The Electro-reduction of Carbon Dioxide in Dimethyl Sulfoxide at

The electro-reduction of carbon dioxide is studied by linear sweep and cyclic .... A solution to eq 13 is sought with the following boundary condition...
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J. Phys. Chem. B 2001, 105, 5253-5261

5253

The Electro-reduction of Carbon Dioxide in Dimethyl Sulfoxide at Gold Microdisk Electrodes: Current | Voltage Waveshape Analysis Peter J. Welford,† Benjamin A. Brookes,† Jay D. Wadhawan,† Hanne B. McPeak,‡ Clive E. W. Hahn,‡ and Richard G. Compton*,† Physical and Theoretical Chemistry Laboratory, Oxford UniVersity, South Parks Road, Oxford OX1 3QZ, United Kingdom, and Nuffield Department of Anaesthetics, Oxford UniVersity, Radcliffe Infirmary, Oxford OX2 6HE, United Kingdom ReceiVed: February 7, 2001

The electro-reduction of carbon dioxide is studied by linear sweep and cyclic voltammetry in DMSO electrolyte solutions and at polycrystalline gold microdisk electrodes. An electrode reaction pathway is suggested. Numerical simulation of the reaction mechanism gives current | potential waveshapes in excellent agreement with those observed experimentally. Kinetic parameters for the reduction process are deduced from this waveshape approach, and the charge-transfer coefficient is found to be approximately 0.43 ( 0.05.

Introduction The electro-reduction of carbon dioxide in nonaqueous solvents at gold electrodes has been extensively proposed as the basis for amperometric sensors for CO2, for example in the measurement of exhaled or blood gases in medicine.1-9 The merits of nonaqueous solvents as opposed to water include the higher solubility of CO2 and improved cathodic potential window, so avoiding hydrogen evolution as a competing reaction. The most popular solvent for this purpose has proved to be dimethyl sulfoxide (DMSO) with tetraethylammonium perchlorate (TEAP) or similar as the supporting electrolyte.3-14 Very recently,6-9 the use of microelectrodes for this purpose has been advocated; a major advantage is the possibility of simultaneous determination of carbon dioxide and oxygen via their electro-reductive currents at different voltages. At macroelectrodes, the two signals are not independent of each other, as chemical reactions involving intermediates derived from CO2 and O2 can occur. At microelectrodes, the kinetics for these reactions are “out run” by the much faster diffusional loss of the species from the electrode | electrolyte interface, and hence the oxygen and carbon dioxide signals become independent of each other. The mechanism of the reduction of CO2 at gold electrodes in nonaqueous solvents is of considerable importance to the sensor design as outlined above. However, surprisingly little is known except that the main reaction products10 are oxalate and/ or CO and CO32-:

2CO2 + 2e- f C2O42-

adsorbed CO2-• is an intermediate.15 In this paper we build upon this observation and examine how the use of current/voltage waveshapes at microdisk electrodes can shed further insight on the mechanism of CO2 reduction in DMSO. Theory We consider the reduction of carbon dioxide at a metallic electrode. Following the work by Vassiliev et al.,16 and Amatore and Save´ant,17 two mechanistic pathways in aprotic media may be envisaged. Mechanism A kD

+e-,fast

(CO2)2-• 98 products Mechanism B kD

2CO2 + 2e f CO + CO3

so that one electron is consumed per molecule of CO2 reacting. For the case of CO2 reduction in DMSO, it is known that * Author to whom correspondence should be addressed. Tel.: +44 (0) 1865 275 413. Fax: +44 (0) 1865 275 410. E-mail: compton@ ermine.ox.ac.uk. † Physical and Theoretical Chemistry Laboratory, Oxford University. ‡ Nuffield Department of Anaesthetics, Oxford University, Radcliffe Infirmary.

+CO2-•,k2,slow

k1

CO2 (bulk) 98 CO2 (surf) 98 CO2-• (ads) 98 products where (surf) refers to a solution species adjacent to the electrode surface. Correspondingly, (ads) refers to a species adsorbed onto the electrode surface. In the above mechanisms, kD refers to the rate of diffusion of CO2 from bulk solution to the electrode surface, which for a macroelectrode may be estimated from eq 1,

kD ) 2-

+CO2,k2,slow

k1

CO2 (bulk) 98 CO2 (surf) 98 CO2-• (ads) 98

D δ

(1)

in which D refers to the diffusion coefficient of CO2 in the solution, and δ defines the diffusion layer thickness of the electrode. The rate of formation of the radical anion created by the heterogeneous transfer of an electron is characterized by the rate constant k1, and k2 parametrizes the rate of the followup reaction to form the reaction products. This latter event may occur either by the reaction of CO2-• and its subsequent slow reaction with carbon dioxide molecules from the diffusion layer of the electrode, immediately followed by the fast heterogeneous

10.1021/jp010467b CCC: $20.00 © 2001 American Chemical Society Published on Web 05/12/2001

5254 J. Phys. Chem. B, Vol. 105, No. 22, 2001

Welford et al.

transfer of a second electron at the electrode surface (Mechanism A), or by the slow, rate-determining dimerization of adsorbed CO2-• molecules (Mechanism B). We consider these two pathways separately. Mechanism A. The rate of diffusion of CO2 to the electrode surface and those for the adsorption and transfer of the first electron to CO2, and the desorption of CO2-• are given by eq 2.

rate of diffusion ) kD([CO2]bulk - [CO2]surf)

(2a)

rate of adsorption and electron transfer ) 0 k1[CO2]surf (1 - ΘCO2-•)e-RF(E-E ′)/RT (2b) rate of reaction ) k2ΘCO2-•[CO2]surf

(2c)

In the above expressions, ΘCO2-• refers to the fractional coverage of adsorbed radical anion, R, the charge-transfer coefficient, F, the Faraday constant, R, the universal molar gas constant, T, the absolute temperature, (E - E0′), the overpotential required for the reduction of CO2 at the electrode, and E0′, the formal potential for the redox reaction. Since the rate-determining step is, by hypothesis, the reaction of CO2-• with unreacted CO2, under steady-state conditions, we may equate eqs 2a,b,c. Thus, from eqs 2b and 2c we obtain a Langmurian expression for the surface coverage of the radical anion,

