noise phenomena caused by reversible adsorption in

KÄTELHÖN ET AL . VOL. 8 ’ NO. 5 ’ 4924–4930 ’ 2014

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April 02, 2014

C 2014 American Chemical Society

Noise Phenomena Caused byReversible Adsorption in NanoscaleElectrochemical DevicesEnno Katelhon,†,^ Kay J. Krause,† Klaus Mathwig,‡ Serge G. Lemay,‡ and Bernhard Wolfrum†,§,*

†Institute of Bioelectronics (PGI-8/ICS-8) and JARA;Fundamentals of Future Information Technology, Forschungszentrum Jülich, 52425 Jülich, Germany,‡MESAþ Institute for Nanotechnology, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands, and §Institute of Physics, RWTH Aachen University,52074 Aachen, Germany. ^Present address: Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road,Oxford OX1 3QZ, United Kingdom.

Adsorption phenomena may impactthe performance of electrochemicaldevices in multiple ways and play a

crucial role in the development of nano-scale sensors. Particularly, the reversible orpermanent adsorption of analyte moleculesat sensing electrodes turns out to be ofincreasing importance at small scales,where analyte transport toward the elec-trode is accelerated through sphericaldiffusion profiles. The same applies to ex-periments involving repeated analyte reac-tions in fast-scan voltammetry1,2 or redoxcycling. In the latter case, similar to nano-electrode experiments, the analyte masstransfer toward the electrode is enhanced,enabling significantly higher reaction ratesin diffusion-limited processes as well as anincreased impact of adsorption effects. Inredox cycling devices the ratio betweenelectrode surface and enclosed volume istypically very high (>107 m�1), representinga good system for the investigation of ad-sorption phenomena. Such devices can be

implemented in a variety of designs,3,4 butalways comprise two individually biasedelectrodes that are located in close proxi-mity to each other. Analyte molecules candiffuse between the electrodes and under-go repeated redox reactions, thus establish-ing a current across the gap. Due to theincreased mass transfer to the electrodes,this effect leads to a significant amplifica-tion of the Faradaic current and representsthe central advantage of this approach.Most reported experiments utilize the

redox cycling effect in two experimentalconfigurations, namely, scanning electro-chemical microscopes (SECMs) and inter-digitated electrodes (IDEs). In SECMs, anultramicroelectrode typically scans acrossa separately biased sample surface.5,6 Thisapproach is widely established todayand applied in a variety of different fieldsof research.7�10 IDEs, on the other hand,feature two comb-shaped electrodes thatare arranged in an interdigitated fashionon a substrate surface.11�14 Due to their

* Address correspondence [email protected].

Received for review February 17, 2014and accepted April 2, 2014.

Published online10.1021/nn500941g

ABSTRACT We theoretically investigate reversible adsorption in

electrochemical devices on a molecular level. To this end, a

computational framework is introduced, which is based on 3D

random walks including probabilities for adsorption and desorption

events at surfaces. We demonstrate that this approach can be used

to investigate adsorption phenomena in electrochemical sensors by

analyzing experimental noise spectra of a nanofluidic redox cycling

device. The evaluation of simulated and experimental results reveals

an upper limit for the average adsorption time of ferrocene

dimethanol of ∼200 μs. We apply our model to predict current noise spectra of further electrochemical experiments based on interdigitated arrays

and scanning electrochemical microscopy. Since the spectra strongly depend on the molecular adsorption characteristics of the detected analyte, we can

suggest key indicators of adsorption phenomena in noise spectroscopy depending on the geometric aspect of the experimental setup.

