Article pubs.acs.org/ac
Charge Transfer Kinetics from Surface Plasmon Resonance Voltammetry Jin Lu and Jinghong Li* Department of Chemistry, Beijing Key Laboratory for Microanalytical Methods and Instrumentation, Tsinghua University, Beijing 100084, China S Supporting Information *
ABSTRACT: On the basis of a quantitative relationship between surface plasmon resonance signal and electrochemical current in the electrochemical surface plasmon resonance (ECSPR), EC-SPR signal measures the semi-integral of faradaic current. We theoretically discussed the electrode potential and charge transfer kinetics to be determined from surface plasmon resonance voltammetry (or potential sweep EC-SPR) signals for the fully reversible, quasi-reversible, and irreversible redox reactions. The results indicated that the electroanalysis of EC-SPR signal is more straightforward than conventional electrochemical current. Then, we studied two model redox reactions of hexaammineruthenium chloride and 4-nitrotoluene, to obtain half wave potential of quasi-reversible redox reaction, transfer coefficient, and standard rate constant of irreversible redox reaction from EC-SPR signals.
S
cally, EC-SPR signal is proportional to the semi-integral of the faradaic current.10 Thus, in the EC-SPR technique, the SPR signal offers a more straightforward way for electrode kinetics and mechanism analysis, rather than electrochemical current. Here, we studied the EC-SPR signals of diffusion controlled fully reversible, quasi-reversible, and irreversible redox reactions. The basic principles of electrode kinetic parameters directly obtained from EC-SPR signal were discussed and verified by the simulations. To demonstrate the applicability of the method, we carried out the EC-SPR measurements on redox reactions of hexaammineruthenium chloride and 4nitrotoluene. From the logarithmical analysis of EC-SPR signal, we were able to obtain the half wave potential of quasireversible redox reaction, transfer coefficient, and standard rate constant of irreversible redox reaction, respectively.
urface plasmon resonance (SPR) is an optical technique with high sensitivity to study the process taking place near the metal film. It has been widely used as a label-free method to monitor the various molecule interactions.1−3 SPR is also an approach that can be combined with other analytical techniques as multifunctional assay platforms.4 Various electrochemical methods, for instance cyclic voltammetry (CV), linear sweep voltammetry (LSV), electrochemical impedance spectroscopy (EIS), and stripping voltammetry, are most commonly combined with SPR in the electrochemical SPR (EC-SPR) technique. EC-SPR has emerged as a powerful tool for investigations of electrochemical and optical properties of adsorbates during the electrochemical process, with various applications to study enzyme activity, self-assembled monolayer, in situ polymerization, and trace metal ion detection at the metal/solution interface.5−9 Meanwhile, Tao and coworkers established a basic formalism of EC-SPR, offering a quantitative relationship between SPR signal and electrochemical current.10 Their work promotes the applications of SPR signals during the electrochemical reactions, that the electrochemical current and impedance can be optically measured from SPR.11,12 CV and LSV are the well established electrochemical techniques to measure the electrode reaction kinetics and mechanisms.13,14 Technically, the semi-integral of the faradaic current is proportional to the diffusing electroactive species concentration and can simplify to some extent the treatment of data for electrode kinetics and mechanisms.15 However, measuring the semi-integral of current is not straightforward; the analog circuits16 or numerical integration computing17 is always needed to facilitate the acquisition and processing of data, which limits its scope of application. On the other hand, SPR detects the refractive index changes or the concentration for a certain chemical species near the metal film. Mathemati© 2014 American Chemical Society
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EXPERIMENTAL SECTION Materials. Potassium chloride, acetonitrile (CH3CN), and 4-nitrotoluene were purchased from Beijing Chemical Reagent Company (China). Hexaammineruthenium(III) chloride (Ru(NH3)6Cl3) was purchased from Alfa Aesar (China). The solutions were prepared using ultrapure water, which was obtained through a Millipore Milli-Q water purification system (Billerica, MA, USA) and had an electric resistivity of >18.3 MΩ·cm. Electrochemical Surface Plasmon Resonance Measurements. BI-2000 SPR instrument (Biosensing Instrument Inc.) was used in the experiments. The SPR sensor chip was a BK7 glass cover slide coated with 2 nm chromium followed by Received: December 18, 2013 Accepted: March 23, 2014 Published: March 23, 2014 3882
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Figure 1. The simulated CV curves (i), EC-SPR responses (ii), and logarithmical analysis of EC-SPR signals (iii) of fully reversible (a) and quasireversible (b) electron transfer processes at different potential sweep rates. Simulation parameters: k0 = 5 cm/s (a) or 0.01 cm/s (b), α = 0.5, E0 = 0 V, DR = DO = 1 × 10−5 cm2/s, CO = 1 mM, CR = 0, electrode area = 1 cm2, and BαO-BαR = 1 mDeg/mM.
