Quantitative nanoscale visualization ofheterogeneous electron transfer ratesin 2D carbon nanotube networksAleix G. Güella,1, Neil Ebejera,1, Michael E. Snowdena, Kim McKelveya,b, Julie V. Macphersona, and Patrick R. Unwina,2

aDepartment of Chemistry and bMolecular Organisation and Assembly in Cells Doctoral Training Centre, University of Warwick, Coventry CV4 7AL,United Kingdom

Edited by Royce W. Murray, University of North Carolina, Chapel Hill, NC, and approved April 11, 2012 (received for review March 1, 2012)

Carbon nanotubes have attracted considerable interest for elec-trochemical, electrocatalytic, and sensing applications, yet thereremains uncertainty concerning the intrinsic electrochemical (EC)activity. In this study, we use scanning electrochemical cell micro-scopy (SECCM) to determine local heterogeneous electron transfer(HET) kinetics in a random 2D network of single-walled carbonnanotubes (SWNTs) on an Si∕SiO2 substrate. The high spatial reso-lution of SECCM, which employs a mobile nanoscale EC cell as aprobe for imaging, enables us to sample the responses of individualportions of a wide range of SWNTs within this complex arrange-ment. Using two redox processes, the oxidation of ferrocenyl-methyl trimethylammonium and the reduction of ruthenium (III)hexaamine, we have obtained conclusive evidence for the highintrinsic EC activity of the sidewalls of the large majority of SWNTsin networks. Moreover, we show that the ends of SWNTs and thepoints where two SWNTs cross do not show appreciably differentHET kinetics relative to the sidewall. Using finite element methodmodeling, we deduce standard rate constants for the two redoxcouples and demonstrate that HET based solely on characteristicdefects in the SWNT side wall is highly unlikely. This is furtherconfirmed by the analysis of individual line profiles taken as theSECCM probe scans over an SWNT. More generally, the studiesherein demonstrate SECCM to be a powerful and versatile methodfor activity mapping of complex electrode materials under condi-tions of high mass transport, where kinetic assignments can bemade with confidence.

Within the family of nanostructured materials, carbon nano-tubes (CNTs) have attracted particular attention because

they are readily synthesised at low cost, have exceptional electro-nic properties, exhibit chemical and mechanical stability, and areamenable to a wide range of simple chemical functionalizationroutes (1–3). These characteristics have led to CNTs being con-sidered ideal substrates for electronics (4), sensing systems (5, 6),electrocatalytic supports (7), and batteries (8). Furthermore, thedifferent configurations in which CNTs can be arranged broadentheir versatility and allow custom design of devices for specificapplications. Individual single-walled carbon nanotubes (SWNTs)(9), 2D networks (10–12), and 3D nanostructures (13) have allbeen employed successfully.

Understanding heterogeneous electron transfer (HET) atCNTs is of considerable importance, due to the wide range ofelectroanalytical and electrocatalytic systems based on CNTs(14–17), and also because electrochemistry provides an attractiveroute to functionalize and tailor the properties of CNTs (18–20).Probing HET in 1D electrode materials is interesting fundamen-tally, given their inherent electronic structure and properties(21, 22). However, as we highlight herein, despite many studiesaimed at characterizing HET at CNTs, substantial questions re-main unanswered, such as the location and rate of HET.

A popular approach for studying electrochemistry at CNTsinvolves drop-casting the material onto an electroactive support(23, 24), but this makes it difficult to unambiguously identify thecontribution from CNTs alone. These voltammetric studies have

led to an interpretation that CNTs are active only at edge-plane-like defects in multiwalled nanotubes (MWNTs) and at the openoxygenated ends of MWNTs and SWNTs (23–25), with the side-wall inactive, even for simple redox couples. A separate approachhas been to study CNTs on an inert substrate to ensure that theelectrochemical (EC) signal measured can be uniquely attributedto the CNT material used. Both 2D networks of SWNTs (12, 26–28) and individual SWNT devices (29, 30) have been employed,and facile HET has been reported for several redox complexes ata majority of SWNTs assessed. Such studies suggest highly activesidewalls, but the measurements are typically averaged over manySWNTs and SWNTcontacts (in the 2D networks) or over a lengthof μm to mm for individual SWNTs.

