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Surface Stress-Charge Response of a (111)-Textured Gold Electrode under Conditions of Weak Ion Adsorption M. Smetanin,*,† R. N. Viswanath,† D. Kramer,† D. Beckmann,† T. Koch,† L. A. Kibler,‡ D. M. Kolb,‡ and J. Weissmu¨ller†,§ Forschungszentrum Karlsruhe, Institut fu¨r Nanotechnologie, Karlsruhe, Germany, UniVersita¨t Ulm, Institut fu¨r Elektrochemie, Ulm, Germany, UniVersita¨t des Saarlandes, Technische Physik, Saarbru¨cken, Germany ReceiVed December 31, 2007. ReVised Manuscript ReceiVed May 5, 2008 We report a cantilever bending investigation into the variation of surface stress, f, with surface charge density, q, for (111)-textured thin films of gold in aqueous NaF and HClO4. The graphs of f(q) are highly linear, and the surface stress-charge coefficients, df/dq, are -1.95 V for 7 mM NaF and -2.0 V for 10 mM HClO4 near the potential of zero charge. These values exceed some previously published experimental data by a factor of 2, but they agree with recent ab initio calculations of the surface stress-charge response of gold in vacuum.
Introduction During the past decade, there has been increased interest in the surface stress, f, of metal electrodes. Possible sensor1–5 and actuator6,7 applications based on variations in f have been not only suggested and demonstrated but also commercialized in the case of sensors.8 Part of the recent work has focused on the origin of the variation of f with the electrode potential, E,9–11 which is documented by experiments using piezoelectric detection,12,13 substrate bending observed with the scanning tunneling microscope,14–16 or with a reflected laser beam,17 or nanomaterial expansion.6,7,18 It has been recognized that the leading terms in f(E) and f(q) at metal electrode surfaces are linear near the potential of zero charge (pzc),6,7,14,16,18–20 contrary to the quadratic variation of the surface tension. Both the magnitude of the surface stress change and the nature of the underlying microscopic processes * Corresponding author. E-mail:
[email protected]. † Forschungszentrum Karlsruhe. ‡ Universita¨t Ulm. § Universita¨t des Saarlandes.
(1) Thundat, T. G. Wachter, E. A. U.S. Patent 5,719,324, filed June 16, 1995. (2) Moulin, A. M.; O’Shea, S. J.; Welland, M. E. Ultramicroscopy 2000, 82, 23–31. (3) Fritz, J.; Baller, M. K.; Lang, H. P.; Rothuizen, H.; Vettiger, P.; Meyer, E.; Gu¨ntherodt, H.-J.; Gerber, Ch.; Gimzewski, J. K. Science 2000, 288, 316–318. (4) Godin, M.; Laroche, O.; Tabard-Cossa, V.; Beaulieu, L. Y.; Gru¨tter, P.; Williams, P. J. ReV. Sci. Instrum. 2003, 74, 4902–4907. (5) Tabard-Cossa, V.; Godin, M.; Beaulieu, L. Y.; Gru¨tter, P. Sens. Actuators, B 2005, 107, 233–241. (6) Weissmu¨ller, J.; Viswanath, R. N.; Kramer, D.; Zimmer, P.; Wu¨rschum, R.; Gleiter, H. Science 2003, 300, 312–315. (7) Kramer, D.; Viswanath, R. N.; Weissmu¨ller, J. Nano Lett. 2004, 4, 793– 796. (8) Concentris GmbH, Basel, Switzerland, offers micromechanical silicon cantilever arrays, a functionalisation unit and a cantilever sensor platform (Cantisens). http://www.concentris.com/. (9) Lipkowski, J.; Schmickler, W.; Kolb, D. M.; Parsons, R. J. Electroanal. Chem. 1998, 452, 193–197. (10) Weissmu¨ller, J.; Kramer, D. Langmuir 2005, 21, 4592–4603. (11) Kramer, D.; Weissmu¨ller, J. Surf. Sci. 2007, 601, 3042–3051. (12) Seo, M.; Ueno, K. J. Electrochem. Soc. 1996, 143, 899–904. (13) Valincius, G. Langmuir 1998, 14, 6307–6319. (14) Haiss, W.; Nichols, R. J.; Sass, J. K.; Charle, K. P. J. Electroanal. Chem. 1998, 452, 199–202. (15) Ibach, H.; Bach, C. E.; Giesen, M.; Grossmann, A. Surf. Sci. 1997, 375, 107–119. (16) Ibach, H. Electrochim. Acta 1999, 45, 575–581. (17) Friesen, C.; Dimitrov, N.; Cammarata, R. C.; Sieradzki, K. Langmuir 2001, 17, 807–815. (18) Viswanath, R. N.; Kramer, D.; Weissmu¨ller, J. Langmuir 2005, 21, 4604– 4609. (19) Haiss, W. Rep. Prog. Phys. 2001, 64, 591–648. (20) Kramer, D. Phys. Chem. Chem. Phys. 2008, 10, 168–177.