47 nm gold by a thermal evaporator at high vacuum (3 × 10−6 Torr). The Au sensor chip was used as the working electrode (WE) and a Pt wire served as the counter electrode (CE). Its potential was controlled with respect to Ag/AgCl reference electrode (RE) by a potentiostat (Model 630B, CH Instruments. Inc.). Potential, current, and EC-SPR signals were collected by Data Acquisition (NI USB-6210, National Instruments) using a program written in MATLAB.
From eq 1, SPR signal is proportional to semi-integral of faradaic current,
Δθ(t ) = b·m(t )
where b = B(αRDR−1/2 − αODO−1/2)·(nF)−1. In the convolution voltammetry, the semi-integral current directly measures the electroactive species concentrations at the electrode surface, with particular advantages to electrochemical analysis of the kinetics and mechanism over conventional LSV or CV methods.18 Eq 3 offers a more convenient way to determine the semi-integral current from SPR signal, without further processing of the electrochemical current data. For the fully reversible redox reaction with pure diffusion control, we simulated the CV curves (Figure 1a (i)) by CH Instrument software. The forward and reverse EC-SPR curves determined by eq 1 coincide at different potential sweep rates (Figure 1a (ii)), indicating that the corresponding EC-SPR signal only depends on the reactant concentrations and potential ranges.10 Similar to convolution voltammetry, the logarithmical analysis of EC-SPR signal (Supporting Information Section 1 for more details)
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RESULTS AND DISCUSSION Theory and Simulation. In the redox reaction with pure diffusion control, O + ne ↔ R
SPR signal (θ) is expressed by the faradaic current (i), as10 Δθ(t ) = B(αR DR −1/2 − αODO−1/2) ·(nFπ 1/2)−1 ·
∫0
t
i(t ′)(t − t ′)−1/2 dt ′
(1)
where αR/αO is the change of refractive index per unit concentration of redox molecule and constant B is the sensitivity of SPR angle to the refractive index changes. This equation implies that SPR signal is a function of convolution integrals of the faradaic current with t−1/2. We define the semiintegral of current as m(t) m (t ) =
1 π
1/2
∫0
t
i(t ′)(t − t ′)−1/2 dt ′
(3)
E = E1/2 +
RT ⎡ θ l − θ(t ) ⎤ ln⎢ ⎥ nF ⎣ θ(t ) ⎦
(4)
gives rise to a straight line (Figure 1a (iii)), where θl is the SPR response plateau when reactant concentration reaches zero as the potential goes to the negative. From the ln [(θl − θ(t))/ (θ(t))] ∼ E curve, the half wave potential (E1/2) will be
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Figure 2. The simulated CV curves (a), EC-SPR responses (b), and logarithmical analysis of EC-SPR signals (c) of irreversible electron transfer process at different potential sweep rates. Simulation parameters: k0 = 2 × 10−5 cm/s, α = 0.5, E0 = 0 V, DR = DO = 1 × 10−5 cm2/s, CO = 1 mM, CR = 0, electrode area = 1 cm2, BαO − BαR = 1 mDeg/mM. All the logarithmical analyses of EC-SPR signals at different potential sweep rates fit to a similar straight line.
Figure 3. The recorded current (a), EC-SPR (b), and logarithmical analysis of EC-SPR signals (c) vs potential of 5 mM Ru(NH3)63+ in 0.5 M KCl at different potential sweep rates.
