J. Phys. Chem. C 2008, 112, 13709–13715
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Unusual Voltammetry of the Reduction of O2 in [C4dmim][N(Tf)2] Reveals a Strong Interaction of O2•- with the [C4dmim]+ Cation Alexander S. Barnes,† Emma I. Rogers,† Ian Streeter,† Leigh Aldous,‡ Christopher Hardacre,‡ Gregory G. Wildgoose,† and Richard G. Compton*,† Department of Chemistry, Physical and Theoretical Chemistry Laboratory, Oxford UniVersity, South Parks Road, Oxford OX1 3QZ, United Kingdom, and School of Chemistry and Chemical Engineering/QUILL, Queen’s UniVersity Belfast, Belfast, Northern Ireland BT9 5AG, United Kingdom ReceiVed: April 17, 2008; ReVised Manuscript ReceiVed: July 3, 2008
Voltammetric studies of the reduction of oxygen in the room temperature ionic liquid [C4dmim][N(Tf)2] have revealed a significant positive shift in the back peak potential, relative to that expected for a simple electron transfer. This shift is thought to be due to the strong association of the electrogenerated superoxide anion with the solvent cation. In this work we quantitatively simulate the microdisc electrode voltammetry using a model based upon a one-electron reduction followed by a reversible chemical step, involving the formation of the [C4dmim]+ · · · O2•- ion-pair, and in doing so we extract a set of parameters completely describing the system. We have simulated the voltammetry in the absence of a following chemical step and have shown that it is impossible to simultaneously fit both the forward and reverse peaks. To further support the parameters extracted from fitting the experimental voltammetry, we have used these parameters to independently simulate the double step chronoamperometric response and found excellent agreement. The parameters used to describe the association of the O2•- with the [C4dmim]+ were kf ) 1.4 × 103 s-1 for the first-order rate constant and Keq ) 25 for the equilibrium constant. 1. Introduction The electrochemical reduction of oxygen has been extensively investigated in numerous different solvents and in nonaqueous media follows the simple one-electron mechanism in which superoxide is generated:1
O2 + e- h O2•-
(1)
The superoxide species (O2•-) is known to readily react with water:2
2O2•- + H2O f O2 + HOO- + HO-
(2)
and the use of aprotic solvents is therefore necessary to produce stable superoxide anions and electrochemically reversible voltammetry. This has previously been reported for the reduction of oxygen in the aprotic solvents acetonitrile (MeCN),3-6 N,Ndimethylformamide (DMF),4-6 dimethyl sulfoxide (DMSO),5,6 acetone,5 pyridine,5 propylene carbonate (PC),7 and methylene chloride.5 The electroreduction of oxygen is an important reaction in conventional protic and aprotic solvents in a range of applications, which include electrosynthesis, metal-air batteries, and fuel cells.8 Recently, room temperature ionic liquids (RTILs) have become increasingly popular as solvents for these applications and for other more general electrochemical investigations. This is due to their near-zero volatility, high thermal and chemical stability, intrinsic conductivity, and wide electrochemical potential window,9-11 and as such, the electroreduction of oxygen in this group of solvents has prompted the publication of a * Corresponding author: Fax +44 (0) 1865 275410; Tel +44 (0) 1865 275413; e-mail
[email protected]. † Oxford University. ‡ Queen’s University Belfast.