ΘCO2-• )

K[CO2]surf 1 + K[CO2]surf

(3)

in which

k1e-RF(E-E ′)/RT 0

K)

k2[CO2]surf

(4)

Equation 3 may be expressed more succinctly as in eq 6 by defining K′ as in eq 5:

K′ ) K[CO2]surf

(5)

K′ ΘCO2-• ) 1 + K′

(6)

Thus, the fractional surface coverage of adsorbed radical anion is a function of the applied electrode potential (E). It follows from eq 2b that the rate of electron transfer is

rate ) k1[CO2]surf

0 1 e-RF(E-E ′)/RT 1 + K′

(7)

adsorbed radical anions, 2 rate of reaction ) k2ΘCO •2

(2d)

Comparing eqs 2b and 2d yields a quadratic equation in terms of the fractional surface coverage of CO2-•, 2 (10) ΘCO •- + K′′[CO2]surfΘCO -• - K′′[CO2]surf ) 0 2 2

in which

k1 -RF(E-E0′)/RT e k2

K′′ )

(11)

Mechanism A at Microdisk Electrodes. We next turn to the numerical modeling of Mechanism A at microdisk electrode geometries, and under steady-state conditions. The diffusiononly mass transport of CO2 to a microdisk electrode is given in cylindrical polar coordinates as

{

∂2a ∂2a 1 ∂a ∂a )D 2+ 2+ ∂t r ∂r ∂z ∂r

}

(12)

where a ) [CO2]/[CO2]bulk, D is the diffusion coefficient of CO2, z is the distance normal to the electrode, and r is the radial coordinate. Equation 12 may be rewritten in dimensionless form at steady-state as

∂2a ∂2a 1 ∂a + + )0 ∂Z2 ∂R2 R ∂R

(13)

where R ) r/re, Z ) z/re, and re is the radius of the electrode. A solution to eq 13 is sought with the following boundary conditions:

a)1 a)1 ∂a/∂Z|Z)0 ) 0

Rg0 Rf∞

Zf∞ Zg0

R>1

Z)0

∂a/∂R|R)0 ) 0

R)0

Zg0

From the proposed mechanism, the diffusive flux of CO2 to the electrode surface at steady-state is equal to the rate of depletion of the surface concentration of CO2 through the electrochemical reaction k2. Hence the electrode boundary condition can be defined as

∂a/∂Z|Z)0 ) k′eff a|Z)0

Re1

Z)0

where k′eff is the dimensionless rate constant such that which can be more conveniently expressed as

rate ) keff[CO2]surf where

keff )

k1 -RF(E-E0′)/RT e 1 + K′

k′eff )

(8)

keffRe D

(14)

We are interested in determining the current at the electrode, and therefore evaluating the equation

(9)

We return to this mechanism below, in the context of predicting the current | potential waveshapes at a microdisk electrode. Mechanism B. Equations 2a and 2b again hold for the rate of diffusion of CO2 to the electrode surface, and for the adsorption and first electron transfer. However, the rate of product formation is given by the surface reaction of two

I ) 2πReFD[CO2]bulk

∂a ∫01(∂Z )Z)0R dR

(15)

where F is the Faraday constant. We may alternatively consider a dimensionless current, ψ, which is given by

ψ)

π 2

∂a ∫01(∂Z )Z)0R dR

(16)

Electro-reduction of CO2 in DMSO

J. Phys. Chem. B, Vol. 105, No. 22, 2001 5255

Previous work suggests using a conformal map devised by Amatore and Fosset18-20 will be an efficient method for solving the above problem. The conformal map demands the following change of variables:

Z ) θtan( /2πΓ), R ) 1

x1 - θ2 cos(1/2πΓ)

Γ is the transformed radial distance, ranging from 0 to 1, corresponding to real distances of 0 and infinity. θ is the transformed angular component sweeping between normal to the electrode (θ ) 0) and parallel to the electrode (θ ) 1). Mass transport eq 13 is transformed to

{

∂2 a ∂ ∂a 4 1 2 π cos ( / Γ) + (1 - θ2) 2 2 2 π 2 2 ∂θ ∂θ [θ + tan ( /2Γ)] π ∂Γ

[

]} )

TABLE 1: Dimensionless Currents for Different Values of k′eff dimensionless current, ψ H

k′eff 0.1

k′eff 1.0

k′eff 10.0

0.04000 0.02000 0.01000 0.00500 0.00250 0.00125

0.850991 0.854080 0.856171 0.857367 0.858006 0.858335

0.425787 0.426148 0.426389 0.426527 0.426602 0.426640

0.072388 0.072393 0.072397 0.072399 0.072400 0.072401

and

λΓd )

4ω cos2(1/2 πΓ) ω(1 - θ2) -ωθ , λ ) , λθs ) θd 2 2 2 ∆θ π (∆Γ) (∆θ)

The discretised finite difference forms of the boundary conditions applicable to eq 19 are

3(Γ, θ)2 a ) 0 (17) and the boundary conditions applicable are

uNJ+1,k ) 1

k ) 1,...NK

uj,NK+1 ) uj,NK

j ) 1,...NJ j ) 1,...NJ

a)1 ∂a/∂q|θ)0 ) 0

1 g θ g 0;

Γ)0

uj,l ) uj,0

θ ) 0;

1gΓg0

∂a/∂R|θ)1 ) 0

θ ) 1;

u1,k ) u0,k 1 +

1gΓg0

2 ∂a ) k′eff a|Γ)0 πθ ∂Γ Γ)0

1 g θ g 0;

Γ)0

( )

(

∫0

1

|

∂a dθ ∂Γ Γ)0

(18)

To find the solution to partial differential eq 17, we approximate the real solution a at locations θk, Γj by the unknown concentration vector u. The location θk, Γj is defined as:

θk ) k∆θ

k ∈ N; 1 e j e Nk

Γj ) j∆Γ

k ∈ N; 1 e k e Nk

∆Γ )

