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J. Phys. Chem. C 2007, 111, 17008-17014
Voltammetry at Nanoparticle and Microparticle Modified Electrodes: Theory and Experiment Ian Streeter, Ronan Baron, and Richard G. Compton* Physical and Theoretical Chemistry Laboratory, Oxford UniVersity, South Parks Road, Oxford, United Kingdom OX1 3QZ ReceiVed: August 29, 2007; In Final Form: September 10, 2007
Electrodes modified with random arrays of nanoparticles and/or microparticles find significant application in electroanalysis. Theory is developed for the diffusional current at nanoparticle-modified electrodes via the diffusion domain approach which is used to model the electrode surface as a randomly distributed assembly of spherical particles. Experiments are reported for the electrocatalytic reduction of protons at a palladium particle modified electrode and shown to behave as predicted theoretically.
1. Introduction The physical and chemical properties of nanoparticles often differ greatly from those of the bulk material.1 When supported on an electrode surface, the nanoparticles can catalyze a heterogeneous electron transfer, and so they are often used in electroanalysis for the detection of species in solution. Nanoparticle-modified electrodes can display a high sensitivity due to the high rate of mass transport to the individual particles and the correspondingly high current density. In this paper, the diffusional current at a particle-modified electrode is studied experimentally and interpreted by comparison with numerical simulations. Potential sweep experiments are studied at different scan rates and for different surface densities of particles. Palladium-covered glassy carbon microspheres (Pd-CMs) are used as the particles because their shape is well-defined, and so the voltammetric response is more easily interpreted. A basal plane pyrolytic electrode (BPPG) is modified by the abrasive attachment of the glassy carbon microspheres.2-4 The system studied is the electrocatalytic reduction of protons at palladium surfaces.5-8 The reaction scheme is illustrated in Figure 1. At an appropriate potential, the electron-transfer takes place only at the interface between the microsphere and the solution; proton reduction at the BPPG electrode surface requires significantly more negative potentials. The Faradaic current at a nanoparticle-modified electrode has been found by numerical simulation, assuming the spherical particles are sufficiently well-spaced that they remain diffusionally independent on the experimental time scale.9 Voltammetry was presented for a reversible electron transfer, and the diffusion limiting current was given by eq 1:
ilim ) -8.71nFDrscb
(1)
where D is the diffusion coefficient of the electroactive species, cb is its bulk concentration, rs is the radius of the spherical particle, and n is the number of electrons transferred. The PdCM modified electrodes investigated here have a range of different surface densities of particles, and the approximation of diffusional independence is not always valid. We develop * Corresponding author. Fax: +44 (0) 1865 275410. Phone: +44 (0) 1865 275413. E-mail:
[email protected].
Figure 1. Schematic representation of the surface of a BPPG electrode with abrasively attached glassy carbon microspheres decorated with palladium shell (Pd-CMs). At an appropriate potential, the proton reduction takes place only at the surface of the Pd-CMs.
Figure 2. Diffusion zones at a spherical nanoparticle on a supporting planar surface. (a) Spherical diffusion zone at short timescales. (b) Hemispherical diffusion zone at long timescales. (c) Diffusion zone overlap expected under some experimental conditions.
the theory for a nanoparticle-modifed electrode by using the diffusion domain approach to model the modified electrode surface under any diffusion regime. 2. Theory Particle-modified electrodes are considered for which the electron transfer occurs only on the surface of the spherical
10.1021/jp076923z CCC: $37.00 © 2007 American Chemical Society Published on Web 10/19/2007
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Figure 4. Simulation space for solution of eq 3.
