Supporting Information Electrochemical Redox Cycling in a ...

Electronic Supplementary Material (ESI) for Nanoscale This journal is © The Royal Society of Chemistry 2013

Supporting Information

Electrochemical Redox Cycling in a Nanoporous Sensor Martin Hüskea, Regina Stockmanna, Andreas Offenhäusserab, and Bernhard Wolfrumab*

a

Institute of Bioelectronics (PGI-8/ICS-8) and JARA—Fundamentals of Future Information Technology, Forschungszentrum Jülich, D-52425 Jülich, Germany b

IV. Institute of Physics, RWTH Aachen University, D-52074 Aachen, Germany

Methods Fabrication The devices are fabricated in our clean room using 4-inch wafer substrates (SiMat p (B), , 7 – 21 Ωcm), on which a 460 nm layer of oxide is thermally grown in an oxidation oven (Tempress) (Scheme 1a). The electrodes are structured in a lift-off process (Scheme 1 b) using a LOR 3B/AZ nLOF 2020 resist stack (MicroChem Corp., MicroChemicals GmbH), which is exposed in a mask aligner (Suess MA 6) and developed in AZ 326 MIF (MicroChemicals

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GmbH). Subsequently, a 70 nm platinum layer with 10 nm titanium top and bottom adhesion layers is deposited via electron beam evaporation (Pfeiffer PLS 500 Physical Vapor Deposition System) to form the bottom electrode. The lift off is performed with EBR PG (MicroChem Corp.). On top of the bottom electrode a 100 nm Si3N4 layer is grown via plasma enhanced chemical vapor deposition PECVD (Scheme 1 c). A 10 nm Ti / 30 nm Pt / 10 nm Ti stack, again structured by lithography, forms the top electrode and its feedlines (Scheme 1d). The whole wafer is then covered by a stack of 3 SiO2 layers, 200 nm each, separated by 2 layers of 100 nm Si3N4, (Scheme 1e). This passivation is successively opened at the contact pads of the top and

Scheme 1. Processing of the silicon wafer includes (a) its oxidation, (b) the deposition of the Pt bottom electrode, (c) the Si3N4 spacing layer, (d) the Pt top electrode and (e) a Si3N4/SiO2 passivation layer, (f) the passivation opening at the contact pads and electrode sites, (g) structuring of the e-beam resist, (h) pattern transfer versus RIE, and (i) deposition of a protecting layer of resist, which is (j) removed after cutting.

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bottom electrodes using reactive ion etching (RIE) (20 ml/min CHF3, 20 ml/min CF4, 200 W, 0.02 mbar) (Oxford Plasmalab 100 Cluster Tool). The etching progress is controlled using a laser interferometer. As a mask, thermally hardened AZ 5214E resist (MicroChemicals GmbH) is used, which is exposed on a mask aligner and developed in AZ 326 MIF. Finally the passivation at the electrode positions is opened using the same process (Scheme 1f)). The nanopores are fabricated via an electron beam lithography process. First, 300 nm of poly(methyl methacrylate) (PMMA, AR P 669.04 (Allresist GmbH)), are spincoated onto the wafer without removing the AZ-resist layer, which covers the whole wafer except the electrode areas. The nanopores are written by electron-beam lithography (Vistec EBPG 5000 plus) system with a dose of 560 µC/cm2 (Scheme 1g). The PMMA is then developed in AR P 600-55 (Allresist GmbH). Hereafter, an Ar/SF6 reactive ion etching process (Ar 40 ml/min, SF6 1 ml/min, 150 W, 0.02 mbar, Oxford AMR System) is used to transfer the pattern to the top electrode. To further etch the Si3N4 insulator and the underlying Ti adhesion layer CHF3 plasma is used in the same device (CHF3 20 ml/min, 200 W, 0.02 mbar). The etching progress is intermediately checked by scanning electron microscope imaging (SEM, Zeiss Gemini 1550). Within the RIE process the structured PMMA is consumed completely. The platinum top electrode is partially thinned (Scheme 1h). During wafer cutting and the following storage period the nanopores are protected by another layer of AZ-resist brought onto the wafer (Scheme 1i). The resist is removed via acetone and the wafer is rinsed in ethanol (Scheme 1j). A brief flame treatment ensures its complete removal. For the recorded concentration-dependent series, glass rings are attached to the chip. The glass rings are carefully wetted with a mixture of dimethylsiloxane and a curing agent (PDMS,

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Sylgard 184, Dow Corning GmbH). After placing the rings on the chip, the polymerization of dimethylsiloxane to PDMS is facilitated by baking the chips at moderate temperatures (60°C 80°C) for about 30 min. Presumably due to the slight variances of fabrications steps associated with RIE etching, the final size of the nanopores varies between different chips. A summary over aperture radii and electrode surfaces of the chips used within this work is therefore given in Tab S1.

sensor

bottom electrode

top electrode

radius

porous basal area

pore radius

active surface

pore radius

porous active surface

rim surface (additional)

signal shape (Figure 2,5)

35 µm

3421 µm2

40 nm

497 µm2

57 nm

2618 µm2

427 µm2

sensitivity (Figure 4)

25 µm 35 µm 50 µm

1661 µm2 3421 µm2 7238 µm2

28 nm 33 nm 29 nm

118 µm2 338 µm2 552 µm2

43 nm 55 nm 44 nm

1459 µm2 2681 µm2 6305 µm2

302 µm2 427 µm2 616 µm2

Table S1. Pore radii and electrode areas of the different sensors used. The top electrode porous surface includes the area of the rounded rims at the pore apertures.

