Differential Capacity of Bromide Anions Adsorption onto Ag(100) in the Absence, and onto Ag(poly) in the Presence of NaClO 4

Transcription

1 V. D. JOVIÆ, Differential Capacity of Bromide Anions Adsorption onto Ag(100), Cm. Biocm. Eng. Q. 23 (1) (2009) 11 Differential Capacity of Bromide Anions Adsorption onto Ag(100) in t Absence, and onto Ag(poly) in t Presence of NaClO 4 V. D. Joviæ Institute for Multidisciplinary Research, Belgrade, P. O. Box 33, Serbia vladajovic@ibiss.bg.ac.yu Original scientific paper Received: June 9, 2008 Accepted: October 5, 2008 In this work, t adsorption of bromide anions onto Ag(100) and Ag(poly) in t absence and presence of NaClO 4 was investigated. T cyclic voltammetry, EIS and C diff vs. E measurement results were analyzed. For t determination of t adsorption parameters, t equivalent circuit containing constant phase element (CPE) instead of t double layer capacity (C dl ) and new equations for t analysis of t anion adsorption, based on a different definition of t CPE, have been developed and used. It was swn that t proposed equivalent circuit and corresponding equations for t differential capacity (C diff ) as a function of frequency () can successfully be applied in t investigated systems. Excellent agreement between t cyclic voltammograms (CVs) and t C diff vs. E curves recorded at frequencies lower than 10 Hz has been detected. T mogeneity of t charge distribution over t real single crystal surfaces, as well as otr parameters of t adsorption process were found to change with t potential. In t presence of t supporting ( non-adsorbing ) electrolyte (0.1 M NaClO 4 ) diffusion-like pnomenon was detected and ascribed to t slow step in exchanging anions adsorbed in t inner Helmltz plane. Key words: Bromide anions adsorption, differential capacity, CPE, surface mogeneity Introduction T determination of t double layer capacities in t available literature is, so far, mainly based on eitr differential capacity measurements (C diff vs. E curves) performed at a single frequency, 1 6 or on impedance measurements performed in a broad range of frequencies and t analysis of impedance diagrams using t adsorption impedance tory developed by M. Sluyters-Rehbach et al. 7 Using equations for t impedance and capacitance defined by this tory 7,8 t equation for t differential capacity is defined as C dl corr Cdiff Ylm 1 (1) 12 / Cad ( 1 Cad ) 12 / ( C ) C ( R 12 / 1 ) 2 ad ad ad wre Y Im corr represents imaginary component of admittance corrected for R s, is t angular frequency ( =2f, f being t frequency), R s represents resistance of t solution, C dl t double layer capacity, while C ad, R ad and correspond to t capacity, resistance and t Warburg coefficient of t anion adsorption, respectively. It suld be noted that in order to obtain t real value for t C dl,solution resistance (R s ) must be subtracted from t total electrode impedance (Y Im corr in t eq. (1)). Taking into account that t Warburg coefficient of t anion adsorption () depends on t concentration (c) and t diffusion coefficient (D) of adsorbing anions, it could be concluded from t eq. (1) that at high frequencies and low concentrations of adsorbing anions, t contribution of t second term in this equation becomes insignificant and t C diff vs. f corresponds to t double layer capacity only. Using t values for C dl =60F cm 2, C ad = 200 F cm 2, R ad =50 cm 2, D = cm 2 s 1 and varying t value of c from 100 mm to 0.01 mm in eq. (1), C diff vs. f diagrams presented in Fig. 1 were obtained. As can be seen, for higr concentrations of anions (1, 10 and 100 mm) tir diffusion has no influence on t shape of t C diff vs. f curves. T total capacitance is independent of frequency and equal to C dl at f 10 2 Hz (point A), while at f <10 0 Hz, t total capacitance is also independent of frequency and equal to t sum C dl + C ad (point B). At lower concentrations (0.1 and 0.01 mm), t differential capacity is again independent of frequency and equal to C dl at f 10 2 Hz (point A), while C diff depends on frequency at frequencies lower than 10 2 Hz, as a consequence of t anion diffusion, and does not represent t sum C dl + C ad (its value cannot reach t sum of C dl + C ad even at f =10 4 Hz). This indicates that t real value of t C ad (independent of frequency)

2 12 V. D. JOVIÆ, Differential Capacity of Bromide Anions Adsorption onto Ag(100), Cm. Biocm. Eng. Q. 23 (1) (2009) cannot be determined from t C diff vs. f curves for tse concentrations of anions. It is important to note that most of t experiments concerning C diff vs. E curves were performed in t solutions of investigated anion concentrations lower than 100 mm, usually of t order of 1 mm in t frequency range between 10 and 20 Hz, 5,6 exactly in t region of frequencies wre C diff increases sharply with decreasing t frequency (frequency region between A and B). In order to decrease t solution resistance in almost all cases a supporting ( non-adsorbing mostly perchlorate) electrolyte was added to t solution. All t above mentioned consideration is valid for t systems wre t double layer capacity behaves as an ideal double layer, i.e. assuming mogeneous electrode surfaces (mogeneous charge distribution over t surface) and t double layer capacity being represented by a parallel plate condenser. 1 8 T introduction of t constant phase element (CPE) instead of t double layer capacity is also discussed in t literature Several pnomena, such as distributed surface reactivity, surface terogeneity, roughness or fractal geometry, electrode porosity and current and potential distribution associated with electrode geometry were attributed to t CPE behavior in t literature T different expressions given for t CPE indicates that its physical meaning is not yet clear. A recent experimental study of Kerner et al. 25 swed that capacitance dispersion on solid electrodes was due to surface disorder (i.e. terogeneities on t atomic scale) ratr than roughness (i.e. geometric irregularities much larger than tse on t atomic scale). Kim et al. 26 also swed that t contribution of surface terogeneity can be much higr than t contribution of t surface irregularity to t capacitance dispersion. Most recently M. Orazem et al. 27 discussed different procedures for t treatment of t distribution of time constants and pointed out that t impedance of an equivalent circuit for parallel connection of CPE and resistance (R) can be expressed by two different equations and R Z( ) (2) 1 ( jcr) Fig. 1 Calculated C diff vs. f curves for t adsorption of anions defined by eq. (1) for t following parameter values: R ad =50 cm 2 ;C dl =60F cm 2 ;C ad = 200 F cm 2 ; D= cm 2 s 1. T concentrations of anions (c) are marked in t figure. R Z( ) (3) 1 ( j) CR It is important to note that eq. (3) was used in all commercially available software for fitting impedance spectra, as well as in our previous paper. 