TABLE 1: Dimensionless Parameters Used for Numerical Simulation
Figure 3. (a) Schematic diagram of diffusion domains for a random distribution of spherical nanoparticles (gray circles). The highlighted diffusion domain is shown again in part (b). The diffusion domain is approximated as a cylinder in part (c).
particles; the supporting planar electrode surface is electrochemically inert. The diffusional behavior observed at the electrode surface is therefore expected to be qualitatively but not quantitatively similar to that described for arrays of microdisc electrodes.10 In a voltammetric experiment at a microdisc array, the electroactive species is consumed at the electrode, and a depletion layer is formed known as a diffusion zone. When neighboring diffusion zones overlap, there is a shielding effect, which reduces the diffusional current as compared with a diffusionally independent microelectrode. A voltammetric experiment at a nanoparticle also generates a diffusion zone. Figure 2 shows a schematic representation of the diffusion zone at a spherical nanoparticle on a planar surface. The diffusion zone is approximately spherical in shape at very short time scales and approximately hemispherical in shape at much longer time scales.9 For a particle-modified electrode of practical surface coverage, we would expect overlapping of the diffusion zones under some experimental conditions. This is expected to affect the diffusional behavior of the electroactive species to the particle surface. The numerical simulation of the current at an isolated spherical nanoparticle is described in detail elsewhere.9 In this work, we model the Pd-covered glassy carbon microspheres as an assembly of particles randomly distributed on a supporting planar surface, such that the diffusion zones of the individual particles are allowed to overlap. This requires a diffusion domain approach, which has also been discussed in detail for other related systems.10-12 Next, we provide a short summary of these concepts for the reader’s convenience. 2.1. Diffusion Domain Approach. Diffusion to a random assembly of nanoparticles is a complicated three-dimensional problem. However, the problem can be simplified by noting that each particle belongs to a diffusionally independent region known as a diffusion domain. The diffusion domain approximation treats these zones as being cylindrical with the particle situated at the axis of symmetry, thus reducing the problem of diffusion to one of only two dimensions. This approximation is illustrated in Figure 3.
parameter
expression
radial coordinate normal coordinate time scan rate potential electrode flux
R ) r/rs Z ) z/rs T ) Dt/rs2 σ ) F/RT νrs2/D θ ) F/RT (E - EfQ) j ) -i/nFDCrs
For a random spatial distribution, each particle’s diffusion domain will be different in size. The distribution of sizes is described by the following probability distribution function:13
f(s) )
343 15
x2π7 (〈s〉s )
5/2
(
exp -
7 s 2 〈s〉
)
(2)
where s is the area of the diffusion domain and 〈s〉 is the mean area. The first step in calculating the current response of a randomly distributed array is to simulate the mass transport at a range of different sized diffusion domains. The current response of each domain is then weighted according to eq 2 and summed to give the total voltammetric response for the whole array. 2.2. Numerical Simulation Method. The numerical simulations performed in this work are for a single step electron transfer at the surface of the spherical particles. The mass transport of the electroactive species through solution is described in eq 3 using the cylindrical radial coordinates r and z:
(
)
∂2c 1 ∂c ∂2c ∂c )D 2+ + ∂t r ∂r ∂z2 ∂r
(3)
where c is its concentration and D is its diffusion coefficient. The product of the electron transfer is considered to be a species in solution with a diffusion coefficient equal to that of the reactant. The concentration profile of the electroactive species can therefore be simulated independently from that of the product.14 We also assume that the electron transfer is fast and reversible such that the concentrations at the particle surface are described by the Nernst equation.15 The system under consideration consists of a sphericle particle with radius rs at the center of a cylindrical diffusion domain of radius r0. Figure 4 shows the simulation space for a single diffusion domain. The simulation space has been normalized using the dimensionless parameters in Table 1. In the normalized space, the particle has radius 1 and the diffusion domain has radius R0. Bulk solution is considered to be at a distance 6xT from the top of the particle.16 Equation 3 is normalized and solved in this simulation space using the alternating direction implicit finite difference method. An expanding simulation grid
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Figure 5. Simulated concentration profiles at a diffusion domain containing a spherical particle. Category 1: σ ) 1000. Category 2: σ ) 10. Category 3: σ ) 1. Category 4: σ ) 0.01. For all categories R0 ) 2. Concentration profiles were taken at the linear sweep’s peak potential.