1 1 and ∆θ ) NJ + 1 NK + 1

We use a second-order central difference approximation to obtain discretised mass transport equations which may be written in 5-point stencil form as

qj,k ) aj,kuj,k-1 + bj,kuj-1,k + cj,kuj,k + dj,kuj,k+1 + ej,kuj+1,k j ) 1...NJ; k ) 1...NK where

aj,k ) λθd - λθs bj,k ) (λΓd)uj-1,k cj,k ) -2λΓd - 2λθd dj,k ) λΓd ej,k ) λθd + λθs qj,k ) 0

(19)

k ) 1,...NK

The resulting NK × NJ linear equations may now be rewritten into a matrix-vector equation as

q ) Mu

The dimensionless current, ψ, in this coordinate system is

ψ)

)

k′effπθ∆Γ 2

(20)

where M is a pentadiagonal matrix. The dimensionless current is evaluated using trapezoid quadrature such that

ψ)

∫0

1

∂u ∂Γ

|

Γ) 0

dθ ≈

[

NK-1 ∆θ 3 3 u1,k + u1,NK u1,1 + ∆Γ 2 2 k)2

∑

]

(21) Note the no flux boundary condition imposed at the center of electrode and insulating surround results in the factor of 3/2 rather than 1/2 for the edge nodes in the summation. Computation To solve eq 20, we employ the NAG library F11 (preconditioned Krylov subspace) methods. These have been tested by Alden for a variety of complex electrochemical reactions20,21 and shown to be successful at solving the ill-conditioned linear system of equations produced with the Amatore transformation where other methods (e.g., Multigrid22) may fail. In particular we use an incomplete LU preconditioner23 (F11ZAF, F11BAF) and the BICGSTAB(l),24,25 CGS,26 and RGMRES27 methods (F11DCF) to solve the resulting linear system of equations. The simulation code was written in C++. Callable IDL was used to display run-time graphical results. The code was run on a Silicon Graphics Indigo2 with an R4400 processor and 192 Mb of RAM. Data were analyzed using MATLAB 5.1. Copies of the program are available on request from the authors. Testing showed that the optimum method28 was to use a modified incomplete LU factorization preconditioner (LFILL ) 0) followed by the BICGSTAB solver (l ) 3). Convergence. The convergence of the dimensionless current was considered for three values of k′eff on increasingly fine grids. Each grid had equal values of NK and NJ such that ∆θ ) ∆Γ ) h. The results are shown in Table 1. To investigate the nature of the convergence, we begin by assuming that the error between

5256 J. Phys. Chem. B, Vol. 105, No. 22, 2001

Figure 1. Working curve for the reduction of CO2 based upon Mechanism A (see text).

the limit of ψ as h tends to 0, and the simulated value of ψ(ψNsimJ,NK) varies as Chn, where C is an unknown constant for each value of k′eff. From the data in Table 1, the empirical values29 of n are 0.722, 0.728, and 0.659 for k′eff 0.1, 1.0, 10.0, respectively. Extrapolation to predict limhf0ψ shows to be accurate to 0.34% for the case where k′eff 0.10. ψ100,100 sim Therefore despite the low rate of convergence, we conclude that the Amatore and Fosset transformation is an accurate method for the determination of the currents for the proposed mechanism. Theoretical Results. To analyze the data, a series of solutions were performed on a grid of size NK ) 100, NJ ) 100 for values for k′eff between 10-4 and 104 to build up a working curve as shown in Figure 1. This illustrates how the steady-state limiting dimensionless current varies between zero at very low values of k′eff, and unity at high values of k′eff. The latter limit represents the transport limited current of a species diffusing from bulk solution to a microdisk electrode. Since both ψ and k′eff are dimensionless, the working curve alone proves sufficient to predict the current, I, for any values of keff, D, and Re by using eqs 14 and 15. Experimental Section Chemical Reagents. Solvents used for electrochemical experiments were dimethyl sulfoxide (DMSO, Spectrosol grade, BDH Chemicals Ltd.), acetonitrile (Fisons, dried and distilled) or demineralized, deionized, and filtered water with a resistivity greater than 18 MΩ cm, taken from an Elgastat water purification system (USF Ltd., Bucks., U.K.). DMSO was carefully purified and dried as outlined below. Supporting electrolytes were tetraethylammonium perchlorate (TEAP), tetrabutylammonium perchlorate (TBAP), tetraethylammonium nitrate (TEAN, all Fluka), tetrabutylammonium nitrate (TBAN) or KCl (both Aldrich). K3Fe(CN)6 and ferrocene were also purchased from Aldrich. These chemicals were all obtained in the highest commercially available grade and used without further purification, except where described below. Carbon dioxide (MG Gases, U.K.) and impurity-free oxygen and nitrogen (BOC, Guildford, Surrey, U.K.) were used for electrochemical experiments as outlined below. Instrumentation. For electrochemical experiments, a commercially available potentiostat (PGSTAT30, Eco Chemie, Netherlands) controlled by a Pentium III computer was used. The small-volume electrochemical cell (ca. 10 cm3) consisted of a three-electrode arrangement with a gold wire counter electrode and, unless otherwise stated, a silver wire pseudoreference electrode (Goodfellow Cambridge Ltd., Cambridge, U.K.). Dry DMSO (vide infra) and TEAP were the chosen solvent and supporting electrolyte from previous work.3,4,6-9 The electrochemical cell was shielded from direct sunlight, to

