Quantitative Analysis of Cyclic Voltammetry of Redox ......Mathematical models that are available for the analysis of cyclic voltammetry fall short of capturing all factors at play

Quantitative Analysis of Cyclic Voltammetry of Redox MonolayersAdsorbed on Semiconductors: Isolating Electrode Kinetics, LateralInteractions, and Diode CurrentsYan B. Vogel,† Angela Molina,‡ Joaquin Gonzalez,*,‡ and Simone Ciampi*,†

†Curtin Institute of Functional Molecules and Interfaces, Curtin University, Bentley, Western Australia 6102, Australia‡Departamento de Quimica Fisica, Universidad de Murcia, Murcia 30003, Spain

*S Supporting Information

ABSTRACT: The design of devices whose functions span fromsensing their environments to converting light into electricity orguiding chemical reactivity at surfaces often hinges around acorrect and complete understanding of the factors at play whencharges are transferred across an electrified solid−liquid interface.For semiconductor electrodes in particular, published values forcharge-transfer kinetic constants are scattered. Furthermore,received wisdom suggests slower charge-transfer kinetics forsemiconductors than for metal electrodes. We have used cyclicvoltammetry of ferrocene-modified silicon photoanodes andphotocathodes as the experimental model system and described asystematic analysis to separate charge-transfer kinetics from diodeeffects and interactions between adsorbed species. Our resultssuggest that literature values of charge-transfer kinetic constants at semiconductor electrodes are likely to be underestimates oftheir actual values. This is revealed by experiments and analytical models showing that the description of the potentialdistribution across the semiconductor−monolayer−electrolyte interface has been largely oversimplified.

Materials that can turn from conductors to insulators arethe basis of our digital technology. From the discoveryof electrical rectification in galena in 1874,1 to top-end silicon-based desktop chips,2 one would be hard-pressed to point to atechnologically relevant material that is not a semiconductor.Where there is the need to gain insights on the “speed” of a

charge-transfer reaction at a semiconductor−liquid interface interms of energy conversion,3,4 chemical catalysis,5 or sensingresearch,6,7 scientists and engineers require an analytical toolfor the kinetic measurement.8 Cyclic voltammetry is by far themost frequently used technique for such studies; it combinesprecise and simple control of potential (i.e., thermodynamicsof the reaction) with a sensitive measurement of current (i.e.,kinetics of the process). Then, to translate experimentalnumbers into quantitative insights, any given electrochemicalmeasurement needs coupling to a theoretical model.Mathematical models that are available for the analysis of

cyclic voltammetry fall short of capturing all factors at play atthe electrified interface: published kinetic data for semi-conductors is highly scattered.9 We believe a contributor tothis problem is the naiv̈e character of the available models forkinetics. Kinetic values reported in the literature for semi-conductor electrodes are usually obtained by analyzing cyclic-voltammetry data through models that are strictly valid onlyfor metal−liquid interfaces.10,11 These models are usedassuming that under strong illumination, a semiconductorbehaves like a metal. Such an assumption is, in most cases, not

valid. Even under strong illumination, the electric field insidethe semiconductor space charge cannot be completelyeliminated. Lewis and co-workers have pioneered a theoreticaldescription of voltammetric curves for redox moleculestethered on semiconductors that accounted for space-charge(i.e., diode) effects for the limiting case of reversible electron-transfer kinetics.12 In other words, Lewis and co-workersdescribed the effects of the semiconductor diode on the shapeand position of the voltammetric curve, but their analysis didnot allow to access kinetic parameters.12 In real systems, besideapparent diode effects that clearly need to be accounted for,the speed of the electron-transfer reaction has a finite value.Further, in real systems, the current−potential relationship isoften complicated by intermolecular and molecule−space-charge interactions.13−16 We have recently developed ananalytical model to interpret cyclic voltammograms byaccounting for the semiconducting nature of the electrode, inparticular for its electrostatic landscape. We showed thatnonidealities, namely, full width at half-maximum

interactions between molecular charges of a tethered redoxprobe and the semiconductor space charge.15