significantnumberofpapersfromdifferentresearchgroups.3,8,9,12-14 One of the first studies of the one-electron reduction of oxygen in room temperature molten salts (imidazolium chloridealuminum chloride) was by Carter et al.,15 who observed that the electrogenerated superoxide species was unstable and the voltammetry was irreversible. Following this, Katayama16 and AlNashef3 looked at the voltammetry of O2 in imidazolium ionic liquids. Although all researchers agreed that O2•- was the electrogenerated species, the stability of this radical anion in the media under consideration was still being investigated. It has been reported that this species is stable in RTILs, such as 1-butyl-3-methylimidazolium hexafluorophosphate, [C4mim][PF6],3 and trimethylhexylammonium bis(trifluoromethylsulfonyl)imide;16 it has also been generated in 1,2-dimethyl-3-nbutylimidazolium hexafluorophosphate, [dmbim][PF6],3 and, as mentioned above, 1-ethyl-3-methylimidazolium aluminum chloride molten salt, [C2mim][AlCl3].15 The strongly nucleophilic, electrogenerated O2•- can potentially undergo a follow-up reaction with the solvent, which contains high concentrations of electropositive imidazolium cations, [Im]+. Strong ion-pairing effects are likely to be observed16,17 after the electron transfer step and hence have the effect of “stabilizing” the reduced species.2 Rapid consumption of the O2•- by [Im]+, i.e., formation of the [Im]+ · · · O2•- ion pair via the following mechanism kf
O2 + e- h O2•- [Im]+ + O2•- y\z [Im]+ · · · O2•-
(3)
kb
impedes the reverse electron transfer for the oxidation of superoxide, and consequently the oxidation peak becomes shifted to a more positive potential and the voltammetry becomes apparently more irreversible than would occur in the absence of the “C” step.2 The reduction of oxygen in imida-
10.1021/jp803349z CCC: $40.75 2008 American Chemical Society Published on Web 08/13/2008
13710 J. Phys. Chem. C, Vol. 112, No. 35, 2008 TABLE 1: Dimensionless Parameters Used for the Numerical Simulationa parameter
expression
concentration radial coordinate normal coordinate time scan rate potential heterogeneous rate constant homogeneous rate constant
u ) [U]/[A]bulk R ) r/rd Z ) z/rd τ ) DAt/rd2 σ ) (F/RT)(νrd2/DA) θ ) (F/RT)(E - Ef) K0 ) k0rd/DA Kf ) kfrd2/DA
a U may refer to the species A, B, or C; all species are normalized to the bulk concentration of species A.
zolium RTILs can be classifed as an electrochemical process with a homogeneous follow-up chemical step,16 i.e., EC. Ion-pairing effects like this have also been observed for the reduction of various 1,n-dinitrobenzenes17 and benzaldehyde18 in 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, [C4mim][N(Tf)2] sthe reduction of the latter being compared with that in the pyrrolidinium ionic liquid 1-butyl1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide, [C4mpyrr][N(Tf)2]. Dramatic anodic shifts were observed for the benzaldehyde in [C4mim][N(Tf)2] compared to the non-aromatic [C4mpyrr][N(Tf)2], which was assigned to the thermodynamic stabilization of the radical anion by interaction processes with [Im]+.18 Islam et al.14 studied the ion-pairing phenomenon in RTILs relative to the more conventional solvent DMSO. They observed qualitatiVely that the reduction of oxygen occurred at a more positive potential in [C4mim][N(Tf)2] than in DMSO, which they attributed to the complexation of superoxide with the imidazolium cation of the ionic liquid. The authors found that increasing cation ([Im]+) concentration caused a positive shift in the half-wave potential for the reaction. The redox peaks of the O2|O2•- became unsymmetrical, and a diffusion coefficient of superoxide, DO2•-, significantly smaller than that of oxygen, DO2, was observed. It was concluded, by consideration of the association constant and the free energy change for the complexation reaction, that ion-pairing of O2•- with [Im]+ is comparable with that observed between O2•- and H2O (in DMSO). The current paper addresses the “strange” voltammetry observed for the reduction of oxygen in the RTIL 1-butyl- 2,3dimethylimidazolium bis(trifluoromethylsulfonyl)imide, [C4dmim][N(Tf)2], and measures a diffusion coefficient and solubility for oxygen (O2) in this ionic liquid. In the experimental voltammetry the oxidative peak is found to be shifted to more positive potential than would be expected for a simple oneelectron transfer. This paper fully and quantitatiVely models the reduction of oxygen as an EC process at a microdisc electrode, and the fitting of the experimental data allows extraction of diffusioncoefficientsforsuperoxide(O2•-)andthecation-superoxide ion pair ([C4dmim]+ · · · O2•-), along with kinetic parameters for the homogeneous and heterogeneous processes. The experi-
Barnes et al. mental work that was carried out, and the simulation strategy that was adopted allows us to gain a detailed understanding of the mechanism of oxygen reduction, which is fully described in this work. 2. Mathematical Model and Numerical Simulation 2.1. Simulation Procedure. The numerical simulation procedure described in this section is used to model the reduction of oxygen and the subsequent association of the electrogenerated radical anion with the solvent cation as an ECrev process. Using the Testa and Reinmuth notation,19 E represents an electrochemical step which is followed by a reversible homogeneous chemical step, C. Here we simulate the one-electron oxidation given in eq 4 at a microdisc electrode of radius rd followed by the homogeneous process given in eq 5. In this work species A corresponds to O2, B to O2•-, and C to the [C4dmim]+ · · · O2•- complex. In this scheme kf and kb represent the first-order rate constants for the forward and reverse homogeneous reactions, respectively. It is worth noting that the follow-up association step is modeled as a first-order process; as such the solvent does not appear in eq 5. This is because in this system the solvent cation is always present in much greater quantities than the superoxide radical anion. As a consequence, the homogeneous rate constants described in this work have units corresponding to a first-order homogeneous process.
