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Adsorbate effects on the surface stress–charge response of platinum electrodes
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Electrochimica Acta 53 (2008) 2757–2767
Adsorbate effects on the surface stress–charge response of platinum electrodes R.N. Viswanath a,∗ , D. Kramer a , J. Weissm¨uller a,b a
Forschungszentrum Karlsruhe, Institut f¨ur Nanotechnologie, Karlsruhe, Germany b Universit¨ at des Saarlandes, Technische Physik, Saarbr¨ucken, Germany
Received 27 June 2007; received in revised form 15 October 2007; accepted 20 October 2007
Abstract The length change in response to changes in the surface stress during scans of the electrode potential was measured for nanoporous platinum samples immersed in aqueous NaF, an electrolyte with weak ion adsorption. The surface stress–charge response may be characterized separately for four different processes, selected by the potential range and by the surface pretreatment: hydrogen adsorption/desorption, oxygen adsorption/desorption (and/or surface oxidation/reduction), and nominally capacitive charging of the Pt surface in two different states, clean and oxide-covered. While each process exhibits a roughly linear response, the magnitude and even the sign of the slope, which determines the surface stress–charge coefficient, ζ, differ. We suggest that the sign of ζ depends on the penetration depth of the excess charge: for strong screening the electronic charge is located outside of the surface, and ζ is negative as found previously for clean metal surfaces. For weaker screening, the wider space charge layer implies a trend for the excess charge to fill bulk-like unoccupied states. These states are here antibonding, giving positive-valued ζ. © 2007 Elsevier Ltd. All rights reserved. Keywords: Platinum; Surface stress; Nanocrystalline; Porous electrodes; Metal–electrolyte actuators
1. Introduction The forces by which a surface interacts with the underlying bulk phase are measured by the surface tension, γ, or by its strain-derivative, the surface stress, f, in the case of fluid or solid surfaces, respectively. While the concept of surface stress at electrodes surfaces remains controversial [1], there is widespread agreement that the two parameters, γ and f, exhibit a distinctly different dependency on the electrode potential, E, or on the superficial charge density, q. Since q and E are energy-conjugate parameters, dγ = −q dE at constant values of the remaining state variables, the first variation of γ(E) must vanish at the potential of zero charge (pzc). The leading term in γ(E) near the pzc is therefore generally quadratic, and the ensuing electrocapillary maximum in γ is embodied in the Lippmann equation. No analogous argument is known for f(E), and indeed the results of the more recent relevant experiments [2–7] show a linear variation of f with E or with q near the pzc. The relevant response param-
∗
Corresponding author. Tel.: +49 7247 82 6737; fax: +49 7247 82 6368. E-mail address: [email protected] (R.N. Viswanath).
0013-4686/$ – see front matter © 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2007.10.049
eter is the surface stress–charge coefficient, ς = ∂f/∂q. Its value and the nature of the underlying microscopic interaction terms are the subject of current research. So far, all reported values of ζ in metals are negative, around −0.4 to −2 V. The most negative values are observed for electrolytes that are believed [5,6,8]1 to absorb more weakly, where a smaller fraction of the total charge q is transferred away from the metal surface and into bonds with adsorbed ions. Furthermore, experiments on Pt surfaces find |ζ| to increase when the adsorption is reduced in dilution series [10]. These observations have prompted ab initio studies of ζ at clean metal surfaces, in the absence of adsorption [11,12]. Magnitude and sign of ζ are found to agree closely with experiments on metal–electrolyte interfaces. Because a Maxwell relation equates ζ to a strainderivative of the work function, W, the negative sign can be rationalized in terms of a weakening of the surface dipole of clean metal surfaces during lateral strain [12] and to the trend 1 Note, however, that questions may be raised as to the usefulness of the particular definition of adsorption strength used in Ref. [6] for measuring the amounts of adsorption and charge transfer under the conditions of the experiment [9].
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of W in metals to increase with increasing electron density, as evidenced by results for Jellium [8,13]. Ab initio computation also points towards a decisive role of coupling between surface stress and surface relaxation (‘stretch’) in response to charging [11]. While the above arguments lend strong support to the notion that sign and magnitude of ζ for capacitive charging of metal electrodes may be understood in terms of the electron theory of clean metal surfaces, it appears also obvious that the interaction of the surface with adsorbates is rarely negligible, and more often decisive in determining the electrode behavior in electrochemical studies. Except for highly idealized conditions, adsorption processes will typically control the charge–potential behavior q(E) in experiment. Even for constant ζ, this propagates immediately to the surface stress–potential variation via f(E) = ζ q(E). Furthermore, important changes in f are observed during studies of adsorption from the vapour phase [5,14,15] and during the underpotential deposition of metals in electrolyte [16–18]. While these processes do involve the transfer of charge between the adsorbate and the metal substrate, it appears unlikely that the same processes which dominate the stress–charge response in weakly adsorbing electrolytes near their pzc act to control the surface stress when, for instance, Cu is deposited on Au. The above considerations imply that it is of interest to study the electrocapillary behavior of metal electrodes in extended potential intervals which include regions where either one of the two processes, capacitive charging or specific adsorption, dominates. Such studies would allow the comparison, for the same electrode/electrolyte combination, of the different electrode processes. Here, we present an experimental study of the surface stress–charge response of polycrystalline Pt which connects to the above issues, using a methodology established previously [6,10]. As the electrolyte we use an aqueous solution of NaF, since this is believed to be weakly adsorbing in certain potential windows [19,20]. Besides probing ζ separately in the regions of O2− /OH− - and H+ -adsorption, we also examine the question, what is the surface stress–charge response when charge is exchanged capacitively at a Pt surface covered by a stable adsorbate layer? This latter study connects to findings, reported separately [21], of a metastable (probably oxide-covered) state of polycrystalline Au surfaces where – contrary to all other reported findings – the value of ζ is found positive in experiments involving weakly adsorbing electrolytes and dominantly capacitive processes. 2. Experimental methods Cylindrical specimens of porous platinum, 1.5 mm in diameter and 1.8 mm in length, were prepared by consolidation of commercial platinum black (Alfa Aesar® ) at ambient temperature and moderate pressure (around 1 MPa), using procedures described previously [6,10]. The particle size – as determined from X-ray line broadening – was (6 ± 1) nm, and the mass-specific surface area of the consolidated samples was αm = 25.3 m2 /g, as determined by gas adsorption. For details of characterization see Ref. [6]. The mass of the porous specimens was 33 mg, giving a total surface area of 0.83 m2 . Thus,
each Coulomb of net charge on the sample implies an equivalent charge density of 1.20 C/m2 , or −0.50 electrons per surface atom (assuming a dense-packed surface layer, 1.50 × 1019 atoms/m2 ). Reference experiments for the planar polycrystalline Pt surface used a commercial Pt (99.95% purity) foil, of 1 cm2 area. For the in situ experiments, a miniaturized electrochemical cell, made of glass, was operated in the sample space of a commercial dilatometer (Netzsch® 402C). The sample compartment, which also contains the Ag/AgCl/3M KCl commercial reference electrode (FLEX-REF, World Precision Instruments, Inc.), is separated from the counter electrode compartment by a glass frit. The reference electrode is in a TeflonTM tube with a KONBOTM (ceramic/conducting polymer) porous membrane at the junction with low electrolyte leakage. Porous platinum (same material as the samples) was used as a counter electrode. Prior to the experiments the cell was cleaned with concentrated nitric acid and then rinsed thoroughly with ultrapure 18.2 M cm grade water to remove all the adsorbed impurities. A steady state temperature of 283 K ± 0.1 K was maintained, by connecting the dilatometer sample space to a bath thermostat. The potential was controlled via a potentiostat (PGSTAT 100, EcoChemie). For synchronization, the dilatometer output signal was fed to the potentiostat’s external input channel, and saved along with current and net charge in a single data file. The net charge, Q, transferred to the sample was determined using the potentiostat’s current integration mode. All values for Q, for the strain, l/l0 , and for the surface stress change, f, are referred to arbitrary reference states. In previous studies [6,10] we had found that repeated cycling is required before reproducible results on the stress–charge behavior can be obtained. Similar to the procedure there, 20 successive scans at 1 mV/s in 0.5 M H2 SO4 in between oxidation and reduction regions (potential range −0.05 to 0.85 V) were instigated with the consolidated porous samples. The samples were then washed repeatedly in ultrapure water (18.2 M cm) to remove any traces of H2 SO4 . The electrolyte used in all in situ dilatometry experiments of this work was 0.7 M solution of NaF (Merck® , 99.9%) in ultrapure water. The electrolyte solution was prepared in air at room temperature (294 K). Prior to the data collection of the in situ experiments, the samples were cycled in NaF (10 successive scans at 1 mV/s in the potential range −0.35 to 0.75 V) in order to ensure a stable and reproducible electrochemical behavior. With one exception (Fig. 5), all scan series shown below started after a 2 h hold at 0.12 V, which is close to the open circuit potential. Potential values in this study are specified relative to the Ag/AgCl/3 M KCl reference electrode used which shifts +200 mV to a standard hydrogen electrode (SHE). Unless stated otherwise, the scan rate is 1 mV/s. 3. Results and discussion of adsorption features 3.1. Overview of charge strain response Here we display an overview of the variation of charge and strain with the electrode potential, inspecting a potential interval, −1.15 to +1.0 V, which includes the regions of adsorption of
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hydrogen as well as oxygen. As a background for the description of the surface stress–charge response, we include a discussion of the most prominent features of the voltammogram at this point, partly anticipating the paper’s Section 4. Fig. 1 displays the time-dependent change in length l of porous platinum and the electrode potential E during nine successive potential cycles. It is seen that the potential variation entails a highly reproducible cyclic deformation. This indicates a stable microstructure of the nanoporous sample in spite of the repeated oxidation/reduction/hydriding/dehydriding cycles of its surface (see below). The reproducibility was similar in all experiments reported here. In some instances, a small drift (either contraction or expansion) was superimposed to the cyclic strain; this was corrected by subtracting a smooth function of time from the l(t) data before further analysis. Importantly, each single potential cycle in Fig. 1 is seen to involve two expansion/contraction cycles of similar amplitude, indicating that the stress–charge coefficient changes sign within the potential interval. This becomes more apparent when the strain is plotted versus the potential or the charge, as discussed below. Fig. 2(a) shows the cyclic voltammogram (CV). The graphs of six successive CVs, shown superimposed in the figure, are practically identical, confirming the reproducibility. The same holds for the graphs (Fig. 2(b)) of the net charge, Q, transferred to the sample as the function of the electrode potential, E. It is noteworthy that these graphs are practically closed, indicating that the charge transfer can be reversed, and that there are no significant net Faradaic currents. Such currents would arise, for instance, if there was gas evolution. The CV in Fig. 2(a) exhibits familiar features of Pt in aqueous electrolytes, namely the oxidative adsorption peaks at the positive end of the anodic scan and adsorption of H at the negative end of the cathodic scan. It is known that the CV of Pt in pH-neutral electrolytes can exhibit a large cathodic shift of the reductive desorption peak [22]. This suggests that the peak at around −0.4 V during the cathodic scan represents reduction
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Fig. 2. Overview of in situ dilatometry studies in the potential interval −1.15 to +1.0 V. (a) Current I vs. electrode potential E. (b) Net charge transfer Q vs. E. (c) Strain l/l0 vs. E. Thin arrows denote direction of scan. Bold arrows provide a rough indication of regimes of dominantly H-adsorption (labeled ‘HA’) and H-desorption (‘HD’) and of dominantly OH-adsorption/desorption or oxidation/reduction (‘OA’/‘OD’); we believe that H+ - and OH− -related processes may occur in intermediate potential intervals. Circles mark features in the graphs associated with the transition between the two suggested regimes. Potential scan rate is 1 mV/s. (d) Strain l/l0 (left ordinate) and the negative of the surface stress change, −f (right ordinate), plotted vs. the charge transfer Q. Note that more positive strain correlates with more negative surface stress. All parts show six successive scans superimposed.
of the oxide film [23,24]2 . The nature of the anodic peaks at around −0.1 and −0.5 V is less obvious. In order to investigate their origin, we find it instructive to inspect the charge transfer, Fig. 2(b).