Electrochemical characterization All experiments presented in this paper are performed in a 100 mM KNO3 electrolyte. The electrolyte further contains redox-active Fc(MeOH)2. All substances are obtained from Sigma and dissolved in bidistilled water (bidest). The amount of electrolyte used is about 50 µl for the non-encapsulated chips and at least 450 µl for the encapsulated ones. During the measurements a platinum wire serves as a counter electrode. Either a housed Ag/AgCl electrode (BASi Inc) or a Warner Instruments “Leak-Free Reference Electrode” (WPI) is used as a reference electrode. The potentials recorded versus the Warner electrode are offset corrected by +65 mV versus the BASi electrode. The current used for plotting and analysis is obtained from the 3rd sweep of a

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particular experiment. The experiments are performed at room temperature (~21 °C). Upon characterization of the sensors, the silicon chips are contacted from the backside to a metal block. Both, the metal block and the bulk electrolyte act as a thermal reservoir to avoid temperature fluctuations. The potential sweeps are performed with a CHI1030B multi-channel potentiostat (CHInstruments). Sweep rates of 50 mV/s and sampling rates of 25 Hz are chosen, corresponding to 2 mV potential steps. The starting potential is either 0 mV vs. Ref. or the minimum potential. The potential of the non-sweeping electrode is kept to maximum or minimum value of the scanned potential window. At least three sweeps are performed. Prior to first use all electrodes where swept at least three times between -650 mV and maximally 550 mV at 200 mV/s. The concentration series are divided into three subseries. At the beginning of each subseries the electrodes are swept in 450 µl pure KNO3 electrolyte. Generally, the sensor response is recorded for two configurations. First the top electrode is swept while the bottom electrode is held at reducing potential. After that, the potential of the top electrode is fixed as the bottom electrode’s potential cycles. For the subsequent voltammograms, 24 µL to 450 µL of a KNO3 containing Fc(MeOH)2 stock solution are added. The Fc(MeOH)2 concentrations of this solution amount to 10 mM, 50 mM or 250 mM depending on the subseries being recorded. This way, a concentration regime reaching from 500 nM to 175 µM can easily be investigated with high accuracy. Between the single subseries the electrolyte is partially removed from the chip. The remaining volume is diluted with bidest water and partially removed again. After a couple of cycles the chip is finally sucked dry completely. Counter and reference electrode are repeatedly washed with bidest water.

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Analysis All data used in the analysis is obtained from the 3rd sweep of a particular measurement. The currents of the cyclic voltammograms presented are not further processed. Only the potentials recorded versus the Warner electrode are offset corrected by +65 mV versus the BASi electrode. This applies to the voltammograms recorded at the un-encapsulated chips as well as to the potentials regarding the redox cycling efficiencies. The currents used for all calculation and fits are averaged values for forward and backward scan at the particular potential. For the determination of the electrodes sensitivities via the concentration series the current of the first sweep in KNO3 is subtracted. The sensitivity for a certain electrode is given by the best linear fit obtained via the least mean square method. All currents plotted plus the offset corrected zero current at zero concentration is included. When fitting the simulated and experiential data of a single sweep or the extended characteristics every 5th or, respectively, every 10th data point is used. Again, the least square method is applied to find the optimal match. To exclude currents deriving from reservoir exchange only the bottom currents are considered. Generally, a current offset is introduced as a free parameter to compensate for a signal baseline like oxygen reduction. Additionally, a common scaling factor is added to fit the extended four-sweep characteristics. Thus, the shape of the simulated curves is optimized rather than for exact signal height. Further, the fitted range is restricted to E0 ± 200 mV. The graphs for the simulated foursweep characteristics are neither scaled nor offset corrected. Here, the adaption factors are used for fitting purposes only. The plot of the simulated bottom current derived from the single top sweep, on the contrary, is offset corrected.

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Numerical simulation Within the article and the SI we investigate the geometrical properties of the sensor array and the single pores. In our numerical calculations we approximate the sensor as a sum of single pores, which are all held in separate hexagonal cells (see Figure S2a). Due to the large number of cells boundary effects at the sensor edge only play a minor part for redox cycling in nanopores. Thus, we can simulate only one cell and derive the final current simply by multiplication with the number of pores. What is beneficial for our calculations is the similarity between a hexagonal and completely radial cell. Adaptations are only necessary at a cell’s outer rim, which barley contributes to the redox cycling signal. We use a cylindrical cell occupying the same size of area as the hexagonal compound. A similar approach has been applied by several groups - partially even with quadratic cells1. All other values, like radii and film thicknesses can be adopted from SEM recordings, like the ones in Figure 1 (article).

The representation of the cell in our

numerical calculations is shown in Scheme S2b. An overview on all parameters is presented in Tab. S2. Values differing from the typical ones given in the table are mentioned in the text.

Scheme S2. The geometric characteristic of the nanoporous array in a) top view and b) lateral view. A hexagonal cell in a) can be treated as a cylindrical element like in b) featuring axial symmetry. Eventually, the sensor largely presents a sum of separate cells.

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Geometry Parameter dint a rvol hvol hvolfine hPttop cPttop hTitop rtop hSiN rbot hTibot rPtbot Rpor

Parameter f F R T α ks ktop, kbot E0 Deq Dred, Dox cred, cox cred0, cox0

Value 200 nm ~115 nm 105 nm 800 nm 50 nm 10 nm 10 nm 10 nm 57 nm 100 nm 40 nm 10 nm 35 nm 33 µm ; 48 µm

Description distance between pore centers (interpore distance) edge length of hexagonal cell radius of the simulated cell holding a pore height of volume above the pore (reservoir) part of reservoir with refined mesh height of top electrode radius of curvature at top aperture height of top adhesion layer radius of aperture at pore’s top height of insulator separating electrodes radius of aperture at insulator’s lower end height of bottom adhesion layer radius of aperture of lower electrode radius of porous area of a sensor site