Welford et al. minimize light-accelerated DMSO disproportionation.30 The working electrode employed was a gold microdisk electrode of various diameters (nominally 5 µm, 10 µm, Microglass Instruments, Greensborough, Australia; 25 µm, constructed in house). These electrodes comprise gold wires sealed in borosilicon glass, the ends of which were polished to reveal the microdisk surface. Platinum and glassy carbon microdisk electrodes with nominal diameters of 10 and 5 µm, respectively, (Microglass Instruments, Greensborough, Australia) were also, for comparative purposes, employed as the working electrode. These microdisk electrodes were all carefully polished31 according to the recipe outlined below. First, the electrode was ground gently over an aqueous 1.0 µm alumina slurry (Buehler, Lake Bluff, IL) on glass using a figure-of-eight movement for ca. 10 s. Second, the electrode was polished over a 1.0 µm alumina slurry on a clean pad (Kermet, Kent, U.K.) for ca. 10 s. This was then followed by polishing for at least 30 s using a 0.3 µm alumina suspension (Buehler, Lake Bluff, IL), diluted by a factor of ca. three, on a clean napped polishing cloth (Microcloth, Buehler, Lake Bluff, IL). Having thoroughly rinsed the electrode with water between polishing procedures, the microdisk surface was briefly polished on a clean damp polishing cloth without alumina to remove surface-bound alumina particles, and subsequently dipped in 10% (v/v) aqueous nitric acid for 10 s to remove any adventitious adsorbates. Last, the electrode was washed in a solution of the solvent and supporting electrolyte into which it was to be used. The electrodes were visually inspected regularly using an optical microscope, to ensure that they were not recessed from the glass surface. Diameters of the microdisks were calibrated electrochemically using either 2 mM ferrocene in acetonitrile, 0.1 M TBAP (using a value for the diffusion coefficient as 2.3 × 10-5 cm2 s-1 as given by Sharp32) or a nitrogen-purged aqueous solution of 2 mM ferricyanide in 0.1 M KCl (with a value of D as33 0.763 × 10-5 cm2 s-1). All experiments were undertaken in a thermostated water bath at 25 ( 3 °C, unless stated otherwise. Carbon dioxide was introduced to the electrochemical cell in selected volume ratios from a Wo¨sthoff (Bochum, Germany) triple gas mixing pump (model 2M 302/a-F) which was accurate to ( 1% relative to the selected ratio. Nitrogen made up the rest of the gas mixture, while oxygen was required to constitute the third input to the pump, although its selected value was kept constant at 0 vol %. The CO2 gas concentrations ranged from 0 to 100 vol %. Gas mixtures were bubbled through DMSO solutions for at least 10 min prior to voltammetric interrogation, to ensure that full equilibration of the gases and solvent could be obtained; the gas supply to the electrochemical cell was stopped for the duration of each voltammetric measurement so as to ensure that measurements were taken in stationary solutions, under diffusion-only conditions. Bubbling was recommenced immediately thereafter. Purification of DMSO. Since DMSO is a hygroscopic liquid,30,34 the purchased material was further purified to remove residual water before use. Following Butler and Cogley,35 5A molecular sieves (Aldrich) were dried, first in an oven at 180 °C for at least 8 h, and then in a furnace at 500 °C for at least 16 h. The sieves were allowed to cool to room temperature in a desiccator containing anhydrous cobalt(II) chloride crystals and under an inert nitrogen atmosphere. Spectrosol grade DMSO was then treated with the cooled sieves for a period of one week. Immediately prior to its use, this DMSO was passed through an alumina column36a (ICN Alumina N-Super I, ICN Biomedicals, Eschwege, Germany). This alumina is also sold as Woelm W 200, neutral super grade I alumina, as recommended by ref

Electro-reduction of CO2 in DMSO

J. Phys. Chem. B, Vol. 105, No. 22, 2001 5257

Figure 2. Schematic of the double sinter reference electrode used for some experiments.

36. Following Parker and Hammerich,36a a leveled spatula of this alumina was added to the DMSO/supporting electrolyte solution before undertaking voltammetric experiments. Reference Electrode for DMSO Electrolyte Solutions. In some experiments, it was necessary to work with a reference electrode that provides a stable potential throughout the electrochemical experiment. There are few reported stable reference electrodes that are suitable for DMSO. The one that is recommended by most texts is the thallium amalgam/TlCl electrode.14,30,34 This was not used on safety grounds. Instead, a novel reference electrode, the design of which is given in Figure 2, was employed. It consists of a silver wire dipping into a 0.1 M solution of silver nitrate in DMSO, which is sealed in a glass tube with a ceramic frit (porosity 4) at one end. This was then placed into another glass cell with a porous frit (porosity 3) containing 0.2 M TBAN, so as to prevent the precipitation of insoluble salts (e.g., AgClO4) at the reference electrode, which would result in a potential drift This reference electrode was employed in cyclic voltammetric experiments with a gold microdisk working electrode and a gold wire counter electrode, as before, in 0.2 M TEAP/DMSO electrolytes.

Figure 3. Linear sweep voltammograms for the reduction of CO2 in 0.2 M TEAP/DMSO at (a) 12.2 µm Pt and (b) 6.1 µm C microdisk working electrodes, using a scan rate of 100 mV s-1. In both cases, (A) 10, (B) 20, (C) 40, and (D) 80 vol % CO2.

Results and Discussion The Solubility of Carbon Dioxide in DMSO Electrolyte Solutions. To calculate a diffusion coefficient for CO2 in DMSO electrolyte solutions from cyclic voltammetric data, the solubility of CO2 in both DMSO and 0.2 M TEAP/DMSO were determined using a dilatometric technique. This method is outlined in the Appendix, and the results are used in the analysis of voltammetric data below. Electrochemical Reduction of Carbon Dioxide at Platinum and Glassy Carbon Microdisk Electrodes. For comparative purposes, the electro-reduction of carbon dioxide was first undertaken at platinum and glassy carbon microdisk electrodes. Previous work in DMSO6 tested both these materials as the cathode. However, although voltammetry was observed at platinum electrodes, none was seen in the range 0 to -2.2 V vs Ag when glassy carbon cathodes were employed. The results of our CO2 reduction experiments using a 12.2 µm (diameter) Pt and a 6.1 µm (diameter) glassy carbon microcathode immersed in a 0.2 M solution of TEAP in DMSO are presented in Figure 3. Well-defined single reduction waves are observed at both platinum and glassy carbon microdisk cathodes, with average half-wave potentials of -1.6 and -1.9 V vs Ag, respectively. The irreversible nature of the electroreduction at both electrodes is illustrated by means of the Tomesˇ criterion37 in Table 2. Since it has been found6 that the electro-reduction on gold exhibits better defined electrochemistry than at platinum or carbon electrodes, we now turn to carbon dioxide electroreduction at gold electrodes; the voltammograms shown in Figure 3 are discussed quantitatively in the below sections, and are compared to the voltammetry at gold working electrodes.