All this suggests that commonly used models are over-simplified. Particularly, metallic models often suggest electron-transfer kinetics at semiconductor electrodes being slower thanat metallic electrodes.9 The slower kinetics has beenhypothesized as being linked to poor coupling between energylevels in the electrode and attached molecules, a low density ofstates, and differences in the molecular packing.9 In the presentwork, we argue that the slower kinetics reported forsemiconducting electrodes is in some cases only apparent,and that it might be just a consequence of using models thatcannot distinguish between electron-transfer kinetics andsemiconductor-related effects in the electrochemical response.We describe a model that simulates current−potential traces ofcyclic voltammograms for electroactive species adsorbed onsemiconductor electrodes, allowing us to retrieve kinetic anddiode parameters from the fitting of experimental data. Thismodel also allows accounting for (i) changes in photocurrents(i.e., open-circuit values) between forward and backwardsweeps and (ii) attractive and repulsive intermolecular forcessensed by the monolayer. By using this model, we haveobtained quantitative insights on the kinetics of a ferrocenemonolayer tethered on amorphous silicon photoanodes andphotocathodes.

■ EXPERIMENTAL SECTIONElectrode modification followed a previously reportedprocedure (details in the Supporting Information).15 Cyclic

voltammograms of ferrocene-modified silicon electrodes wererecorded with a CHI650E potentiostat (CH Instruments)using a three-electrode, single-compartment PTFE cell fittedwith Ag/AgCl (saturated KCl) as the reference electrode and aplatinum mesh as the counter electrode. All potentials arereported versus the reference electrode. Ohmic contact to themodified silicon electrode was ensured by using emery paperto grind a thin layer of indium−gallium eutectic on its backsideand then pressing it against a copper plate. A rectilinear cross-section gasket defined the active area of the working electrodeto be 0.28 cm2. An aqueous solution of perchloric acid (1.0 M)was used as the electrolyte. Light was shined from theelectrolyte side using a red LED (M625L3 source coupled to aSM1P25-A collimator adapter, Thorlabs). The light intensitywas regulated through the LED driver (LEDD1B, Thorlabs)and measured with a light meter (LM-200LED, Amprobe).Models and simulations of experimental data were written andperformed in GFortran and Mathcad 14.

■ RESULTS AND DISCUSSIONDevelopment of the Analytical Model. The voltam-

metric model described below is applicable to electroactivespecies attached on a semiconductor electrode and with finiteelectron-transfer kinetics. The electrified semiconductor−monolayer−electrolyte interface is modeled as two polarizableinterfaces that are arranged in series: a photodiode in serieswith an ideal metal electrode with surface-attached redoxspecies that follow Butler−Volmer kinetics (see Figure 1a). Akey feature of the model is that it accounts for the balance of

Figure 1. Theoretical landscape and simulated electrochemical responses for the limiting case of reversible kinetics without electrostaticinteractions for a photoanode. (a) Representation of the potential drop across the space-charge layer (SCL), Helmoltz layer (HL), and double layer(DL). In the model, the potential drop across the SCL behaves as an ideal diode. (b) Shape of the voltammetric curves as a function of θ assuminginfinite electron-transfer kinetics and neglecting molecular interactions. For curves a−e, the values of θ are 7.8 × 10−3, 7.8 × 10−2, 0.156, 0.389, and0.519. (c) Peak-position dependence on the open-circuit potential, which is a function of the I0/(I0 + IL) ratio (see eq 7). I0 is 10

−9 A, v is 0.1 V/s,Q is 8 × 10−6 C, and IL drops progressively from curve a to curve d (1, 0.1, 0.01, and 0.001 A, respectively). For all the curves, θ < 10−2, whichresults in no changes to the curve shapes. (d) Effect of changes to the interaction parameter on values of θ for a Nernstian charge transfer. Repulsivemolecular interactions (negative G) lower θ, and attractive interactions (positive G) increase θ. The sweep rate is 0.1 V/s, Q is 8 × 10−6 C, IL is 1μA, and I0 is 1 × 10−11 A.