Electrochemistry Value Description f = F / RT 96485.3365 C/mol Faraday constant 8.3144621 J/(mol K) universal gas constant 298 K temperature 0.50 ; 0.70 – 0.95 transfer coefficient 0.01 cm/s – 25.60 cm/s heterogeneous electron transfer constant 0.01 cm/s – 6.40 cm/s separate transfer constants for top / bottom electrode 250 mV redox potential vs. Ag/AgCl 0.64 10-9 m2/s diffusion constant 0.45 10-9 m2/s , 0.91 10-9 m2/s distinct diffusion constants for reduced / oxidized species – concentration of reduced / oxidized species 0 µM, 50 µM initial concentration and, if used, boundary 50 µM, 0 µM conditions of reduced / oxidized species Voltammetry

Parameter Etop,bot Esw Emin, Emax v Estep tstep

Value Emin, Emax, Esw Emin … Emax -25 mV, -50 mV 575 mV, 550 mV 50 mV/s 5 mV, 10 mV 0.1 s, 0.2 s

Description potential of top / bottom electrode potential of sweeping electrode minimum / maximum potentials vs. Ag/AgCl sweep rate voltage steps time stepping

Table S2. Parameters used within the numerical calculations and their typical values. The actual values might differ depending on the specific case. Please refer to the according paragraph. The numerical calculations are carried out with time dependent “transport of diluted species” model in COMSOL. The modeling of the sensor is done within the program, while parametric sweeps used for fitting are performed via LiveLink from MATLAB or higher.

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The calculations are based on Fick’s law of diffusion within the electrolyte and the flux defining Butler-Volmer behavior at the electrodes. Eventually, the emulated flux used for plotting and fitting is also derived from the Butler-Volmer equation in conjunction with the surfaces concentrations at the electrodes. The mesh is manually adapted to reach element sizes from below 1 nm at the electrodes apertures up to 15 nm at the reservoirs upper boundary. The time steps for calculation are strictly 0.1 s, which corresponds to steps of 5 mV/s for the electrodes sweeping with 50 mV/s. For performance purposes the mesh size was increased by a factor of about 2 during manual fitting experimental results. The according mesh is presented in Figure S1a. To find the parameters of the four-sweep characteristics the temporal binning was further enlarged to 0.2 s. Initial concentration are chosen to be cred = 1, cox = 0 or vice versa depending on the starting potential of the electrodes. The sweeps are emulated in forward direction only. For calculations including species dependent diffusion constants the volume is extended to (rvol = 105 nm, hvol = 400 µm) for linear diffusion and (rvol = 400 µm, hvol = 400 µm) for radial diffusion. For the latter case 2 µm rim is simulated around the single pore. A complete list of the parameters and the values used can be found in the supporting information. To validate the applied mesh, the size of its finite elements is varied2. For this purpose, the upper and lower limit of the element sizes is modulated by a factor ζ while the number of elements defined at the inter-volume boundaries (Figure S1a, (i) and (ii)) and the electrodes is varied by 1/ζ. The finest mesh tested (ζ = 0.125) holds elements of maximally 1.1 nm edge length within the fine volume up to 50 nm. At the electrodes the element extensions reach down to 0.3 nm. As we can see from Figure S1b,c for the electrochemical parameters ktop = 0.8 cm/s, kbot = 0.6 cm/s and α = 0.90 (compare Figure 7, article) the current obtained for the varied meshing parameters changes by only a view per mille compared to the parameters used for

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fitting. This is true for all sweep configurations. When changing the time stepping no change in current is observed. This fact can be attributed to the quasi-steady state of the concentration distribution correlating with slow sweep rates and the small volume dimensions. Consequently, the discretization used provides a good representation of the analytical redox cycling model.

Figure S1. Mesh applied to fit transfer rates and the transfer coefficient using the Butler-Volmer approach (a) and maximum deviations found when tuning the size of the mesh elements by a common factor (b,c) for the parameters ktop = 0.8 cm/s, kbot = 0.6 cm/s and α = 0.90. Regardless of the sweep configuration, the expected errors using the grid shown in (a) (relative element size = 1.0) only amount to a few per mille compared to a mesh with element sizes approaching zero.

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Varying Operating Modes The cyclic voltammograms presented within the article are always recorded in a mode, with one sweeping electrode and one electrode held to at a fixed reducing or oxidizing potential. There are, however, other operation modes that can characterize the sensor. One is the single sweep mode, where only one electrode potential is swept while the other electrode unbiased so that the electrode potential is floating. The resulting currents for a 50 µm electrode, comparable to the ones used for the concentration series in Figure 4, article, are presented in Figure S2a,b. In principle, top and bottom electrode feature typical voltammograms of sweeping microelectrodes. Superimposed by background currents, the analyte currents adjust to two distinct plateau phases at the two opposing overpotentials. Sweeping the potentials across the redox potential E0 at about 250 mV causes a steady change between the maximum states. A characteristic current overshoot indicates the conversion of the analyte species accumulated at the vicinity of the electrode during the prior plateau phase. Interestingly, the analyte currents at top and bottom are comparable in magnitude. Implying perfect conversion at the top electrode and the nanoporous bottom electrode array a linear behavior between radius and limiting current should be given 3,4. As the radius of the top electrode (50 µm) is close to the distance of the outer nanopores to the electrode center (48 µm) the bottom currents should reach about 1.44 nA for 1.50 nA top currents. The fact, that the bottom currents reach only about 1.25 nA simply illustrates that not all of the reduced molecules diffusing towards the electrode are converted at the outer pores. Instead, the analyte is partially oxidized closer to the center of the porous array. This is hardly surprising as due to the small openings towards the bottom electrode (rbot ~ 29 nm) the bottom electrode covers less than 8% of the porous area. Accordingly, lower bottom currents might indicate even smaller apertures. Contrary to the analyte currents at the bottom electrode

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Figure SY. Cyclic voltammograms obtained for different sweeping configurations. Either top electrode (a) or the bottom electrode (b) is swept separately while the opposing electrode is unbiased or both electrode are swept simultaneously across the same potentials (c,d). Sweeping one electrode, here the top electrode, while keeping the other at a constant potential yields the typical switching between redox cycling off- and on state (e). The non-redox cycling currents of the top electrode (Itop + Ibot) are plotted in (f). Signals are recorded with a 50 µm sensors in 100 µM Fc(MeOH)2 using a aqueous 100 mM KNO3 electrolyte. Sweep rates are 50 mV/s.

