Electroactive self-assembled monolayers: Laviron's interaction model extended to non-random distribution of redox centers

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Electroactive self-assembled monolayers: Laviron's interaction model extended to non-random distribution of redox centers

Olivier Alévêque, Pierre-Yves Blanchard, Christelle Gautier, Marylène Dias, Tony Breton ⁎ , Eric Levillain ⁎

Laboratoire CIMA, Université d'Angers-CNRS, 2 boulevard Lavoisier 49045, Angers cedex, France

a b s t r a c t a r t i c l e i n f o

Article history:

Received 30 June 2010

Received in revised form 13 July 2010 Accepted 22 July 2010

Available online 12 August 2010 Keywords:

Tempo

Self-assembled monolayers Cyclic voltammetry Interaction model

The Laviron's interaction model, dedicated to randomly distributed electroactive adsorbed species, was extended to a non-random distribution in order to extract the current–voltage characteristics from any surface distribution of electroactive centers on self-assembled monolayer (SAM). Confronted to electro- chemical behaviour of nitroxyl radical SAMs, theagreement observed betweentheoryand experiments provides evidence of a distribution independence of the interaction parameters.

© 2010 Elsevier B.V. All rights reserved.

1. Introduction

Since the pioneering work by Nuzzo and Allara in 1983[1], self- assembled monolayers (SAMs) of alkanethiols have gained much attention in the interfacial electrochemistry and other researchfields [2]. Previous works [3] were dedicated to confront Laviron's interaction model and electrochemical data from nitroxyl radical SAMs on gold in order to provide evidence of a random distribution of electroactive centers on surface. To extend this approach to non- random distribution of electroactive sites on SAMs, we developed an empirical numerical model combined with electrochemical data from nitroxyl radical SAMs. This work allowed to differentiate a random distribution from a non-random distribution[4].

Here, we propose to develop an extension of the Laviron's model to a non-random distribution in order to extract the current–voltage characteristic (i–E) from any surface distribution of electroactive centers.

2. Experimental procedures

2.1. Compounds

The synthesis and electrochemical characterizations of nitroxyl radical (TEMPO) derivative 1 (N-(TEMPO)16-mercaptohexadecana- mide) were described in reference[5].

Elaboration and electrochemical characterizations of SAMs pre- pared from Route 1 and from Route 2 were described in references [3,4].

Route 1: Successive adsorptions of 1 and dodecanethiol (C12) for the formation of binary SAMs were performed by immersing the Au/

glass substrate for 15 min in a millimolar solution of 1 in dichlor- omethane and then in a millimolar solution of C12 in dichloro- methane. The time in the C12 solution varied from 1 min to 48 h in order to obtain the expected1surface coverage.

Route 2: Partial desorption of a densely packed SAM of 1 was performed by immersing the Au substrate for 15 min in a millimolar solution of 1 in dichloromethane and then in pure dichloromethane under ultrasonication (40 kHz) for a time varying from 5 to 120 min to obtain the desired 1 surface coverage.

2.2. Numerical models

The SAMs were modeled by a square matrixM(X,Y) composed of

“1” (site occupied by an electroactive species) and of“0” (site not occupied or site occupied by a non-electroactive species). The relation between the number of “1” and the “total number of sites” experimentally corresponds to the normalized surface coverageθT

[0,1]. A matrix exclusively composed of“1” corresponds to a SAM whose number of electroactive sites is maximum withθT=θmax= 1. A mixed SAM is represented by a matrix whoseθTis included in the interval [0,1[. To generate a non-unitary matrix with afixedθTvalue from a unitary matrix, we used a pseudorandom number generator (PRNG).

Electrochemistry Communications 12 (2010) 1462–1466

⁎Corresponding authors. Tel.: +33 241735095; fax: +33 241735405.

E-mail addresses:tony.breton@univ-angers.fr(T. Breton), eric.levillain@univ-angers.fr(E. Levillain).

1388-2481/$–see front matter © 2010 Elsevier B.V. All rights reserved.

doi:10.1016/j.elecom.2010.07.039

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Electrochemistry Communications

j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e l e c o m

2.3. Surface distribution

Two numerical models were developed[4]in order to generate two different molecular surface distributions. The RND model was dedicated to random distribution and the CNT model to phase segregation. The two models were used to generate matricesM(X,Y) with a normalized surface coverageθTbetween 0 and 1. The binary images from calculated matrices are represented inFig. 1for a 0.5 normalized surface coverage.

