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Cyclic Square Wave Voltammetry of Surface-Confined Quasireversible Electron Transfer Reactions Megan A. Mann and Lawrence A. Bottomley* School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States

Downloaded by NEW YORK UNIV on September 4, 2015 | http://pubs.acs.org Publication Date (Web): August 21, 2015 | doi: 10.1021/acs.langmuir.5b01684

S Supporting Information *

ABSTRACT: The theory for cyclic square wave voltammetry of surface-confined quasireversible electrode reactions is presented and experimentally verified. Theoretical voltammograms were calculated following systematic variation of empirical parameters to assess their impact on the shape of the voltammogram. From the trends obtained, diagnostic criteria for this mechanism were deduced. These criteria were experimentally confirmed using two well-established surface-confined analytes. When properly applied, these criteria will enable non-experts in voltammetry to assign the electrode reaction mechanism and accurately measure electrode reaction kinetics.

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INTRODUCTION Redox active adsorbates have been studied for over five decades. The impetus for these studies included: (1) gaining insight into monolayer formation and the associated isotherm for its formation, (2) exploring the reason(s) behind preferential accumulation of the adsorbate on the surface of one electrode material over another, (3) pre-concentration of analyte on the electrode for quantitative purposes, and (4) measuring kinetic parameters associated with the surfaceconfined species.1,2 Voltammetric methods have been employed to characterize this family of electrode reactions.3−6 Recent interest has focused on the application of pulse voltammetric techniques for characterizing redox active adsorbates.7−11 The reason for moving to the pulse techniques is straightforward. The diagnostic criteria put forth originally by Randles,12 Ševčik,13 Nicholson and Shain14 for identifying electrode reactions was developed when analog instrumentation was commonplace. Current instrumentation is digital; cyclic voltammograms acquired with digital instruments are actually cyclic staircase voltammograms. The applicability of theory developed for analog instruments to data acquired with digital instruments depends upon when the current is sampled during the potential pulse.15 The “correct” sampling point depends upon the electrode reaction mechanism.16,17 This leads to the experimental conundrum of what sampling point to select if one does not know the electrode reaction mechanism. Square wave voltammetry (SWV) has been shown to be particularly useful in identifying electrode reaction mechanisms in general18,19 and especially for kinetically controlled surfaceconfined redox active analytes.19−25 Even though a strong theoretical basis for using SWV to identify the electrode © 2015 American Chemical Society

reaction exists, the application of this theory has been limited to a small number of electrochemists. Our goal is to broaden the use of SWV for mechanistic determinations by electrochemists as well as non-experts in electrochemistry who make occasional use of voltammetry. Cyclic square wave voltammetry (CSWV) is a pulse technique originally described 3 decades ago26,27 that combines the virtues of SWV and cyclic voltammetry (CV).28,29 The merits of CSWV include lower limits of detection (in comparison to CV) and a more straightforward means for determining the formal potential and kinetic parameters (in comparison to SWV). In our opinion, the latter feature will attract more non-experts into using square wave voltammetry as a mechanistic tool. It should be noted that, in some cases, the results obtained for CSWV are equivalent to those obtained by conventional SWV followed by reverse scan SWV. In others (e.g., for chemically coupled electron transfer reactions), they are not. Our current effort is focused on identifying the specific mechanisms where CSWV provides a more straightforward means for determining the mechanism and associated kinetic parameters without having to analyze the individual (and net) currents for each potential step. In previously published work, we identified diagnostic criteria for diffusion-controlled reversible and quasireversible mechanisms using CSWV.28,29 The goals of this work are to develop diagnostic criteria for surface-confined electron transfer processes, to verify experimentally these criteria in determining Received: May 8, 2015 Revised: July 31, 2015 Published: August 21, 2015 9511

DOI: 10.1021/acs.langmuir.5b01684 Langmuir 2015, 31, 9511−9520

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standard heterogeneous electron transfer rate constant in units of s −1 . The current response was converted into a dimensionless current to remove the electrode area and the surface excess magnitude using the equation

kinetic parameters for a strongly adsorbed redox active analyte, and to compare the criteria to that for a non-surface confined quasireversible reaction. For this mechanism, CSWV enables accurate measures of E0 and k0 and the electron transfer coefficient, α, compared to SWV.


