In-Situ Optical Quantification of Adsorbates and Surface Charges on

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

In-Situ Optical Quantification of Adsorbates and Surface Charges on Copper Crystals and their Impact on the Hydrogen Evolution Reaction in Hydrochloric Electrolytes Miao-Hsuan Chien, Saul Vazquez-Miranda, Reza Sharif, Kurt Hingerl, and Christoph Cobet J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b01149 • Publication Date (Web): 26 Mar 2018 Downloaded from http://pubs.acs.org on March 26, 2018

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The Journal of Physical Chemistry

In-Situ Optical Quantication of Adsorbates and Surface Charges on Copper Crystals and their Impact on the Hydrogen Evolution Reaction in Hydrochloric Electrolytes †,¶

Miao-Hsuan Chien,

Saul Vazquez-Miranda,

‡,†

Christoph Cobet

†Center

Reza Sharif,

†

†

Kurt Hingerl,

and

∗,†

for Surface- and Nanoanalytics (ZONA), Johannes Kepler Universität, Altenbergerstr 69, A-4040, Linz, Austria

‡Instituto

de Investigacióen Comunicación Óptica, Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, SLP 78000, San Luis Potosí, México

¶Current

address: Institute of Sensor and Actuator Systems (ISAS), Technische

Universität Wien, Gusshausstrasse 27-29, A-1040, Wien, Austria

E-mail: [email protected]

1

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Abstract In-situ

spectroscopic ellipsometry is combined with cyclic voltammetry to disco-

ver and quantify potential dependent surface adsorbates and the electronic charge on copper single crystals in HCl solution. In comparison with electrochemical scanning tunneling microscopy it is demonstrated that ellipsometry provides not only an extremely high nger print sensitivity to sub-monolayer surfaces modications but that it is furthermore possible to determine qualied values with an appropriate optical model. As a critical bench mark we use the amount of adsorbed Cl at the Cu(111) surface. In this context we found clear optical evidence for a densied water layer at the Cu(111) surface. A particular attention is drawn to the potential range of the hydrogen evolution reaction and the catalytic eciency of the relatively stable Cu(111) and the more open corrugated (110) surface. With the introduced ellipsometric method we disclose a step-like increase of the surface electron excess and a decreasing lateral surface electron mobility at the onset of the hydrogen evolution reaction. Both is explained by a protonation of the surface or the adsorbed water layer and demonstrate an unexpected inhibiting eect to the hydrogen evolution reaction.

1

Introduction

Whenever the principles of electrochemical reactions are discussed, for example in connection with corrosion or electro-catalytic processes, experimental evidence about the structure of the solid-liquid interface on the atomic scale is requested. But many surface sensitive techniques, which could provide such information about surfaces in vacuum, cannot be applied in liquid environments. Thus, it is not surprising that the microscopic background of basic electrode reactions like the hydrogen reduction at metal electrodes, is still a subject of ongoing discussions. 1,2 Examples of fruitful experimental developments regarding the solid-liquid interface analytics are the electrochemical scanning tunneling microscope (EC-STM), X-ray scattering and X-ray standing wave methods as well as (near) ambient pressure photo-emission 2


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spectroscopy. In this work we use spectroscopic ellipsometry (SE) in the visible spectral range in order to determine the surface charging and adsorbate structures on single crystal copper surfaces in hydrochloride solutions. It is well known that the change of the light polarization upon reection at a boundary and in particular the change of the relative phase between distinct polarization components is a sensitive measure concerning ultra thin lms and sub mono-layer adsorbates. 36 Furthermore, it is a considerable advantage of optical reection techniques that they are applicable in dierent environments and at opaque materials electrodes in electrolytes. Ellipsometry is, therefore, widely used as an

id est

in-situ

on metal

monitoring

tool in vacuum and gas phase environments. 79 Also it's applicability for the investigation of electrochemical processes especially in terms of single wavelength experiments is known for decades. 10 In most of the cases where ellipsometry is used

in-situ

in electro-chemistry, the

formation of relatively thick surfaces lms are investigated. 1113 But there are also examples where mono layer coverages are studied al.

e.g.

by internal reection ellipsometry. 14 Prato

et

could demonstrate sub mono layer sensitivity with a conventional ellipsometer while

depositing copper on gold electrochemically. In case of sub mono layer coverages, however, a quantication of material parameters based on the optical response is dicult. A decent optical model has to include a correct description of the electrolyte near the surface, of the adsorbate, of electro-modulation eects 1517 in the electrode surface and if necessary the morphology of the surface. 18,19 A promising model for the adsorption of anions on dierent amorphous metal electrodes was described by Chiu and Genshaw 20 as well as by Paik and Bockris et al. 21 With the help of EC-STM, the adsorbate structures of anions and in particular of halides on single crystalline electrodes are meanwhile relatively well known. 22 It was shown for √ √ example, that Cl adsorbs on Cu(111) in acidic solutions within ( 3× 3)R30◦ structure. 23 The more reactive Cu(110) surface has shown, on the other hand, a more complex behavior upon chloride adsorption which includes morphology transformation. 24,25 The comparison 3



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of both surfaces provides in this work crucial information for the qualitative understanding of the

in-situ

ellipsometric response at cathodic potentials close to the hydrogen evolution

reaction. In the discussion section we introduce an optical model for a comprehensive quantitative analysis of the obtained data. The EC-STM results are used here as a critical test of the model. The results are nally used in order to adapt the optical model and to study surface adsorbates and excess electrons apart from the Cl adsorption with particular attention on the hydrogen evolution reaction.

2

Experimental

2.1 Sample preparation Copper single crystals with (111) and (110) orientation and 99.9999% purity from MatecK GmbH were used in the measurements. The dimension of the samples was 8 mm by 20 mm with a thickness of 1 mm as-cut. The orientation accuracy is ensured by the vendor within 1◦ , and the roughness at delivery was below 0.03 µm. Additional, the samples were annealed in a hydrogen atmosphere in order to minimize sulfur contaminations. To obtain oxide-free, mirror-like copper surfaces for highly-sensitive measurements, electrochemical polishing processes were done in 85% ultra-high pure phosphoric acid (Fluka-Analytical, TraceSELECT Ultra with ppb impurity level) each time before the

in-situ

experiments. The whole elec-

tropolishing process was carefully monitored by a potentiostat (Ivium Technologies B.V., CompactStat), and the polishing potential was optimized by a linear scan within the electrochemical window of water before polishing. For the subsequent polishing we have used a potential in passivation plateau region about 600 mV below the onset of the oxygen generation. At this potential a minimized stable polishing current could be achieved. 2628 The averaged current density for polishing measured by the potentiostat is between 4-5 mA/cm2 , consistent with the current density of passivation plateau in previous literature. The electrochemically polished sample was then cleaned with ultra pure deaerated water (18.2 MΩ/cm) 4


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inside of a ultrasonic bath in Ar environment to remove phosphate contaminations from the surface. It was then transfered immediately into the electrochemical cell with a pure water droplet covered on-top to prevent any further oxidization of the fresh surface. According to diusion calculations, a water layer of 2-3 mm in thickness is proven to be an eective protection of the surface against atmosphere for several seconds. 29,30

2.2 Cyclic Voltammetry The electrochemical experiments were realized in a closed half-lled electrochemical cell, containing three electrodes with inlet and outlet windows for the ellipsometric probing light as depicted in the graphical abstract. During measurements the upper part of the cell was continuously purged with Argon 5.0. To observe the atomic interaction between Cl and Cu, the reagent HCl (Merck KGaA, Suprapur) with impurities below several ppb was diluted in ultra pure water (18.2 MΩ-cm) to 10 mM/L as electrolyte in all measurements. Before the measurements, the electrolyte was externally deaerated with Argon 5.0 for at least two hours. The working electrode (WE) id est the copper sample at the bottom of the cell was contacted from the backside. The surface exposed to the electrolyte has an eective area of ≈0.7 cm2 . All currents measured by cyclic voltammetry (CV) are normalized, in the following, to the eective area of the sample and are presented as current densities j but denominated in short as "current". An Ag/AgCl wire prepared by electrochemical deposition of Cl onto Ag was adopted as quasi-reference electrode, and was placed ≈1 mm above the sample surface. 31 The reported potentials in the following have been shifted +130 mV to be in agreement with commercially available Ag/AgCl quasi-reference electrodes (RE) in 3 M/L NaCl. The oset with respect to the standard hydrogen electrode is thus 209 mV. 32 A long, winding platinum wire was used as counter electrode (CE) in a distance of about 1 cm above the WE.

