, one could not observe significant shift of Eecm vs Epzc. Of course, precise and simultaneous measurements of the estansograms and double layer capacity in the systems involving low melting point metals
6318 Langmuir, Vol. 14, No. 21, 1998
would provide a more clear picture of the processes responsible for the closeness of the Eecm to Epzc in this case. Anyhow, one may conclude that closeness of the Eecm to Epzc does not necessarily mean that classical Lippmann electrocapillary equation is valid for this group of metals and that these metals possess the properties of liquids of very high viscosity. The case of silver should be discussed separately. As already mentioned, a number of investigators have found9,45-47 the zero of estance to be near -0.7 V (SHE). This value coincides well with a value of Epzc found by using differential capacity measurements on a polycrystalline Ag electrode.55 Nevertheless, the general shape of estansograms of Ag46,47 is surprisingly similar to the shapes of Au estansograms found in this work. The estansograms of Ag possess one zero point at Eecm ) -0.70 V and a well-pronounced step some 0.3 V more positive than Eecm. It prompts the supposition that actual values of the Epzc of polycrystalline Ag specimens that were used by authors45-47 could be more positive than -0.7 V. The more so, no special differential capacity measurements have been performed by these authors in order to establish the real value of Epzc from the capacity minimum. The authors simply ascertained that the potential of Eecm, found from estansograms, coincides well with a value of Epzc widely accepted in the literature.18 Nevertheless, as was pointed out by Trasatti,56 the actual value of the Ag polycrystalline surface could be strongly dependent on the purity of the silver sample as well as the pretreatment of the electrode before differential capacity measurements. According to him, a value of Epzc) -0.44 V (SHE) fits better to the well-known correlation between work function and potential of zero charge.56 More positive experimental values of Epzc were also found by the scrape method (in situ renewal of Ag surface)17 and recently by the X-ray photoelectron spectroscopy (XPS) technique.57 Sometimes, more positive values of Epzc of the silver electrode are assigned to the oxidized surface.58 Anyhow, the question about coincidence of the Eecm with Epzc in the case of polycrystalline silver remains open until thorough and simultaneous measurements of estance and differential capacity will be performed. Comparison with Data of Other Authors. The results of the present work are in very good agreement with the results obtained by the group of Beck.19,20,32 As seen, unexplained “discrepancy” between Eecm and Epzc could be interpreted by using a modified electrocapillary equation. In essence, the experimental results of the present work agree well with ones presented in ref 25. The authors interpreted their results assuming contribution of the second term in eq 5 is negligible as compared with that of the first term. This assumption did not allow them to explain the negative shift of the Eecm with respect to the Epzc. Nevertheless, there are a number of thorough works21,22,27,28,44 in which the coincidence of Eecm and Epzc has been observed. This essential discrepancy between present work and cited works cannot be explained by trivial reasons (purity of solutions, different polycrystalline samples, etc.). In our opinion, the only essential difference between experimental conditions is the measurements in refs 21, 22, 27, 28, and 44 were carried out using thin evaporated gold electrodes while, in the present work, we (55) Valette, G.; Hamelin, A. J. Electroanal. Chem. 1973, 43, 301. (56) Trasatti, S. J. Electroanal. Chem. 1971, 33, 351. (57) Hecht, D.; Strehblow. H.-H. J. Electroanal. Chem. 1997, 436, 109. (58) Aleksandrova, D. P.; Sevastjanov, E. S.; Andrusev, M. M.; Leikis, D. I. Elektrokhimiya 1975, 11, 648.