Figure 4. Cyclic voltammograms (100 mV s-1 scan rate) for the reduction of CO2 in 0.2 M TEAP/DMSO at a 9.0 µm Au microdisk working electrode. (A) 10, (B) 15, (C) 20, (D) 40, and (E) 80 vol % CO2.

TABLE 2: Steady-State Cyclic Voltammetric Data for the Reduction of CO2 in DMSO at Gold, Platinum, and Glassy Carbon Microdisk Electrodes (A scan rate of 100 mV s-1 was employed.) electrode type and size

E1/2 /V vs Ag

E3/4 - E1/4| /mV vs Ag

Au 9.0 µm Pt 12.0 µm C 6.1 µm

-2.05 ( 0.01 -1.60 ( 0.05 -1.88 ( 0.02

141 ( 20 202 ( 40 284 ( 40

Electrochemical Reduction of CO2 in DMSO at Gold Microdisk Electrodes. Figure 4 shows the current | voltage curves corresponding to the reduction of various amounts of carbon dioxide at a 9.0 µm (diameter) gold microdisk electrode in dimethyl sulfoxide (DMSO) containing 0.2 M tetraethylammonium perchlorate (TEAP). The observed well-defined, sigmoidal-shaped curves are in agreement with previous

5258 J. Phys. Chem. B, Vol. 105, No. 22, 2001

Welford et al.

studies,6-9 which suggested that a one-electron-transfer process occurs. The average half-wave potential (E1/2) for this process is -2.0 ( 0.1 V vs Ag. At a scan rate of 100 mV s-1, the near superimposition of the forward and reverse sweeps suggests that the reduction and reoxidation processes occur under steadystate conditions. The process is electrochemically irreversible,37 with average |E3/4 - E1/4| ) 141 ( 20 mV at 25 °C. The cathodic potential window limit occurs between -2.4 and -2.8 V vs Ag, and can be attributed to supporting electrolyte discharge at the working electrode.17 Hahn et al.6 and Kilmartin and co-workers9 have shown that the limiting current observed for the reduction of CO2 at gold microdisk electrodes is linear with solution concentration of carbon dioxide. Analysis of the data in Figure 4 was undertaken in a similar manner, viz., the limiting current (ilim) was found to be proportional to vol % CO2, with a gradient of 226.3 nA (vol %)-1, and a Pearson’s Product Moment Correlation Coefficient (R) of 0.9998, confirming the assumption of Henry’s Law. Analogous plots for the 4.4 µm and 26.0 µm electrodes were also linear with the following characteristics:

to the DMSO solution resulted in only a slight potential shift, when added in excess (ca. 1-2 vol %); little effect upon the magnitude of the limiting current was observed. The system therefore appears to be relatively insensitive to water present in the system, a fact that has important implications in using this type of system as a gas sensor in many possible applications.1,6,7 Not all of the experimental voltammograms at gold microdisk electrodes consisted of a single reduction plateau; the occasional and random occurrence of two poorly resolved CO2 reduction waves were observed with half-wave potentials of -2.4 ( 0.1 and -3.05 ( 0.05 V vs Ag | Ag+. Other studies6,11,13 have also sometimes observed two signals, although this occurrence is poorly understood. Kinetic Waveshape Analysis of the Current | Potential Curves. Simple analytical expressions for quasi-reversible steady-state voltammetry describing the nonuniform accessibility of microdisk electrodes have been deduced previously,38-41 for the case of a simple, chemically uncomplicated electron-transfer process:

4.4 µm gradient ) 93.1 nA (vol %)-1 R ) 0.9991

A(soln) + e- h B(soln)

26.0 µm gradient ) 530.0 nA (vol %)-1 R ) 0.9989

In the approach by Oldham et al,40 the shape of the quasireversible steady-state voltammogram is characterized by two parameters, θ and κ,

The magnitude of the steady-state diffusion-limited current at microdisk electrodes is given by eq 22:

ilim ) 4nFDre[CO2]

(23)

θ ) 1 + enF(E-E ′)/RT 0

(24)

(22)

where the symbols have their usual meanings. From solubility measurements of CO2 in DMSO/electrolyte solutions (see Appendix), and the gradient of the ilim-vol % CO2 plot, a value of the diffusion coefficient, D, was estimated as 1.02 × 10-5 ( 0.1 cm2 s-1 assuming that a one-electron process occurs. The value of D determined in this way is in reasonable agreement with that deduced by Albery and Barron3 (1.45 × 10-5 cm2 s-1). The limiting current at both Pt and C cathodes were also found to be directly proportional to the vol % concentration of carbon dioxide, with gradients of 333.2 nA (vol %)-1 (Pt) and 115.5 nA (vol %)-1 (C), and Pearson’s Product Moment Correlation Coefficients of 0.9994 and 0.9753, respectively. From these data, mutatis mutandis for Au electrodes, a value for the diffusion coefficient of CO2 in DMSO was calculated to be 1.25 × 10-5 cm2 s-1 (Pt) and 8.7 × 10-6 cm2 s-1 (C). These values are consistent with that calculated for the gold cathode. The above experiments were all undertaken using a 0.2 M solution of TEAP in DMSO. The reduction process will be affected by changes in the viscosity of the electrolyte solution, as a change in this parameter necessarily results in changes in both the diffusion coefficient of CO2 and in the solubility of CO2 in the electrolyte solution. Accordingly, the effects of varying the supporting electrolyte concentration and the solution temperature upon the reductive voltammetry of CO2 were investigated. Changing the temperature by as much as 20 K (to 40 °C) was shown to have only little effect upon the voltammetric signals, suggesting that the diffusion coefficient of CO2 in 0.2 M TEAP/DMSO has a low thermal energy of activation. Decreasing the TEAP concentration from 0.2 to 0.05 M effectively “stretches” the voltammetric response, consistent with a decrease in the conductivity of the electrolyte (“ohmic distortion”). It is therefore best to work with a DMSO solution containing at least 0.2 M background electrolyte. Adding water