Fig. 1. Change in length l (bottom part of figure) and potential E (top part) during nine successive potential cycles in the interval −1.15 V < E < +1 V. Scan rate is 1 mV/s.
2 In the case of Pt oxidation in H SO , there is evidence that the oxidized 2 4 Pt surface contains chemisorbed O or anhydrous PtO rather than hydroxide [23,24], although other experiments indicate OH-adsorption at low coverage [25]. While the presence of adsorbed OH or of Pt(OH)2 is rather less likely for the almost neutral solution used here, we still would like to use the wellestablished term ‘OH adsorption’, explicitly emphasizing that this is meant to describe the adsorption of an oxygen species (OH− or H2 O) which might be immediately de-protonated.
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In view of the established phenomenology of the electrochemical oxidation of Pt (see, for instance, Refs. [26,27]) we may safely assume that the charge which is accumulated after the central anodic peak, i.e. for E > +0.2 V, during the anodic scan (circle in Fig. 2(a)) is due to oxidation (‘OH-adsorption’), with a small contribution from capacitive processes. The charge accumulated at more anodic potential must therefore be balanced by an equal and opposite charge from oxide species desorption or reduction in the cathodic scan (plus a contribution from capacitive discharging). The circles in Fig. 2(b) illustrate the corresponding values of Q, and vertical lines link them to the features of the CV in Fig. 2(a). It is seen, that our assumption requires OH-desorption/reduction to continue well into the peaks at the negative end of the cathodic scan (until E < −0.85 V). If – consistently with the above – we assume that H-adsorption starts no later than at E ≤ −0.85 V, then an analogous inspection of the charge balance indicates that hydrogen desorption cannot be complete until E ≥ +0.15 V in the anodic scan (circle in Fig. 2(a)). This argument suggests strongly that the peaks near the centre of the anodic scan represent hydrogen desorption. The arrows in Fig. 2 illustrate this picture. The interaction of Pt surfaces with hydrogen is not known to involve such strong hysteresis. This might be seen as evidence that the notion of a clear separation between the regimes of H+ and OH− exchange is unrealistic, and that a more appropriate scenario would have to allow for an overlap of the two regimes. However, the strain data – to be discussed below – are well compatible with a clear separation. It is emphasized that, compared to planar polycrystalline Pt electrodes, the features of the CV of Fig. 2(a) are shifted considerably on the potential axis. This is evident in a comparison of the respective CVs in Fig. 3, which illustrates the cathodic shift of the OH-desorption and H-adsorption peaks, as well as the anodic shift of the H-desorption and OH-adsorption. Also shown in Fig. 3 is a CV of porous Pt at the slower scan rate of 30 V/s. The peak positions are here generally intermediate between those for porous Pt at 1 mV/s and those of the planar electrode. This indicates that the transport kinetics in the
pore space limit the rate of the electrode processes. This may be due to the potential gradient in the pore space arising from the electrical resistance of the solution, which is larger than that of highly acidic solutions for which such considerable potential shifts have not been observed [6]. Furthermore, the almost pH-neutral electrolyte (pH 8.5) suffers changes in pH during the adsorption and desorption processes, which equilibrate slowly and shift the adsorption/desorption potentials. Fig. 2(c) shows strain versus potential. The most apparent features are a large hysteresis and a cross-over, related to regions of both positive and negative slope. In the spirit of the above discussion, the strain–potential graph can be related to the exchange of H+ and oxygen species in an obvious way: the onset of ‘OH-adsorption’ at +0.2 V anodic coincides with the onset of expansion, and the net expansion strain corresponds to an equal and opposite contraction strain associated with the oxygen desorption peak. Arrows labeled ‘OA’ and ‘OD’ indicate the processes in the figure. Even more obvious are the onset of expansion, coinciding with the above tentative onset-potential for dominant H-adsorption (around −0.85 V) in the cathodic scan, and the completion of the corresponding contraction at around +0.2 V, which coincides with the end of the suggested Hdesorption feature near the centre of the anodic scan. We believe, that this discussion suggests a plausible picture of the potential regimes where two separate adsorption/desorption processes, both associated with expansion during adsorption, are dominant in separate regimes of the voltammogram. The graph of strain versus charge, Fig. 2(d) agrees with the above observations. Most notably, there are two roughly linear regimes with strain–charge response of opposite sign. Though the cathodic and anodic branches do not perfectly agree, the hysteresis of the strain–potential plot has essentially been removed by plotting the strain versus the charge. This trend agrees with previous observation for Pt [6,10] and Au [7] in various electrolytes, suggesting that the strain is essentially a function of the superficial charge density. It is noteworthy that the large hysteresis between oxidation and reduction enables scans where, depending on the potential regime at which the sample was equilibrated before the cycle, capacitive (or pseudo-capacitive) processes can be conducted either with or without an oxide layer in place. The data presented below explore this behavior. Because the hydrogen adsorption/desorption does not involve a similarly clear hysteresis, no analogous experiment was possible on Pt–H. 3.2. Charge strain response, oxidation/reduction cycle
Fig. 3. Cyclic voltammograms for platinum samples in 0.7 M NaF electrolyte. (a) Porous Pt at 1 mV/s; (b) porous Pt at 30 V/s; (c) planar Pt surface at 50 mV/s.
Here we inspect the charge–strain response during scans in the potential interval −0.5 to +0.9 V, which includes the oxidation and reduction of the surface, but which excludes hydrogen adsorption. The measurement was done on a ‘fresh’ sample, conditioned as described in Section 2. The cyclic voltammogram (Fig. 4(a)) shows that the cycle comprises here the formation and reduction of an oxidized Pt surface (and adsorption and desorption of oxygen species). Note in particular the absence of the peak near 0 V in the anodic scan
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Fig. 5. Variation of strain l/l0 from the length change l of porous platinum (left ordinate) and the negative of the surface stress change, −f (right ordinate), vs. change in surface charge Q measured during the in situ charging of porous platinum immersed in 0.7 M NaF electrolyte measured between −0.5 and 0.92 V at 30 V/s. Note that more positive strain correlates with more negative surface stress.
than by slow oxidation or reduction kinetics. For reference in the section describing the analysis of the surface stress–charge response (see below) we point out that the ratios of the peakto-peak amplitudes, strain amplitude over charge amplitude, are closely similar for the two very different scan rates. The observation confirms our previous suggestion, that the measurement of ζ is not significantly affected by the limitations on the transport kinetics [10]. The strain amplitude of ∼0.14% obtained at 30 V/s is consistent with our previous reported strain, 0.14%, measured for nominally identical sample material but with a different electrolyte, 1 M KOH [6]. 3.3. Charge strain response, oxide-covered surface Fig. 4. Results of in situ dilatometry studies of porous platinum immersed in 0.7 M NaF electrolyte measured between −0.5 and 0.9 V at 1 mV/s. (a) Cyclic scans of current I vs. potential E. (b) Charge transfer Q vs. E. (c) Strain l/l0 vs. E. (d) Strain l/l0 (left ordinate) and the negative of the surface stress change, −f (right ordinate), plotted vs. the charge transfer Q. Note that more positive strain correlates with more negative surface stress. All graphs show 10 successive cycles superimposed.
of Fig. 2(a). This supports our discussion of this feature in terms of hydrogen desorption. Fig. 4(b) shows the change of the net charge, Q, versus potential, E. The plots of strain versus potential (Fig. 4(c)) and strain versus charge (Fig. 4(d)) confirm the sample expansion during positive charging. Fig. 5 shows the strain versus charge plot measured at the much smaller scan rate of 30 V/s under otherwise identical conditions. It is seen that the hysteresis is here considerably reduced, in support of the notion that the strain and the underlying capillary parameter, the surface stress (see below) are functions of the charge. The finding that the amplitudes of charge and strain at 30 V/s are both about three times as large compared with the 1 mV/s scans indicate that the equilibration is incomplete during the faster scan. Since Fig. 3 demonstrates that the kinetics of the charge transport is slow, probably due to the limited electrical conductivity of the almost pH-neutral solution and due to the restricted transport in the pore space, it is likely that the charging current is limited rather by the transport
Here we exploit the large hysteresis between oxidation (‘OH-adsorption’) and reduction for studying the stress–charge response during pseudo-capacitive charging of an oxide-covered surface.
Fig. 6. Coulombmetric signature of oxidation treatment. Main frame shows 12 successive voltammograms of current I vs. electrode potential E. Current decreases from scan to scan. Inset shows cumulative charge transferred after the end of each scan. Ordinate gives scan number on logarithmic scale. Note the linear increase, indicating that there is no saturation oxide coverage.
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the potential cycles. Fig. 7(a) shows the cyclic voltammogram. Fig. 7(b) shows the net charge transferred to the sample as a function of electrode potential. Here, the graphs are closed, indicating that the remaining process that was not reversed in the preceding series of oxidation scans was related to the strong increase in anodic current beyond +1.0 V. By inspection of Fig. 2(a) it is seen that the present potential range is entirely on the anodic side of the ‘OH-desorption’ peak. Thus, the adsorbate or oxide is expected to remain in place during this cycle, so that charge transfer is dominantly due to capacitive processes, possibly with a contribution from cyclic adsorption/desorption of more weakly bound ions on top of the chemisorbed (oxide) layer, which remains in place during the present cycles. The dominant feature in the in situ strain measurements is a cyclic expansion/contraction when the electrode potential
Fig. 7. Results of in situ dilatometry studies of partially oxidized porous platinum immersed in 0.7 M NaF electrolyte. (a) Cyclic scans of current I vs. potential E. (b) Charge transfer Q vs. E. (c) Strain l/l0 vs. E. (d) Strain l/l0 (left ordinate) and the negative of the surface stress change, −f (right ordinate), plotted vs. the charge transfer Q. Note that the slope is of opposite sign to that in Fig. 4. Also, note that more positive strain correlates with more negative surface stress. All graphs show 15 successive cycles superimposed.