28 In such a case CPE was considered as an independent element of t equivalent circuit and its impedance 29,30 was defined as Z CPE = 1/[Y 0 (j) ], while t values of Y 0 and were obtained by fitting procedure, with t constant Y 0 having dimension 1 cm 2 s. Accordingly, its value suld be corrected by t procedure defined in t paper of Hsu et al. 31 in order to obtain correct dimension for t capacity, by following equation max 1 CY0( lm ) (4) with Im max being t frequency of t maximum on Z Im vs. log dependence, independent of t value of. Eq. (4) is a result of t application of eq. (2) in t case of t analysis of t equivalent circuit with t parallel connection between CPE and R. If t value of Im max cannot be determined (in t case wre t maximum on Z Im vs. log dependence, i.e. t maximum on t semi-circle of t complex plane Z Im vs. Z Re does not exist, which is almost always t case on tse diagrams obtained for anion adsorption, t real (dimensionally correct) value of t capacity cannot also be determined. In such a case t following equation suld be used. 1 C[ Y ( R) 1 ] / 0 (5) Eqs. (2), (4) and (5) assume that both parameters, C and R depend on in t same way. T frequency dispersion of t capacity as a consequence of t surface terogeneity (expressed as ) is closely related to t charge distribution over t same surface and tse two parameters are mutually dependent. Such a statement is also pointed out by Van Meirhaege 32 in t analysis of t capacity of semiconductors. 33 According to tse two references, t frequency dependence of t capacity must be accompanied by a frequency-dependent parallel resistance.

3 V. D. JOVIÆ, Differential Capacity of Bromide Anions Adsorption onto Ag(100), Cm. Biocm. Eng. Q. 23 (1) (2009) 13 T model and t equivalent circuit for anion adsorption onto real single crystals After t in situ STM technique is introduced in t processes of t double layer and anion adsorption investigation onto single crystal surfaces, 34 it was obvious that even single crystal surfaces are not perfectly flat, but to t contrary, it is swn that ty consist preferentially of a significant number of atomically flat terraces separated by monoatomic steps (for t best surface) A typical example is demonstrated in Fig. 1 of Ref. 35, swing not only monoatomic steps, but also t presence of much more pronounced irregularities on t real single crystal surfaces of Ag(111) and Ag(100). It is also swn that during t process of anion adsorption, t first step is adsorption of anions at t monoatomic steps accompanied by t dynamic change of t STM image and movement of t monoatomic steps and terraces along t electrode surface, indicating t presence of terogeneous charge distribution over t single crystal surface. Simultaneously with t adsorption of anions at t monoatomic steps, adsorption of anions also takes place at t flat terraces with a formation of 2D islands of (most probably ordered) adsorbed structures (mogeneous charge transfer distribution over t terrace), while t movement of monoatomic steps and terraces along t electrode surface still occurs After reaching t potentials of t sharp peaks on t CVs, in all cases ordered adsorbed structures were detected all over t electrode surface and t movement of monoatomic steps and terraces was not so pronounced Hence, in such a case it would be reasonable to assume that tse two processes, t adsorption on t terogeneous and t mogeneous part of t electrode surface, occur simultaneously during t anion adsorption in a certain potential region. In our previous papers, it was swn for t Ag(111) in 0.01 M NaCl 28 and Cu single crystals in 0.1 M NaOH 46 that C diff vs. E curves are very sensitive to t frequency altugh t process of anion adsorption is not controlled by anion diffusion, indicating that even single crystal surfaces cannot be treated as being mogeneous and that, instead of C dl,acpe suld be introduced in t analysis of C diff vs. curves. Accordingly, considering all above mentioned, it could be concluded that t equivalent circuit for t anion adsorption onto real single crystal surfaces suld be represented by t one swn in Fig. 2, with R ad and CPE dl corresponding to t adsorption resistance and constant phase element on t terogeneous part of t surface respectively (practically t inner Helmltz layer, including t outer Helmltz layer on t wle surface) and Fig. 2 Equivalent circuit for t anion adsorption onto real single crystal surfaces: R s solution resistance; R ad charge transfer resistance corresponding to t adsorption of anions on t terogeneous part of t surface; CPE dl constant phase element corresponding to t adsorption of anions on t terogeneous part of t surface; R ad charge transfer resistance corresponding to t adsorption of anions on t mogeneous part of t surface; C ad capacitance corresponding to t adsorption of anions onto mogeneous part of t surface. R ad and C ad corresponding to t adsorption resistance and capacity on t mogeneous part of t surface respectively. By analysis of t equivalent circuit presented in Fig. 2, t following equation was obtained for t C diff (after subtraction of t solution resistance, R s, as in eq. (1)): 1 1 Ylm Cdiff ( Cdl ) ( R ad ) sin 2 C (6) ad ( C ) ( R ) Using t values for C dl =60F cm 2, C ad = 200 Fcm 2, R ad =50 cm 2 and R ad = 5000 cm 2 and varying t value of from 1.00 to 0.80, t diagrams presented in Fig. 3a were obtained. As can be seen, this dependence is very sensitive to t value of (as well as to t otr parameters) in a wle range of frequencies, being characterized by two inflection points (marked in t figure as A and B, as in t case of Fig. 1). In t range of high frequencies (f >10 2 Hz for given equivalent circuit parameters) C diff slightly changes with f down to t inflection point A for all values < 1. Between t inflection points A and B sharp, a non-linear increase of C diff with f occurs, while with furtr decrease of frequency C diff exponentially increases, with this increase being more pronounced at lower values of. T values of C diff at inflection points are defined by t values of C dl (A) and C ad + C dl (B). T position of t inflection points on t frequency axis (not swn in this work) is also sensitive to t values of t resistances R ad and R ad. It suld be noted re that eq. (6) is dimensionally correct, i.e. its dimension is capacitance per unit area. Hence, it could be concluded that if C diff vs. f function is dependent on frequency in t wle ad ad