κ)

πrek0 -RnF(E-E0′)/RT e 4D

(25)

where the diffusion coefficients (D) of the oxidized and reduced species are have been assumed to be identical, and re is the radius of the microdisk electrode. The current | potential characteristics for the quasi-reversible process are then given by eq 26:

i)

[

)]

(

ilim π 2κθ + 3π 1+ θ κθ 4κθ + 2π2

-1

(26)

Bard and Mirkin41 solved eq 26 numerically in terms of two quartile potential parameters: ∆E1/4 ) |E1/2 - E1/4| and ∆E3/4 ) |E3/4 - E1/2| and tabulated their results to output three kinetic parameters, specifically, the charge-transfer coefficient, R, a parameter dependent upon the standard rate constant and the diffusion coefficient of the oxidized species, λ ) (rek0/D), and a parameter that depends on the formal electrode potential for the reduction, n∆E0′ ) n|E0′ - E1/2|. From these kinetic parameters, the current | voltage characteristics may be deduced from their insertion into eq 26. In particular, this model anticipates well-defined, sigmoidal voltammograms for electrochemical processes at microdisk electrodes, which are characterized by rapid rise of |i| with |E| up to the half-wave potential, followed by a tailing off in the upper quartile. That is to say,

〈dEdi 〉

E1/2 E1/4

>

〈dEdi 〉

E1/2

E3/4

(27)

This analysis was undertaken for the voltammograms shown in Figure 4, and is illustrated in Figure 5. It can be seen that although steady-state voltammograms are observed via this type of analysis, with limiting currents that are more or less identical to those observed experimentally, the characteristics of current

Electro-reduction of CO2 in DMSO

J. Phys. Chem. B, Vol. 105, No. 22, 2001 5259 being equal, we draw initial satisfaction that this dimensionless plot, effectively of current against voltage, exhibits characteristics that are the exact opposite of inequality 27, and thereby are consistent with those observed experimentally. Deduction of the electrode kinetic parameters for the quasiirreversible reduction of CO2 in DMSO at gold microdisk electrodes may only be made via the comparison of the working curve data with those obtained from experiment. However, this is not trivial, and necessitates the iteration of the unknown parameters (R, E0′, k1, and k1/k2), for each value of the applied electrode potential, so as to calculate a value for keff′. Comparison with the data in Figure 1 permits the inference of a current. A measure of the fit of the experimentally observed and the theoretically fitted currents is obtained through the evaluation of the mean-scaled absolute deviation (MSAD),

MSAD )

1 n

∑n |iexpt - itheory|

(28)

where n is the number of experimental points that are produced during the reductive scan. By definition, the best fit of the experimental and theoretical values corresponds to the case of minimum MSAD. To this end, a program was written in MS Visual Basic 6.0 in MS Excel 2000 to sequentially iterate the four parameters R, E0′, k2, and the ratio k1/k2. However, the problem was first simplified to a three-parameter iterative process, by writing keff as follows:

keff )

kh1e-(RF/RT)E kh1 1 + e-(RF/RT)E k2

(29)

where kh1 ) k1e(aF/RT)E0′. This simplification combines the formal electrode potential for CO2 reduction with the rate constant associated with the fast transfer of the first electron. The three independent parameters are then R, k2, and kh1, which were sequentially iterated within the following ranges:

0.2 e R e 0.6 Figure 5. Waveshapes corresponding to the reduction of CO2 in 0.2 M TEAP/DMSO at a 9.0 µm Au microdisk working electrode. (a) 10, (b) 20, (c) 40 vol % CO2. The theoretical curve has been simulated assuming adsorption to the electrode is not significant (see text).

| potential plot are significantly different from those predicted by inequality 27. In the current | potential waveshapes simulated from the experimental data, there is a slow rise of |i| with |E| up to the half-wave potential, followed by a rapid tailing off in the upper quartile, the exact opposite of inequality 27. This discrepancy is not due to poor-quality experimental voltammogramssohmic distortions of the voltammetric signals are negligible. Instead, it is likely to be due to the application of a model not consistent with observation; eq 25 has assumed that adsorptive processes do not occur. We now turn to the numerical simulation of the experimental voltammograms based upon the theory described above. The theoretical working curve shown in Figure 1 illustrates how a dimensionless current parameter, Ψ, varies as a function of a dimensionless parameter, keff′, that is dependent upon the potential applied to the electrode (E), the charge-transfer coefficient (R), and the relative rates of formation of CO2-• (k1)and of its reaction with CO2 (k2) for Mechanism A. Other things

10-25 e k2/m s-1 e 10-10 10-37 e kh1/m s-1 e 10-23 This allowed the comparison to good-quality experimental data to yield a best fit as shown in Figure 6 and Table 3. It can be seen that there are good agreements between the experimental and theoretical waveshapes, suggesting that Mechanism A may be the mechanism by which carbon dioxide is electrochemically reduced at gold microdisk electrodes in DMSO-electrolyte solutions. The kinetic data for this quasi-irreversible reduction process are given in Table 3. Conclusions The voltammetry of carbon dioxide in DMSO electrolyte solutions at gold microdisk electrodes has been shown to be accountable by a reaction mechanism in which the ratedetermining step is reaction of CO2-• with CO2 (Mechanism A). Numerical simulation of the experimental voltammograms permits the extraction of kinetic data; the charge-transfer coefficient is found to be 0.43 ( 0.05sgreater than the 0.3

5260 J. Phys. Chem. B, Vol. 105, No. 22, 2001

Welford et al. We thank Frank Marken, Barry Coles, Colin Bain, Horatio Corti, Robin Chaplin, Tony Wragg, Alan Bond, Derek Pletcher, Uwe Schro¨der, and Nathan Lawrence for valuable discussions and advice. Appendix

Figure 6. Waveshapes corresponding to the reduction of CO2 in 0.2 M TEAP/DMSO at a 9.0 µm Au microdisk working electrode. (a) 10, (b) 20, (c) 40 vol % CO2. The theoretical curve has been simulated assuming Mechanism A (see text).