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the top electrode currents are almost independent of the sensor. In any case the analyte currents are superimposed by background currents, particularly at low reducing potentials. As these currents presumably reflect diffusively non-limited surface reactions, they are larger by a factor of about 12, which matches the ratio of the surface area of both electrodes. Another feature of the sensor is unveiled when simultaneously sweeping top and bottom electrode. This way, both electrodes compete for the analyte supply from the sensor. As we can see from Figure S2c,d the top currents barely differ from the single sweep, while changes in the flux towards the bottom electrode are far from neglectable. Indicated by the drastically reduced on-step around 250 mV the current induced by analyte conversion does not exceed about 0.05 nA though the step in single sweep mode amounts to almost 2 nA. Consequently, we find again that the bottom electrode is strongly shielded from the reservoir by the top electrode. Eventually, top and bottom electrode can be operated in redox cycling or generation-collection mode. In the example in Figure S2e,f the top electrodes are swept versus the bottom electrodes, which are fixed at -50 mV. We find the typical redox cycling behavior described in the article (Figure 2a, article). Additional currents detected at the top electrode (Figure S2f) can again be attributed to single-electrode effects at the top electrode as in Figure S2a. This includes diffusive flux from the reservoir, electrolyte reduction at low potentials and charging of the electrode/electrolyte interface. As to expect, the non-redox cycling currents in Figure S2f are all equal in magnitude. The magnitudes of the redox cycling currents, on the contrary, correlate to the current magnitudes of the separately sweeping bottom electrodes in Figure S2b. Therefore, the currents are mostly determined by the integrated kinetics of the bottom electrode and probably by the exact pore sizes of different sensors.

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Comparison to transfer rates in literature The investigations performed in the article give a nice insight into the reactions at a nanoporous sensor. What might be surprising, though, is the asymmetric transfer coefficient α = 0.9 we find in our experiments. Using a nanocavity device Zevenbergen et al. report α to be in the range of 0.49 and 0.55 for KCl and LiClO4 electrolytes of varying concentrations. Though they do not investigate the reactions in a KNO3-electrolyte one might expect a better agreement between the results. We can argue that the symmetry constant α is not easily to obtain from characteristics of a symmetric sensor. This applies especially to reactions with high kinetics, where the signal is largely limited by diffusion. As mentioned in the article, we find that simulated flux with α = 0.5 and α = 0.85 look quite alike. Transfer coefficients for ferrocenederivatives in aqueous solution reported in literature do vary significantly. Using micro- and nanoelectrodes, for instance, the values for the transfer coefficient in different electrolytes amount to α = 0.2-0.9 for the Fc(MeOH)1-couple5–8. Studies on TMAFc yield values up to α = 0.799. The exact value might not only depend on electrolyte type and concentration but also on the processes involved in sensor fabrication and the electrochemical history of the electrodes. Eventually nanoporous redox cycling sensors deliver a tool to precisely determine the transfer coefficient α in agreement with the Butler-Volmer model and reproduce the observed behavior numerically. The transfer rates obtained from our fit are further in good agreement with the rates of Fc(MeOH)2 (k0 = 1.5-15.0 cm/s)10. Still, it is of special interest to know which phenomenon causes the high transfer coefficient.

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Non-ideal behavior In the following four paragraphs we discuss effects that possibly influence the redox cycling current recorded, but are not included by the Butler-Volmer equations and diffusion. Since effects are obviously manifold, only a few are treated in a rather compact way. Special attention is paid to mediator adsorption and the influence of the titanium layer.

Adsorption of Redox Cycling Species In principle there are multiple processes to impair electron transfer at an electrode’s surface. Changes happening on timescales that are large compared to the timeframe of single measurements can be captured by adapting the heterogeneous transfer rate. Processes taking place during measurements are of greater interest. They could have an impact on the determined transfer coefficient. For the redox mediator used in our experiments, for instance, potential depended adsorption has been reported11. From the amount molecules reported to adsorb we can deduce Fc(MeOH)2 to form layers with maximum up to about 1 molecule / 15 nm2. Within the nanochannels, which the Lemay-group uses for their investigations, adsorption would cause a depletion of the number of freely moving molecules. Consequently, the redox cycling current was decreased until the cavity is repopulated by molecules diffusing in from the reservoir. When stepping down the potential, the adhered species could be released from the electrodes again. As a result changes in signal amplitude and noise characteristics could be seen. This is exactly was has been observed in the experiments performed in Lemay’s group. In our case, however, a signal modification caused by a depletion of redox cycling molecules was unlikely. Using a nonporous sensor the coupling to the reservoir is strong. Still, when

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recording cyclic voltammograms in redox-cycling mode we see hysteresis effects. The behavior can be nicely tracked by the curves recorded at the concentration series (Figure S3 a)). Especially for sweeps of the bottom electrode versus -50 mV the current magnitude of a backward sweep is lower than the one for a forward sweep. It might be speculated that we see here a potential dependent passivation of the electrode, which itself is caused by mediator adsorption. Like for the nanochannels the hysteresis is largest around 300 mV vs. Ag/AgCl. However, considering the occupied area of an adsorbed Fc(MeOH)2 molecule to be (0.3 nm)2 we barely reach a substantial coverage of the surface. One would further expect the adsorbed molecules to be in some kind of equilibrium with the molecules in solution. Thus, the number of adsorbed molecules should increase with the concentration and the degree of passivation was to increase as well. Consequently, the detected signal should not increase linearly with the concentration. Since this is not in agreement with our observations (Figure S3b) adsorption of the redox cycling molecules are not believed to be of major importance for the detected signal.