Analytical Chemistry Article

DOI: 10.1021/acs.analchem.9b00336Anal. Chem. XXXX, XXX, XXX−XXX

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intermolecular attractive and repulsive forces (which are oftenevident in the experiments14,15,17), with the thermodynamicsof these interactions introduced through the Frumkinisotherm, as well as for dynamic changes in diode parametersfrom the forward to the backward scan.The potential, E, is applied between the ohmic back contact

made to the semiconductor electrode and the referenceelectrode. E is distributed between the space-charge layer, Ed,and the monolayer−electrolyte interface, Ee:

= +E E Ed e (1)

and the current passing through the two interfaces is identical:

= =I I Id e (2)

In order to describe the current−potential (I−E) relation-ship for this system (Figure 1a), we need to know the I−Eexpressions for each independent element (i.e., the seriesarrangement of a photodiode and the monolayer−electrolyteinterface). These two elements are described for photoanodesand photocathodes (i.e., monolayer systems tethered on n- andp-type substrates, respectively) by the following.For the first element of the circuit we can use the ideal-diode

equation for the photodiode steady-state I−E relationship,which is given by

photoanode

= + − −I I InFERTD

1 expd L 0d

Ä

Ç

ÅÅÅÅÅÅÅÅÅikjjj

y{zzzÉ

Ö

ÑÑÑÑÑÑÑÑÑ (3)photocathode

= + −I I InFERTD

exp 1d L 0d

Ä

Ç

ÅÅÅÅÅÅÅÅÅikjjj

y{zzz

É

Ö

ÑÑÑÑÑÑÑÑÑ (4)where IL and I0 are the photogenerated current and thereverse-saturation diode current, respectively, and D is thediode ideality factor, which typically varies from 1 to 2. IL islogically related to the intensity of irradiated light. We couldassume that this relationship is linear18 through a factor f I; thatis, IL,net = f IIL with 0 < f I < 1, where the lower limit, zero,corresponds to no illumination, and the upper limit, unity,corresponds to “full” illumination.Equations 3 and 4 can be rearranged as

photoanode

+= − − −

II I

nFRTD

E E1 exp ( )dL 0

e OC

Ä

ÇÅÅÅÅÅÅÅÅ

É

ÖÑÑÑÑÑÑÑÑ (5)

photocathode

− += − −

II I

nFRTD

E Eexp ( ) 1dL 0

e OC

Ä

ÇÅÅÅÅÅÅÅÅ

É

ÖÑÑÑÑÑÑÑÑ (6)

where EOC is the open-circuit potential given by

photoanode

=+

EDRT

nFI

I IlnOC

0

L 0

ikjjjjj

y{zzzzz (7)

photocathode

=| | +

EDRT

nFI I

IlnOC

L 0

0

ikjjjjj

y{zzzzz (8)

The second element of the circuit is equivalent to a redoxcouple attached onto a metallic electrode. The I−E relation-ship for a cyclic-voltammetry experiment when interactions ofthe attached redox species (in the oxidized, O, and reduced, R,forms) are not negligible was developed by Laviron assuming aFrumkin isotherm:10,11

=

− −

η − − − +

− − + −

InQ

k f

f

1e e

(1 )e

F

y G f G s

y s f G s

red R( ) ( )

R( ) ( )

e R

R

ÄÇÅÅÅÅÅÅ

ÉÖÑÑÑÑÑÑ (9)

where

= + +G a a ao r or (10)

= −s a ar o (11)

= +y a ao r (12)

where ao, ar, and aor are interaction coefficients expressing therepulsive O−O interactions, the repulsive R−R interactions,and the attractive O−R interactions, respectively. G describesthe overall interaction, s describes the difference between theO−O and R−R interactions, and y describes the overallinteraction magnitude. The total amount of charge transferred(in coulombs) is QF, and ηe is defined as

η = − ′nFRT

E E( )e e0

(13)

with E0′ being the formal potential of the process. Consideringthe Butler−Volmer kinetic approach, kred is given by

= αη−k k ered et e (14)

with ket and α being the conditional rate constant (the value ofthe rate constant for electro-reduction or electro-oxidation at E= E0′) and the charge-transfer coefficient, respectively.Equation 9 can be rearranged as

= [ − −αη η− − −InQ

k f fe e e e (1 )eF

sf G f Gfet,ap R

(1 )R

e,ap R e,ap R RÉÖÑÑÑÑÑÑ(15)

where

η

= =

= −

= +

− − −

′

′ ′

k k k

nFRT

E E

E ERTnF

s

e e

( )

s y s G aet,ap et et

2

e,ap e ap0

ap0 0

or|

}

oooooooooo

~

oooooooooo (16)ket,ap is an apparent rate constant, and its value changesdepending in the values of the interaction parameters.The current in terms of the variation of f R (i.e., the changes

to the surface coverage of the species R) can be written as

= −InQ

vf

E

d

dF

R

e (17)

where v is the scan rate.Equation 9 can then be rewritten in a dimensionless way as

follows:



