Molecularly-tunable nanoelectrode arrays created by harnessing intermolecular interactions

Intermolecular interactions play a critical role in the binding strength of molecular assemblies on surfaces. The ability to harness them enables molecularly-tunable interfacial structures and properties. Herein we report the tuning of the intermolecular interactions in monolayer assemblies derived from organothiols of different structures for the creation of nanoelectrode arrays or ensembles with effective mass transport by a molecular-level perforation strategy. The homo- and hetero-intermolecular interactions can be fully controlled, which is demonstrated not only by thermodynamic analysis of the fractional coverage but also by surface infrared reflection absorption and X-ray photoelectron spectroscopic characterizations. This understanding enables controllable electrochemical perforation for the creation of ensembles or arrays of channels across the monolayer thickness with molecular and nanoscale dimensions. Redox reactions on the nanoelectrode array display molecular tunability with a radial diffusion characteristic in good agreement with theoretical simulation results. These findings have implications for designing membrane-type ion-gating, electrochemical sensing, and electrochemical energy storage devices with molecular level tunability.


Introduction
The fabrication of nanoelectrode ensembles and arrays has gained increasing interest in development of highly sensitive and miniaturized electrochemical devices and sensors. 1a Template synthesis of nanoporous membranes is an important pathway for the fabrication of ensembles of nanoscopic electrodes (e.g., metal nanotube membranes) towards ionpermselective membrane. 1b Both bottom-up and top-down approaches have been used in the fabrication of nanopore electrode arrays or ensembles potentially viable for chip-based nano-electrochemical sensing applications. 1c The nano-conned space of nanoporous electrodes enhances electrochemical efficiency between redox probes and the electrode surface with enhanced nanoporous mass transport tunable by size, shape, and charge. The effective mass transport is also exploited for electrochemical energy conversion and storage devices, 2,3 and materials, 2a including self-supported 1D/2D nanoarrays with different geometries for supercapacitors with high specic capacitance. Imparting nanostructure to electrodes is also desired for energy storage reactions 2b by improvement of mass transport with nanoelectrode arrays. Experimental and theoretical studies of diffusion domains based on microelectrode arrays 3 have highlighted the importance of radial diffusion compared to microelectrode arrays and the strong dependence on the size. Major challenges for fabrication include the high-cost or complicated fabrication processes and low active-mass loading per unit area. Nanoelectrode ensembles or arrays for electrochemical applications 4 are fabricated by both top-down electron-beam lithography or nano-imprinting for ordered arrays, and bottom-up template and self-assembly methods for random ensembles. The mass transport by radial diffusion at individual nanoelectrodes, arrays, ensembles or nanopores not only emulates transmembrane ion transport processes but also enhances the surface spatial imaging 5 where a given footprint of a functional device could enable a larger number of active interaction points at the interface.
For the bottom-up approach to nanoelectrode fabrication by exploring the atomic and molecular structures on surfaces and interfaces, especially self-assembled systems, [6][7][8][9][10][11][12][13] a key question is how the surface or interface can be tuned precisely for the creation of specially-structured functionality. In self-assembled monolayers (SAMs), there has been a large body of work focusing on the well-dened single-phase structural character, including earlier spectroscopic, microscopic and electrochemical studies 6 and recent studies 7-13 of the molecular structures of these systems. There has been limited understanding for binary or mixed SAMs due to the complexity of intermolecular interactions. In situ ellipsometry study of mixed monolayers showed evidence for the formation of a low refractive index region aer desorption of the monolayer component. 14 In a lateral force microscopy study of some binary monolayers formed on planar polycrystalline gold, 15 portions of 2-aminoethanethiol were removed by selective reductive desorption and backlled with 11-mercaptoundecanoic acid. Phase formation in mixed alkanethiol monolayers 16 was also revealed by electrochemical quartz crystal nanobalance. For homogeneously mixed SAMs of mercaptoalkanoic acids of different chain lengths on Au(111), 17 a pH-sensitive supramolecular switch function was revealed by breaking or restoring the hydrogen bond interaction in basic or acidic solutions. For SAMs on gold nanoparticles, recent Monte Carlo study 18 showed that the hexanethiolate/tetradecanethiolate mixture yields Janus-like arrangement when the ligands are conned to a single nanoparticle. Atomistic simulation study 19 showed that mixed hydrophilic and hydrophobic alkylthiols on gold nanoparticles exhibit domains of surface hydrophilicity, serving as a platform not only for structural characterizations but also for electrochemical applications. Despite the progress, the question of how the intermolecular interactions can be controlled to pin down the interfacial molecular or nanoscale functionalities remains elusive.