KEYWORDS: nanoelectrochemistry . noise spectroscopy . adsorption spectroscopy . redox cycling . nanofluidics

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comparably simple fabrication and easy lab-on-a-chipintegration, IDEs are now used in a wide range ofapplications.15�18 Other on-chip approaches includepore-based sensors19�24 that are formed through aninterpenetrated electrode stack. Additionally, preciselyoverlapping electrode faces can be implemented innanofluidic or nanocavity sensors by removing a sacri-ficial layer between two closely spaced electrodes.25,26

Such devices will be addressed first in this paper.Even though redox cycling sensors are widely used,

there are only a few publications that focus on theirnoise characteristics. Most of these studies investigatethe fluctuation of the Faradaic current or the stochasticsensing of single molecules in either SECM experi-ments27,28 or nanofluidic devices.29�31 In previousstudies we analyze the origin of different types of noisethat can be found in the current response of nano-fluidic sensors.32�34 Here, we expand recent work onthe simulation of noise phenomena34 by investigatingthe impact of molecular adsorption on the noisespectra of redox cycling sensors. We first show thatour simulation model reproduces theoretical expecta-tions in simple geometries. We then take a further stepand simulate the spectrum of a realistic nanofluidicelectrochemical sensor. We compare the experimentaldata with simulated spectra and find a close match ofthe results. The analysis yields an upper boundary forthe average adsorption times of redox-active mol-ecules. In the last part of this work, we apply our modelto more complex geometries that cannot be easilysolved analytically. We predict the noise spectra ofadsorbing interdigitated arrays as well as of an absorb-ing scanning electrochemical microscope tip near abiased conducting surface. Our simulations reveal newapplications in noise spectroscopy predicting discreteboundaries for observing adsorption times.

THEORY

In former studies, three origins of current noise havebeen described for nanofluidic redox cycling sensors.These are namely number fluctuation noise, adsorp-tion noise, and shot-like redox cycling noise. In thefollowing, we will shortly discuss their nature and setour adsorption model in relation to the current state ofresearch.

Number Fluctuation Noise. Number fluctuation noiseresults from active molecules that diffusively enter andleave the sensor. The change in number of moleculesinside the sensor then also leads to fluctuations in thenumber of molecules that participate in redox cyclingand causes a certain type of noise in the low-frequencyregime that can be described analytically.32,39 For thecase of adsorbing electrodes, an effective diffusionconstant (Deff) can be assumed inside the channel thatreduces the frequency of the fluctuation noise, whilepreserving the spectrum's shape.32,33 Deff can herebybe determined either from the variance of a current

trace or through a spectral analysis and turns out to bea convenient measure to determine the ratio betweenaverage adsorbed and desorbed times. This behaviorcan also be observed in our simulation approach. Dueto adsorption at electrodes, the diffusion constantalong the nanochannel is effectively lowered, sincemolecules reversibly adsorb after an average free timewhile diffusion is halted. The effective diffusion con-stant between the electrodes of a nanofluidic sensor isthen given by

Deff ¼ D1

1þ τaτd

(1)

where τd and τa represent the average time amoleculediffuses freely and spends adsorbed, respectively.32

However, the effective diffusion constant in our modelis not assumed to behomogeneous butmay vary insidethe nanochannel. It depends on whether the moleculeis enclosed between two electrodes, one electrode anda nonconducting surface, or two nonconducting sur-faces and the device geometry. Our model can there-fore be used for arbitrary designs without the need ofdefining area-specific diffusion constants.

Adsorption Noise. In contrast to fluctuation noise,adsorption noise impacts the number of moleculesparticipating in redox cycling through reversible ad-sorption at the electrodes. Analytically, this process canbe described through a two-state Markov process,32

in which molecules either participate in redox cyclingand contribute a certain current to the overall sensorcurrent or are adsorbed. In the case of an ideal nano-fluidic channel, this model is fully captured by oursimulation. Therefore, analytical findings can then bedirectly transferred to verify our simulation approach.

Shot-like Redox Cycling Noise. Shot-like redox cyclingnoise is caused by the Brownian motion of activemolecules in between the electrodes and dependssolely on the average number of free molecules insidethe sensor and the interelectrode distance in the caseof nonadsorbing electrodes.34 It features a white noisespectrum34 and is typically smaller than the formerlymentioned sources of noise in the low-frequencyregime.