Figure S3. a) Cyclic voltammograms recorded for a 50 µm electrode at varying Fc(MeOH)2 concentrations for a sweeping bottom electrode (dashed lines) and a reducing top electrode (straight lines), which is set to Etop = -50 mV. b) Concentration series for the currents of the top electrode at Ebot = 450 mV for different electrode sizes.

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Reactions at nanoelectrodes As mentioned above, measurements performed with nanoelectrodes can yield a wide range of kinetic parameters for the exact same ferrocene redox-couple. Partially, these variances can be explained by the dimensions of the system used. It is known that pure diffusive species transport as well as classical Butler Volmer kinetics breaks down at nanometer-sized electrodes or small electrode distances in redox cycling systems12–14. On the one hand potential dependent attraction and repulsion of a charged analyte becomes increasingly important15, on the other hand electron tunneling can result in electron transfer nanometers away from the electrode periphery13. Regarding our experiments, tunneling of electrons beyond the plane of closest approach could explain the slight yet continual increase in current at high overpotentials. Since the species can undergo reduction and oxidation further away from the surface the necessary shuttling length for the redox molecules is shortened with increasing potential. Tunneling effects, however, cannot be the cause of an asymmetric transfer coefficient. It is not obvious how the redox cycling currents would be highly dependent on the orientation of the opposing overpotentials. Interestingly, electrostatic interactions between electrode and the the Fc(MeOH)2+-species and the consideration of the effective potential at the plane of reaction (known in combination as the Frumkin effect) might provide an explanation for α >> 0.5. For high enough electrolyte concentrations14 the electrode reactions can be written by a modulation of the Butler-Volmer equation:

((

)

(

))

This leads to an electrode flux of

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)

((

[

((

)

)

(

))

(

(

)) ]

meaning that the charge number zox = +1 of the oxidized molecule takes over the function of alpha in the pure Butler-Volmer terms. The transfer rate alpha - along with the potential of zero charge at the electrode - simply affects the apparent potential independent transfer rate. This picture might even hold up when including electrode tunneling.16 However, also the relevance of tunneling effects is potential dependent. Furthermore, the potential of zero charge was introduced as a novel parameter. Here, potential dependent adsorption of electrolyte ions might influence the potential at the Helmholtz plane and therefore alter electrode kinetics. Accordingly, adsorption effects seem likely due to the hysteresis shown in Figure S3a. As it is unclear to what degree this behavior would influence the signal, we restrict our considerations to simpler phenomenological Butler-Volmer model. Nevertheless, the high value of alpha could correlate to the charge of the oxidized analyte and thus be partially included by the Frumkin effect.

Surface morphology In studies performed on TMAFc, height variations of the surface are cited by the authors as the probable reason for the obtained variety of kinetic parameters. Velmurugan et al. further show that polishing nanoelectrodes in a suspension of alumina nanoparticles results in CV-curves, which can be fitted with a rather symmetric transfer coefficient7. Recordings with Fc(MeOH)1 at unpolished surfaces, on the contrary, yield signals that could be interpreted by α >> 0.5. It might therefore be speculated that our value for the transfer coefficient could be the result of a higher

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surface roughness. In studies performed on nanofluidic redox cycling devices for instance, chemical etching is used to release the electrodes and obtain a relatively planar surface17. The reactive ion etching process we used, on the other hand, can leave a rougher surface. Height variations alone, however, cannot cause distinct current magnitudes at maximum overpotentials. For the ‘Top +550 mV vs. Bot. -50 mV’ state and its inverse configuration the signals should be identical. Comparing both configurations in case of α = 0.5 we would simply find an inverted concentration ratio of oxidized and reduced species. Reversed reactions at the electrodes would still yield the same current amplitude.

Electrode passivation by titanium One might also consider the transfer coefficient to be affected by the titanium adhesive layer. Not only can titanium diffuse though a platinum layer and influence the signal, in our case, both titanium adhesion layers are also directly facing the electrolyte. Regarding potentials dependent electrode passivation, however, titanium seems an unlikely candidate, since the redox potential of titanium lays around -525 mV and a once oxidized surface layer is hard to be reduced. Titanium might only contribute to general fouling of the electrode by diffusing towards the electrode surface. The passivation might particularly happen at the edges of the electrodes, where titanium is facing the electrode at the front as well. Due to the relatively large amount of electron transfer events around the rim a degradation of the electrode edges was easily reflected in the redox cycling signal. We therefore test the impact that is expected by the rim passivation. Figure S4 shows the cyclic voltammograms that is to be expected from electrodes with ktop,bot = 1.2 cm/s. While we see in Figure S4a the outcome with the unmodified geometry used before

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Figure S4b-d represent electrodes with locally modified kinetics. In our case, we simply assume a ring of 5 nm width at the wall side of the electrodes, which is completely passivated. As expected, a direct comparison between Figures S4a and S4b shows that the signal amplitude is decreasing for all sweep configurations. The main cause regarding the modified top electrode might be the larger distance (~10%) molecules have to travel to complete a full redox cycle. At the pore bottom the additional restriction of the electrode area is believed to be of greater importance for the signal strength. The differing effects are again reflected in the distinct variance in the sweeps of the particular electrodes. So the current of a top sweep still appears rather diffusion limited when assuming rim passivation. A bottom sweep, on the contrary, results in a wider redox-cycling on-step. Eventually, the difference in the maximum currents is even

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Figure S2. Emulated redox-cycling currents of (a) a sensor with homogenous electron transfer and (b) – (d) influenced by a possible local fouling of the electrodes for different transfer coefficients. For (b) – (d) a completely inactive 5 nm zone at the in-pore edges is assumed. The parameters are E0 = 250 mV, ktop,bot = 1.2 cm/s and Deq = 0.64×10-5 cm2/s.

increased compared to the unmodified model. Therefore, hypothetical localized passivation might indeed affect the determination of the transfer coefficient α. Yet again, it cannot be the cause for the asymmetry, since symmetric kinetics would still lead to matching currents at maximum overpotentials.