We demonstrate here the ability to harness the intermolecular interactions and a molecular-level perforation strategy for the creation of molecularly-tunable nanoelectrode arrays or ensembles. In contrast to previous studies of mixed monolayers, 16,20-24 the controllability of the intermolecular interactions and binding strength of the two-component monolayer to gold surface enables the molecular level tunability. Fig. 1A(a) illustrates how the overall binding strength depends on the intermolecular interactions of the two components with subtle differences in their packing structure and functional group. In other words, the overall binding strength is determined by the lateral interactions through the molecular packing structure and the functional group (end group). Fig. 1A(b) shows selected examples of the combinations to create differences in terms of the binding strength (E * b , also see Table S1 †) based on density functional theory (DFT) calculations 25,26 in several recent reports, 27,28 which could also involve molecular packing as shown in our recent work. 25 These differences are harnessed by tuning the alkyl chain, aromatic moiety, and functional groups in terms of hydrophobic, guesthost, protonation, hydrogen-boding, or electrostatic interactions for a wide range of sensor applications. [29][30][31][32] The selected combination of thiolate molecules highlight the differences in molecular structure, chain length, and functional groups. It is the resulting difference in binding strength that constitutes the basis for manipulation of their intermolecular interactions and phase structures for the selective desorption by controlling the E * b , which determines the desorption peak potential (E p ). 28,[33][34][35] The basis for the selective reductive desorption is that E p depends on the molecular structure, chain length, and functional groups. For example, the potential shis negatively by $20 mV per (-CH 2 ) group for n-alkanethiolate monolayers at annealed gold. By holding the applied potential (E app ) at a value between the two waves corresponding to the two different components, the desorption of the short chain component is preferentially induced. This removal therefore denes the size  Table S1 †). (c) Illustration of competitive adsorption of two thiols forming a monolayer on Au(111). (B-D) Dependence of fractional coverages, q 1 and q 2 , vs. their concentration ratio in the solution for TP (C 1 ) and ET (C 2 ) (B); MUA (C 1 ) and HDT (C 2 ) (C); and MBA (C 1 ) and MHA (C 2 ) (D). The dashed lines represent fitting curves based on eqn (3a) and (3b) with the fitting parameters: (B) K 2 /K 1 ¼ 0.7, a a ¼ 0.05, a b ¼ 2.05, and a c ¼ À2.0; (C) , and a c ¼ 0.9. and shape of the channels, whereas the retained long chain component functions as an impermeable framework surrounding each nanochannel, creating nanoelectrode arrays or assembles with molecular tunability.

Results and discussion
As illustrated in Fig. 1A(a) and (b), the general design principle to tune the nanoelectrode pore size and interpore distance starts from controlling the mixing ratio of two host-guest thiol components in terms of lateral interaction and binding energy (see also Table S1 †). The key is the ability to harness the intermolecular interactions and the overall binding properties. A stronger binding strength leads to a more negative desorption potential, whereas a stronger cross intermolecular interaction leads to a better mixing of the two components. These control parameters are assessed in the following subsections rst in terms of the co-adsorption isotherm analysis, then the electrochemical desorption manoeuvring, and nally the nanoelectrode array evaluation.