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http://dx.doi.org/10.1021/acs.analchem.9b00336

ψ

η

=

= − −

= − ̅ − −η− −

II

Gf

G k f f

(4 2 )d

d

(4 2 ) e ( e e (1 )e )sf G f Gf

p,rev

R

red,ap R(1 )

RR e,ap R R

(18)

with

= ±−

IH G1 1

4 2p,rev (19)

=H RTn Fv Q

1

F2

(20)

̅ = ̅ αη−k k ered,ap et,ap e,ap (21)

̅ =kk

nFv RT( )/( )et,apet,ap

(22)

Note that Ip,rev given by eq 19 corresponds to the peakpotential of a monolayer at a metallic electrode underNernstian conditions (i.e., for a very fast redox conversion ofthe electroactive couple). It will be used as a reference value.With eqs 7, 8, and 18, we have the equations necessary to

obtain the current−potential expressions for photoanodes andphotocathodes:

photoanode

θ= − − −

II

nFDRT

E E1

1 exp ( )dp,rev

d OC

lmono

Ä

ÇÅÅÅÅÅÅÅÅ

É

ÖÑÑÑÑÑÑÑÑ|}o~o (23)

photocathode

θ= − −

II

nFDRT

E E1

exp ( ) 1dp,rev

d OC

lmono

Ä

ÇÅÅÅÅÅÅÅÅ

É

ÖÑÑÑÑÑÑÑÑ

|}o~o (24)

with θ defined as

θ =| | +

I

I Ip,rev

L 0 (25)

In order to solve eq 18, the values of at least one of the twopotential drops, Ee or Ed, have to be determined to calculate ψ.We can, for example, work on Ed, which can be obtained fromeq 23 or 24:

photoanode

θψ= − −E E DRTnF

ln(1 )d OC (26)

photocathode

θψ= + +E E DRTnF

ln(1 )d OC (27)

by taking into account that

− = − −′ ′E E E E Ee ap0

ap0

d (28)

From eqs 26−28, we can write the following:photoanode

θψ= −η ηe e (1 )De eff (29)

photocathode

θψ=

+η

ηe

e(1 )D

eeff

(30)

where

η = − −′nFRT

E E E( )eff ap0

OC (31)

By inserting eq 29 or 30 into eq 18, two differentialequations are obtained:

photoanode

ηθψ

θψ

− = ̅ −

× − − −

αη α

η

− − −

−

fk

f f

d

de (1 ) e

( e e (1 ) (1 )e )

D sf

G f D Gf

Ret,ap

R(1 )

R

eff R

R eff R

(32)

photocathode

η θψ

θψ

− = ̅+

×+

− −

αη

α

η

−

−−

−

fk

ff

d

de

(1 )e

e e

(1 )(1 )e

Dsf

G f

DGf

Ret,ap

R(1 )

R

effR

R eff

R

lmooonooo

|}ooo~ooo (33)

Equations 32 and 33 have no algebraic solution and have tobe solved numerically. This can be done by using the Eulermethod for the determination of ψ, for which the derivate in eq18 can be changed to

ψη η η−

= ≈ΔΔ

=−

Δ−

G

f f f f

4 2

d

di iR R R, R, 1

(34)

where the subscript i indicates the potential being considered.By inserting eq 34 into eqs 32 and 33, an algebraic implicitequation is obtained that can be solved by iteration.