5



2.3 In-situ Spectroscopic Ellipsometry For the

in-situ

ellipsometric measurements we used a spectroscopic rotating compensator

instrument (J.A. Woollam Co., Inc., M-2000DI). The incident angle of 68◦ was predened by the electrochemical cell geometry. The change in the light polarization upon reection on the sample is recorded by means of the ellipsometric angles Ψ and ∆ which account for a polarization rotation and the phase shift between polarization components parallel and perpendicular to the plane of incidence. The rotating compensator (PCR SA) conguration of the instruments enables a full-range determination of ∆ with uniform sensitivity. 4 A possible strain induced birefringence in the fused-silica cell windows was determined with a standard Si wafer before each experiments and all presented results are corrected to that eect. Two spectrograph's as well as a combined tungsten-halogen and deuterium light source allow a parallel measurement at 700 wavelengths covering a spectral range from 193 to 1690 nm (6.4-0.76 eV). The ellipsometric spectra were recorded synchronized with CV in order to obtain a real-time

in-situ

optical responses for variable electrochemical potentials.

The integration time for each spectrum was chosen to be 5 s. The latter intervals still allow a time resolved monitoring of interface processes if we regard potential sweep rates around 5 mV/s. All measurements were performed at room temperature. The Cu(110) sample was mounted with the [001] in-plane surface direction 45◦ rotated against the intersect line of the surface plane and the plane of light incidence. Eects of the surface anisotropy 24 have been tested and are negligibly small.

3

Results

3.1 Cu(111) Figure 1 shows the cyclic voltammetry (CV) results for Cu(111) in 10 mM/L HCl solution measured with dierent scan rates of 2 mV/s, 5 mV/s, 10 mV/s, and 20 mV/s. The potential

6


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window is limited between 50 mV and -750 mV by exponentially increasing currents which correspond to the Cu2+ dissolution in anodic and the hydrogen evolution reaction (HER) in cathodic scan direction. The characteristic peaks of specic adsorption and desorption of Cl are labeled in gure 1 with A in the anodic and with A' in the cathodic scans, respectively. This assignment is based on previous studies of the Cu(111)-HCl system. The potential √ √ range above peak A and A' is a double layer region with a ( 3× 3 )R30◦ Cl adsorbate structure which was conrmed by EC-STM. 23,3335 At more negative potentials before peak A and after A' a (1×1) bare Cu(111) surface is observed. 23,33 The peak currents in CV systematically increase with the scan rate due to higher over potentials. But the overall integrated charge transfer in A remains almost the same. The increasing separation of peak A and A' in CV's with higher scan rates is, accordingly, a consequence of nite time constants in the Cl adsorption/desorption process. The equilibrium standard potential E0 of the Cl adsorption/desorption reaction on Cu(111) is obtained by extrapolating this trend to an innitesimal slow scan rate. The shift of A and A' follows an exponential trend (not shown here) and the tting yields in an intersect with E0 =-558 mV (vs. Ag/AgCl in 3M/L NaCl). √ √ An ideal ( 3× 3)R30◦ coverage of the Cu(111) surface with Cl comprises 5.87×1014 Cl ions per cm2 which corresponds to an ionic charge in the inner Helmholtz layer (IHL) of QI − =94 µC/cm2 . For comparison, we have determined the electronic charge transfer upon adsorption of Cl at peak A by an integration of the current measured in CV. For the 5 mV/s scan, we obtained an electronic charge transfer of ∆Qe =-102 µC/cm2 between point (1) and (2) as dened in gure 1). Almost the same value is obtained also for all other scan rates with respectively chosen integration limits. The near agreement of QI − and ∆Qe provides a rst evidence that the electron excess in the copper surface decrease equivalent with the amount of adsorbed Cl ions. As we will discuss later in more detail, point (1) is believed to be a potential where no or a minimum amount of ions are absorbed at the surface. 7



Respective calculations for the charge transfer in case of the Cl desorption in peak A' require a decoupling of the overlapping Faraday current of the HER. Therefore the exponential Faraday current was subtracted from the total cathodic current as shown in the inset of gure 1. But, the charge transfer ∆Qe remained, nevertheless, roughly a factor of two larger than in the Cl adsorption peak A. This inequality of the electron charge transfer was already observed in previous studies of the Cu surface in acidic environments. 23,34,36 It is attributed to the so called Frumkin eect 3739 which describes a charge inversion at the electrode surface resulting from specic anion adsorption at cathodic potentials. The latter anions create a negative proximity and thus enhance the adsorption and catalytic reduction of hydrogen. The attraction of cations like H+ or H3 O+ to the Cu(111) surface thus increases the exchange current density of the HER. Vice versa, a desorption of the Cl reduces also the exchange current density of the HER which explains the apparent discrepancy in the amplitude of peak A', even after subtracting the measured exponential increasing Faraday current at more cathodic potentials. In parallel to CV, we recorded in-situ the ellipsometric angles Ψ and ∆ spectroscopically for all dierent scan rates. The ellipsometric spectra are reversible over many cycles and the observed potential dependencies appear independent from the scan speeds. Only the position of changes in Ψ and ∆ moves consistently with the respective A and A' peak shifts. Therefore we restrict our analysis in the following to the results obtained from 5 mV/s scans. The spectral line shape of Ψ and ∆ (black dotted line) is exemplary shown in gure 2 (a) for the potential of 520 mV in anodic scan direction (position (1) in gure 1). The surface sensitivity of the ellipsometric measurements is demonstrated by means of dierence Ψ and ∆ spectra which were measured at potential (1) and a more cathodic potential (3) 135 mV below (Fig. 2 (b)). Therefore, Ψ and ∆ were averaged over respective potentials from 5 cycles. At point (3) one can consider an increased electron and cation surface excess in connection with the HER. The peculiarity of the chosen potential (3) is again not yet apparent but will be discussed later in more detail. However, the ellipsometric 8


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angle ∆ shows signicantly larger sensitivity against the potential induced changes than Ψ. Such a behavior is typical for very thin layers if the imaginary part of the constituent dielectric functions are small or vanishing. 40 Reectance measurements under such conditions would thus have a very low sensitivity upon surface modications. The phase ∆ shows a maximal variation of 0.25◦ in the photon energy range from 2.1 to 2.3 eV. The latter spectral range matches with the onset of d-band transitions in Cu. 41 In the following we use, therefore, transients at 2.1 eV in order to examine the potential dependency of ∆. Figure 3 shows the time-dependence of the ellipsometric angle ∆ (black dotted and green line) at 2.1 eV recorded in parallel to CV sweeps with a scan rate of 5 mV/s. The (Faraday) current is plotted in blue in a time-dependent representation while the related potentials are plotted in the upper panel (a) of gure 3. The plot contains two cycles in order to demonstrate the reproducibility of the experiment. Within these two cycles one can clearly observe a correlation between the Faraday current at the Cu(111)-HCl interface and ∆. The exponential increase of the anodic Faraday current above around -100 mV at the beginning of the transient is a Tafel current attributed to the Cu2+ dissolution. This process coincides with an exponential decrease in ∆. It should be mentioned that we could neither observe a change in the intensity nor a depolarization of the reected light (not shown here). A roughening of the surface is therefore excluded although it would correspond to a decrease in ∆ as well. In the following cathodic scan the Cu2+ redeposition is generating a negative Faraday current which exponentially decays. Apart from the opposite sign, the ellipsometric

∆ retraces again the exponential behavior of the current and resembles even the slightly slower decay of the current to the old value. A decrease in ∆ is in general explainable by any surface layer which is optically more dense than the electrolyte and less dense than the bulk copper. A possible explanation for the change in ∆ at these potentials is the increasing Cu2+ concentration near the surface but needs to be conrmed in further experiments. In continuation of the cathodic scan after 190 s, ∆ increase signicantly in close connection to the negative current peak A' which is attributed to the Cl desorption (Fig. 1). 9