TABLE 3: Kinetic Parameters, Obtained as the Best Fit between Experiment and Simulation, for the Reduction of CO2 in 0.2 M TEAP/DMSO at a 9.0 µm Au Microdisk Electrode under Steady-State Conditions (100 mV s-1) vol % CO2

R

k2/m s-1

10 15 20 40 80

0.48 0.44 0.43 0.40 0.40

2.05 × 10-13 2.74 × 10-13 4.22 × 10-13 3.16 × 10-13 1.00 × 10-13

inferred by Haynes and Sawyer12 from simple Tafel theory applied without correction for the chemical complexity for the reaction. Acknowledgment. We are grateful to the EPSRC for studentships for B.A.B. and J.D.W., and to AµC Sensing, Ltd. for providing financial support for this project via the SMART scheme. B.A.B. acknowledges support from Windsor Scientific.

The Solubility of Carbon Dioxide in Dimethyl Sulfoxide. Methods for the determination of the solubility of carbon dioxide in dimethyl sulfoxide have been used for over fifty years.3,11-13,42-46 For electrochemical studies of carbon dioxide in DMSO, it is vital to have an accurate knowledge of this parameter, so that accurate diffusion coefficients may be inferred from experimental data. However, literature values of the latter parameter vary significantlyssee for example Table 1 of ref 9. In part, this may be due to an erroneous determination of CO2 solubility in the DMSO/electrolyte medium. In addition, previous determinations of the diffusion coefficient11,12 have been undertaken using chronopotentiometirc measurements of questionable reliability. The techniques used for the determination of CO2 solubility in DMSO or other aprotic media may be divided into three categories, each of which is outlined below. (i) Methods Based upon Titration.3,11-13,42-44 These are essentially based upon the procedure outlined by Pieters44 in 1948, and generally involve the addition of a known aliquot of a CO2-saturated DMSO/electrolyte solution to a known amount of standard aqueous alkali. This sample is then back-titrated with standardized acid, using an appropriate indicator (e.g., phenolphthalein or m-cresol purple). The concentration of a CO2-saturated DMSO solution containing 0.03 M electrolyte has been estimated to be 0.128 M,11 while one containing 0.1 M electrolyte has been deduced to be between 82 and 132 mM!12,43 (ii) Methods Based upon Pressure Changes.45,47 In these methods, known amounts of degassed solvent and the gas that the solubility coefficient is unknown are continually mixed together. A manometer connected to the setup measures the total pressure of the gas and the solvent vapor. The pressure falls to an equilibrium value from which the amount of dissolved gas may be deduced. In this manner, a saturated solution of CO2 in DMSO was found to be 0.128 M.45 (iii) The Gas Chromatographic Technique.46 Vianello and coworkers46 measured the solubility of carbon dioxide in DMSO as a function of temperature and supporting electrolyte concentration, using a gas chromatographic technique. Effectively this involved recording the gas chromatographic trace of a CO2saturated DMSO solution using 1,4-dioxane as a reference solvent (as it has an accurately known CO2 solubility). Integration of the traces allows quantitative determination, found to be 0.138 ( 0.003 M at 25 °C, and compared well to that determined using the titration method above: 0.134 ( 0.006 M. The effect of adding supporting electrolyte (TBAP) was found to be negligibly small; the Henry constant decreased from 101.6 atm (pure solvent) to 100.1 atm (0.1 M TBAP/DMSO), effecting a slight increase in CO2 solubility. It was also found that the CO2 solubility was found to obey, over the small temperature range 20 - 50 °C, the well-known48 empirical relationship

-T ln(xCO2) ) A + BT

(30)

in which T is the absolute temperature, xi refers to the mole fraction of species i, and the constants A ) -1495 ( 20 and B

Electro-reduction of CO2 in DMSO

Figure 7. Apparatus for the determination of the solubility of CO2 in DMSO electrolyte solutions.

) 9.62 ( 0.07. Thus, the concentration of CO2-saturated DMSO at 30 °C is ca. 0.12 M. (iV) The Dilatometric Technique. The variance in the literature data for the CO2 solubility prompted further independent determination. Furthermore, knowledge of the latter permits the inference of diffusion coefficients from electrochemical measurements. Thus, the CO2 solubility was determined using a method similar to that used by Dymond45 and Postigo et al.47 Figure 7 shows the apparatus used. The whole system was maintained at ambient temperature (23 ( 3 °C). First, the whole system was thoroughly flushed with CO2, and ensured to be leak-free. The syringe at A was filled with CO2. An initial amount of DMSO (ca. 1.0 mL) was introduced through the seal into the round-bottom flask, so that there was a DMSO vapor pressure. A magnetic flea was employed to mix the solvent and solute. A DMSO drop (ca. 0.2 mL) was then introduced into the graduated pipette at point B. Its position was adjusted using the syringe at A and noted. A 0.5 mL aliquot of DMSO was then injected into the round-bottom flask through its neck. This caused the DMSO drop in the pipet to be displaced by 0.5 mL away from the round-bottom flask. Dissolution of CO2 was then observed by means of a displacement in the opposite direction. This was followed with time, until there was no further displacement. The final position was noted. The solubility was observed to be 0.113 ( 0.008 M (neat DMSO) and 0.125 ( 0.013 M (0.2 M TEAP/DMSO), in agreement with other results.6,8-10 As these two values are within experimental error, we may infer (like Vianello et al.46) that the supporting electrolyte does not significantly affect the solubility of CO2 in DMSO. References and Notes (1) For a review, see Hahn, C. E. W. Analyst 1998, 123, 57R. (2) Zhou, Z.-B.; Zhou, Y. M. Wuhan Daxue, Xuebao, Ziran Kexueban 1999, 45, 135. (3) Albery, W. J.; Barron, P. J. Electroanal. Chem. 1982, 138, 79. (4) Albery, W. J.; Clark, D.; Drummond, H. J. J.; Coombs, A. J. M.; Young, W. K.; Hahn, C. E. W. J. Electroanal. Chem. 1992, 340, 99. (5) Albery, W. J.; Clark, D.; Young, W. K.; Hahn, C. E. W. J. Electroanal. Chem. 1992, 340, 111. (6) Hahn, C. E. W.; McPeak, H.; Bond, A. M.; Clark, D. J. Electroanal. Chem. 1995, 393, 61. (7) Hahn, C. E. W.; McPeak, H.; Bond, A. M. J. Electroanal. Chem. 1995, 393, 69.