In order to oxidize the surface, the porous platinum sample was repeatedly cycled in NaF in the potential range +0.25 to +1.1 V, anodic of the surface reduction peak. The CV, Fig. 6, illustrate that the broad adsorption feature is essentially suppressed after the first cycle, indicating that the corresponding O-adsorption sites are essentially saturated. However, a net charge transfer persists during all successive cycles, diminishing only slowly. In fact, the cumulative charge transferred to the sample increases linearly with the logarithm of the scan number (see inset in Fig. 6), indicating that there is no saturation of the oxidation process. The net charge transferred after 12 scans, about 6 C, translates into about three electrons per Pt surface atom, or around 1½ equivalent monolayers of oxide. In situ strain measurements were now performed during potential cycles in the interval +0.1 to +1.0 V. Fig. 7 shows 15 successive scans superimposed; their reproducibility supports the notion that the surface oxide remains in place during
Fig. 8. Results of in situ deformation studies of nominally oxide-free porous platinum (after reduction) in the potential interval −0.2 and 0.5 V. (a) Cyclic scans of current I vs. potential E. (b) Charge transfer Q vs. E. (c) Strain l/l0 vs. E. (d) Strain l/l0 (left ordinate) and the negative of the surface stress change, −f (right ordinate) plotted vs. the charge transfer Q. Note that more positive strain correlates with more negative surface stress. All graphs show 11 successive cycles superimposed.
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(Fig. 7(c)) or the charge (Fig. 7(d)) is varied, similar to Fig. 4. The most important observation is here that the plot of strain versus charge shows contraction during the anodic scan, in striking contrast to the expansion found invariably in previous studies of Pt and Au surfaces in the capacitive regime, including Figs. 4 and 5 here. Note that the strain measurements of Fig. 7 cannot be explained by oxidation/reduction cycles, since the experiment of Fig. 4 shows that the sample expands in the anodic scan when oxidized.
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4. Discussion of surface stress–charge response The central observation of the previous section is the existence of different regimes, each with a roughly linear dependence of strain on charge, but with slopes of different magnitude and sign. Table 1 summarizes the potential ranges along with the peak-to-peak changes of charge transfer, q, strain, l/l0 , and surface stress, f. We now resume our discussion of the underlying adsorption/desorption processes, and proceed to discuss the surface stress–charge response and possible mechanisms.
3.4. Charge strain response, clean surface 4.1. Nature of the different surface states The next step of our experimental sequence aimed at recovering and investigating the clean Pt surface. To this end, the potential was cycled to more negative values, between −0.55 V and −0.1 V, still using NaF as the electrolyte. Multiple cycles were performed, using a scan rate of 1 mV/s, until the imbalanced reduction current became imperceptible. In situ experiments were then carried out in the potential range −0.2 V and 0.5 V, which includes a regime of constant capacitance as well as weak cyclic adsorption/desorption features. The CV, Fig. 8(a), agrees closely with the relevant section of the CV for larger potential window, Fig. 2(a). The peak at −0.1 V in the anodic scan is unexpected in view of the absence of this feature in scans covering a somewhat wider potential interval, Fig. 4. Conceivably, the absence of the peak in Fig. 4(a) is related to a more disordered state of the surface there, with incomplete reduction during the cathodic scan. However, a conclusive statement about the origin of the current maximum around −0.1 V is not possible here. Fig. 8(b–d) shows the results for surface charge versus potential, strain versus potential and strain versus charge, respectively. It is seen that the sample expands during the anodic scan, so that the strain charge response of Fig. 4 is recovered. In other words, one can repeatedly switch between an oxide-covered surface, showing contraction during positive charging, and a clean surface, showing charge–strain response of opposite sign.
Several processes are involved in the oxidation of the Pt surface [23,24,27]: (i) adsorption of oxygen species in the form of ad-molecules on the Pt surface (according to [23,24] rather H2 O and Oads than OHads ), (ii) de-protonation processes, e.g. Pt–OH2 → Pt–O + 2H+ + 2e− and (iii) an inward movement of oxygen and an outward displacement of Pt (‘place exchange’ [23] or ‘replacement-turnover’ between adsorbed O and Pt [28]), during which a thin ‘quasi three-dimensional’ film is formed where O is buried underneath Pt atoms on the surface, giving anhydrous PtO [24]. The formation of this film may set in at only fractional surface coverage, and may continue to several monolayers in thickness. Conway [27] emphasizes that during the interaction of Pt electrodes with oxygen highly reversible processes concur with ‘irreversible’ ones, which exhibit a strong hysteresis and slow desorption kinetics. The hysteretic process is believed to be related to desorption of the buried oxygen species and the removal of the place-exchanged layer. The reversible process is attributed to sub-monolayer adsorption, and it is found both on the clean and on the oxide-covered Pt surface. This process contributes a pseudo-capacitive component to the CV, on top of the capacitive double-layer charging proper. The findings from our cyclic voltammograms are well compatible with the above picture. The most notable implication is
Table 1 Summary of parameters and results for the four processes as listed in the first column Potential range (V)
q (C/m2 )
ne e− /Pt
l/l0 (10−4 )
f (N/m)
ζ (V)
Oxidation/reduction −0.85 to +1.0 (Fig. 3) −0.50 to +0.90 (Fig. 4) −0.50 to +0.92 (Fig. 5)
2.2 1.8 3.8
0.90 0.75 1.56
6.9 5.4 14.1
−1.62 −1.27 −3.35
−0.75 −0.71 −0.90
Mean
−0.79
Hydrogen desorption/adsorption −1.15 to +0.20 (Fig. 3)
1.15
0.48
−7.3
1.73
+1.51
Capacitive (oxygen-covered surface) +0.10 to +1.0 (Fig. 7)
0.29
0.12
−2.0
0.47
+1.60
Capacitive (clean surface) −0.20 to +0.50 (Fig. 8)
0.47
0.20
2.2
−0.50
−1.06
q, ne , l/l0 , peak-to-peak changes (amplitude and sign corresponding to a change E > 0) of charge density, electron per Pt surface atom, strain and surface stress, respectively; ζ, surface stress–charge coefficient. See Section 2 for details on referring experimental net charge value to surface area and to number of surface atoms.
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that the ‘oxide-covered’ state of the surface involves a placeexchanged layer, in which at least part of the oxygen occupies sub-surface sites. The pseudo-capacitive process on the oxidecovered surface can then be attributed to double-layer charging plus reversible adsorption. The current view of hydrogen adsorption on Pt does not allow for place exchange: the existence of noticeable amounts of H on sub-surface sites has been speculated upon [29,30], but has remained without firm experimental support so far. Ab initio simulation [31] indicates that the adsorption of H as well as O on Pt(1 1 1) relaxes the tensile surface stress of pure Pt, in agreement with the trend for expansion during hydrogen- as well as oxygen adsorption found here. 4.2. Surface stress–charge responses
(1)
where VS and A denote, respectively, the volume of the solid and the total wetted surface area, and the brackets denote the respective averages. For a linear surface stress–charge relation, f = ζ q, and for linear elastic response, P = −KVS /VS with K the bulk modulus, one obtains −3KVS = 2ζAqA = 2ζQ.
(2)
In situ X-ray diffraction on porous Pt samples similar to the ones investigated here [6] suggests the relative volume change of the solid (as inferred from the lattice parameter) scales with the macroscopic length change according to 3l/ l0 =
ΔVS . VS
(3)
Using VS = m/ρ where m and ρ denote the sample mass and the mass–density of the solid, respectively, we can relate ζ to the measured quantities, the macroscopic strain l/l0 , the transferred charge Q, and the sample mass m via ζ=−
9Km l . 2ρl0 Q
(4)
This relation, along with Eq. (2), connects ζ to measurable data in a simple way, which is largely independent of the scale and geometry of the microstructure. In particular, its analysis does not require that the specific surface area or the porosity are known. We have determined (l/l0 )/Q from straight-line fits to the in situ dilatometry data – including anodic and cathodic 3
4.3. Magnitude of surface stress variation The relations discussed above can be combined into a relation between strain and surface stress, from which the change, f, in surface stress can be estimated provided that the specific surface area, αm , is known: f A = −
We have previously shown how the surface stress–charge coefficient, ζ, can be determined from the in situ strain measurements [6,10]. The analysis exploits the fact that the volumetric mean of the pressure, P, in the bulk of the material is related to the area average surface stress via [32,33]3 3VS PV = 2Af A ,
branches – in the respective intervals. Table 1 shows values of ζ obtained by inserting this data into Eq. (4), using K = 283 GPa for bulk Pt. Since these results have been obtained from the linear plots of strain versus charge (after carefully selecting the scan range by inspection of the voltammograms), they are not affected by possible shifts of pH and of adsorption potentials (as visible in Fig. 3).
The more general version of Eq. (1) in [31,32] refers to absolute values of pressure and of surface stress due to all interfaces, including grain boundaries. Here, the contribution of grain boundaries drops out when computing differences, since their surface stress may safely be assumed to remain constant during potential cycling.
