Single Collision Events of Conductive Nanoparticles Driven byMigrationJun Hui Park,⊥ Aliaksei Boika, Hyun S. Park, Heung Chan Lee, and Allen J. Bard*

Center for Electrochemistry, Department of Chemistry and Biochemistry, The University of Texas at Austin, Austin, Texas 78712,United States

*S Supporting Information

ABSTRACT: We report that conductive single nanoparticle (NP)collisions can involve a significant component of the mass transportto the electrode of the charged NPs by migration. Previously,collision events of catalytic NPs were described as purely diffusionalusing random walk theory. However, the charged NP can also beattracted to the electrode by the electric field in solution (i.e.,migration) thereby causing an enhancement in the collisionfrequency. The migration of charged NPs is affected by thesupporting electrolyte concentration and the faradaic current flow. Asimplified model based on the NP transference number is introduced to explain the migrational flux of the NPs. Experimentalcollision frequencies and the transference number model also agreed with more rigorous simulation results based on the Poissonand Nernst−Planck equations.

1. INTRODUCTION

We report a strong effect of migration in explaining singlenanoparticle (NP) collision events of charged metal particles.Migration of the NP increases the particle flux to the electrode,resulting in an increase in the sensitivity of NP detection overpreviously reported current amplification (amperometric)1−8

and potentiometric techniques.9 In this previous work, NPmass transport only by diffusion (Brownian or random walkmotion) was considered. This random process depends on thediffusion coefficient, which follows the Stokes−Einsteinrelation.10

Characterizing single particle collision events electrochemi-cally has been suggested as a means of analysis of lowconcentrations, using particles as labels. However, the detectiontime can be quite long when the concentration of the particlesin solution is low (e.g., attomolar or smaller) when the arrival ofparticles at the electrode only occurs by random motion(diffusion). To measure low analyte concentrations foranalytical applications (e.g., in biomarker detection), a drivingforce of a single particle to the electrode is needed.11 Extensivestudies on analyte collection at electrodes have been carriedout. Magnetic nanoparticles are frequently used to tag theanalyte, because they can be attracted by a magnetic field.12

Microfluidic systems utilize convection by pumping orelecroosmosis to produce flow through a microfluidicchannel.13 Migration of the nonconductive particles, e.g., latexor polystyrene beads, or silica particles, produce a decrease inthe ferrocene methanol oxidation current of Pt ultramicroe-lectrodes (UMEs) by blocking the electroactive area.14,15

However, the migration of conductive particles in collisionexperiments has not previously been considered.

Here, we show that catalytic metal NP collisions can becontrolled by migration. Catalytic NPs colliding and adheringto an inert Au UME show steplike current increases uponcollision events.2 The total flux of particles is substantiallyenhanced by the migration effect, and the migrational flux ofNPs was often larger than the diffusional flux in ourexperiments. Migrational collision frequencies were estimatedbased on the transference number of the NPs. A Multiphysicssimulation was performed to calculate the NP flux using thePoisson and Nernst−Planck equations that take into accountboth diffusion and migration at the same time. Finally, a quickcalculation method is suggested to estimate migrating NPfrequency without simulation. The simulation results matchwell with both the experimental data and the suggested quickcalculation results.

2. EXPERIMENTAL SECTION

Reagents. Sodium phosphate dibasic anhydrous(Na2HPO4, 99.5%), sodium phosphate monobasic monohy-drate (NaH2PO4·H2O, 99.5%), and potassium chloride (KCl,99.6%) were obtained from Fisher Scientific (Pittsburgh, PA).Hexachloroplatinic acid hexahydrate (H2PtCl6·6H2O, 99%) wasobtained from Alfa Aesar (Ward Hill, USA). Hydrazineanhydrous (N2H4, 98%), citric acid (99.5%), L-ascorbic acid(99%), ferrocene methanol (97%), trisodium citrate dihydrate(99%), and sodium borohydride (NaBH4, 98%) were obtainedfrom Sigma-Aldrich. All chemicals were used as received.Millipore water (18 MΩ) was used in all experiments. Platinum