J. Phys. Chem. B, Vol. 105, No. 22, 2001 5261 (8) McPeak, H.; Hahn, C. E. W.; Bond, A. M. J. Electroanal. Chem. 2000, 487, 25. (9) Dawson, G. A.; Hauser, P. C.; Kilmartin, P. A.; Wright, G. A. Electroanalysis 2000, 12, 105. (10) Electrochemical and Electrocatalytic Reactions of Carbon Dioxide; Sullivan, B. P., Ed.; Elsevier: Amsterdam, 1993. (11) Roberts, J. L., Jr.; Sawyer, D. T. J. Electroanal. Chem. 1965, 9, 1. (12) Haynes, L. V.; Sawyer, D. T. Anal. Chem. 1967, 39, 333. (13) Eggins, B. R.; McNeill, J. J. Electroanal. Chem. 1983, 148, 17. (14) Sawyer, D. T.; Sobkowiak, A.; Roberts, J. L., Jr. Electrochemistry for Chemists, 2nd ed.; Wiley: New York, 1995; p 199 ff. (15) Sawyer, D. T.; Sobkowiak, A.; Roberts, J. L., Jr. Electrochemistry for Chemists, 2nd ed.; Wiley: New York, 1995; p 438. (16) Vassiliev, Y. B.; Bagotzky, V. S.; Khazova, O. A.; Mayorova, N. A. J. Electroanal. Chem. 1985, 189, 295. (17) Amatore, C. A.; Save´ant, J. M. J. Am. Chem. Soc. 1981, 103, 5021. (18) Amatore, C. A.; Fosset, B. J. Electroanal. Chem. 1992, 328, 21. (19) Brookes, B. A.; Lawrence, N. S.; Compton, R. G. J. Phys. Chem. B 2000, 104, 11258. (20) Alden, J. A.; Compton, R. G. J. Phys. Chem. B 1997, 101, 9606. (21) Alden, J. A.; Compton, R. G. J. Phys. Chem. B 1997, 101, 8941. (22) Alden, J. A. D. Phil Thesis, Oxford University, 1997. (23) Meijerink, J.; Van der Vorst, H. Math. Comput. 1977, 31, 148. (24) Van der Vorst, H. SIAM J. Sci. Statist. Comput. 1989, 13, 631. (25) Sleijpen, G. L. G.; Fokkema, D. R. Electron Trans. Numer. Anal. 1993, 1, 11. (26) Sonneveld, P. SIAM J. Sci. Statist. Comput. 1989, 10, 36. (27) Saad, Y.; Schultz, M. SIAM J. Sci. Statist. Comput. 1986, 7, 856. (28) Defined by the CPU time (NAG ROUTINE F05BAF) for a particular solution of eq 20 on a given grid size. (29) Values of n were calculated by minimizing (in hn) the residuals from the least squares regression fit of ψsim(hn). (30) See, for example, Dimethyl sulfoxide; Martin, D., Hanthanl, H. G., Eds.; Akademie-Verlag: Berlin, 1971, and references therein. (31) Cardwell, T. J.; Mocak, J.; Santos, J. H.; Bond, A. M. Analyst 1996, 121, 357. (32) (a) Sharp, P. Electrochim. Acta 1983, 28, 301. (b) Kuwana, T.; Bublitz, D. E.; Hoh, G. J. Am. Chem. Soc. 1960, 82, 5811. (33) Adams, R. N. Electrochemistry at Solid Electrodes; Marcel Dekker: New York, 1969; p 219 ff. (34) See, for example, Butler, J. N. J. Electroanal. Chem. 1967, 14, 89, and references therein. (35) (a) Cogley, D. R.; Butler, J. N. J. Phys. Chem. 1968, 72, 1017. (b) Cogley, D. R.; Butler, J. N. Study of the Kinetics of Alkali Metal Deposition and Dissolution in Non-Aqueous SolVents; Air Force Cambridge Research Laboratories, AFCRL-68-0560, 1968, AD 681453. (36) (a) Hammerich, O.; Parker, V. D. Electrochim. Acta 1973, 18, 537. (b) Lines, R.; Jensen, B. S.; Parker, V. D. Acta Chim. Scand. 1978, 32, 510. (c) Kiesele, H. Anal. Chem. 1981, 53, 1952. (d) Heinze, J. Angew. Chem. 1984, 23, 831. (e) Aojula, K. S.; Pletcher, D. J. Chem. Soc. Faraday Trans. 1990, 86, 1851. (37) Tomesˇ, J. Collect. Czech. Chem. Commun. 1937, 9, 81. (38) See, for example, Montenegro, M. I. Res. Chem. Kinetics 1994, 2, 299. (39) Aoki, K.; Tokuda, K.; Matsuda, H. J. Electroanal. Chem. 1987, 235, 87. (40) Oldham, K. B.; Myland, J. C.; Zoski, C. G.; Bond, A. M. J. Electroanal. Chem. 1989, 270, 79. (41) Mirkin, M. V.; Bard, A. J. Anal. Chem. 1992, 64, 2293. (42) Ayres, G. H. QuantitatiVe Chemical Analysis; Harper and Row: New York, 1969; p 607. (43) Schmidt, M. H.; Miskelly, G. M.; Lewis, N. S. J. Am. Chem. Soc. 1990, 112, 3420. (44) Pieters, H. J. Anal. Chim. Acta 1948, 2, 263. (45) Dymond, J. H. J. Phys. Chem. 1967, 71, 1829. (46) Gennaro, A.; Isse, A. A.; Vianello, E. J. Electroanal. Chem. 1990, 289, 203. (47) Postigo, M. A.; Katz, M. J. Solution Chem. 1987, 16, 1015. (48) Wilhelm, E.; Battion, R. Chem. ReV. 1973, 73, 1.