9K l . 2αm ρ l0
(5)
This emphasizes the linear relation between the strain as measured by dilatometry and the surface stress. In fact, all strain data shown in the diagrams of the preceding section are converted to surface stress changes by multiplying the strain values in the ordinate with a (negative-valued) constant, c = −2390 N/m. Table 1 shows the peak-to-peak changes (amplitudes plus sign for a change E > 0) of surface stress, f, obtained in this way. We shall now discuss selected aspects of these findings. 4.4. Comparison of surface stress–charge phenomenology to previous findings The ζ-values for oxidation–reduction and for pseudocapacitive processes on clean Pt have been investigated previously. Our findings agree with the trends found in these studies: for oxidation/reduction, our value of about −0.8 V compares to −0.7 V for oxidation/reduction in KOH [6], whereas our −1.1 V for the pseudo-capacitive process compares well to data in [8] for gold and to −1.2 V as interpolated in Fig. 4 of Ref. [10] for Pt in NaF of the present molarity. The change in sign of the surface stress–charge behavior in the hydrogen adsorption region has first been reported by Seo et al. [34], though the surface stress was not quantified. Feibelman [31] has studied the effect of H- and O-adsorption on the surface stress of Pt(1 1 1) surfaces (in vacuum) by density functional theory (DFT). Our observation of more negative f for both H- and O- (or OH) adsorption in the electrolyte agrees qualitatively with the DFT results (f < 0 for H-adsorption which requires E < 0, in spite of the positive sign of f in Table 1). In the case of hydrogen, the present results imply – by extrapolation from the actual coverage of about 0.5 monolayer as indicated by the charge transfer – that one monolayer of adsorbed hydrogen would correspond to a surface stress change of −3.3 N/m. This compares to a quite similar value, −4.6 N/m, found by DFT. The ab initio work finds a linear dependence of surface stress on coverage, which is also well compatible with our findings. For oxygen, the results in Ref. [31] imply −3.2 N/m for saturation coverage of 1/4 monolayer, in other words the effect per atom is about four times that of hydrogen. This is not born out by the present findings at electrode surfaces: even if we
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admit a charge transfer of two electrons per O (as opposed to one electron per OH), we find that the surface stress change per adsorbate atom or molecule is at best the same, if not less, than for H. Apparently, the processes probed during the electrochemical surface oxidation/reduction cycle differ from simple oxygen adsorption on Pt as studied in Ref. [31]. This is well compatible with a partial lifting of the oxygen-induced surface stress via place exchange in our experiments. 4.5. Origin of the stress–charge response An overview of various models for the effects of cleavage and of adsorption in vacuum on the surface stress of noble metal surfaces can be found in Ref. [31]. In one way or another, each relates the tensile surface stress of clean metal surfaces to a charge deficiency near the atoms of the outermost plane. Obviously, this concept on its own cannot explain the surface stress variation during capacitive charging of the clean surface, where negative charging – while removing part of the charge deficiency – makes f even more tensile (more positive). As mentioned in Section 1, two suggestions have been made for the origin of the surface stress–charge response during capacitive charging of clean metal surfaces [11–13], i.e. for conditions where adsorption effects are absent or negligible. One is based on the strain-derivative of the work function, W, which is related to ζ via a Maxwell relation. Lateral straining changes the electron density, ρe , and a systematic increase in W with ρe is implied by Jellium data. For Jellium, a negative value of ζ is obtained in this way, in agreement with experiments on clean noble metal surfaces. However, the predicted numerical magnitude (about ζ = −0.1 V for Au)4 largely underestimates the experimental value, and the approach fails to account for the dependency of ζ on the surface orientation [12]. By contrast, ab 4 The link between the surface stress–charge coefficient, ς, and the variation of the work function, W, with the conduction electron density, ρe , of metals has been considered independently by Haiss et al. [8] and by Ibach [13]. Both references withhold details of the derivation. The basis is the result of a DFT analysis of Jellium [35], W ≈ 4.63 eV−0.38 eV × rS /rB , where rS and rB denote the electron’s Wigner-Seitz radius and the Bohr radius, and 4πrS3 /3 = ρe−1 . Since ρe varies when the material is strained, the relation may be used to estimate the strain-derivative of W and, through the Maxwell relation [8,12,13] ∂f/∂q|e = q0−1 ∂W/∂e|q (q0 is the elementary charge), the value of ς near the pzc. The underlying assumption is that three issues may be neglected, (i) the details of atomic structure and bonding, which depend on the surface orientation, (ii) the break in lattice symmetry ensuing from the tangential character of the strain, and (iii) the possible role of atomic relaxation. Allowing for transverse contraction of the bulk during a tangential strain, ␦e = ␦A/A, at constant normal stress (which is the appropriate form for processes at constant pressure in the electrolyte), we have ␦ρe /ρe = (2υ−1)(1−υ)−1 ␦e. With the Jellium result for W we then obtain dW/de = 0.13 eV (2υ − 1)(1 − υ)−1 rS /rB . For gold, which has rS = 3.0 rB and Poisson number υ = 0.42, one estimates ς = −0.10 V. This is considerably smaller than the results quoted by Haiss et al. (−0.45 V) and by Ibach (−0.38 V), who both apparently ignored the important effects of transverse contraction. While predicting the sign of ς correctly, the argument largely underestimates the parameter’s experimental magnitude (−0.9 to −2 V for weak adsorption). One is lead to conclude that details of the atomic and electronic structure and/or relaxation, which are ignored by the Jellium model, must contribute decisively to the surface stress–charge response.
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initio computation of the work function strain dependence for fully relaxed Au surfaces predicts ζ in quantitative agreement with experiment, emphasizing the importance of crystallography and relaxation [12]. In fact, the second suggested model (see below) proposes a normal relaxation of the surface layer as the primary response to surface charging [11]. According to this picture, which remains speculative in the absence of dedicated studies of stress and relaxation at charged metal surfaces, the forces and the surface stress represents a secondary effect, which may be understood in terms of transverse contraction tendency of solids. These considerations agree at least qualitatively with the present findings, with the notable exception that the positive sign of ζ which we find here for the (pseudo-)capacitive process on the oxide-covered surface is unexpected. We believe that a detailed atomistic simulation is required for establishing a reliable explanation. However, we find it instructive to discuss the findings in relation to two limiting cases of the excess charge distribution, specifically the depth of penetration of the excess charge. In the first limiting case, the excess charge is taken to be essentially localized outside the surface. This appears a realistic model on dense-packed surfaces of noble metals, where the efficient electronic screening prevents noticeable penetration of the excess charge into the bulk. Here, an obvious interaction mechanism is a shift of the electrostatic centre of gravity of the surface Wigner-Seitz cell, which prompts an outward relaxation (‘stretch’) of the ion cores when the excess charge is negative (i.e., positive excess of electrons) [11]. In as much as the excess charge does not directly enter the orbitals that are responsible for the bonding between the surface atoms, the most important effect of charging on surface stress could here be indirect: the electronic charge is redistributed as the result of the outward stretch, away from the bonds between the surface and first sub-surface layer of atoms, and into the inplane bonds. This would result in more tensile (positive) surface stress during negative charging, in agreement with the observation of ζ < 0 at clean noble metal surfaces. The process would be quite analogous to the one which controls the transverse contraction of bulk matter, and in fact the coupling between surface stress and surface stretch at gold surfaces is in reasonable quantitative agreement with simple transverse contraction [11,12]. As the opposite limiting case let us consider a semiconductor with weak screening, where the excess charge penetrates several atomic layers into the bulk. Here, it is expected that the excess charge occupies the unfilled states of the bulk density of states (DOS) just above the Fermi energy. The effect on the surface stress may then be understood in terms of the character, bonding or antibonding, of these orbitals. In other words, the excess charge affects the bonding directly, as opposed to the indirect effect, mediated by stretch, in the case of strong screening. We believe that the observations of charge-induced strain in graphite [36,37] may serve to illustrate this situation. Here, the Fermi energy is in a minimum of the DOS, between the bonding valence band and the antibonding conduction band. Due to the small conduction electron density, weak screening is expected.
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Excess electrons (negative charging) are expected to populate the antibonding conduction band states of graphite, while a deficit of electrons (positive charging), depletes the bonding valence band states. Both processes are expected to decrease the net bond strength. Indeed, graphite is found to expand when charged, irrespective of the sign of the excess charge [36,37]. Similar behavior would be expected for ‘true’ semiconductors such as Si or Ge. In relation to the present experiments it is noteworthy that the surface oxide on Pt electrodes is known to be semiconducting [28]. This suggests the screening on Pt–O is less efficient than on the clean surface, so that the excess charge can penetrate deeper. The positive-valued ζ might then be understood in terms of the filling (depletion) of antibonding valence band states if the oxide-covered surface is charged more negatively (positively), as would be the case if the Fermi energy near the surface was pinned below the valence band edge. While the above argument was designed to rationalize some of the aspects of the surface stress–charge response during capacitive charging, we note that it is not without contact to the behavior during adsorption, if that includes a change in the occupancy of bonding or antibonding band states of the metal [5].
5. Summary We have presented in situ dilatometry results for the surface stress–charge response of platinum immersed in aqueous NaF. While the electrolyte is believed to exhibit weak anion adsorption, the potential range under study included regions of extensive oxygen and hydrogen adsorption. We find that the surface stress–charge response may be characterized separately for four different processes, selected by the potential range and by the surface pretreatment: hydrogen adsorption/desorption, oxygen adsorption/desorption (and/or surface oxidation/reduction), and nominally capacitive charging of the Pt surface in two different states, clean and oxidecovered. While each process exhibits a roughly linear surface stress–charge response, the magnitude and even the sign of the slope, which determines the surface stress–charge coefficient, ζ, differ. Besides these most obvious features, in situ strain graphs such as Figs. 1 and 2 exhibit a significant and highly reproducible sub-structure. This indicates the presence of additional electrode processes that may deserve attention in future studies. The highly reproducible resolution of these details emphasizes the robustness and sensitivity of strain measurements on nanoporous samples as probes for the electrocapillary behavior of solid surfaces. We suggest that the sign of ζ depends on the penetration depth of the excess charge: for strong screening the electronic charge is located outside of the surface, and ζ is negative as found previously for clean metal surfaces. For weaker screening, the wider space charge layer implies a trend for the excess charge to fill bulk-like unoccupied states. These states are here antibonding, giving positive-valued ζ.