Received: December 21, 2012Revised: February 27, 2013Published: March 8, 2013

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(99.99%) and gold (99.99%) wires, 10 μm in diameter, fromGoodfellow (Devon, PA) were used to fabricate the UMEs.Preparation of UMEs. Pt and Au UMEs were prepared

following the general procedure developed previously. Briefly, a10 μm diameter metal (Au, Pt) wire was sealed in a borosilicatecapillary tube (0.75 mm i.d. 1.5 mm o.d., FHC, Brunswick, ME)after rinsing with ethanol and water. The electrode was thenpolished on an abrasive pad (Buehler, Lake Bluff, IL), followedby polishing to a mirror finish in alumina powder watersuspension on microcloth pads (Buehler, Lake Bluff, IL). Thesurface area of electrodes was confirmed by standard redoxelectrochemistry of ferrocene methanol.Instrumentation. The electrochemical experiments were

performed using a CHI model 630 potentiostat and 920cpotentiostat (CH Instruments, Austin, TX) with the three-electrode cell placed in a Faraday cage. A 3 mm diametercarbon rod was used as the counter electrode and the referenceelectrode was Ag/AgCl in a saturated KCl solution. Allpotentials are quoted versus Ag/AgCl. Pt NP mobility wasmeasured by electrophoretic light scattering using a ZetasizerNano ZS (Malvern Instruments, Malvern, UK).Preparation of Metal Nanoparticles (NPs). The Pt NPs

(diameter 32 ± 3 nm) solutions were prepared by theprocedure reported previously.9 A seed-mediated growthprocedure was used to prepare stable citrate-capped large PtNPs. Seed particles were prepared as follows. H2PtCl6·6H2O(3.8 mM, 7 mL) was added to boiling water (90 mL) whilestirring. After 1 min, 2.2 mL of solution containing 34 mMtrisodium citrate and 2.6 mM citric acid was added, followed bya quick addition of freshly prepared sodium borohydride (21mM, 1.1 mL). After 10 min, the solution was cooled to roomtemperature. For 32 nm particles, 1 mL of Pt seed solution wasadded to 29 mL of water with stirring. H2PtCl6·6H2O (0.4 M,0.045 mL) was added, followed by addition of 0.5 mL solutioncontaining 34 mM trisodium citrate and 71 mM ascorbic acid.The temperature was slowly increased to the boiling point (∼5°C/min). The reaction time was 1 h with a reflux condenser.NPs were washed twice with water by precipitation in acentrifuge at 14 000 rpm for 10 min. A recent study showedthat citrate adsorbed during synthesis (at 100 °C) is stable onthe Pt NP even after the washing step.16 From the measuredzeta-potential value, ∼−50 mV, we obtained approximately−190 charges per Pt NP (32 nm in diameter) in 5 mMmonovalent supporting electrolyte solution.17 For calculatingthe charge of NP, the interested reader is referred to Ohshimaet al.18

Multiphysics Simulation. The simulation was performedby solving the Poisson and Nernst−Planck equations usingCOMSOL Multiphysics 3.5a software. The electrostatics andNernst−Planck without charge neutrality modules were used.An adaptive free triangular mesh element was used. The meshsize at the UME surface was set to 5 nm. The followingparameters were used at room temperature (298 K). In thePoisson equation the relative permittivity of the medium (εr)was set to 80, space charge density (ρ) was set as ∑ziCi and ε0was the vacuum permittivity (8.854 × 10−12 F/m). Diffusioncoefficients (D) of ions were assumed to be the ideal infinitedilution values; D(Na+) = 1.33 × 10−5 cm2/s, D(HPO4

2‑) =7.59 × 10−6 cm2/s, D(H2PO4

−) = 9.59 × 10−6 cm2/s, D(N2H4)= 1.39 × 10−5 cm2/s, D(H+) = 9.31 × 10−5 cm2/s, D(Pt NP) =1.02 × 10−7 cm2/s.19,20 The diffusion coefficient of the Pt NPwas determined from the mobility that was measured by lightscattering using a Zetasizer. Mobilities of ions (ui) were

calculated from the diffusion coefficients using the Einsteinrelation, ui = ziDi(F/RT),

10 where zi and Ci represent the chargeand concentration of the species i. zNP itself is not important inthis simulation because it is already reflected in the uNP.