4 14 V. D. JOVIÆ, Differential Capacity of Bromide Anions Adsorption onto Ag(100), Cm. Biocm. Eng. Q. 23 (1) (2009) range of applied frequencies, is lower than 1 and, accordingly, C dl suld be replaced with CPE in t equivalent circuit. For t results presented in Fig. 3a it was assumed that t adsorption process was under activation control (higr concentration of anions than 1 mm). If t diffusion, represented by t Warburg impedance, was introduced in t equivalent circuit (in series with C ad and R ad ), t following equation for t C diff vs. was obtained. 1 Cdiff ( Cdl ) ( R ad ) sin 2 12 / (7) Cad ( 1 Cad ) 12 / ( C ) C ( R 12 / 1 ) 2 ad ad ad Using t same parameter values as in Fig. 3a for t concentration (c) of 0.1 mm, t C diff vs. f dependences swn in Fig. 3b were obtained. As can be seen, inflection points A and B are defined only for = 1, while for all otr values of practically exponential dependence is obtained in t wle range of frequencies. Hence, if t diffusion pnomena are involved and t charge distribution is not mogeneous, it is practically impossible to determine t values of t adsorption parameters by plotting C diff vs. E curve for a single frequency. In this paper, t dependences of t C diff vs., as well as C diff vs. E for t systems Ag(100)/0.01 M NaBr and Ag(poly)/0.01 M NaBr M NaClO 4, using t above-mentioned approach, were analyzed and discussed. Experimental Fig. 3 (a) C diff vs. f curves calculated using eq. (6): R ad =50 cm 2 ;R ad = 5000 cm 2 ;C dl =60F cm 2 ;C ad = 200 F cm 2. T values of a are marked in t figure. (b) C diff vs. f curves calculated using eq. (7): R ad =50 cm 2 ;R ad = 5000 cm 2 ;C dl =60F cm 2 ;C ad = 200 F cm 2 ;c= 0.1 mm. T values of are marked in t figure. All experiments were carried out in a two-compartment electrocmical cell at t temperature of 25 1 o C. T single crystal and polycrystalline electrodes (Monocrystals Company, d = 0.9 cm) were sealed in an epoxy resin (resin EPON hardener TETA) in such a way that only t disc surfaces were exposed to t solution (0.636 cm 2 ). T counter electrode was a Pt set and was placed parallel to t working electrode surface. T reference electrode was a saturated calomel electrode (SCE) placed in a separate compartment and connected to t working compartment by means of a Luggin capillary. Solutions were made from pure NaBr ( % Aldrich) and NaClO 4 (99.98 % Aldrich) cmicals and extra pure UV water (Smart2PureUV, TKA). All potentials are given vs. SCE. T single and polycrystalline surfaces were prepared by a mechanical polishing procedure followed by cmical polishing in t solution containing NaCN and H 2 O 2 as explained in detail in previous papers. 28,46,47,62 65 Before each experiment, t electrolyte was purged with high purity nitrogen ( %) for 45 min, while a nitrogen atmospre was maintained over t solution during t experiment to prevent contamination with oxygen. T cyclic voltammetry experiments were performed using a universal programmer PAR M-175, a potentiostat PAR M-173 and an X-Y recorder (Houston Instrument 2000R). A potentiostat Reference 600 and a software EIS300 version 5.0 (Gamry Instruments) were used to perform EIS and differential capacity measurements with an amplitude of 10 mv.

5 V. D. JOVIÆ, Differential Capacity of Bromide Anions Adsorption onto Ag(100), Cm. Biocm. Eng. Q. 23 (1) (2009) 15 T differential capacity vs. potential curves for t system Ag(100)/0.01 M NaBr were obtained by t following procedure: Potential of t electrode was changed in steps of 50 mv starting from 1.2 V and finishing at 0.1 V; at each applied potential t values of t real and imaginary components of t impedance were recorded at different frequencies (1000, 700, 400, 200, 100, 70, 40, 20, 10, 7, 4, 2, 1, 0.7, 0.4, 0.2 and 0.1 Hz); tse values were corrected for t solution resistance R s (determined from t high frequency intercept on t Z Re axis of Z Im vs. Z Re diagrams, see Figs. 5 and 9) and converted into C diff. For each potential t C diff vs. curves were plotted. T EIS measurements at three different potentials were performed in t frequency range from 0.01 Hz to 10 khz with 10 points per decade and t same amplitude. Fitting of C diff vs. curves was performed using t commercially available Origin 6.1 program. One of t most powerful and complex components of t Origin program is its nonlinear least squares fitting (NLSF) capability. Its nonlinear regression metd is based on t Levenberg-Marquardt (LM) algorithm and is t most widely used algorithm in nonlinear least squares fitting. T NLSF always reported t reduced chi 2 value, varying from to , as well as t coefficient of determination (R 2 ), varying from to with no weighting function. T curves connecting experimental points presented in Figs. 4a, 5, 7, 8b, 9 and 11 were obtained by using B-spline function (smoothing t curve) defined in t Origin program. In t case of t system Ag(poly)/0.01 M NaBr M NaClO 4, CV and EIS were recorded using t Gamry Reference 600 potentiostat. Instead of using t previously described procedure, t EIS measurements were performed at different potentials (in steps of 50 mv) from 1.0 V to 0.05 V (in t frequency range from 0.1 Hz to 10 khz with t amplitude of 10 mv). For each potential, t C diff vs. curves were plotted and analyzed by t same procedure as for t Ag(100)/0.01 M NaBr system (using Origin program). In order to plot C diff vs. E curves, t C diff values at certain frequencies (0.1, 1, 10 and 100 Hz) were used. It suld be emphasized that t value of t differential capacity was calculated in all cases using t equation C diff corr lm Y Zlm ( ZRe Rs ) ( Zlm ) 2 2 (8) Each experiment was repeated three times and t average values presented in this paper. T variation of t results was 5%. Results System Ag(100)/0.01M NaBr T CV recorded for t Ag(100) in 0.01 M NaBr solution at a sweep rate of 100 mv s 1 is swn in Fig. 4a. As can be seen, t voltammogram is in good agreement with t results of otr autrs, 48,49 being characterized by almost reversible pairs of broad and sharp peaks. Fig. 5 sws t results of t EIS measurements performed for t same system at three constant potentials (frequencies are in Hz). T high frequency ends of t Z Im vs. Z Re diagrams are presented in t inset of t figure. T solution resistance was determined by linear extrapolation to t Fig. 4 (a) CV of Ag(100) in 0.01 M NaBr recorded at a sweep rate of 100 mv s 1. (b) Corresponding C diff vs. E curves recorded at different frequencies (marked in t figure in Hz).