is used, which has its highest mesh density in the region of the particle in order to mimic its curved surface.9 A zero-flux boundary condition is implemented at the supporting planar surface (Z ) 0), at the axis of symmetry (R ) 0), and at the diffusion domain boundary (R ) R0). The current is calculated by the diffusional flux of the electroactive species through the particle surface. Because the simulation grid is rectangular, the flux must be found from the sum of its components in the R and Z directions.9 2.3. Categorization of Diffusional Behavior. The mass transport to a random assembly of spherical particles can be described in terms of the four categories originally defined by Davies et al. for the partially blocked electrode17 and subsequently used in many other studies on spatially heterogeneous surfaces.10,18 Figure 5 shows a numerically simulated concentration profile to illustrate each category of diffusion. The concentration profiles were calculated using a diffusion domain of size R0 ) 2 and various values of the dimensionless scan rate, σ, which is defined in Table 1. For category 1, the particles must be diffusionally independent, and the diffusion layer thickness must be much smaller
than the particle radius. Under these conditions, diffusion to the particle surface is approximately planar. This behavior is unlikely to be observed at conventional scan rates for particles of micrometer or nanometer dimensions. Category 2 also requires the particles to be diffusionally independent. The diffusion layer thickness may be any size compared with the particle radius, provided neighboring diffusion zones do not overlap. The diffusion limiting current under category 2 condtions is given by eq 1. As the diffusion zone grows and overlap begins, the diffusion is described as category 3. In this regime, the particles experience a shielding effect from their neighbor, and the flux of the electroactive species to the particle is reduced. Category 4 represents the limiting situation of category 3 when neighboring diffusion zones overlap to such an extent that the overall concentration profile is planar. The current response is equal to that of planar diffusion to the supporting macroelectrode, even though the electrode surface remains electrochemically inert. 2.4. Results of Numerical Simulation. The particle-modified electrodes are discussed here in terms of their fractional surface coverage, Θ. This is defined in eq 4 and describes the fraction
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Figure 8. SEM images of glassy carbon microspheres: (A) shows the nonmodified microspheres, and (B) and (C) show the microspheres with a Pd shell (Pd-CMs).
Figure 6. Simulated linear sweep voltammetry of a reversible electron transfer at a spherical particle modified electrode. Scan rate σ ) 0.01, Θ varies from 10-4 to 0.1.
Figure 7. Peak current, jp, versus square root of the scan rate, σ1/2. Simulated data is shown by circles, the solid line the shows RandlesSˇ evcˇ´ık values for planar diffusion. (a) Θ ) 0.2 and (b) Θ ) 0.05.
of the supporting planar electrode that lies directly underneath a spherical particle.
Θ)
Nπrs2 A
(4)
where A is the area of the supporting electrode and N is the number of spherical particles present on its surface. The wave shape of a simulated voltammogram depends on only two parameters: the dimensionless scan rate, σ, and the fractional surface coverage of particles, Θ. The simulated voltammetry
presented in this section shows the dimensionless diffusional flux, j, as a function of the dimensionless potential, θ, both of which are defined in Table 1. It should be noted that the flux j applies to a single particle; its value is not normalized per unit area. Figure 6 shows a selection of flux-potential plots for a scan rate of σ ) 0.01 and various values of Θ. With a surface coverage of Θ ) 10-4, there is no significant overlap between neighboring diffusion zones. The voltammogram is that expected for an isolated spherical particle, as already characterized.9 Lowering the value of Θ any further has negligible effect on the simulated flux. This diffusional behavior is therefore described as category 2. At this slow scan rate, the wave shape is approximately that expected for steady-state diffusion, with a maximum flux close to the value of 8.71 predicted by eq 1. As the surface density of particles increases, the simulated voltammograms in Figure 6 decrease in magnitude and become more peak shaped. This is attributed to a change in diffusional behavior from category 2 to category 3. There is more significant overlapping of diffusion