Valincius
used massive electrodes. The thickness of the electrodes used by Heusler et al.59 was in the range of 30-60 nm, and the magnitude of the strain was ca. 10-4, i.e., some 105 times greater than that reported in the present work. It is quite possible that under such strain sputtered gold film behaves like plastic material (maybe partially plastic). Slow equilibration of the measured signal observed by authors26-28 confirms this possibility. If this presumption is true, the discrepancy between results of present work and the results in refs 21, 22, 27, 28, and 44 disappears. Moreover, the seeming discrepancy only proves that plastic and elastic electrocapillary behavior of gold (and other solids) may be appreciably different. Finally, it is worth comparing the data of present work with data obtained by using monocrystalline gold surfaces. As mentioned above, up to now, there was only one recent attempt to measure electrocapillary properties of the monocrystalline surface of Au in a similar electrochemical system (ideally polarizable electrode).29 The authors did not observe the maximum of electrocapillary curve at all in the investigated potential region. Instead, they observed monotonic upraise of interface stress curves for Au(111) surface from the most positive potentials up to potentials of ≈-0.1 V (hereinafter recalculated to Ag/AgCl reference electrode scale). It is clear, these results are not in contradiction with the present work because the maximum of the surface stress curve was not observed near the Epzc ) 0.37 V of the Au(111) surface.60 It is quite possible that Eecm of Au(111) could be found at more negative potentials than -0.1 V. The surface stress curves of a freshly prepared Au(100) surface are very flat.29 After several potential scans their shape becomes similar to the Au(111) surface stress curve. As in the previous case, no maximum of the surface stress curve is observed near the Epzc ≈ 0.10 V of Au(100).61 This leads to the conclusion that the negative shift of the Eecm vs Epzc could be not only the specific feature of polycrystalline surface of Au but also one of the monocrystalline surfaces. Conclusions Summarizing the material presented above, one may draw out several conclusions: (i) It follows from the results of the simultaneous measurements of estance and differential capacity that the potential of the electrocapillary maximum and potential of the zero charge of solid electrodes do not necessarily coincide. In the case of polycrystalline gold the value of Eecm is shifted negatively with respect to Epzc by some 0.3 V. The potential of electrocapillary maximum corresponds to the surface charge density -11 ( 1 µC/ cm2. (ii) The experimentally observed shift of Eecm can be explained by using a modified electrocapillary Lippmann equation that is supplemented by second term, which estimates possible influence of the variation of surface properties on elastic strain. (iii) In the case of gold the positive value of the second electrocapillary term in the potential region E < Epzc could be assigned to the variation of the electronic dipole layer charge density with the elastic stretching. It is unlikely that the surface dipole layer of water molecules has any direct contribution to the second term in this potential range. (59) Heusler, K. E.; Pietrucha, J. J. Electroanal. Chem. 1992, 329, 339. (60) Lecoeur, J.; Bellier, J. P.; Koehler, C. Electrochim. Acta 1990, 35, 1383. (61) Hamelin, A. J. Electroanal. Chem. 1995, 386, 1.
Properties of Polycrystalline Gold
Langmuir, Vol. 14, No. 21, 1998 6319
(iv) At the potentials positive of Epzc, the additional term strongly depends on both pH and concentration of perchlorate anions. This suggests that perchlorate anions, commonly accepted as surface inactive ions, appreciably influence structure of the double layer in this potential region. Appendix Derivation of Equation 5. An arbitrary increase of the surface excess of Gibbs energy in the system containing an ideally elastic electrified solid surface, at constant number of particles at the interface, temperature, and pressure, is
dG ) EdQ + γdΩ
(A2)
or in terms of charge density q
(∂E/∂e)q ) (∂γ/∂q)e
(A6)
dE ) (∂E/∂Q)Ω dQ + (∂E/∂Ω)Q dΩ
(A7)
Taking into account the equality eq A2 and dividing eq A6 by eq A7 under condition Ω ) const, one obtains
(∂γ/∂E)Ω ) (∂γ/∂Q)Ω (∂Q/∂E)Ω ) (∂E/∂Ω)Q (∂Q/∂E)Ω (A8) According to eq A7, the product (∂E/∂Ω)Q (∂Q/∂E)Ω is
(∂E/∂Ω)Q (∂Q/∂E)Ω ) - (∂Q/∂Ω)E
(A1)
where E is potential difference between two phases, Q is total excess charge of the solid, γ is generalized surface intensive parameter, and Ω is total surface area of the solid. The dG is total differential of two independent extensive variables Q and Ω. The second mixed partial derivatives of eq A1 are equal (the only requirement is: function must be finite and continuos in the interval of differentiation). That is why equality is valid:
(∂E/∂Ω)Q ) (∂γ/∂Q)Ω
dγ ) (∂γ/∂Q)Ω dQ + (∂γ/∂Ω)Q dΩ
(A3)
(A9)
Thus, from eqs A8 and A9 the following equation is obtained
(∂γ/∂E)Ω ) - (∂Q/∂Ω)E
(A10)
The total surface charge Q is
Q ) qΩ
(A11)
where q is surface charge density. Differentiating eq A11 with respect to surface area Ω and fixing the condition E ) constant one obtains
(∂Q/∂Ω)E ) q + Ω (∂q/∂Ω)E ) q + (∂q/∂e)E
(A12)
Equation A3 is eq 6 in the text. As mentioned, it was proved experimentally. The intensive parameters of eq A1 are in a certain functional relationship with the extensive parameters:
(note: de ) dΩ/Ω is an elastic strain) Substituting eq A12 into eq A10, one obtains electrocapillary equation
γ ) γ (Q,Ω)
(A4)
-(∂γ/∂E)e ) q + (∂q/∂e)E
E ) E(Q,Ω)
(A5)
which is eq 5 in the text, under conditions P,T,n ) constant.
The total differentials of eqs A4 and A5 are
LA980440S