An open issue is the possible effect of surface roughening, for instance by the formation of adatoms during the removal of the place-exchanged oxide layer. It is conceivable that the surface stress and its response to charging are affected by this detail of the surface defect structure. Such a process could contribute in an as yet unknown way to the cyclic surface stress variation observed here. On the other hand, the large number of step edges in nanoporous materials provides efficient sinks for adatoms, so that the surface roughness is not too severely affected by the cyclic oxidation/reduction processes. Acknowledgments Support by the Deutsche Forschungsgemeinschaft (Center for Functional Nanostructures) and by the Landesstiftung Baden-W¨urttemberg (Kompetenznetz Funktionelle Nanostrukturen) and discussions with L. Kibler are gratefully acknowledged. References [1] D. Kramer, J. Weissm¨uller, Surf. Sci. 601 (2007) 2042. [2] W. Haiss, J.-K. Sass, Langmuir 12 (1996) 4311. [3] N. Vasiljevic, T. Trimble, N. Dimitrov, K. Sieradzki, Langmuir 20 (2004) 6639. [4] H. Ibach, C.E. Bach, M. Giesen, A. Grossmann, Surf. Sci. 375 (1997) 107. [5] W. Haiss, Rep. Prog. Phys. 64 (2001) 591. [6] J. Weissm¨uller, R.N. Viswanath, D. Kramer, P. Zimmer, R. W¨urschum, H. Gleiter, Science 300 (2003) 312. [7] D. Kramer, R.N. Viswanath, J. Weissm¨uller, Nano Lett. 4 (2004) 793. [8] W. Haiss, R.J. Nichols, J.K. Sass, K.P. Charle, J. Electroanal. Chem. 452 (1998) 199. [9] K. Sieradzki, Private communication (2007). [10] R.N. Viswanath, D. Kramer, J. Weissm¨uller, Langmuir 21 (2005) 4604. [11] F. Weigend, F. Evers, J. Weissm¨uller, Small 2 (2006) 1497. [12] Y. Umeno, C. Els¨asser, B. Meyer, P. Gumbsch, M. Nothacker, J. Weissm¨uller, F. Evers, Europhys. Lett. 78 (2007) 13001. [13] H. Ibach, Physics of Surfaces and Interfaces, Springer, 2006, Section 4.2.4. [14] R. Berger, E. Delamarche, H.P. Lang, Ch. Gerber, J.K. Gimzewski, E. Meyer, H.-J. G¨untherodt, Science 276 (1997) 2021. [15] M. Godin, P.J. Williams, V. Tabard-Cossa, O. Laroche, L.Y. Beaulieu, R.B. Lennox, P. Gr¨utter, Langmuir 20 (2004) 7090. [16] C. Friesen, N. Dimitrov, R.C. Cammarata, K. Sieradzki, Langmuir 17 (2001) 807. [17] M. Seo, M. Yamazaki, J. Electrochem. Soc. 151 (2004) E276. [18] G.R. Stafford, U. Bertocci, J. Phys. Chem. B 110 (2006) 15493. [19] W.-B. Cai, C.-X. She, B. Ren, J.-L. Yao, Z.-W. Tian, Z.-Q. Tian, J. Chem. Soc., Faraday Trans. 94 (1998) 3127. [20] V.A. Marichev, Prot. Met. 38 (2002) 431. [21] S. Parida, H.J. Jin, D. Kramer, J. Weissm¨uller (in preparation). [22] D.M. Kolb, Private communication (2007). [23] G. Jerkiewicz, G. Vatankhah, J. Lessard, M.P. Soriaga, Y.-S. Park, Electrochim. Acta 49 (2004) 1451. [24] M. Alsabet, M. Grden, G. Jerkiewicz, J. Electroanal. Chem. 589 (2006) 120. [25] M. Teliska, W.E. O’Grady, D.E. Ramaker, J. Phys. Chem. B 109 (2005) 8076. [26] H. Angerstein-Koslowska, B.E. Conway, W.B.A. Sharp, J. Electroanal. Chem. 43 (1973) 9. [27] B.E. Conway, Prog. Surf. Sci. 49 (1995) 331. [28] A. Sun, J. Franc, D.D. Macdonald, J. Electrochem. Soc. 153 (7) (2006) B260. [29] P. L´egar´e, Surf. Sci. 559 (2004) 169.
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Adsorbate effects on the surface stress–charge response of platinum electrodes R.N. Viswanath a,∗ , D. Kramer a , J. Weissm¨uller a,b a
Forschungszentrum Karlsruhe, Institut f¨ur Nanotechnologie, Karlsruhe, Germany b Universit¨ at des Saarlandes, Technische Physik, Saarbr¨ucken, Germany
Received 27 June 2007; received in revised form 15 October 2007; accepted 20 October 2007
Abstract The length change in response to changes in the surface stress during scans of the electrode potential was measured for nanoporous platinum samples immersed in aqueous NaF, an electrolyte with weak ion adsorption. The surface stress–charge response may be characterized separately for four different processes, selected by the potential range and by the surface pretreatment: hydrogen adsorption/desorption, oxygen adsorption/desorption (and/or surface oxidation/reduction), and nominally capacitive charging of the Pt surface in two different states, clean and oxide-covered. While each process exhibits a roughly linear response, the magnitude and even the sign of the slope, which determines the surface stress–charge coefficient, ζ, differ. We suggest that the sign of ζ depends on the penetration depth of the excess charge: for strong screening the electronic charge is located outside of the surface, and ζ is negative as found previously for clean metal surfaces. For weaker screening, the wider space charge layer implies a trend for the excess charge to fill bulk-like unoccupied states. These states are here antibonding, giving positive-valued ζ. © 2007 Elsevier Ltd. All rights reserved. Keywords: Platinum; Surface stress; Nanocrystalline; Porous electrodes; Metal–electrolyte actuators
1. Introduction The forces by which a surface interacts with the underlying bulk phase are measured by the surface tension, γ, or by its strain-derivative, the surface stress, f, in the case of fluid or solid surfaces, respectively. While the concept of surface stress at electrodes surfaces remains controversial [1], there is widespread agreement that the two parameters, γ and f, exhibit a distinctly different dependency on the electrode potential, E, or on the superficial charge density, q. Since q and E are energy-conjugate parameters, dγ = −q dE at constant values of the remaining state variables, the first variation of γ(E) must vanish at the potential of zero charge (pzc). The leading term in γ(E) near the pzc is therefore generally quadratic, and the ensuing electrocapillary maximum in γ is embodied in the Lippmann equation. No analogous argument is known for f(E), and indeed the results of the more recent relevant experiments [2–7] show a linear variation of f with E or with q near the pzc. The relevant response param-
∗
Corresponding author. Tel.: +49 7247 82 6737; fax: +49 7247 82 6368. E-mail address: [email protected] (R.N. Viswanath).
0013-4686/$ – see front matter © 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2007.10.049
eter is the surface stress–charge coefficient, ς = ∂f/∂q. Its value and the nature of the underlying microscopic interaction terms are the subject of current research. So far, all reported values of ζ in metals are negative, around −0.4 to −2 V. The most negative values are observed for electrolytes that are believed [5,6,8]1 to absorb more weakly, where a smaller fraction of the total charge q is transferred away from the metal surface and into bonds with adsorbed ions. Furthermore, experiments on Pt surfaces find |ζ| to increase when the adsorption is reduced in dilution series [10]. These observations have prompted ab initio studies of ζ at clean metal surfaces, in the absence of adsorption [11,12]. Magnitude and sign of ζ are found to agree closely with experiments on metal–electrolyte interfaces. Because a Maxwell relation equates ζ to a strainderivative of the work function, W, the negative sign can be rationalized in terms of a weakening of the surface dipole of clean metal surfaces during lateral strain [12] and to the trend 1 Note, however, that questions may be raised as to the usefulness of the particular definition of adsorption strength used in Ref. [6] for measuring the amounts of adsorption and charge transfer under the conditions of the experiment [9].
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of W in metals to increase with increasing electron density, as evidenced by results for Jellium [8,13]. Ab initio computation also points towards a decisive role of coupling between surface stress and surface relaxation (‘stretch’) in response to charging [11]. While the above arguments lend strong support to the notion that sign and magnitude of ζ for capacitive charging of metal electrodes may be understood in terms of the electron theory of clean metal surfaces, it appears also obvious that the interaction of the surface with adsorbates is rarely negligible, and more often decisive in determining the electrode behavior in electrochemical studies. Except for highly idealized conditions, adsorption processes will typically control the charge–potential behavior q(E) in experiment. Even for constant ζ, this propagates immediately to the surface stress–potential variation via f(E) = ζ q(E). Furthermore, important changes in f are observed during studies of adsorption from the vapour phase [5,14,15] and during the underpotential deposition of metals in electrolyte [16–18]. While these processes do involve the transfer of charge between the adsorbate and the metal substrate, it appears unlikely that the same processes which dominate the stress–charge response in weakly adsorbing electrolytes near their pzc act to control the surface stress when, for instance, Cu is deposited on Au. The above considerations imply that it is of interest to study the electrocapillary behavior of metal electrodes in extended potential intervals which include regions where either one of the two processes, capacitive charging or specific adsorption, dominates. Such studies would allow the comparison, for the same electrode/electrolyte combination, of the different electrode processes. Here, we present an experimental study of the surface stress–charge response of polycrystalline Pt which connects to the above issues, using a methodology established previously [6,10]. As the electrolyte we use an aqueous solution of NaF, since this is believed to be weakly adsorbing in certain potential windows [19,20]. Besides probing ζ separately in the regions of O2− /OH− - and H+ -adsorption, we also examine the question, what is the surface stress–charge response when charge is exchanged capacitively at a Pt surface covered by a stable adsorbate layer? This latter study connects to findings, reported separately [21], of a metastable (probably oxide-covered) state of polycrystalline Au surfaces where – contrary to all other reported findings – the value of ζ is found positive in experiments involving weakly adsorbing electrolytes and dominantly capacitive processes. 2. Experimental methods Cylindrical specimens of porous platinum, 1.5 mm in diameter and 1.8 mm in length, were prepared by consolidation of commercial platinum black (Alfa Aesar® ) at ambient temperature and moderate pressure (around 1 MPa), using procedures described previously [6,10]. The particle size – as determined from X-ray line broadening – was (6 ± 1) nm, and the mass-specific surface area of the consolidated samples was αm = 25.3 m2 /g, as determined by gas adsorption. For details of characterization see Ref. [6]. The mass of the porous specimens was 33 mg, giving a total surface area of 0.83 m2 . Thus,
each Coulomb of net charge on the sample implies an equivalent charge density of 1.20 C/m2 , or −0.50 electrons per surface atom (assuming a dense-packed surface layer, 1.50 × 1019 atoms/m2 ). Reference experiments for the planar polycrystalline Pt surface used a commercial Pt (99.95% purity) foil, of 1 cm2 area. For the in situ experiments, a miniaturized electrochemical cell, made of glass, was operated in the sample space of a commercial dilatometer (Netzsch® 402C). The sample compartment, which also contains the Ag/AgCl/3M KCl commercial reference electrode (FLEX-REF, World Precision Instruments, Inc.), is separated from the counter electrode compartment by a glass frit. The reference electrode is in a TeflonTM tube with a KONBOTM (ceramic/conducting polymer) porous membrane at the junction with low electrolyte leakage. Porous platinum (same material as the samples) was used as a counter electrode. Prior to the experiments the cell was cleaned with concentrated nitric acid and then rinsed thoroughly with ultrapure 18.2 M cm grade water to remove all the adsorbed impurities. A steady state temperature of 283 K ± 0.1 K was maintained, by connecting the dilatometer sample space to a bath thermostat. The potential was controlled via a potentiostat (PGSTAT 100, EcoChemie). For synchronization, the dilatometer output signal was fed to the potentiostat’s external input channel, and saved along with current and net charge in a single data file. The net charge, Q, transferred to the sample was determined using the potentiostat’s current integration mode. All values for Q, for the strain, l/l0 , and for the surface stress change, f, are referred to arbitrary reference states. In previous studies [6,10] we had found that repeated cycling is required before reproducible results on the stress–charge behavior can be obtained. Similar to the procedure there, 20 successive scans at 1 mV/s in 0.5 M H2 SO4 in between oxidation and reduction regions (potential range −0.05 to 0.85 V) were instigated with the consolidated porous samples. The samples were then washed repeatedly in ultrapure water (18.2 M cm) to remove any traces of H2 SO4 . The electrolyte used in all in situ dilatometry experiments of this work was 0.7 M solution of NaF (Merck® , 99.9%) in ultrapure water. The electrolyte solution was prepared in air at room temperature (294 K). Prior to the data collection of the in situ experiments, the samples were cycled in NaF (10 successive scans at 1 mV/s in the potential range −0.35 to 0.75 V) in order to ensure a stable and reproducible electrochemical behavior. With one exception (Fig. 5), all scan series shown below started after a 2 h hold at 0.12 V, which is close to the open circuit potential. Potential values in this study are specified relative to the Ag/AgCl/3 M KCl reference electrode used which shifts +200 mV to a standard hydrogen electrode (SHE). Unless stated otherwise, the scan rate is 1 mV/s. 3. Results and discussion of adsorption features 3.1. Overview of charge strain response Here we display an overview of the variation of charge and strain with the electrode potential, inspecting a potential interval, −1.15 to +1.0 V, which includes the regions of adsorption of
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hydrogen as well as oxygen. As a background for the description of the surface stress–charge response, we include a discussion of the most prominent features of the voltammogram at this point, partly anticipating the paper’s Section 4. Fig. 1 displays the time-dependent change in length l of porous platinum and the electrode potential E during nine successive potential cycles. It is seen that the potential variation entails a highly reproducible cyclic deformation. This indicates a stable microstructure of the nanoporous sample in spite of the repeated oxidation/reduction/hydriding/dehydriding cycles of its surface (see below). The reproducibility was similar in all experiments reported here. In some instances, a small drift (either contraction or expansion) was superimposed to the cyclic strain; this was corrected by subtracting a smooth function of time from the l(t) data before further analysis. Importantly, each single potential cycle in Fig. 1 is seen to involve two expansion/contraction cycles of similar amplitude, indicating that the stress–charge coefficient changes sign within the potential interval. This becomes more apparent when the strain is plotted versus the potential or the charge, as discussed below. Fig. 2(a) shows the cyclic voltammogram (CV). The graphs of six successive CVs, shown superimposed in the figure, are practically identical, confirming the reproducibility. The same holds for the graphs (Fig. 2(b)) of the net charge, Q, transferred to the sample as the function of the electrode potential, E. It is noteworthy that these graphs are practically closed, indicating that the charge transfer can be reversed, and that there are no significant net Faradaic currents. Such currents would arise, for instance, if there was gas evolution. The CV in Fig. 2(a) exhibits familiar features of Pt in aqueous electrolytes, namely the oxidative adsorption peaks at the positive end of the anodic scan and adsorption of H at the negative end of the cathodic scan. It is known that the CV of Pt in pH-neutral electrolytes can exhibit a large cathodic shift of the reductive desorption peak [22]. This suggests that the peak at around −0.4 V during the cathodic scan represents reduction
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Fig. 2. Overview of in situ dilatometry studies in the potential interval −1.15 to +1.0 V. (a) Current I vs. electrode potential E. (b) Net charge transfer Q vs. E. (c) Strain l/l0 vs. E. Thin arrows denote direction of scan. Bold arrows provide a rough indication of regimes of dominantly H-adsorption (labeled ‘HA’) and H-desorption (‘HD’) and of dominantly OH-adsorption/desorption or oxidation/reduction (‘OA’/‘OD’); we believe that H+ - and OH− -related processes may occur in intermediate potential intervals. Circles mark features in the graphs associated with the transition between the two suggested regimes. Potential scan rate is 1 mV/s. (d) Strain l/l0 (left ordinate) and the negative of the surface stress change, −f (right ordinate), plotted vs. the charge transfer Q. Note that more positive strain correlates with more negative surface stress. All parts show six successive scans superimposed.
