J. Phys. Chem. C 2008, 112, 1933-1937
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Gold Nanoparticle-Modified Carbon Nanotubes-Modified Electrodes. Using Voltammetry to Measure the Total Length of the Nanotubes Ian Streeter, Lei Xiao, Gregory G. Wildgoose, and Richard G. Compton* Physical and Theoretical Chemistry Laboratory, Oxford UniVersity, South Parks Road, Oxford, United Kingdom OX1 3QZ ReceiVed: September 24, 2007; In Final Form: NoVember 13, 2007
A carbon nanotube (CNT)-modified electrode is made in which a glassy carbon macroelectrode is partially covered with a layer of gold nanoparticle-modified CNTs. The carbon surfaces are passivated so that only the gold nanotubes are electroactive. Linear sweep voltammetry of ferrocyanide is studied using the modified electrode, and the results are interpreted by numerical simulation. It is shown that the voltammetric measurements can measure the total length of the CNTs present on the surface.
1. Introduction Voltammetric measurements have long been used to make temporal measurements. Examples include the precise inference of diffusion coefficients and rate constants,1 both heterogeneous and homogeneous. Only more recently voltammetry has found application in the domain of spatial explorations, notably the introduction of scanning electrochemical microscopy evolving from the work of Engstrom et al.,2,3 who were the first to show that a microelectrode could be employed as a local probe to map the concentration profiles of species near a larger, active electrode. Recently, we have been interested to explore complementary experiments in which particles located on or near an electrode surface can be sized, shaped, and located via voltammetric experiments only. Initially, we determined the average size of inert particles at about the micron level deposited on a macroelectrode.4 Linear sweep voltammetry (LSV) was used to study a reversible redox couple on the partially blocked electrode at a range of scan rates, and finite difference methods were used to numerically simulate the voltammetric response. With knowledge of the total mass of the particles and a value for their density, the particle size could be calculated. A similar approach was used to accurately size a single spherical particle placed at the center of a microdisc electrode.5 The concept was extended to three dimensions by depositing an inert sphere adjacent to a microdisc electrode; chronoamperometric measurements of a simple redox system were compared with lattice Boltzmann simulations to derive the radius of the sphere and its distance from the electrode.6 The sphere could be located to a higher degree of accuracy by using a three-electron array in a triangulation experiment.7 Taking this idea further, we studied hemispherical microdroplets immobilized on a regular array of hydrophobic polymer blocks of a partially blocked electrode.8 Potential step experiments were compared to finite difference simulations to determine an accurate droplet radius. These experiments build on ideas implied in scanning electrochemical microscopy and those developed for measuring film thickness.9,10 Finally, we note that the use of photoelectrochemical measurements allows the measurement of the size of objects without the need for them to be immersed in a solution.11 * Corresponding author. Email:
[email protected]. Fax: +44 (0) 1865 275410. Tel: +44 (0) 1865 275413.
Figure 1. Schematic diagram of gold-modified MWCNTs randomly distributed on a glassy carbon macroelectrode.
In the present paper, we seek to explore the voltammetric measurement of objects of “nano” dimensions. In particular, we are concerned with making a carbon nanotube (CNT)modified electrode in which the latter is partially covered with a layer of gold nanoparticle-modified CNTs. The modifying material is chosen to be electroactive toward the oxidation of ferrocyanide at potentials at which the substrate electrode can be made inactive. It is shown that voltammetric measurements alone can measure the total length of the CNTs present on the surface. This measurement can be compared to the total length estimated by scanning electron microscopy (SEM) imaging to give information on the electrochemical activity of the CNTs. 2. Theory Figure 1 shows a schematic diagram of the modified electrode. Carbon nanotubes modified with gold nanoparticles (AuCNTs) lie flat on a glassy carbon (GC) macroelectrode. The carbon surfaces are passivated by the physisorption of anthraquinone-2,6-disulfonic acid. At an appropriate potential, the electron transfer occurs only at the gold nanoparticles;12 oxidation of ferrocyanide at the passivated carbon surfaces requires a significantly more positive overpotential. In this work, we treat the modified electrode as a randomly distributed array of parallel band electrodes, the bands being the AuCNTs. Figure 2 shows a schematic diagram of this model. The model ignores the three-dimensional structure of the nanotubes, which is justified because the diffusion layer thickness is considerably greater than the nanotubes’ height above the electrode surface.