Degradation can only amplify the transfer coefficient specific

separation. In our example, an adaption of the transfer coefficient to α = 0.85 already yields a more than sufficient compensation (Figure S4c). Similar effects, of course are expected from any

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kind of electrode fouling preferably taking place at their edges. Still, the effects of effective electrode size and transfer coefficient are distinguishable. Even when further decreasing alpha (Figure S4d) a larger separation around 300 mV persists, as this difference is ascribed to the differing electrode sizes.

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Significance of sensor dimensions The nanoporous sensor presented offers the opportunity to closely investigate electrochemical electrode reactions. As shown in the main article, the parameters involved in the redox cycling process effect the current derived from voltammetric studies in a particular way. The impacts are noticeable even for high transfer rates up to ktop,bot ~ 6.0 cm/s. However, when discussing the effects of different electrode areas and circumferences as well as the importance of transfer rates and transfer coefficients one should keep in mind the significance of the most important geometrical factor, namely the pores’ structure sizes. Firstly, the electrode spacing must be small enough to be in a kinetically limiting regime. The axial extension therefore should not exceed values around 100 nm. Secondly, the lateral dimension of structure must be far below the micrometer regime. When using a micropore sensor, differing sizes of top and bottom electrode only have a small impact on the signal. The reactions further take place closer to the circumference and the overall surface area becomes less important. Assuming a constant slope at the pores flank, the ratio of both electrodes’ circumference approximates unity with increasing diameter. An asymmetric behavior could not be restored by slower falling edges. Above a certain deviation of the pore wall’s orientation from the perpendicular upper and lower electrode were apart by a distance at which diffusion would dominate the process. Consequently, the strong dependence on the pore size is a typical characteristic of nanopores. In pores with approximate radii of r ~ 250 nm, the kinetic effects we found for Fc(MeOH)2 are barely noticeable (see supporting information). Eventually, the electrochemical parameters cannot be determined when using devices with larger pores. To underline the importance of the sensor dimensions we simulate a sensor with the radii rtop = 250 nm, rbot = 225 nm and an insulator thickness of hpore =

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200 nm. These values reflect the geometrical parameter of sensors, which have been previously introduced by the groups of Stelzle and Schuhmann18. Further assuming a cell radius of rvol = 500 nm we obtain the characteristics presented in Figure S5. Figure S5a reflects the result expected for fast and symmetric kinetics, Figure S5b shows the strongly asymmetric case with lowered kinetics. Though the top and bottom radii are clearly different, hardly any curve separation at high overpotentials can be seen. Also the separation around 300 mV, which in our case is caused by the different electrode areas is missing. It is interesting, however, that we see the current of the bottom sweep slightly exceeding the top sweep’s current. This might indicate, that also the orientation of the electrodes is reflected in the voltammograms of large pores. Due to the lower reaction rate at the top electrode at high overpotentials, reduced species might not react at the top rim as easily and might therefore take a detour through the bulk medium. The chances of leaving the electrode are significantly smaller at the pore bottom. Considering the nature of experiments, however, it is unlikely to identify these effects in laboratory setups.

Figure S5. Simulated signals derived from a pore modeled according to Neugebauer et al.18 (hpore = 200 nm, rpore ~ 250 nm) for a) fast and symmetric kinetics and b) slower asymmetric electrode reactions. Common parameters are E0 = 250 mV and Deq = 0.64×10-5 cm2/s.

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Asymmetric Reactions in a Symmetric Sensor When trying to determine transfer rates of electrode reactions, the effort to do so increases with increasing transfer rates. The reason is that one needs to investigate a system, where the overall process is not limited by diffusion, but the electrode kinetics can be derived from the nonNernstian behavior at the electrodes. Nanochannels with two opposing electrode represent such a system. However, diffusion limitation can still become the predominant factor for sufficiently fast reactions. The determination of the transfer coefficient might then be rather challenging as well. Regarding the data analysis typically the channel height used for the calculations is adapted in regard to the current at an overpotential (e.g. +450 mV for Fc(MeOH)2 in 250 M KCl). For sufficiently fast kinetics and a transfer coefficient of about 0.5 one can assume this current to be limited by diffusion only. Adapting the channel height by the signal amplitude, concentration, and diffusion coefficient is then justified. Dealing with geometries, however, in which the transfer kinetics might be the restricting factor, the situation behaves differently. Based on a numerical model of the channel, one will find the current for α >> 0.5 to still rise at 450 mV. (This behavior is similar to, though less extreme than the bottom-sweep vs. -50 mV in Figure 5,6b (article).) Therefore, the reaction is intrinsically assumed to be symmetric by employing the current at 450 mV as the limiting current and adapting the channel height accordingly. As a direct consequence, the fitted curves feature transfer coefficients close to 0.5. Impacts on the transfer constants k0 are believed to be less severe, since the transfer rates derived should scale rather linearly with the estimated electrode distance. The increase in shuttling time with the square distance of the electrodes is partially compensated by the linearly increasing number of molecule within the channel.