RESULTS

Adsorption Noise. In order to first study adsorptionnoise isolated from number fluctuation noise, we startour investigations using a simple redox cycling systemthat solely consists of two infinite parallel electrodes,as shown in Figure 1a. Here the number of moleculesbetween the electrodes remains constant throughoutthe simulation. The resulting current is therefore af-fected only by adsorption noise and shot-like redoxcycling noise.

Figure 1b presents the simulated power spectraldensities in comparison to the analytical solution.

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In the case of adsorbing electrodes, graphs are calcu-lated for different average adsorption times τa whilethe ratio between adsorbed and desorbed moleculesremains constant. Spectra are further normalized to asingle free molecule present between the electrodes.For the adsorption-free case, we obtain the expectedwhite spectrum of shot-like redox cycling noise thatwas previously described.34 With an increase in τa,however, we find a growing plateau in the low-frequency regime that extends up to a transitionfrequency ftrans. This transition frequency decreaseswith an increase in τa. Above ftrans, there is a decreaseof the power spectral density according to 1/f 2 until asecond transition frequency, above which the spectraare again dominated by shot-like redox cycling noise.Overall, we find a close agreement between the simu-lated power spectra (after subtraction of the shot-likeredox cycling noise) and the analytical solution.

Modeling Nanofluidic Redox Cycling Sensors. To validatethe presented simulation model, we compare thesimulation results to experimental data. In a previousstudy,34 our simulation did not consider any adsorp-tion effects and we had to analytically compensatefor the impact of adsorption by processing the simula-tion data according to Singh et al.33 This required a

rescaling of the frequency axis to model the shift in theeffective diffusion constant. In contrast, we now de-monstrate that our simulation framework is capableof modeling the full sensor response solely based onadsorption modeled at the molecular level. This en-ables the application of our simulations to arbitrarydesigns and also allows modeling noise effects thatresult from molecular properties. The latter aspectfurther allows derivingmolecular properties fromnoisespectra, as we will show below.

For the experiments, we used the nanofluidic redoxcycling device specified in the Experimental Methods.Since the sensor exhibits symmetry with respect to thelongitudinal cross section, we model half of the deviceat doubled analyte concentration to increase compu-tational efficiency, as shown in Figure 2a.

Figure 2b presents simulated data for the case of noadsorption and compares it to experimental data. Wecan find that the spectra feature a similar shape thatresults from the geometry of the access channels ofthe device and the dead volume aside the channel,in which the electrodes do not overlap. However, thesimulated spectrum appears to be shifted to higherfrequencies. This result is in line with our expectations,since adsorption is not considered in the simulationand the lateral diffusion constant along the channeltherefore exceeds the effective diffusion constant thatis observed in the experiment.

In order to address this issue, we first calculate theratio between free and adsorbed molecules from theaverage current and the standard deviation of theexperimentally recorded trace.31 Hereby, we first com-pute the number of free molecules (nfree) betweenthe electrodes from the average redox cycling current(Irc)

23 and use this value to calculate the averagenumber of adsorbed molecules (nads) as follows:

31

nads ¼ ÆIrcæ2

I2rc, std� nfree (2)

The ratio between adsorbed and desorbed mol-ecules then equals the ratio between the averageadsorbed and desorbed times. Therefore we can cal-culate that the ratio τa/τd during the experiment was3.37,whereas the absolute values still remain unknown.Figure 2c shows the simulated spectra for differentaverage adsorption times, with the ratio betweenadsorbed and desorbed molecules inside the channelis set to the formerly determined experimental condi-tions. In the plot, we find that the transition frequency(ftrans) decreases with an increase in the average ad-sorption time (τa), while the height of the plateau thatspreads up to ftrans increases with τa. At an adsorptiontime of τa = 50 μs, the adsorption noise is dominated bythe fluctuation noise of the sensor and cannot be seenany more in the spectra below 150 Hz. In this case, thesimulated spectrum closely matches the experimental

Figure 1. Simulations basedon a parallel platemodel that isused to investigate the adsorption and shot-like redoxcycling noise separately from number fluctuation noise.(a) Illustration of the geometry. (b) Simulated power spec-tral densities in comparison to the analytical model. Differ-ent colors represent different average adsorption times.The power spectral density is normalized to a single freemolecule. The simulations assume a diffusion coefficient ofD = 10�9 m2/s. All further parameters can be found in theSupporting Material 1.