zones when the value of Θ is large. This has a shielding effect, and so the flux of the electroactive species to the particle surface is lower. For a very high surface coverage of particles, we expect to see category 4 diffusional behavior, which occurs with extreme overlapping of neighboring diffusion zones. Under this diffusional regime, the current response can be predicted by a planar diffusion model. For a reversible electron transfer, the peak current under planar diffusion conditions is given by the Randles-Sˇ evcˇ´ık equation,16 and its value is proportional to the square root of the scan rate. Figure 7 shows the simulated peak current, jp, plotted against σ1/2 for two different values of Θ. Category 4 behavior can be observed at the low scan rates where overlapping of the diffusion zones is greatest. With a surface coverage of Θ ) 0.05, there is a negative deviation from the planar diffusion peak current at higher scan rates. This indicates incomplete overlapping of diffusion zones and a transition into category 3 diffusional behavior. With a surface coverage of Θ ) 0.2, there is a positive deviation of the simulated peak current from the planar diffusion value at higher scan rates. This contrasts with the behavior observed at arrays of flat microdisc10 and flat microband18 electrodes and at flat partially blocked electrodes.12 For these two-dimensional surfaces, the current was found to tend toward the Randles-Sˇ evcˇ´ık value at high surface coverage but was not found to go above this limit. The spherical particles considered here are able to draw a higher current because their height above the electrode surface makes them diffusionally accessible to a greater region of the solution on a short experimental time scale. 3. Experimental Section 3.1. Reagents and Materials. Hydrazine (35 wt % in water), palladium(II) chloride (99.999%), hydrochloric acid (37 wt % solution in water), ammonium hydroxide (100%), ethylenediamine tetraacetic acid (EDTA, +99.4%), and potassium bromide
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Figure 9. Cyclic voltammetry in 3 mM HCl, 0.1 M KCl at a 5 mm diameter BPPG electrode modified by the abrasive attachment of different amounts of Pd-CMs. The fractional surface coverage of particles is (A) 0.445, (B) 0.118, and (C) 7.64 × 10-3 cm2. For each graph curves (a), (b), and (c) correspond respectively to voltammograms recorded at 10, 100, and 500 mV s-1.
(KCl, 99.5%) were supplied by Sigma-Aldrich and used without further purification. Glassy carbon spherical powder (15 ( 5 µm, type 1) was purchased from Alfa Aesar (Heysham, U.K.). The deionized water used for the preparation of the solutions had a resistivity of not less than 18.2 MΩ cm at 25 ( 2 °C (Vivendi Water Systems, U.K.). 3.2. Electrochemistry. A standard three electrode cell was used. The reference electrode was an aqueous saturated calomel electrode (Radiometer Analytical) and the auxiliary electrode was a carbon graphite rod. The working electrodes were a 5 mm disc diameter basal plane pyrolytic graphite electrode (BPPG, Le Carbone Ltd, Sussex, U.K.) and a 1 mm diameter disc bulk Pd electrode (Pd wire insulated in epoxy). The electrochemical investigations were performed using an Eco Chemie µ-Autolab potentiostat connected to a computer. All experiments were performed at 22 ( 2 °C under a nitogen atmosphere. For voltammetry at the Pd-CMs, all of the measurements were made in aqueous solutions with HCL, 3 mM, and using KCl, 0.1 M, as the supporting electrolyte. Each cyclic voltammetry measurement included, after the cathodic scan, an anodic scan up to 0.5 V. This ensured that both the adsorbed and the absorbed hydrogen atoms were oxidized before a subsequent measurement was made and thus that the palladium surface was in the same reproducible condition for all of the measurements. 3.3. Synthesis and Characterization of a Palladium Shell on Glassy Carbon Microspheres. The synthesis and characterization of a palladium “shell” on the glassy carbon microspheres was made by an electroless deposition method. The shell is formed by growing a large number of palladium nanoparticles on the microsphere surface until they form a continuous layer. The procedure involved immersing 0.3 g of glassy carbon spherical powder into 80 cm3 of water. Then 0.286 g of PdCl2,