At this point it is worth to remember that the current density j (charges per time and unit area) measured in CV is proportional to the change of the surface charge density (electron excess) j = dQe /dt plus contributions from surface catalytic reactions like the HER. The ellipsometric response, on the other hand, is determined only by the instantaneous interface properties. A direct relation of the current measured in CV and the ellipsometric response is thus only appropriate if the current measured in CV would originate exclusively from interface modications. In the latter case the rst derivative of ∆ with respect to time should be proportional to the measured current. A maximum in the current should thus coincide with a change in ∆ as observed around peak A'. Remarkable in this connection are the small "overshoot peaks" in ∆ before and after the Cl desorption (asterisks in Fig. 3 (b)). A negative slope should generate a positive peak in the current. Such a correlation is in fact observable at ≈190 s where the small decrease in delta correlates with the weak but reproducible hump in current. An explanation of the "overshoot peaks" in ∆ again may require some additional work. In the remaining cathodic scan the negative current is exponentially increasing due to the HER. But, ∆ appears almost not inuenced by this Faraday current and remains nearly constant. Also after turning in the anodic scan direction, ∆ responds only with a small negative slope. This "saturation" in ∆ is proven by additional measurements on amorphous copper samples where the scan range was extended to much more negative potentials (not shown here). Even the formation of a limited number of H2 bubbles does not inuence the measured ∆ and is only detectable by a decreasing overall intensity of the reected light. Signicant changes in ∆ in the anodic scan direction emerge rst after 250 s, above -600 mV, where the Faraday current is already relatively small. A closer inspection of the strong negative slope in ∆, additionally, reveals a distinct step which is reproducible over many cycles and dierent scan speeds (point (1) in Fig. 3 (b) and (c)). The dominating surface related changes in ∆, thus, arise from two dierent processes which separate only in the anodic scans, where just the second part after 275 s is correlating to peak A and 10


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therefore to the Cl adsorption.

3.2 Cu(110) Figure 4 shows a CV recorded at the Cu(110) surface with a scan rate of 5 mV/s. The scan range from -100 mV to -690 mV is again limited by the Cu2+ dissolution in the anodic and by the hydrogen evolution reaction (HER) in cathodic scan, respectively. In case of the Cu(110) surface, high Cu2+ dissolution as well as hydrogen evolution rates are avoided in order to prevent irreversible surface modications. 24 In between we observe two characteristic peaks in anodic as well as in cathodic scan direction in agreement with previous studies. 24,25,42,43 Both relate to the Cu(110)-surface reactions with Cl-ions and are labeled with A/A' and B/B', respectively (Fig. 4). A and A' are assigned to a Cl adsorption and desorption. The amplitude and shape of the peaks labeled by B and B' depend, in contrast to A and A', strongly on the scan speed. B and B' as well as the "plateau region" with elevated Faraday current at potentials more positive then B and B' results from reactions where precipitates Cu-Cl near the surface. The following reaction steps are accepted: 24,44 Cl− (aq) Cl(ad) ,

(1)

− Cu(bulk) + Cl(ad) + Cl− (aq) [CuCl2 ](aq) ,

(2)

Cu(bulk) + Cl(ad) CuCl(s) .

(3)

Reaction 3 creates a passivating aggregate layer which covers the Cu surface and thus inhibits the further Cu-Cl interactions. It was also shown in Ref. 24 that the adsorption of Cl initiates a sequence of morphology transformations at the (110) surface. An unambiguous assignment of peaks in the Faraday current to the adsorption of Cl (Eq. 1) is therefore dicult. The

in-situ

ellipsometric measurement on Cu(110) are presented in gure 5 again in

11



terms of a transient of ∆ at 2.1 eV. The scan rate was kept at 5 mV/s, the same as in the plotted Cu(111) transient. The changes in ∆ can likewise be related to current peaks in CV. The plotted transient starts with an increase in ∆ after switching from the anodic to the cathodic scan direction

id est

at potentials where a Cu2+ redeposition takes place. Worth

mentioning is the fact that ∆ increases although the absolute value of the Faradaic current remains positive. The latter behavior is explainable by an ongoing transformation of bulk copper according to equation 3 and 2 during the redeposition of near the surface Cu2+ . The copper "redeposition" from the CuCl precipitate and CuCl2 is following after 350 s below -300 mV (peak B') along withe a strong increase of ∆. The redeposition is observed in close vicinity to the subsequent Cl desorption (peak A'). Both processes are therefore almost not distinguishable in ∆ and manifest themselves only in slightly dierent slope. The same holds for the opposite processes in the anodic scan. ∆ decreases by the same amount at peak A and B after about 500 s. It was already mentioned 24 that the Cl adsorption induces morphology transformation on the (110) surface which nalize in a faceting. This faceting is also contributing to the decrease in ∆ like a surface roughening. The natural corrugation and the higher instability of the (110) surface is responsible for a generally higher surface "roughness" which explains the overall smaller absolute values of ∆ in comparison to Cu(111) (Fig. 3). The HER takes place around 430 s and 675 s (below -600mV). The exponential increase of the Faraday current is now accompanied by an increasing ∆ although the current remains about 20 times smaller than the maximum value measured on Cu(111). The observation of a distinct change in ∆ at relatively small HER rates compared to Cu(111) highlights again that the change in ∆ at these potentials is not a result of the diluted H2 or H2 bubbles. The optical eect of diluted H2 should be the same at both surfaces and should scale with the increasing current. Worth mentioning is also the relatively large potential separation of Cl adsorption/desorption (peak A/A') and the HER. At the Cu(110) surface it becomes apparent that ∆ changes at the onset of the HER due to an additional adsorption/desorption 12


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process. The potential range of low activity between both processes gives rise to a shoulder in the transient of ∆ (e.g. at point (1) in Fig. 5 (b)).

4

Discussion

√ √ It was mentioned already that the smooth ( 3× 3)R30◦ termination at Cu(111) is equivalent to a Cl surface excess ΓCl− ) of 5.87×1014 ions per cm2 or 94 µC/cm2 in the IHL under the assumption of a vanishing electron transfer across the WE boundary. The latter ionic charging is 8 µC/cm2 smaller than the respective electron transfer measured by CV (∆Qe = of 102 µC/cm2 ) in connection to the Cl absorption. In a rigorous discussion the change of the surface charge density (the electron accumulation/depletion at the WE surface) depends on the number of ions adsorbed on an unit area (surface excess Γ) as well as on the applied potential E : 45 dQe =

δQe δE

dE +

X δQe

Γ

i

δΓi

dΓi .

(4)

E,Γj6=i

In the particular case we consider three dierent possible surface adsorbates namely Cl , a not yet specied cation I+ , and eventually a dielectric H2 O layer. If we reasonably assume, furthermore, a linear relationship between adsorbate coverage and electron excess as well as a decoupled contribution of the dierent adsorbates, dQe can be approximated by: dQe ≈

δQe δE

dE + qe (αH2 O dΓH2 O + αI + z dΓI + + αCl− dΓCl− ).

(5)

Γ

The above mentioned deviation of 8 µC/cm2 can be thus explained by means of the potential dierence between point (1) and (2) (the contribution of the rst term in Eq. 4), by varying contributions from a water and cation adsorbate (second and third term in Eq. 4), or by an electrosorption valence αCl− dierent from minus one. In the remaining discussion we will determine the dierent contributions within a quantitative evaluation of the ellipsometric and CV data.

13



The HER and the Cl desorption strongly overlap in cathodic scan direction at Cu(111) (Fig. 3(b)). In the anodic scan both appear separated in CV as well as in the ∆ transient and we could distinguish two subsequent adsorption/desorption signatures (Fig. 3(c)). At potentials where the Faraday current of the HER is already very small ∆ decreases at rst by a value of 0.15◦ . Immediately after this rst drop, follows a 0.25◦ decrease in ∆ due to the Cl adsorption. The rst drop of ∆ in the anodic scan after 250 s is attributed to an additional surface modication and the question remains whether it is an adsorption or desorption process. At rst glance the HER seems to be not inuenced by the optical detected process. In the acidic HCl solution it is, nevertheless, likely a desorption of a cation like H+ . At the Cu(110) surfaces, the HER and the Cl adsorption/desorption are well separated in anodic as well as in cathodic scan direction and we observe also in cathodic scans an increase in ∆ at the onset of the HER (Fig. 5(b)). In order to prevent an irreversible surface degradation, we had to stop the cathodic scan at -690 mV. At this potential ∆ has increased by 0.1◦ without indications of a saturation. We associate this signature to the same cationic adsorption as discussed for the (111) surface although the adsorbate does not reach the maximum coverage in the scanned potential range. Instead, the correlation with the onset of the HER is now more evident. Between the discussed cation desorption and the Cl adsorption we assume a minimum of adsorbed ions. Point (1) as denoted in gure 3 for Cu(111) and in gure 5 for Cu(110) is assigned to this potentials. As we seek for an optical model which describes the measured ∆ and Ψ values by means of interface quantities, it is appropriate to start at this potential. In the rst attempt, we consider an optical model with a single interface namely the boundary between the electrolyte and the copper sample. Under such conditions, the dielectric function (DF) of the copper can be determined by the known Fresnel equations for the reection coecients rp parallel and rs perpendicular to the plain of incidence. For the upper half space we use the refractive index of water from Ref. 46. The measured Ψ and ∆ are related 14