⎡ αnF ⎤ k f (E) = k0exp⎢ − (E − E Θ )⎥ ⎣ RT ⎦
determined as x-intercept of the line and the slope equal to nF/ RT (= 38.9 in Figure 1a (iii)) In the real electrochemical systems, fully reversible electron transfer kinetics are not always strictly followed, as the commonly used redox molecules Fe(CN)64−/3− and Ru(NH3)62+/3+. We simulated the CV and EC-SPR curves of quasi-reversible redox reaction in Figure 1b (i, ii). The forward and reverse EC-SPR curves do not coincide, with the increasing gap at higher potential sweep rate. Although the logarithmical analysis (ln[(θl − θ(t))/(θ(t))] ∼ E) is also a straight line (Figure 1b (iii)), it does not follow the eq 4. The slope of the line is not equal to nF/RT, especially at higher sweep rates. However, at the lowest sweep rate, the average of x-intercepts of the forward and reverse lines is still a good estimation of E1/2. For the irreversible redox reaction with pure diffusion control, the simulated CV and EC-SPR response are shown in Figure 2a,b. Considering the charge transfer kinetics expression in convolutive technique18 and the relationship between SPR and semi-integral current (Supporting Information Section 1 for more details), we have ⎡ θ − θ (t ) ⎤ ln k f (E) = ln D1/2 − ln⎢ l ⎥ ⎣ i(t ) ·b ⎦
(6)
the logarithmical analysis of EC-SPR signal E − EΘ =
RT ⎛ k0 ⎞ RT ⎡ θ l − θ(t ) ⎤ ln⎜ 1/2 ⎟ + ln⎢ ⎥ αnF ⎝ D ⎠ αnF ⎣ i(t ) ·b ⎦
(7)
gives a straight line (Figure 2c). Here, the current i(t) is directly calculated from SPR signal θ(t) according to eq 1, rather than electrochemical recording. Once the diffusion coefficient and standard potential is known, we can derive the transfer coefficient (α) and the standard rate constant (k0) from the slope and intercept of the line. The calculated results from Figure 2c, α = 0.50 and k0 = 1.97 × 10−5 cm/s, are constant with simulation parameter values. The above theoretical analyses and simulations show that, in the simple redox reaction system with pure diffusion control, EC-SPR signals, which are proportional to the semi-integral of faradaic current, can significantly simplify the charge transfer kinetics studies unlike conventional LSV or CV methods. Experimental Analysis of Quasi-Reversible Electrode Reaction. We studied EC-SPR response of Ru(NH3)63+ redox reaction, as a model of quasi-reversible electrode reaction. To remove interferences from supporting electrolyte, CV and ECSPR responses of the supporting electrolyte were subtracted
(5)
if the Butler−Volmer kinetics is followed 3884
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Figure 4. The recorded current (a), EC-SPR (b), and logarithmical analysis of EC-SPR signals (c) vs potential of 1 mg/mL 4-nitrotoluene in 0.5 M KCl + 10% CH3CN at different potential sweep rates. All the logarithmical analyses fit to a straight line (c, gray solid line) well. The transfer coefficient (α) and the standard rate constant (k0) were calculated from linear fitting coefficients.