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i(t ) =

EXPERIMENTAL SECTION

Two analytes were used to validate the diagnostic criteria presented below: (15-mercapto-N-pentadecyl)ferrocenecarboxamide, hereafter abbreviated as (Fc)CONH(CH2)15SH, and the disodium salt of anthraquinone disulfonic acid, hereafter abbreviated as AQDS. This compound was used as received from Sigma-Aldrich (St. Louis, MO). A monolayer of (Fc)CONH(CH2)15SH was assembled onto a gold electrode (area = 0.20 cm2) via a previously established method.30−33 A Pt mesh served as the counter electrode; the reference electrode was Ag/AgClO4 located behind a frit filled with 0.1 M NaClO4. The electrolyte used for all CV and CSWV experiments was 0.1 M HClO4. A monolayer of AQDS was assembled onto the surface of a hanging mercury drop connected to a PerkinElmer 303A SMDE (Waltham, MA) by exposing a fresh drop (area = 0.027 cm2) to 5 μM AQDS in 0.1 M acetate buffer (pH 4.5). A Pt wire served as the counter electrode, and the reference electrode was Ag/AgCl located behind a frit filled with a saturated KCl solution. A new mercury drop was used for each scan; the potential was held at 150 mV (versus Ag/AgCl) for 30 s before each scan. CSWV data were acquired using a Pine Instruments (Durham, NC) WaveNano potentiostat. No solution resistance compensation was used because this capability is not an option on the WaveNano potentiostat. Pine Instruments software program Aftermath was used to set experimental parameters, record voltammograms, and analyze the data. Oxygen was removed from all solutions by sparging with N2.

(k τ − = 0

Ψm

k0τ 2L

m−1

)

∑i = 1 Ψi e−αφ − 1+

k0τ −αφ e 2L

+

k0τ 2L

m−1

∑i = 1 Ψie(1 − α)φ

k0τ (1 − α)φ e 2L

(4)

where τ is the period, L is the number subintervals on the step, and Ψm is the dimensionless current for each time increment with the serial number m. A detailed explanation of this derivation is provided in the Supporting Information. Computation of theoretical voltammograms was performed in MATLAB. The recursive calculation of current on each step for every step in the voltammogram was performed by systematic variation over the following intervals: 1 ms ≤ τ ≤ 5 s, 10 ≤ ESW ≤ 90 mV, 1 ≤ δE ≤ 25 mV, 0 ≤ Eλ ≤ 1000 mV, and L = 20 over each period. Period limits were set in consideration of typical potentiostat rise times, commonly encountered solution resistances, and electrode double-layer capacitances, as well as the time duration required per scan. Amplitude limits were set in accordance with the range typically used in SWV. Increment limits were set in consideration of the number of points to define the peak. Switching potential limits were set in consideration of the potential windows normally encountered in non-aqueous electrolytes. Specific values of each parameter are given in the Supporting Information and in the caption of many figures. The predicted difference current, ΔΨ, is determined by subtracting Ψforward pulse from Ψreverse pulse and is plotted versus the average of the potentials (Estep) at which both currents were calculated. Throughout this work, the forward difference current, ΔΨf, will denote the difference currents acquired over the interval Einitial to the switching potential Eλ, and the difference current, ΔΨr, will denote difference currents acquired over the reverse potential sweep from Eλ to the final potential, Efinal. To capture the effect of period as it relates to current, ΔΨs is used throughout this work where

RESULTS AND DISCUSSION Theory. The CSWV waveform used herein is the one found on most commercial instruments with the capability of performing CSWV (e.g., Pine Instruments). It is characterized by the following empirical parameters: period (τ), increment (δE), switching potential (Eλ), and amplitude (ESW). Readers unfamiliar with this waveform are referred to Figure 1 in our previous publication for full details.29 For experimentalists using instruments that describe the voltammogram in terms of frequency, period is inversely related to frequency. The generalized reaction for a surface-confined redox active species is (1)

The surface concentrations of the oxidized and reduced forms are potential- and time-dependent. Underlying assumptions in this work are that no interactions exist between redox moieties on the electrode surface and that the electroactive molecules may be present as a either single or multiple monolayers so long as no concentration gradient exists within the layer(s) on the time scale of the voltammetric experiment.34 Derivation of an equation for predicting current as a function of potential and time begins by applying appropriate boundary conditions for this electrode reaction. The resultant expressions for surface concentrations were inserted into the Butler−Volmer relationship i = nFAk0[ΓOxe−αϕ − ΓRede(1 − α)ϕ]