In order to more fully assess and understand the electro-chemical behavior of SWNTs, it is necessary to measure HETofdifferent components, e.g., sidewalls and ends, at very high spatialresolution, allowing the spread of activity to be identified. Herein,we use scanning electrochemical cell microscopy (SECCM) (31,32), which utilizes a theta pipet probe filled with an electrolytesolution and a quasi-reference counter electrode (QRCE) in eachchannel, for the EC interrogation of a substrate. The meniscuscreated at the end of the probe defines a local and mobile EC cell,confining the measurement of the substrate to the dimensionsof the pulled pipet (33), approximately 250 nm diameter herein(34). Using feedback protocols, the tip maintains a constant dis-tance from the sample to produce EC maps (vide infra), specifi-cally of redox reactions at the SWNT network biased at a definedpotential with respect to the QRCEs. This allows EC data to becollected across a range of characteristic SWNTsites while acces-sing only a very small part of the electrode material at a time.In parallel, finite element method modeling (33) of SECCM al-lows the quantitative assignment of standard HETrate constantsfor the redox reactions of interest.

The focus herein was 2D networks of SWNTs grown by che-mical vapor deposition (CVD) on insulating substrates (SiO2).In addition to the pristine and low-defect nature of such SWNTs(26, 35), this arrangement exposes a large quantity of character-istic sidewalls, cross-points and ends for investigation, and a ran-dom population of semiconducting and metallic SWNTs (36).The use of an inert substrate avoids any possible EC contributionfrom the substrate. Two-dimensional networks of SWNTs are alsoof interest for at least two further reasons: (i) There is now ampleevidence that such an electrode arrangement is optimal for max-

Author contributions: A.G.G., N.E., J.V.M., and P.R.U. designed research; A.G.G. and N.E.performed research; N.E., M.E.S., and K.M. contributed new reagents/analytic tools;A.G.G., N.E., M.E.S., and K.M. analyzed data; and A.G.G., N.E., M.E.S., K.M., J.V.M., andP.R.U. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1A.G.G. and N.E. contributed equally to this work.2To whom correspondence should be addressed. E-mail: P.R.Unwin@warwick.ac.uk.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1203671109/-/DCSupplemental.

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imizing signal to noise in voltammetric and amperometric mea-surements (26, 37), and so understanding the intrinsic activity isvaluable; and (ii) this arrangement presents a rather challengingarray of closely spaced active elements for electrochemical ima-ging and highlights the capabilities of SECCM in resolving suchcomplexity. More generally, we also show that the configurationof SECCM and an SWNTon an inert substrate leads to ultrahighmass-transport rates that allow incredibly high HET rate con-stants to be quantitatively determined while also permitting dis-tinction between different models of EC activity.

Results and DiscussionA scheme of the SECCM setup is depicted in Fig. 1A. Taking intoaccount the characteristic separation between SWNTs, it wasessential that the SECCM probe was of the order of ca. 250 nmin diameter (SEM image in Fig. 1A), since this dimension definesthe size of the EC cell (33) when the electrolyte at the end ofthe pipet comes into contact with the substrate. At this lengthscale, individual SWNTs could be resolved, and it should be pos-sible to distinguish between sidewalls, nanotube ends, and cross-ing SWNTs. The 2D SWNT network is comprised of randomlydistributed interconnected SWNTs, as seen in Fig. 1B. EachSWNT is grown from a single catalytic nanoparticle that is em-bedded at one end of the SWNT (38, 39). The density of SWNTswas above the metallic percolation threshold (40), so after estab-lishing macroscopic electrical contacts to the network, the samplewas ready to be used without any need of postprocessing cleaningsteps. This was particularly important because the number ofdefects present in the SWNTs remains at the intrinsic value.Naturally, SWNTs contain no edge-plane-like sites of the typeheld responsible for the EC response in MWNTs (41); also, forSWNTs grown by CVD, the ends are likely to be closed, whichmight be expected to lead to very slow HET kinetics (24, 25).The only other type of defect site that one could reasonably con-sider is point defects in the sidewall, identified through electro-deposition (42). These have a spacing of 100 nm–4 μm (averagingapproximately 400 nm) along the sidewall.