Co-adsorption isotherm
A novel element of our strategy is to harness the intermolecular interactions of a two-component monolayer assembly on the surface of a substrate. Consider rst the equilibrium for competitive adsorption for surface sites between two thiols in a solution (sol) and the surface assembly by adsorption (ads) (1 and 2, Fig. 1A(c)), which is represented by eqn (1): 1 sol + 2 sol 4 1 ads + 2 ads (1) We further consider Frumkin adsorption isotherm, 36 which derives from Langmuir isotherm by inclusion of attractive and repulsive intermolecular interactions between neighboring adsorbates. 37 For the formation of a full monolayer at each mixing ratio of the two-component solutions (q 1 and q 2 are the fractional surface coverages of 1 ads and 2 ads ), eqn (2a) and (2b) can be derived, 38 expð Àa 11 q 1 À a 12 q 2 Þ (2a) where C 1 and C 2 are the solution concentrations of 1 sol and 2 sol (at a constant total concentration), and K 1 and K 2 are the adsorption equilibrium constants. Eqn (2a) and (2b) introduce the intermolecular interactions between 1 and 2, 1 and 1, and 2 and 2, which are described by the interaction parameter (a ij ). The intermolecular interaction is attractive when a ij > 0, and repulsive when a ij < 0. By recasting a ij as a a ¼ a 11 + a 22 À 2a 12 , a b ¼ a 22 À a 12 , and a c ¼ a 11 À a 12 , dividing eqn (2a) by eqn (2b), and rearranging the result, we obtain eqn (3a) and (3b) in terms of q 1 and q 2 . An equation in terms of q 2 can be obtained by replacing q 1 in eqn (3a) with q 2 , where q 2 ¼ 1 À q 1 .
The relative homo-and hetero-molecular interactions are assessed by comparing the magnitude and sign of these values. The relative coverages of the two components in the monolayer are assessed from the voltammetric reductive desorption. 39 The theoretical reductive charge is 70 mC cm À2 , corresponding to the 7.2 Â 10 À10 mol cm À2 coverage for a fully formed monolayer (O3 Â O3)R30 on gold. 40 The fractional coverage of two components in the monolayer controlled by the precursors in the solution. A small fraction of double-layer charge in the overall reductive charge has little impact on the analysis of the fractional coverage (q) since the double-layer charges are largely canceled in the coverage calculation.
We systematically determined the coverages of several twocomponent monolayer assemblies on Au(111) surfaces (q 1 and q 2 ) as a function of concentrations in the solution (C 1 and C 2 ) by voltammetric measurements, including: (1) TP/ET monolayer assembly, where TP (thiophenol) features an aromatic moiety while ET (ethanethiol) features a hydrophobic end group with approximately similar molecular length as TP (Fig. S1A †); (2) MUA/HDT monolayer assembly, where MUA (11-mercaptoundecanoic acid) features an alkyl chain with -CO 2 H end group whereas HDT (hexadecanethiol) features a longer alkyl chain with a hydrophobic -CH 3 group ( (4) MBA/MHA monolayer assembly, where MBA (mercaptobenzoic acid) maintains the same aromatic structure as FTP but introduces a -CO 2 H group whereas MHA features a long-alkyl chain host-like molecules with -CO 2 H end groups in the monolayer (Fig. S2B †).
Based on simulations using Frumkin isotherms, 36 the faradaic current contributes largely to the total integrated charge, whereas the capacitive current produces a charge less than 10-20% of the total charge. The latter is supported by a double-layer charge of 15-20 mC cm À2 at the desorption potential. Also, in agreement with previous simulations, 41,42 the width and potential are dependent on the adsorbate-adsorbate interactions, which constitutes the basis for assessing the thermodynamic correlation between surface coverages and the relative amounts of the two precursors in solution. By analysis of the reductive desorption potentials (E p ), we observed an excellent agreement between the DFT calculated binding strength and the reductive desorption potential in terms of their relative differences (see Fig. 1A(b) and S3 †).
As shown in Fig. 1B, the general agreement for the tting of the predictions by eqn (3) to the electrochemical data for the monolayer mixed with TP and ET (Fig. S1A †) establishes the thermodynamic correlation between the surface and solution species. The tting parameters for TP (1) and ET (2) yield a a ¼ 0.05, a b ¼ 2.05, and a c ¼ À2.0. In comparison, a similar agreement between the theoretical prediction and experimental data is also found for monolayers of longer-chain MUA(1)/ HDT(2) system ( Fig. S1B †), yielding a a ¼ 2.8, a b ¼ 2.5, and a c ¼ 0.3 (Fig. 1C). In addition, the analysis of the isotherm for mixing short and long RSHs with distinctive structural difference but the same functional groups, e.g., MBA/MHA ( Fig. S2B †), yields a a ¼ 3.8, a b ¼ 2.9, and a c ¼ 0.9 (Fig. 1D), displaying a clear shi of the cross point to a higher C 1 /C 2 ratio ($25). The results demonstrate a 22 > a 11 > a 12 .