3.5 g of EDTA, and 20 mL of NH4OH were added under stirring. Finally, 1 mL of N2H4 1 M was added dropwise to the reaction medium, and the reaction was allowed to proceed for 2 h at 45 °C. After the allowed reaction time, the reaction mixture was filtered and rinsed with water to remove any unreacted species. The resulting powder was dried in the oven overnight at 45 °C. The characterization of the glassy carbon microspheres was done using scanning electron microscopy (SEM) imaging and was carried out using a JEOL JMS model 6500F scanning electron microscope. 3.4. Abrasive Attachment of Carbon Microspheres on a Basal Plane Pyrolytic Graphite Electrode. The abrasive attachment of glassy microspheres on a basal pyrolytic graphite electrode was achieved by gently rubbing the electrode surface onto a thin layer of microspheres laying on a filter paper. The excess of non-attached microspheres on the electrode surface is then removed by throughly washing the electrode surface with water. The electrode surface can be renewed before modification by pressing cellotape on the electrode surface and removing it along with several surface layers of graphite. 3.5. Estimation of the Number of Particles on the Electrode Surface. For each modification of the BPPG electrode, the total surface area of palladium is estimated from the reduction of surface oxides. A cyclic voltammetry experiment is performed between 0.2 and 1.2 V in phosphate buffer 0.1 M, pH 7. A reduction peak is obtained in the backward scan. The integration of this reduction peak indicates the charge necessary to reduce the surface oxides, and the total surface of palladium is estimated using a value of 424 µC cm-2.2,3,19 The total number of spheres present on the electrode surface is estimated assuming a particle radius of 15 µm. This calculation assumes that surface area of a palladium covered
Voltammetry at Nanoparticle Modified Electrodes
J. Phys. Chem. C, Vol. 111, No. 45, 2007 17013 in shape with diameter 15 ( 5 µm. Various amounts of the Pd-CMs were abrasively attached to the surface of the BPPG electrode using the method described in section 3.4. The current generated in the voltammetric experiments confirms that this method is sufficient to obtain an electrical contact between the Pd-CMs and the BPPG surface. Figure 9 presents a selection of experimentally recorded voltammograms for the reduction of protons on the Pd-CMs. The peak shapes and peak heights indicate that the diffusional behavior of the protons is different depending on the experimental conditions. With a surface coverage of Θ ) 0.445 (Figure 9a), the plot of peak current, ip, versus the square root of the scan rate, ν, is linear, and the wave shape is that expected for transient voltammetry. This is the behavior expected for category 4 diffusion. At this high particle density, there is considerable overlapping of neighboring diffusion zones to the extent that they have formed a planar diffusion layer. With a surface coverage of Θ ) 7.64 × 10-3 (Figure 9c), the plot of ip versus ν1/2 deviates from linearity, especially at higher scan rates. This suggests there is much less significant overlapping of diffusion zones with this relatively low surface particle density. The voltammetric wave shape suggests nearsteady-state diffusion, which is consistent with the higher rates of mass transport expected when the particles are diffusionally independent. This suggests the diffusional behavior is approximately category 2. With a surface coverage of Θ ) 0.118 (Figure 9b), the voltammetry is transient in terms of its wave shape, which suggests overlapping of diffusion zones. However, the plot of ip versus ν1/2 deviates from linearity, which shows that the overlap is not sufficient to induce overall planar diffusion to the electrode surface. The voltammetry in this figure is therefore attributed to category 3 behavior. The diffusional current at a single particle can be found by dividing the linear sweep’s forward scan peak height by the number of particles present on the electrode surface. Figure 10 shows the variation of this quantity with fractional surface coverage. Simulated linear sweep voltammetry is also shown for a range of values of Θ and using values of σ that correspond to the experimental conditions. Simulations used the literature value of D ) 7.9 × 10-5 cm 2 s-1 for the proton diffusion coefficient20,21 and a value of rs ) 15 m for the sphere radius. Figure 10 shows that a single particle generates the highest current when the surface distribution is sparse and there is little overlap between neighboring diffusion zones. The simulated and experimental data show agreement in the general trend with varying Θ. The discrepancy between the two data sets is attributed to the complexities of the electron-transfer mechanism which are not accounted for in our simple model and the inaccuracies in counting the number of microspheres.
