The Stripping Voltammetry of Hemispherical Deposits Under

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J. Phys. Chem. C 2009, 113, 2846–2854

The Stripping Voltammetry of Hemispherical Deposits Under Electrochemically Irreversible Conditions: A Comparison of the Stripping Voltammetry of Bismuth on Boron-Doped Diamond and Au(111) Electrodes Sarah E. Ward Jones,† Kathryn E. Toghill,† Susan H. Zheng,‡ Sylvie Morin,‡ and Richard G. Compton*,† Department of Chemistry, Physical and Theoretical Chemistry Laboratory, Oxford UniVersity, South Parks Road, Oxford, OX1 3QZ, United Kingdom, and Department of Chemistry, York UniVersity, 4700 Keele Street, Toronto, Ontario, Canada M3J 1P3 ReceiVed: October 22, 2008; ReVised Manuscript ReceiVed: December 19, 2008

A study of the stripping voltammetry of hemispherical deposits under electrochemically irreversible conditions is presented. Experiments show a difference in the stripping voltammetry of bismuth from a single crystal Au(111) electrode where the bismuth covers the surface in relatively flat film and a boron-doped diamond (BDD) electrode where the hemispherical deposits are seen on the surface. It is shown using mathematical modeling and numerical simulation that this difference cannot be accounted for by simply considering the different distributions of bismuth on the electrode surfaces. Rather, it is concluded that the difference in voltammetry is mainly due to the morphology/orientation of the deposits formed leading to differences in the kinetics and thermodynamics of the stripping process. 1. Introduction Bismuth modified electrodes have been extensively studied as possible replacements for mercury electrodes for the detection of trace toxic heavy metal ions such as Pb2+, Cd2+, and Zn2+ using stripping voltammetry. Both in situ and ex situ fabrication methods and a range of electrode substrates have been investigated.1-9 The characteristics of the deposited bismuth and the potential at which bismuth stripping occurs effects the electrodes success as a sensor and the potential window available for the detection of other ions and molecules. The electrochemical deposition of metal deposits on an electrode surface can be influenced by a number of factors including the nature of the electrolyte, solvent, pH, and the electrode substrate. In this paper, we investigate the effect on the stripping voltammetry of bismuth changing from the single crystal Au(111) electrode used in our previous paper10 to a boron-doped diamond (BDD) electrode. In our previous paper,10 the stripping of a bismuth film from a Au(111) single crystal electrode was found to have slow kinetics (k0 ) 4 × 10-7 cm s-1) and a mechanism that has a chemical rate-determining step that likely involves a change in solvation of a Bi+ intermediate. STM and X-ray diffraction have been used to characterize the bismuth deposit and suggest that a film is epitaxial and that it covers the whole electrode surface, although this film is rough and not of a uniform thickness.11-13 On Au(111), a UPD layer is observed indicating that deposition of a monolayer of bismuth on Au(111) is more favorable than the deposition of bismuth on itself. Similar voltammetry to that of bismuth on a Au(111) electrode has been reported in the literature14 on a Pt(111) electrode. Boron-doped diamond (BDD) is an electrode material where deposition of metals has been observed to start with * Corresponding author. E-mail: [email protected]. Tel: +44(0) 1865 275 413, Fax: +44(0) 1865 275 410. † Oxford University. ‡ York University.

nucleation on the surface leading to randomly spaced hemispherical deposits being observed.7,15-18 The absence of a UPD layer indicates that the deposition of bismuth on BDD is less favorable than deposition of bismuth on itself. Depositing bismuth will therefore preferentially grow where it has already nucleated rather than grow evenly over the whole electrode surface. The BDD surface is also known to be heterogeneous with some areas being more active than others due to the orientation of the BDD and a variation of boron-doping levels. These differences along with defects in the surface determine where the bismuth nucleates on the surface. The difference between these observations on BDD and those on Au(111) suggest that the bismuth deposition will vary substantially between the two different electrode substrates and this may affect the stripping voltammetry, as is indeed observed experimentally, as reported below. The target of this paper is to investigate whether the differences in the stripping voltammetry of bismuth on a Au(111) and a BDD electrode can be explained by the difference in the distribution of bismuth on the electrode surface. In this paper, we use mathematical modeling and numerical simulation to investigate the effect on the voltammetry of stripping hemispherical metal deposits compared to uniform films under electrochemically irreversible conditions.

2. The Basic Mathematical Model Full details of the n electron stripping voltammetry mathematic model and details of the computational aspects of the numerical simulations can be found in our previous paper.10 A brief summary is provided here. Bismuth deposition and stripping occurs via a net three electron transfer according to the equation below:

10.1021/jp809355n CCC: $40.75  2009 American Chemical Society Published on Web 01/26/2009

Stripping Voltammetry of Hemispherical Deposits ka

Bi3+(aq) + 3e- y\z Bi(s)

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kd 19,20

The process is assumed to follow Butler-Volmer kinetics according to the equations below where ka is the rate constant for addition to the surface and kd is the rate constant for dissolution:

(E - E )) ( R′F RT (n - R′)F k ) k [A] exp( (E - E )) RT ka ) k0 exp 0

0 f

0 f

0

d

ΓBi ) 0 for 0 e r e rd

(1)