from Ru(NH3)63+ solution, respectively (Supporting Information, Figure S1). The corresponding EC-SPR responses are shown in Figure 3b. SPR detected the refractive index change between the oxidized and reduced forms of the reactant. When the potential drops from 0 to −0.4 V, the SPR signal decreases as Ru(II) complex has a smaller contribution of refractive index than that of Ru(III). At a lower potential, SPR signal tends toward a plateau (θl), where Ru(III) complex depletes near the electrode surface. This value (θl) is independent with the potential sweep rate at a fixed potential sweep range. Figure 3c shows the logarithmical analysis of Ru(NH3)63+ EC-SPR signal. The plots of ln[(θl − θ(t))/(θ(t))] ∼ E are satisfactorily linear from all potential sweep rates. The increasing gaps between forward and reverse profiles (Figure 3b,c) at higher potential sweep rate indicate the quasi-reversible electron transfer kinetics of Ru(NH3)63+/2+, as the simulated response in Figure 1b (ii, iii). For the quasi-reversible Ru(NH3)63+/2+ EC-SPR process, E1/2 was estimated from average x-intercepts of linear profiles at 0.09 V/s, and the value is −0.19 V, which is in good agreement with published data.19 Experimental Analysis of Irreversible Electrode Reaction. 4-Nitrotoluene (4-NT) reduction was used as an irreversible electron transfer model to analyze the EC-SPR response. Similar supporting electrolyte signal subtractions were done to the CV and EC-SPR responses (Supporting Information, Figure S2) and used for the further analyses. From CV curves in Figure 4a, the reduction peak potentials shift more negative as the potential sweep rate increases, and the reduction peak current is proportional to the square root of sweep rate (Supporting Information, Figure S3), demonstrating a diffusion controlled irreversible 4-NT reduction. The EC-SPR signal increases as the potential drops from −0.5 to −0.9 V, indicating the reduction product has larger contribution of refractive index than 4-NT. This was confirmed by the measurements of BαR(BαO) values by experiment (Supporting Information Section 4). The SPR response plateau (θl) at −0.9 V is dependent on the potential sweep rate. This may be caused by the redox molecule adsorption or unsubtracted interface capacitance effects. Figure 4c shows the logarithmical analysis of EC-SPR signal according to eq 7. The SPR derived current (eq 1), rather than recorded electrochemical current, was used to plot the ln[(θl − θ(t))/(i(t)·b)] ∼ E curves. All the curves at different potential sweep rates fit to a similar straight line (linear fitting in Figure 4c) well, similar to the simulated trends shown in Figure 2c.
Here, we assumed that the standard potential is practically equal to the Ep (−0.635 V) at lower sweep rate (0.2 V/s, Supporting Information, Figure S3). The diffusion coefficient of 4-NT is 0.808 × 10−5 cm2·s−1.20 From these values and the linear fitting coefficients (Figure 4c), the transfer coefficient (α) of 4-NT reduction is 0.57 ± 0.01, and the standard rate constant (k0) is (9.22 ± 3.54) × 10−3 cm·s−1. These values are reasonable, compared to published results by electrochemical measurements.21,22 Practically, it is not always necessary to determine the constant b (or BαR, BαO) of a certain redox molecule to determine the electrode kinetic parameters. The constant b was reducible in the logarithmical analysis of EC-SPR signal as shown in eqs 4 and 7. Thus, these analyses mentioned above are applicable to all kinds of redox reactions with diffusion control, as long as there are distinct refractive index differences between reduction and oxidation states of redox molecule to generate the EC-SPR signals.
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CONCLUSION We demonstrate the basic principles of electrode potential and charge transfer kinetic parameters directly obtained from ECSPR signal in the SPR voltammetry. Theoretically, EC-SPR signal in a diffusion controlled electrode process is proportional to the semi-integral of the faradaic current. We discuss logarithmical analysis of EC-SPR signal in fully reversible, quasi-reversible, and irreversible redox reactions to determine the half wave potential, transfer coefficient, and the standard rate constant. The theoretical discussion is validated by the simulated EC-SPR response. Then, we carried out the EC-SPR measurements on redox reactions of hexaammineruthenium chloride and 4-nitrotoluene, as the models of quasi-reversible and irreversible electron transfer processes, and obtained corresponding electrochemical parameters experimentally. Compared to traditional convolution voltammetry, the EC-SPR signal in the SPR voltammetry is more straightforward to determine the charge transfer kinetics. Furthermore, this method is ready to work in imaging mode, as EC-SPR imaging study. After logarithmical analysis of ECSPR images pixel-by-pixel, the mapping of local charge transfer kinetics of interface with lateral resolution is obtained, as a powerful tool to characterize the electrochemical properties of heterogeneous interface quantitatively. 3885
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Article
ASSOCIATED CONTENT
S Supporting Information *
Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org.
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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 This work was financially supported by National Basic Research Program of China (No. 2011CB935704) and the National Natural Science Foundation of China (No. 21235004, No. 21327806).