(3)

where Γ* is the total surface concentration of Ox(ads) and Red(ads) and A is the electrode area. The Nicholson−Olmstead method was used to replace the integrals with summations expressing the dimensionless current equation numerically.35 The final equation is

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Ox (ads) + ne− ⇌ Red(ads)

nFA Γ* Ψ(t ) τ

ΔΨ s = ΔΨ/τ =

i(t ) nFA Γ*

(5)

The physical meaning of ΔΨs is the normalized real current emanating from the electron transfer. The plotting convention used herein treats reduction currents as positive values and oxidative currents as negative values. Consequently, the net currents on the cathodic sweep, ΔΨsf , are positive currents, and the net currents on the anodic sweep, ΔΨsr, are negative currents. Peak currents are designated as ΔΨsp,f and ΔΨsp,r. The peak ratio is calculated as ΔΨsp,r/ΔΨsp,f. Similarly, Ep,f and Ep,r are used to represent peak potentials, while peak separation can be calculated by ΔEp = Ep,r − Ep,f. Peak widths (W1/2,f and W1/2,r) are measured at half peak currents.

(2)

where ϕ = nF/RT(Eapplied − E ), α is the transfer coefficient, ΓOx and ΓRed represent the surface excess at equilibrium for the oxidized and reduced forms, respectively, n is the number of electrons transferred, F is the Faraday constant, and k0 is the 0

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with period can be used to discern a diffusional from a surfaceconfined quasireversible mechanism. Effect of Increment, δE. The effect of increment on the shape and magnitude of the voltammogram is shown in Figure 2. For comparison to CV, the effective potential sweep rate is


In the following sections, the impact of each empirical parameter on the shape of the voltammogram is examined and compared to the diffusional quasireversible mechanism for the specific case where n = 1. Then, a protocol for discerning this mechanism from empirical data is provided followed by experimental validation of this protocol using two redox active, surface-confined analytes. Note that the theoretical trends delineated below are applicable to both planar and spherical electrodes.34 Also note that trends for the forward sweep are identical to those one would obtain using conventional SWV.19−25 Effect of Period, τ. A series of voltammograms in which the period is varied is shown in Figure 1. Determination of the

Figure 2. Effect of increment on the shape of the voltammogram when log k0 = −1, α = 0.5, period = 50 ms, amplitude = 50 mV, and increment = 1 mV (red), 5 mV (orange), 10 mV (gold), 15 mV (green), and 20 mV (cyan).

increment divided by period. Thus, an increase in increment is equivalent to increasing the potential sweep rate. However, the number of points defining the voltammogram decreases as the increment increases. As a consequence, the peaks become less rounded and more jagged. As increment increases, ΔΨsp and W1/2 increase and Ep,f and Ep,r shift away from E0. As a result, s ΔEp increases with increment. ΔΨratio remains at unity throughout the variation of increment. As reported in the previous section, peak currents, potentials, and widths depend upon the period. The variation of both period and increment and the resultant peak currents, peak ratios, peak potentials, peak separations, and peak widths are shown in Figures S-1−S3. Several key differences in the effect of increment on voltammograms for the diffusional and surface-confined cases can be identified. Peak currents slightly increase in a curvilinear fashion for the diffusional case, whereas they increase in a linear fashion for the surface-confined case. Peak ratios decrease with increasing increment for the diffusional mechanism, while peak ratios are invariant with increasing increment for the surfaceconfined case. Although peak potentials shift away from the formal potential for both mechanisms, the magnitude of the shift differs for each mechanism. The shift is also dependent upon period (compare Figures S-2 in this and our previous work29). Thus, the dependence of peak currents and potentials on increment can be used to distinguish the diffusional and surface-confined mechanisms. It is interesting to note that the trends observed for period are the inverse of those observed for increment. For example, ΔΨsp values decrease with period but increase with increment. Similarly, while Ep values shift toward E0 with period, they shift away from E0 with increment. Effect of Switching Potential, Eλ. The effect of switching potential on voltammograms for the surface-confined mechanism is shown in Figure S-4. As the switching potential is