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data, which allows us to draw first conclusions regard-ing τa: since the adsorption plateau cannot be seen inthe experiment, we can find an upper limit for theadsorption time (τa

max) that is given at the adsorptiontime τa, at which the adsorption plateau first disap-pears within the bandwidth of the experimentallydetermined spectrum. The spectrum is then only af-fected through the impact of adsorption on the fluc-tuation noise. By this means, we find that the averageadsorption time in this experiment is smaller than200 μs.

Figure 2d presents the experimentally obtainedcurrent trace in comparison to a simulated trace thatuses a short average adsorption time of 50 μs. In theplot it can be seen that now both power spectra are inclose agreement.

Noise Spectra of SECM Experiments and IDAs. Havingshown that our simulation can reproduce experimentalmeasurements, we take a step further and apply ourmodel to other sensor designs. Since all effects areimplemented on the molecular level and no furtherpostprocessing of the simulated data is required, weare not limited to idealized systems but may predictnoise spectra of nanoscaled redox cycling sensors withalmost arbitrary geometry. For this work, we choose

two common designs: an interdigitated array anda scanning electrochemical microscope tip above aconducting surface; see Figure 3a and b. We find thatboth designs are particularly interesting for determina-tion of average adhesion times in the millisecondrange.

The noise spectra of a simulated IDE are given inFigure 3c, where differently colored graphs indicatedifferent average adsorption times. In contrast to thenanofluidic sensors discussed above, the spectra of theIDE do not exhibit any impact of adsorption above atransition frequency of 10 Hz. However, noise levels atlow frequencies significantly depend on the simulatedadsorption parameters. In the case of no adsorption,we find a flat plateau that spreads up to ∼40 Hz,but with increasing adsorption times, the noise below10 Hz increases with adsorption. Accordingly, thissection of the spectra can be used to determine theadsorption characteristics of molecules that typicallyadsorb longer than 10ms. The data below 10Hz herebyserve as a direct measure for the average residencetime, while the higher frequency components can beused as a calibration of the model.

We additionally simulated the adsorption noiseexpected in an SECM experiment, as shown in

Figure 2. Comparison between simulation and experiment. (a) Illustration of the simulated design. Attached to the accesschannel on the upper right, a cubic bulk reservoir is added to mimic a bulk reservoir. Dimensions are not to scale. (b)Comparison between experimental data and a simulation that does not consider adsorption effects. (c) Simulationsemploying different average adsorption times. The ratio between the average adsorbed and desorbed time is held constanttomatch the experimentally obtained value of 3.37. (d) Comparison between an experimentally obtained current trace and asimulated trace that features an average adsorption time below200 μs. The simulations are based on a diffusion coefficient ofD = 6.7 � 10�10 m2/s. Further simulation parameters are given in Supporting Material 1.

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Figure 3d. The spectra show an impact in a wideadsorption regime of average residence times be-tween 3 and 300 ms. In comparison to the spectra ofa nonadsorbing sensor, adsorption here induces anadditional plateau between 1 and 300 Hz that shiftsto higher frequencies and lower amplitudes with anincrease in average residence time. Similar to theabove specified spectroscopy method based on anIDE, one can utilize this plateau to identify the adsorp-tion characteristics of the analyte under investigation.Thus, we predict that adsorption phenomena on thistime scale should become apparent in SECM experi-ments and hope that in the future our simulations canbe confirmed experimentally by the SECM community.