(2) (3)

k0 is the rate constant, R′ is the effective transfer coefficient, n is the number of electrons, Ef0 is the formal potential, and [A]0 ) 1 × 10-3 mol cm-3 is a standard concentration included to take account of the different standard states adopted by thermodynamics for aqueous Bi3+ and solid Bi.21 R is the ideal gas constant (8.314 J mol-1 K-1), F is the Faraday constant (96 485 C mol-1), and T is the temperature in K. The active area, which may be the whole electrode surface in the case of a film or a single hemispherical deposit on the surface, is modeled as a disk of radius rd, and this gives cylindrical symmetry to the system. The problem can therefore be considered as two-dimensional with r representing the coordinate axis that runs parallel to the electrode/deposit surface from the center of the electrode/deposit out into the solution. z represents the coordinate axis that is perpendicular to the electrode surface with z ) 0 being the electrode/deposit surface. In the case of a film across the whole electrode, rd takes the value of the electrode radius, whereas in the case of a hemispherical deposit, it takes the value of the initial radius of the hemisphere. Table 1 gives the general boundary and surface conditions for this model. The diffusion of Bi3+ within the solution is given by Fick’s second law,19 which is also included in Table 1. In this model, it is assumed that the rate of dissolution of bulk Bi from the surface is independent of the position-dependent surface coverage of Bi, ΓBi, whereas the rate of deposition is dependent on the solution concentration of Bi3+. The second surface boundary condition is needed to ensure that the stripping stops once all the bismuth has run out and that the coverage of bismuth on the surface does not drop below zero. The initial condition for solution which is used in each simulation is

[Bi3+] ) [Bi3+]bulk for 0 e r e rmax and 0 e z < zmax (4) whereas the position-dependent surface coverage, ΓBi, depends on the experiment being simulated. When deposition is included, the initial condition is

(5)

In cases when only the stripping step is considered, ΓBi reflects the nature of the deposit. The surface coverage is modeled as having an infinitely small height. This approximation is suitable when you have a relatively uniform layer; however, this approximation starts to break down when uneven or incomplete layers are considered, as it does not give a true description of the surface area and its changes during the scan. The system of partial differential equations that define this model as a solution using a fully implicit finite difference scheme22 combined with Newton’s method and an extended version of the Thomas algorithm.23,24 The current flowing at the electrode surface due to the stripping of a deposit can be calculated using the following equation:

I ) -2πnF

∫0r

d

∂ΓBi rdr ∂t

(6)

When a number of separate hemispherical deposits are present on the electrode surface, it is necessary to simulate each deposit, taking into account their proximity to other deposits, and add the resulting current signals together. This model will be adapted later in this paper to consider modeling hemispherical deposits. 3. Bismuth Stripping Voltammetry at Au(111) and BDD Electrodes: Experimental Results Details of the bismuth stripping voltammetry experiments carried out on a Au(111) electrode can be found in our previous paper.10 The amount of bismuth deposited on the Au(111) at suitably high overpotentials has been simulated using the model described in Section 2. Figure 1 shows a plot of stripping peak potential against deposition time at fixed deposition potentials of -0.2 and -0.25 V. The plot shows the experimental results, the results from the simulation outlined in Section 2, and the value calculated using eq 7 below and the parameters given in Table 2.

Ep ) E0f +

RT RT (n - R′)FΓ + ln ln υ (7) (n - R′)F RTkd (n - R′)F

Equation 7 is an equation derived by Brainina25-27 for the dissolution of metal under electrochemically irreversible conditions. The equation has been modified so that all symbols have the same meaning as in the mathematical model in Section 2. υ is the scan rate of the stripping potential sweep. In this equation, Γ refers to the initial average surface coverage of the deposited layer (which must be approximately uniform). From Figure 1, it can be seen that there is good agreement among the simulated results, eq 7, and the experimental results. This shows that the mathematical model and parameters in Table 2

TABLE 1: General and Surface Boundary Conditions and Fick’s Second Law for the Model Described in Section 2 equations [Bi ] ) 0 ∂[Bi3+]/∂r ) 0 ∂[Bi3+]/∂r ) 0 ∂[Bi3+]/∂z ) 0 3+

boundary region 0 e r e rmax r ) 0 r ) rmax rd < r e rmax

z 0 0 z

) zmax e z < zmax e z < zmax ) 0

Surface Boundary Conditions (∂ΓBi)/(∂t) ) DBi3+(∂[Bi3+])/(∂z) ) ka[Bi3+ ]z)0 - kd 0 e r e rd z ) 0 kd∂t ) -∂ΓBi + ka[Bi3+]z)0∂t If (∂ΓBi)/(∂t) > ka[Bi3+ ]z)0 - kd Fick’s Second Law (∂[Bi3+])/(∂t) ) D((∂2[Bi3+])/(∂r2) + (1)/(r)(∂[Bi3+])/(∂r) + (∂2[Bi3+])/(∂z2))

0 e r e rmax

0 e z < zmax

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Figure 1. A comparison of experimentally recorded stripping peak potential, Ep, against deposition time for the deposition and stripping of bismuth on a Au(111) electrode from a 1 mM Bi3+/0.1 M HClO4 solution, scan rate 20 mV s-1, and a deposition potential of -0.2 or -0.25 V with the results of simulations and the predicted results from eq 7 both using the parameters in Table 2.