3. EXPERIMENTAL RESULTSWe previously reported NP collision events using catalyticproton reduction with Pt NPs,1 water oxidation with IrOx NPs,

3

hydrazine oxidation with Pt NPs,2 and sodium borohydrideoxidation on Au NPs.4 Reported collision events werecontrolled by diffusion (Brownian motion) of the particlesbecause of the relatively high supporting electrolyte concen-tration (e.g., 100 mM), which suppressed the migration effect.Under these conditions, the collision frequency of the NPs( fdiff) was determined from the flux of the adhering particles tothe UME, jdiff, which is a function of DNP, the diffusioncoefficient of the particles, CNP, the concentration of theparticles and r0, the radius of the UME disk electrode accordingto eq 1. Note that the frequency of NP is obtained simply bymultiplying by Avogadro’s number ( fdiff = jdiffNA).

=j D C r4diff NP NP 0 (1)

=NPf

fvalid NP ratio( )ratio

diff,ex

diff (2)

The ratio in eq 2, fdiff,ex/fdiff, is an estimate of the number ofobservable collisions, and is obtained by comparing thecollision frequency calculated with eq 1 and the experimentalobserved collision frequency, fdiff,ex, with 50 mM supportingelectrolyte (where migration is negligible). This ratio (2) was∼13%. The observed diffusional collision frequency depends onthe state of the surface of the NP and UME,21 the NP contactwith the UME, and NP size. For a more accurate calculation, abetter estimate of the NP concentration is required. Ananalogous valid ratio of NP would also apply to the migrationalflux of NP; this ratio must be considered when comparing thecomputed (or simulated) data to the experimental data.One can increase the collision frequency by enhancing mass

transport (e.g., by migration) of the NPs to the UME. Tochange the collision system from the diffusional dominance toone with a larger migrational component, (1) electrodepotential, (2) faradaic current, (3) supporting electrolyteconcentration (ionic strength), and (4) sign and magnitudeof the particle charge should be considered.The total flux of NPs is the sum of the migrational and

diffusional fluxes, as shown in eq 3.

= +j j jtotal diff mig (3)

where jtotal is total flux of NP and jmig is migrational flux of NP.If we assume that jdiff is given at steady state by eq 1, under theconditions of the experiments discussed here with lowelectrolyte, the total flux is mainly controlled by jmig.

Effect of Electrode Potential and Background Current.Figure 1 shows Pt NP collision events using the hydrazineoxidation reaction at a Au UME at different electrode potentialsand background currents that affected the Pt NP collisionfrequency. At −100 mV (background current ∼1 nA) (Figure1b) the frequency of the collision events was ∼17 times largerthan that at −150 mV (background current ∼90 pA) (Figure1a). The increase in the collision frequency can be attributed tothe migration effect, because diffusional collisions are notaffected by the electrode potential in the diffusion-limited

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region as indicated by eq 1. The two different collisionfrequencies with the same Pt NP concentration resulted fromthe increased anodic background current, ∼10 times, so the fluxof the negatively charged NPs increased (when the supportingelectrolyte concentration was low (5 mM)) to supply theneeded charge at the electrode to maintain electroneutrality(Scheme 1). With 50 mM supporting electrolyte, there was nomigration effect at different electrode potentials. Deciding theproper supporting electrolyte concentration for a migrationeffect requires consideration of several factors, thus, one needsto do a simulation. For an estimate, the transference number ofthe NP can be used to determine the supporting electrolyteconcentration needed to observe a migration effect, asdiscussed below.