6 16 V. D. JOVIÆ, Differential Capacity of Bromide Anions Adsorption onto Ag(100), Cm. Biocm. Eng. Q. 23 (1) (2009) Fig. 5 Z Im vs. Z Re diagrams recorded at potentials of 1.10 V (), 0.50 V () and 0.30 V () in t frequency range from 0.01 to Hz for t system Ag(100)/0.01 M NaBr. T high frequency ends of Z Im vs. Z Re diagrams, used for determination of R s, are presented in t inset. Frequencies are marked in Hz. Z Re axis, wreby t value R s = 102 cm 2 was obtained for all potentials. As can be seen, none of t impedance diagrams is even close to t shape typical for ideal double layer behavior. Some of t obtained C diff vs. E curves are swn in Fig. 4b. T dispersion of points on t C diff vs. E curves at t frequencies f > 400 Hz was significant and tse results were not used for furtr analysis (at high frequencies t difference between t values of Z Re and R s is very small and, accordingly, t value of Z Re -R s becomes very sensitive to t measured Z Re and extrapolated R s, producing dissipation of points on t C diff vs. E curves). As can be seen, C diff was found to depend on frequency in t wle range of investigated frequencies, as it was t case with Ag(111) in 0.01 M NaCl (Ref. 28, Fig. 5). Using t values of C diff at a constant potential (from t C diff vs. E curves), C diff vs. curves were plotted, some of which have been presented in Fig. 6. In order to obtain t values for C dl, C ad, R ad, R ad and, fitting of t C diff vs. curves was performed using eq. (6), as explained in t experimental section. T experimental points are presented by squares, circles, triangles, etc., while t lines represent t fitting curves. Potentials are marked in t figure for each curve. As can be seen, good fits were obtained with very high values of t coefficient of determination (R 2 ) (see experimental). Identical results were obtained for t rest of t C diff vs. curves, not presented in Fig. 6. T dependences of t parameters C dl, C ad, (C dl + C ad ), R ad, R ad and on potential are swn in Fig. 7. As can be seen in Fig. 7a, only C ad vs. E curve coincide well with t corresponding CV, wreas t value of sharply decreases at t maximum on t C ad vs. E () curve, indicating significant terogeneity of t charge distribution over t electrode surface at potentials more positive than t potential of t sharp peak on t CV (Fig. 4a). Resulting R ad vs. E and R ad vs. E dependences are also different, as swn in Fig. 7b. Fig. 6 C diff vs. curves for different potentials (marked in t figure) obtained from t C diff vs. E curves for t system Ag(100)/0.01 M NaBr. T squares, circles, triangles, etc. represent t experimental points, while t full lines represent t fitted curves obtained by using eq. (6). Fig. 7 Results obtained by fitting t C diff vs. curves for different potentials with eq. (6) for t system Ag(100)/0.01 M NaBr; (a) C ad vs. E (), C dl vs. E (), (C dl +C ad )vs.e() and vs. E () curves. (b) C ad vs. E (), R ad vs. E () and R ad vs. E () curves.

7 V. D. JOVIÆ, Differential Capacity of Bromide Anions Adsorption onto Ag(100), Cm. Biocm. Eng. Q. 23 (1) (2009) 17 T charge recorded under t anodic part of t voltammogram swn in Fig. 4a, as well as t charges obtained by t integration of C dl vs. E, C ad vs. E and (C dl + C ad ) vs. E curves presented in Fig. 7a are given in Table 1. Table 1 Charge recorded under corresponding curves for t system Ag(100)/0.01 M NaBr. Toretical charge for c(2x2) = 96 C cm 2 (assuming complete charge transfer). Curve Charge Anodic part of t CV 105 C cm 2 C ad vs. E 31 C cm 2 C dl vs. E 32 C cm 2 (C dl +C ad ) vs. E 63 C cm 2 System Ag(poly)/0.01 M NaBr M NaClO 4 T CV recorded at t Ag(poly) in 0.01 M NaBr M NaClO 4 solution at a sweep rate of 100 mv s 1 is swn in Fig. 8a, while C diff vs. E curves are swn in Fig. 8b (frequencies are in Hz). As can be seen, t CV is in good agreement with t C diff vs. E curves recorded for low frequencies (< 10 Hz), particularly with t curve recorded for f = 0.1 Hz. T CV (as well as C diff vs. E curves) is characterized with three different regions, double layer region (A) and adsorption regions (B) and (C). At t potentials close to zero, a nucleation loop reflecting formation of 3D layer of AgBr is detected. Fig. 9 sws t EIS measurements performed for this system at four constant potentials. T high frequency ends of t Z Im vs. Z Re diagrams are presented in t inset of t figure. T solution resistance was determined by linear extrapolation to t Z Re axis, wreby t value R s = 8.16 cm 2 was obtained for all potentials. As in a previous case, none of t impedance diagrams is even close to t shape typical for ideal double layer behavior. Some of t C diff vs. curves were plotted in Fig. 10. As can be seen, t shape of tse curves depends on t potential regions, being sensitive to t potential in t regions (A) and (B), and practically insensitive to t potential in t region (C). In order to obtain values for C dl, C ad, R ad, R ad, and, fitting of t C diff vs. curves was performed using eq. (7) since t use of eq. (6) could not give good results (see discussion). T experimental points are presented by squares, circles, triangles, etc., while t lines represent t fitting curves. Potentials are marked in t figure for each Fig. 8 (a) CV of Ag(poly) in 0.01 M NaBr M NaClO 4 recorded at a sweep rate of 100 mv s 1. (b) Corresponding C diff vs. E curves recorded at different frequencies (marked in t figure in Hz). Fig. 9 Z Im vs. Z Re diagrams recorded at different potentials (marked in t figure) in t frequency range from 0.01 to Hz for t system Ag(poly)/0.01 M NaBr M NaClO 4. T high frequency ends of Z Im vs. Z Re diagrams, used for determination of R s, are presented in t inset.