A h B + e-
(4)
kf
B {\} C
(5)
kb
The normalized mass transport equations for the species involved in the EC mechanism are presented in eqs 7-9. The ∇2 term describes mass transport; this derives from a consideration of Fick’s second law in the cylindrical coordinate system we are using and is given by eq 6.
∇2 )
∂2 ∂2 1 ∂ + + ∂R2 ∂Z2 R ∂R
(6)
The remaining terms arise from the coupled homogeneous process.
∂a ) ∇2a ∂τ
(7)
∂b ) ∇2b - Kf b + Kbc ∂τ ∂c ) ∇2c - Kbc + Kf b ∂τ
(8) (9)
In this model, space is described by the normalized (R,Z)coordinate system, where the normalized radial coordinate, R, is given by r/rd and the normal coordinate, Z, is given by z/rd. Species A, B, and C are described by their normalized concentrations, a, b, and c, and time, t, is normalized to the dimensionless τ as defined in Table 1. The homogeneous
TABLE 2: Boundary Conditions for Linear Sweep Cyclic Voltammetry boundary
condition for A
condition for B
τ ) 0, all r, z z ) 0, r > rd z ) 0, r e rd z g 0, r ) 0 z f ∞, r g 0 z g 0, r f ∞
a)1 (∂a/∂z) ) 0 (∂a/∂z) ) K0(e-Rθa0 - e(1-R)θb0) (∂a/∂r) ) 0 a)1 a)1
b)0 (∂b/∂z) ) 0 DA(∂a/∂z) ) -DB(∂b/∂z) (∂b/∂r) ) 0 b)0 b)0
condition for C c)0 (∂c/∂z) ) 0 (∂c/∂z) ) 0 (∂c/∂r) ) 0 c)0 c)0
Reduction of O2 in [C4dmim][N(Tf)2]
J. Phys. Chem. C, Vol. 112, No. 35, 2008 13711
TABLE 3: Electrode Boundary Conditions for Double Step Chronoamperometry, i.e., Where r e rd boundary
condition for A
condition for B
condition for C
τ e τf/2
a)0
(∂c/∂z) ) 0
τ > τf/2
DA(∂a/∂z) ) -DB(∂b/∂z)
DA(∂a/∂z) ) -DB(∂b/∂z) b)0
(∂c/∂z) ) 0
TABLE 4: Boundary Conditions for Double Step Chronoamperometry boundary τ ) 0, all r, z z ) 0, r > rd z g 0, r ) 0 z f ∞, r g 0 z g 0, r f ∞
condition for A
condition for B
condition for C
a)1 (∂a/∂z) ) 0 (∂a/∂r) ) 0 a)1 a)1
b)0 (∂b/∂z) ) 0 (∂b/∂r) ) 0 b)0 b)0
c)0 (∂c/∂z) ) 0 (∂c/∂r) ) 0 c)0 c)0
rate constants, kf and kb, are expressed as the dimensionless rate constants Kf and Kb defined in Table 1, and the ratio of these parameters is of course the dimensionless equilibrium constant for the coupled chemical step, Keq ) Kf/Kb. The mass transport equations are discretized over an appropriate simulation grid and solved using the alternating direction implicit (ADI) method20 coupled with the Thomas algorithm21 adapted for a seven diagonal matrix. The simulation grid is constructed such that the mesh density is greatest around the singularity at R ) 1 and adjacent to the electrode surface at Z ) 0. The exponentially expanding grid spacings are described by the mesh spacing adjacent to these points, h0, and the expansion factor, γ, as described by Gavaghan.22 Therefore, the spacing at the jth line is given by h0γj. We obtain the concentration profiles for species A, B, and C by solving the normalized mass transport equations subject to the boundary conditions given in Tables 2-4 depending on the electrochemical technique being modeled. The dimensionless diffusional flux is calculated from the concentration profile of species A using second-order finite difference methods and eq 10.