Figure 2. Comparison of the stripping voltammetry of bismuth from a Au(111) and a BDD electrode. The dotted line indicates a simulation of the BDD electrode experiment using the parameters in Table 2 (which are for stripping voltammetry on a Au(111) electrode) and assuming that a smooth layer of bismuth is deposited.

TABLE 2: Simulation Parameters from ref 10 for the Simulation of the Stripping Voltammetry of Bismuth on a Au(111) Electrodea

bismuth on Au(111). It can be seen that the main part of this peak is at a higher peak potential and is narrower than the experimental peak from the BDD electrode experiment. Despite the difference in deposition time and potential, the simulated BDD electrode peak is in a similar position to the experimental peak from the Au(111) electrode. This suggests that the nature of the bismuth deposition and stripping depends on the electrode substrate. The mathematical simulation used in Figure 2 does not take the effects of nucleation into account and assumes that bismuth has no preference as to where it deposits on the BDD surface, and a smooth film of bismuth is therefore deposited. Figure 3 shows the atomic force microscopy (AFM) image of the BDD electrode after the 120 s deposition at -1.2 V in a 1 mM Bi3+ solution. From the image, it is obvious that the bismuth does not cover the whole electrode with a continuous layer but is instead present as a large number of hemispherical deposits with spaces between them. This is in contrast to bismuth deposition at the Au(111) where the whole electrode surface is covered. This difference in the distribution of material on the electrode surface is one possibility for the differences observed in the stripping peaks at the two different electrodes and will be investigated in the following section. The parameters obtained in our previous paper10 showed that the bismuth stripping on the Au(111) electrode is electrochemically irreversible, and therefore in the next section, we investigate the mathematical modeling of the stripping hemispheres under these irreversible conditions.

parameter

value

diffusion coefficient, D number of electrons transferred, n effective transfer coefficient, R′ rate constant, k0 formal potential (vs SCE), Ef0 temperature, T scan rate, υ starting potential, E1 end potential, E2 molar density, d

5.5 × 10-6 cm2 s-1 3 2 4 × 10-7 cm s-1 0.015 V 293 K 0.02 V s-1 - 0.5 V + 0.5 V 0.0468 mol cm-3

a

These parameters are used for the simulations in Sections 3 and 4.

fit the experimental data well for deposition on a Au(111) electrode and that the kinetics are slow enough for the process to follow the equation for stripping under electrochemically irreversible conditions. Experimental details of the boron-doped diamond experiments can be found in the Supporting Information. All potentials quoted in this paper are versus the SCE electrode. Figure 2 show a comparison of the voltammetry at a borondoped diamond electrode after a 120 s deposition at -1.2 V in a 1 mM Bi3+ solution with the voltammetry from a 60 s deposition at -0.25 V at a Au(111) electrode. The data from the Au(111) electrode have been scaled to represent the same electrode size as that used in the BDD experiments. The experimental stripping peak of the BDD electrode occurs at a more negative potential than that of the Au(111) electrode. The BDD electrode peak is also wider and more symmetrical than the Au(111) peak. The area of the BDD peak is larger than that of the Au(111) peak, which is expected due to the longer deposition time. At the deposition potentials used in these experiments, the deposition is expected to be diffusion controlled for the majority of the deposition phase. Also shown in Figure 2 is the simulated voltammetry, using the model presented in Section 2, expected for the boron-doped diamond experiment using the mechanism and parameters determined in our previous paper10 (and listed in Table 2) for

4. Electrochemically Irreversible Stripping of Hemispheres Three different ways of modeling shrinking hemispheres are proposed in this section. To model the three-dimensional shape of the hemisphere would be computationally difficult, as the size of the hemisphere changes throughout the scan, leading to a moving solid/liquid boundary. To avoid this and to model experimental data, three different approximation models for shrinking hemispheres under electrochemically irreversible conditions are proposed and evaluated. These models all involve modeling the hemisphere as a flat disk which has a different size and position dependent coverage for each model. Stripping hemispheres under irreversible conditions will mean that dif-

Stripping Voltammetry of Hemispherical Deposits


Figure 3. AFM image of the BDD electrode surface after a 120 s deposition at -1.2 V in 1 mM Bi3+/0.1 M HClO4 solution.