Figure 1. Effect of the period on the shape of the voltammogram when log k0 = −1, α = 0.5, amplitude = 50 mV, increment = 10 mV, and period = 10 ms (red), 20 ms (orange), 50 ms (gold), 100 ms (green), 200 ms (cyan), 500 ms (blue), 1000 ms (purple). The inset presents peak potentials versus log period for the voltammograms depicted in this figure (black squares represent Ep,f, and red circles represent Ep,r).

mechanism using CV requires variation in the potential sweep rate. In SWV and CSWV, the effective potential sweep rate is increment divided by period. Thus, increasing period is equivalent to decreasing the potential sweep rate. As the period increases, Ep,f and Ep,r shift toward the formal potential (see inset of Figure 1) and ΔΨsp decreases linearly with period−1, while the peak ratio remains constant at unity. ΔEp approaches zero as the period is elongated. Peak widths remain constant, increase to a maximum, and then decrease as the period is increased. Comparison of the trends for ΔΨsp and Ep as a function of the period reveals several differences between the surfaceconfined and diffusional mechanisms. Trends in peak potentials with period are similar between these two mechanisms, whereas peak currents and peak ratios differ. As period increases, ΔΨsp decreases linearly with period−1. For the diffusional case, ΔΨ+p decreases linearly with period−1/2 (where ΔΨ+ = ΔΨ/τ1/2). Peak ratios increase to unity as period is increased for the diffusional case but remain constant at unity for the surfaceconfined case. Thus, trends in peak currents and peak ratios 9513


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magnitude of peak potential shift can be used for the identification of surface-confined mechanisms. In some instances, when amplitude is varied, a different trend emerges. As shown in Figure 3b, ΔΨsp,f and ΔΨsp,r increase with amplitude, reach a maximum, then decrease, and split into two separate peaks. This phenomenon is unique to a quasireversible surface-confined mechanism.19 Amplitude, k0, and period values determine when the peak split will occur. Splitting is observed at small k0 values when using long periods and high amplitudes. It is also observed at large k0 values when using short periods and low amplitudes, but the peak currents under these conditions are quite low (see section below on effects of k0). Thus, peak splitting is an additional indicator of a surfaceconfined mechanism. Effect of k0. The impact of heterogeneous kinetics on the shape of the voltammogram depends upon the magnitude of k0 relative to τ. Previous investigators have treated the effects of SWV frequency and k0 (or period and k0) as a single dimensionless kinetic parameter.19,20,22,24,25 We have elected to treat these quantities individually to assist non-specialists in interpreting the voltammetric trends and assigning the proper mechanism. In practice, one varies τ and determines k0 from changes in the shape of the voltammograms. The kinetic parameter k0 is intrinsic to the analyte undergoing an electron transfer reaction at a particular electrode immersed in a specific electrolyte. Therefore, varying k0 at a fixed value of τ is, in effect, comparing responses for different analytes and/or different electrode/electrolyte combinations. Figure 4 depicts a set of calculated voltammograms for which period is held constant at 50 ms and log k0 is varied from −6 to


shifted positively, peak currents and potentials remain constant until the switching potential occurs before the current can return to the baseline. Peak ratio decreases at this point, and peak separation is slightly decreased. Similarly, peak widths are unaffected until the switching potential occurs before the current can to return to baseline. At this point, peak widths decrease. Further inspection of the effect of switching potential and period on voltammograms is shown in Figures S-5−S-7. The effect of switching potential on the voltammogram for the surface-confined mechanism is very similar to that of the diffusional case. Peak currents and peak potentials are only affected when the switching potential occurs prior to the current to baseline. Thus, the variation of switching potential cannot be used to distinguish between these two electrode reaction mechanisms. Effect of Amplitude, ESW. Figure 3a presents the effect of amplitude on the shape of the voltammogram for the surface-

Figure 3. Effect of amplitude on the shape of the voltammogram when α = 0.5, increment = 10 mV, and amplitude varied from 10 mV (red) to 90 mV (gray) in 10 mV steps: (a) log k0 = −1 and period = 50 ms and (b) log k0 = 1 and period = 200 ms.