Quantitative Analysis of an Experimental Model. Thepotential applied across the semiconductor−molecular mono-layer−electrolyte interface is distributed between two polar-izable interfaces: the semiconductor space-charge layer and themolecular monolayer−electrolyte interface. These interfacescan be described by two electrical elements in series: a diodethat follows the Shockley relationship (eqs 3 and 4) and amolecular monolayer of an attached redox molecule withelectron-transfer kinetics following Laviron’s formalism (eq15). This is schematically depicted in Figure 1a for aphotoanode. The semiconductor potential drop is only afunction of the ratio θ = Ip,rev/(I0 + IL), where Ip,rev is the peakcurrent for a Nernstian process, IL is the photocurrent, and I0 isthe reverse saturation current of a diode. Figure 1b showssimulated cyclic voltammograms for different values of θ in thecase of a redox couple under infinitely fast kinetics. The currentaxis in the simulated voltammograms have been normalized tothe dimensionless current ψ (eq 18) and the abscissarepresents the voltage, E, relative to the redox formal potential,E0′, corrected for the open-circuit potential, EOC (i.e., E − E0′− EOC). For θ values lower than ca. 10−2, the shapes of thecurves appear identical to those for metal electrodes. It isevident from Figure 1b (photoanode) that the anodic peak ismore sensitive to changes in θ than the cathodic peak. For aphotocathode, the situation is reversed: the cathodic peak ismost sensitive to changes in θ. The peak position is defined by



D


EOC, which is a logarithmic function of the I0/(I0 + IL) ratio, asshown in eq 7. Figure 1c shows changes in the peak position asa consequence of changes in the open-circuit potential (i.e.,changes in the I0/(I0 + IL) ratio) when θ < 10

−2, that is, whenthe shapes of the voltammograms on semiconductors are likethose on metallic electrodes.As discussed above, θ affects the shape of the cyclic

voltammogram (for θ > 10−2), and EOC affects its position, andthey are ultimately functions of three parameters: Ip,rev, I0, andIL. Ip,rev is the peak intensity for a Nernstian process whendiode effects are not present and is a function of the scan rate;increasing the scan rate increases Ip,rev, as is shown in eqs 17and 18. The magnitude of Ip,rev also depends on theinteractions (either repulsive or attractive) experienced bythe tethered redox centers through the Frumkin isotherm andits parameter, G: repulsive interactions will decrease themagnitude of Ip,rev, and attractive interactions will increase it(eqs 17 and 18). Figure 1d plots the dependence of diodeparameter, θ, on the interaction parameter, G, and shows thatdiode effects are more evident as interactions move in favor ofattractions (positive G). I0 is the current under dark conditionsand is characteristic for a given system at constant temper-ature; for higher I0 values, the more the system becomes“metallic”. The photocurrent, IL, is linearly and directlydependent on the light intensity18,19 and diode effects; thatis, effects that make the system become less metallic are morerelevant at low IL values (i.e., under low light intensity; see eq23). As θ depends on Ip,rev, IL, and I0 (see eq 25), the practicalchallenge resides in determining them separately. Ip,rev can bedetermined in the Nernstian limiting behavior from eqs 17 and18 once G is known (G can be determined independently atlow scan rates, vide infra). I0 has a given value for the system atconstant temperature and can be calculated from the currentunder dark conditions. Once Ip,rev and I0 are known, IL can becalculated from θ using eq 23. The shape of the voltammogramis affected by changes in θ, as shown by the curves in Figure1b. Figure 2 summarizes the effects of changes in θ on the

characteristic features of the current−potential curves fordifferent values of G and under infinite kinetics. Namely,Figure 2 shows the effect of θ on peak potentials (Ep, Figure2a), peak separation (Ep,a−Ep,c, Figure 2b), peak currents (Ip,as denoted in general from now on, Figure 2c), and values offull width at half-maximum (fwhm, Figure 2d). As discussedabove, for a photoanode, the anodic peak is affected more thanthe cathodic peak (and the opposite for a photocathode). It isnoteworthy that an increase in θ splits the positions of theanodic peak with respect to the cathodic peak (Figure 2b).This type of peak-to-peak separation is therefore purely asemiconductor effect, as it can be completely associated withchanges in θ and is not related to electron-transfer kinetics.This is in contrast with monolayers attached on metallicelectrodes, where the magnitude of peak separation is anindication of the electron-transfer kinetics and from which thekinetic constant ket,ap is estimated.