10.1021/jp0776661 CCC: $40.75 © 2008 American Chemical Society Published on Web 01/12/2008
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Figure 2. Schematic diagram of a section of a randomly distributed electroactive band array.
It also assumes that the nanotubes are electroactive along their entire length, which is a reasonable assumption for a high coverage of gold nanoparticles. The theory of diffusion to a randomly distributed array of microband electrodes was described in a previous paper.13 The theory also applies here, although the band electrodes under consideration are of nanometer rather than micrometer dimensions. In a voltammetric experiment, a “diffusion zone” is created at each electroactive nanotube as the diffusing species is consumed. As the time of the experiment progresses, these diffusional zones extend further into solution, often to the extent that they overlap with those of neighboring nanotubes. For microband arrays, different diffusional behaviors were identified depending on the extent of this overlap.13,14 The diffusion is described as “category 1” when the diffusion layer thickness is much smaller than the width of the electroactive band. This behavior is unlikely to be observed at conventional scan rates for bands of nanometer dimensions. “Category 2” requires the electroactive nanotubes to be diffusionally independent with no overlapping of diffusion zones. As the diffusion zone grows and overlap begins, the diffusion is described as “category 3”. In this regime, the nanotubes experience a shielding effect from their neighbor, and the flux of the electroactive species to the nanotube 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 overall planar diffusion to the supporting macroelectrode, even though the regions between the electroactive nanotubes remain electrochemically inert. In our previous paper,13 a zone diagram was presented to describe which is the active diffusion category for a wide range of scan rates and microband separation distances. 3. Numerical Simulation Category 1 and category 4 diffusional behaviors both involve planar diffusion, so the linear sweep current response can be calculated by a relatively trivial one-dimensional approach.15 Category 2 diffusion is simply that of an isolated band electrode for which the current response is also well understood.16-19 Category 3 provides a slightly more complicated problem, because the electroactive nanotubes cannot be considered in isolation of each other. The numerical methods used to simulate the current at a microband array under any diffusion category have been described in detail in our previous papers.13,14 We provide a short summary here for the reader’s convenience. The problem of simulating a large array of electroactive bands is simplified by using a diffusion domain approach, as illustrated in Figure 3. In this approach, the array is partitioned into smaller units with the boundaries being the planes at the center of each band and at the midpoint of each electroinactive region between the bands. The approximation is made of zero net flux across these planes, so that each resulting diffusion domain may be considered independently. For a randomly distributed array, these diffusion domains will all be of different sizes. Equation
Figure 3. Cross section of a diffusion domain.
TABLE 1: Boundary Conditions for Equation 2 boundary
condition
initial conditions center of microband (x ) 0) domain boundary (x ) s) electroinactive surface bulk solution electroactive band
c ) c* ∂c/∂x ) 0 ∂c/∂x ) 0 ∂c/∂Z ) 0 c ) c* eq 3
1 presents the probability distribution function that describes the different sizes
( )
f(s) ) exp -
s 〈s〉
(1)
where s is the width of the diffusion domain, and 〈s〉 is the mean width over the whole array. To calculate the total current response at our surface modified electrode, mass transport is first simulated at a range of different sized diffusion domains. The current response of each domain is then weighted according to eq 1. The sum of these weighted current responses gives the voltammetric response for the whole electrode surface. Mass transport in a diffusion domain is described by Fick’s second law of diffusion using the coordinates x and z, which are defined in Figure 2 as
(
∂2c ∂2c ∂c )D 2+ 2 ∂t ∂x ∂z
)
(2)
where c is the concentration of the electroactive species, and D is a diffusion coefficient, which is assumed to be equal for both the reactant and product of the electron transfer. The electron transfer at the nanotube-solution interface is described by Butler-Volmer kinetics as
FE FE ∂c ) k0c exp (1 - R) - k0(c* - c) exp -R ∂z RT RT
(
)
(
)
(3)
where k0 is the standard heterogeneous rate constant, and c* is the concentration of the electroactive species in bulk solution. Equation 2 is discretised and solved by the alternating direction implicit finite difference method subject to the boundary conditions in Table 1. This yields concentration profiles from which the current, i, is calculated using eq 4
i ) 2FlD
dx ∫0w/2 ∂c ∂z
(4)