A dimensionless quantityϕ,“segregation factor”, representative of the average number of lateral interactions per electroactive site, allowed quantifying distributions from RND and CNT models.

For the RND model;ϕRNDð ÞθT =N θT

For the CNT model;ϕCNTð ÞθT =N θT

1 +θT

0:4

exp 1:44 θT

1 +θT

4

ð1Þ with N= the maximum number of nearest neighbours on a full- covered surface (θT=θmax= 1).

3. Results and discussion

3.1. Interactions calculation

The influence of the initial molecular distribution on the molecular distribution of reduced and oxidized species during the oxidation (or reduction) step was studiedviaa reversiblen-electron redox reaction of adsorbed electroactive species:

R_ads⇄O_ads+n e ð2Þ

Hypotheses[6,7]were the following:

• The sum of surface concentrationsΓOandΓRofOandRrespectively, is constant and equal toΓT.Γmaxdesignates the maximal steady

state surface coverage ofOand R. The coverageθOandθRbeing defined by:θO=ΓO/Γmax,θR=ΓR/ΓmaxandθT=ΓT/Γmax,

• The surface occupied by one molecule ofOis equal to the surface occupied by one molecule ofR.

For a givenθTmatrix image, with random (RND) or non-random (CNT) distribution, and initially composed ofRspecies (θR=θT), the oxidation process is simulated by the random replacing ofRspecies by Ospecies (Fig. 1). At each step of the replacement (i.e.for variousθO), we calculated interactions between redox species by means of four dimensionless quantities ϕOO(θO,θT), ϕOR(θO,θT), ϕRR(θO,θT), and ϕRO(θO,θT). ϕij(θO,θT), representative of the average number of interactions between a speciesi(OorR) and a speciesj (OorR).

Taking into account only the nearest neighbours interactions, ϕij

(θO,θT) can be expressed by:

ϕijðθO;θTÞ=

∑^X

x ∑^Y

y ∑

M_θO;θTðX;YÞ=i

M_θ

O;θTðX;YÞN_jðX;YÞ

∑^X

x ∑^Y

y ∑

M_θO;θTðX;YÞ=i

M_θ

O;θTðX;YÞ

ð3Þ

with

M_θO,_θT(X,Y) Matrix generated for given surface coveragesθOandθT.

Nj(X,Y) Number of direct neighboursjclose toM(X,Y)

Φij(θO,θT) varies between 0 andN. In our case, with a square matrix, N= 4.

ϕij(θO,θT) valuesvs.θTwere calculated from RND and CNT models. In both models, numerical simulations exhibited a linear dependence of ϕij(θO,θT)vs.θT(Fig. 2), leading to:

ϕijðθO;θTÞ= ϕ θð ÞT

θT θj ð4Þ

Fig. 1.Binary images obtained from calculated matrix during an oxidation step forθT= 50%. (Up) random and (Down) segregated distribution of electroactive centers for different values ofθO. For each matrix,Rspecies are represented in blue,Ospecies are represented in red and free sites are represented in white. he size of the matrix is (100 × 100).

with ϕ(θT) =ϕij(θO=θT,θT), “segregation factor”, i.e. the average number of interactions between an electroactive species and directly adjacent electroactive species (OandR).

For a random distribution,ϕij(θO,θT) is proportional toθj: ϕijðθO;θTÞ=ϕRNDð ÞθT

θT θj= NθT

θT θj=Nθj ð5Þ

3.2. Modification of Laviron's interaction model 3.2.1. Surface activities

Based on the Frumkin isotherm, Laviron developed an interaction model to predict (i–E) characteristic of adsorbed electroactive mole- cules, focusing exclusively on non-idealities caused by lateral interac- tions when redox centers are randomly distributed on substrate[6].

Using the formalism of Laviron and Frumkin[8,9], the surface activities of the oxidized and reduced species can be expressed according to:

γi=Γiexp ∑

k 2a_ikθk

with i;k=O;R ð6Þ

The interactions among adsorbed molecules[10,11]are included in the interaction term

a_ik= Nεik

2RT ð7Þ

withεik= the interaction energy of one molecular pair between two speciesiand k,N= the maximum number of nearest neighbours on a full-covered surface (θT=θmax= 1).

