The electron as a probe to measure the thickness distributions of electroactive films

A theoretical model combined to an experimental study shows that the morphology of electron conducting films can be quantified directly from the analysis of cyclic voltammetry data.


Introduction
Redox-active or conductive lms assembled from synthetic 1,2 or natural materials 3 are ubiquitous as matrices for the immobilization and electrical wiring of catalysts or of light absorbing materials for technological applications. The most prominent of these are thin lms based on perovskites and organic semiconductors 4 for photovoltaics, 5 as well as inorganic catalysts for reactions such as proton reduction and water oxidation. 6,7 In addition, redox lms containing biological or molecular catalysts immobilized on electrode surfaces have found numerous applications in sensing, 1 and recently, have also attracted interest in energy conversion [8][9][10][11][12] as well as in the electrosynthesis of small molecules. 13 While design and optimization is oen focused on the active components embedded within the lm, the geometry and dimensions of the redox-active matrix also play a central role in the resultant catalytic or photoactive properties. [14][15][16][17] For example, lm thickness can be modulated to maximize the overall performance with respect to electron transfer, mass transport and catalyst loading and thus exploit catalytic systems to their full potential. Recently, the properties and thickness of a redoxactive lm were engineered to provide protection to sensitive catalysts, 10,12,18 and may eventually serve to control reaction selectivity 19 by regulating the local supply of electrons and reactants. Theoretical models describing reaction/diffusion processes in these systems, 6,[15][16][17] as well as mechanisms for protection 12,14 with lm thickness as a major design parameter, are in place to enable the rational optimization of their catalytic properties.
The central role of lm thickness also means that the homogeneity of its distribution will likewise have a major impact on catalytic performance. For instance, a lm with a highly heterogeneous thickness is detrimental because it may include areas where mass transport limits the catalytic performance due to excessive thickness, while on other areas of the same electrode, the catalyst loading may be limiting due to insufficient thickness. Therefore, for the optimization of such lms, the homogeneity of the electroactive lm thickness must be known.
A variety of confocal or atomic force microscopy (AFM) methods exist to characterize lm morphology. 20 However, these methods are oen too complex for routine implementation or deliver only partial information. For instance, AFM is oen applied, but only yields the top roughness of the sampled fraction of the lm. Estimation of the thickness distribution is possible through prole measurements, but this requires partial lm removal as an additional destructive step. Moreover, essential information, such as the thickness distribution of the electroactive fraction of the lm, which is most relevant for electrocatalytic or light-induced charge transfer processes, remains inaccessible through AFM or confocal microscopy investigations.
Here, we propose a straightforward and non-destructive electroanalytical method, based on linear sweep voltammetry, that delivers the electroactive lm thickness distribution directly, and under the conditions relevant for the catalytic processes being optimized. Since the lms under consideration for these applications are intrinsically electron conducting, we can use the electron as a probe for quantifying the locations of the lm boundaries with respect to the electrode.
Within redox-active lms, electrons are transported by a hopping mechanism between the tethered redox moieties at a rate which is dened by the apparent diffusion coefficient of the electron 21 (D). For a given time scale (q) dened by the scan rate (n), the electron will travel a distance determined by the diffusion layer thickness (d) dened as d ¼ (Dq) 1/2 ¼ (DRT/nFn) 1/2 . The key feature of our method is that the current response related to the electron transfer within the lm depends on the relative dimension of d with respect to the lm thickness d (Fig. 1). In contrast to a smooth lm (Fig. 1A), the time scale window corresponding to d values that reaches the outermost lm boundaries is larger for rough lms (Fig. 1B). Accordingly, the current response for a rough lm deviates from the one obtained for a smooth lm ( Fig. 1C and D).
We exploit these deviations in peak currents obtained from linear sweep voltammograms to directly quantify the lm thickness distribution. We demonstrate that the arrangement of the surface features does not signicantly impact the accuracy of the thickness distribution determination when counterion transport is non-limiting. Major advantages of using this electrochemical method include (i) its simplicity, since only voltammetric measurements are required, (ii) its scope, since the thickness distribution is obtained for the entire lm in contrast to a limited sampled area, and (iii) its relevance to the intended electrocatalytic application, since it specically probes the electroactive fraction of the lm.