in experiments near the pzc remain the subject of discussion. The surface stress-charge coefficient, ς ) df/dq|e (where e denotes a tangential strain) quantifies the response of f to surface charging. Experimental studies quote values for ς on the order of -1 V,6,14,19 on the basis of the simultaneous measurement of ∆f and ∆q. Because a typical value for the double-layer capacitance, c, of Au near the pzc is 30 µF/cm2, the results for ς imply values of around -0.3 C/m2 for the surfacestress potential coefficient df/dE|e, which is the parameter quoted in other studies. It obeys df/dE|e ) cς. However, considerably larger experimental values are reported, -0.9 to -1.6 C/m2.21 At the same time, estimates based on the Jellium model, which might be appropriate in relation to simple metals, provide ς values of around -0.1 V (cf. ref 22 and references therein) whereas a DFT calculation for Au(111) suggests ς ) -1.9 V.23 Thus, the experimental situation and its relation to theory are far from clear. Along with the above unresolved issues, there are conflicting views about the microscopic origin of the surface stress-charge response. Bonds with adsorbates,17,24 changes in the water dipole orientation,25 and the effect of the excess charge proper18,23,26 have all been suggested to be decisive for the surface stresscharge response. Here, we present experimental results for the charge and potential dependence of f for Au(111) at the pzc, emphasizing the quantitative evaluation of ς. Our interest is in conditions where that fraction of the net excess charge, q, that is transferred away from the metal and into bonds with adsorbates remains at a minimum. We are therefore using solutions of fluoride and perchlorate anions, which are considered to be weakly adsorbing on gold surfaces.27 Because the number density of adsorbates per charge decreases with increasing dilution,18 we use electrolytes (21) Vasiljevic, N.; Trimble, T.; Dimitrov, N.; Sieradzki, K. Langmuir 2004, 20, 6639–6643. (22) Viswanath, R. N.; Kramer, D.; Weissmu¨ller, J. Electrochim. Acta 2008, 53, 2757–2767. (23) Umeno, Y.; Elsa¨sser, C.; Meyer, B.; Gumbsch, P.; Nothacker, M.; Weissmu¨ller, J.; Evers, F. Europhys. Lett. 2007, 78, 13001-p1–13001-p5. (24) Ibach, H. Surf. Sci. Rep. 1997, 29, 195–263. Ibach, H. Surf. Sci. Rep. 1999, 35, 7173 (Erratum) (25) Heaton, Th.; Friesen, C. J. Phys. Chem. C 2007, 111, 14433–39. (26) Weigend, F.; Evers, F.; Weissmu¨ller, J. Small 2006, 2, 1497–1503. (27) Hamelin, A.; Vitanov, T.; Sevastyanov, E.; Popov, A. J. Electroanal. Chem. 1983, 145, 225–264.
10.1021/la704067z CCC: $40.75 2008 American Chemical Society Published on Web 07/11/2008
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Figure 1. Experimental setup. (a) Schematic illustration of the experimental setup. Electrochemical cell made of Teflon: Cantilevered working electrode (WE) made from a 100 µm (100) silicon wafer with 40 nm of evaporated gold gently fixed at one end and immersed into the electrolyte. The reference electrode (RE) SCE was connected to the cell through a Luggin Capillary. A gold plate was used as the counter electrode (CE). The cell was sealed using an optically transparent glass plate and a Teflon coated O-ring. The laser path was (1) a He-Ne laser, (2) x and y etalons, (3) the electrochemical cell, (4) glass, (5) a Teflon coated O-ring, (6) wafer holder clamps, (8) a CCD camera, where R is the angle between the incident beam and the sample surface, L is the sample-CCD camera distance, and d0 is the distance between laser spots reflected from the WE. (b) Illustration of the two bending radii, Rx and Ry.
that are comparatively dilute though of sufficient concentration to allow a useful amplitude of q and, hence, measurable surface stress changes.