confined mechanism. Mirčeski et al.19 have established that the voltammetric response depends upon the product nESW. This section presents a discussion of the effect of amplitude for n = 1. Readers encountering systems with n > 1 should refer to the text by Mirčeski et al. As amplitude increases, ΔΨsp,f and ΔΨsp,r increase curvilinearly and both Ep,f and Ep,r shift toward E0. The peak ratio remains constant at unity, and ΔEp decreases as amplitude increases. W1/2 increases with amplitude. The effect of both period and amplitude on waveform parameters can be found in Figures S-8−S-10. Systematic variation of amplitude leads to several similar trends for the surface-confined and diffusional mechanisms. Peak potentials shift toward E0, while ΔEp decreases for both cases. However, the magnitude of the shift differs for each mechanism (compare Figure S-9 in this work to Figure S-6 in our previous work29). Peak currents and peak widths increase with amplitude for both cases. However, peak ratios for the surface-confined case remain constant at unity, while peak ratios increase with amplitude for the diffusional case. Thus, examining the effect of amplitude on the peak ratio and the

Figure 4. Effect of k0 on the shape of the voltammogram when α = 0.5, amplitude = 50 mV, increment = 10 mV, period = 50 ms, and log k0 = −6 (red), −5 (orange), −4 (gold), −3 (green), −2 (cyan), −1 (blue), 0 (purple), 1 (magenta), and 2 (black).

2 in decades. These limits encompass the range historically associated with an irreversible and reversible process. Figure 5 presents the dependence of peak potentials upon log k0. Peak potentials shift toward E0 as log k0 increases linearly from −6 to 0 and then curvilinearly from 0 to 1. Peak potentials equal E0 over the range 1 ≤ log k0 ≤ 1.7. At log k0 > 1.7, the peak in each scan direction splits into two. Consequently, peak potential separations decrease with increasing log k0, reaching zero at log k0 = 1. After the peak splitting occurs, ΔEp for each pair remains at zero. 9514


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is in sharp contrast with CV. In CV using analog instrumentation, a peak is observed regardless of k0 and its magnitude is proportional to the potential sweep rate. However, in cyclic staircase voltammetry (i.e., CV with digital instrumentation), the peak magnitude markedly depends upon when the current is sampled on the step. Figure 6b presents the dependence of peak widths on log k0. Peak widths are equal to 127 mV and remain constant over the range −6 < log k0 < −1. They increase to 133 mV as log k0 increases from −1 to 0 and then decrease to 101 mV at log k0 = 1.3. At log k0 > 1.3, the peak widths rise as a result of peak splitting. Several differences in the effect of k0 on the voltammogram for quasireversible diffusional and surface-confined cases can be identified. Peak potentials and peak separation are dependent upon log k0 for both mechanisms but with slightly differing slopes. Quasireversible diffusional processes have leak-over peaks29 at small values of k0, whereas surface-confined processes never have leak-over peaks. For diffusional processes, peak currents increase with log k0 in a sigmoidal fashion, whereas peak currents reach a maximum and then fall with a surface-confined process. Peak splitting is only observed with surface-confined processes; the point at which peak splitting occurs depends upon period, amplitude, and k0. Peak widths decrease with increasing log k0 in a sigmoidal fashion for diffusional processes, but both increase and decrease with increasing log k0 for surface-confined processes. Thus, log k0 affects the shape and magnitude of the voltammogram differently for diffusional and surface-confined processes. The range in log k0 accessible with CSWV is limited by the range in τ and whether the experimenter is using peak separation or peak current maxima. Effect of the Transfer Coefficient. The transfer coefficient, α, describes the symmetry of the overlap of the two potential wells of the reaction coordinate for electron transfer. The transfer coefficient is a property that is inherent to a particular electron transfer process. Hence, this value cannot be varied by an experimenter, but CSWV experiments can be executed to identify the transfer coefficient for a given reaction. An α value of 0.5 denotes a perfectly symmetrical overlap. Because α ranges from 0 to 1, values other than 0.5 indicate that the overlap of the potential energy−reaction coordinate curves leans toward one well or the other. Figure 7 presents the effect of α on the shape of a voltammogram. As α increases, ΔΨsp,f increases, while ΔΨsp,r decreases. ΔΨsratio decreases with increasing α. Ep,f and Ep,r shift positively with increasing α but with differing magnitudes. W1/2,f decreases with increasing α; W1/2,r increases with α. Thus, α strongly affects the shape and magnitude of the voltammogram. Figure 8 presents the combined effect of α and period on the shape of the voltammogram. For α = 0.5 (Figure 8c), peak potentials are symmetrically displaced from the formal potential; peak currents are of equal and opposite magnitude, while W1/2,f = W1/2,r. For α < 0.5 (panels a and b of Figure 8), peak potentials are shifted negatively compared to values for α = 0.5. ΔΨsp,f values are smaller for α < 0.5 compared to α = 0.5; ΔΨsp,r values are greater than values expected for α = 0.5. W1/2,f are greater than the values obtained for α = 0.5, and W1/2,r values are smaller than the values obtained for α = 0.5. For α > 0.5 (panels d and e of Figure 8), peak potentials are shifted positively compared to values for α = 0.5. ΔΨsp,f values are larger for α < 0.5 compared to α = 0.5; ΔΨsp,r values are smaller