CONCLUSIONS

In conclusion, we introduce a computationalframework for the modeling of adsorption effects in

nanoscaled electrochemical sensors. Adsorption ishereby implemented through a model based on fixedadsorption and desorption probabilities at electrodeswhile each analyte molecule is simulated individually.This approach elucidates the impact of specific molec-ular adsorption phenomena on the resulting sensorresponse. A distinct advantage over simplifying analy-tical concepts is further given by the applicability toalmost arbitrary designs. In this work, we first demon-strate that our simulations closely match experimen-tally obtained data sets and place quantitative limitson the analytes' adsorption properties. Having shownthis, we proceed and predict adsorption-dependentnoise spectra of IDEs and SECM tips.We further suggestcertain features in the noise spectra to be used as keyindicators in methods of adsorption spectroscopy. Weshare our simulation code with other researchers andlook forward to seeing it used for different applications.

METHODSSimulation Framework. We employ an approach that is based

on a previously described computational framework.34 In short,the Brownian motion of redox-active molecules is modeledthrough individual random walks, while molecular trajectoriesare reflected upon collisions with boundaries. Redox-activemolecules can further adopt two oxidation states and partici-pate in redox reactions whenever they come in contact withan appropriately biased electrode. In the simulation, analyte

molecules feature equal diffusion coefficients in both oxidationstates. Since we investigate noise in the low-frequency regime,different diffusion coefficients affect only the value of thecurrent obtained per molecule that is located between theelectrodes and do not impact the analyzed noise characteristics.A detailed study on the impact of unequal diffusion coefficientswas published previously.35

In this work, we expand this simulation by a model ofadsorption: in the employed random walk model, molecules

Figure 3. Simulations of other designs. (a and b) Illustrations of the simulated designs of an IDE and an SECM tip. Dimensionsare not to scale. (c) Simulated noise spectrumof an IDE for different adsorption times. (d) Simulated noise spectrumof a SECMprobe for different adsorption times. All spectra are normalized to a single free molecule. For the simulations, a diffusioncoefficient of D = 10�9 m2/s is assumed.

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can adsorb in collisions at electrode surfaces with a fixedprobability pa. Hence, a linear adsorption isotherm is assumed,for which the ratio of surface concentration and bulk concen-tration is always constant. A detailed analysis of the depen-dency of the adsorption of different redox species onexperimental conditions can be found in a previously publishedstudy.36 We discuss the exact meaning of pa below. In experi-ments, the mean free path of a diffusing molecule is muchsmaller than the maximal resolution employed computers canmodel in a reasonable time. Therefore, pa has to be consideredas the average molecular adsorption probability within thetemporal random walk step width dt, while the respectivemolecule is located in a cubic space at the electrode thatfeatures an edge length dx equaling the one-dimensional stepwidth of the random walk. The resulting adsorption rate ka istherefore a function of the random walk step width and pa.Since the random walk resolution is usually limited by thecomputational power of computers employed, pa can beadjusted to match realistic reaction rates. At a given step width,pa can then be calculated from the desired reaction rate ka as

ka ¼ pa2

dxdt

S pa ¼ 2kadtdx

(3)

The product kacbulkA then provides the rate of the absolutenumber of adsorbing molecules, where cbulk is the bulk con-centration of molecules and A the electrode surface. After eachtemporal step of the random walk, adsorbed molecules candesorb again with the probability pd. The distribution of themolecules' residence times then follows the geometrical dis-tribution: the probability of detachment after the nth step forn > 1 is given by pdetach(n) = (1� pd)

n�1pd. It features an averageresidence time τa of

τa ¼ dtpd

(4)

where dt represents the temporal step width of the randomwalk. This approach resembles the common model of anadsorbed molecule that oscillates due to its thermal energyand hits an energy barrier at the frequency of its oscillations.However, due to the available computing capacity, dt has to bechosen to be significantly higher. Therefore, pd represents thetotal desorption probability of all desorption attempts a mole-cule performs within dt, while the resulting desorption rate isagain linked to the random walk parameters. In order to derivethis reaction rate, we have to consider the discrete nature ofthe random walk, which does not allow surface concentrationsbut limits the analysis to volume concentrations. The volumeconcentration at the electrode surface therefore has to beconverted into a surface concentration by division throughdx. The rate of desorption is then given by

kd ¼ 1τd

¼ pddt

(5)

Here, the product kdcsurfaceA provides the rate of the absolutenumber of molecules being released, where csurface is the sur-face concentration.