The model
Linear sweep voltammetry with normalized parameters and a characteristic plot For the case of planar diffusion in a perfectly smooth lm, 22 the theoretical position of the diffusion layer thickness (d) with respect to the lm thickness (d) can be expressed in terms of a dimensionless parameter (w 1/2 ) according to eqn (1). Since w 1/2 is proportional to n 1/2 , w 1/2 can be regarded as a normalization of the square root of the scan rate.
R is the gas constant, T is the temperature, F is the Faraday constant and n is the number of electrons exchanged. The peak current (i p ) obtained at a given scan rate is normalized according to eqn (2), and can be plotted against the dimensionless parameter (w 1/2 ), given by eqn (1), to prepare the characteristic plot for this system. . At the slowest scan rates, the diffusion layer goes beyond the outermost film boundary (d 3 ). (C) Corresponding LSVs (w avg 1/2 ¼ 10, 2 and 0.4) and (D) normalized peak current (i p ) plot, for a smooth film (solid line, shape factor ¼ 100), and for a rough film (blue circles, shape factor ¼ 2). The difference in current responses (Di p , shaded blue areas) at intermediate diffusion layer thicknesses, allows for determination of the underlying film thickness distribution.
A is the surface area of the electrode and C is the concentration of the redox-active species within the lm. Although there are several variables in these expressions, a plot of i p,n vs. w 1/2 can be regarded as essentially the normalization of an i p /n 1/2 vs. n 1/2 plot (Fig. 1D).

Weibull distribution for the parameterization of lm thickness variations
We use the Weibull distribution 23 for the parameterization of lm thickness distributions due to its ability to characterize lms with extremely high inhomogeneity. The Weibull distribution is usually given as a shape factor (SF) which directly correlates with the relative standard deviation of the lm thickness (see details in ESI Section S1 †). Low values of the shape factor correspond to high relative standard deviations. Therefore, low shape factors correspond to rough lms, and high shape factors correspond to smooth lms.

The deconstruction method for a planar electron diffusion reference
A straightforward approach for the prediction of the peak current for a rough lm is to "deconstruct" it into a series of independent and perfectly smooth lm sub-sections ( Fig. 2A).
The underlying assumption of planar (one-dimensional) electron transfer within each sub-section allows for the use of an algebraic equation for the peak current for a smooth lm (eqn (S3) †) for each of the sections, and then for the total current to be determined by taking the average. The theoretical electrochemical response of a perfectly smooth lm in an LSV experiment was previously solved analytically using the Laplace Transform technique, resulting in integral equations for the theoretical LSV current-potential curves. 22 This includes an algebraic expression for the peak current vs. w 1/2 (eqn (S2) †), with a stated accuracy of 0.5% when compared to the results obtained from the evaluation of the integral equations. An algebraic equation with tighter agreement was needed for this work. Therefore, an updated algebraic equation for peak current was obtained (see details in ESI Section S2 †).
The nite element method for the time and space dependent concentration proles The nite element method 24 (FEM), was used by means of the Matlab® Differential Equations Toolbox to account for edge effects and non-planar diffusion. In contrast to the deconstruction method, in which the lm is represented as a series of independent sections, the nite element method treats the entire lm as one complete piece. In this approach, the time and space-dependent concentration proles within the lm are determined by solution of a partial differential eqn (3), where the value for w 1/2 from the problem for smooth lms is replaced by w avg 1/2 according to eqn (4), because the characteristic lm thickness (d) is now the average lm thickness (d avg ): For each time point, the current was calculated by evaluating the concentration gradient at the electrode surface (C r is the concentration of the reduced form of the redox species within the lm) and integrating the result according to eqn (5), where (g lh ) is the geometric length to height ratio of the lm. The complete dimensionless formulation of the problem, as well as additional details regarding the nite element method implementation are included in ESI Sections S3 and S4. †