TABLE 3: Comparison of the “Flat Cone” Model with a Real Hemisphere at Different Stages in the Stripping Process. Figure 4. Schematic diagram of the stripping of a hemisphere and the three models considered in this paper.

radius of hemisphere

radius of cone

height of cone

volume of shape

surface area

(2πr3)/(3) (9πr3)/(32) (πr3)/(12) (πr3)/(96)

2πr2 (18πr2)/(16) (πr2)/(2) (πr2)/(8)

(2πr3)/(3) (9πr3)/(32) (πr3)/(12) (πr3)/(96)

2πr2 (18πr2)/(16) (πr2)/(2) (πr2)/(8)

Hemisphere

fusion within the solution does not have any influence on the rate of stripping, as the irreversible nature of the process implies no back reaction. The voltammetry can therefore be simulated by considering only the metal on the electrode surface. Figure 4 shows a schematic diagram of the stripping of a real hemisphere under electrochemically irreversible conditions (Figure 4a) and the three approximate models that simulate the hemisphere as a flat disk. Figure 4b shows the “uniform layer” model. The radius of the flat disk, rd, is kept equal to that of the hemisphere, rh, and the average coverage of metal on the electrode surface is assigned across the whole layer so that at the beginning of the scan the amount of metal present is the same as that in the hemisphere. The initial condition of the position-dependent coverage, Γ, on the disk is Γ ) (2/3)rhd for 0 < r < rd where d is the molar density (in mol cm-3) of the metal. Figure 4c shows the “hemispherical distribution” model. In this model, the radius of the flat disk, rd, is kept equal to that of the hemisphere, rh, and the position-dependent coverage has a distribution of metal on it that represents the amount of metal above that point in the real hemisphere. The initial condition of the position-dependent coverage, Γ, on the disk is Γ ) drh2 - r2 for 0 < r < rd. Figure 4d shows the “flat cone” model. Under irreversible electrochemistry, it is possible to specify the initial conditions of the simulation so that the flat disk area represents the surface area of the hemisphere. The position-dependent coverage is then set to represent the distribution of material over the flat disk so that the total amount of material present is equal to that of the hemisphere being modeled. This is done in such a way that the surface area of the flat disk with a nonzero coverage of metal decreases with the total amount of metal on the surface in a way that mirrors the shrinking of a hemisphere that maintains its hemispherical shape through the dissolution (Figure 4a). This involves a conical distribution of material over the flat disk and is hence going to be referred to as the “flat cone” model. Under

r (3r)/(4) (r)/(2) (r)/(4) r (3r)/(4) (r)/(2) (r)/(4)

2r (3 × 2r)/(4) (2r)/(2) (2r)/(4)

Cone r (3r)/(4) (r)/(2) (r)/(4)

irreversible conditions, it would be expected that the hemisphere would retain its shape during dissolution, as unequal diffusion in solution will not have a role in the dissolution rate. The exception to this would be when stripping metal off the electrode substrate is less favorable than stripping off the metal from itself. The transformation needed for the “flat cone” model described above involves modeling the hemisphere as a flat disk with a conical distribution of material on a flat disk with the radius, rd, equal to 2rh. The “height” of the cone is equal to the radius of the original hemisphere, rh. The “height” is incorporated into the position-dependent coverage (in mol cm-2) when modeling the cone as flat and has a maximum value of rhd, where dis the molar density (in mol cm-3) of the metal and r is the radius of the hemisphere (in cm). The initial condition of the positiondependent coverage, Γ, on the disk is Γ ) drh[1 - r/(2rh)] for 0 < r < rd. When R is the radius of the hemisphere at any given time, the volume of a hemisphere is 2/3πR3 and the surface area of the curved surface is 2πR2. The volume of a cone is 1/3πR2h and the area of the base of a cone, which represents the surface area in the “flat cone” model, is πR2. r is the initial radius of the hemisphere. Table 3 shows how the “flat cone” represents the hemisphere at different stages during the stripping processes as defined by the radius of the hemisphere at that moment in time. In contrast to the “uniform layer” and “hemispherical distribution” models, it can be seen that the “flat cone” model


Figure 5. Simulated voltammetry of the stripping voltammetry of a 1 µm radius hemisphere using the “uniform layer”, “hemisphere distribution”, and “flat cone” models. The material is stripping into a blank solution. All other simulation parameters are given in Table 2.

accurately represents both the surface area and the amount of material left of the shrinking hemisphere under irreversible conditions at all times during the stripping process. Figure 5 shows the simulated voltammetry for the stripping of a 1 µm radius hemisphere into a blank solution using the parameters given in Table 2 for each of the models proposed above. The “hemispherical distribution” model gives a more rounded peak and a lower peak current than the “uniform layer” model but has the same peak potential. The peak from the “hemispherical distribution” model is also wider than for the “uniform layer” model, as there is still some material left on the electrode surface after the peak maximum because the maximum occurs when the decrease in the covered area of the flat disk is greater than the increase in the rate of dissolution. In the “uniform layer” model, all of the material runs out at the peak maximum. The low potential part of the stripping peak is the same for these two models, as they have the same surface area exposed to the solution. From Figure 5, it can also be seen that the “flat cone” model has a lower peak potential and a lower peak current than both of the other models. The “flat cone” model peak rises faster than the other models at the beginning of the scan due to the larger surface area of the flat disk in this model. The surface area of the disk in this case is equal to the surface area of the hemisphere rather than the area of its base. The peak is broader at its half-peak height than the “hemisphere distribution” model peak; however, the potential difference between the start and the end of the stripping peak is about the same. Figure 4 also shows how the amount and distribution of material on the surface has reduced after a set amount of time, which corresponds to the radius of the real hemisphere becoming half of its original value. Out of the three models considered in this paper, the “flat cone” model is the most accurate for representing the shrinking of the hemisphere over the whole stripping potential sweep, as it takes account of both the correct and changing surface area as well as the amount of material left on the surface. This “flat cone” model will be used in the rest of this paper for the modeling of hemisphere deposits under electrochemically irreversible conditions. In circumstances where the hemisphere will not retain its shape during the stripping potential sweep, such as when the material has stronger interactions with the electrode surface material than itself, this model will not be as accurate.