Insight from the Transference Number. The trans-ference number (tj) indicates the fraction of the total currentcarried by the anions and cations in electrolysis as shown in eq4.22 The transference number of a NP represents the relativeflux of charged NPs in the electrolyte solution.

=| |

∑ | |t

z u C

z u Cjj j j

i i i i (4)

In considering the overall conduction, the NP transferencenumber, tNP, is usually neglected because its value is muchsmaller than those of the supporting electrolyte ions, tNa+ ortH2PO4

2−, as shown in Scheme 1a. This indicates that thefraction of current in the bulk solution transported by Pt NPs isnegligible. However, even this tiny transference number, tNP,becomes important when the electrode reaction is controlledby the flux of NP to the electrode and the diffusionalcontribution to the mass transport of NPs is also tiny (becausethe NP diffusion coefficient value and the concentration are

Figure 1. Chronoamperometric curves for single Pt NP (radius ∼16nm) collisions at the Au UME (radius 5 μm) in the presence of 7.5pM Pt NPs in 5 mM phosphate buffer (pH 7.0) and 15 mM hydrazine.Applied potentials are (a) −0.15 V and (b) −0.1 V (vs Ag/AgCl).Data acquisition time was 50 ms.

Scheme 1. (a) Migration Portion of Balance Sheet for the Electrochemical Cell, and (b) Pictorial Illustration of the Two MajorParticle Fluxes of Diffusion (Brownian Motion) and Migrationa

aCharge of Pt NP was assumed to be −190 for this estimation.

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very small). Under such conditions the NP migrational collisionfrequency becomes important.Origin of Migration: Effect of Current. Migration (as

also in electrophoresis) arises because of the effect of theelectric field on a charged species in the bulk solution (Scheme1a) and also near the electrode surface (i.e., within the diffusionlayer) (Scheme 1b). This field develops because of the flow offaradaic current at the electrode, so that the migration effectdepends on the magnitude of the faradaic current (which is afunction of the electrode potential). Figure 2 shows three

consecutive Pt NP collision chronoamperograms withpotentials −0.2 V, −0.1 V, and then back to −0.2 V appliedin sequence. While the same potential was applied (−0.2 V),the observed collision frequency differed due to the history ofthe electrode. A clean Au UME in the first experiment onlyshows a few collision events within a 400 s window at −0.2 Vwith a small hydrazine oxidation current (∼100 pA). At asubsequent more positive potential, −0.1 V, the oxidationcurrent is larger. This mainly involves the kinetically controlledincrease following Butler−Volmer behavior, and also the factthe electrode now has some Pt NPs attached from the earlierexperiment. This increased oxidation current enhances themigrational flux of the negatively charged Pt NPs toward the AuUME and the collision frequency is larger. After many Pt NPshave stuck on the Au UME by collision events at −0.1 V, theattached catalytic Pt NPs increase the hydrazine oxidationcurrent at −0.2 V on Au UMEs. When the potential is againswitched to −0.2 V, the faradaic current at the Au UME ismuch larger (∼1.5 nA) than in the initial −0.2 V experiment,and this leads to a larger collision frequency at −0.2 V.Effect of Supporting Electrolyte Concentration. In

addition to the current, the supporting electrolyte concen-tration is an important factor in migration, since it determinestNP. One can expect the Pt NP collision frequency will decreasewith an increase in the supporting electrolyte concentration.Figure 3 shows a Pt NP collision experiment at −0.1 and −0.05V, applied potentials in the region where a large catalyticcurrent difference exists between Au and Pt, with differentsupporting electrolyte concentrations. At a high concentrationof the supporting electrolyte condition (50 mM) in Figure 3a,the Pt NP collision frequency was ∼0.017 pM−1 s−1 for the first

100 s. By lowering the supporting electrolyte concentration to 5mM, the Pt NP collision frequency increased to ∼0.14 pM−1

s−1. This frequency difference is consistent with the about 10times larger tNP at 5 mM compared with tNP at 50 mMsupporting electrolyte concentration. Thus, the Pt NP collisionfrequency with 50 mM supporting electrolyte is controlledmainly by diffusion, with negligible migration of the Pt NPs,while at 5 mM the NP mass transfer is controlled mainly bymigration. In Figure 3b, the faradaic current at the Au UMEincreased at the more positive potential, causing an increase inthe NP collision frequency at all concentrations of supportingelectrolyte. This demonstrates that adjustment of both thesupporting electrolyte concentration and the applied potentialis important in controlling the Pt NPs collision frequency at aAu UME.