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REFERENCES
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Charge Transfer Kinetics from Surface Plasmon Resonance Voltammetry Jin Lu and Jinghong Li* Department of Chemistry, Beijing Key Laboratory for Microanalytical Methods and Instrumentation, Tsinghua University, Beijing 100084, China S Supporting Information *
ABSTRACT: On the basis of a quantitative relationship between surface plasmon resonance signal and electrochemical current in the electrochemical surface plasmon resonance (ECSPR), EC-SPR signal measures the semi-integral of faradaic current. We theoretically discussed the electrode potential and charge transfer kinetics to be determined from surface plasmon resonance voltammetry (or potential sweep EC-SPR) signals for the fully reversible, quasi-reversible, and irreversible redox reactions. The results indicated that the electroanalysis of EC-SPR signal is more straightforward than conventional electrochemical current. Then, we studied two model redox reactions of hexaammineruthenium chloride and 4-nitrotoluene, to obtain half wave potential of quasi-reversible redox reaction, transfer coefficient, and standard rate constant of irreversible redox reaction from EC-SPR signals.
S
cally, EC-SPR signal is proportional to the semi-integral of the faradaic current.10 Thus, in the EC-SPR technique, the SPR signal offers a more straightforward way for electrode kinetics and mechanism analysis, rather than electrochemical current. Here, we studied the EC-SPR signals of diffusion controlled fully reversible, quasi-reversible, and irreversible redox reactions. The basic principles of electrode kinetic parameters directly obtained from EC-SPR signal were discussed and verified by the simulations. To demonstrate the applicability of the method, we carried out the EC-SPR measurements on redox reactions of hexaammineruthenium chloride and 4nitrotoluene. From the logarithmical analysis of EC-SPR signal, we were able to obtain the half wave potential of quasireversible redox reaction, transfer coefficient, and standard rate constant of irreversible redox reaction, respectively.
urface plasmon resonance (SPR) is an optical technique with high sensitivity to study the process taking place near the metal film. It has been widely used as a label-free method to monitor the various molecule interactions.1−3 SPR is also an approach that can be combined with other analytical techniques as multifunctional assay platforms.4 Various electrochemical methods, for instance cyclic voltammetry (CV), linear sweep voltammetry (LSV), electrochemical impedance spectroscopy (EIS), and stripping voltammetry, are most commonly combined with SPR in the electrochemical SPR (EC-SPR) technique. EC-SPR has emerged as a powerful tool for investigations of electrochemical and optical properties of adsorbates during the electrochemical process, with various applications to study enzyme activity, self-assembled monolayer, in situ polymerization, and trace metal ion detection at the metal/solution interface.5−9 Meanwhile, Tao and coworkers established a basic formalism of EC-SPR, offering a quantitative relationship between SPR signal and electrochemical current.10 Their work promotes the applications of SPR signals during the electrochemical reactions, that the electrochemical current and impedance can be optically measured from SPR.11,12 CV and LSV are the well established electrochemical techniques to measure the electrode reaction kinetics and mechanisms.13,14 Technically, the semi-integral of the faradaic current is proportional to the diffusing electroactive species concentration and can simplify to some extent the treatment of data for electrode kinetics and mechanisms.15 However, measuring the semi-integral of current is not straightforward; the analog circuits16 or numerical integration computing17 is always needed to facilitate the acquisition and processing of data, which limits its scope of application. On the other hand, SPR detects the refractive index changes or the concentration for a certain chemical species near the metal film. Mathemati© 2014 American Chemical Society
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EXPERIMENTAL SECTION Materials. Potassium chloride, acetonitrile (CH3CN), and 4-nitrotoluene were purchased from Beijing Chemical Reagent Company (China). Hexaammineruthenium(III) chloride (Ru(NH3)6Cl3) was purchased from Alfa Aesar (China). The solutions were prepared using ultrapure water, which was obtained through a Millipore Milli-Q water purification system (Billerica, MA, USA) and had an electric resistivity of >18.3 MΩ·cm. Electrochemical Surface Plasmon Resonance Measurements. BI-2000 SPR instrument (Biosensing Instrument Inc.) was used in the experiments. The SPR sensor chip was a BK7 glass cover slide coated with 2 nm chromium followed by Received: December 18, 2013 Accepted: March 23, 2014 Published: March 23, 2014 3882
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Figure 1. The simulated CV curves (i), EC-SPR responses (ii), and logarithmical analysis of EC-SPR signals (iii) of fully reversible (a) and quasireversible (b) electron transfer processes at different potential sweep rates. Simulation parameters: k0 = 5 cm/s (a) or 0.01 cm/s (b), α = 0.5, E0 = 0 V, DR = DO = 1 × 10−5 cm2/s, CO = 1 mM, CR = 0, electrode area = 1 cm2, and BαO-BαR = 1 mDeg/mM.