of the oxide film [23,24]2 . The nature of the anodic peaks at around −0.1 and −0.5 V is less obvious. In order to investigate their origin, we find it instructive to inspect the charge transfer, Fig. 2(b).
Fig. 1. Change in length l (bottom part of figure) and potential E (top part) during nine successive potential cycles in the interval −1.15 V < E < +1 V. Scan rate is 1 mV/s.
2 In the case of Pt oxidation in H SO , there is evidence that the oxidized 2 4 Pt surface contains chemisorbed O or anhydrous PtO rather than hydroxide [23,24], although other experiments indicate OH-adsorption at low coverage [25]. While the presence of adsorbed OH or of Pt(OH)2 is rather less likely for the almost neutral solution used here, we still would like to use the wellestablished term ‘OH adsorption’, explicitly emphasizing that this is meant to describe the adsorption of an oxygen species (OH− or H2 O) which might be immediately de-protonated.
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In view of the established phenomenology of the electrochemical oxidation of Pt (see, for instance, Refs. [26,27]) we may safely assume that the charge which is accumulated after the central anodic peak, i.e. for E > +0.2 V, during the anodic scan (circle in Fig. 2(a)) is due to oxidation (‘OH-adsorption’), with a small contribution from capacitive processes. The charge accumulated at more anodic potential must therefore be balanced by an equal and opposite charge from oxide species desorption or reduction in the cathodic scan (plus a contribution from capacitive discharging). The circles in Fig. 2(b) illustrate the corresponding values of Q, and vertical lines link them to the features of the CV in Fig. 2(a). It is seen, that our assumption requires OH-desorption/reduction to continue well into the peaks at the negative end of the cathodic scan (until E < −0.85 V). If – consistently with the above – we assume that H-adsorption starts no later than at E ≤ −0.85 V, then an analogous inspection of the charge balance indicates that hydrogen desorption cannot be complete until E ≥ +0.15 V in the anodic scan (circle in Fig. 2(a)). This argument suggests strongly that the peaks near the centre of the anodic scan represent hydrogen desorption. The arrows in Fig. 2 illustrate this picture. The interaction of Pt surfaces with hydrogen is not known to involve such strong hysteresis. This might be seen as evidence that the notion of a clear separation between the regimes of H+ and OH− exchange is unrealistic, and that a more appropriate scenario would have to allow for an overlap of the two regimes. However, the strain data – to be discussed below – are well compatible with a clear separation. It is emphasized that, compared to planar polycrystalline Pt electrodes, the features of the CV of Fig. 2(a) are shifted considerably on the potential axis. This is evident in a comparison of the respective CVs in Fig. 3, which illustrates the cathodic shift of the OH-desorption and H-adsorption peaks, as well as the anodic shift of the H-desorption and OH-adsorption. Also shown in Fig. 3 is a CV of porous Pt at the slower scan rate of 30 V/s. The peak positions are here generally intermediate between those for porous Pt at 1 mV/s and those of the planar electrode. This indicates that the transport kinetics in the
pore space limit the rate of the electrode processes. This may be due to the potential gradient in the pore space arising from the electrical resistance of the solution, which is larger than that of highly acidic solutions for which such considerable potential shifts have not been observed [6]. Furthermore, the almost pH-neutral electrolyte (pH 8.5) suffers changes in pH during the adsorption and desorption processes, which equilibrate slowly and shift the adsorption/desorption potentials. Fig. 2(c) shows strain versus potential. The most apparent features are a large hysteresis and a cross-over, related to regions of both positive and negative slope. In the spirit of the above discussion, the strain–potential graph can be related to the exchange of H+ and oxygen species in an obvious way: the onset of ‘OH-adsorption’ at +0.2 V anodic coincides with the onset of expansion, and the net expansion strain corresponds to an equal and opposite contraction strain associated with the oxygen desorption peak. Arrows labeled ‘OA’ and ‘OD’ indicate the processes in the figure. Even more obvious are the onset of expansion, coinciding with the above tentative onset-potential for dominant H-adsorption (around −0.85 V) in the cathodic scan, and the completion of the corresponding contraction at around +0.2 V, which coincides with the end of the suggested Hdesorption feature near the centre of the anodic scan. We believe, that this discussion suggests a plausible picture of the potential regimes where two separate adsorption/desorption processes, both associated with expansion during adsorption, are dominant in separate regimes of the voltammogram. The graph of strain versus charge, Fig. 2(d) agrees with the above observations. Most notably, there are two roughly linear regimes with strain–charge response of opposite sign. Though the cathodic and anodic branches do not perfectly agree, the hysteresis of the strain–potential plot has essentially been removed by plotting the strain versus the charge. This trend agrees with previous observation for Pt [6,10] and Au [7] in various electrolytes, suggesting that the strain is essentially a function of the superficial charge density. It is noteworthy that the large hysteresis between oxidation and reduction enables scans where, depending on the potential regime at which the sample was equilibrated before the cycle, capacitive (or pseudo-capacitive) processes can be conducted either with or without an oxide layer in place. The data presented below explore this behavior. Because the hydrogen adsorption/desorption does not involve a similarly clear hysteresis, no analogous experiment was possible on Pt–H. 3.2. Charge strain response, oxidation/reduction cycle
Fig. 3. Cyclic voltammograms for platinum samples in 0.7 M NaF electrolyte. (a) Porous Pt at 1 mV/s; (b) porous Pt at 30 V/s; (c) planar Pt surface at 50 mV/s.
Here we inspect the charge–strain response during scans in the potential interval −0.5 to +0.9 V, which includes the oxidation and reduction of the surface, but which excludes hydrogen adsorption. The measurement was done on a ‘fresh’ sample, conditioned as described in Section 2. The cyclic voltammogram (Fig. 4(a)) shows that the cycle comprises here the formation and reduction of an oxidized Pt surface (and adsorption and desorption of oxygen species). Note in particular the absence of the peak near 0 V in the anodic scan
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Fig. 5. Variation of strain l/l0 from the length change l of porous platinum (left ordinate) and the negative of the surface stress change, −f (right ordinate), vs. change in surface charge Q measured during the in situ charging of porous platinum immersed in 0.7 M NaF electrolyte measured between −0.5 and 0.92 V at 30 V/s. Note that more positive strain correlates with more negative surface stress.
than by slow oxidation or reduction kinetics. For reference in the section describing the analysis of the surface stress–charge response (see below) we point out that the ratios of the peakto-peak amplitudes, strain amplitude over charge amplitude, are closely similar for the two very different scan rates. The observation confirms our previous suggestion, that the measurement of ζ is not significantly affected by the limitations on the transport kinetics [10]. The strain amplitude of ∼0.14% obtained at 30 V/s is consistent with our previous reported strain, 0.14%, measured for nominally identical sample material but with a different electrolyte, 1 M KOH [6]. 3.3. Charge strain response, oxide-covered surface Fig. 4. Results of in situ dilatometry studies of porous platinum immersed in 0.7 M NaF electrolyte measured between −0.5 and 0.9 V at 1 mV/s. (a) Cyclic scans of current I vs. potential E. (b) Charge transfer Q vs. E. (c) Strain l/l0 vs. E. (d) Strain l/l0 (left ordinate) and the negative of the surface stress change, −f (right ordinate), plotted vs. the charge transfer Q. Note that more positive strain correlates with more negative surface stress. All graphs show 10 successive cycles superimposed.
of Fig. 2(a). This supports our discussion of this feature in terms of hydrogen desorption. Fig. 4(b) shows the change of the net charge, Q, versus potential, E. The plots of strain versus potential (Fig. 4(c)) and strain versus charge (Fig. 4(d)) confirm the sample expansion during positive charging. Fig. 5 shows the strain versus charge plot measured at the much smaller scan rate of 30 V/s under otherwise identical conditions. It is seen that the hysteresis is here considerably reduced, in support of the notion that the strain and the underlying capillary parameter, the surface stress (see below) are functions of the charge. The finding that the amplitudes of charge and strain at 30 V/s are both about three times as large compared with the 1 mV/s scans indicate that the equilibration is incomplete during the faster scan. Since Fig. 3 demonstrates that the kinetics of the charge transport is slow, probably due to the limited electrical conductivity of the almost pH-neutral solution and due to the restricted transport in the pore space, it is likely that the charging current is limited rather by the transport
Here we exploit the large hysteresis between oxidation (‘OH-adsorption’) and reduction for studying the stress–charge response during pseudo-capacitive charging of an oxide-covered surface.