Collision Frequency Calculation. The transferencenumber indicates the fraction of current, tNP, carried in thebulk solution by each species (where tNP = iNP/iTotal and iTotal isthe total current flowing during a collision). The producttNPiTotal represents a measure of current by the NP. The currentof NPs can be converted to the flux of NPs by multiplying by1/(zPtNPF). From the transference number and the faradaiccurrent flow, one can estimate the flux of Pt NPs migrating tothe Au UME per second by eq 5, where iavg is the averagecurrent flow at Au UME, zNP is the charge of Pt NP, and F isthe Faraday constant.

=jt i

z FNPmigrational flux of Pt NP ( )mig

NP avg

NPratio

(5)

The collision frequency was proportional to the averagecurrent, at a given supporting electrolyte concentration when

Figure 2. Chronoamperometric curves for single Pt NP (radius ∼16nm) collisions at the Au UME (radius 5 μm) at various potentials(−0.2, −0.1, and −0.2 V vs Ag/AgCl; by time sequence) in thepresence of 7.5 pM Pt NPs, 5 mM phosphate buffer (pH 7.0), and 15mM hydrazine. Data acquisition time was 50 ms.

Figure 3. Chronoamperometric curves for single Pt NP (radius ∼16nm) collisions at the Au UME (radius 5 μm) with various phosphatebuffer concentrations (50, 25, 10, and 5 mM; pH 7) in the presence of7.5 pM Pt NPs and 15 mM hydrazine at −0.1 V (a) and −0.05 V (b)(vs Ag/AgCl). Data acquisition time was 50 ms.

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the NP has the same transference number (i.e., at a givensupporting electrolyte concentration), as shown in Figure 4.

The average current used in Figure 4 was obtained from theexperimental result in Figure 3 by integrating the current toobtain the total charge and dividing it by the time. The slopesin Figure 4 represent the relative transference numbermagnitude. The relation between migrating NP and iavg implieseq 5 is qualitatively correct. The line for a smaller supportingelectrolyte concentration has a steeper slope. With 50 mMphosphate buffer, diffusion dominates, and the collisionfrequency is almost independent of the current. The interceptsof these plots should represent the diffusional component. Theapplicability of eq 5 was studied by a model for calculatingmigration based on a Multiphysics simulation.Simulation. A Multiphysics simulation was performed to

obtain the expected collision frequency using a steady-statecurrent (i.e., the average experimental current) at the UME. Weassume the UME reaction is hydrazine oxidation (N2H4 → N2+ 4H+ + 4e) and neglect mechanistic complications. ThePoisson and Nernst−Planck equations, eqs 6 and 7,respectively, were used to describe the NP collision eventunder migration and diffusion.

ε ε ρ−∇ ∇ =V0 r (6)

= − ∇ − ∇J r z D C r z u C r z V r z( , ) ( , ) ( , ) ( , )i i i i i (7)

where ε0 is the vacuum permittivity, εr is the relativepermittivity, V is the electric potential, ρ is space chargedensity, Ji is the flux of each species, Di is the diffusioncoefficient, Ci is the concentration, and ui is the electricalmobility of the ionic species.In the simulation the space dimension was taken as 2D axial

symmetry, with electrostatics and nonconservative Nernst−Planck steady-state equation selected.23 Simulation details areshown in the Experimental Section and the SupportingInformation. Figure 5 shows the experimental collisionfrequency and simulated frequency as a function of thesupporting electrolyte concentration. Every parameter valuewas the same for the two simulation sets except for the averagecurrent. The simulated Pt NPs collision frequencies agree fairlywell with the two experimental data sets in Figure 3.