Results and discussion
Normalized peak current plots for lms of increasing inhomogeneity in their thickness Prediction of the peak current for a given experimental time scale was carried out with the deconstruction method ( Fig. 2A Fig. 1). The extent of the linear region depends on the shape factor, but within the linear region, the peak currents at high w avg 1/2 values are identical for all shape factor values. At high w avg 1/2 values, i p,n is independent of w avg 1/2 and also identical for all shape factor values. This plateau region corresponds to the time scale for which the electrons do not reach any of the boundary (d ( d, d 1 in Fig. 1). The transition between the linear and plateau regimes holds the information on the relative positions of the boundaries (d z d, d 2 in Fig. 1), i.e. the lm thickness distribution. The i p,n values deviate from the linear region sooner and reach the plateau later as the shape factor decreases because the rst boundaries are reached sooner and the last boundary is reached later as the lm inhomogeneity increases. This trend is clearly visible for lms with shape factors from 100 to 3.5 in Fig. 2B. The i p,n values also eventually reach the plateau for all other shape factors at high w avg 1/2 values.
The substantial changes observed in the transition region, where the diffusion layer passes through the roughness features of the lm, allow for the use of the i p,n vs. w avg 1/2 plot for deducing the lm thickness distribution based on experimental data. The thickness distribution can then be obtained from the shape factor of the theoretical i p,n vs. w avg 1/2 plot matching the experimental i p,n vs. w avg 1/2 plot. In order to make the shape factor determination more accurate, a correlation was constructed, using the dimensionless peak current value at a reference line at w avg 1/2 ¼ 2 (Fig. 2C). In addition, FEM was used to calculate the entire LSVs for visualization of the effect of the shape factor (Fig. 2D). Besides the peak current that decreases as the shape factor decreases, the shape of the entire LSV also changes when varying the shape factor when all other parameters are held constant.

Quantitative evaluation of hemispherical diffusion contributions
Although the calculation procedure afforded by the deconstruction method is especially fast and convenient for obtaining the normalized peak current variation as a function of normalized scan-rate (i p,n vs. w avg 1/2 plot), the accuracy of the resulting lm thickness distribution is bound to the assumption of planar electron diffusion through the lm. In order to quantitatively account for the contribution of hemispherical electron diffusion, the nite element method (FEM) was used for generating the concentration proles and gradients for a lm thickness distribution with a shape factor of 1.5 (Fig. 3). This shape factor was selected because the effects of hemispherical diffusion were greatest at this value, according to the comparison of deconstruction and FEM results for the entire range of Weibull distribution shape factors (see details in ESI Section S5.2 †).
The lm sub-sections were rstly arranged in an ascending order to reveal insights into the contour line curvature. For the case of planar electron transfer, the contour lines of the concentration prole would be entirely at throughout the lm. Instead, the concentration prole for the ordered arrangement ( Fig. 3A) revealed curvature, which can be attributed to contributions from hemispherical diffusion. This was conrmed by the non-planar direction of the electron ow depicted in the ow prole (Fig. 3B). Moreover, comparison of the concentration prole from an arrangement having a strong planar diffusional character (Fig. 3C) with the one from a highly disordered arrangement having strong hemispherical character (Fig. 3D) showed substantial differences in their curvatures. This qualitatively demonstrates that lm sub-section arrangements have an impact on the resulting electron-transfer within the lm. This implies that the various possible arrangements of the lm sub-sections for a single thickness distribution affect the resulting normalized peak currents from which the shape factor is extracted.
For a quantitative evaluation of the effect of lm sub-section arrangement on the resulting hemispherical diffusion, a set of 100 sub-sections for a lm with a shape factor of 1.5 was generated and shuffled randomly between two extreme congurations containing minimum and maximum disorder (Fig. 3E). The objective was to identify the minimum and maximum i p,n values obtained for a given shape factor as a function of the arrangement and, by extension, the minimum and maximum thickness distribution values related to these i p,n values. The normalized peak currents were calculated and plotted versus the normalized total perimeter, which was used as a general measure of lm sub-section disorder. The minimum i p,n value (0.320) was obtained from a cluster of values with a perimeter ratio of 2.6, while the maximum i p,n (0.334) was derived from a cluster of values with a perimeter ratio of 8.7. The minimum value, being closest to the deconstruction result (black dashed line in Fig. 3E), represents the lm conguration that corresponds to a condition of mostly planar diffusion, and the maximum value represents the lm conguration that corresponds to a maximum contribution from hemispherical diffusion.
Through these calculations, the impact of hemispherical diffusion on i p,n was quantied, allowing for the calculation of a correlation between i p,n and shape factor based on FEM results that includes lower and upper condence limits. For the calculation of these limits, one representative conguration from the minimum and maximum value clusters was identied ( Fig. 3C and D). Then, for each shape factor, the sampled subsections were rearranged according to these limiting congurations before calculation of the i p,n values by FEM, and the difference between this result and the deconstruction result (which was used as an internal standard that depends on planar diffusion only), was used to add lower and upper limits to the correlation (Fig. 3F). The average of the two results is reported as the center line. Probability distribution functions (PDFs) at the lower and upper limits at three points in the correlation (nominal shape factor ¼ 0.5, 1.5, and 7.0) were compared and did not look substantially different (see ESI Section S5.3 †). This means that although the lm sub-section arrangement impacts the peak current and thus the resulting lm thickness distribution value, it remains relatively minor.
While it is possible to determine the shape factor (and therefore the distribution) using only the value of i p,n at w avg 1/2 ¼ 2 (Fig. 3F), a peak current overlay plot similar to that of Fig. 2B, but which uses FEM and deconstruction was calculated (Fig. S9 †) to enable extraction of the shape factor using i p,n values at any w avg 1/2 values in the transition region. This is useful when the exact value of i p,n at w avg 1/2 ¼ 2 is not available experimentally (the exact value of the scan rate corresponding to w avg 1/2 ¼ 2 cannot be predicted beforehand since the value of d avg is typically unknown, see eqn (4). In Fig. S9, † deconstruction was used for shape factors below 0.75 and FEM was used for shape factors 0.75 and greater. This was possible because the average FEM values (when using deconstruction as an internal standard) were the same as the deconstruction values for shape factors below 0.75 (see ESI Fig. S8 and ESI Section S5.4 †). Physically, this means that the effects of hemispherical diffusion are negligible for shape factors below 0.75.