The fact that the competitive adsorption theory ts well with the two-component thermodynamic description rules out the presence of disuldes. Based on a 22 > a 11 , the attractive interactions between alkylthiolate-adsorbates are stronger than those between benzylthiolate-adsorbates, and the attractive interactions between long chains are larger than those between short chains, leading to K 2 being greater than K 1 . This is consistent with the narrower desorption wave for stronger attractive interactions than those with weak ones for the mixed monolayers in Fig. S1 and S2. † The effect of the intermolecular interactions on the overall binding strength is in fact consistent with the shi in E p vs. mixing ratio.
Considering the summative nature of a a , a b , and a c in terms of a 11 , a 22 , and a 12 , the nding that a c ¼ À2.0 (Fig. 1B) means that TP-TP interaction is smaller than TP-ET interaction, reecting the dominance of van der Waals interaction in the mixed monolayer, as supported by the small value of a a . For MUA/HDT and MBA/MHA, a c values are not negative but quite small (0.3 and 0.9), suggesting again the important role of van der Waals interactions, a detailed insight into which may be provided by molecular dynamics modeling in the future work.
Electrochemical perforation (A) Component removal and rell. To achieve well-dened voltammetric deposition waves with a low effective level of a defect-associated current, annealing temperature was systematically varied from room temperature to 400 C, we found that gold lms annealed at $300 C exhibit the optimal performance based on comparisons of leakage current and desorption voltammetric waves. For electrochemically-driven selective desorption for MUA/HDT ( Fig. 2A), the desorption of MUA is clearly not detectably destructive to the architecture dened by HDT monolayer (Fig. 2B). Two partially overlapping waves are evident (a) where the more positive wave is for the desorption of MUA and the more negative is for that of HDT. By sweeping from À0.2 to À1.0 V and holding the potential at À1.0 V while agitating the solution, MUA is desorbed (b). This is substantiated by the post-MUA-desorption wave (c), showing that the wave for MUA is virtually undetectable aer its selective desorption in (b). The wave in (c) is effectively the same as the more negative one in (a). As shown by the general similarities of the two major waves in the monolayer for the other combinations (TP/ET and MBA/MHA) ( Fig. S1 and S2 †), the changes in their reductive desorption curves are basically similar to those in Fig. 2B.
The structural integrity of the longer chain component aer perforation is supported by the similarities in peak width, peak potential and integrated charges for the wave in Fig. 2B. Aer desorbing MUA, the integrated charge for the remaining HDT is estimated at $23 mC, demonstrating the maintenance of structural integrity of HDT component in the MUA/HDT assembly aer perforation, which stems from the strong cohesive intermolecular interactions. We further examined whether the resulting channels from the desorption of MUA in MUA/ HDT could be relled by testing three different species: S 2À (a), MPA (b) and MUA (c) (Fig. 2C). In each case, two desorption waves are observed prior to the onset of solvent reduction. The more negative wave corresponds to that for the desorption of HDT, whereas the more positive waves reect the desorption of the reconstituting adsorbate.