47 nm gold by a thermal evaporator at high vacuum (3 × 10−6 Torr). The Au sensor chip was used as the working electrode (WE) and a Pt wire served as the counter electrode (CE). Its potential was controlled with respect to Ag/AgCl reference electrode (RE) by a potentiostat (Model 630B, CH Instruments. Inc.). Potential, current, and EC-SPR signals were collected by Data Acquisition (NI USB-6210, National Instruments) using a program written in MATLAB.
From eq 1, SPR signal is proportional to semi-integral of faradaic current,
Δθ(t ) = b·m(t )
where b = B(αRDR−1/2 − αODO−1/2)·(nF)−1. In the convolution voltammetry, the semi-integral current directly measures the electroactive species concentrations at the electrode surface, with particular advantages to electrochemical analysis of the kinetics and mechanism over conventional LSV or CV methods.18 Eq 3 offers a more convenient way to determine the semi-integral current from SPR signal, without further processing of the electrochemical current data. For the fully reversible redox reaction with pure diffusion control, we simulated the CV curves (Figure 1a (i)) by CH Instrument software. The forward and reverse EC-SPR curves determined by eq 1 coincide at different potential sweep rates (Figure 1a (ii)), indicating that the corresponding EC-SPR signal only depends on the reactant concentrations and potential ranges.10 Similar to convolution voltammetry, the logarithmical analysis of EC-SPR signal (Supporting Information Section 1 for more details)
■
RESULTS AND DISCUSSION Theory and Simulation. In the redox reaction with pure diffusion control, O + ne ↔ R
SPR signal (θ) is expressed by the faradaic current (i), as10 Δθ(t ) = B(αR DR −1/2 − αODO−1/2) ·(nFπ 1/2)−1 ·
∫0
t
i(t ′)(t − t ′)−1/2 dt ′
(1)
where αR/αO is the change of refractive index per unit concentration of redox molecule and constant B is the sensitivity of SPR angle to the refractive index changes. This equation implies that SPR signal is a function of convolution integrals of the faradaic current with t−1/2. We define the semiintegral of current as m(t) m (t ) =
1 π
1/2
∫0
t
i(t ′)(t − t ′)−1/2 dt ′
(3)
E = E1/2 +
RT ⎡ θ l − θ(t ) ⎤ ln⎢ ⎥ nF ⎣ θ(t ) ⎦
(4)
gives rise to a straight line (Figure 1a (iii)), where θl is the SPR response plateau when reactant concentration reaches zero as the potential goes to the negative. From the ln [(θl − θ(t))/ (θ(t))] ∼ E curve, the half wave potential (E1/2) will be
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Figure 2. The simulated CV curves (a), EC-SPR responses (b), and logarithmical analysis of EC-SPR signals (c) of irreversible electron transfer process at different potential sweep rates. Simulation parameters: k0 = 2 × 10−5 cm/s, α = 0.5, E0 = 0 V, DR = DO = 1 × 10−5 cm2/s, CO = 1 mM, CR = 0, electrode area = 1 cm2, BαO − BαR = 1 mDeg/mM. All the logarithmical analyses of EC-SPR signals at different potential sweep rates fit to a similar straight line.
Figure 3. The recorded current (a), EC-SPR (b), and logarithmical analysis of EC-SPR signals (c) vs potential of 5 mM Ru(NH3)63+ in 0.5 M KCl at different potential sweep rates.