Comparison of the Simulation and the Simplified(Transference Number) Treatment for CalculatingCollision Frequencies. A simplified model for predictingconditions needed for a given collision frequency based on eq 5is quicker and easier than carrying out the more rigorousMultiphysics simulation. One only needs the faradaic currentfor the electrode reaction (A → A+ + e; A is a unchargedoxidizable redox mediator (e.g., ferrocenemethanol, hydra-zine)) that drives the migration and the transference numbersof all species in the starting solution. The collision frequency asa function of supporting electrolyte concentration computedfrom the simulation and from eq 5 with diffusion coefficients ofA, A+, and supporting electrolyte ions of 1 × 10−5 cm2 s−1 andthat of the Pt NPs of 1.02 × 10−7 cm2 s−1 are plotted in Figure6. The two results match quite well in this case. However, thetransference number approach is not rigorously correct underall possible conditions, because it does not account for the roleof electrogenerated species.24 The transference number in thebalance sheet assumes constant bulk solution concentrationsand a steady state. However, it does not consider theproduction of ions by the faradaic reaction that leads tochanges in the ionic concentrations (and hence the electricfield) in the diffusion layer. Thus, in the example, the diffusioncoefficient of A+ governs the concentration profile near theelectrode surface, as shown in Figure 7a. The NP collision

Figure 4. Collision frequency vs average current at three differentphosphate buffer concentrations (5, 10, and 50 mM) at variouspotentials (−150, −100, −50, and 0 mV), which set the backgroundcurrent. Collision frequency was counted for the first 100 s afterparticle injection. The average current was obtained from integratingthe charge and dividing by time. Data obtained by 3−5 replicatemeasurements.

Figure 5. Experimental (triangles) and computed (circles. fromMultiphysics simulation based on Poisson and Nernst−Planckequations) collision frequency as a function of the supportingelectrolyte concentration at an applied potential of (a) −0.1 V and(b) −0.05 V. Average current in (a) is 3.4 nA (5 mM), 1.6 nA (10mM), 0.66 nA (25 mM), and 0.4 nA (50 mM). Average current in (b)is 9.8 nA (5 mM), 3.6 nA (10 mM), 1.3 nA (25 mM), and 0.67 nA (50mM). The average current and collision frequency were considered forthe first 100 s after particle injection. Diffusion coefficient of ionicspecies used in here is obtained from the literature19,20 which isdescribed in detail in the Experimental Section.

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frequency is inversely proportional to the diffusion coefficientof A+ as shown in Figure 7b, as obtained from Multiphysicssimulation under the same conditions except for D(A+). Sincethe transference number balance sheet approach does not

consider D(A+), it can lead to differences between thesimulation and the transference number approaches. In thesystem under consideration, where the electrode reaction ishydrazine oxidation, one H+ is produced per electrontransferred. In a buffer solution, the generated H+ reactsrapidly with the buffer base, and it is this ion that contributes tothe electric field in the diffusion layer, so that the D of thebuffer ion should be considered rather than that of H+. Figure 8

shows the collision frequency obtained from the Multiphysicssimulation and from eq 5 using the indicated D-values andmobility parameters. The results in Figure 8 show a deviation ofabout 30%.