Jones et al.

Figure 6. Plot showing the stripping of 2, 4, 6, 8, and 10 1-µm-radius hemispheres under irreversible conditions (black lines) and a comparison with uniform layers (dotted lines) containing the same amount of material but with a constant base area equal to that of 10 1-µm-radius hemispheres. The material is stripping into a blank solution. All other simulation parameters are given in Table 2.

Under irreversible kinetics, the difference between the a uniform layer and the “flat cone” model for hemisphere stripping can act as an approximate comparison between a flat uniform deposit and a rough deposit that covers the whole surface at the beginning of the stripping process. It can therefore be concluded by looking again at Figure 5 that the distribution of metal on the surface has a large effect on the shape and position of the stripping peak. The surface area, maximum height, and unevenness of the deposit all have an effect on the peak shape. The following subsections investigate the effects of different distribution material on the electrode surface. 4.1. Changing the Number Density of Hemispheres. Figure 3 shows that on the boron-doped diamond electrode the whole electrode surface is not covered with bismuth metal deposits. Hemispheres of bismuth are present with gaps between then. The number density is the number of hemispheres present on a fixed total electrode area. Simulations run using the mathematical model detailed in Section 2 and the parameters listed in Table 2 can be used to compare the expected voltammetry for a uniform layer (using the “uniform layer” model) and a distribution of hemispheres (using the “flat cone” model) with the same total amount of bismuth present and a fixed total electrode area. Figure 6 shows the effect on the voltammetry of increasing the number of 1 µm hemispheres on an electrode surface with a fixed area. As we are considering electrochemically irreversible conditions, the decreasing spacing between particles does not have an effect on the voltammetry, as no redeposition of bismuth will take place. Increasing the number of hemispheres on the surface simply increases the magnitude of the current, but the peak potential and shape of the peak remain the same; in other words, the voltammetry from N hemispheres is simply N times that of a single hemisphere. Figure 6 also shows the effect of having the same amount of material present in the form of a uniform layer that covers the whole electrode surface. The area of the electrode has been assigned the value equal to the area covered by 10 1-µm-radius hemispheres. As the amount of material on the electrode surface is increased in the same way as increasing the number of hemispheres on the surface, the result is that the uniform layer gets thicker. The beginning of the peak and the general shape are the same for all thicknesses; however, the peak potential shifts to more positive values as



Figure 7. Plot showing a comparison of 0.25-, 0.5-, and 1-µm-radius hemispheres (black lines) with uniform layers (dotted lines) containing the same amount of material and with the same base area. This acts as an example comparing a smooth layer to an uneven layer with the whole surface covered at the beginning. The material is stripping into a blank solution. All other simulation parameters are given in Table 2.

Figure 8. Different sized hemispheres with the same total amount of material. From left to right, 1000 0.1-µm-radius hemispheres, 64 0.25µm-radius hemispheres, 8 0.5-µm-radius hemispheres, and 1 1-µmradius hemisphere (black lines). Also shown is a uniform layer (dotted line) with the same total volume and a base area equal to that covered by 1000 0.1-µm-radius hemispheres. The material is stripping into a blank solution. All other simulation parameters are given in Table 2.

the thickness of the deposit increases and the peak becomes wider and the peak current increases. The peak shape is much sharper than for the hemispheres, as the material on the surface is depleted at the same time at all places on the electrode surface, resulting in a sharp drop. With low numbers of particles in the same area, the thin uniform layer with the same total amount of material has a less positive peak potential than when considering the hemispheres. With higher numbers of particles, the peak potential of the equivalent uniform layer is more positive than with the hemispheres. Figure 6 shows that there is a large difference between the voltammetry of a uniform layer and a distribution of hemispheres. 4.2. Changing the Size of Hemispheres. Figure 7 shows the effect on the voltammetry of increasing the size of a hemisphere on the electrode surface. 0.25-, 0.5-, and 1-µm-radii hemispheres are shown along with a corresponding uniform layer that has the same total amount of material in and has the same electrode area as the base of the hemisphere in each case. The difference in peak potential between the uniform layer and the hemisphere does not seem to depend on the size of the hemisphere. The change in surface area and maximum height between the two models seems to create a constant shift regardless of particle size. As the hemisphere size increases, the uniform layer thickness also increases, and therefore, the peak potential in both cases shifts toward more positive potentials. The peak potential increases with hemisphere size and layer thickness, as it takes longer for the material on the surface to run out. 4.3. Changing the Size of Hemispheres with the Same Total Amount of Material. Figure 8 shows the effect on the voltammetry of changing the size of the hemispheres while changing the number present so that the same total amount of material is on the electrode surface. The simulated voltammetry for 1000 0.1-µm, 64 0.25-µm, 8 0.5-µm and 1 1-µm-radius hemispheres is shown in the figure. The peak current remains constant as the size of the hemispheres is increased; however, the peak potential shifts toward more positive potentials. Also shown in Figure 8 is the simulated voltammetry for a uniform layer containing the same amount of material as the hemisphere and has a surface area equal to the area covered by 1000 0.1µm-radius hemispheres. For small particles, the peak potential