where w and l are the width and length of the nanotube, respectively. 4. Experimental Section 4.1. Reagents and Equipment. All reagents were purchased from Aldrich (Gillingham, U.K.) with the exception of potas-
Au Nanoparticle-Modified CNTs-Modified Electrodes sium chloride (Reidel de Ha¨en, Seelze, Germany). “Bamboolike” multiwalled carbon nanotubes (b-MWCNTs) were purchased from Nanolab (Brighton, MA)20 and consist of tubes 30 ( 15 nm in diameter and 2-20 µm in length. The term bamboolike refers to the fact that the tubes are periodically closed along their length. Electrochemical measurements were recorded using a computer-controlled Autolab potentiostat (EcoChemie) with a standard three electrode configuration in solutions containing 0.1 M KCl as supporting electrolyte. A GC electrode with a geometric area of 0.07 cm2 (BAS Technicol) was used as a working electrode, a platinum wire as a counter electrode, and a saturated calomel reference electrode (SCE, Radiometer, Copenhagen, Denmark) completed the cell assembly. Prior to modification with the AuCNTs, the GC electrode was polished with diamond spray (Kemet, Kent, UK) using decreasing sizes from 3 to 0.1 µm. The electrode was then sonicated for 5 min in pure water. All experiments were carried out at 20 ( 2 °C. SEM images were recorded using a JSM 6300 microscope, using an acceleration voltage of 20 kV and an operating distance of 15 mm. Transmission electron microscopy (TEM) images were recorded using a JEOL 2000FX microscope with a tungsten filament as the electron source using an acceleration voltage of 200 kV. 4.2. Preparation of Gold-Modified Multiwalled Carbon Nanotubes. The procedure used for modification of the bMWCNTs was adapted from reports previously published.21 First, 50 mg of the b-MWCNTs was activated by refluxing in a 3 M solution of 1:1 (HNO3/H2SO4) at 80 °C for 5 h and was washed thoroughly with pure water. Next, the b-MWCNTs were suspended in a solution of 1% SDS (surfactant) at 1 mg/mL concentration and sonicated for 30 min. Finally, gold nanoparticles were deposited onto the activated CNTs by mixing the suspension with 500 µL of 1% HAuCl4‚H2O followed by 500 µL of 0.75% NaBH4 dropwise while stirring. The mixture was stirred for another 5 min, filtered with a membrane filter (0.45 µm, Millipore), and washed with pure water. 4.3. Immobilization of the AuCNTs onto the Working Electrode and Passivation of the GC and MWCNT Surfaces. To immobilize the AuCNTs onto the GC electrode, a “casting” solution of 1 µg/mL of the AuCNTs suspended in chloroform and sonicated for 30 min was used. A 20 µL aliquot of the casting suspension was then placed onto the GC electrode surface, and the solvent was allowed to evaporate at room temperature leaving the AuCNTs immobilized onto the GC surface. Next, any exposed GC substrate and bare regions of the MWCNTs were passivated so that only the gold nanoparticles remain as the electroactive sites on the electrode surface. To this end, the AuCNT-modified GC electrode was immersed in a 10 mM aqueous solution of anthraquinone-2,6-disulfonic acid according to a literature procedure.12
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Figure 4. An SEM image of the AuCNT-modified GC electrode.
Figure 5. A TEM image of a gold nanoparticle-modified MWCNT.
5. Results and Discussion
Figure 6. Overlaid linear sweep voltammograms of a bare GC electrode; a GC electrode after passivation with physisorbed anthraquinone; and a AuCNT modified GC electrode (again, after passivation of the carbon substrate with anthraquinone) in 1 mM potassium ferrocyanide. Scan Rate 100 mV s-1.
The gold nanoparticle-modified carbon nanotubes have been characterized previously using high-resolution transmission electron microscopy and cyclic voltammetry.22 An example TEM image is shown in Figure 5. The b-MWCNTs are uniformly encrusted in gold nanoparticles with an average diameter of 10 nm. The total diameter of the AuCNT including the contribution from the nanoparticles is estimated from the TEM images to be 40 nm. Next, the AuCNT-modified GC electrode surface was examined using SEM. Figure 4 shows that the AuCNTs are dispersed onto the GC electrode surface as a sparse monolayer, which allows one to approximate the
electrode as a random array of gold nanoband electrodes as discussed above. From this and several other SEM images, the mean separation of the nanotubes was estimated to be 3.0 µm. Next the linear sweep response of 1 mM potassium ferrocyanide was studied on the following three electrode surfaces: a bare GC electrode, a b-MWCNT-modified GC electrode passivated with physisorbed anthraquinone, and the AuCNTmodified GC electrode with passivated carbon surfaces. Figure 6 shows the resulting linear sweep voltammograms. It is apparent that the electron-transfer kinetics at the underlying carbon surface and b-MWCNT support has been slowed down
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Figure 7. Concentration profiles at a diffusion domain of size s ) 1.5 µm. The scan rates are (a) ν ) 10 V s-1, and (b) ν ) 0.05 V s-1. The concentration profile is recorded at the peak potential. Electroactive bands of width 40 nm are located at x ) 0 and x ) 3 µm.