Experimental example and comparison with AFM
As an experimental example showing the usefulness of the electroanalytical approach, as well as its complementarity with AFM, both methods were applied for the characterization of redox-active lms assembled from viologen modied  Fig. S11. † For panels (A-E), the shape factor was 1.5. Counter-ion transport is assumed to be non-limiting.
macromolecules. We compare previously reported data 20 for smooth lms (Fig. 4) assembled from the drop-casting of viologen-modied dendrimers (Fig. 4A) as well as for rough lms (Fig. 5) made from the drop-casting of viologen-modied polymers (Fig. 5A). Optical microscopy of the smooth lm revealed surface homogeneity over a large area (Fig. 4B), which was conrmed by AFM on a smaller sampled area (Fig. 4C). The probability distribution function of the surface height (Fig. 4D) and roughness parameters were calculated using Gwyddion soware. 25 The average value of the surface height is 0.75 mm and the root mean square roughness is 0.20 mm. For electrochemical determination of the thickness distribution, the peak currents were extracted from both the anodic and cathodic scans of the cyclic voltammograms obtained for the same redox lm at various scan rates (Fig. 4E). The normalized dimensionless peak values obtained according to eqn (2), are plotted against the normalized scan-rates obtained according to eqn (4) (Fig. 4F). The experimental data are in close agreement with the theoretical i p,n vs. w avg 1/2 plot (black solid trace) expected for a perfectly homogenous lm. Using the i p,n value at w avg 1/2 ¼ 2, a Weibull distribution shape factor value of 14 was directly determined based on the correlation given in Fig. 3F and was used to generate the probability distribution function (see ESI Section S1.1 †) shown in Fig. 4G. The relative standard deviation for the thickness distribution of the electroactive fraction of the lm obtained directly from the shape factor (Fig. S1 †) was 9%.
In the case of this smooth lm, both of the limiting regions (the linear dependence at low scan rates and the plateau at high scan rates) are experimentally accessible (Fig. 4F). Information from the two limiting regions (the slope at low scan rates and the plateau value at high scan rates) were used for the determination of two combinations of variables (d avg /D 1/2 and CD 1/2 ) which can be used to convert the i p /n 1/2 vs. n 1/2 plot to the normalized plot of i p,n vs. w avg 1/2 (see ESI Section S6.1 †). This means that the peak currents from the voltammetric measurements alone directly enable the determination of the lm thickness distribution without the need to determine any of the individual parameters used for normalization of the peak current and of the scan rate. An additional benet of the independence of the lm thickness distribution from lm parameters such as D, d avg , and C is that the method is independent of the electrolyte composition which can impact the values of those same parameters. Knowledge of D, however, is useful for extracting the absolute lm thickness d avg from the electrochemical data according to a previously reported method 14 or more conveniently from the intersection of the extrapolated plateau and linear regions in Fig. 4F (see ESI Section S6.2 †). In the case of this particular lm based on redox-active dendrimers, the value of D was determined previously. 20 The resulting d avg value extracted from the electrochemical data is 1.2 mm, and was used to dimensionalize the probability distribution function of the lm thickness (Fig. 4G). To allow for a direct comparison with AFM surface measurements, the lm thickness distribution can be further converted to a dimensional surface distribution (see ESI Section S1.3 †). The resulting average surface height value (0.88 mm) and the root mean square roughness (0.10 mm) are in good agreement with the corresponding values obtained from AFM considering the different characterization conditions (dry vs. solvated state).
One additional parameter of interest is the resolution of the electrochemical method. This was determined by analyzing the variations of the electrochemistry derived lm thickness distributions (relative standard deviations). Aer preparation of a single smooth lm, a series of nine successive CVs (Fig. S10 †) were taken at a scan rate corresponding to w avg 1/2 ¼ 2 for this lm preparation (n ¼ 10 mV s À1 ). Data treatment for each CV was then performed separately, resulting in a series of nine individual shape factor determinations with their corresponding normalized RSD values. The standard deviation of these nine RSD values was found to be 1% (Table S1 †).
In the case of rough lms (Fig. 5) with very low shape factors, the two limiting regimes for the experimental i p,n vs. w avg 1/2 plot may not be accessible. This is illustrated with the example based on a lm fabricated through drop-casting of a viologen modied polymer. Both the optical (Fig. 5B) and AFM (Fig. 5C) images revealed the presence of large polymer aggregates. The probability distribution function of the height features on the surface was subsequently extracted using Gwyddion soware 25 (Fig. 5D). The average value of the surface height is 0.31 mm and the root mean square roughness is 0.17 mm.
The cyclic voltammetry measurements of this same lm (Fig. 5E) were used for extraction of the peak currents and for construction of the experimental i p,n vs. w avg 1/2 plot (Fig. 5F).