Experimental Procedures Preparation and Characterization. A gold film on a silicon single-crystal wafer was used as a working electrode for the wafer bending experiment. A (100)-oriented silicon wafer of nominal thickness 100 µm and with a thermally grown 100-nm-thick oxide layer was obtained from CrysTec GmbH. Rectangular pieces of dimension (8 × 36) mm2 were cut with a diamond cutter. Measurements of mass and area confirmed the thickness of h ) (100 ( 2) µm. The metal films were deposited by thermal evaporation in a vacuum chamber with a base pressure of 1 × 10-9 mbar. During evaporation, the pressure was 1 × 10-8 mbar with a deposition rate of 0.01 nm/s, controlled by a quartz microbalance, and a substrate temperature of 220 K. Around 2 nm of Ti was deposited for better adhesion, and then Au was deposited to a thickness of 40 nm. The deposition covered one side of the wafer entirely, except for a small fraction in the clamping area. X-ray diffraction was performed with a powder diffractometer (Philips X’Pert) with Cu KR radiation and a solid-state detector. The surface topology of the film was studied by atomic force microscopy (AFM) (Digital Instruments NanoScope III) in contact mode. Auger electron spectroscopy on as-deposited films provided no evidence of metallic impurities at the surface. In Situ Electrochemical Cell. The setup for the laser-based measurement of substrate bending during in situ electrochemical charging is schematically shown in Figure 1a. The rectangular cell of about 150 mL capacity, made of electronicgrade Teflon, contained the horizontal cantilever as the working electrode and a coplanar gold plate with a surface area of 10 cm2
Smetanin et al. as the counter electrode. A saturated calomel electrode (SCE) as the reference was connected to the cell through a Teflon Luggin capillary sealed with a Teflon-coated O-ring. In the interest of charging kinetics and low uncompensated resistance between the reference and working electrodes, it would be desirable to arrange the Au-coated side of the cantilever down, facing the counter electrode. However, the low reflectivity of the back side of the wafer prevented a meaningful evaluation of the reflected laser beams (see below) in this configuration; the cantilever was therefore arranged with the Au film (which had good reflectivity) facing up. The cell was completely filled with electrolyte so that the cantilever was wetted on all sides, and the cell was closed with a glass plate sealed with a Teflon-coated O-ring. The active Au surface area for different samples varied between 2.4 and 2.9 cm2. The unsupported length of the cantilever was 3.2 cm, and the laser beam array illuminated an area of 6 × 6 mm2 centered at the far end from the clamp, 2.8 cm away from it (Figure 1b). To diminish mechanical constraints further, the clamp was tightened with the minimum force required to fix the wafer. Screws and clamp were made from Teflon. Electrical contact with the film was provided by a thin (∼100 µm diameter) gold wire. Prior to the experiment, the cell was cleaned with a standard cleaning solution (5 volume parts conc. H2SO4 + 1 part 30% H2O2) and then rinsed thoroughly with ultrapure 18.2 MΩ cm grade water (Arium 611, Sartorius) to remove adsorbed ions. The same water, plus HClO4 (Suprapur, Merck) or NaF (Suprapur, Merck), was used to prepare the electrolytes. All cyclic voltammetry was performed with a PGSTAT 10 potentiostat (Eco Chemie); the charge transfer to the electrode was computed for by integrating the current using the potentiostat’s “current integration” mode. All experiments were carried out at 25 °C. Potential of Zero Charge. The pzc was determined from the potential-dependent ac capacitance curve for an as-deposited film sample, measured at 18 Hz and a potential scan rate of 1 mV/s by means of the hanging meniscus method.28 An Ag/AgCl capillary electrode in saturated KCl was used as the reference in this experiment, but all potentials are referred to the saturated calomel electrode (SCE) using the potential offset value of 45 mV. The capacitance was measured after the potential had been cycled several times in the same potential interval that was used for the measurement (-0.4 to +0.6 V). Determination of the Surface Stress from Differential Spot Spacing. Changes in the cantilever curvature in response to surface stress were determined in situ by means of a commercial laser-based device (Multi-Optical Stress Sensor, k-Space).29,30 The surface was illuminated by an array of 4 × 4 parallel laser beams (Figure 1b). The spots that correspond to each reflected beam were recorded with a charge coupled device (CCD) camera. Changes in the local curvature, κ, of the irradiated region of the cantilever give rise to a change, ∆d/d0, in the characteristic spot spacing d0, which was monitored in real time by image analysis software. We found that a significantly improved signal-to-noise ratio could be obtained when air convection in the (vertical) laser path was suppressed by inserting a plastic tube between the cell and the optics unit. The primary data from the image analysis were two timedependent values for the differential spot spacing, ∆d, measured along two orthogonal directions (x and y in Figure 1b). The spot spacing relates to changes in the resolved curvature along the respective direction, parallel to the long (curvature κy) and short (κx) axes of the cantilever, respectively. Each value individually satisfies (28) (a) Dickertmann, D.; Koppitz, F. D.; Schultze, J. W. Electrochim. Acta 1976, 21, 967–971. (b) Hamelin, A. In Modern Aspects of Electrochemistry; Conway, B. E.,. White, R. E., Bockris, J. O’M., Eds.; Plenum: New York, 1987; Vol. 16. (29) Floro, J. A.; Chason, E. Mater. Res. Soc. Symp. Proc. 1996, 406, 491– 496. (30) Floro, J. A.; Chason, E.; Lee, S. R.; Twesten, R. D.; Hwang, R. Q.; Freund, L. B. J. Electron. Mater. 1997, 26, 969–979.