Figure 5. Effect of k0 on Ep,f and Ep,r and voltammogram shape when amplitude = 50 mV, increment = 10 mV, period = 50 ms, α = 0.5, and log k0 = from −6 to 2. The current magnitudes for voltammograms depicted on top of the plot are normalized for display purposes. They are not indicative of the variation of current with k0.

Figure 6. Effect of k0 on (a) ΔΨsp,f (red) and ΔΨsp,r (orange), and (b) W1/2,f (red) and W1/2,r (orange) when amplitude = 50 mV, increment = 10 mV, period = 50 ms, α = 0.5, and log k0 = from −6 to 2.

Figure 6a presents the dependence of peak currents upon log k0. Peak currents remain unchanged up to log k0 equal to −0.7. At higher values of log k0, peak currents increase to a maximum at log k0 = 1.2. After the maximum, the peak current decreases until it splits into two (vide supra) and then falls rapidly into the baseline. As the rate of electron transfer increases, the time required to convert Oxads to Redads at a given potential decreases. When the period is longer than the time required for this conversion, peak currents will approach zero. Previous reports have established the quasireversible maximum in SWV as an indicator of a surface-confined process.19,36−38 This trend 9515


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Figure 7. Effect of α on the shape of the voltammogram when log k0 = −1, period = 50 ms, amplitude = 50 mV, increment = 10 mV, and α is 0.9 (gray), 0.7 (purple), 0.5 (cyan), and 0.3 (gold).

Figure 9. Plot of (a) peak potential versus log period and (b) Ep,f versus Ep,r as a function of α when log k0 = −1, amplitude = 50 mV, increment = 10 mV, and α is 0.3 (gold), 0.4 (green), 0.5 (cyan), 0.6 (blue), and 0.7 (purple).

increased. Similarly, peak potential separation depends upon both α and period (see Figure S-12). Note that the trace for α = 0.4 in Figure S-12 is identical to that for α = 0.6. The traces for α = 0.3 and 0.7, 0.2 and 0.8, and 0.1 and 0.9 overlap as well. We have previously shown that the value of α for a diffusional quasireversible electrode reaction can be determined from systematic variation of period.29 A plot of Ep,f versus Ep,r constructed from measurements made over a range in period (while keeping amplitude, increment, and switching potential constant) provides a straightforward means for calculating α. This method is also applicable to the surface-confined reaction. Figure 9b illustrates that a linear relationship is obtained between Ep,f versus Ep,r (when ΔEp ≥ 100 mV) and the marked dependence of the slope upon α. Thus, the slope of the line can be used to calculate α. α slope of Ep,f versus Ep,r = (6) 1−α For all of the voltammograms depicted in Figure 8, ΔΨsp decreases with increasing period. Figure S-13 shows that ΔΨsp is linearly related to period−1; the slope of this trace depends upon α. This contrasts with the diffusional quasireversible mechanism where ΔΨ+p decreases with the square root of period. Thus, plots of peak currents versus period−1 and period1/2 are diagnostic indicators of each reaction mechanism and the value of α. Diagnostic Criteria for Identifying a Surface-Confined Reaction. The peak currents, potentials, and shapes of cyclic square wave voltammograms have been shown to be a complex function of α, k0, increment, period, switching potential, and amplitude. The effects of these various parameters on the voltammograms for a surface-confined electrode reaction have enabled the discovery of diagnostic criteria for this mechanism. These are listed in Table 1. Also included in this table are diagnostic plots that will enable rapid identification of the electrode reaction using CSWV.