From Eqs.(6) and (7), we obtain:

γi=Γiexp ∑

k

εik

RTNθk

ð8Þ

In this expression, each termNθkis related to the average number of nearest neighbour of a species i with species k randomly distributed with a normalized surface coverage θk. This term is exactly equal to ϕij(θO,θT) calculated in the case of a random distribution.

Based on this result, we propose to generalize the expression of surface activities assuming:

γi=Γiexp ∑

k

εik

RTϕikðθO;θTÞ

=Γiexp ∑

k 2a_ikϕⁿikðθO;θTÞ

ð9Þ

withϕⁿikðθ^O;θ^TÞ=^ϕikðθ_N^O;θTÞ∈½0;1

Using Eqs.(4) and (9), the surface activity of the two redox species are given by:

γO=ΓOexp 2aOOϕⁿð ÞθT

θT θO2aORϕⁿð ÞθT

θT θR

γR=ΓRexp 2a_RRϕⁿð ÞθT

θT θR2a_ROϕⁿð ÞθT

θT θO

8>

>>

<

>>

>:

ð10Þ

withϕⁿð ÞθT = ^{ϕ θð Þ}_N^T ∈½0;1

Fig. 2.(Black short-short lines) Dimensionless quantitiesϕvs.θTand (Red lines)ϕOO(θO,θT) valuesvs.θOat differentθT(25% (A) and (D), 50% (B) and (E) and 75% (C) and (F)), calculated from binary images modeled from RND ((A), (B) and (C)) and CNT ((E), (F) and (G)) models.

O. Alévêque et al. / Electrochemistry Communications 12 (2010) 1462–1466

3.2.2. Cyclic voltammetry parameters for a reversible system

Thei–Echaracteristic (IUPAC convention) can be expressed[12]:

i tð Þ=nFAk_s γOexp αnF RTEE^0′

γRexp ð1αÞnF RTEE^0′

=nFAk_s γOη^αγ^1αR

ð11Þ

withη=exph_RT^nFEE^0′i

Using surface activity of the two redox species, Eq.(10), we reach:

i tð Þ=nFAk_sΓ_max

θOð Þηt ^αexp2aOO

ϕⁿð Þθ_T

θ_T θOð Þ t 2a_ORϕⁿð Þθ_T θ_T θRð Þt

θRð Þηt ^1αexp2aRRϕⁿð ÞθT

θT

θRð Þ t 2aROϕⁿð ÞθT

θT

θOð Þt

0 BB BB

@

1 CC CC A i tð Þ=nFAdΓ_O

dt =nFAΓmax

dθ_O dt 8>

>>

>>

>>

>>

<

>>

>>

>>

>>

>:

ð12Þ

wheren,F,A,R,ks,T, andE^0′have their usual meanings.

For a fast reversible system (k_s→+∞), the Nernst equation is applicable:

γO

γR

=η=exp nF

RTEE^0′

ð13Þ

From Eqs.(2), (10) and (13), we obtain:

exp nF RTEE⁰⁰

= θO

θTθO

exp 2ϕⁿð ÞθT

θT

GθO+θTða_ORa_RRÞ

ð Þ

ð14Þ with interaction parametersG=aOO+aRR−aOR−aROandS=aOO− aRR+aOR−aRO.

aOO, aRR, aOR and aRO are the interaction constants between molecules of O, molecules ofRand molecules ofOandRrespectively (a_iis positive for an attraction and negative for a repulsion; thea values are assumed to be independent of the potential)[6,7].

In order to extract the i–E characteristic (cyclic voltammetry, E=Ei+v t), the differentiation of Eq. (14)in t andθO respectively leads to:

nF RTv

dt= θT

θOðθTθOÞ2Gϕⁿð ÞθT

θT

dθO ð15Þ

From Eqs.(12) and (15), the current can be expressed:

ið ÞθO = n²F²AvΓmax

RT

θTθOðθTθOÞ

θ²T2GθOϕⁿð ÞθT ðθTθOÞ ð16Þ For a full reversible reaction (ks→+∞) and from Eqs.(14) and (16), peak potential (Ep) and peak current (ip) can be extracted for θO=θT/ 2.

Epð ÞθT =E^0′RT

nFSϕⁿð ÞθT ð17Þ

i_pð ÞθT =n²F²vAΓmax

RT

θT

2 2ð Gϕⁿð ÞθT Þ ð18Þ

For a full reversible reaction (ks→+∞) and from Eqs.(14), (16), (17) and (18), full width at half maximum (FWHM) can be extracted fori=i_p/ 2.