is less positive than for a uniform layer with the same total volume; however, for larger particles with a lower surface coverage, the peak potential is more positive than for the thin uniform layer. This is mainly due to the increase in the maximum thickness of the particle but is also due to the decreasing surface area. The effect of the decreasing surface area with increasing hemisphere size accounts for the difference in the magnitude of the current near the start of the stripping peak. 4.4. A Mixture of Hemisphere Sizes. From Figure 3, it can be seen that there is a range of sizes of bismuth hemisphere deposits on the BDD electrode. If the stripping of the bismuth deposits take place under electrochemically irreversible conditions, as it does with a Au(111) electrode,10 the proximity of the deposits to each other will have no effect on the stripping signal observed, as diffusion within the solution is irrelevant. This allows a mixture of hemisphere sizes to be considered by simply adding together the currents for a range of hemisphere sizes, which have been weighted according to the number of each size present. The voltammetry is also not effected by whether metal is stripped into a blank solution or into a solution already containing the metal ions as long as the solution concentration does not get too close to the saturation solubility limit. Figure 9 shows the effect on the voltammetry of a mixture of hemisphere sizes on the electrode surface and is compared to the voltammetry with the same amount of material present in the form of single-sized hemispheres. In this example, the voltammetry for 1000 0.1-µm, 64 0.25-µm, 8 0.5-µm, to 1 1-µmradius hemispheres are shown individually and are compared with the voltammetry for the same total amount of material made up from a mixture of the different-sized hemisphere. The mixture is such that a quarter of the material comes from each of the 0.1, 0.25, 0.5, and 1-µm-radius hemispheres. It can be seen from Figure 9 that the mixture of particle sizes broadens the peak and also reduces its peak current compared to the voltammetry expected when the same amount of material is present in a number of particles with the same size. The voltammetry from the simulation of a mixture of particle sizes is very bumpy because there is not a smooth change in particle size. This voltammetry also indicates that, if there is a noncontinuous distribution of hemisphere deposit sizes that


Jones et al.

Figure 9. Comparison of the effect of a quarter of the material present being of each of 4 different-sized hemispheres to create a voltammetric signal with the voltammetry of all the material being present as each of 4 different-sized hemispheres. The hemispheres have a radius of 0.1, 0.25, 0.5, and 1 µm. The material is stripping into a blank solution. All other simulation parameters are given in Table 2.

Figure 10. A comparison of the experimentally recorded voltammetry for the stripping of bismuth from a BDD after deposition from a 1 mM Bi3+/0.1 M HClO4 solution for 120 s at -1.2 V (scan rate ) 20 mV s-1) and the simulated stripping results using the “flat cone” model with either a 3.8 × 108 45-nm-radius hemisphere or 4.3 × 109 20-nmradius hemisphere, both being stripped into a blank solution. The other simulation parameters as listed in Table 2.

covers a large range of sizes, split peaks or peak shoulders might be observed. In this section, it has been shown that under electrochemically irreversible conditions the distribution of material on the surface makes a big difference in the shape and position of the stripping peak. The broadening of peaks can be explained by a distribution of hemisphere sizes along with the effects of having hemispheres instead of a flat layer. The following section uses this information to assess whether the difference in the distribution of bismuth on a Au(111) and a BDD electrode can explain the difference in the experimental voltammetry discussed above.

flat layer on the electrode surface. The simulation peak has a higher peak current and is thinner, as it does not take into account the range of hemisphere sizes. Even if the extreme case of all the material being present as 4.3 × 109 20-nm-radius hemispheres, as shown by the dotted line in Figure 10, is considered, the simulated peak still does not shift to the position of the experimental peak. The change in hemisphere size does show that the distribution of hemisphere sizes on the BDD electrode is wide enough to cause a difference in the voltammetry, and a lowering of the peak current and broadening of the peak would be expected as was seen in Figure 9. The simulation was done using a blank solution, as otherwise the initial distribution of material is altered so much that peaks are completely different sizes and the distribution no longer represents a hemisphere. If the solution concentration is important because the process does not have completely irreversible kinetics, the presence of metal ions in the solution would push the simulation peak further to the right. It can therefore be concluded that consideration of the distribution of metal on the surface alone cannot explain the difference in the voltammetry on Au(111) and BDD. Other possible reasons for the difference may include a change in kinetics, thermodynamics, or mechanism. Returning to Figure 2, it can be seen that the experimental results from the experiment on boron-doped diamond look more “electrochemically reversible” than on the Au(111) electrode, as the voltammetry does not form a plateau with I ) 0 between the deposition stage at the beginning of the scan and the stripping peak at the end. It is therefore appropriate to now consider changing the kinetics for the stripping voltammetry of bismuth on the BDD electrode. Figure 11 shows an approximate simulation fit of the experimental data for the stripping of bismuth from a BDD electrode after deposition in a 1 mM Bi3+/0.1 M HClO4 solution for 120 s at -1.2 V (scan rate ) 20 mV s-1) obtained using the following values: k0 ) 1 × 10-5 cm s-1, Ef0 ) -0.044 V with all other parameters remain unchanged from Table 2. These parameters represent the same mechanism as is used to fit the data from the Au(111) electrode experiments but faster kinetics and a slight change in formal potential. The dashed line shows the fit using the “flat cone” model with 3.8 × 108 45-nm-radius