Guidelines for Designing a Migrational CollisionSystem for Analytical Applications. We have suggestedthe use of electrocatalytic NPs as labels in analyticalapplications, where observation of collisions could extendanalyses to very small concentrations. Conditions wheremigration contributes significantly to the NP mass transferand thus increasing the collision frequency increases thesensitivity of the analytical method. The conditions needed tomaximize the collision current and frequency are the following:(1) transference number of NP should be maximized (i.e., highcharge and small radius); (2) the charge of the redox reactant,A, for the faradaic reaction should be zero; (3) a large reactantconcentration will enhance the faradaic current; (4) a small Dof the reaction product, A+, or its product in a followingreaction increases the electric field in the diffusion layer; (5) thesign of the NP charge must match the direction (anodic orcathodic) of the UME reaction; (6) low supporting electrolyteconcentration.On the basis of this study, citrated Pt NPs or Ag NP

collisions, where the NPs are negatively charged, will not showa migration effect with the proton reduction as the NPreaction,1,6 and an anodic electrocatalytic reaction is preferable.Similarly, negatively charged IrOx NP collisions with wateroxidation will show a migrational effect. The Ag NP oxidativefaradaic collision6 is not subject to migration enhancement,because ideally no reaction happens until the Ag NP arrives atthe electrode, so no current flows. It might be possible,

Figure 6. Quickly calculated and computer simulated (triangles fromeq 5 (NPratio = 1), and circles from Comsol simulations using Poissonand Nernst−Planck equations, respectively) collision frequency as afunction of the supporting electrolyte concentration. Average currentvalue used in both computations was 3.4 nA (5 mM), 1.6 nA (10mM), 0.66 nA (25 mM), and 0.4 nA (50 mM), which is obtained fromexperimental results in Figure 3a. D(A), D(A+), and D(supportingelectrolyte ions) are 1 × 10−5 cm2 s−1 and D(Pt NPs) is 1.02 × 10−7

cm2 s−1.

Figure 7. (a) Steady-state concentration profile of A+ at the anodedepending on diffusion coefficient of A+ (D(A+), from top to bottom 1× 10−5, 2 × 10−5, 3 × 10−5, 4 × 10−5, and 5 × 10−5 cm2 s−1) and (b)NP collision frequency as a function of the diffusion coefficient of A+.D(A) and D(supporting electrolyte ions) are 1 × 10−5 cm2 s−1. D(PtNPs) is 1.02 × 10−7 cm2 s−1.

Figure 8. Computed (triangles from eq 5 (NPratio = 1), circles fromComsol simulation based on Poisson and Nernst−Planck equations)collision frequency as a function of the supporting electrolyteconcentration. Average current value used in both computations was3.4 nA (5 mM), 1.6 nA (10 mM), 0.66 nA (25 mM), and 0.4 nA (50mM) which is obtained from experimental results in Figure 3a.Diffusion coefficient of ionic species used here is obtained from theliterature19,20 which is described in detail in the Experimental Section.

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however, to purposely introduce an electroactive reactant tocreate a background current in this case.

4. CONCLUSIONIn electrochemical detection of single NP events on anelectrode, the collision frequency can be increased under theright experimental conditions. The relative migration contribu-tion for the Pt NP/Au UME/hydrazine oxidation system isaffected by the supporting electrolyte concentration and thebackground current (determined by the applied potential). TheNP collision frequency can be simulated by a Multiphysicsprogram using the Poisson and Nernst−Planck equations andalso calculated from a simple transference number-balancesheet approach from the mobility of the NP and the averagetotal current. This technique could be used in designing the NPcollision system for sensitive analytical detection (e.g., at theaM or lower level) with proper system design.

■ ASSOCIATED CONTENT*S Supporting InformationSimulation information. This material is available free of chargevia the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*Fax: 512-471-0088. Tel.: 512-471-3761. E-mail: ajbard@mail.utexas.edu.Present Address⊥Department of Chemistry Education, Chonbuk NationalUniversity, Jeonbuk 560-756, Republic of Korea.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSWe appreciate support from the Robert A. Welch Foundation(F-0021), the National Science Foundation (CHE-1111518),and the Department of Defense, Defense Threat ReductionAgency (Contract No. HDTRA1-11-1-0005), for support of theexperimental studies. The content of the information does notnecessarily reflect the position or the policy of the federalgovernment, and no official endorsement should be inferred.

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dx.doi.org/10.1021/jp3126494 | J. Phys. Chem. C 2013, 117, 6651−66576657