8 18 V. D. JOVIÆ, Differential Capacity of Bromide Anions Adsorption onto Ag(100), Cm. Biocm. Eng. Q. 23 (1) (2009) Fig. 10 C diff vs. curves for different potentials (marked in t figure) obtained from t EIS measurements for t system Ag(poly)/0.01 M NaBr M NaClO 4. T squares, circles, triangles, etc. represent t experimental points, while t full lines represent t fitted curves obtained by using eq. (7). curve. Identical results were obtained for t rest of t C diff vs. curves, not presented in Fig. 10. T dependences of t parameters C dl, C ad, (C dl + C ad ), R ad, R ad, and as a function of potential are swn in Fig. 11. From Fig. 11a it can be seen that t value of C dl is practically negligible, and that (C dl + C ad ) vs. E and C ad vs. E curves are identical, coinciding well with t corresponding CV, wreas t value of is much smaller in comparison with t one detected for t Ag(100) (see Fig. 7a, before t sharp peak on t CV), decreasing at t maximum on t C ad vs. E () curve. Such behavior of indicates significant terogeneity of t charge distribution over t electrode surface in t entire investigated potential range, as suld be expected for t polycrystalline surface. Hence, in t presence of t supporting, non-adsorbing electrolyte, C dl is practically independent of potential. T R ad vs. E and C ad vs. E dependences, swn in Fig. 11b, possess t shapes expected for a serial connection of R ad and C ad. Altugh t process of bromide anions adsorption cannot be diffusion controlled, t high value of t Warburg constant, swn in Fig. 11c, indicates that some diffusion-like pnomenon is involved in t process of anion adsorption. Discussion Fig. 11 Results obtained by fitting t C diff vs. curves for different potentials with eq. (7) for t system Ag(poly)/0.01 M NaBr M NaClO 4 ; (a) C ad vs. E (), C dl vs. E (), (C dl +C ad )vs.e() and vs. E () curves. (b) C ad vs. E () and R ad vs. E (). (c) C ad vs. E () and vs. E () curves. T bromide anions are known as strongly adsorbing species characterized by t formation of ordered adsorbate structures on all investigated single crystal faces It is important to note that, except in our recent papers 28,46 and papers of Kerner et al. 13 and Pajkossy, 12,14,15 in all previous 1 8 and later investigations it was assumed that t double layer behaves as an ideal double layer, neglecting t possibility of terogeneity of t electrode surface. Different techniques were employed in tse investigations: LEED-Auger, 51 in situ STM, 43,45 in situ XAFS, 52 in situ X-ray, 53,54 EIS, differential capacity measurements, trmodynamic analysis chronocoulometric curves and

9 V. D. JOVIÆ, Differential Capacity of Bromide Anions Adsorption onto Ag(100), Cm. Biocm. Eng. Q. 23 (1) (2009) 19 cyclic voltammetry in all papers Most of t experiments were performed in t presence of t non-adsorbing supporting electrolyte (mainly KClO 4 or HClO 4 ) with t addition of a low concentration of bromide anions (up to 10 mm), while in a few of tm one component (KBr, NaBr, HBr) electrolytes were used 43,51,53 respectively, and adsorption of bromide anion was investigated in t absence of t supporting electrolyte. A common feature of t experiments performed in t presence of non-adsorbing supporting electrolyte is t appearance of peaks on CVs for pure supporting electrolyte, corresponding to t specific adsorption of ClO 4 anions to some extent ,55 57 Also, in all papers with differential capacity measurements, t C diff vs. E curves were recorded only at one constant frequency (1 Hz or 18 Hz) at t sweep rate of 10 mv s 1 and 10 mv peak-to-peak amplitude. T. Wandlowski et al. 48 clearly stated that differential capacity vs. potential curves do not provide equilibrium data for Br adsorption onto Ag(100) surface in t low and medium concentration regions, with this comment being relevant to t curves recorded at one frequency only. It suld also be stated re that t differential capacity dispersion, recorded even in a pure supporting electrolyte (0.1 M HClO 4 ), as well as in t presence of adsorbing anions in a very narrow frequency range (12 Hz < f < 80 Hz), has been observed by Hamelin and coworkers on perfect single crystals. 5 All autrs employing trmodynamic analysis assumed that t adsorption of anions from t supporting electrolyte is negligible. It is characteristic that, in all tse cases, t values of t electrosorption valence () were smaller than 1, indicating partial charge transfer during bromide anions adsorption. On t otr hand, in only one paper 53 was t value of = for bromide anions adsorption onto Au(111) obtained by t analysis of G vs. E curves at different anion concentrations. It is characteristic that in some papers employing EIS, 6 8,56,57 Z Im vs. Z Re diagrams were used for fitting experimental results with corresponding equivalent circuit for t diffusion control of anion adsorption. It is important to note re a statement of D. Eberhardt et al. 55 concerning t fitting procedure for such a case: Altugh t resulting equivalent circuit represents very well t surface processes occurring at t interface, it suld be pointed out that t employment of such a complicated combination of elements conduces to ratr high correlation factor between t fitted values, so that t individual elements can be determined only with a fairly large uncertainty. Hence, t generally accepted explanation for t frequency dependence of t interfacial differential capacity ( capacity dispersion ) could be given as: this pnomenon is a consequence of eitr adsorption of organic or certain inorganic species 58,59 or molecules, 60,61 or surface roughness and terogeneity, 9 15,28,46 or specific adsorption of anions. 