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to rp and rs 15,47 by:

rp = tan Ψeı∆ . rs

(6)

The line shape of the real and imaginary part of the DF calculated in such way

e.g.

for the

Cu(111) is similar to those plotted in gure 7. It shows the known features of the Drude like free electron resonance and above ∼2 eV structures of d-band excitations. 41 In a second step, the real and imaginary part of the obtained DF (ε1 and ε2 ) is tted with a parametric model consisting of a sum over several generalized Kramers-Kronig consistent Lorenz oscillators and a Drude dispersion upon the photon energy E . The Drude part with the electron density

Ne and the electron mobility µ is given by: 4

εDrude (E) =

−~qe2 Ne µ . ε0 (µ m∗ E 2 + ıqe ~E)

(7)

Ne and µ are used as t parameters while the eective electron mass m∗ was taken as 1.49×me . 48 The vacuum permittivity is ε0 and qe is the elementary charge of the electron. With the applied simple two phase model, we obtained an electron density which is about 3% larger than the expected value of 8.46 × 1022 cm−3 relating to one free electron per Cu atom. The discrepancy is explainable by the fact that the potential with a minimum of surface adsorbate's (point (1)) is found at -520 mV and thus likely several 100 mV below the expected point of zero charge (PZC). In reference 49 the PZC is

e.g.

tabulated for amorphous copper

in 20 mM/L Cl solutions at -122 mV (vs. Ag/AgCl). It should be noted, however, that the PZC in the presence of specic adsorbates is sometimes not consistently dened. As we measure with SE the electron excess at the surface of the Cu electrode, it is actually the point of zero total charge (PZTC)

i.e.

the potential of zero surface electron excess which we

expect at much more positive potentials. Accordingly we should consider at potential (1) an electron accumulation layer (EAL) at the copper side of the boundary which is accompanied in the Gouy-Chapman model by a positively charged diuse layer (DL) at the other side 15



of the interface (Fig. 6(a)). The electrochemical determined PZC in the Gouy-Chapman description, on the other hand, often refers to the point of zero free charge where the ionic charge in the DL vanishes.

√ √ The potential denoted by (2) in gure 1 is assigned to the ( 3× 3)R30◦ Cl structure on the (111) surface. In HCL solution Cl adsorbs on Cu by means of a super-equivalent (contact) adsorbate already well below the point PZTC; 50 a concept which was mentioned already in connection with the Frumkin eect. Thus, the electric double layer structure at potential (2) consists of an EAL and another negatively charged layer at the electrolyte side of the boundary (IHL) containing the specically adsorbed Cl ions. The positively charged counterpart is given by the DL (Fig. 6(b)). At point (3), nally, we assume a specic adsorption of cations in the IHL which change the interface capacity and thus introduce a step like increase of the electron accumulation (Fig. 6(c)). For the evaluation of the ellipsometric results, such a surface double layer structure can be described with an (optical) layer model by assuming sharp boundaries. Each layer is considered to be homogeneous with an eective DF εˆ. The charge or ion distribution perpendicular to the surface is ignored. It was shown that such an approximation is reasonable since the optical response is mainly determined by the integrated dierential refractive index R (nambient − nlayer (y))dy . 21,51 The reection coecients rp and rs as dened in equation 6 for a single boundary are replaced by generalized coecients rp,s which depend on the bulk water DF εH2 O , the eective DF of the DL εˆDL , the eective DF of the IHP εÎHP , the DF of the EAL εEAL , the DF of bulk copper εCu , and the respective layer thicknesses dDL , dIHP , and dEAL . The generalized rp,s coecients are calculated with the Berreman transfer matrix algorithm 4,47 which is implemented in the used CompleteEASE ellipsometer software. In the following three paragraphs, we discuss the used approximations for the electron accumulation layer, the inner Helmholtz layer, and diuse layer.

16


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4.1 Electron Accumulation Layer At the copper side of the boundary, we approximate in all cases a homogeneous layer with a reduced or increased electron density (electron excess). The DF εÊAL of this layer is almost identical to the DF of the bulk copper. We expect that only the electron density Ne of the Drude part (Eq. 7) of the parameterized DF is modied. This approximation is worthwhile since we expect an increasing electron concentration in the discussed potential range. The Mott criterion (the screening length is smaller than the Bohr radius) is therefore always satised and the copper surface layer remains metallic. An estimation of the screening is given by the Thomas-Fermi screening length: 52

s λT F =

π 2 ~2 ε0 1 (3π 2 Ne )− 3 , 2 m e qe

(8)

With an electron density of 8.46 × 1022 cm−3 , λT F is 0.055 nm and reduces with increasing electron excess. In terms of a layer thickness representing the area of modied electron density in the optical model, the Thomas-Fermi screening length λT F turned out to be not an appropriate. The calculated value for the screening of single ions is much to small to be applicable as a layer thickness and is in contradiction to the observed ellipsometric data. Self-consistent (quantum mechanical) calculations show, on the other hand, that the charge distribution at metal surfaces varies more likely in the order of 1/2 of the Fermi wavelength. 53 The Fermi vector in copper is kF = 1.36 × 108 cm−1 . The thickness of the electron accumulation layer will be thus approximated by dEAL = π/kF ≈ 0.2 nm. The electron excess Γe =

(Ne − 8.46 × 1022 cm−3 ) ∗ dEAL will be used in the following as a t parameter.

4.2 Inner Helmholtz Layer Specically adsorbed ions at the WE surface are approximated by ridged spheres in the IHL. For the optical model calculations, it is suitable to dene a layer thickness indepen17



Page 18 of 49

dent from the number of adsorbed ions. We use the doubled Van der Waals radius rV W (rVClW =180 pm) 20,54 of the ions as the thickness of the IHL. The eective (macroscopic) DF −

εÎHL of the IHL can be calculated with the local polarizability of all entities in the layer if each entity retains the local electronic orbitals. This model was already suggested in an earlier ellipsometric investigations of halide ion adsorption on amorphous metal-electrolyte interfaces. 20,21 Accordingly, the layer DF can be obtained with the Clausius-Mossotti relation by means of the molar refractivity (molar polarizability) R [cm3 mol−1 ] and the number of moles per unit volume M (molar density [mol cm−3 ]) of all entities. The Clausius-Mossotti relation is also known as the Lorenz-Lorentz equation if the DF is √ expressed by the refractive index n ˆ = εˆ. The denition of a layer with homogeneous optical properties is appropriate because of the huge wavelength of the incident light in comparison to atomic distances. In the following discussion just one type of adsorbed ions surrounded by water molecules is considered and the Clausius-Mossotti relation takes the form:

εÎHL − 1 = MI RI + MH2 O RH2 O . εÎHL + 2

(9)

The number of moles per unit volume of each entity in our system is determined according to the occupation of the surface area. A complete mono layer of the ions is dened in this model by the most dense packing of ridged spheres in a hexagonal arrangement. 21 In such a conguration each ion covers a surface area AI of:

√ AI = 2 3rV2 W .

(10)

The reciprocal value is the maximum number of ions per unit area. The molar density MImax of such a complete mono layer can be dened as the number of ions per unit area divided by the IHL thickness as dened above according to:

1 MImax = √ 3 , 4 3rV W NA 18


(11)

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where NA is the Avogadro constant. In case of sub-mono layer coverages the molar density reduces linearly with the occupied surfaces area by: (12)

MI = θMImax = ΓI AI MImax ,

where ΓI is the to be determined number of ions adsorbed on an unit area (surface excess). The value of ΓI , however, has to be always smaller than the maximum number of ions on the unit area dened by the reciprocal of equation 10. θ is thus a number between zero and one which represents a relative surface coverage. The remaining surface area, which is not covered by the ions, should contain water. The molar density of pure water MH2 Omax is obtained as the reciprocal value of the molar volume

VmH2 O =18.02 cm3 /mol. 54 The remaining molar density of the water in the IHL is then given by:

MH2 O = (1 − θ)MH2 Omax = QI AI

1 VmH2 O

.