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To illustrate our point we calculate the current to expect from the nanochannel depending on the electrochemical parameters. Except for the geometry we use the same model that is applied for the nanopores. Again, only a segment of the sensor is considered, which is given by a volume with the radius rvol = 105 nm. Within this volume upper and lower boundaries represent top and bottom electrode. Their flux is defined by the Butler-Volmer equation. The vertical boundaries hold a no-flux condition. All other parameters, including channel height h = 53 nm, transfer rate k0 = 6.0 cm/s and transfer coefficient α = 0.49, are taken from Zevenbergen et al10. For the simulations using a transfer coefficient of α = 0.85 the channel height is also changed to hchan = 50 nm. As we can see from Figure S6a the currents for (hchan = 53 nm, α = 0.50) and (hchan = 50 nm, α = 0.85) match each other quite well. The agreement at 450 mV is of particular importance,

Figure S6. Calculated currents in a nanochannel for a) an electrode sweeping versus a reducing electrode (Ebot = 50 mV) with differing parametric sets of channel height h and transfer coefficient α. Graph b) depicts a full characterization like performed at the nanoporous sensors for the parameter set (h = 50 nm, α = 0.85). The Reaction rate is assumed to be k 0 = 6.0 cm/s, other values are E0 = 251 mV and Deq = 0.67×10-5 cm2/s.

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since this potential is used to determine the channel height. Assuming a transfer coefficient α ~ 0.85 for a channel height of hchan = 53 nm, on the contrary, would yield currents largely deviating from the recorded signal. Consequently, the characteristics obtained from an asymmetric transfer coefficient are more likely to be fitted with α ~ 0.50 when assuming hchan = 53 nm. Thus, a modification of the channel height has a direct impact on the derived transfer coefficient. Interestingly, the 50 nm-sized electrode gap exactly represents the channel height aimed at during fabrication. Additionally, one can observe that the currents of the cyclic voltammogram in the nanofluidic channel slightly increase at high positive overpotentials10. An asymmetric transfer coefficient would thereby also explain the different current magnitudes for the sweeps versus 50 mV and 550 mV. Corresponding to overpotentials of about -200 mV and +300 mV, respectively, the redox cycling process at E0 - 200 mV is not saturated, while at E0 + 300 mV the maximum flux is obtained. The calculated four-sweep characterization is presented in Figure S6b. The previous considerations, however, is only based on the available graphs. Other than for the nanoporous sensor the influences of the transfer coefficient α on the curve shapes are difficult to discern. Still, it is possible that the measurements presented by Zevenbergen et al. actually point at an asymmetric transfer coefficient as well.

Aspects of varying kinetics, transfer coefficient, and redox potential To exclude the possibility of any electrochemical parameter other than α to cause the observed behavior we have performed numerical investigations on their impact on cyclic voltammograms. The results are also summarized in the supporting information.

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Figure S7. Calculated effects of non-instant electrode reactions. If not stated differently the electrochemical parameters are E0 = 250 mV, ktop,bot = 1.2 cm/s and α = 0.90, while the diffusion constant for both species is Deq = 0.64×10-5 cm2/s.

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With high and symmetric kinetics (ktop,bot = 4.8 cm/s, α = 0.50) we find currents that are almost independent of the electrode sweeping (Figure S7a). Cyclic voltammograms recorded versus an oxidizing electrode are further exchangeable with the recordings taken versus a reducing potential. The graphs only have to be mirrored at E0. Assuming a reduced transfer rate of ktop,bot = 1.2 cm/s the slope due to the onset of redox cycling is less steep and shifted towards larger overpotentials of the cycling electrode (Figure S7b). Due to the differing sizes of the electrodes the current derived by a sweep of the bottom electrode is affected more severely. Changing only the transfer rate of one electrode will almost exclusively impact the cyclic behavior of that particular electrode (Figure S7c). Down to about 0.01 cm/s the transfer rates of an electrode biased to a fixed potential are still high enough to ensure full analyte conversion at ±300 mV overpotential. For the same reason a redox potential differing from the assumed one does not have an impact on the signal shape (Figure S7e). By setting E0 from 250 mV to 275 mV we only find a shift of all graphs towards a correspondingly higher potential. Changes in the joint diffusion coefficient Deq mainly affect the current amplitude (Figure S7f). For kinetics large enough we find a linear correlation. However, with a growing Deq the kinetic limitations become increasingly important for the signal shape. Like for a decreasing transfer rate, we find a broadening and a shift of the redox cycling on-step.

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Effects of unequal diffusion coefficients Investigations on the impact of distinct diffusion coefficients for two species of a redox-couple prove to be more complex. Due to the differing transport properties from and towards an electrode performing species conversion, the analyte molecules will either deplete or enrich at the sensor surface19. For redox cycling with identical diffusion coefficients only the specially restricted species exchange between bottom and top electrode has to be considered. Here, we also have to cover the molecule exchange towards a large reservoir via the appropriate diffusive coupling. In Figure S8 we present two exemplary cases. First, we present a simulated response of a single nanopore with the usual dimensions (rtop = 57 nm, rbot = 40 nm) in the centre of a mircodisc with a 2.1 µm-sized radius (Figure S8a). The pore is coupled to an extended reservoir (rvol = 400 µm, hvol = 400 µm), which consequently facilitates radial diffusion. The current maxima are again independent of the sweeping electrode.

Figure S8. Simulated cyclic voltammograms with different diffusion coefficients for the reduced (Dred ≈ 0.91×10-5 cm2/s) and oxidized (Dox ≈ 0.45×10-5 cm2/s) species. The pore is coupled to (a) a quasi-infinite hemispherical and (b) a quasi-infinite cylindrical volume. The electrochemical parameters are E0 = 250 mV, ktop,bot = 1.2 cm/s and α = 0.50. In (a) not the top currents, but the inverted bottom currents (light grey) are plotted.