(B) Spectroscopic characterizations. The effectiveness of removing one component without affecting the other component in the monolayer was further demonstrated by spectroscopic characterizations of FTP/MHA. To remove the FTPcomponent in the mixed monolayer (Fig. 3A), the applied potential was held at the midpoint between the two desorption waves in Fig. 3B(a) (i.e., À0.8 V) for $2 min while agitating the electrolytic solution with a stream of argon. The subsequent scan (Fig. 3B(b)) is devoid of FTP-desorption wave, while the wave for MHA-desorption remains largely unchanged. Upon removing both FTP and MHA, the voltammetric curve is devoid of any waves (Fig. 3B(c)). The spectra in the S(2p) region are also in general agreement with the expected sample compositions, and are consistent with earlier assignments to gold-bound thiolates. 7,8 There is, however, an additional piece of structural detail evident in the spectrum for the FTP-derived monolayer in Fig. 3D. The appearance of the lower energy shoulder in (b), as opposed to the usual doublet-shaped peak in (a), reveals the presence of a small relative amount of adsorbed atomic and oligomeric sulfur, as described in the discussion of the voltammetric data of Fig. S2A. † The deconvoluted data included with the data further clarify this interpretation. That is, two S(2p) couplets are evident in (b) and only one couplet in (a). The S(2p) couplet at high energy (S(2p 3/2 ) $ 162.0 eV and S(2p 1/2 ) $ 163.2 eV) are assigned to sulfur bound to gold as a thiolate and the S(2p) couplet at (S(2p 3/2 ) $ 161.1 eV and S(2p 1/2 ) $ 162.2 eV) to sulfur bound to gold in its atomic and oligomeric forms. Aer treatment at an applied potential of À0.8 V, the absence of a detectable ($0.1 monolayer detection limit) F(1s) band in Fig. 3D(d) is diagnostic of the removal of the FTP component from the monolayer. The decrease of the intensities of the S(2p) couplet in spectrum (d) relative to (c) also supports the decrease in the total sulfur coverage at the gold surface. Furthermore, the absence of a detectable sulfur S(2p) peak for the sample aer the À1.2 V-treatment (e) reects the exhaustive removal of the remaining portion of the original mixed monolayer, and is in strong agreement with the electrochemical and IRRAS data in Fig. S2A † and 3C. This analysis proceeds by comparing the integrated band intensities for the deconvoluted S(2p) couplets of the thiolate species before and aer the removal of the FTPderived component, which were normalized using the intensities of the bands for the corresponding single-component spectra to estimate for the effects of attenuation. This analysis yields a mixing ratio of FTP to MHA $ 0.43, in close agreement with the value determined from the electrochemical data.
Nanoelectrode arrays (A) Voltammetric characteristics. It is well established that non-linear diffusion can be induced by a partial blockage of an electrode surface towards electron transfer, 37 where microelectrode phenomena 38 may appear when the average size of the active sites is very small and the average distance between the unblocked areas is relatively large. These microelectrodes are of molecular or nano-dimensions in size. The access of redox probes to the underlying electrode may thus be externally gated by pH-tuning of the terminal group between protonated carboxylic acid form and negatively-charged carboxylate form, leading to a change in electrostatics around the rim of the channel. This is demonstrated with two ionic redox probes, Ru(NH 3 ) 6 3+/2+ and Fe(CN) 6 3À/4À . Fig. 4A(b) (Fig. 4A(d) and (e)) show a clear dependence on pH, exhibiting sigmoidal current at low pH (d) and diminished current at pH above 10 (e). This result is consistent with protonation/deprotonation of -CO 2 H groups of the MHA skeleton at the rim of the microchannels. While MBA/MHA assembly acts as an effective barrier between the redox probe and the underlying substrate, the perforated assembly aer removal of MBA exhibits a pH-tunable sigmoidal-shaped voltammetric curve (c) for Fe(CN) 6 3À , which is characteristic of radial diffusion of a microelectrode array or ensemble. 43 The half-wave potential for curve (b) is similar to that estimated from the formal reduction potential for Fe(CN) 6 3À/4À (a).
The dependence on pH for the positively-charged redox probe, Ru(NH 3 ) 6 3+ , is shown in Fig. 4B. The voltammetric curve of the redox couple at a bare gold electrode is included for comparison (a). The key observation is that the redox current increases upon increasing pH (b-d), a nding not observed prior to perforation. This result is consistent with the expectation based on the pH-induced electrostatic gating mechanism. We also note that the voltammetric curves show peak-shaped and widely-separated redox waves that are not characteristic of a radial diffusion-controlled process. We attribute this result to a signicant reduction of the apparent heterogeneous electron transfer rate constant (k app s ) for the redox probe at the monolayer-assembled electrode. 37 Indeed, an estimate of k app s based on the peak separation 44 at pH 10 (DE p $ 500 mV) yields a value of 5.9 Â 10 À4 cm s À1 , which is at least three orders of magnitude lower than that for the solution-phase rate constant. Further investigations are needed to gain an improved understanding of this observation.