⎡ αnF ⎤ k f (E) = k0exp⎢ − (E − E Θ )⎥ ⎣ RT ⎦
determined as x-intercept of the line and the slope equal to nF/ RT (= 38.9 in Figure 1a (iii)) In the real electrochemical systems, fully reversible electron transfer kinetics are not always strictly followed, as the commonly used redox molecules Fe(CN)64−/3− and Ru(NH3)62+/3+. We simulated the CV and EC-SPR curves of quasi-reversible redox reaction in Figure 1b (i, ii). The forward and reverse EC-SPR curves do not coincide, with the increasing gap at higher potential sweep rate. Although the logarithmical analysis (ln[(θl − θ(t))/(θ(t))] ∼ E) is also a straight line (Figure 1b (iii)), it does not follow the eq 4. The slope of the line is not equal to nF/RT, especially at higher sweep rates. However, at the lowest sweep rate, the average of x-intercepts of the forward and reverse lines is still a good estimation of E1/2. For the irreversible redox reaction with pure diffusion control, the simulated CV and EC-SPR response are shown in Figure 2a,b. Considering the charge transfer kinetics expression in convolutive technique18 and the relationship between SPR and semi-integral current (Supporting Information Section 1 for more details), we have ⎡ θ − θ (t ) ⎤ ln k f (E) = ln D1/2 − ln⎢ l ⎥ ⎣ i(t ) ·b ⎦
(6)
the logarithmical analysis of EC-SPR signal E − EΘ =
RT ⎛ k0 ⎞ RT ⎡ θ l − θ(t ) ⎤ ln⎜ 1/2 ⎟ + ln⎢ ⎥ αnF ⎝ D ⎠ αnF ⎣ i(t ) ·b ⎦
(7)
gives a straight line (Figure 2c). Here, the current i(t) is directly calculated from SPR signal θ(t) according to eq 1, rather than electrochemical recording. Once the diffusion coefficient and standard potential is known, we can derive the transfer coefficient (α) and the standard rate constant (k0) from the slope and intercept of the line. The calculated results from Figure 2c, α = 0.50 and k0 = 1.97 × 10−5 cm/s, are constant with simulation parameter values. The above theoretical analyses and simulations show that, in the simple redox reaction system with pure diffusion control, EC-SPR signals, which are proportional to the semi-integral of faradaic current, can significantly simplify the charge transfer kinetics studies unlike conventional LSV or CV methods. Experimental Analysis of Quasi-Reversible Electrode Reaction. We studied EC-SPR response of Ru(NH3)63+ redox reaction, as a model of quasi-reversible electrode reaction. To remove interferences from supporting electrolyte, CV and ECSPR responses of the supporting electrolyte were subtracted
(5)
if the Butler−Volmer kinetics is followed 3884
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Figure 4. The recorded current (a), EC-SPR (b), and logarithmical analysis of EC-SPR signals (c) vs potential of 1 mg/mL 4-nitrotoluene in 0.5 M KCl + 10% CH3CN at different potential sweep rates. All the logarithmical analyses fit to a straight line (c, gray solid line) well. The transfer coefficient (α) and the standard rate constant (k0) were calculated from linear fitting coefficients.