j)
∂a ∫01 ( ∂Z )z)0R dR
(10)
The corresponding Faradic current, I, is related to the dimensionless flux by eq 11.
i ) 2πnFDard[A]bulk j
(11)
The simulation procedure described is now applied to the cases of linear sweep cyclic voltammetry and double potential step chronoamperometry at a microdisc electrode. 2.2. Linear Sweep Cyclic Voltammetry. When simulating cyclic voltammetry, the dimensionless potential, θ, defined as (F/RT)(E - Ef), is swept from an initial value, θi, to a more reducing potential, θf, and then back to the initial value. The value of θ is therefore calculated at any time on the forward sweep using eq 12 and on the reverse sweep using eq 13, where σ is the dimensionless scan rate and τ is the dimensionless time as defined in Table 1.
θ ) θi + στ
(12)
θ ) 2θf - θi - στ
(13)
The boundary conditions appropriate to the simulation of linear sweep cyclic voltammetry are given in Table 2. The boundary condition at the electrode surface given in eq 14 derives from Butler-Volmer kinetics describing electron transfer where K0
Figure 1. Dimensionless potential-time plot for the double potential step experiment.
is the dimensionless heterogeneous rate constant defined in Table 1 and R is the transfer coefficient.
( ∂a∂z ) ) K (e
-Rθ
0
a0 - e(1-R)θb0)
(14)
2.3. Double Step Chronoamperometry. When performing a double step chronoamperometric experiment, the potential is held at a value corresponding to negligible current flow until the start of the experiment at τ ) 0. Here the potential is instantaneously stepped to a value at which diffusion-controlled reduction of species A f B occurs. The potential is held at this value until τ ) τf/2, at which point it is instantaneously stepped back to the initial value (corresponding to diffusion-controlled oxidation of B f A) and is held here until τ ) τf. A generalized potential-time scheme for the experiment is given in Figure 1. In this simulation we employ an expanding time grid in order to reduce the overall number of timesteps and therefore computation time while maintaining a high density of timesteps after the changes in potential. We require this mesh density of timesteps because immediately after the potential steps occur the concentration gradient adjacent to the electrode surface is changing rapidly. At longer times the response is almost steady state, and so the concentration gradient at the electrode surface is undergoing much smaller changes; this permits the use of a more widely spaced time grid with negligible loss of accuracy. The time grid expands as τ in line with diffusion layer thickness and was found to be stable and fully converged. When simulating the double step experiment, the mass transport equations are solved using the procedure described in section 2.1 subject to the boundary conditions given in Tables 3 and 4. For 0 e τ e τf/2 the boundary condition at the electrode surface is a ) 0; this corresponds to a large negative potential which causes diffusion-controlled reduction of A to B. For τf/2 < τ e τf the boundary condition at the electrode surface is b ) 0, which corresponds to a large positive potential which drives the diffusion-limited oxidation of B back to A. 3. Experimental Section 3.1. Chemical Reagents. Ferrocene (Fe(C5H5)2, Fc, Aldrich, 98%), acetonitrile (Fischer Scientific, dried and distilled, >99%), tetra-n-butylammonium perchlorate (TBAP, Fluka, Puriss electrochemical grade, >99%), and oxygen (BOC, Surrey, UK) were used as received without further purification. 1-Butyl-2,3dimethylimidazoliumbis(trifluoromethylsulfonyl)imide,[C4dmim]-
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Barnes et al.
Figure 2. Structure of the cation and anion used as the RTIL in this study.