(B) Theoretical modeling. To provide a more quantitative description of the nanoelectrode array formed by electrochemical perforation, the number of microchannels in the array can be determined from the fractional coverage of the desorbed component (q m ) or the non-desorbed component (q block ) (q m + q block ¼ 1) by integrating the charge under each of the desorption waves by q m ¼ Q m /(Q m + Q block ), where Q m is the charge for the desorbed component upon perforation, and Q block corresponds to the charge for the non-desorbed component. Experimentally, however, an extremely small fraction (i.e., q m ¼ $0.02) of the shorter length component is mixed into the monolayer in order to generate highly dispersed nanoelectrodes which is undetectable in the desorption voltammetry. For this reason, we estimate the surface density of the microelectrode-like channels based on models of microelectrode arrays, either disk-shaped microelectrodes with an average radius of r a , or strip-shaped microelectrodes with an average width of r a (Scheme S1 †). The charge transfer is considered to occur at a partially blocked electrode surface, 36 and has been applied to the simulations of  ) for A-c using r a ¼ 2.0 nm, R 0 ¼ 482 nm, D ¼ 3.20 Â 10 À6 cm 2 s À1 , and k ¼ 2 (D, a); for A-d using r a ¼ 20 nm, R 0 ¼ 1950 nm, D ¼ 3.20 Â 10 À6 cm 2 s À1 , and k ¼ 2 (D, b); and for B using r a ¼ 0.7 nm, R 0 ¼ 545 nm, D ¼ 8.43 Â 10 À6 cm 2 s À1 , and k ¼ 2 at pH $ 3.5 (E, a); r a ¼ 7.5 nm, R 0 ¼ 2160 nm, D ¼ 2.0 Â 10 À5 cm 2 s À1 , and k ¼ 2 at pH $ 6.0 (E, b); and r a ¼ 600 nm, R 0 ¼ 5.70 Â 10 4 nm, D ¼ 3.0 Â 10 À4 cm 2 s À1 , and k ¼ 2 at pH $ 10.0 (E, c). defects in monolayer systems. In an idealized model, 2r a and 2R 0 represent the average diameter of the perforated electrodes and the average distance between them (Fig. 4C). If the fractional coverage of the blocking architecture (q block ) is close to unity, i.e., q / 1, the voltammetric current plateau (I lim ) of the array can be expressed as: where n is the electron transfer number, F is the Faraday constant, A is the electrode surface area, D is the diffusion coefficient, and C 0 is the concentration of the redox probe; the coverage function, dened as f(1 À q), equals 0.3(1 À q) À1/2 . In the model (Scheme S1 †), the electrode radius (r a ) À interelectrode distance (2R 0 ) are related to the surface coverage of the electrodes (1 À q) by r a ¼ R 0 (1 À q) 1/2 (disk-type), or r a ¼ R 0 (1 À q) (strip-type). The dimensionless equation of current (i)$ potential (E) (see ESI †) depends on the function of f(1 À q), numerical solution of which is used for the simulations of the experimental data in terms of the nanoelectrode parameters. on the perforated MBA/MHA ( Fig. 4D(b)), the disk-model showed an excellent t to the experimental data in the entire potential range. The nanoelectrode array features disks with about 20 nm in radius and about 3900 nm in the nearest-neighbor distance. Apparently, the nanoelectrode is 10Â larger and the inter-disk spacing is 4 times greater than those for the perforated MUA/HDT, showing 12Â higher active area. Note that the strip-model did not show any good t to the experimental data for both perforated MUA/ HDT and MBA/MHA (see Fig. S4 †). Fig. 4E shows the theoretical modelling results with the diskmodel for the reduction of Ru(NH 3 ) 6 3+ at three different pH values on the perforated MBA/MHA. In these cases, the diskmodel simulation result showed tting to the experimental data at potentials before reaching current-peak/plateau potentials, yielding r a ¼ 0.7 nm and R 0 ¼ 545 nm for pH $ 3.5 (a); r a ¼ 7.5 nm and R 0 ¼ 2160 nm for pH $ 6.0 (b); and r a ¼ 600 nm and R 0 ¼ 5.70 Â 10 4 nm for pH $ 10.0 (c). In comparison with the D value for Fe(CN) 6 3À on the perforated MBA/MHA (Fig. 4D(b)), the value of D for the reduction of Ru(NH 3 ) 6 3+ is increased, which is somewhat surprising. Since the diffusion coefficient D is referred to near the electrode surface, it is not