Surface Stress-Charge Response of a Gold Electrode
∆κ )
∆d cos R d0 2Ln
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(1)
where R is the angle included by the laser beam and the cantilever normal, L is the distance from the sample to the CCD camera, and n is the electrolyte index of refraction. The ratio L/cos R was calibrated as (107 ( 3) cm using mirrors with known radii of curvature (10 m and infinite for the planar one); the value agrees with a direct measurement of the path length (around 105 cm) and of R (3°). Because we used dilute electrolytes, the value of n was identified with that of pure water, 1.33. When the electrode potential is changed, then the surface stress tensor, s, at the electrode surface varies and the compensating stress in the cantilever gives rise to bending. By symmetry, s must be isotropic on 111-oriented surfaces of fcc crystals so that we can identify each of the resolved values with the scalar surface stress value, f (half the trace of the tensor). By identifying f with the stress-thickness product in Stoney’s equation,31,32 we obtain
∆κ ) -
6∆f Mh2
(2)
where M refers to the substrate biaxial modulus and h represents the substrate thickness. We used M ) Y/(1 - ν) with the values of Young’s modulus, Y ) 130.2 GPa, and Poisson’s ratio, V ) 0.279, of 100-oriented Si.33 Applying eq 2 separately to each of the two experimental curvature values κx and κy and solving for f provides two independent measurements for the nominally identical quantity f. The derivation of Stoney’s equation for biaxial bending makes use of the classical lamination theory, which requires that the normal displacements are much less than the beam thickness. Here, this requires κb2 , h, where b is the dimension of the cantilever orthogonal to the bending direction. In the present experiments, the maximum curvature change corresponded to radii of around 500 m. With b ) 8 and 36 mm, the condition was well satisfied for bending along both directions. The experimental error in f may be estimated as follows: The uncertainties quoted above for hS, L, and R contribute a systematic uncertainty of around 5%. The statistical experimental uncertainty as estimated from the scatter in individual measurements was about 1% (see below). As was found, apparently the largest source of possible systematic error arises from the partial suppression of the transverse bending due to constraints from clamping. To minimize this effect, the laser spot array probed the curvature near the free end of the cantilever, about 2.6 cm or 3 times the wafer width, from the clamp. According to ref 34, free biaxial bending is expected as long as the distance is larger than the wafer width. Nevertheless, a noticeable anisotropy in the curvature was found, and the surface stress value inferred from the transverse bending component was less than the longitudinal one by about 10% (see below). Because symmetry requires s to be isotropic, the result suggests that noticeable clamping effects remain. Because the longitudinal curvature component and the surface stress value determined from it are not affected by clamping, this data was selected as more reliable and was used for quantitative analysis.
Results Microstructure and pzc. Figure 2 shows results of AFM characterization of an as-prepared film. The image suggests a characteristic lateral feature size of around 80 nm. The surface height profile standard deviation is 3 nm after correction for drift. Thus, height gradients are small, and the surface may be qualified as reasonably smooth. To verify this conclusion, we (31) Stoney, G. G. Proc. R. Soc. London, Ser. A 1909, 82, 172–175. (32) Doerner, M. F.; Nix, W. D. CRC Crit. ReV. Solid State Mater. Sci. 1988, 14, 225–268. (33) Brantley, W. A. J. Appl. Phys. 1973, 44, 534–535. (34) Dahmen, K.; Lehwald, S.; Ibach, H. Surf. Sci. 2000, 446, 161–173.
Figure 2. AFM micrograph of 1 × 1 µm2 area of the working electrode surface in the as-prepared state. The inset shows height h versus position rx on a characteristic cross section.
Figure 3. X-ray characterization of the Au electrode. Intensity I versus scattering angle 2θ in a Bragg-Brentano θ-2θ scan. (Inset) Rocking curve of I versus angle of inclination ω for the (111) reflection.