[N(Tf)2] (see Figure 2 for structure), was prepared using standard literature methods23 from the corresponding chloride salt. 3.2. Instruments. Electrochemical experiments were performed using a computer-controlled µ-Autolab potentiostat (EcoChemie, Netherlands). A conventional two-electrode arrangement was employed to study the voltammetry, with a platinum electrode (10 µm diameter) as the working electrode and a silver wire (0.5 mm diameter, Goodfellow Cambridge Ltd.) quasireference electrode. Alumina slurry (1.0 and 0.3 µm) on soft lapping pads (both Buehler, Illinois) was used to polish the electrode surface. The electrode diameter was calibrated electrochemically by analyzing the steady-state voltammetry of a 2 mM solution of ferrocene in acetonitrile containing 0.1 M TBAP, using a value for the diffusion coefficient of 2.3 × 10-9 m2 s-1 at 298 K.24 A small section of disposable pipet tip was used to modify the working electrode, creating a cavity into which a drop (ca. 20 µL) of ionic liquid solvent was placed. The electrodes were housed in a glass cell25,26 specially designed for investigating microsamples of ionic liquids under a controlled atmosphere. All experiments were carried out in a Faraday cage, thermostated at 298 ( 1 K, which also served to minimize background noise. The ionic liquid was purged under vacuum until the baseline showed little or no traces of impurities. At this point, oxygen gas was introduced via one arm of the T-cell. The gas was then left to diffuse through the sample of the ionic liquid until equilibration between gaseous and dissolved oxygen was reached (typically after 10 min). An outlet gas line led from the other arm of the cell into a fume cupboard to avoid buildup of gas in the Faraday cage. 3.3. Double Potential Step Chronoamperometric Experiments. Double potential step chronoamperometric transients for the reduction of oxygen were achieved using a sample time of 0.001 s. The potential was held (pretreated) at -0.60 V (corresponding to zero faradaic current) for 20 s, after which the experimental transients were obtained by stepping the potential to a position after the reduction peak, and the current was measured for 0.50 s. The potential was then stepped back to the starting potential (-0.60 V), and the current was measured for a further 0.50 s. A nonlinear curve fitting function available in OriginPro 7.5 (Microcal Software Inc.) was used to extract diffusion coefficient and solubility data from the first potential step of the experimental transients. The data were theoretically fitted using the Shoup and Szabo27 approximation for the timedependent current response at microdisc electrodes. The equations used in this approximation (eqs 15-17) sufficiently describe the current response to within 0.6% accuracy.
I ) -4nFDcrd f(τ)
(15)
-1/2
+ 0.2146 exp(-0.7823τ
τ)
4Dt rd2
f(τ) ) 0.7854 + 0.8863τ
-1/2
) (16) (17)
where n is the number of electrons transferred, F is the Faraday constant, D is the diffusion coefficient, c is the initial concentra-
Figure 3. CV for the reduction of oxygen on a platinum microelectrode (diameter 10 µm) in [C4dmim][N(Tf)2] at varying scan rates (10, 20, 50, 100, 200, 400, 700, 1000, 2000, 4000, 7000, and 10 000 mV s-1). Inset is the experimental (s) and fitted theoretical (O) chronoamperometric transients recorded for the reduction of O2. The potential was stepped from -0.50 to -1.75 V.