FWHMð ÞθT =2RT nF ln

1 +

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Gϕⁿð Þ θT 2 Gϕⁿð Þ θT 4 s

1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Gϕⁿð Þ θT 2 Gϕⁿð Þ θT 4 s

0 BB BB B@

1 CC CC CAGϕ θð ÞT

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Gϕⁿð Þ θT 2 Gϕⁿð Þ θT 4 s

2 66 66 64

3 77 77 75 ð19Þ

We pointed out that, for |Gϕⁿ(θT)|b1, FWHM varies quasi-linearly withGθTand can be determined from Eq.(6)(viaa Taylor series at Gϕⁿ(θT) = 0):

FWHMð ÞθT = RT

nF 2ln 2 ffiffiffi p2 + 3

3 ffiffiffi p2

2 Gϕⁿð ÞθT

" #

ð20Þ

3.3. Model vs. experimental data

Fig. 3 exhibits cyclic voltammograms (CVs) of SAMs in 0.1 M nBu4NPF6/CH2Cl2 prepared from Route 1 and from Route 2. As previously observed[4], Routes 1 and 2 favour random distribution and phase segregation respectively.

To confront theory and experimental data, E_p, FWHM and i_p parameters were extracted from experiment CVs[3,4]for each route (Fig. 4). For Route 1,GandSparameters were previously estimated from Eqs.(17), (18) and (20)by a linear regression with an RND distribution (ϕRND, Laviron model)[3]:G= 1.13± 0.03 andS= 1.14 ± 0.04 at 293 K.

For Route 2,GandSparameters are estimated by non-linear regression with a CNT distribution (ϕCNT):G= 1.13 ± 0.04 andS= 1.19 ± 0.06 at 293 K.

Fig. 3.(A) Experimental CVs of SAMs of1in 0.1 M nBu4NPF6/CH2Cl2, prepared from Route 1, leading to 4.6, 3.7, 2.8, 2.1, 1.4 and 0.8 × 10⁻¹⁰mol cm⁻²[3]. (B) Simulation of these experimental CVs calculated from Laviron's model withG= 1.10,S=−1.1, ks= 90 s⁻¹andθ= {1.00, 0.79, 0.59, 0.44, 0.30, 0.17}[3]. (C) Experimental CVs of SAMs of1in 0.1 M nBu4NPF6/CH2Cl2, prepared from Route 2, leading to 4.6, 3.8, 3.3, 2.7, 1.8, 1.5 and 0.6 × 10⁻¹⁰mol cm⁻²[4]. (D) Simulation of these experimental CVs calculated from Laviron's extended model withG= 1.10,S=−1.1, ks= 90 s⁻¹andθ= {1.00, 0.83, 0.72, 0.58, 0.39, 0.32, 0.13}.

The distribution independence ofGandSparameters confirms that the interaction parameters are not governed by the nature of the distribution of redox centers, and are only linked to the system considered.

FromGandSparameters deduced from mathematical regressions, simulated CVs are in qualitative (i.e. shape) and quantitative (i.e.

intensities) agreement with CV experiments of SAMs for random and segregated distributions (Fig. 3).

4. Conclusion

The Laviron's model was extended to any distributions of redox centers on SAMs. This model can be used in the case of electroactive monolayers presenting lateral interactions, and more precisely, when electrochemical characteristics deviate from the theoretical values.

This approach could be applied to monolayers of molecules for which intermolecular interactions are known. The non-ideality of CV shapes of nitroxyl radical SAMs on gold provides a simple way to illustrate the random and segregated distributions of electroactive sites.

Acknowledgments

This work was supported by the Centre National de la Recherche Scientifique (CNRS-France), the“Agence Nationale de la Recherche”

(ANR-France), and the “Région des Pays de la Loire” (France). The authors thank Flavy Alévêque for her critical reading of the manuscript.

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Fig. 4.Route 1[3]: (A) anodic apparent potential (Epa) as a function of the surface coverage; (B) anodic peak intensity (ipa) as a function of the surface coverage; (C) anodic full width at half maximum (FWHMa) as a function of the surface coverage. Route 2[4]: (D) anodic apparent potential (Epa) as a function of the surface coverage; (E) anodic peak intensity (ipa) as a function of the surface coverage; (F) anodic full width at half maximum (FWHMa) as a function of the surface coverage.

O. Alévêque et al. / Electrochemistry Communications 12 (2010) 1462–1466