(13)

By inserting equation 10 and 13 in equation 9 we obtain the IHL dielectric function εÎHL depending on the number of ions adsorbed on an unit area of the copper surface ΓI . All other parameters are reference values from literature. Molar refractivities are tabulated for many substances at the sodium-vapor emission line at 589.3 nm (2.10 eV). Commonly they are used in chemistry in connection to refractive index bench mark measurements. For our work it is a rather helpful coincidence that the sodium-vapor emission line ts perfect to the wavelength of maximal sensitivity of our ellipsometric angle ∆ upon surface adsorbates on copper. The here used molar refractivities are summarized in Table 1. To ensure a consistent model we have calculated the molar polarizability of pure water from the data base spectral dielectric function of water. 46 The bulk electrolyte is approximated by pure water due to the small ion concentration of 10 mM/L. With equation 9 and a vanishing ion concentration, we obtained a water molar polarizability of 3.70 cm3 mol−1 which slightly deviates from the literature value listed in table 1. 19



Page 20 of 49

Table 1: Molar refractivity (polarizability) of processed molecules and ions at 589 nm (2.105 eV), the wavelength of the principal sodium line.

H2 O 55,56 R [ cm mol ] 3.72 3.70 (cal.) 3

Cl

H 3 O+

9.06 55

≈ 3.0 57

4.3 Diuse Layer The optical eect of the diuse layer (DL) is expected to be very small. This could be justied by two arguments. First, the thickness of the DF layer is probably best described in the Gouy-Chapman model by the Debye (screening) length. This ionic screening length for the symmetric monovalent HCl solution this is given by:

s λD =

εH2 O ε0 kB T . 2NA qe2 cHCl

(14)

The static dielectric constant of water εH2 O is assumed to be 80. The quantities kB and

NA denote the Boltzmann and Avogadro constant, respectively. At T =300K and for the considered HCl concentration cH Cl =10mMol/l, the Debye length λD is ≈3 nm. Typical double layer charging values are in the order of 1015 per cm2 . If such an amount of ions is distributed in a 3nm thick layer, we obtain a concentration increase of ≈5.5 Mol/l which is just 10% of the pure water molar concentration (≈55.5 Mol/l). Second, the DF of the DL is considered only at potentials where we presume an excess of hydrogen or more precisely an excess of hydronium ions (H3 O+ ). The polarizability of hydronium diers from pure water just by 20% (Tab. 1)). Both together, the low concentration and the similar polarizability, conrms in sum a negligible impact of the DL to the ellipsometric results.

20


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4.4 Discussion of the "Pristine" Copper Surface With the above dened approximations, the ellipsometric results obtained at potential (1) (Fig. 1 and 4) can be analyzed now in more detail. As discussed above, we assume at this potential a minimum of adsorbed ions and the DL is not contributing to the optical response. The ellipsometric angles are thus only dened by the copper bulk DF and a surface electron accumulation. The measured spectral line shape of the ellipsometric angles, is accordingly tted within a parametric model. It includes now the DF of the copper bulk represented by 5 Kramers-Kronig consistent generalized critical points (containing 18 parameters in total) 58,59 and the Drude dispersion part as dened in equation 7. Again we use an eective electron mass m∗ of 1.49∗me . 48 The electron density Ne is set to the theoretical value of

8.46 × 1022 cm−3 . The electron mobility µ is retained as a t parameter. Additionally a surface EAL is dened (Fig. 6(a)). As argued in paragraph 4.1, it has the same DF as the bulk copper and dier just in the electron density Nes which is used as an additional t parameter. The thickness of the EAL is approximated with dEAL =0.2 nm. The thereby tted ellipsometric angles are shown by red and blue lines in the upper part of gure 2. The bulk DF of Cu(111) obtained in this way is shown in gure 7. The contributions of the generalized Lorenz oscillators to ε2 are shown as dotted lines. The solid black line is the contribution of the Drude free electrons. Within this model, we obtained an electron mobility of 7.53 cm2 V−1 s−1 which is just a little smaller than the value determined by Johnson et al. 48 The electron density in the surface layer is determined to Ne = 2.26 ± 0.02 ×1023 cm−3 ; a value which has still a small but, as we will discuss in the following section, essential systematic error. Under consideration of the chosen layer thickness we obtain thus in this second approximation a surface electron excess of Γe =2.83×1015 electrons per cm2 (453 µ C/cm2 ). It was pointed out already by Paik et al., 21 that the optical model appears robust concerning variations in the chosen layer thickness. A factor of two in the layer thickness causes variations of less than ≈10% in the calculated electron excess. In other words, it is optically not relevant whether the excess electrons are distributed over a thicker or thin 21



Page 22 of 49

surface layer. In this framework it is also evident that the expected electron spill out at the meal-electrolyte boundary is almost not contributing to the optical response. Whether this value is realistic or not is tested by means of the double layer capacity. The Gouy-Chapman theory provides an approximation for the capacity of the double layer without surface adsorbates where just the rst term in equation 4 is considered. In a symmetric monovalent solution, as it is the case for HCL, the capacity is given by: 45

CGC

εε0 cosh = λD

qe (E − EP ZC ) 2kB T

(15)

.

The surface charge at the working electrode can be now calculated by an integration of the potential dependent capacity starting from the PZC (PZTC) to the potential of interest according to:

Z

E

2εε0 kB T CGC (E ) dE = sinh Qe = λD qe EP ZC 0

0

qe (E − EP ZC ) 2kB T

.

(16)

With equation 16 and the ellipsometric determined surface charge, thus, a hypothetical PZTC is estimated for a system without chloride adsorption. We believe that this value is equivalent to the "PZFC" which was found close to the Cu dissolution potentials in electrochemical impedance experiments. 60 For the Cu(111) surface we obtain as a rst approximation -157 mV and with a later discussed additional small corrections a value of -148 mV vs. Ag/AgCl. These values are just slightly lower than literature value of

e.g.

-122 mV for

amorphous Cu. 49 At Cu(110) we identied the point with a minimum of adsorbed ions in the IHL around the potential of -450 mV which is again labeled by (1)(Fig. 4). The ellipsometric results at this potential are analyzed with the same model calculation as used before for the (111) surface. We obtained thus a charge accumulation of Γe =9.04×1014 electrons per cm2 (Qe =145 µC/cm2 ) which is about 300-400 µC/cm2 smaller than on the (111) surface. The calculation of the PZFC (the hypothetical PZTC without super-equivalent absorption of Cl) 22


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yields -166 mV, which is just slightly smaller than the value of the (111) surface. This result is somehow surprising, because the PZC and the work function in units of eV are believed to be strongly correlated. In a rough approximation they interrelate only by the factor of the elementary charge and a common constant oset. The work functions of Cu(111) and (110) are 4.98 eV and 4.48 eV, 61 respectively. Thus we would actually expect a dierence in the PZC of several 100 mV. At this point, it is worth mentioning that the determination of the absolute electron excess at the copper surface is also directly linked to the absolute accuracy in the determination of the ellipsometric angle ∆ which may include some systematic errors. A critical test of the experiment and the calculation of absolute numbers for the electron excess is subject of ongoing work. But, relative changes in ∆ are, nevertheless, obtained precisely; a fact which is used in the following discussion.

4.5 Cl adsorption and water surface layers The evaluation of the ellipsometric response from Cu(111) at potential (2) could serve as a critical test of the optical model. EC-STM experiments have proven already that the Cl overlayer structure contains 5.87×1014 Cl ions per cm2 . The ellipsometric model contains now the copper bulk DF, an EAL, and an IHL containing the adsorbed Cl ions in a matrix of water (Fig.