tion of parent species, rd is the radius of the disc electrode, and t is the time. By fixing the value for the radius of the electrode (determined previously from calibration), it is possible to obtain values for diffusion coefficient (D) of the species and the product of the number of electrons multiplied by concentration (nc). The experimental data for the second chronoamperometric potential step were utilized in the simulation process detailed in section 2. 4. Results and Discussion After purging the ionic liquid under vacuum to remove all atmospheric oxygen and water vapor, oxygen was added to the T-cell (described in section 3.2) in controlled amounts, and cyclic voltammograms were recorded periodically to ensure that the reduction wave due to added oxygen had reached a maximum (this occurred after ∼10 min for 20 µL of ionic liquid). Electrochemical measurements were made only after full equilibration had occurred. 4.1. Electrochemical Reduction of Oxygen in [C4dmim][N(Tf)2]. Figure 3 shows typical cyclic voltammetry for the reduction of oxygen at a 10 µm diameter Pt microelectrode in [C4dmim][N(Tf)2]. Oxygen is reduced by one electron to give stable superoxide, O2•-, at a peak potential of -1.58 V vs Ag, which is subsequently reoxidized to oxygen at a potential of -0.88 V (at 10 000 mV s-1), corresponding to eq 1. The asymmetry of the voltammetry is discussed in section 4.2. Potential step chronoamperometric techniques were performed to determine values for the diffusion coefficient, D, and solubility, c, of oxygen in this RTIL, and the resulting reductive transient (s) is shown as an inset to Figure 3 along with the best theoretical fit (O) to the Shoup and Szabo27 equation. The potential was stepped from -0.60 to -1.75 V (and then back to -0.60 V) vs Ag, and upon analysis of the transient for the reduction of O2, average values of (3.90 ( 0.07) × 10-10 m2 s-1 and 5.34 ( 0.06 mM were determined for D and c of oxygen in [C4dmim][N(Tf)2] (88 cP)28 at 298 K, respectively. These values are in good agreement with those published previously in this ionic liquid (D of 2.10 × 10-10 m2 s-1 and c of 7.20 mM at 293 K,29 bearing in mind that an increase in temperature is expected to provoke both an increase in diffusion coefficient and a decrease in gas solubility, owing to a reduction in the viscosity of the ionic liquid). Diffusion coefficients have also been reported in other RTILs, and they are all comparable in magnitude to values determined experimentally in this work: 7.30 × 10-10, 2.20 × 10-10, and 1.50 × 10-10 m2 s-1 for [C2mim][N(Tf)2]12 (28 cP),10 [C4mim][PF6]3 (275 cP),10 and
Reduction of O2 in [C4dmim][N(Tf)2] [N6, 2, 2, 2][N(Tf)2]12 (167 cP)10 at room temperature, with solubilities of 3.90, 3.60, and 11.60 mM, respectively. A diffusion coefficient of 4.80 × 10-11 m2 s-1 was also reported for oxygen in an imidazolium chloride-aluminum chloride molten salt at 298 K (21 cP).15 Note that the usual Stokes-Einstein relationship30 (inverse proportionality between diffusion coefficient, D, and viscosity, η), which applies for organic molecules,31 ferrocene,32 and cobaltocenium hexafluorophosphate,32 does not apply for oxygen diffusion in ionic liquids,13 as the O2 molecule is too smallsthis is also the case for H2,33 SO2,34 and H2S.35 These values are 1-2 orders of magnitude slower than the diffusion coefficient of oxygen in water (19.0-21.2) × 10-10 m2 s-1)36,37 as well as various aprotic solvents (21 × 10-10 m2 s-1 in DMSO, 47.5 × 10-10 m2 s-1 in DMF, and 110 × 10-10 m2 s-1 in MeCN6), and this is reasonable considering the differences in viscosities (η) of the solvents (28-275 cP10 for RTILs vs 0.34-2.00 cP38 for aqueous and aprotic solvents, all at 298 K). 4.2. Discussion of Experimental Voltammetry. As mentioned in section 4.1, Figure 3 shows the cyclic voltammetry for the reduction of oxygen and subsequent oxidation of superoxide in [C4dmim][N(Tf)2]. The asymmetry of the CV observed is due to a difference in the diffusion type of the neutral and radical anion oxygen species. The reduction of O2 to O2•is dictated by quasi-hemispherical diffusion as a result of the faster diffusion rate of oxygen through the solvent and leads to more steady-state-like behavior. The charged superoxide species diffuses more slowly through the ionic liquid media compared to the neutral species,12 and so the oxidation of O2•- to O2 is dictated by more planar diffusion, resulting in a reverse wave which is more peak shaped (transient).13 The differences in diffusion between the two species leads to a large discrepancy in the diffusion coefficients of O2 and O2•-; they vary by up to a factor of 30 in RTILs compared to just 3 in acetonitrile.12 As discussed above and by Evans et al.,13 the voltammetry observed is asymmetric, with a marked positive shift in the potential of the back peak. This result is typical of a system in which strong association between the electrogenerated superoxide species and the RTIL cation is is encountered; in this system the ion pair formed is [C4dmim]+ · · · O2•-. The formation of this ion pair is most likely due to the electrostatic interaction of O2•- with [C4dmim]+ onlyshydrogen bonding is not possible because the imidazolium ring lacks an acidic hydrogen on the 2-position carbon. The formation of the complex impedes the back-electron transfer, and the oxidation peak becomes shifted to a more positive potential than would be expected if this follow-up chemical step did not occur. 