Samples were routinely characterized with atomic force micro-scopy (AFM), confirming a typical coverage of SWNTof approxi-mately 4 μm∕μm2 (SWNT length / substrate area) and heights ofapproximately 1 nm, with high monodispersity (vide infra). SomeSWNT bundles were also observed, as shown in the zoomedimage of Fig. 1B, where the splitting of a bundle is seen. Furtheranalysis of the sample with Raman spectroscopy (Fig. S1) con-firmed the presence of high quality SWNTs.

Two simple one-electron processes with widely different redoxpotentials were employed: ferrocenylmethyl trimethylammo-nium (FcTMAþ) oxidation and ruthenium (III) hexaamine

(RuðNH3Þ6 3þ) reduction (in phosphate buffer pH 7.2 as support-ing electrolyte). Fig. 2 A and B show EC current maps, togetherwith linescans, for these processes, with the SWNT substratesbiased at the formal potential of the redox couple (Fig. S2). Ineach case, the EC activity of the substrate is clearly similar to thecharacteristic topography of SWNT network geometries. Thedata show that the EC activity is mostly uniform along the lengthof SWNTs.

The EC map for FcTMAþ oxidation (Fig. 2A) shows only asmall variation in current across the nanotubes. This is consistentwith the similar density of states of metallic and semiconductingnanotubes (29) at this positive potential, so that electrochemistrywith this mediator is relatively insensitive to the electronic natureof the SWNT. Although a highly active SWNT network is alsoevident for RuðNH3Þ6 3þ reduction (Fig. 2B), there also appearsto be a small proportion of SWNTs with lower ET activity (forexamples, see the left hand side of the line profile in Fig. 2B,the EC current histogram in Fig. 3A; Fig. S3). This could be be-cause the formal potential of RuðNH3Þ6 3þ∕2þ lies in the chargedepletion region of some of the semiconducting SWNTs (43),diminishing HET activity (44); and because some SWNTs maybe highly defective or poorly connected (45) in the network.

SECCM also acquires three complementary maps (Figs. S4,S5, S6) simultaneously with the EC maps: z-piezo displacement,ion conductance, and the AC component of the ion conductance(Materials and Methods, SI Text). These extra data can be viewedto confirm the stability of the meniscus size and the constancyof the tip-sample separation during an SECCM scan. To furtherensure that the images did not contain artifacts, and to demon-strate the high reproducibility of the method, we recorded sometrace and retrace EC maps (example, Fig. S3). We show, alongwith the trace image in Fig. 2B, examples of trace and retrace line-scans, with each line comprising points obtained every 4 nm. Thetrace and retrace linescans overlay, confirming the consistency ofthe measurements, accurate tracking of the surface, the absence ofblocking or fouling of the SWNT, and of meniscus dragging effects.

To assign standard HET rate constants, k0, a finite elementmethod model of the SECCM system was developed (33)(Materials and Methods, SI Text). We approximated the cylindricalSWNT (diameter, dnt) by a band electrode in the plane of theinert substrate, with an equivalent width wnt ¼ ðπ∕2Þ · dnt anda length defined by the substrate-meniscus contact area, as shownin Fig. 1A. A band approximation is reasonable (46), especiallywhen the HET kinetics are close to surface-limited (vide infra).When the SWNT lies across the center of the SECCM meniscus,the relative orientation between the SWNT and the SECCMprobe barrels (defined by the orientation of the septum) wasfound to be negligible (SI Text). Thus, unless stated otherwise,

Fig. 1. Depiction of the SECCM setup and the 2D SWNT network samples on which studies were performed. (A) Schematic (not to scale) of the SECCM setup,showing the SECCM tip with QRCEs over a 2D SWNT network sample connected as the working electrode with a gold contact. FE-SEM image of a typical SECCMtip and the geometry for the FEM is also shown [3D simulation, making use of the symmetry plane perpendicular to the tip septum (33)]. (B) RepresentativeAFM image of SWNT network samples, with an expanded image of a junction and a bundle splitting. Catalyst particles can be seen in the AFM image but arenot connected to the SWNTs and are electrochemically inactive.

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the SWNTwas considered to be parallel with the septum betweenthe SECCM probe barrels (Fig. 1A). Based on our previous ex-perimental studies (31–33), typical tip-substrate separations inSECCM are between 25% and 50% of the tip radius, and we con-sidered a tip-substrate separation of 50 nm in the present study,which was most consistent with the ion current response (35).Further simulations (Fig. S7) proved that the effect on the currentat the formal potential of changing the tip-substrate separation byup to �20 nm was less than 3% for a constant ion current.