Figure 10. Variation of linear sweep peak height per particle with surface coverage of particles. Scan rates: (a) 0.01, (b) 0.1, (c) 0.5 V s-1. Simulated data is shown by a solid line; experimental data is shown by connected squares.
microsphere is given by 4πr2s ; it ignores the roughness of the Pd-CM surface. With an estimated value for the number of spheres, the microsphere-modifed arrays can be discussed in terms of their fractional coverage, Θ. 4. Results and Discussion Figure 8 shows SEM images of the glassy carbon particles before and after their modification with a palladium shell. The images confirm that the particles are approximately spherical
5. Conclusions The experimental voltammetry at the Pd-CMs illustrated how different diffusional behaviors are observed at a particlemodified electrode depending on the experimental conditions. The highest total current output was found with a high surface coverage of the microspheres. Conversely, the highest rates of mass transport to a single microsphere was found with a low surface coverage such that neighboring diffusion zones did not overlap. The nature of diffusion to a nanoparticle-modified electrode can therefore be tuned by varying the experimental conditions. Diffusion to a nanoparticle-modified electrode can be simulated numerically for any surface coverage by using a diffusion
17014 J. Phys. Chem. C, Vol. 111, No. 45, 2007 domain approach. The numerical simulations in this work confirmed the basic trends that were observed experimentally. Acknowledgment. I.S. thanks the EPSRC for a studentship. Lei Xiao is thanked for the SEM imaging. References and Notes (1) Welch, C. M.; Compton, R. G. Anal. Bioanal. Chem. 2006, 384, 601-619. (2) Sˇ ljukic´, B.; Baron, R.; Salter, C.; Crossley, A.; Compton, R. G. Anal. Chim. Acta 2007, 590, 67-73. (3) Baron, R.; Sˇ ljukic´, B.; Salter, C.; Crossley, A.; Compton, R. G. Electroanalysis 2007, 19, 1062-1068. (4) Baron, R.; Sˇ ljukic´, B.; Salter, C.; Crossley, A.; Compton, R. G. Russ. J. Phys. Chem. 2007, 81, 1443-1447. (5) Breiter, M. W. J. Electroanal. Chem. 1980, 109, 253-260. (6) Mengoli, M.; Fabrizio, M.; Manduchi, C.; Zannoni, G. J. Electroanal. Chem. 1993, 350, 57-72. (7) Batchelor-McAuley, C.; Banks, C. E.; Simm, A. O.; Jones, T. G. J.; Compton, R. G. Chem. Phys. Chem. 2006, 7, 1081-1085. (8) Liang, H. P.; Lawrence, N. S.; Jones, T. G. J.; Banks, C. E.; Ducati, C. J. Am. Chem. Soc. 2007, 129, 6068-6069. (9) Streeter, I.; Compton, R. G. J. Phys. Chem. C, 2007, accepted. (10) Davies, T. J.; Compton, R. G. J. Electroanal. Chem. 2005, 585, 63-82.
Streeter et al. (11) Reller, H.; Kirowa-Eisna, E.; Gileadi, E. J. Electroanal. Chem. 1982, 138, 65-77. (12) Brookes, B. A.; Davies, T. J.; Fisher, A. C.; Evans, R. G.; Wilkins, S. J.; Yunus, K.; Wadhawan, J. D.; Compton, R. G. J. Phys. Chem. B 2003, 107, 1616-1627. (13) Ja´rai-Szabo´, F.; Ne´da, Z. arXiV Condens. Matter e-prints 2004, 06, 116. (14) Streeter, I.; Compton, R. G. Phys. Chem. Chem. Phys. 2007, 9, 862-870. (15) We note the limitations of these assumptions in describing the mechanism of the reduction of protons at the Pd-CMs; however the variation of peak current with particle size and coverage is likely to be predicted to a good approximation. (16) Bard, A. J.; Faulkner, L. R. Electrochemical Methods, Fundamentals and Applications; John Wiley and Sons: New York, 2001. (17) Davies, T. J.; Banks, C. E.; Compton, R. G. J. Solid State Electrochem. 2005, 9, 797-808. (18) Streeter, I.; Fietkau, N.; del Campo, J.; Mas, R.; Mun˜oz, F. X.; Compton, R. G. J. Phys. Chem. C 2007, 111, 12058-12066. (19) Burke, L. D.; Nagle, L. C. J. Electroanal. Chem. 1999, 461, 5264. (20) Macpherson, J. V.; Unwin, P. R. Anal. Chem. 1997, 69, 20632069. (21) Daniele, S.; Lavagnini, I.; Baldo, M. A.; Magno, F. J. Electroanal. Chem. 1996, 404, 105-111.