4.3. Fitting of Experimental Data. Initially, our simulations were based upon a simple one-electron reduction model in the absence of coupled homogeneous kinetics. However, this approach completely failed to provide a set of parameters (k0, R, DA, and DB) giving an acceptable fit for both the forward and reverse peaks simultaneously. Therefore, in this section we make use of the ECrev simulation procedure described fully in section 2. This models the association of the superoxide radical anion with the solvent cation as observed experimentally in ref 14 as a coupled reversible homogeneous step. Therefore, the parameters used to fit the forward and reverse peaks are k0, R, DA, DB, DC, kf, and Keq. The optimized parameters used to simulate the voltammetry shown in Figure 4 were k0 ) 1.1 × 10-5 m s-1, R ) 0.3, DA ) 3.90 × 10-10 m2 s-1, DB ) 3.51 × 10-11 m2 s-1, DC ) 7.02 × 10-12 m2 s-1, kf ) 1.44 × 103 s-1, and Keq ) 25. These values are found to provide an excellent fit over a wide range of scan rates and are in good
J. Phys. Chem. C, Vol. 112, No. 35, 2008 13713
Figure 4. Comparison of experimental (O) and simulated (s) voltammograms for (a) 100 mV s-1 and (b) 1000 mV s-1.
agreement with work published previously for similar systems. Evans et al.13 report values of k0 ) 8.0 × 10-6 m s-1 and R ) 0.35 for the reduction of oxygen in [Py14][N(Tf)2], and in the experimental work carried out by Islam14 an equilibrium constant of 13.5 M-1 is estimated independently for the following process: [C4mim]+ + O2•- h [C4mim]+ · · · O2•-. The dielectric constant for [C4dmim][N(Tf)2] has been reported as 11.5.39,40 The value of Keq obtained from the simulations is consistent with that expected for strong ion pairing in a low dielectric medium. Attempts to fit the experimental voltammetry shown in Figure 3 without accounting for the interaction of the electogenerated radical anion with the solvent cation resulted in a simulated reverse peak situated at a more negative potential than that of the experimental reverse peak. This result is observed at all scan rates but is most noticeable at faster scan rates. The inclusion of coupled homogeneous kinetics is therefore essential if a satisfactory fit is to be achieved for both the forward and reverse peaks simultaneously. This is illustrated in Figure 5, which
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Figure 6. Comparison of experimental (O) and simulated (s) results for the complete double potential step experiment. Simulation was performed using the parameters described in section 4.3. At very short times after both potential steps the experimental response is distorted by double-layer charging effects, as such these points have been omitted from the plot.
parameters completely describing the system. These parameters have been shown to provide an excellent fit over a wide range of scan rates and have been utilized to independently fit the double potential step response. The excellent agreement between the simulated and experimental double potential step gives support to our suggested mechanism for the reduction of oxygen in [C4dmim][N(Tf)2]. The successful application of the ECrev mechanism to this system supports previous work on the role of ion pairing in RTIL electrochemistry, and this model will be useful for future work in this field. References and Notes
Figure 5. Comparison of experimental (O) and simulated (s) voltammograms without a follow-up reversible chemical step for (a) 100 mV s-1 and (b) 1000 mV s-1.
compares the experimental voltammetry to that simulated without accounting for ion-pairing effects. To further support the optimized parameters found from the simulations they were used to simulate the double step chronoamperometic response without any further refinement. Figure 6 shows good agreement between the simulated and experimental transients and as such completely supports the values found from fitting the voltammetry and our suggested mechanism. 5. Conclusions In this work we have successfully modeled the experimental voltammetry obtained for the reduction of oxygen in [C4dmim][N(Tf)2]. The success of this model has been shown to be the result of including a follow-up homogeneous step accounting for the strong ion-solvent pairing effects observed in these RTILs. This strategy has enabled us to fit the forward and reverse peaks simultaneously and to extract a set of
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