Figure 4. Differential capacitance vs potential curves for (111)-textured Au in 7 mM NaF (dashed line, left axis) and 10 mM HClO4 (dotted lie, right axis). Arrows denote the potential of zero charge, Epzc, which is (0.18 ( 0.01) V in NaF and (0.20 ( 0.01) V in HClO4.
have computed the root-mean-square inclination angle along the surface by analysis of the AFM data. The value, 19°, confirms the essentially planar nature of the surface. The (200) reflection was absent in θ-2θ X-ray scans, indicating a (111) crystallographic texture. This is confirmed by rocking curves (inset in Figure 3) that yield a full-width at half-maximum of 3.2° for the (111) reflection. Figure 4 shows the differential capacitance curves in 7 mM NaF and 10 mM HClO4. Because we were interested in the pzc value during the curvature measurement, the capacitance was
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Figure 5. Electrode potential, E, (top) and variation of the differential spot spacing, δd/d0, (bottom) as a function of the measurement time, t, during 11 successive voltammograms in 10 mM HClO4. The curves at the bottom part represent the change in curvature of the wafer in the longitudinal (blue, dotted lines) and transverse (red, solid lines) directions (cf. Figure 1).
measured after several potential cycles. The two curves exhibit a pronounced minimum that is attributed to the pzc. A quadratic fit in the vicinity of the capacitance minimum yields Epzc ) (180 ( 10) mV versus SCE for NaF and Epzc ) (200 ( 10) mV versus SCE for HClO4. This is in good agreement with values reported in the literature, namely, 230 mV versus SCE for a bulk-terminated gold single crystal in 0.01 M HClO4.35 The pzc of reconstructed Au(111)-(3 × 22) is considerably more positive, 320 mV versus SCE both in 0.01 M HClO435 and in 0.01 M NaF.27 The comparatively negative value found here suggests that the surface of the present Au films was bulk-terminated. Differential Spot Spacing. A representative graph of the timedependent differential spot spacing, δd/d0, during cyclic variation of the electrode potential E is shown in Figure 5. One can see that δd/d0 varies reproducibly in phase with E and that the signalto-noise ratio is excellent. The two curves of δd/d0 represent the results for the two orthogonal bending directions. They illustrate the reduced amplitude in the transverse direction, as discussed above. Only the longitudinal signal will be used in the data analysis below. Surface Stress in NaF. In situ surface stress-charge measurements were carried out in 0.007 M NaF at a 10 mV/s scan rate and in a potential range of 0.4 V centered near the pzc. Figure 6 displays the current density, j, charge density, q, and surface stress change, ∆f, versus the potential. The cyclic voltammogram (CV) of Figure 6a shows featureless behavior, indicating the dominance of double-layer charging. The graph of charge density, q, (Figure 6b) is nearly closed, indicating that charge is conserved. Figure 6c shows the change in surface stress, ∆f, versus E. Note the noticeable hysteresis and the good reproducibility. Figure 6d displays a graph of ∆f versus q. It is seen that the relation is quite accurately linear. The hysteresis seems to vanish in this representation; a small amount of hysteresis might be hidden in the noise. A linear regression of the graph of f(q) gives the surface stress-charge coefficient for this particular experiment, ς ) (-1.95 ( 0.01) V. Surface Stress in HClO4. By analogy to Figure 6, Figure 7 shows the results of the in situ experiment in 10 mM HClO4 at a 10 mV/s scan rate in the potential range of 0.05 to 0.6 V. Both f(E) and f(q) exhibit hysteresis yet f(q) exhibits reasonably linear behavior, and by linear regression we obtain here ς ) (-2.01 ( 0.01) V. (35) Kolb, D. M.; Schneider, J. Electrochim. Acta 1986, 31, 929–936.
Figure 6. Results of the experiment in 7 mM NaF (scan rate 10 mV/s). (a) Cyclic voltammogram. (b) Change in charge density, ∆q, versus E. (c) Surface stress change, ∆f, versus E. (d) ∆f versus ∆q. The straight dashed line is the best fit and has a slope of –1.95 V. Parts c and d show 12 successive cycles superimposed.
Reproducibility. Our results are based on experimental data obtained for several independent runs using five separate gold samples (three and two for NaF and HClO4, respectively), each using the same procedure as in the examples above. Figure 8 illustrates that the results are compatible, with a standard deviation of about 1%. When including the uncertainties in wafer thickness and optical path length (see above), we estimate the net uncertainty in ς to be around 5%. Thus, our experimental results for ς are (-1.95 ( 0.1) V (NaF) and (-2.00 ( 0.1) V (HClO4). Our experimental observations also show that the quality of the film is crucial to the measurement. For instance, in a few cases, a deviation from linearity of f(q) was observed when the film started to detach from the substrate, in agreement with the observations in ref 19. Furthermore, a common artifact after extended cycling (typically, for 24 h) was a significant decrease in the amplitudes of both f and q for a given potential interval. We find it noteworthy that, in a typical example, the two amplitudes dropped by about 30% each, whereas their ratio, ς, was reduced by only 10%. This indicates that as compared to df/dE the parameter df/dq is significantly more robust with respect to artifacts due to the degradation of the film, provided that the charge amplitude is measured in situ along with the surface stress variation.