SECCM images were analyzed to extract current values wherethe pipet most likely passed over individual SWNTs and cross-points of SWNTs in networks. These data are summarized inFig. 3 as histograms of peak currents in the images at these loca-tions. A corresponding AFM of SWNT height (equivalent to

diameter, dnt) is also shown for comparison. The working curvesof EC current vs. logðk0Þ (with a transfer coefficient of α ¼ 0.5)for dnt ¼ 1 nm (wnt ¼ 1.57 nm) used to analyze these data areshown in Fig. 3 B and C (pipet radius of 125 nm). These curvesindicate that, if SWNT heights are well-defined, k0 approaching30 cm s−1 may be accessible (where the current is ca. 90% of themaximum transport-limited value and so distinguishable fromthe limit). The modal value of the current distribution for theindividual SWNTs with RuðNH3Þ6 3þ∕2þ (Fig. 3A) is iwe ¼ 4 pA(�1 pA accounts for 40% of the values) yielding k0 ¼ 4�2 cm s−1. For FcTMAþ∕2þ, a modal current of iwe ¼ 1.8 pA(�0.2 pA accounts for 42% of the values) yields k0 ¼ 9�2 cm s−1. Confidence in these assignments is high because thesekinetic values are so far away from the reversible limit with thehigh mass-transport rates of SECCM. Interestingly, the value de-termined for RuðNH3Þ6 3þ∕2þ is of the order of that found on goldnanoelectrodes, k0 ¼ 13.5� 2 cm s−1 (47). For FcTMAþ∕2þ,k0 ¼ 4� 2 cm s−1 has been found for individual SWNT devices,and we previously estimated k0 > 1.0� 0.6 cm s−1 or k0 > 2�1 cm s−1 for this couple (37, 48).

The samples used for the present study were found to have anarrow range of SWNT heights, as shown in Fig. 3A (blue histo-gram). To investigate how this variation might impact on the ECresponse, simulations were performed for the range of nanotubeheights (converted to wnt in the model) for dnt between 0.8 nmand 2.75 nm, using k0 ¼ 4� 2 cm s−1 for RuðNH3Þ6 3þ∕2þ and9� 2 cm s−1 for FcTMAþ∕2þ. The results, presented in Fig. S8,indicate that the EC response changes with nanotube diameter,from 3.5 pA to 7.5 pA for RuðNH3Þ6 3þ∕2þ and from 1.7 pA to2.4 pA for FcTMAþ∕2þ. This variation is thus a plausible expla-nation for the main part of the distributions of peak current, inwhich more than half of the values lie, although we recognize thatthis is a simple analysis and that k0 may change with nanotubeheight (22).

On the other hand, particularly for RuðNH3Þ6 3þ∕2þ, there is asmall but detectable population of low currents that cannot beaccounted for simply from the height distribution. This can rea-sonably be attributed to the presence of some semiconductingSWNTs (vide supra) and SWNTs with high resistance dropwithin parts of the ensemble. Indeed, SWNT densities fromSECCM (2.6� 0.3 μm∕μm2) are lower than densities from AFM(3.8� 0.4 μm∕μm2). While this difference could partly be due tothe lower spatial resolution of SECCM, it is also reasonable topostulate a proportion of SWNTs not being electrically connected(26) and low HET rates at some semiconducting nanotubes(vide supra).

One of the characteristic features of 2D SWNT networks is thepresence of nanotube junctions (vide supra). The mapping featureof SECCM allowed us to readily view the EC activity of sucharrangements. We observed a slight increase in the modal currentcompared to the individual SWNTcase (Fig. 3A), but taking ac-count of the extra active area (compare individual and crossedSWNT working curves in Fig. 3B), the corresponding k0 valuewas similar, k0 ¼ 3� 2 cm s−1.

It has been suggested (24, 25, 41, 49, 50) that sidewalls are elec-trochemically inactive in CNTs and that only edge-plane-like sitesand open oxygenated nanotube ends are active. Our work showsthis earlier hypothesis is incorrect. For the SWNT network, wehave no obvious edge-plane sites, and the ends are most likelyto be closed (38). We see high and similar activity across differentsites in SWNT networks.