28,46 50,62,63 It suld be emphasized re that, except in our previous papers, 28,46 t capacity dispersion as a consequence of both anion adsorption and surface terogeneity, has not been considered in t literature. This work considers both cases: adsorption of only one anion (solution of pure NaBr salt) in t absence of supporting electrolyte, and adsorption of t same anion of t same concentration in t presence of non-adsorbing supporting electrolyte (0.1 M NaClO 4 possible competitive adsorption). At t same time, t possibility for diffusion-controlled adsorption of anions is avoided by using concentrations at which t adsorption process is under activation control. System Ag(100)/0.01 M NaBr As can be seen, t CV swn in Fig. 4a is in good agreement with t results of otr autrs T shape of t impedance diagrams swn in Fig. 5 indicates deviation from t ideal double layer behavior Impedance diagram recorded at 0.3 V vs. SCE () is very similar to t one that might correspond to diffusion-controlled adsorption, 7 but an attempt to fit this diagram with t corresponding equation for diffusion-controlled impedance was not possible, and this is one more argument for t statement that such a shape of t impedance diagram could be a consequence of surface terogeneity, as well as specific anion adsorption. T importance of t solution resistance subtraction suld be emphasized re. As can be seen in t inset of Fig. 5, values of Z Re at frequencies lower than 1 khz are very close to t value of R s and if R s is not subtracted, lower values for C diff would be obtained (see eq. (8)). T C diff vs. E curves as a function of frequency are presented in Fig. 4b. T shape of t C diff vs. E curves is practically identical to t shape of CV at low frequencies (lower than 10 Hz). T influence of t frequency on t shape of this dependence is also evidence of t deviation from t ideal double layer behavior, while t similarity between t shape of C diff vs. f curves simulated and presented in Fig. 3a and t experimentally obtained ones (C diff vs. presented in Fig. 6) could only be ascribed to t presence of both specific adsorption of anions and t surface terogeneity. Comparing (C dl + C ad ) vs. E curve (Fig. 7a) with C diff vs. E curves (Fig. 4b), it could be con-

10 20 V. D. JOVIÆ, Differential Capacity of Bromide Anions Adsorption onto Ag(100), Cm. Biocm. Eng. Q. 23 (1) (2009) cluded that C diff vs. E curves sw higr values for t capacity than t one presented in Fig. 7a. Hence, it seems that neitr of t curves presented in Fig. 4b could be considered relevant for t system Ag(100)/0.01 M NaBr. Only after fitting C diff vs. curves recorded at different potentials was t correct differential capacity vs. potential curve, (C dl + C ad ) vs. E obtained. Considering t results presented in Fig. 7a, it could be concluded that t shape of t C ad vs. E curve is much more similar to t shape of CV than t otr two curves. Fig. 7a illustrates that C dl increases with potential up to 0.75 V and tn sharply decreases to t very small values of about 3 5 F cm 2. At t position of a maximum on t C ad vs. E curve, C dl is practically negligible and at potentials more positive than 0.60 V a total capacity (C dl + C ad ) is practically determined by t value of C ad. T value of sharply decreases from about 0.95 at 0.70 V to about 0.45 at 0.10 V. This system has already been analyzed by Wandlowski et al. 48 and it was swn by SXS analysis that with increasing electrode potential, bromide undergoes a phase transition from a lattice gas to an ordered c(2x2) structure, and that this structure is formed at t potential of t sharp peak on both t CV and C diff vs. E curves. Taking into account that, in t case of bromide adsorption, incommensurate adsorbed structures, compressing uniformly with increasing potential, have been detected after t commensurate ordered structures were formed (sharp peak on t CV), such a change of t surface mogeneity, i.e. t change of, could be expected. At t same time, it is important to note that at potentials close to 0.0 V vs. SCE a nucleation loop can be detected (not swn in this figure), indicating t formation of 3D layer (see Fig. 8a) of AgBr (similar to behavior of Ag(111) in 0.1 M NaCl 64 ). It is quite reasonable to assume that t transformation of ordered c(2x2) adsorbed structure into 3D layer suld be accompanied by t change of t charge distribution, i.e. t mogeneity of t electrode surface. Concerning t R ad vs. E and R ad vs. E curves it is seen that t values of R ad and R ad are of t same order of magnitude, varying between 0.1 and 4.5 k cm 2 (Fig. 7b). At t beginning of t adsorption process, t R ad is high, wreas R ad is low, indicating faster adsorption of bromide anions at t monoatomic steps. In t region of sharp peaks on C ad vs. E curve, R ad sharply decreases, while R ad sharply increases, as it could be expected. It is important to note that in this case t shapes of C ad vs. E and R ad vs. E curves are far from being a mirror-image of one anotr. 28 Such a behavior is most likely t consequence of t formation of incommensurate adsorbed structures at potentials more positive than t potential of sharp peak on t CV, i.e. a sharp decrease of surface mogeneity (decrease of ). Finally, considering charges presented in Table 1, it could be concluded that t charge under t anodic part of t CV is higr than that obtained by integration of (C dl + C ad ) vs. E curve. At t same time, charges corresponding to t C ad vs. E and C dl vs. E curves are almost identical. Taking into account that for a formation of ordered c(2x2) structure t toretical charge needed (assuming complete charge transfer) amounts to 96 C cm 2,it appears that for t formation of this structure = 0.32 (31 C cm 2 over 96 C cm 2 ). Hence, this analysis clearly indicates that neitr t charge under t CV, nor that under C diff vs. E curve recorded at a single frequency and C ad vs. E and C dl vs. E curves, can be considered relevant for determining eitr t structure of adsorbed anions or t value of. At t same time, in order to define correct charges corresponding to t adsorption on t terogeneous and t mogeneous part of t surface (as well as correct values of C dl and C ad )itis necessary to know exactly t corresponding surface area (on t atomic level), which