Fig. 6. Coulombmetric signature of oxidation treatment. Main frame shows 12 successive voltammograms of current I vs. electrode potential E. Current decreases from scan to scan. Inset shows cumulative charge transferred after the end of each scan. Ordinate gives scan number on logarithmic scale. Note the linear increase, indicating that there is no saturation oxide coverage.
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the potential cycles. Fig. 7(a) shows the cyclic voltammogram. Fig. 7(b) shows the net charge transferred to the sample as a function of electrode potential. Here, the graphs are closed, indicating that the remaining process that was not reversed in the preceding series of oxidation scans was related to the strong increase in anodic current beyond +1.0 V. By inspection of Fig. 2(a) it is seen that the present potential range is entirely on the anodic side of the ‘OH-desorption’ peak. Thus, the adsorbate or oxide is expected to remain in place during this cycle, so that charge transfer is dominantly due to capacitive processes, possibly with a contribution from cyclic adsorption/desorption of more weakly bound ions on top of the chemisorbed (oxide) layer, which remains in place during the present cycles. The dominant feature in the in situ strain measurements is a cyclic expansion/contraction when the electrode potential
Fig. 7. Results of in situ dilatometry studies of partially oxidized porous platinum immersed in 0.7 M NaF electrolyte. (a) Cyclic scans of current I vs. potential E. (b) Charge transfer Q vs. E. (c) Strain l/l0 vs. E. (d) Strain l/l0 (left ordinate) and the negative of the surface stress change, −f (right ordinate), plotted vs. the charge transfer Q. Note that the slope is of opposite sign to that in Fig. 4. Also, note that more positive strain correlates with more negative surface stress. All graphs show 15 successive cycles superimposed.
In order to oxidize the surface, the porous platinum sample was repeatedly cycled in NaF in the potential range +0.25 to +1.1 V, anodic of the surface reduction peak. The CV, Fig. 6, illustrate that the broad adsorption feature is essentially suppressed after the first cycle, indicating that the corresponding O-adsorption sites are essentially saturated. However, a net charge transfer persists during all successive cycles, diminishing only slowly. In fact, the cumulative charge transferred to the sample increases linearly with the logarithm of the scan number (see inset in Fig. 6), indicating that there is no saturation of the oxidation process. The net charge transferred after 12 scans, about 6 C, translates into about three electrons per Pt surface atom, or around 1½ equivalent monolayers of oxide. In situ strain measurements were now performed during potential cycles in the interval +0.1 to +1.0 V. Fig. 7 shows 15 successive scans superimposed; their reproducibility supports the notion that the surface oxide remains in place during
Fig. 8. Results of in situ deformation studies of nominally oxide-free porous platinum (after reduction) in the potential interval −0.2 and 0.5 V. (a) Cyclic scans of current I vs. potential E. (b) Charge transfer Q vs. E. (c) Strain l/l0 vs. E. (d) Strain l/l0 (left ordinate) and the negative of the surface stress change, −f (right ordinate) plotted vs. the charge transfer Q. Note that more positive strain correlates with more negative surface stress. All graphs show 11 successive cycles superimposed.
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(Fig. 7(c)) or the charge (Fig. 7(d)) is varied, similar to Fig. 4. The most important observation is here that the plot of strain versus charge shows contraction during the anodic scan, in striking contrast to the expansion found invariably in previous studies of Pt and Au surfaces in the capacitive regime, including Figs. 4 and 5 here. Note that the strain measurements of Fig. 7 cannot be explained by oxidation/reduction cycles, since the experiment of Fig. 4 shows that the sample expands in the anodic scan when oxidized.
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4. Discussion of surface stress–charge response The central observation of the previous section is the existence of different regimes, each with a roughly linear dependence of strain on charge, but with slopes of different magnitude and sign. Table 1 summarizes the potential ranges along with the peak-to-peak changes of charge transfer, q, strain, l/l0 , and surface stress, f. We now resume our discussion of the underlying adsorption/desorption processes, and proceed to discuss the surface stress–charge response and possible mechanisms.
3.4. Charge strain response, clean surface 4.1. Nature of the different surface states The next step of our experimental sequence aimed at recovering and investigating the clean Pt surface. To this end, the potential was cycled to more negative values, between −0.55 V and −0.1 V, still using NaF as the electrolyte. Multiple cycles were performed, using a scan rate of 1 mV/s, until the imbalanced reduction current became imperceptible. In situ experiments were then carried out in the potential range −0.2 V and 0.5 V, which includes a regime of constant capacitance as well as weak cyclic adsorption/desorption features. The CV, Fig. 8(a), agrees closely with the relevant section of the CV for larger potential window, Fig. 2(a). The peak at −0.1 V in the anodic scan is unexpected in view of the absence of this feature in scans covering a somewhat wider potential interval, Fig. 4. Conceivably, the absence of the peak in Fig. 4(a) is related to a more disordered state of the surface there, with incomplete reduction during the cathodic scan. However, a conclusive statement about the origin of the current maximum around −0.1 V is not possible here. Fig. 8(b–d) shows the results for surface charge versus potential, strain versus potential and strain versus charge, respectively. It is seen that the sample expands during the anodic scan, so that the strain charge response of Fig. 4 is recovered. In other words, one can repeatedly switch between an oxide-covered surface, showing contraction during positive charging, and a clean surface, showing charge–strain response of opposite sign.
Several processes are involved in the oxidation of the Pt surface [23,24,27]: (i) adsorption of oxygen species in the form of ad-molecules on the Pt surface (according to [23,24] rather H2 O and Oads than OHads ), (ii) de-protonation processes, e.g. Pt–OH2 → Pt–O + 2H+ + 2e− and (iii) an inward movement of oxygen and an outward displacement of Pt (‘place exchange’ [23] or ‘replacement-turnover’ between adsorbed O and Pt [28]), during which a thin ‘quasi three-dimensional’ film is formed where O is buried underneath Pt atoms on the surface, giving anhydrous PtO [24]. The formation of this film may set in at only fractional surface coverage, and may continue to several monolayers in thickness. Conway [27] emphasizes that during the interaction of Pt electrodes with oxygen highly reversible processes concur with ‘irreversible’ ones, which exhibit a strong hysteresis and slow desorption kinetics. The hysteretic process is believed to be related to desorption of the buried oxygen species and the removal of the place-exchanged layer. The reversible process is attributed to sub-monolayer adsorption, and it is found both on the clean and on the oxide-covered Pt surface. This process contributes a pseudo-capacitive component to the CV, on top of the capacitive double-layer charging proper. The findings from our cyclic voltammograms are well compatible with the above picture. The most notable implication is
Table 1 Summary of parameters and results for the four processes as listed in the first column Potential range (V)
q (C/m2 )
ne e− /Pt
l/l0 (10−4 )
f (N/m)
ζ (V)
Oxidation/reduction −0.85 to +1.0 (Fig. 3) −0.50 to +0.90 (Fig. 4) −0.50 to +0.92 (Fig. 5)
2.2 1.8 3.8
0.90 0.75 1.56
6.9 5.4 14.1
−1.62 −1.27 −3.35
−0.75 −0.71 −0.90
Mean
−0.79
Hydrogen desorption/adsorption −1.15 to +0.20 (Fig. 3)
1.15
0.48
−7.3
1.73
+1.51
Capacitive (oxygen-covered surface) +0.10 to +1.0 (Fig. 7)
0.29
0.12
−2.0
0.47
+1.60
Capacitive (clean surface) −0.20 to +0.50 (Fig. 8)
0.47
0.20
2.2
−0.50
−1.06
q, ne , l/l0 , peak-to-peak changes (amplitude and sign corresponding to a change E > 0) of charge density, electron per Pt surface atom, strain and surface stress, respectively; ζ, surface stress–charge coefficient. See Section 2 for details on referring experimental net charge value to surface area and to number of surface atoms.
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that the ‘oxide-covered’ state of the surface involves a placeexchanged layer, in which at least part of the oxygen occupies sub-surface sites. The pseudo-capacitive process on the oxidecovered surface can then be attributed to double-layer charging plus reversible adsorption. The current view of hydrogen adsorption on Pt does not allow for place exchange: the existence of noticeable amounts of H on sub-surface sites has been speculated upon [29,30], but has remained without firm experimental support so far. Ab initio simulation [31] indicates that the adsorption of H as well as O on Pt(1 1 1) relaxes the tensile surface stress of pure Pt, in agreement with the trend for expansion during hydrogen- as well as oxygen adsorption found here. 4.2. Surface stress–charge responses
(1)
where VS and A denote, respectively, the volume of the solid and the total wetted surface area, and the brackets denote the respective averages. For a linear surface stress–charge relation, f = ζ q, and for linear elastic response, P = −KVS /VS with K the bulk modulus, one obtains −3KVS = 2ζAqA = 2ζQ.
(2)
In situ X-ray diffraction on porous Pt samples similar to the ones investigated here [6] suggests the relative volume change of the solid (as inferred from the lattice parameter) scales with the macroscopic length change according to 3l/ l0 =
ΔVS . VS
(3)
Using VS = m/ρ where m and ρ denote the sample mass and the mass–density of the solid, respectively, we can relate ζ to the measured quantities, the macroscopic strain l/l0 , the transferred charge Q, and the sample mass m via ζ=−
9Km l . 2ρl0 Q
(4)
This relation, along with Eq. (2), connects ζ to measurable data in a simple way, which is largely independent of the scale and geometry of the microstructure. In particular, its analysis does not require that the specific surface area or the porosity are known. We have determined (l/l0 )/Q from straight-line fits to the in situ dilatometry data – including anodic and cathodic 3
4.3. Magnitude of surface stress variation The relations discussed above can be combined into a relation between strain and surface stress, from which the change, f, in surface stress can be estimated provided that the specific surface area, αm , is known: f A = −
We have previously shown how the surface stress–charge coefficient, ζ, can be determined from the in situ strain measurements [6,10]. The analysis exploits the fact that the volumetric mean of the pressure, P, in the bulk of the material is related to the area average surface stress via [32,33]3 3VS PV = 2Af A ,
branches – in the respective intervals. Table 1 shows values of ζ obtained by inserting this data into Eq. (4), using K = 283 GPa for bulk Pt. Since these results have been obtained from the linear plots of strain versus charge (after carefully selecting the scan range by inspection of the voltammograms), they are not affected by possible shifts of pH and of adsorption potentials (as visible in Fig. 3).