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We only see the point of maximum slope to be shifted by about 15 mV towards higher potentials. With the diffusion coefficient of the oxidized species being smaller than the one of the reduced molecules (Dox = 0.5×Dred) the parameters are chosen in a way, that the number of molecules builds up with higher potentials. Consequently, the increasing current of the redox cycling on-step is overlaid by the increase of analyte molecules. The concentration at the nonsweeping electrode stays constant. The pore connected to a reservoir with rvol = 105 nm and hvol = 400 µm, as a second example, exhibits shifted slopes as well. The exact positions of the points of maximum rise, however, are somewhat more diverse. This is likely due to the remarkable configuration dependence of the signal amplitude. The current maxima differ by a factor of sqrt(Dox/Dred). As it turns out, the restricted analyte supply, which comes along with the weak linear coupling, is insufficient to increase the concentration at the sensor surface without decreasing the concentration at the bottom electrode. The changes at both electrodes apparently equalize to values to be obtained for Deq = sqrt(Dox*Dred). In the inverse case only the concentration at the bottom electrode changes, whereas the concentration at the sensor periphery matches the one of the bulk. Consequently, an overall increase in current can be observed. The detailed mechanisms will be subject of a separate paper. Here, we only present the interesting outcome being unique for distinct diffusion coefficients in a nanoporous sensor. As a closer look reveals, the graphs calculated do not match the case observed for a high transfer coefficient. Despite the differing maximum currents we do not obtain a clear bend at about 50 mV above the redox potential, which is typical for α ~ 0.9 (Figure 8d). We further find that, within a reasonable range of electron transfer rates, the separation for different diffusion

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constants is facilitated and not inhibited by higher kinetics. We conclude that possible diverging diffusion coefficients cannot be the essential cause for the recorded signal shape. Finally, we can state that an adaption of the transfer coefficient to α = 0.78-0.90 returns by far the best results. The congruence between experimental and theoretical curves is almost perfect. Modifications of all other model parameters lead to comparable results only if changing α along with them. Else, a variation of any of those parameters yields very specific changes in the current characteristics.

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References 1. Nanoelectrode Arrays and Limitations of the Diffusion Domain Approach: Theory and Experiment. J. Phys. Chem. C 2009, 113, 11119–11125. 2. Cutress, I. J.; Dickinson, E. J. F.; Compton, R. G. Analysis of Commercial General Engineering Finite Element Software in Electrochemical Simulations. J. Electroanal. Chem. 2010, 638, 76–83. 3. Aoki, K.; Osteryoung, J. Diffusion-controlled Current at the Stationary Finite Disk Electrode: Theory. J. Electroanal. Chem. Interfacial Electrochem. 1981, 122, 19–35. 4. Shoup, D.; Szabo, A. Chronoamperometric Current at Finite Disk Electrodes. J. Electroanal. Chem. Interfacial Electrochem. 1982, 140, 237–245. 5. Miao, W.; Ding, Z.; Bard, A. J. Solution Viscosity Effects on the Heterogeneous Electron Transfer K c f c h D hy S f x −W x J. Phys. Chem. B 2002, 106, 1392–1398. 6. Sun, P.; Mirkin, M. V. Kinetics of Electron-Transfer Reactions at Nanoelectrodes. Anal. Chem. 2006, 78, 6526–6534. 7. Velmurugan, J.; Sun, P.; Mirkin, M. V. Scanning Electrochemical Microscopy with Gold Nanotips: The Effect of Electrode Material on Electron Transfer Rates. J. Phys. Chem. C 2009, 113, 459–464. 8. L Y g D Zh g P E c ch c f 1−3 P D k Electrodes. Anal. Chem. 2009, 81, 5496–5502. 9. Watkins, J. J.; Chen, J.; White, H. S.; Abruña, H. D.; Maisonhaute, E.; Amatore, C. Zeptomole Voltammetric Detection and Electron-Transfer Rate Measurements Using Platinum Electrodes of Nanometer Dimensions. Anal. Chem. 2003, 75, 3962–3971. 10. Zevenbergen, M. A. G.; Wolfrum, B. L.; Goluch, E. D.; Singh, P. S.; Lemay, S. G. Fast ElectronTransfer Kinetics Probed in Nanofluidic Channels. J Am Chem Soc 2009, 131, 11471–11477. 11. Kang, S.; Mathwig, K.; Lemay, S. G. Response Time of Nanofluidic Electrochemical Sensors. Lab. Chip 2012, 12, 1262. 12. Smith, C.; White, H. Theory of the Voltammetric Response of Electrodes of Submicron Dimensions - Violation of Electroneutrality in the Presence of Excess Supporting Electrolyte. Anal. Chem. 1993, 65, 3343–3353. 13. White, R. J.; White, H. S. Electrochemistry in Nanometer-Wide Electrochemical Cells. Langmuir 2008, 24, 2850–2855. 14. Dickinson, E. J. F.; Compton, R. G. Influence of the Diffuse Double Layer on Steady-state Voltammetry. J. Electroanal. Chem. 2011, 661, 198–212. 15. Soestbergen, M. van Ionic Currents Exceeding the Diffusion Limitation in Planar Nano-cavities. Electrochem. Commun. 2012, 20, 105–108. 16. Gavaghan, D. J.; Feldberg, S. W. Extended Electron Transfer and the Frumkin Correction. J. Electroanal. Chem. 2000, 491, 103–110. 17. Wolfrum, B.; Zevenbergen, M.; Lemay, S. Nanofluidic Redox Cycling Amplification for the Selective Detection of Catechol. Anal Chem 2008, 80, 972–977. 18. Neugebauer, S.; Müller, U.; Lohmüller, T.; Spatz, J. P.; Stelzle, M.; Schuhmann, W. Characterization of Nanopore Electrode Structures as Basis for Amplified Electrochemical Assays. Electroanalysis 2006, 18, 1929–1936. 19. Mampallil, D.; Mathwig, K.; Kang, S.; Lemay, S. G. Redox Couples with Unequal Diffusion Coefficients: Effect on Redox Cycling. Anal. Chem. 2013.

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