5. Comparison of Theoretical and Experimental Data Section 4 studied the distribution of material on the surface and has shown that the shape and position of the peak can reflect this. This information can next be used to try and simulate the BDD taking the size distribution of hemispheres observed by AFM into account but still using the parameters and mechanism found for bismuth stripping from a Au(111) electrode. From the experimental voltammetry, it can be calculated that there are 3.4 × 10-9 mol of bismuth on the BDD surface (area ) 0.0707 cm2) giving an average coverage of 4.75 × 10-8 mol cm-2. However as seen in Figure 3, this material does not form a uniform layer but is instead present as separate hemispherical deposits. The average-sized hemisphere has a radius of 45 nm; however, the sizes range from 20 to 70 nm. Given the average 45 nm radius and the total amount of bismuth on the surface, it is predicted that there are on the order of 3.8 × 108 particles on the surface, which is roughly consistent with the number seen in the AFM image, as 480 particles are expected and approximately 600 can be counted. Figure 10 shows the simulated voltammetry using the parameters listed in Table 2 and the “flat cone” model with 3.8 × 108 45-nm radius hemispheres and the experimental voltammetry from the stripping of bismuth from a BDD after deposition from a 1 mM Bi3+/0.1 M HClO4 solution for 120 s at -1.2 V (scan rate ) 20 mV s-1). The simulation, using an average hemisphere radius size of 45 nm, does not give a peak in the correct place with stripping occurring at a more positive potential than observed experimentally. This is a similar difference to that observed when modeling the bismuth as a


Figure 11. An approximate simulation fit of the experimental data from the stripping of bismuth from a BDD after deposition from a 1 mM Bi3+/0.1 M HClO4 solution for 120 s at -1.2 V (scan rate ) 20 mV s-1) obtained using the following k0 ) 1 × 10-5 cm s-1 and Ef0 ) -0.044 V with all other parameters remaining unchanged from Table 2. The dashed line shows the simulation of 3.8 × 108 45-nm-radius hemispheres stripping into a blank solution, and the dotted line shows the full ASV simulation, assuming that the whole BDD surface has the same activity and the solution concentration of Bi3+ is 1 mM.

hemispheres being stripped into a blank solution. This fit is approximate as the “flat cone” model starts to break down as the kinetics get faster and the stripping process becomes more reversible, as diffusion within the solution starts to play an important role. The shape of the peak will also change if the full distribution of hemisphere sizes is considered. It is therefore difficult to judge whether there may also be a change in mechanism. The dotted line shows the anodic stripping voltammetry (ASV) simulation using the same parameters but includes the deposition step, the correct solution concentration of 1 mM, but assumes that the whole BDD surface has the same activity. With this new set of parameters, the crossover between deposition and stripping occurs at the correct point and the peak has approximately the correct area; however, the peak is too sharp, as the distribution of metal on the surface is not correct. The full ASV simulation has a peak potential less positive than using the “flat cone” model. This is because the complete layer of material formed during the simulation of the deposition is thinner than the average coverage in areas where a hemisphere is present. The results in this section suggest that the difference in the voltammetry may be due to a difference in the structure of the bismuth deposits formed rather than just the distribution on the electrode surface, and hence a change in the kinetics and thermodynamics of the deposition process. 6. Discussion of Results Section 5 has shown that it is not possible to model the data for bismuth stripping voltammetry on BDD using the mechanism and parameters determined in our previous paper on Au(111). When deposition of metal occurs on a foreign substrate, there are a number of different growth processes that can happen. The balance of these processes depends on the electrode substrate and the experimental conditions and can lead to different morphologies and orientations of the metal deposit, which may in turn lead to a change in the observed voltammetry. A difference in the stripping voltammetry of bismuth on different electrode materials can be seen by comparing voltammetry from