totally unreasonable considering similar values reported in the literature, 47 and the strong electrostatic attraction by the positive redox probe's charge and the negative charge (-CO 2 À groups of MHA) at the entrance of the nanoelectrode channel. This interpretation however needs further conrmation. At pH $ 6.0, the nanoelectrode array features disks with about 8 nm in radius and about 4320 nm in nearest-neighbour distance. The radius is increased by a factor of 80 at pH $ 10.0 but reduced by a factor of $10 at pH $ 3.5. The disk radius at pH $ 10.0 is much larger than the radius of Ru(NH 3 ) 6 3+ ($0.4 nm), resulting in a peak-shaped voltammetric wave. Interestingly, the D value is shown to increase with pH, coinciding with the increase of the electrostatic attraction at higher pH. Again, the experimental data cannot be tted using the strip-model (see Fig. S5 †). While the nanoelectrode pore size, shape and interpore distance are derived from the theoretical simulation, there have been extensive AFM (atomic force microscopy) studies of SAMs or mixed SAMs, 6,7,14,48 though with limited resolution under ambient condition, for measuring the pore sizes. One relevant example involves AFM study of mercaptopropionic acid (MPA)-MUA monolayer assembled from 1 : 4 ratio of MPA : MUA. 49 The monolayer aer reductive desorption of MPA showed nanopores with diameters of 12-19 nm, supporting the formation of nanopores in the monolayer which is similar to our MBA/MHA monolayer. Moreover, in a recent eld ion microscopy (FIM) study of a mixed monolayer of octanethiol (ODT) and per-uorodecanethiol (PFDT), 50 PFDTs are shown to arrange in a patchy type of domains surrounded by ODTs due to the cross intermolecular interaction with the homogeneous inter-chain interaction energy being larger than the cross-interaction energy, supporting our assessment of the homo and heterointermolecular interactions.
Consider further the array performance by analyzing the limiting current (i lim ) for the radial diffusion at a microelectrode, 43 which is given by: where N m is the number density of nanoelectrodes. The total limiting current (I lim ) density is the sum of the limiting current from all individual nanoelectrodes. 43 Based on eqn (5), the theoretical single nano-electrode limiting current is calculated (i theory ). As shown in Table S2, † the result is quite comparable with the simulation results (i simulated ) aer taking the number of nanoelectrode into consideration (N m ). The i theory and i simulated values are quite comparable (Table S2 and  The above results have demonstrated the general micro/ nano electrode characteristics of the nanoelectrode arrays, 43 which not only show the radial diffusions at the nanoelectrode arrays, but also the characteristics of pH-insensitive and pHsensitive interfaces for the arrays (Scheme 1). Considering the Debye length at the electrolyte concentration, 44 the xed negative charges of the carboxylate groups are effectively screened by cations at a distance of a few angstroms, which is reasonably consistent with the average diameters of the redox probes. This nanoelectrode array or ensemble indeed features molecularlyand chemically-tunable characteristics.

Conclusions
Taken together, the intermolecular interactions are shown to play a critical role in creating the nanoscale channels with nanoelectrode functionality. The strategy of electrochemical perforation by rational combinations of homo-/heterointermolecular interactions not only opens an intriguing avenue for the creation of nanochannel-like nanoelectrode at a molecular level, but also offers the capacity for manipulation of the nanoelectrode properties by relling the perforation sites with a pre-selected molecular functionality or dimension. The array or ensemble of such nanoelectrodes is potentially capable of functioning as an articial membrane for molecularlycontrollable and tunable ion-gating, which could lead to a paradigm shi in the design of biosensors.