The more general version of Eq. (1) in [31,32] refers to absolute values of pressure and of surface stress due to all interfaces, including grain boundaries. Here, the contribution of grain boundaries drops out when computing differences, since their surface stress may safely be assumed to remain constant during potential cycling.
9K l . 2αm ρ l0
(5)
This emphasizes the linear relation between the strain as measured by dilatometry and the surface stress. In fact, all strain data shown in the diagrams of the preceding section are converted to surface stress changes by multiplying the strain values in the ordinate with a (negative-valued) constant, c = −2390 N/m. Table 1 shows the peak-to-peak changes (amplitudes plus sign for a change E > 0) of surface stress, f, obtained in this way. We shall now discuss selected aspects of these findings. 4.4. Comparison of surface stress–charge phenomenology to previous findings The ζ-values for oxidation–reduction and for pseudocapacitive processes on clean Pt have been investigated previously. Our findings agree with the trends found in these studies: for oxidation/reduction, our value of about −0.8 V compares to −0.7 V for oxidation/reduction in KOH [6], whereas our −1.1 V for the pseudo-capacitive process compares well to data in [8] for gold and to −1.2 V as interpolated in Fig. 4 of Ref. [10] for Pt in NaF of the present molarity. The change in sign of the surface stress–charge behavior in the hydrogen adsorption region has first been reported by Seo et al. [34], though the surface stress was not quantified. Feibelman [31] has studied the effect of H- and O-adsorption on the surface stress of Pt(1 1 1) surfaces (in vacuum) by density functional theory (DFT). Our observation of more negative f for both H- and O- (or OH) adsorption in the electrolyte agrees qualitatively with the DFT results (f < 0 for H-adsorption which requires E < 0, in spite of the positive sign of f in Table 1). In the case of hydrogen, the present results imply – by extrapolation from the actual coverage of about 0.5 monolayer as indicated by the charge transfer – that one monolayer of adsorbed hydrogen would correspond to a surface stress change of −3.3 N/m. This compares to a quite similar value, −4.6 N/m, found by DFT. The ab initio work finds a linear dependence of surface stress on coverage, which is also well compatible with our findings. For oxygen, the results in Ref. [31] imply −3.2 N/m for saturation coverage of 1/4 monolayer, in other words the effect per atom is about four times that of hydrogen. This is not born out by the present findings at electrode surfaces: even if we
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admit a charge transfer of two electrons per O (as opposed to one electron per OH), we find that the surface stress change per adsorbate atom or molecule is at best the same, if not less, than for H. Apparently, the processes probed during the electrochemical surface oxidation/reduction cycle differ from simple oxygen adsorption on Pt as studied in Ref. [31]. This is well compatible with a partial lifting of the oxygen-induced surface stress via place exchange in our experiments. 4.5. Origin of the stress–charge response An overview of various models for the effects of cleavage and of adsorption in vacuum on the surface stress of noble metal surfaces can be found in Ref. [31]. In one way or another, each relates the tensile surface stress of clean metal surfaces to a charge deficiency near the atoms of the outermost plane. Obviously, this concept on its own cannot explain the surface stress variation during capacitive charging of the clean surface, where negative charging – while removing part of the charge deficiency – makes f even more tensile (more positive). As mentioned in Section 1, two suggestions have been made for the origin of the surface stress–charge response during capacitive charging of clean metal surfaces [11–13], i.e. for conditions where adsorption effects are absent or negligible. One is based on the strain-derivative of the work function, W, which is related to ζ via a Maxwell relation. Lateral straining changes the electron density, ρe , and a systematic increase in W with ρe is implied by Jellium data. For Jellium, a negative value of ζ is obtained in this way, in agreement with experiments on clean noble metal surfaces. However, the predicted numerical magnitude (about ζ = −0.1 V for Au)4 largely underestimates the experimental value, and the approach fails to account for the dependency of ζ on the surface orientation [12]. By contrast, ab 4 The link between the surface stress–charge coefficient, ς, and the variation of the work function, W, with the conduction electron density, ρe , of metals has been considered independently by Haiss et al. [8] and by Ibach [13]. Both references withhold details of the derivation. The basis is the result of a DFT analysis of Jellium [35], W ≈ 4.63 eV−0.38 eV × rS /rB , where rS and rB denote the electron’s Wigner-Seitz radius and the Bohr radius, and 4πrS3 /3 = ρe−1 . Since ρe varies when the material is strained, the relation may be used to estimate the strain-derivative of W and, through the Maxwell relation [8,12,13] ∂f/∂q|e = q0−1 ∂W/∂e|q (q0 is the elementary charge), the value of ς near the pzc. The underlying assumption is that three issues may be neglected, (i) the details of atomic structure and bonding, which depend on the surface orientation, (ii) the break in lattice symmetry ensuing from the tangential character of the strain, and (iii) the possible role of atomic relaxation. Allowing for transverse contraction of the bulk during a tangential strain, ␦e = ␦A/A, at constant normal stress (which is the appropriate form for processes at constant pressure in the electrolyte), we have ␦ρe /ρe = (2υ−1)(1−υ)−1 ␦e. With the Jellium result for W we then obtain dW/de = 0.13 eV (2υ − 1)(1 − υ)−1 rS /rB . For gold, which has rS = 3.0 rB and Poisson number υ = 0.42, one estimates ς = −0.10 V. This is considerably smaller than the results quoted by Haiss et al. (−0.45 V) and by Ibach (−0.38 V), who both apparently ignored the important effects of transverse contraction. While predicting the sign of ς correctly, the argument largely underestimates the parameter’s experimental magnitude (−0.9 to −2 V for weak adsorption). One is lead to conclude that details of the atomic and electronic structure and/or relaxation, which are ignored by the Jellium model, must contribute decisively to the surface stress–charge response.
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initio computation of the work function strain dependence for fully relaxed Au surfaces predicts ζ in quantitative agreement with experiment, emphasizing the importance of crystallography and relaxation [12]. In fact, the second suggested model (see below) proposes a normal relaxation of the surface layer as the primary response to surface charging [11]. According to this picture, which remains speculative in the absence of dedicated studies of stress and relaxation at charged metal surfaces, the forces and the surface stress represents a secondary effect, which may be understood in terms of transverse contraction tendency of solids. These considerations agree at least qualitatively with the present findings, with the notable exception that the positive sign of ζ which we find here for the (pseudo-)capacitive process on the oxide-covered surface is unexpected. We believe that a detailed atomistic simulation is required for establishing a reliable explanation. However, we find it instructive to discuss the findings in relation to two limiting cases of the excess charge distribution, specifically the depth of penetration of the excess charge. In the first limiting case, the excess charge is taken to be essentially localized outside the surface. This appears a realistic model on dense-packed surfaces of noble metals, where the efficient electronic screening prevents noticeable penetration of the excess charge into the bulk. Here, an obvious interaction mechanism is a shift of the electrostatic centre of gravity of the surface Wigner-Seitz cell, which prompts an outward relaxation (‘stretch’) of the ion cores when the excess charge is negative (i.e., positive excess of electrons) [11]. In as much as the excess charge does not directly enter the orbitals that are responsible for the bonding between the surface atoms, the most important effect of charging on surface stress could here be indirect: the electronic charge is redistributed as the result of the outward stretch, away from the bonds between the surface and first sub-surface layer of atoms, and into the inplane bonds. This would result in more tensile (positive) surface stress during negative charging, in agreement with the observation of ζ < 0 at clean noble metal surfaces. The process would be quite analogous to the one which controls the transverse contraction of bulk matter, and in fact the coupling between surface stress and surface stretch at gold surfaces is in reasonable quantitative agreement with simple transverse contraction [11,12]. As the opposite limiting case let us consider a semiconductor with weak screening, where the excess charge penetrates several atomic layers into the bulk. Here, it is expected that the excess charge occupies the unfilled states of the bulk density of states (DOS) just above the Fermi energy. The effect on the surface stress may then be understood in terms of the character, bonding or antibonding, of these orbitals. In other words, the excess charge affects the bonding directly, as opposed to the indirect effect, mediated by stretch, in the case of strong screening. We believe that the observations of charge-induced strain in graphite [36,37] may serve to illustrate this situation. Here, the Fermi energy is in a minimum of the DOS, between the bonding valence band and the antibonding conduction band. Due to the small conduction electron density, weak screening is expected.
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Excess electrons (negative charging) are expected to populate the antibonding conduction band states of graphite, while a deficit of electrons (positive charging), depletes the bonding valence band states. Both processes are expected to decrease the net bond strength. Indeed, graphite is found to expand when charged, irrespective of the sign of the excess charge [36,37]. Similar behavior would be expected for ‘true’ semiconductors such as Si or Ge. In relation to the present experiments it is noteworthy that the surface oxide on Pt electrodes is known to be semiconducting [28]. This suggests the screening on Pt–O is less efficient than on the clean surface, so that the excess charge can penetrate deeper. The positive-valued ζ might then be understood in terms of the filling (depletion) of antibonding valence band states if the oxide-covered surface is charged more negatively (positively), as would be the case if the Fermi energy near the surface was pinned below the valence band edge. While the above argument was designed to rationalize some of the aspects of the surface stress–charge response during capacitive charging, we note that it is not without contact to the behavior during adsorption, if that includes a change in the occupancy of bonding or antibonding band states of the metal [5].
5. Summary We have presented in situ dilatometry results for the surface stress–charge response of platinum immersed in aqueous NaF. While the electrolyte is believed to exhibit weak anion adsorption, the potential range under study included regions of extensive oxygen and hydrogen adsorption. We find that the surface stress–charge response may be characterized separately for four different processes, selected by the potential range and by the surface pretreatment: hydrogen adsorption/desorption, oxygen adsorption/desorption (and/or surface oxidation/reduction), and nominally capacitive charging of the Pt surface in two different states, clean and oxidecovered. While each process exhibits a roughly linear surface stress–charge response, the magnitude and even the sign of the slope, which determines the surface stress–charge coefficient, ζ, differ. Besides these most obvious features, in situ strain graphs such as Figs. 1 and 2 exhibit a significant and highly reproducible sub-structure. This indicates the presence of additional electrode processes that may deserve attention in future studies. The highly reproducible resolution of these details emphasizes the robustness and sensitivity of strain measurements on nanoporous samples as probes for the electrocapillary behavior of solid surfaces. We suggest that the sign of ζ depends on the penetration depth of the excess charge: for strong screening the electronic charge is located outside of the surface, and ζ is negative as found previously for clean metal surfaces. For weaker screening, the wider space charge layer implies a trend for the excess charge to fill bulk-like unoccupied states. These states are here antibonding, giving positive-valued ζ.
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