10 The immediate con-sequence of the peak separation when observed in semi-conductor electrodes is that it will be wrongly attributed to akinetic effect and interpreted as slow electron transfer. Webelieve this is a commonly encountered error in the literature,which in most cases reports slower kinetic values forsemiconducting systems.9 We argue that the slower kineticsreported for semiconductors, compared against metals, mightbe at least in part a misconception. Voltammetric waves insemiconductors can be separated because of the diodecharacter of the electrode and not because of a low value ofket,ap. For an accurate kinetic analysis of a diffusionless redoxprocess at a semiconductor−liquid interface, it is therefore veryimportant to be able to separate kinetic from diode effects. It isalso key to note that the self-interaction parameter, G, affectsnot only Ip and fwhm (Figure 2c,d), as expected for a metalelectrode, but also has an influence on the peak-to-peakseparation (Figure 2b).Figure 3 shows two voltammetric waves simulated under

finite kinetics and in absence of interactions (G = 0) using themodel developed in the previous section. Both voltammetric

Figure 2. Dependence of the diode parameter, θ, on the voltammogram shape for different G values under infinite kinetics for a photoanode.Voltammogram shapes as defined by (a) peak potential, (b) peak separation, (c) peak current, and (d) fwhm. The solid and dashed lines are for theanodic and cathodic waves, respectively, and the different colors are for different G values (magenta: G = −1, blue: G = −0.5, green: G = 0, red: G =0.5, and black: G = 1). I0 is set to 10

−6 μA, and IL is 10 μA.



E


curves show equal electron-transfer kinetics (ket,ap = 1.0 s−1),

but one takes into account the semiconductor nature of theelectrode (dotted line), whereas the other does not (solidline). It is clear that part of the peak separation in thevoltammograms in Figure 3 (dotted line) is due to the diodenature of the electrode and not to its electron-transfer kinetics.If ket,ap is calculated (dotted line) using the Laviron model for ametal electrode,10 the obtained value (ket,ap = 0.2 s

−1) is 1order of magnitude lower than the actual one (ket,ap = 1.0 s

−1).From this theoretical example, it can be concluded that correctkinetic analysis of redox couples tethered at a semiconductor−

liquid interface requires considering the diodelike nature of theelectrode.Figure 4 shows the influence of k̅et,ap on the peak parameters

(Ep, ΔEp, Ip, and fwhm) at different values of θ and in theabsence of interactions (G = 0). Figure S1 (SupportingInformation) shows this plot for different values of G. Theseplots can be used to get a rough estimation of k̅et,ap; however, acomplete simulation analysis is recommended because of thecomplexity of the process (i.e., the presence of interdependentfactors such as kinetics, interactions, and diode effects). As canbe seen in Figure 4, there are three clear regions correspondingto very fast (Nernstian, log k̅et,ap ≥ 1), quasireversible (−1.5 ≤log k̅et,ap < 1), and fully irreversible (log k̅et,ap < − 1.5) charge-transfer reactions. Moreover, in the absence of interactioneffects on the voltammograms, the evolution of the peakparameters with k̅et,ap is qualitatively the same, regardless of thevalue of θ. As stated above, in the Nernstian region, an increaseof θ leads to a decrease in the anodic peak current much moremarked than that observed for the cathodic one (the oppositeis true for a photocathode).For the above-mentioned example not to remain a

theoretical exercise, we developed an experimental model byattaching a ferrocene monolayer on an amorphous siliconsemiconductor electrode by a previously reported method20

(see the scheme in Figure 5a). The amorphous silicon wasdeposited on either n-type or p-type crystalline silicon. Thedoping type of the crystalline substrate determines thephotoanode (n-type) or photocathode (p-type) behavior ofthe electrode. In practice, the challenge when interpretingcyclic-voltammetric curves remains in distinguishing andisolating kinetic effects, defined by ket,ap, from semiconductoreffects, defined by θ, and electrostatic interactions, defined by

Figure 3. Semiconductor versus metallic electrode under the samekinetics. Simulated cyclic-voltammetry curves for a metallic electrode(solid line) and for an n-type semiconductor electrode in the presenceof diode effects (dotted line, θ = 0.7). The sweep rate is 0.1 V/s, α is0.5, and ket,ap is set to 1 s

−1.