Sample preparation
The substrates were prepared by the vapor deposition of 300 nm of gold (99.9% purity) onto freshly cleaved mica sheets (B & M Trading Inc.) or pre-cleaned glass slides using an Edwards 306A cryopumped evaporator. The glass slides were primed with 15 nm of chromium prior to gold deposition. In both cases, gold was deposited at a rate of $0.3 nm s À1 . The pressure in the evaporator was less than 1 Â 10 À6 Pa before deposition. The mica-supported gold lms were subsequently annealed at 300 C for $4 h, a process that yields a surface composed of large (100-200 nm 2 ) atomically smooth Au(111) crystallites. The roughness factor, as determined by a comparison of the surface area from the oxidative stripping of iodide to the exposed geometric area of the electrode, is 1.1 AE 0.1. Monolayers were formed by immersing the gold substrates into ethanolic solutions with a controlled thiol concentration. Typically, the monolayers were obtained using thiol concentrations of >1 mM, assembly time of >12 hours and room temperature (25 C), which are important for achieving not only thermodynamic equilibrium but also better molecular packing in the SAMs. The use of 5 mM total concentration is for the purpose of well-dened thermodynamic analysis by varying the mixing ratio of the two components while xing the total concentration. All samples were thoroughly rinsed with ethanol and dried under argon before characterization. We also note that the reduction peak can be displayed on polycrystalline gold surface without annealing to form Au(111), but the multiple peaks due to the presence of multiple facets (e.g., 111, 110, 100) 41 complicate the controllability. Polycrystalline gold could be used if the rst component's desorption is separated from the second one.

Instrumentation
Electrochemical measurements were performed using a CV-27 potentiostat, including electrochemical reductive desorption 51 and cyclic voltammetry. A conventional three-electrode cell was employed, with a platinum coil as auxiliary electrode and an Ag/ AgCl (sat'd KCl) electrode as reference electrode; all potentials are given with respect to this reference electrode. The geometric area of the working electrode, 0.60 cm 2 , was dened by an Oring which denes the diameter on the working electrode (0.88 cm). The supporting electrolyte was an aqueous solution of KOH (0.5-1.0 M) that was deaerated with ultrahigh purity argon before electrochemical measurements. The pH of the solution was controlled by adding aliquots (a few mL) of 1.0 M HCl or 1.0 M KOH into the solution while maintaining the high ionic concentration (1.0 M KCl). For the coverage analysis, the voltammetric peaks and integrated charges were determined by deconvolution with mixed Lorentzian-Gaussian curves. The measurement of the reductive desorption potential is reproducible within AE5%, and the integrated desorption charge is reproducible within AE10%. 42 Infrared reection absorption spectroscopy (IRRAS) was acquired with a Nicolet 760 ESP FTIR that was purged with boiloff from liquid nitrogen and equipped with a liquid nitrogencooled HgCdTe detector. The spectra were obtained in an external reection mode using p-polarized light incident at 80 with respect to the surface normal, and with 500 scans at 2 cm À1 Scheme 1 Illustrations of radial diffusion as the nanoelectrode arrays, and pH-sensitive and insensitive interfacial characteristics.
resolution. An octadecanethiolate-d 37 monolayer was used as the reference.
A Physical Electronics Industries 5500 surface analysis system was used for the X-ray Photoelectron Spectroscopy (XPS) characterizations. This system is equipped with a hemispherical analyzer, toroidal monochromator, and multichannel detector. The sampling area was $2 mm 2 . A pass energy of 29.35 eV was used with a resolution of $0.3 eV. Monochromatic Al K a -radiation (1486.6 eV) at 300 W was used for excitation. Photoelectrons were collected at 45 from the surface normal with acquisition times less than 10 min. The Au(4f7/2) emission band served as an internal reference for binding energies. The base pressure of the XPS chamber was less than 9 Â 10 À10 torr during all analyses. The XPS spectral couplet in the S(2p) region was tted using a doublet with a Gaussian prole. This doublet is the result of spin-orbit coupling which splits the S(2p) band into 2p 3/2 -and 2p 1/2 -components separated by 1.2 eV with halfheight widths of 0.9 AE 0.05 eV, differing in intensity by a factor of two (2p 3/2 > 2p 1/2 ). 52

Author contributions
HWC carried out the data analysis and theoretical simulation, and performed part of the data acquisition. SW carried out part of the simulation and data analysis. MDP and CJZ conceived and supervised the research. CJZ designed the experimental measurement and theoretical simulation, and directed the manuscript writing and revision. All co-authors assisted in writing and revising the manuscript. All co-authors read and approved the nal manuscript.

Conflicts of interest
There are no conicts of interests to declare.