Figure 8. Effect of α and period on the shape of the voltammogram when log k0 = −1, amplitude = 50 mV, increment = 10 mV, α is (a) 0.3, (b) 0.4, (c) 0.5, (d) 0.6, and (e) 0.7, and period = 1 ms (red), 2 ms (orange), 5 ms (gold), 10 ms (green), 20 ms (cyan), 50 ms (blue), 100 ms (purple), 200 ms (magenta), 500 ms (light gray), 1 s (gray), 2 s (black), and 5 s (brown).

than values expected for α = 0.5. W1/2,f values are smaller than the values obtained for α = 0.5, and W1/2,r values are greater than the values obtained for α = 0.5. Interested readers are referred to Figure S-11 for a further analysis of peak widths as a function of α and period. Figure 9a displays peak potentials as a function of α and log period corresponding to the voltammograms found in Figure 8. Peak potentials are linearly related to period so long as log period ≤ −0.5. For log period > −0.5, peak potentials curvilinearly approach zero and remain constant as the period is 9516


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Table 1. Diagnostic Plots and Protocol for Assessing a Quasireversible Surface-Confined Electrode Reaction by CSWV

a

Zero slope indicates reversible reaction.

Experimental Verification of Predicted Trends for a Surface-Confined Mechanism. To experimentally validate the trends delineated above, the oxidation of (Fc)CONH(CH2)15SH adsorbed on a gold electrode was investigated by CSWV. This molecule was selected because it is wellestablished that the molecule chemisorbs to the gold surface through a Au−S−C linkage and remains bound to the surface when the ferrocenyl moiety is oxidized at least over the potential range from −0.2 to 0.45 V versus Ag/AgClO4.30−33 Voltammograms were acquired with systematic variation in period, increment, switching potential, and amplitude. The following trends in peak currents and potentials were obtained. As period increased, peak current decreased. Figure S-14 presents a plot of peak current versus the reciprocal of period; the expected linear relationship is obtained (compare Figure S14 to Figure S-13). As period increased, peak potentials shifted toward an E0 = 0.25 V versus Ag/AgClO4 with a corresponding decrease in peak separation. As increment was increased, peak currents increased in a manner consistent with theory (compare Figure S-15 to Figure S-1). As increment increased, peak potentials shifted away from E0 with a corresponding increase in peak separation. Peak currents and potentials were not affected by variation of switching potential (data not shown). Trends in amplitude were dependent upon period. At a period of 20 ms, peak currents increased curvilinearly, while Ep,f and Ep,r shifted negatively with amplitude (see Figures S-16 and S-17). The peak widths significantly broaden with increasing amplitude. The peak current and Ep,r trends align with theory; the apparent Ep,f trend did not. At a period of 200 ms, peak currents increased to a maximum, decreased slightly, and then split into two peaks in each scan direction, i.e., Ep,f1, Ep,r1, Ep,f2,

and Ep,r2 (see Figures S-18 and S-19). As expected, peak widths at half-maximum broadened with increasing amplitude. Prior to the peak splitting, Ep,f and Ep,r shifted negatively with amplitude. After the peak splitting occurred, the separation between Ep,f1 and Ep,f2 as well as Ep,r1 and Ep,r2 increased with amplitude (see Figure S-19). The predicted trend is that the peak potentials remain at or near E0 until peak splitting occurs. We speculate that the apparent negative shift in Ep,f at low amplitude is due to inaccuracies in peak potential measurement caused by unresolvable split peaks. Earlier, we presented a method for determining α from peak potentials as a function of period. This method is most applicable when ΔEp ≥ 100 mV. The maximum peak separation that we observed for (Fc)CONH(CH2)15SH was only 50 mV for parameter combinations investigated. Mirčeski and co-workers19 have also presented a method for determining α from square wave voltammetry data for a surface-confined analyte. Their method scans the potential in one direction and plots the individual anodic and cathodic currents versus potential. For oxidative electrode reactions, they compute the ratio of the maximum cathodic current over the maximum anodic current to determine α. These currents are different from the net peak currents discussed above. Using their method, we found α to be 0.49 ± 0.01 for oxidation of a monolayer of (Fc)CONH(CH2)15SH on gold, a value consistent with the literature.30 We also presented a method for determining k0 from peak potentials as a function of period. Again, this method is most applicable when ΔEp ≥ 100 mV. Because the observed ΔEp for (Fc)CONH(CH2)15SH was only 50 mV, this method is inapplicable in this instance. Komorsky-Lovrić and Lovrić36 have an alternative method for determining k0 from SWV data. 9517