6(b)). As a template we use the before obtained copper DF and surface

electron density from potential (1). In such a model, just one t parameter is remaining, if the adsorption of Cl ions at the surface presupposes an electron depletion of equal amount on the other side of the interface. 21,62 It is the change in the surface electron density −∆Qe which is equal to Cl ion density ∆QI . With this model we obtained by ellipsometry a

Γe = ΓI of 3.08×1014 cm−2 . The remaining discrepancy of almost a factor of two is attributed to the insucient assumption of a "pristine" surface at potential (1). Regardless of the presence of remaining adsorbed ions, it turned out to be necessary to include a water surface layer with dierent 23



optical properties. It was demonstrated already in Ref. 50 that the interaction of the dipole moment of the water molecules with a metal surface could result in a surface layer with more than 30% higher density in comparison to the bulk water. As a consequence also the refractive index of the water layer near the surface increases. The value of the refractive √ index n ˆ = εˆ for dierent densities can be calculated by means of the molar polarizability of water with equation 9 (MI = 0). For a 30% higher density n ˆ H2 O increase for example from 1.33 to 1.344. If such a water layer is considered in the calculations for the "pristine" (111) surface, the respective electron excess at potential (1) increase and also the calculated amount of adsorbed Cl ions at potential (2) increases towards the expected value. With the known Cl excess determined by EC-STM (ΓCl− =5.87×1014 ions per cm2 ) and the known change in the electron excess between potential (1) and (2) determined from CV (∆Qe =102 µC/cm2 ) the observed dependency of the ellipsometric angle ∆ can be nally used in order to obtain an approximation for the water layer density on the Cu(111) electrode. The presumption of an one-to-one exchange of the electron excess by the negative charge of the Cl ions (electrosorption valence αCl− =-1), was motivated by previous experiments on mercury electrodes 62 and is likely not perfectly correct for copper. But if we would roughly approximate (δQe /δE)Γ = (δQe /δΓH2 O )E ≈ 0, the hereby determined electrosorption valence of αCl− = ∆Qe /∆QCl− = 1.1 is still close to one and matches with X-ray diraction results on Cu(110) which predict a small or negligible electron transfer from the Cl ions to the copper WE. 63 The surface electron excess and the water layer density at potential (1) is determined in a simultaneous t by assuming that the water layer at potential (1) is partially replaced at potential (2) by a 0.36 nm thick Cl layer containing the 5.87×1014 Cl ions per cm2 . The thereby determined density appears again relatively robust against the assumed layer thickness. We obtained water layer densities which are 1.8 to 2.2 times larger than in the bulk liquid phase depending on whether a thicknesses between 0.4 and 1.0 nm is assumed. A thickness of 0.8 nm would roughly comprise 3 water mono-layers. That such an extreme 24


Page 24 of 49

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densication is realistic was demonstrated already by Toney et al. 64 at a silver (111) electrode in X-ray scattering experiments. Depending on the voltage they got doubled density in the rst water layer with an exponentially decreasing consolidation over the rst 3-4 layers. If we compare, on the other hand, our t result with the number copper atoms at the (111) surface (1.76×1015 cm−2 ) it is conspicuous that an increase of the water density by 76% coincides with a situation where each copper atom is decorated by one water molecule. For comparison, ab-initio calculations for Cu(110) in equilibrium with ambient water vapor pressures disclosed several stable surface adsorbate structures which all comprise a water layer density according to the number of copper atoms at the (110) surface. 65 The electron excess at potential (1) under consideration of a water layer with two times higher density increases in comparison to the calculations without water overlayer from Γe =2.83×1015 (1)

(1)

electrons per cm2 (453 µ C/cm2 ) to Γe =3.4×1015 cm−2 (Qe =540 µC/cm2 ). Quite in general it is worth mentioning that the observed change in the ellipsometric angle ∆ is mainly depending on the change of the electron density at the copper electrode surface. The Cl layer with 5.87×1014 ions per cm2 has a calculated refractive index of 1.64 at 2.1eV. The proposed water layer with a density of 1.76 would have a refractive index of 1.61. Hence, the optical properties are similar and the contribution of the overlayer to the change in ∆ upon a partially exchange of the water layer with Cl is small. Furthermore it is worth mentioning that ∆ is in a good approximation linearly depending on the surface and electron excess which can be proven by means of a Taylor series representation of the optical model. In case of Cu(110), a quantitative discussion concerning the Cl adsorption is unfortunately much more complicated. The observed faceting of the surface would require a more complex optical model with additional unknown parameters. Nevertheless, it is worthwhile to note that ∆ decreases by about 0.15◦ in connected with the Cl adsorption is almost a factor of two less than on the (111) surface (0.25◦ ). The faceting has a similar eect like a statistical roughening of the surface and is expected to generate an even stronger decrease 25



in ∆ at 2.1 eV. A smaller decrease of ∆ is, thus, neither a result of the morphology transformations nor a result of the formation of an aggregate layer. More likely is a considerably smaller amount of adsorbed Cl at the (110) surface compared to (111). The uppermost layer of the more open Cu(110) surface contains only 1.08×1015 /cm2 copper atoms. Therefore also the water overlayer density is expected to be smaller if the water molecules arrange again in a "1×1 structure" with respect to this upper most copper layer. 65,66 The surface water lm would have almost the same density as bulk water and the charge accumulation calculated in the previous paragraph 4.5 for the pristine (110) surface (point (1)) remains correct. Based on the CV we measure between potential (1) and (2) an integrated charge transfer of about 150 µC/cm2 . The considerably higher value in comparison to the (111) surface (102 µC/cm2 ) is especially surprising as the optical results indicate a smaller amount of adsorbed Cl . The larger charge transfer can be explained either by an increasing surface area due to the faceting of the surface and/or with contributions of the overlapping Cu dissolution in form of CuCl or CuCl. 24

4.6 H+ accumulation upon HER potentials It was mentioned already that both copper surfaces arm through the ellipsometric angle ∆ a signature of a specic adsorption at potentials of the HER. The value of ∆ increases at the onset of the HER but saturates at a certain level in contrast to the exponentially increasing HER Faraday current measured by CV. The variations in ∆ have been primarily attributed to modications of the electron excess. Variations in the ion excess in the IHL contribute only to a small amount. But a double layer charging according to the Gouy-Chapman theory without specic adsorption (rst term in Eq. 4) would result just in a monotonous increase of the raising electron excess (Eq. 15 and Eq. 16) and thus can not explain a step like modication in ∆ (before point (1); g. 3c). The eect of the Gouy-Chapman double layer charging can be observed for example in gure 3 between 100 and 175 s or between 300 and 350 s. The observed step like change in ∆ has to be the result of an adsorption (second 26


Page 26 of 49

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term in Eq. 4). With the approximation of equation 5 and the obtained linear relationship between ∆ and the overall electron excess, we further conclude that the step like change in

∆ is proportional to the variation in the ionic surface excess including the respective electron excess at the metal side of the boundary. The adsorption/desorption of an anion species like OH− is in the deaerated acidic solution and at this potential unlikely. Therefore we rather consider the absorption of an cation as an explanation for the increase in ∆. But the straightforward assumption of an absorption of bare H+ is also questionable in particular under consideration of the before discussed adsorption of water at the (metal) copper surfaces. Broeckmann et al. 67 have studied the HER on Cu(111) already by EC-STM in dilute sulfuric acid. At potentials below the sulfate anion adsorption they found a narrow potential window with a 1×1 copper surface which was interpreted as a pristine surface. At more negative potentials in the onset of the HER, they observed an increasing decoration with a quasi-commensurate adsorbate structure. This structure is discussed in terms of an adsorption of H2n+1 O+ n clusters since the authors believe that the hydronium ion H3 O+ is further screened in a hydration shell. Under consideration of the above discussed adsorbed/densied water layer even on pristine copper, it seems likely that this water layer is protonated at more negative potentials in the HER range. Evidence for the existence of a dense water lm on Cu(111) and it's protonation upon the HER was obtained also by Ito et al. based on surface X-ray diraction and infrared reection adsorption experiments. 68 According to their structure model, the water density near the surface increases by a factor of 1.63 due to a reduced distance between the rst water mono layers. The appearance of the adsorbed water in EC-STM as a quasi-commensurate structure upon HER could be explained by the charging which may result in a repulsive interaction in the layer. That the preceding pure water layer is not visible in EC-STM, is perhaps connected to the supposed 1×1 coverage structure. If we further assume that pristine water with a considerable surface mobility is not visible in the background of the bulk electrolyte, the absence of a signature in EC-STM appears likely. 27



Page 28 of 49

According to a commonly accepted model, the HER on copper in acidic solutions is believed to obey the so called Volmer-Heyrovsky mechanism. 45 This includes at st a hydrogen adsorption by means of a proton-transfer step within the so called Volmer reaction: H3 O+ + e− H(ad) + H2 O,

(17)

which is followed by the Heyrovsky step with the release of hydrogen gas: H(ad) + H3 O+ + e− H2(g) + H2 O.