J. Phys. Chem. C, Vol. 113, No. 7, 2009 2853 literature; however, in most cases a direct comparison is very hard to make, as different electrolytes, pH, and solution concentrations are used as well as the different electrode materials. An example of the difference between carbon paste and a gold electrode can be seen in ref 28. The deposit on Au(111) is made of crystalline Bi with the Bi(012) plane parallel to the Au(111) surface for bulk deposits.13 On the BDD electrode, there is an absence of a UPD layer or any other surface interactions that would force the depositing bismuth to adopt a set orientation, and therefore, the bismuth deposits formed may be randomly orientated. This may result in a more active surface of the bismuth being in contact with the solution, leading to the faster kinetics suggested in Section 5. The bismuth deposit might also have a different morphology. Needle-like structures have been observed for bismuth on Au(111) where inclusion of new atoms can only occur at the needle tip.13 Different morphologies will have different surface structures and may therefore affect the kinetics and thermodynamics for the stripping/deposition process. There is also a possibility that different morphologies of bismuth might have a different mechanism for growth and dissolution. Electrodeposited bismuth has been observed in other studies to form different morphologies depending on the experimental conditions used and electrode substrate.29 7. Conclusions Experiments show a difference in the stripping voltammetry of bismuth from a single crystal Au(111) electrode and a BDD electrode. It has been shown using mathematical modeling and numerical simulation that this difference cannot be accounted for by just considering the different distributions of bismuth on the electrode surface. It is therefore concluded that the difference in voltammetry is mainly due to the morphology/orientation of the deposits formed leading to differences in the kinetics and thermodynamics for the stripping process. Acknowledgment. S.E.W.J. thanks the NERC for a studentship (NER/S/A/2005/13354). K.T. thanks the EPSRC and Asylum Research for funding and support. S.H.Z. and S.M. gratefully acknowledge financial support from the Natural Sciences and Engineering Research Council (NSERC) of Canada and York University. S.M. also acknowledges the financial support from the Canada Research Chair Program. Supporting Information Available: Experimental details of the experiments on boron-doped diamond. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Banks, C. E.; Kruusma, J.; Hyde, M. E.; Salimi, A.; Compton, R. G. Anal. Bioanal. Chem. 2004, 379, 277. (2) Hocevar, S. B.; Ogorevc, B.; Wang, J.; Pihlar, B. Electroanalysis 2002, 14, 1707. (3) Kachoosangi, R. T.; Banks, C. E.; Ji, X.; Compton, R. G. Anal. Sci. 2007, 23, 283. (4) Kadara, R. O.; Tothill, I. E. Anal. Bioanal. Chem. 2004, 378, 770. (5) Kruusma, J.; Banks Craig, E.; Compton Richard, G. Anal. Bioanal. Chem. 2004, 379, 700. (6) Pauliukaite, R.; Hocevar, S. B.; Ogorevc, B.; Wang, J. Electroanalysis 2004, 16, 719. (7) Toghill, K. E.; Wildgoose, G. G.; Moshar, A.; Mulcahy, C.; Compton, R. G. Electroanalysis 2008, 20, 1731. (8) Wang, J. Electroanalysis 2005, 17, 1341. (9) Wang, J.; Lu, J.; Hocevar, S. B.; Farias, P. A. M.; Ogorevc, B. Anal. Chem. 2000, 72, 3218. (10) Ward Jones, S. E.; Zheng, S. H.; Jeffrey, C. A.; Seretis, S.; Morin, S.; Compton, R. G. J. Electroanal. Chem. 2008, 616, 38.

2854 J. Phys. Chem. C, Vol. 113, No. 7, 2009 (11) Zheng, H. M. Sc Thesis, York University, 2005. (12) Jeffrey, C. A.; Harrington, D. A.; Morin, S. Surf. Sci. 2002, 512, L367. (13) Jeffrey, C. A.; Zheng, S. H.; Bohannan, E.; Harrington, D. A.; Morin, S. Surf. Sci. 2005, 600, 95. (14) Valsiunas, I.; Gudaviciute, L.; Steponavicius, A. Chemija 2005, 16, 21. (15) Simm, A. O.; Ji, X.; Banks, C. E.; Hyde, M. E.; Compton, R. G. ChemPhysChem 2006, 7, 704. (16) Hyde, M. E.; Banks, C. E.; Compton, R. G. Electroanalysis 2004, 16, 345. (17) Hyde, M. E.; Jacobs, R. M. J.; Compton, R. G. J. Electroanal. Chem. 2004, 562, 61. (18) Hyde, M. E.; Jacobs, R. M. J.; Compton, R. G. J. Phys. Chem. B 2002, 106, 11075. (19) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications, 2nd ed.; John Wiley & Sons: New York, 2001. (20) Compton, R. G.; Banks, C. E. Understanding Voltammetry; World Scientific: Singapore, 2007.

Jones et al. (21) Chevallier, F. G.; Goodwin, A.; Banks, C. E.; Jiang, L.; Jones, T. G. J.; Compton, R. G. J. Solid State Electrochem. 2006, 10, 857. (22) Strikewerda, J. C. Finite Difference Schemes and Partial Differential Equations; Prentice Hall: New York, 1973. (23) Kreiszig, E. AdVanced Engineering Mathematics; John Wiley and Sons, Inc.: New York, 1962. (24) Svir, I. B.; Klymenko, O. V.; Compton, R. G. Radiotekhnika 2001, 118, 92. (25) Brainina, K. Z. Stripping Voltammetry in Chemical Analysis; Halsted: New York, 1974. (26) Brainina, K. Z.; Lesunova, R. P. Zh. Anal. Khim. 1974, 29, 1302. (27) Brainina, K. Z.; Vydrevich, M. B. J. Electroanal. Chem. 1981, 121, 1. (28) Baldrianova, L.; Svancara, I.; Vlcek, M.; Economou, A.; Sotiropoulos, S. Electrochim. Acta 2006, 52, 481. (29) Jiang, S.; Huang, Y.-H.; Luo, F.; Du, N.; Yan, C.-H. Inorg. Chem. Commun. 2003, 6, 781.

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The Stripping Voltammetry of Hemispherical Deposits Under

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