We now consider whether other possible defects in the sidewallcould be solely responsible for the SECCM observations. Giventhe defect density attributed from selective electrodeposition(42), vide supra, the SECCM pipet would be expected to encoun-ter only one defect when passing over an SWNT. We thusconsider this case, simulating a defect (at most) as a square oflength 1 nm positioned in the plane of an inert substrate, for

Fig. 2. Experimental data obtained using SECCM of the SWNT network.SECCM images (2.5 μm × 2.5 μm) of SWNT networks at the formal potentialfor FcTMAþ∕2þ (2 mM) (A) and RuðNH3Þ6 3þ∕2þ (5 mM) (B). Representativetrace (A, B) and retrace (B) linescans are shown below.

Fig. 3. Summary of experimental peak EC current data and simulationresults. (A) The SWNT height distribution from the AFM images. Histogramsof peak current populations from SECCM images for RuðNH3Þ6 3þ reductionand FcTMAþ oxidation from regions of the image where individual SWNTpeaks were identified. For RuðNH3Þ6 3þ reduction the peak current popula-tion is also shown for points where more than one nanotube is under thetip (crossed SWNT). (B) and (C) Working curves of EC current vs. standard rateconstant for HET at a fully active individual SWNT of height 1 nm withRuðNH3Þ6 3þ and FcTMAþ as the redox mediator, respectively. The simulationswere at the formal potential and a transfer coefficient of α ¼ 0.5 was as-sumed.

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RuðNH3Þ6 3þ∕2þ. The resulting working curve (Fig. 4A) of ECcurrent vs. logðk0Þ at the formal potential provides two importantobservations: (i) the discernible range of k0 values is now up to1;000 cm s−1, due the very high mass transport to a nm-scale elec-trode; and (ii) the maximum mass-transport limited current for a1 nm sized defect is 0.46 pA (for k0 > 1;000 cm s−1), an order ofmagnitude lower than the modal value observed experimentally,and this is for an unfeasibly high rate constant.

Next we considered an increase in the number of side-walldefects, up to three in the area under interrogation, to simulatea maximum possible EC response for an SWNT with defectsspaced ca. 100 nm. The EC current vs. logðk0Þ working curve forthis case yields a maximum current iwe ¼ 1.5 pA, but only fork0 > 1;000 cm s−1. This rate constant is unfeasibly high, yet thiscurrent and lower values are only evident in <10% of the nano-tubes visualized. Thus, the overwhelming majority of SWNTshave an EC activity that can only reasonably be explained basedon considerable intrinsic SWNT sidewall activity.

The high spatial resolution of SECCM during scanning (seeMaterials and Methods) allowed tracking of EC currents acrossindividual SWNTs. The resulting peak profiles also indicatethat the EC current response is best explained by HET activityintrinsic to SWNT sidewalls. Fig. 4B compares a simulation forscanning over a fully active SWNT (wnt ¼ 1.5 nm and k0 ¼4 cm s−1) with a typical, and frequently observed, experimentalexample linescan for RuðNH3Þ6 3þ reduction. It is evident thatthere is a good match to the shape and magnitude of the profile,assuming a uniformly active tube. Note that such profiles providean excellent test of the uniformity of SWNTactivity as the SWNT

length accessed changes in a systematic manner as the SECCMmeniscus scans over it.

Simulations of moving the SECCM probe across an SWNTcontaining one and three sidewall defects with an exaggeratedvalue of k0 ¼ 100 cm s−1 were also performed and compared(Fig. 4B). Besides the large difference in the EC response com-pared to the sidewall active case, there is also a significant differ-ence in the shape of the line scan profile, with an abrupt change incurrent for the defect, depending on whether or not a defect isaccessed. Furthermore, there is negligible variation of the ECcurrent response for the single active site. Note, additionally, thatthe defect simulations are for the most favorable case where thedefect is located central to the scanned meniscus of the SECCMpipet. On this basis, we can further deduce that the most appro-priate model for electrochemistry at pristine, untreated SWNTs isone where the large majority of the sidewalls display high intrinsicEC activity.