(18)

With the suggested water layer we would add to this reaction scheme a proton transfer from the DL to the adsorbed water layer: H2 O(ad) + H+ H2n+1 O+ n (ad) ,

(19)

which increases the overall capacity of the double layer region and is observed in ellipsometry due to the adsorbed ions and/or the change in the surface electron excess. Whether the subsequent Volmer reaction (Eq. 17) is relying on the H+ adsorbed in the surface water layer is a remaining question which will be discussed in a comparison of the CV and ellipsometric results. The molar density as well as the molar polarizability (Tab. 1) of the adsorbed water is eventually just slightly decreasing after the proton transfer. Hence it is a good approximation if we keep the optical properties of the water layer constant. The observed variation in ∆ is consequently only a result of the respective change in the electron excess. The optical layer model in this potential range (Fig. 6(c)) is thus the same as it is used for the potential (1) ((Fig. 6(a))). The change in the ellipsometric angle ∆ can be expressed according to equation 5 by: H3 O+ (ad)

d∆

=

δ∆ δQe

H 3 O+ (ad)

dQe

≈ ξαH3 O+ dΓH3 O+ . (ad)

28


(ad)

(20)

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The electrosorption valence αH3 O+

(ad)

is unfortunately an unknown scaling factor while ξ ≈

δ∆/δQe is determined by the optical layer model. With ellipsometry, we can thus quantitatively measure ∆Qe between two potentials independent from CV and not convoluted with the Faraday current of the HER. For the calculation we use potential (1) as a reference. The second potential is denoted as point (3) in gure 1 and 3. It is chosen in the anodic scan direction just before the respective proton desorption. For the Cu(111) surface we obtain thus a ∆Qe of 109 µC/cm2 which (3)−(1)

corresponds to a change in the electron excess of ∆Γe

=6.8±0.2 ×1014 cm−2 for the

maximal protonation. If we consider also the ellipsometric angle Ψ, we can determine furthermore a variation in the electron mobility. The correlation factor of the two quantities is smaller than 0.05. It turns out that the electron mobility decreases by a factor of two upon the protonation process. A explanation could be the scattering of the free surface electrons at the adsorbed (hydronium) cations. Right now, the surface electron excess and mobility is obtained by a t at 2.1 eV. Whether the optical model and a t with just two parameters at a single wavelength is appropriate can be tested by means of the calculation of the complete spectral response. Therefore we have calculated the dierence Ψ and ∆ spectra between point (1) and (3). These are the red and blue curves in gure 2b. The agreement with the experiment (black symbols) concerning the spectral line shape and amplitude is remarkable. The deviations in the spectral range below 2eV are caused by a rapidly increasing inuence of systematic errors while Ψ tends to 45◦ . Next, we compare the CV's of Cu(111) and Cu(110) in the HER range in more detail. Therefore the Faraday currents are depicted together in the inset of gure 4 in terms of a Tafel plot (logj vs. potential). Both surfaces display almost the same linear slope in this range and the HER apparently obeys the Tafel equation:

j = −j0 exp

−βc zqe (E − Er ) , kb T 29


(21)


Page 30 of 49

with a common charge transfer coecient βc of ≈0.4. The Tafel currents are shifted by about 30 mV. This shift corresponds to deviations in exchange current density j0 and is therefore a measure of the catalytic eect of the copper surface. The shift between the two (111)

Tafel currents indicates that j0

(110)

is about 2.6 times larger than j0

. Notice, the standard

potential E0 of the HER dose not depend on the WE and that j0 just scales with a constant factor depending on the arbitrarily chosen reference potential Er . For the comparison of the ellipsometric results we choose for Cu(110) a potential denoted as point (3) with the same current density of the HER as at the respective potential (3) for Cu(111) (inset in Fig. 4). For Cu(110) we found thus a surface charge density increase of ∆Qe (3)−(1)

of 37 µC/cm2 which corresponds to a change in the electron excess of ∆Γe

=2.3±0.3

×1014 cm−2 . This is almost a factor of three less than on Cu(111) at the same HER current density and we conclude that also the respective protonation of the water layer is a factor of three smaller. Furthermore we nd that the electron mobility increases which is the opposite behavior compared to the (111) surface where the electron mobility decreases. As pointed out already by Kötz and Kolb 16 the (110) surface depicts a natural surface corrugation which causes a reduced mobility of the surface electrons. With increasing cathodic potentials the surface electron excess increases and the electrons are pushed outward and smooth out the corrugation. In conjunction with a less dense water layer and the measured much smaller proton transfer (H+ adsorption) an increasing electron mobility is logically consistent. Finally it is remarkable that on one hand the exchange current density j0 of the HER on Cu(110) is about 2.6 times smaller than those on Cu(111). On the other hand also the protonation value of the (I)HL is more than 3 times smaller on the (110) surface if we compare potentials where the current density j of the HER is the same. Therefore, the proton transfer to the adsorbed water layer (Eq. 19) seems not to be a preceding step for the Volmer reaction (Eq. 17). This conclusion is further supported by the fact that the value of the exchange current density factor j0 at the (111) surface rather increases with the deprotonation of the surface. This behavior is depicted in gure 8, where we compare the 30


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current density j of the HER in a Tafel-plot with the changing ellipsometric angle ∆ which is proportional to the surface excess. The deprotonation itself as well as the subsequent Cl adsorption at even higher potentials should induce a positive current and can thus not explain the observed increase in the Tafel current of the HER towards more negative values. In search of correlation eects for the catalytic activity upon the HER, transition metals are often arranged in a so called volcano plot where the logarithm of the exchange current density is plotted against the free energy of adsorption of hydrogen on the respective metal. 45 For metals like copper, logj0 increases linearly with a decreasing absorption energy i.e. if less energy is needed to establish the metal-hydrogen-bond in the Volmer reaction (Equ. 17). In this empirical framework, one would expect that a protonation of the water layer supports the HER if it is interpreted as a preliminary step before the hydrogen adsorbs at the copper surfaces. But the opposite is observed. The protonation seems to suppress the HER.

5

Summary

In this work we determined quantitatively the surface termination and charge accumulation at copper single crystal surfaces in HCl solution and at dierent electrochemical potentials. Therefore we have used

in-situ

ellipsometry in comparison to EC-STM and CV. First of

all, we could demonstrate that the thereby measured ellipsometric angles Ψ and ∆ possess a sucient sensitivity in order to monitor surface processes in the space charge region at a level of sub-mono layer coverages. In this connection it is important that the phase parameter ∆ reveals a much higher sensitivity than Ψ regarding

e.g.

the surface electron excess. Hence,

simple reection experiments can not gain comparable results. In ellipsometric transient experiments, we could thus identify the optical signature of the adsorption of a sub-mono layer of Cl on Cu(111) which was before identied by EC-STM √ √ as a ( 3× 3)R30◦ structure. At more cathodic potentials, we found, furthermore, on the Cu(111) as well as on (110) surfaces a signature of an adsorption process at the onset of the

31



Page 32 of 49

hydrogen evolution reaction. At more anodic potentials we could observe a dependency of the ellipsometric response which correlates linearly with the copper dissolution. However, the latter is not further discussed and the subject of subsequent investigations. A quantitative insight in the surfaces processes is obtained from ellipsometry within an optical layer model calculation which assumes in the space charge region between the bulk copper WE and the bulk electrolyte two homogeneous layers with modied dielectric properties. At the metal side of the boundary we anticipated a near surface layer which has the same optical properties as bulk copper but with a modied free electron density and mobility. The dielectric response at the ionic side of the boundary,

i.e.

in the Helmholtz

layer, are calculated by means of the local polarizability of the contributing ions and the water molecules. 21 It is shown that the diuse layer is optically not contributing in the investigated system. Hence, the ellipsometric response is attributed to an electromodulation eect and the adsorption of ions. The ellipsometric angle ∆ exposes in a good approximation a linear dependency on the electron and ion excess. Herein, the biggest contribution is from the surface free electron density. Worth mentioning is the relatively small eect of the assumed thickness of the articially dened homogeneous electron accumulation layer on the calculated electron excess. Important to note is that ellipsometry maps only near surface modications. It enables in comparison to

e.g.