Both the linear region and the plateau were not accessible experimentally via the scan rate. Nevertheless, the transition region was sufficient for the determination of the lm thickness distribution because the normalization of i p,n and w avg 1/2 can be performed independently of these regions. In such a case, the values of D, d avg , and C which are needed for normalization must be determined individually from separate experiments. The value of D for lms made of the same redox polymer was determined previously 14 and was used to determine C. The value of d avg (7.32 mm) was obtained from C and the surface concentration in viologen according to a previously reported procedure. 14,20 The dimensionless normalized i p,n vs. w avg 1/2 plot (Fig. 5F) constructed based on D, d avg , and C values was used for extraction of the value of i p,n at w avg 1/2 ¼ 2, from which a Weibull distribution shape factor of 0.60 was directly determined, using the correlation given in Fig. 3F. The probability distribution function corresponding to the determined shape factor was then generated (Fig. 5G) as described in ESI Section S1.1. † The relative standard deviation for the lm thickness distribution obtained from the shape factor using the correlation in Fig. S1 † was 176%. To allow for a direct comparison with AFM results, as in the case of the dendrimer, the dimensional lm thickness distribution was generated (Fig. 5G) and then converted into a surface distribution (see ESI Section S1.3 †). The average surface height value (7.32 mm) and the root mean square roughness (12.87 mm) are substantially different from the corresponding values obtained from AFM. This discrepancy is attributed to the selection of a relatively smooth region for AFM imaging (orange frame in Fig. 5B) in comparison to the large aggregates in other regions of the same sample as observed in the optical image (Fig. 5B). This result highlights an important advantage of the electrochemical method in that it is naturally an ensemble method, whereby the entire surface is sampled as opposed to a small subsection. Although direct observation of the surface by AFM or optical methods is highly desirable, in particular, for its ability to show the sizes and spatial locations of aggregates, the results are highly dependent on the selection of the sampling area (typically only up to 100 mm Â 100 mm). Conversely, although the electrochemistry measurements are representative of the entire surface, the exact locations and geometries of the aggregates are not available. This emphasizes the complementary nature of the two methods and highlights the unique information derived from electrochemistry.
Moreover, the electrochemical method measures from the bottom of the lm at the electrode surface upwards through the lm. Therefore, it naturally probes the lm thickness distribution, in contrast to AFM which directly gives surface roughness information but requires scratching of the sample to access thickness information. Furthermore, while AFM can be performed on solvated samples or in the presence of electrolytes, so samples such as the hydrogel lms used in the present study can be particularly challenging to image. 26 The electrochemical method, in contrast, is intrinsically performed in the presence of the electrolyte, which correspond to the operational conditions for the applications of the lm. Therefore, optimization of the solvent composition and the evaluation of solvent effects is convenient when using the electrochemical method.
Although the method presented in this work is broadly applicable to redox-active lms, the limitations of the scope of this model should be noted. Firstly, the time scale of the electron transfer within the lm needs to be sufficiently slow so that the diffusional regime is accessible within the time scale of the linear sweep voltammetry experiment. In other words, diffusion layer thicknesses with dimensions in the range of the thicknesses of all lm sub-sections must be accessible via the scan rate (see eqn (1)). Generally, lms in which electrons are transported by diffusional or "electron-hopping" mechanisms are covered by this model. Secondly, the accuracy of the peak current analysis depends on the ease of subtraction of the baseline related to the capacitive current. In particular, possible interferences may arise from non-uniform capacitance (i.e. potential dependent capacitance at the underlying electrode) that would distort the cyclic voltammograms and therefore adversely affect the peak current analysis. Additionally, since the model assumes electrochemical reversibility for the electron transfer at the electrode/lm interface, peak currents from lms that have slow heterogeneous electron transfer rates cannot be analyzed with the current version of the model.
In general, the design requirements of redox active lms for electrocatalytic applications include high loading of the redox moiety (catalyst and/or electron relays) and fast charge transfer at the electrode interface, implying that the peak to baseline ratio is signicant and that the reversibility condition is usually fullled, which makes this method useful for the characterization of a broad range of modied electrodes. Moreover, the analysis of lms that display signicant and non-uniform capacitive current and/or slow heterogeneous charge transfer can in principle also become accessible by adapting the model to the analysis of the current response obtained by potential step voltammetry. This method would in principle also enable characterization of very thick lms that are not conveniently accessible in the time scale of linear sweep voltammetry.
Future development of the method may also take advantage of the counter ion transport associated with the electron transport, purposely making the former limiting to deliver the arrangement of the surface features of the lms, which is currently not accessible via the electrochemical method. As a nal note, pin-holes which do not enable any electron transport are not included in the scope of this work. In this case, methods are available which make use of rotating disk electrodes with variable rotation rates 27 or scanning electrochemical cell microscopy. 28