ConclusionsWe have shown that the intrinsic EC activity of a complex elec-trode, comprising a random network of interconnected SWNTson an Si∕SiO2 substrate, can be resolved by SECCM. By measur-ing the EC currents as a function of probe position at the formalpotential of two redox couples, we have found that the majorityof SWNTs are more or less uniformly active on the length scale ofhigh resolution SECCM. The images herein provide strikingquantitative information on EC activity across different types ofsites in SWNTs (sidewall and ends) and in 2D networks (cross-points). Quantitative information has not only come from theanalysis of peak currents in SECCM maps (when the SWNT liesunder the center of the SECCM pipet) but also from the analysisof line profiles in which the line shape across an SWNT runningacross the Si∕SiO2 substrate perpendicular to the linescan direc-tion can be fitted to a single rate constant for a uniformly ac-tive SWNT.

We have also demonstrated that SECCM accesses very highmass-transport rates, which allows the ready assignment of rateconstants with high accuracy, and proves that a high proportionof the SWNTs detected had k0 in the narrow range 4� 2 cm s−1for RuðNH3Þ6 3þ∕2þ and 9� 2 cm s−1 for FcTMAþ∕2þ. Further-more, for both couples, all SWNTs detected by SECCM showk0 > 0.1 cm s−1. Thus, in practical terms, SWNT sidewalls willshow fast HET for most common electrochemical techniques thatoperate with much lower mass transport coefficients than thesestandard rate constants. As such, SWNTs should be viewed ashighly active electrochemical materials, at least for outer-sphereredox couples of the type studied herein. This new understandingof electrochemistry at SWNTs clarifies misconceptions that havearisen from different views in the literature on the electroactivityof SWNT materials; also, it has implications for related materialssuch as graphene and graphite.

Materials and MethodsSynthesis of SWNT Network Samples. SWNTs were grown by catalytic chemicalvapor deposition (cCVD) on silicon/silicon oxide substrates (IDB TechnologiesLtd., n-type Si, 525 μm thick with 300 nm of thermally grown SiO2) asreported elsewhere (12). Fe nanoparticles served as the metal catalyst (35),deposited from aqueous solutions of horse spleen ferritin (Sigma Aldrich),diluted from the original concentration in a ratio of 1∶200. To establishmacroscopic electrical contact to the SWNT networks, 100 nm Au (with anadhesion layer of 4 nm Cr) was thermally evaporated (Moorfield Miniboxevaporator) on the SWNT samples, partly covered by a stencil shadow mask.AFM characterization of the SWNT networks was performed using a VeecoEnviroscope AFM (Bruker) with Nanoscope IV controller, in tapping mode.Raman spectra were acquired with a 514 nm Ar laser microRaman (RenishawinVia, United Kingdom) and a 50x optical lens.

Solutions. Solutions were prepared using Milli-Q water (Millipore Corp.) andconsisted of either 2 mM trimethyl(ferrocenylmethyl)ammonium (as the hex-afluorophosphate salt, synthesized in house) (51) or 5 mM hexaamineruthe-

Fig. 4. Comparison of experimental data with simulated data for fully activeSWNT sidewall, one defect and three defects. (A) Working curves of EC cur-rent vs. standard rate constant for HET of a fully active individual SWNT, onepoint defect and three point defects (with the SWNT central under the pipetmeniscus). (B) Experimental (points) for the current response of an SECCMprobe translated over a portion of an individual SWNT, compared to simula-tions for full sidewall activity (blue, k0 ¼ 4 cm s−1), one active defect (red,k0 ¼ 100 cm s−1) and three active defects (green, k0 ¼ 100 cm s−1).

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nium (III) chloride salt (Sigma Aldrich, 98%). In each case phosphate bufferpH 7.2 (Sigma Aldrich) served as supporting electrolyte.

SECCM Instrumentation and Protocols. Tip fabrication. SECCM tips were pulledfrom quartz theta capillaries (o.d. 1.2 mm, i.d. 0.9 mm, Sutter Instrument) in alaser puller (P-2000, Sutter Instrument) to yield pipets of ca. 250 nm internaldiameter at the end. Tip dimensions, including taper angle, were measuredaccurately using field emission-scanning electron microscopy (FE-SEM; Zeiss-SUPRA 55-VP) as shown, for example, in Fig. 1A. The outer walls of the tipswere silanized with dimethyldichlorosilane (Fluka).