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Mirčeski and co-workers.19 Using this method, we determined α = 0.53 for AQDS for the specific pH, electrolyte, and electrode examined. This value is in agreement with previous reports.52

Their method involves plotting net peak current versus the log of square wave frequency to determine the eponymous quasireversible maximum. From the frequency at maximum current, k0 can be determined. Unfortunately, this method is not applicable here because we did not find a quasireversible maximum over the range in period investigated. Instead, we examined the current decay on each and every pulse over the potential range from 0.210 to 0.300 V versus Ag/AgClO4. Plots of ln(I) versus time on each pulse were constructed. As shown in Figure S-20a, curvature was observed consistent with a previous report on electroactive monolayers.39−41 We followed the example by Creager and Weber and computed kf + kb from the linear portion over the second half of each pulse.41 A plot of kf + kb versus Epulse was constructed (see Figure S-20b) analogous to a Tafel plot. An asymmetric curve was observed with the slope of the cathodic portion being less steep than that of the anodic portion. Creager and Weber41 have also observed this asymmetry. They attribute this to the following phenomena: the chemisorbed monolayer is almost completely uncharged through the cathodic branch and almost completely charged through the anodic branch. The minimum on this curve represents the point where the monolayer is undergoing large changes in surface charge. We have observed that the minima depend upon period and amplitude. For example, at an increment of 3 mV and a period of 20 ms, (kf + kb)min equal to 98.3, 111, and 116 s−1 were measured at amplitudes of 10, 20, and 30 mV, respectively. In comparison, at a period of 50 ms, a (kf + kb)min of 64.4 s−1 was measured for a 20 mV amplitude at an increment of 3 mV. These rates are in close agreement with those previously reported for a complete monolayer of (Fc)CONH(CH2)15SH.41 Lower rates have been reported for submonolayer coverage of this ferrocene alkanethiol.30−33 Variation of empirical parameters should have resulted in peak ratios of 1 for the surface-confined process modeled in this work. However, this trend was not obtained. Because a peak ratio of unity over a wide range of scan rate was obtained from CV on the same monolayer, we attribute this deviation from theory to non-ideal behavior, i.e., interactions between the surface-confined molecules, ion-solvation energies, and ion spatial distribution that result from our use of a full monolayer of (Fc)CONH(CH2)15SH.33,41−51 AQDS, another well-characterized surface-confined analyte, was also investigated.8,11,52−56 Even though the AQDS electrode reaction is complicated by pH-dependent chemical reactions,57,58 we have selected it to highlight how variation of amplitude distinguishes a surface-confined process. A linear relationship between current and scan rate was observed by CV (results not shown) confirming surface confinement of both the oxidized and reduced forms. With increasing CSWV amplitude, peak currents grew to a maximum, began to decrease and broaden, and finally, split into two separate peaks, as shown in Figures S-21 and S-22. This peak split is in agreement with theory, as reported in this paper (see Figure 3b) and by others.19,36 Peak ratios ranged from 1.0 to 1.2 (see Figure S23), which is indicative of coupled chemical reactions. Diagnostic criteria for chemically coupled electrode reactions will be addressed in detail in a forthcoming paper. Peak potentials remained at the formal potential until the peaks split, and peak separation was less than the increment (see Figure S24). All trends with amplitude are consistent with a fast, surface-confined electron transfer. From the peak currents after peak splitting has occurred, α can be calculated using the previously established method by

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CONCLUSION In this work, theory for a surface-confined, kinetically controlled electrode reaction has been developed for CSWV. This theory is applicable to both planar and spherical electrodes. Diagnostic criteria to assist experimenters in identifying this mechanism from CSWV data have been presented (see Table 1). These criteria were experimentally verified using two well-characterized surface-confined analytes. For this particular mechanism, the trends observed for CSWV are comparable to those obtainable with SWV coupled with reverse scan SWV. However, this is not the case for chemically coupled electron transfer reactions. Diagnostic criteria for distinguishing chemical reactions preceding and following electron transfers by CSWV will be presented elsewhere. The forthcoming report will further demonstrate the utility of CSWV for identifying the electrode reaction mechanism and measuring associated kinetic parameters.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.5b01684. Additional information including figures and our theoretical derivation as noted in the text (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Prof. Stephen E. Creager of Clemson University for the kind donation of (Fc)CONH(CH2)15SH.

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REFERENCES

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