compared to a clean, bare GC as demonstrated by the increased overpotential required to oxidize the ferrocyanide. However, at the AuCNT-modified GC electrode, ferrocyanide is oxidized at a less positive potential, indicating that for our purposes the gold nanoparticles can be considered as the principal electroactive sites on this heterogeneous electrode surface. The LSV response of the AuCNT-modified GC electrode was examined at various scan rates from 0.05 to 10 V s-1, and the peak current was recorded for comparison with the simulated peak currents. Our theoretical treatment of the modified GC electrode assumes the width of the AuCNTs is 40 nm and they have an average spacing 3.0 µm. The literature value of D ) 6.3 × 10-6 cm2 s-1 is used for the diffusion coefficient of ferrocyanide,23 and a value of k0 ) 0.013 cm s-1 is used for the rate constant of its oxidation on gold.12 The zone diagrams presented in our previous paper predict that for these dimensions the diffusional behavior is category 3.13 Numerical simulations must therefore be used to interpret the current response under this category of diffusion, as described in Section 3. Figure 7 shows simulated concentration profiles for scan rates of 0.05 and 10 V s-1. For both scan rates, there is significant overlapping of diffusion zones, consistent with category 3 diffusion. For the scan rate 0.05 V s-1, the overall diffusion profile looks approximately planar, suggesting the diffusion is close to the category 4 limit. The current is calculated from the simulated concentration profiles using eq 4. To implement this equation, a value is needed for the total combined length of all the nanotubes. The simulated voltammetry is compared to the experimental voltammetry, and by using the method of least-squares the best fit between the two data sets is found when a total length of 230 cm is used. The total length of nanotubes can also be estimated by using the SEM images such as that shown in Figure 4. The use of this method suggests a total nanotube length of 160 cm.
Figure 8. Simulated voltammetry at three different scan rates.
This is within reasonable agreement with the electrochemically “measured” value, indicating that the nanotubes are electrochemically active along their entire length. The simulations were repeated with varying values of the tube diameter and average spacing to account for the error in measuring these values. The best fit total length was found to be relatively insensitive to the value used for tube diameter, but slightly more sensitive to the average spacing. For all values used, the electrochemically measured length was within reasonable agreement of the SEM measured length. The simulated currents presented in the figures in this section use a value of 230 cm for the total length. Figure 8 shows simulated voltammetry for a range of scan rates. The voltammograms all have the distinctive peaked shape associated with approximately planar diffusion. Figure 9 shows a comparison of the peak currents for experimental and simulated data. The experimental peak currents have been baseline corrected to account for the capacitive current. Also shown in Figure 9 are the peak currents predicted by a planar
Au Nanoparticle-Modified CNTs-Modified Electrodes
J. Phys. Chem. C, Vol. 112, No. 6, 2008 1937 Note Added after ASAP Publication. This article was published ASAP on January 12, 2008. The caption of Figure 6 has been modified. The correct version was published on January 16, 2008. References and Notes
Figure 9. Peak currents as a function of scan rate at the modified electrode. Experimental and simulated data are shown by squares and circles, respectively. The planar diffusion peak currents found using Digisim24 are shown by a solid line.
diffusion model, which were found by using the commercial simulation package Digisim.24 The planar diffusion simulations use the same values of D and k0 as for our two-dimensional simulations and a total electrode area of 0.07 cm2. It can be seen that the experimental peak currents are close to the planar diffusion values at slow scan rates for which there is considerable overlapping of neighboring diffusion zones and the diffusional behavior is close to the category 4 limit. At faster scan rates where overlapping of diffusion zones is less significant, the peak currents deviate much further from planar diffusion behavior. The numerically simulated peak currents in Figure 9 show good agreement with the experiment. 6. Conclusions The abilities of voltammetric measurements for the “sizing” of gold nanotubes modifying an electrode surface has been demonstrated and shown to be quantitative. Acknowledgment. I.S. and L.X. thank the EPSRC for studentships. G.G.W. thanks St John’s College, Oxford for a Junior Research Fellowship.
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