CV a clear distinction between adsorbates

and electrocatalytic surface reactions like the HER. As a critical test of the optical model we used the Cl adsorption on Cu(111). Therefore the ellipsometric response was analyzed between two potentials where EC-STM has proven √ √ a pristine Cu(111) surface and a ( 3× 3)R30◦ Cl structure, respectively. Thus we obtained an electron/Cl excess in a t of the optical data which is just deviating by a factor of two from the expected value of 5.87×1014 Cl ions per cm2 . The deviation could be explained by the existence of a densied water layer at the copper surface which modies the optical response even at potentials where EC-STM is indicating a "pristine" surface. Because the changes in the electron and Cl excess are 32


Page 33 of 49 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


actually determined independently by CV and EC-STM, we could quantify the water layer density. By assuming a layer thickness of 0.4 nm the determined water density appears 1.8 times larger on Cu(111) than in bulk liquid phase. The adsorption signature detected by ellipsometry at the (111) and (110) surfaces at the onset of the HER (the H+ reduction at the copper surface) is attributed to a protonation of the adsorbed water layer. The optical properties of the water layer are assumed to be almost unaected by the protonation and the optical eect is thus determined by the induced variation in the surface free electron properties. At both surfaces we observe an increasing surface electron excess upon protonation. In case of Cu(111) it saturates at increasing cathodic over potentials while the Faraday current of the HER increases continuously. The respective increase of the electron excess is determined as 6.8×1014 electrons per cm− (109 µC/cm2 ). Parallel to the increasing electron excess (protonation) we could determine optically a decreasing lateral mobility of the surface electrons. In this connection it is remarkable that the Cu(110) surface possess at potentials with the same HER current density an almost three times smaller protonation of the near surface area than the Cu(111). Furthermore we found in a comparison of the ellipsometric results with the CV an increasing exchange current density factor of the HER upon the desorption of H3 O+ on Cu(111). Both ndings together let us conclude that the supposed protonation of the densied water layer, is not an initiating step of the HER. In contrary is rather seen as a suppressing factor.

Acknowledgement This work was supported by the European Union's Horizon 2020 research and innovation program under grant agreement No.692034 (TwinFusyon). Furthermore, we gratefully acknowledge nancial support and a fellowship for Saul Vazquez-Miranda by the Mexican National Council of Science and Technology (CONACYT).

33



Page 34 of 49

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Graphical TOC Entry

41



5 0 (3 )

2 5

C u (1 1 1 )

(1 )

(2 )

5 2 0 m V

3 9 0 m V

6 5 5 m V

in 1 0 m M /L H C l

A

)

0 2

-2 5

j ( µA / c m

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 42 of 49

-5 0 -7 5

A '

-1 0 0 A '

-7 5 0

-7 0 0

-6 5 0

-6 0 0

-1 2 5 -8 0 0

-7 0 0

-6 0 0

-5 0 0

-4 0 0

-3 0 0

-2 0 0

-1 0 0

0

E ( m V v s . A g / A g C l in 3 M / L N a C l) Figure 1: Cyclic current-potential plots for Cu(111) in 10 mM/L HCl recorded at dierent scan rates (2 mV/s pink, 5 mV/s blue, 10 mV/s red, 20 mV/s black). The inset shows an expected current evolution without the Faraday current caused by the HER with a dashed curve. The potentials (1) at -520 mV, (2) at -390 mV, and (3) at -655 mV label points of characteristic surface conditions.

42


1 2 0

4 0

1 0 0

3 5

8 0

3 0

Y

D (°)

4 5 a

1 4 0

b 0 .2

0 .1

0 .1

0 .0

0 .0

-0 .1

-0 .1

1

-Y

1

(°)

(°)

0 .2

Y

3

D 3-D

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(°)

Page 43 of 49

2

3

4

5

6

p h o to n e n e rg y (e V ) Figure 2: Cu(111) - Ellipsometric angles Ψ and ∆ (black symbols) in comparison to the parametric optical model (red and blue lines). The upper panel (a) shows the spectral dependency at the potential (1) (Fig.1) where we assume a negligible amount of ionic surface adsorbates. The lower panel (b) shows dierence spectra of Ψ and ∆ between potential (1) and a more cathodic potential (3) (Fig.1). The optical model assumes a modied electron density and mobility at the surface of the WE.

43



E (m V )

0 a

-2 0 0 -4 0 0 -6 0 0

c

b

9 3 .2

* 1

5 0

9 3 .1

9 2 .9

A

A '

2

-5 0

)

0

2

9 3 .0

j ( µA / c m

3

∆(° ) a t 2 .1 e V

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 44 of 49

9 2 .8 9 2 .7

-1 0 0

*

9 2 .6 0

1 0 0

2 0 0

3 0 0

4 0 0

5 0 0

6 0 0

T im e ( s e c . ) Figure 3: Cu(111) - In-situ ellipsometric transient of ∆ at 2.1 eV (black dotes, panel (b) and (c)) and the Faraday current (blue line, panel (b)) both recorded simultaneously to a cyclic voltage sweep (black line, panel (a)) with 5mV/s. The green line shows a segment by segment smoothed ∆ transient in order to emphasize the characteristic line shape.

44


Page 45 of 49

1

6

C u (1 1 0 )

C u (1 1 0 )

3

5

in 1 0 m M /L H C l

C u (1 1 0 )

A

C u (1 1 1 )

4

2

1 0

3 3

B

C u (1 1 1 )

2

)

2

j ( µA / c m

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-7 0 0

1

-6 5 0

-6 0 0 1

0 -1 3

-2 -3 -4

A '

-5 -8 0 0

-7 0 0

-6 0 0

-5 0 0

-4 0 0

B ' -3 0 0

-2 0 0

-1 0 0

E ( m V v s . A g / A g C l in 3 M / L N a C l) Figure 4: Cyclic current-potential plots for Cu(110) in 10 mM/L HCl recorded at with a scan rate of 5 mV/s. The inset shows in a Tafel plot the evolution of the logarithm of the current in the potential range of the HER in comparison to the results from Cu(111). The potentials (1) at -420 mV, (2) at -290 mV, and (3) at -690 mV label points of characteristic surface conditions.

45


Page 46 of 49

a

-2 0 0 -4 0 0 -6 0 0 b 1

9 2 .6 5

A B 2

9 2 .6 0 0 2

)

9 2 .5 5 3

9 2 .5 0 9 2 .4 5 9 2 .4 0

2

B '

-2

j ( µA / c m

∆(° ) a t 2 .1 e V

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

E (m V )


-4

A ' -6

9 2 .3 5 3 0 0 3 5 0 4 0 0 4 5 0 5 0 0 5 5 0 6 0 0 6 5 0 7 0 0 7 5 0

T im e ( s e c . ) Figure 5: Cu(110) - In-situ ellipsometric transient of ∆ at 2.1 eV (black dotes, panel (b)) and the Faraday current (blue line, panel (b)) both recorded simultaneously to a cyclic voltage sweep (black line, panel (a)) with 5mV/s. The green line shows a segment by segment smoothed ∆ transient in order to emphasize the characteristic line shape.

46


e-

(a)

10 mM/L HCl

e-

H+

e-

Cu

e-

e-

(c)

eeee-

Cu

eee-

H+

H+

H+

Cu

DL 10 mM/L HCl H+ H+

H+ H+

e-

Cl-

e-

EAL IHL

10 mM/L HCl H+ H+

H+

H+ H+

e-

Cl-

H+

ee-

(b)

Cl-

dEAL= 0.20 nm dIHL= 0,36 nm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


H+

H+

H+ H+

λDebye ≈ 3 nm

Page 47 of 49

H+

H+ H+

Figure 6: Optical layer models of the electrochemical double layer region. (a), (b), and (c) represent the three characteristic surface congurations at the potentials (1), (2), and (3) (Fig. 1 and 4).

47



0 7

-5 6

-1 0 5

-1 5 1

2

4

e

-2 0

e

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 48 of 49

3

-2 5 2

-3 0 1

-3 5 1

2

3

4

5

6

0

p h o to n e n e rg y (e V ) Figure 7: Real (blue) and imaginary part (red) of the dielectric function of bulk single crystal Cu measured at the (111) surface in 10 mM/L HCl solution at 520mV (vs. Ag/AgCl in 3 M/L NaCl). The chosen potential ensures a negligible amount of adsorbed ions. The surface electron excess at this potential is considered by a surface layer EAL (Fig. 6). The black solid and black dotted lines represent the free electron contributions, described with a Drude dispersion, and the bound electrons, described by generalized Lorenz oscillators.

48


Page 49 of 49

1

9 3 .2 0 C u (1 1 1 )

9 3 .1 5

2

)

3

j ( µA / c m

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1 0 1

9 3 .1 0

9 3 .0 5

1 0 0 -7 0 0

-6 5 0

-6 0 0

-5 5 0

E ( m V v s . A g / A g C l in 3 M / L N a C l) Figure 8: Cu(111) - Comparison of the potential dependency of Faraday current (blue line) and the ellipsometric angle ∆ (green line). Both where recorded in anodic scan direction with 5 mV/s at the onset of the HER. The Faraday currents are presented within a Tafel plot in a logarithmic scale. The black lines are used as a guide for the eye.

49


In-Situ Optical Quantification of Adsorbates and Surface Charges on

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