Figure 4. Effect of changes to the electron-transfer kinetics, k̅et,ap, on the voltammogram shape in the presence of diode effects, θ (photoanode), andin the absence of lateral interactions. (a) Ep vs k̅et,ap. (b) ΔEp vs k̅et,ap. (c) Ip vs k̅et,ap. (d) fwhm vs k̅et,ap. The values of θ for the different curves are 7.8× 10−3 (black lines), 7.8 × 10−2 (red lines), 0.156 (green lines), 0.389 (blue lines), and 0.519 (pink lines). The sweep rate is 100 mV s−1, α is 0.5,and G = s = 0. Solid lines correspond to the direct scan (anodic scan), and dashed lines correspond to the reverse (cathodic scan).



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G. Bringing changes to θ without affecting ket,ap would allowdecoupling one effect from the other. From the parametersthat affect θ, IL can be easily and predictably changed bychanging the intensity of the light on the semiconductor.Moreover, IL in theory is not dependent on ket,ap (see theprevious section) and is linearly dependent on the light

intensity18,21 (Figure S2, Supporting Information). Therefore,the light intensity can be assumed to not affect the electron-transfer kinetics in the system here studied, and then θ can beadjusted by studying the voltammograms at different lightintensities. Figure 5b shows cyclic voltammograms taken atdifferent light intensities (solid lines) and their fittings (dots).Table S1 (Supporting Information) resumes the parametersused for these fittings. Once the semiconductor θ parameter isknown, the electron-transfer rate constant, ket,ap, can beobtained by studying the influence of the voltammetric curveswith the scan rate, v, as shown in Figure 5c. The parametersused for these fittings are listed in Table S2 (SupportingInformation).For instance, considering our experimental data, the error

that one would make by using a metallic model to calculaterate constants in a semiconductor would be close to 81%. For aphotoanode operating at the highest light intensity (i.e., whendiode effects are less notable), the value of ket,ap refined usingLaviron’s equations is more than 5 times lower than the valueobtained with our model to account for diode effects (14 vs 75s−1). The ket,ap value of 75 s

−1 is in accordance with literaturevalues reported for highly doped semiconductor electro-des.22−24 The Laviron model underestimates the electron-transfer constant, wrongly sensing a slower electron transferthan the actual one as a consequence of the potential dropacross the semiconductor space-charge layer. If the Lavironmodel is applied at the lowest light intensity, the calculatedelectron-transfer constant is 75 times lower (ket,ap = 1 s

−1) thanthe one obtained applying the model we developed here.Moreover, the Laviron model would wrongly suggest thatkinetics depends upon light intensity. It is likely that valuesreported in literature have similar errors because of thesemiconductor nature of the electrode. It is well-known thatelectron-transfer constants reported for semiconductor siliconelectrodes systematically show smaller electron transferscompared with those for gold electrodes.9 This has beenattributed to differences in the electronic coupling between theattached molecules and the surface and density of states. Ourresults show that the slower electron transfer for semi-conductor electrodes, compared with that of metallic electro-des, is at least in part a consequence of using a model notapplicable to semiconductors.The introduction of the Frumkin isotherm in the model

allows us to sense electrostatic interactions experienced by theattached electroactive molecules.11 Interactions have beenbroadly observed in the literature,9 with the fwhm beingbroader or narrower than the theoretical 90.6 mV for aNernstian process, indicating repulsive or attractive forces,respectively. The degree of interaction is accounted throughthe G parameter (where G < 0 is indicative of repulsions, andG > 0 is indicative of attractions) and directly related to thefwhm in a Nernstian process and a metallic electrode.11

However, under finite kinetics and diode effects, the fwhm isnot only a function of G but also of θ and ket, as shown inFigures 2d and 4d, respectively. Therefore, for the determi-nation of G, one needs to ensure that kinetic and diode effectsare not present by moving to the parts of the graphs of Figures2d and 4d where the fwhm does not depend on ket,ap or on θ.For practical situations, this criteria is met when −log θ > 1.3and the dimensionless rate constant ket,ap > 3 s

−1, which in theexperimental model we have studied here corresponds to scanrates of v < 100 mV·s−1 for a true rate constant in the range 1−

Figure 5. Photoanode systems. (a) Light-assisted hydrosilylation of1,8-nonadiyne (1) at a Si−H electrode and attachment ofazidomethylferrocene (2) via CuAAC reactions to yield redox-activemonolayers. (b) Experimental (solid lines) and fitted (dots) cyclicvoltammograms (0.1 V s−1) taken at different light intensities (1, 2, 4,11, and 27 mW cm−2). (c) Experimental (solid lines) and fitted(dots) cyclic voltammograms taken at different scan rates underillumination (27 mW cm−2). In the fittings, ket and G are assumed tobe independent of the light intensity. Best-fit values are ket,ap = 75 s