In most redox cycling experiments, the average adsorptionand desorption times are unknown. However, if the employeddevice features two fully overlapping parallel electrodes thatare separated by the distance h, this ratio can be calculated fromthe currents' variance.33 For this reason, we also provide theratio of adsorption and desorption times as a function of thesimulation parameters. If we combine eqs 3 and 5, we obtain

τaτd

¼ papd

dxh

(6)

In all simulations, the lateral step width of the random walkis chosen significantly smaller than the smallest design features.The power spectral densities were calculated from the squareof the absolute value of the Fourier transform of the simulatedcurrent traces and averaged over 10 spectra.

Experimental Methods. Devices were fabricated as reportedpreviously.37,38 In short, Pt electrodes as well as a sacrificial Crlayer defining the nanochannel were consecutively deposited

on an oxidized silicon wafer by electron-beam evaporation andpatterned by photolithography and lift-off processes. After-ward, the structure was buried in Si3N4 and access channelswere dry-etched into this passivating layer. The nanochannelwas released directly before the experiment by wet etching thesacrificial layer (chromium etchant solution, Selectipur, BASF),and electrode surfaces were subsequently cleaned with 0.5 MH2SO4 (Sigma-Aldrich). The device features a nanofluidic chan-nel of 10 μm length, 5 μmwidth, and 60 nm height. The channelhas access to the bulk reservoir via two 2 � 4 μm2 wide accesschannels in the passivation layer. The electrodes inside thenanochannel overlap in an area of 30 μm2.

In the measurement, the nanofluidic device was connectedto a reservoir enclosed in polydimethylsiloxane. The reservoirwas filled with the analyte solution, in which a Ag/AgCl refer-ence electrode was immersed. Both top and bottom electrodeswere connected to LabVIEW-controlled Femto DDPCA-300transimpedance amplifiers used as current meters as well asvoltage sources operating at potentials of 450 and 50mV for thetop and bottom electrode, respectively. The analyte, 1,1-ferro-cene dimethanol, Fc(MeOH)2, was acquired from Sigma-Aldrichand prepared in a 20 μM solution in Milli-Q water using 1 M KCl(Sigma-Aldrich) as background electrolyte. Ten-second-longcurrent�time traces were recorded at a 150 Hz bandwidthand a 1000 Hz acquisition rate.

Conflict of Interest: The authors declare no competingfinancial interest.

Acknowledgment. We gratefully acknowledge funding bythe Helmholtz Young Investigators Program, The NetherlandsOrganization for Scientific Research (NWO), and EuropeanResearch Council (ERC).

Supporting Information Available: Detailed parameters of allsimulations (Supporting Material 1). Simulation source codeincluding installation instructions (Supporting Material 2a�f).This material is available free of charge via the Internet at http://pubs.acs.org.

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ARTIC

LE

NoisePhenomenaCausedbyReversible

AdsorptioninNanoscaleElectrochemical

Devices

Enno Kätelhön, Kay J. Krause, Klaus Mathwig, Serge G. Lemay, and Bernhard Wolfrum

Supporting Material 1

Detailed parameter tables for all simulations.

• Figure 1b

Number of active molecules 250

Spatial step width 5 nm

Diffusion constant 10-9

m2/s

Temporal step width 12.5 ns

Number of iterations 16*108

Simulated time interval 20 s

Sum over iterations 800

Sampling frequency 100 kHz

Ratio between the average adsorbed and desorbed time 20

Number of traces averaged 6

• Figure 2b



Diffusion constant 6.7*10-10

m2/s


Number of iterations 107.2*108





• Figure 2c/d



Diffusion constant 6.7*10-10

m2/s






Ratio between the average adsorbed and desorbed time 3.37


• Figure 3c




m2/s

Temporal step width 50 ns

Number of iterations 12*108



Sampling frequency 33.3 kHz



• Figure 3d




m2/s

Temporal step width 1.25 s







noise phenomena caused by reversible adsorption in

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