Discussion Magnitude of S. Our finding of a linear correlation between surface stress and charge is in agreement with previous experiments for single-crystal gold surfaces in electrolytes of higher concentra-
Surface Stress-Charge Response of a Gold Electrode
Figure 7. Results of the experiment in 10 mM HClO4 (scan rate 10 mV/s). (a) Cyclic voltammogram. (b) Change in charge density, ∆q, versus E. (c) Surface stress change, ∆f, versus E. (d) ∆f versus ∆q. The straight dashed line is the best fit and has a slope of -2.01 V. Parts c and d show 12 successive cycles superimposed.
Figure 8. Compilation of results for the surface stress-charge coefficient, ς, in 7 mM NaF and 10 mM HClO4. Each data point represents an average over about 12 successive scans. Different symbols denote results obtained with different samples. Error bars represent a combination of systematic and statistical errors; see the text for details.
tions.14,15 The present results put the value of ς for conditions of weak adsorption at around -2.0 V. This is remarkable in view of the fact that most direct measurements of ς for Au that have been reported so far indicate a value that is smaller in magnitude by at least the factor of 2.14,15,16,19 Note, however, that independent observations support the larger magnitude of the present work: (i) As mentioned in the introduction, the results in ref 21, although quoting df/dE|e rather than ς, are poorly compatible with the smaller magnitude of previously published ς values. In fact, df/dq for Au(111) can be estimated by combining data for surface stress and charge density (measured ex situ) in Figures
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5 and 3, respectively, of that reference using ς ) c-1 df/dE|e. In this way, we obtain about -2.3 and -2.5 V for ς in 0.1 M NaF and 0.1 M Na2SO4, respectively. In view of the uncertainties involved in our extraction of data from the graphs and in combining data for f and q from different experiments, the result may be considered to support our results and the suggestion that the value of ς is closer to -2 V than to -1 V; this is confirmed for 0.1 M HClO4.36 (ii) The first experiments with Pt, using more concentrated solutions, put the surface-stress-charge response for that metal at ς ) -0.9 V. However, later measurements using a dilution series18 to reduce the amount of adsorption arrived at values of larger magnitude, up to -1.9 V. (iii) The ab initio calculation for Au(111) in vacuum suggests ς ) -1.89 V.23 This agrees closely with the present result. For a large value of ς at the pzc, that contribution to the variation of f(q) that is linear in charge is expected to dominate the f(q) curve.20 Therefore, the large ς is in line with our interpretation of a linear f(q). We shall now comment on a possible microscopic scenario underlying these observations. Presence of Adsorption. As a preliminary remark, it is emphasized that the electrolytes in question, though nominally weakly adsorbing, do exhibit noticeable cyclic anion adsorption/ desorption in voltammograms. NaF was chosen because F- ions have a low tendency for specific adsorption because of their strongly bound solvation shell.37 Perchloric acid is believed to have a somewhat higher adsorption strength, at least at high potentials. It is still considered to be very weakly adsorbing close to the pzc,27 but a small amount of adsorption is documented in the literature.38 For both electrolytes, specific adsorption is apparent in the time dependence of the electrode behavior: the quite different capacitances inferred from the ac experiment in Figure 4 (18 Hz) as compared to the cyclic voltammograms shown in Figures 6 and 7 (0.02 Hz), suggest that some electrode processes require thermal activation, as would be expected for specific adsorption. The observations on hysteresis illuminate another aspect of this issue: the hysteresis of f(q) in HClO4 shows that the state of the electrode is here not uniquely defined by the value of q. Hysteretic specific adsorption appears to be an obvious explanation, in agreement with the statements above. By contrast, we note that the apparent hysteresis in the voltammograms, and in particular in q(E), may partially reflect the potential gradient between reference and working electrodes as a result of the uncompensated resistance of the intermediary electrolyte. This feature is therefore likely not, or not entirely, related to microscopic processes at the electrode, such as specific adsorption. We note that a relatively slow scan rate was used in the present study, namely, 10 mV/s as compared to 40 mV/s15 and even 200 mV/s14 in previous work. Yet, inasmuch as the capacitances deduced from the voltammograms are quite similar, the difference does not seem to have a significant effect on the amount of adsorption. Intrinsic Stress-Charge Coefficient: Role of Charge Transfer. The excellent agreement between the present experiments and the ab initio computation in ref 23 suggests that the same processes may govern the surface stress-charge response at the Au-electrolyte and Au-vacuum interfaces. In other words, electric charge alone, without specific adsorption, can apparently (36) Tabard-Cossa, V.; Godin, M.; Burgess, I. J.; Monga, T.; Lennox, R. B.; Gru¨tter, P. Anal. Chem. 2007, 79, 8136–8143. (37) Bockris, J. O’M., Reddy, A. K. N. Modern Electrochemistry, Vol. 2; Plenum Press, New York, 1970, p. 744. (38) Hamelin, A. J. Electroanal. Chem. 1986, 210, 303–309.