Instrumentation. Two instruments were used, the first of which has been pre-viously reported in detail (31–33). The second instrument was similar, but hadthe SECCM tip mounted on a one-axis piezoelectric positioner (P-753.31C,Physik Instrumente), with the sample positioned vertically below the tip ina humidity cell on a two-axis piezoelectric stage (P-622.1CD, Physik Instru-mente). The SECCM tip was oscillated normal to the surface (200 Hz,30 nm peak to peak) by an ac signal generated from a lock-in amplifier(SR830, Stanford Research Systems). The AC component of the barrel current(used for distance control) was measured using the same lock-in amplifierand recorded through the FPGA card (7852R, National Instruments).

Imaging procedure. For the studies herein, the bias between the two QRCEs inthe SECCM pipet was 500 mV, inducing an ion current between the two bar-rels. The conductance cell was floated with respect to the working electrodesurface, held at ground, so that the driving force for HET was at the formalpotential for the particular redox couple of interest. A meniscus forms at theend of the SECCM tip and acts as the electrochemical cell that is scannedacross the sample (31–33).

The first instrument (31) used for the FcTMAþ∕2þ studies produced an im-age with data points evenly spaced (typically 50 nm). The second instrumentemployed a continuous scanning method, providing higher spatial resolutionin the tip-scan direction. The SECCM tip speed was 300 nms−1, and datawere acquired at a rate of 78 Hz, yielding a spatial resolution of ca. 4 nmin the direction of the line scan. This imaging procedure was used forRuðNH3Þ6 3þ∕2þ studies. Data analysis was performed in Matlab (R2010b,Mathworks). Points where the tip was directly above a carbon nanotubewereidentified as peaks in the substrate current.

Simulations. Following the methodology we have reported recently for finiteelement method (FEM) modeling of mass transport within an SECCM probe(33), we approximated the SECCM probe geometry to a circular-based cone

of radius 125 nm. In contrast to our previous studies (33), we applied a two-step solver for computational efficiency. Initially, the potential field and ionmigration current between the two QRCEs in the SECCM pipet were deter-mined in the absence of a working electrode reaction by solving the steady-state Nernst–Planck equations:

∇ð−Dj∇cj − zjujFcj∇V Þ ¼ 0 [1]

∑j

zjcj ¼ 0 [2]

where Dj , cj , zj , and uj are the diffusion coefficient, concentration, charge,and ionic mobility of species, j, respectively. F is the Faraday constant, and V isthe electric field (provided by the bias applied between QRCE1 and QRCE2, Ef ,as depicted in Fig. 1A). The boundary conditions were as outlined previously(33) and the potential field was calculated for a solution containing either2 mM FcTMAþ as the PF6

− salt or 5 mM RuðNH3Þ6 3þ as the chloride saltin 50 mM phosphate buffer at pH 7.2 using ion mobilities and diffusion coef-ficients obtained from the literature (52, 53) and summarized in Table S1.

To determine the EC response at the formal potential, we considered themajority of the substrate to be insulating, with the SWNT defined as a rec-tangle of widthwnt in the plane of the substrate with a length determined bythe substrate-meniscus contact area. The width of the rectangle was relatedto the height of the SWNT, dnt, as defined earlier. Butler-Volmer kinetics wereapplied to the SWNT electrode, assuming a transfer coefficient α ¼ 0.5, withthe remainder of the surface (Si∕SiO2) inert. Mass transport to the workingelectrode surface was calculated by solving Eq. 1 for the electrode reactantand product species, for a typical barrel current of ca. 1 nA, using protocolsdescribed in full (33).

ACKNOWLEDGMENTS. We thank Dr. Alex Colburn for the design and buildof instrumentation amplifiers. The European Research Council has providedfinancial support under the European Community’s Seventh FrameworkProgramme (FP7 / 2007–2013) /ERC—2009—AdG2471143—QUANTIF). A.G.G.was further supported by a Marie Curie Intra-European Fellowship (project236885 “FUNSENS”). Support from Engineering and Physical SciencesResearch Council for studentships to N.E. (CTA scheme with the NationalPhysical Laboratory, United Kingdom) and K.M. (Molecular Organisationand Assembly in Cells Doctoral Training Centre) and Grant EP/H023909/1 isgratefully acknowledged. Some of the equipment used in this work was ob-tained through the Science City Advanced Materials project with supportfrom Advantage West Midlands and the European Regional Develop-ment Fund.

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