−1,G = 0.8, I0 = 10

−5 A, IL,a = 750 μA, IL,c = 250 μA, and s = −1, and αwas set to 0.5. For the light-intensity study, we introduce a correctionfactor, f I, such that the values of IL,a and IL,c are now ( f I × IL,a) and ( f I× IL,c), with 0 < f I < 1 (a value of 1 corresponds to full illumination,and 0 to no light). The obtained values of f I are 0.05, 0.125, 0.20,0.55, and 1 for 1, 2, 4, 11, and 27 mW·cm−2, respectively. Theelectrolyte is 1.0 M HClO4.



G

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10 s−1 using the highest light intensity (Figure S3, SupportingInformation).The model is also applicable to photocathodes (vide supra in

Development of the Analytical Model), and Figure S4(Supporting Information) shows this for experimentalvoltammetric curves (solid lines) and fittings (dots) forferrocene monolayers on p-type electrodes operating underdifferent light intensities (Figure S4a) and scan rates (FigureS4b). Tables S3 and S4 list the fitting parameters.

■ CONCLUSIONSIn summary, we have developed a theoretical model that allowsquantitative determination of the electron-transfer constants ofstrongly adsorbed electroactive monolayers at semiconductorphotoelectrodes and describes the shapes of experimentallyencountered cyclic-voltammetry curves. This model expandsprevious work developed by Laviron10,11 and Santangelo etal.12 and will aid the kinetic analysis of redox reactions atchemically modified semiconductor electrodes. The model isintended to lead advancement in the fields of energyproduction and storage and light-addressable electrochemis-try.25 It is also of relevance to the field of molecular electronics:silicon has just entered this area with STM single-moleculebreak-junctions experiments made technically possible in2017.26 To date, reported kinetic values of these systemsshow slower electron-transfer kinetics than metals, which weargue is most likely due to inaccurate analysis of thevoltammetric curves. The implication of the findings reportedhere are that accurate descriptions of the electron transfer ofelectroactive species attached at semiconductors require theuse of a model that accurately describes the potentialdistribution at the semiconductor−electrolyte interface.We have described a step-by-step analytical procedure to

separate diode currents, kinetic rate constants, and intermo-lecular-interaction parameters by adjusting the light intensityand scan rates during cyclic-voltammetry experiments onsemiconducting electrodes. At strong illumination and slowscan rates, fwhm values are independent of the diode-related θparameter, and the Frumkin interaction parameter, G, can beobtained. At slow scan rates the peak separation is independentof the rate constant, and θ can be obtained by analyzing datarecorded at different light intensities. Finally, once G and θ areknown, the electron-transfer rate constant is obtained througha scan-rate study at high light intensity.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.anal-chem.9b00336.

Detailed experimental procedure for surface modifica-tion, chemicals and material used, theoretical depend-ence of ket and G on voltammogram shape, experimentaldependence of IL with light intensity, parameters usedfor the fittings, and theoretical dependence of fwhm on θat different values of G (PDF)

■ AUTHOR INFORMATIONCorresponding Authors*E-mail: [email protected] (S.C.).*E-mail: [email protected] (J.G.).

ORCIDYan B. Vogel: 0000-0003-1975-7292Angela Molina: 0000-0002-9661-1660Joaquin Gonzalez: 0000-0001-6848-074XSimone Ciampi: 0000-0002-8272-8454NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis work was financially supported by the Australian ResearchCouncil (DP190100735). A.M. and J.G. greatly appreciate thefinancial support provided by the Fundacioń Seńeca de laRegioń de Murcia (Project 19887/GERM/15) as well as bythe Ministerio de Economiá y Competitividad (Projects CTQ-2015-65243-P). We thank Vinicius R. Gonca̧les and J. JustinGooding for the preparation and generous supply ofamorphous silicon substrates.

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H

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(26) Aragones̀, A. C.; Darwish, N.; Ciampi, S.; Sanz, F.; Gooding, J.J.; Díez-Peŕez, I. Nat. Commun. 2017, 8, 15056.



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