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cause changes in surface stress that are comparable to those in the experiment. Our striving toward conditions of weak adsorption was motivated in part by the intention to verify this picture. We base our discussion of the role of adsorption on Haiss’ suggestion19 that the surface stress variation is determined only by the effective charge density, qM, on the metal surface, even when there is adsorption. Within our description in terms of the stress-charge coefficient, this implies that
δf ) ςMδqM
(3)
where ςM is the stress-charge coefficient of the clean metal surface. The relevant effect of specific adsorption is here simply to transfer charge between the metal and the adsorbate so that qM may differ from the net electrode charge, q, which is experimentally accessible as the time integral of the current in a voltammogram. F- or ClO4- has been suggested19 to be a good approximation to the ideal reference adsorbate with no charge transfer across the interface so that qM ) q. Yet in view of the measurable adsorption effects on the voltammogram for the corresponding electrolytes, one is led to suspect that even those weakly adsorbing ions may not entirely meet the condition. As a background for further discussion, we find it here useful to cast the corrections to eq 3 that ensue in the presence of adsorption into equations. For an ion of valence z, the possible transfer of a noninteger number λ of electrons has been described by the electrosorption-reaction equation39–42
νM-OH2 + Sz(aq) f Mν - Sz+λ + λe-(met) + νH2O(aq) where S refers to the adsorbing substance. Obviously, if this reaction were to occur at constant q, then it would lead to a change in the charge within the metal, qM, that is proportional to λ and to the superficial density, Γ, of specifically adsorbed ions. It has been suggested that the dependence of the chargetransfer coefficient λ on the potential is small39 and might be neglected. Then42
qM ) q - λFΓ
(4)
where F denotes the Faraday constant. The coefficient λ is closely related to the concept of electrosorption valency γ. The details of this relation, which involve considerations of adsorbate position and dipole terms of adsorbate and water, can be found in refs 39-42. A nontrivial part of Haiss’ hypothesis is its focus on chargeinduced changes in bond forces within the metal only. In a more general scenario, it would have to be admitted that the total surface stress change contains an extra contribution, δfΓ, due to metal-adsorbate and adsorbate-adsorbate bond forces. For instance, one might formally write δfΓ ) (φMA + φAAΓ) δΓ, with constants φMA and φAA representing the respective forces. Haiss’ hypothesis here requires that δfΓ/δq , ςM. The net experimental stress-charge response ς will then be related to the intrinsic stress-charge response ςM and to a combination of the partial charge-transfer coefficient λ and the amount of specific adsorption via
ς)
δf δΓ ) ςM(1 - λF ) δq δq
(5)
This expression illustrates two implications of the hypothesis: (i) The surface-stress-charge response might be used to estimate the charge-transfer factor λ, a quantity that is notoriously difficult to access in experiments.42 (ii) Experiments aimed at measuring ςM should pursue either or both of the strategies minimizing the net charge transfer: the
use of an anion with small λ or the use of an electrolyte with a low tendency for specific adsorption (small δΓ/δq). We note that a dependency of Γ on the anion concentration, X, in the bulk of the electrolyte must be admitted; in other words, Γ ) Γ(q, X). Therefore, simple scaling between ς and λ or γ cannot be inferred from eq 5. As was pointed out in ref 18 when both the inner Helmholtz layer and the bulk electrolyte can be approximated as dilute solutions of the adsorbing species, Γ at a given value of E depends linearly on X. The double-layer capacitance varies more slowly as X according to the Gouy-Chapman theory. Thus, δΓ/δq in eq 5 tends to zero, and ς approaches ςM in the limit of high dilution. The quite noticeable difference between the ς obtained by different authors using different X14,16,19 suggests that a significant amount of chemisorption remains at the higher concentrations. This is indeed confirmed by the dilution series in ref 18, which shows ς for Pt in the NaF electrolyte to become independent of concentration only for X < 0.1 mol/L. So far, experimental observations near the nominally capacitive regime of the voltammogram, allowing for weak anion adsorption, also agree with the trend predicted by eq 5: experiments with different anions find ς to be enhanced for ions with a smaller expected λ,14,19 the dilution series finds ς to be initially enhanced and then to saturate, presumably at the value ςM, as the dilution is increased, and the ab initio work, which computes ςM because adsorption is excluded, finds a large stress-charge response. The present results for conditions of weak adsorption (small λ and small δΓ/δq) confirm the