Conclusions
In this work, a novel electrochemical method based on linear sweep voltammetry was developed as a highly complementary method to AFM for the characterization of electroactive lms. By measuring the peak currents in a series of linear sweep voltammograms, going from low to high scan rate, the underlying lm thickness distribution in terms of the Weibull distribution shape factor can be determined from a plot of the normalized peak current vs. the experimental time scale. From the shape factor, the probability distribution function can be constructed as a quantitative description of the lm thickness distribution. As an "ensemble" method, it samples the complete surface and is therefore not sensitive to the location of the sampling area.
Furthermore, as an electrochemical method, it focuses on the electroactive portion of the lm on the electrode, which is of particular relevance to lms which are actively participating in redox or electro-catalytic processes. Finally, this information is provided in the solvated state which is relevant for the nal working conditions of the modied electrode. This is ultimately useful for the optimization of the performance of these lms, in which the lm thickness is a critical parameter, dening the catalytic or light-induced current output, and the fraction of catalyst effectively contributing to the reaction.

Materials and methods
Unless stated otherwise, all reagents used in experiment were purchased from Sigma-Aldrich. All the materials were directly used as received without further purication.

Film preparation
The preparation and characterization procedure for the redoxactive lms used to illustrate the application of the present method for determination of the thickness distribution was previously reported in detail. 20 We recall here the lm preparation corresponding to the specic data used in the present study: viologen modied dendrimer 18 (200 mg cm À2 ) was cast from a 2 mL droplet onto a gold electrode (2 mm diameter) with 0.5 mL Tris-buffer (0.1 M, pH 9.0), and allowed to dry in a closed container at room temperature under a water saturated atmosphere for 24 h. The electrode was then dried in the air for another hour. Viologen modied polymer 10 (200 mg cm À2 ) was cast from a 2.5 mL droplet onto a glassy carbon electrode (3 mm diameter), and dried using the same conditions as that of the dendrimer.

Electrochemical characterization
Cyclic voltammograms were performed in phosphate buffer (0.1 M, pH 7.2) under anaerobic conditions at room temperature using Gamry Potentiostats and an Autolab PGSTAT12 Bipotentiostat. A platinum wire and Ag/AgCl/3 M KCl were used as the counter and reference electrodes, respectively. Before preparation of the characteristic normalized peak current plot, interactions were accounted for using slow scan-rate LSVs, in which the experimentally determined peak currents were converted to their Langmuir equivalents (see details in ESI Section S7 †).

AFM characterization
The AFM measurements were conducted in the AC mode by NanoWizard 3 (JPK) with cantilever of the type NSC15 (MikroMasch).

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