is practically impossible using present techniques for t surface characterization. System Ag(poly)/0.01 M NaBr M NaClO 4 In t case of polycrystalline surface, sharp peaks for ordered adsorbed structures cannot be expected, as can be seen on t CV swn in Fig. 8a. Comparing CVs recorded for single crystal surfaces 48 60,65 one can conclude that in t region (B) adsorption on t terogeneous part of t surface takes place, while, most probably, ordered structures are formed in t region (C). T nucleation loop at potential close to 0.0 V vs. SCE is a consequence of t formation of 3D layer of AgBr. 64 A similar conclusion can be drawn from t shape of t C diff vs. E curves, swn in Fig. 8b. T EIS results (Fig. 9) clearly sw deviation from t ideal double layer behavior at all investigated potentials, as well as much lower value of R s in t presence of t supporting electrolyte (inset of Fig. 9) in comparison with t one recorded for t system Ag(100)/0.01 M NaBr. Altugh t solution resistance is much smaller in t presence of 0.1 M NaClO 4, t importance of its subtraction is as significant as in t system Ag(100)/0.01 M NaBr, since at high frequencies Z Re values are also very close to t value of R s and t precision of t R s determination is very important. A very good fit of t experimentally recorded C diff vs. curves (Fig. 10) clearly indicates that for this system eq. (7) must be used. Resulting values

11 V. D. JOVIÆ, Differential Capacity of Bromide Anions Adsorption onto Ag(100), Cm. Biocm. Eng. Q. 23 (1) (2009) 21 of adsorption parameters, presented in Fig. 11 as a function of potential, confirm that in t presence of 0.1 M NaClO 4 different dependences were obtained in comparison with tse recorded in a pure NaBr salt. T (C dl + C ad ) vs. E curve is practically identical to t C ad vs. E curve, while t value of C dl is almost independent of potential and much smaller than expected for t ideal double layer capacity (C dl =20µFcm 2, Fig. 11a). At t same time, as it might be expected, charge distribution over t polycrystalline surface is terogeneous, reaching maximum value of = 0.8 (Fig. 11a). Considering t shapes of C ad vs. E and R ad vs. E curves, one can conclude that ty are more or less a mirror-image of one anotr 28 (Fig. 11b). T most interesting is vs. E dependence. Taking into account that t constant represents t presence of Warburg-like impedance and that t diffusion of anions from t bulk of solution is excluded at such anion concentration, it seems most likely that t diffusion pnomenon is connected with t replacement and exchange of anions in t inner Helmltz plane. Actually, ClO 4 anions are already adsorbed on t electrode surface wn Br anions start to adsorb. Since t adsorption of Br anions is much stronger, ClO 4 anions must be desorbed and replaced with bromides. This process is obviously slow step in t overall reaction, being expressed as t diffusion-like pnomenon, and accordingly eq. (7) must be used to fit experimentally recorded C diff vs. curves (Fig. 10). According to t results presented in Fig. 11c, this effect is more pronounced in t region of ordered (more dense) adsorbed structure formation (potential region C), wre all ClO 4 anions must be removed and replaced with bromides. It is most likely that removed ClO 4 anions again adsorb on t bromide layer, as it was t case in UPD of Cd onto Cu(111) 66 and Cd onto Ag(111) in t presence of chloride anions. 67 A similar effect has recently been recognized by T. Pajkossy and D. M. Kolb 68 in t double layer region of Pt(111) and Ir(111) in t presence of only one anion (much simpler case) and ty attributed t frequency dependence of t interfacial capacitance to t relatively slow exchange of anions between t outer and inner Helmltz planes. At this moment a convincing explanation for t observed pnomenon is missing and it will be t subject of furtr investigations. Conclusion For t determination of t adsorption parameters, a new equivalent circuit and corresponding equation for analyzing anion adsorption, based on a different definition of t constant phase element, has been developed and used in this work. It is swn that such analysis can successfully be applied in t case of bromide anions adsorption in two systems: Ag(100)/0.01 M NaBr and Ag(poly)/0.01 M NaBr M NaClO 4. Homogeneity of t charge distribution over t electrode surface was found to change as a consequence of t adsorption of bromide anions in both cases. It was swn that in t presence of t supporting electrolyte (0.1 M NaClO 4 ) Warburg impedance must be introduced in t equivalent circuit (and corresponding equation for C diff ) in order to fit experimentally recorded C diff vs. curves. This pnomenon was explained by t slow step of replacement of already adsorbed perchlorate anions with bromide anions. Symbols C capacitance, F cm 2 c concentration of adsorbing anions, M C ad adsorption capacitance, µf cm 2 C diff differential capacitance, µf cm 2 C dl double layer capacitance, µf cm 2 CPE constant phase element CPE dl constant phase element of t terogeneous part of t surface D diffusion coefficient of adsorbing anions, cm 2 s 1 f frequency, Hz R resistance, cm 2 R ad adsorption resistance, cm 2 R ad adsorption resistance on t terogeneous part of t surface, cm 2 R ad adsorption resistance on t mogeneous part of t surface, cm 2 R s solution resistance, cm 2 Y Im imaginary component of admittance, 1 cm 2 Y 0 constant, 1 cm 2 s Z Re real component of impedance, cm 2 Z Im imaginary component of impedance, cm 2 Z CPE impedance of t CPE factor of t charge distribution mogeneity Warburg coefficient, cm 2 s 1/2 angular frequency, s 1 References 1. Reeves, R., T Double Layer in t Absence of Specific Adsorption, in Bockris,J.O M.Conway,B.E., and Yeager, E. (Eds.), Comprensive Treatise of Electrocmistry, Vol. 1, Plenum, New York and London, 1980, pp Valette, G., Hamelin, A., J. Electroanal. Cm. 45 (1973) Gouy, G., J. Phys. 9 (1910) Gouy, G., C. R. Acad. Sci. 149 (1910) 654.