above arguments by agreement with the ab initio result. Furthermore, in spite of the different adsorption behavior of the two anions under study, practically identical ς values are found. This is again consistent with eq 5 if we admit that these experiments probe the limit where the correction term that represents the charge transfer has become negligible. In other words, the surface concentration of adsorbed anionic species for both electrolytes may be so low that the space charge in the metal will indeed control the surface stress change. Stress-Potential Response. We find it noteworthy that the agreement in ς for the two electrolytes does not extend to the surface stress-potential response, ∆f/∆E. For scans in similar potential intervals, the net change of the surface stress, ∆f, was 0.22 N/m in NaF, which is considerably less than the 0.8 N/m in HClO4. Accordingly, the values of ∆f/∆E are 0.4 and 1.5 C/m2, respectively, which is a difference of a factor of almost 4. The finding is readily reconciled with essentially identical values of ς if we consider that the effective capacitances, ∆q/∆E, exhibited the same difference as ∆f/∆E. We emphasize that the capacitances are governed by a combination of adsorption and processes in the diffuse layer of the electrolyte. The ς values appear to be insensitive to these processes, which are apparently noticeably different between the solutions of NaF and HClO4. This is again consistent with a stress-charge response that is governed by interactions within the metal. Possible Experimental Artifacts. As arguments in favor of the present, larger value of ς, we advertise the fact that known artifacts, such as film delamination, parasitic capacitance, and constraints on the deformation due to clamping, will either diminish the apparent surface stress variation or increase the apparent charge transfer. This implies that the experimental value represents a lower limit for the true value of ς. We also refer to (39) Vetter, K. J.; Schultze, J. Berichte Bunsenges. Phys. Chem. 1972, 76, 920–927. (40) Schultze, J. W.; Rolle, D. J. Electroanal. Chem. 2003, 552, 163–169. (41) Rikvold, P. A.; Wandlowski, Th.; Abou Hamad, I.; Mitchell, S. J.; Brown, G. Electrochim. Acta 2007, 52, 1932–1935. (42) Schultze, J. W.; Vetter, K. J. J. Electroanal. Chem. 1973, 44, 63–81.
Surface Stress-Charge Response of a Gold Electrode
our finding that the simultaneous measurement of changes in surface stress and surface charge, as in the present work, significantly diminishes experimental error due to film degradation. An as yet poorly explored issue concerns the effect of surface roughness on the surface stress measurement. None of the available discussions43,44 apply to the present situation of a singlephase layer that is essentially isotropic on the macroscopic scale and in which, a priori, a general 3D surface-induced stress state must be admitted. Yet both approaches predict that surface corrugation acts to reduce the effect of surface stress on cantilever bending. Preliminary results of a continuum mechanics investigation dedicated to the present problem, to be published separately, confirm this trend. At the same time, because the area of a rough surface is larger than the geometric area that underlies our analysis, the charge density may be overestimated here. Both of the above effects contribute to a trend in experimental results, including the present one, to underestimate the true magnitude of the stress-charge coefficient.
Summary For Au(111) under conditions of weak adsorption, there is a linear correlation between surface stress and charge in a significant (43) Spaepen, F. Acta Mater. 2000, 48, 31–42. (44) Pao, C.-W.; Srolovitz, D. J. J. Mech. Phys. Solids 2006, 54, 2527–2543.
Langmuir, Vol. 24, No. 16, 2008 8567
potential interval around the pzc. Identical values for the surface stress-charge coefficients are found for two dilute electrolytes, ς ) (-1.95 ( 0.1) V in 7 mM NaF and (-2.0 ( 0.1) V in 10 mM HClO4. These values are numerically larger than some previously published ones. They do, however, exhibit good agreement with results of recent ab initio computation for ς of Au(111) in vacuum and with reported trends of enhanced stresscharge response when the amount of adsorption is reduced. We inspect the hypothesis that the surface stress change is controlled by the contribution of surface excess charge to the bond forces between metal atoms in the surface and not due to forces arising from bonds with adsorbates. For the present experimental situation, gold in weakly adsorbing electrolytes near the pzc, the experiment appears to support this picture. Acknowledgment. We thank K. Soliman for his support in establishing procedures for the pzc measurement, S. Walheim for assistance with the AFM characterization and film thickness measurement, E. Nold for Auger spectroscopy analysis, and S. Lebedkin for useful suggestions on our optical system. Landesstiftung Baden-Wu¨rttemberg is gratefully acknowledged for financial support. LA704067Z