from Ru(NH3)63+ solution, respectively (Supporting Information, Figure S1). The corresponding EC-SPR responses are shown in Figure 3b. SPR detected the refractive index change between the oxidized and reduced forms of the reactant. When the potential drops from 0 to −0.4 V, the SPR signal decreases as Ru(II) complex has a smaller contribution of refractive index than that of Ru(III). At a lower potential, SPR signal tends toward a plateau (θl), where Ru(III) complex depletes near the electrode surface. This value (θl) is independent with the potential sweep rate at a fixed potential sweep range. Figure 3c shows the logarithmical analysis of Ru(NH3)63+ EC-SPR signal. The plots of ln[(θl − θ(t))/(θ(t))] ∼ E are satisfactorily linear from all potential sweep rates. The increasing gaps between forward and reverse profiles (Figure 3b,c) at higher potential sweep rate indicate the quasi-reversible electron transfer kinetics of Ru(NH3)63+/2+, as the simulated response in Figure 1b (ii, iii). For the quasi-reversible Ru(NH3)63+/2+ EC-SPR process, E1/2 was estimated from average x-intercepts of linear profiles at 0.09 V/s, and the value is −0.19 V, which is in good agreement with published data.19 Experimental Analysis of Irreversible Electrode Reaction. 4-Nitrotoluene (4-NT) reduction was used as an irreversible electron transfer model to analyze the EC-SPR response. Similar supporting electrolyte signal subtractions were done to the CV and EC-SPR responses (Supporting Information, Figure S2) and used for the further analyses. From CV curves in Figure 4a, the reduction peak potentials shift more negative as the potential sweep rate increases, and the reduction peak current is proportional to the square root of sweep rate (Supporting Information, Figure S3), demonstrating a diffusion controlled irreversible 4-NT reduction. The EC-SPR signal increases as the potential drops from −0.5 to −0.9 V, indicating the reduction product has larger contribution of refractive index than 4-NT. This was confirmed by the measurements of BαR(BαO) values by experiment (Supporting Information Section 4). The SPR response plateau (θl) at −0.9 V is dependent on the potential sweep rate. This may be caused by the redox molecule adsorption or unsubtracted interface capacitance effects. Figure 4c shows the logarithmical analysis of EC-SPR signal according to eq 7. The SPR derived current (eq 1), rather than recorded electrochemical current, was used to plot the ln[(θl − θ(t))/(i(t)·b)] ∼ E curves. All the curves at different potential sweep rates fit to a similar straight line (linear fitting in Figure 4c) well, similar to the simulated trends shown in Figure 2c.
Here, we assumed that the standard potential is practically equal to the Ep (−0.635 V) at lower sweep rate (0.2 V/s, Supporting Information, Figure S3). The diffusion coefficient of 4-NT is 0.808 × 10−5 cm2·s−1.20 From these values and the linear fitting coefficients (Figure 4c), the transfer coefficient (α) of 4-NT reduction is 0.57 ± 0.01, and the standard rate constant (k0) is (9.22 ± 3.54) × 10−3 cm·s−1. These values are reasonable, compared to published results by electrochemical measurements.21,22 Practically, it is not always necessary to determine the constant b (or BαR, BαO) of a certain redox molecule to determine the electrode kinetic parameters. The constant b was reducible in the logarithmical analysis of EC-SPR signal as shown in eqs 4 and 7. Thus, these analyses mentioned above are applicable to all kinds of redox reactions with diffusion control, as long as there are distinct refractive index differences between reduction and oxidation states of redox molecule to generate the EC-SPR signals.
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CONCLUSION We demonstrate the basic principles of electrode potential and charge transfer kinetic parameters directly obtained from ECSPR signal in the SPR voltammetry. Theoretically, EC-SPR signal in a diffusion controlled electrode process is proportional to the semi-integral of the faradaic current. We discuss logarithmical analysis of EC-SPR signal in fully reversible, quasi-reversible, and irreversible redox reactions to determine the half wave potential, transfer coefficient, and the standard rate constant. The theoretical discussion is validated by the simulated EC-SPR response. Then, we carried out the EC-SPR measurements on redox reactions of hexaammineruthenium chloride and 4-nitrotoluene, as the models of quasi-reversible and irreversible electron transfer processes, and obtained corresponding electrochemical parameters experimentally. Compared to traditional convolution voltammetry, the EC-SPR signal in the SPR voltammetry is more straightforward to determine the charge transfer kinetics. Furthermore, this method is ready to work in imaging mode, as EC-SPR imaging study. After logarithmical analysis of ECSPR images pixel-by-pixel, the mapping of local charge transfer kinetics of interface with lateral resolution is obtained, as a powerful tool to characterize the electrochemical properties of heterogeneous interface quantitatively. 3885
dx.doi.org/10.1021/ac404101w | Anal. Chem. 2014, 86, 3882−3886
Analytical Chemistry
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Article
ASSOCIATED CONTENT
S Supporting Information *
Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org.
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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 This work was financially supported by National Basic Research Program of China (No. 2011CB935704) and the National Natural Science Foundation of China (No. 21235004, No. 21327806).
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REFERENCES
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