12 22 V. D. JOVIÆ, Differential Capacity of Bromide Anions Adsorption onto Ag(100), Cm. Biocm. Eng. Q. 23 (1) (2009) 5. Hamelin, A., Double-layer properties at sp and sd metal single-crystal electrodes, in Conway, B. E., White, R., Bockris, J. O M. (Eds.), Modern Aspects of Electrocmistry, Vol. 16, Plenum, New York, 1985, pp El-Aziz, A. M., Kibler, L. A., Kolb, D. M., Electrocm. Comm. 4 (2002) Sluyters-Rehbach, M., Sluyters, J., Sine Wave Metds in t Study of Electrode Processes, in Bard, A. (Ed.), Electroanalytical Cmistry, Vol. 4, Marcel Dekker, New York, 1970, pp Kerner, Z., Pajkossy, T., Kibler, L. A., Kolb, D. M., Electrocm. Comm. 4 (2002) Sluyters-Rehbach, M., Pure & Appl. Cm. 66 (1994) Nyikos, L., Pajkossy, T., Electrochim. Acta 35 (1990) Mandelbrot, B. B., T Fractal Geometry of Nature, Freeman, San Francisco, Pajkossy, T., Solid State Ionics 94 (1997) Kerner, Z., Pajkossy, T., Electrochim. Acta 46 (2000) Pajkossy, T., Heterogeneous Cm. Rev. 2 (1995) Pajkossy, T., J. Electroanal. Cm. 364 (1994) Moto, A. J., Sadkowski, A., Neves, R. S., J. Electroanal. Cm. 430 (1997) Zoltowski, P., J. Electroanal. Cm. 443 (1998) Sadkowski, A., Moto, A. J., Neves, R. S., J. Electroanal. Cm. 445 (1998) Láng, G., Heusler, K. E., J. Electroanal. Cm. 457 (1998) Zoltowski, P., J. Electroanal. Cm. 481 (2000) Sadkowski, A., J. Electroanal. Cm. 481 (2000) Láng, G., Heusler, K. E., J. Electroanal. Cm. 481 (2000) Sadkowski, A., J. Electroanal. Cm. 481 (2000) Jorcin, J.-B., Orazem, M. E., Pébère, N., Tribollet, B., Electrochim. Acta 51 (2006) Kerner, Z., Pajkossy, T., J. Electroanal. Cm. 448 (1998) Kim, C.-H., Pyun, S.-I., Kim, J. H., Electrochim. Acta 48 (2003) Orazem, M. E., Shukla, P., Membrino, M. A., Electrochim. Acta 47 (2002) Joviæ, V. D., Joviæ, B. M., J. Electroanal. Cm. 541 (2003) Macdonald, J. R., Impedance Spectroscopy Emphasizing Solid Materials and Systems, Wiley, New York, Chicster, Brisbane, Toronto, Singapore, Brug, G. J., Van Eeden, A. L. G., Sluyters-Rehbach, M., Sluyters, J., J. Electroanal. Cm. 176 (1984) Hsu, C. H., Mansfeld, F., Corrosion 57 (2001) Van Meirhaeg, R. L., Dutiot, E. C., Cardon, F., Gomes, W. P., Electrochim. Acta 20 (1975) Morrison, S. R., Electrocmistry at Semiconductor and Oxidized Metal Electrodes, Plenum Press, New York, Moffat, T. P., Scanning tunneling microscopy studies of metal electrodes, in Bard, A. J., Rubinstein, I. (Eds.), Electroanalytical Cmistry: a Series of Advances, Vol. 21, Marcel Dekker Inc., New York, Basel, 1999, pp Schweizer, M., Kolb, D. M., Surf. Sci. 544 (2003) Garcia, S. G., Salinas, D. R., Mayer, C. E., Lorenz, W. J., Staikov, G., Electrochim. Acta 48 (2003) Kunze, J., Streblow, H.-H., Staikov, G., Electrocm. Comm. 6 (2004) Wilms, M., Broekmann, P., Kruft, M., Park, Z., Stuhlmann, C., Wandelt, K., Surf. Sci (1998) Wan, L., Suzuki, T., Sashikata, K., Okada, J., Inutai, J., Itaya, K., J. Electroanal. Cm. 484 (2000) Maurice, V., Streblow, H.-H., Marcus, P., Surf. Sci. 458 (2000) Kunze, J., Maurice, V., Klein, L. H., Streblow, H.-H., Marcus, P., J. Phys. Cm. B 105 (2001) Streblow, H.-H., Maurice, V., Marcus, P., Electrochim. Acta 46 (2001) Broekmann, P., Anastesescu, M., Spaenig, A., Lisowski, W., Wandelt, K., J. Electroanal. Cm. 500 (2001) Li, W. H., Wang, Y., Ye, J. H., Li, S. F. Y., J. Phys. Cm. B 105 (2001) Cuesta, A., Kolb, D. M., Surf. Sci. 465 (2000) Joviæ, V. D., Joviæ, B. M., J. Electroanal. Cm. 541 (2003) Joviæeviæ, J. N., Joviæ, V. D., Despiæ, A. R., Electrochim. Acta 29 (1984) Wandlowski, Th., Wang, J. X., Ocko, B. M., J. Electroanal. Cm. 500 (2001) Hamad, I. A., Wandlowski, T., Brown, G., Rikvold, P. A., J. Electroanal. Cm (2003) Beltramo, G., Santos, E., J. Electroanal. Cm. 556 (2003) Reniers, F., Fairbrotr, D.-H., Wu, S., Lipkowski, J., Surf. Sci (1999) Endo, O., Matsumura, D., Kohdate, K., Kiguchi, M., Yokoyama, T., Ohta, T., J. Electroanal. Cm. 494 (2000) Magnussen, O., Ocko, B. M., Adiæ, R. R., Wang, J. X., Phys. Rev. B 51 (1995) Magnussen, O., Ocko, B. M., Wang, J. X., Adiæ, R. R., J. Phys. Cm. B 100 (1996) Eberhardt, D., Santos, E., Schmickler, W., J. Electroanal. Cm. 419 (1996) Pajkossy, T., Wandlowski, T., Kolb, D. M., J. Electroanal. Cm. 414 (1996) Kerner, Z., Pajkossy, T., Electrochim. Acta 47 (2002) Lorenz, W., Möckel, F., Z. Elektrocm. 60 (1994) Armstrong, R. D., Rice, W. C., Thirsk, H. R., J. Electroanal. Cm. 16 (1968) Van Houng, C. N., Hinnen, C., Dalbera, J. P., Parsons, R., J. Electroanal. Cm. 125 (1981) Lipkowski, J., Van Houng, C. N., Hinnen, C., Parsons, R., Cvalet, J., J. Electroanal. Cm. 143 (1983) Joviæ, V. D., Joviæ, B. M., Parsons, R., J. Electroanal. Cm. 290 (1990) Joviæ, V. D., Parsons, R., Joviæ, B. M., J. Electroanal. Cm. 339 (1992) Joviæ, B. M., Joviæ, V. D., Draiæ, D. M., J. Electroanal. Cm. 399 (1995) Joviæ, B. M., Draiæ, D. M., Joviæ, V. D., J. Serb. Cm. Soc. 64 (1999) Stulmann, C., Park, Z., Bach, C., Wandelt, K., Electrochim. Acta 44 (1998) Joviæ, V. D., Joviæ, B. M., Electrochim. Acta 47 (2002) Pajkossy, T., Kolb, D. M., Electrocm. Comm. 9 (2007) 1171.