Phase segregation on electroactive self-assembled monolayers: a numerical approach for describing lateral interactions between redox centers

(1)

Phase segregation on electroactive self-assembled monolayers:

a numerical approach for describing lateral interactions between redox centers

Olivier Ale´veˆque, Christelle Gautier, Maryle`ne Dias, Tony Breton* and Eric Levillain*

Received 31st March 2010, Accepted 24th June 2010 DOI: 10.1039/c0cp00085j

A numerical method is proposed in order to diﬀerentiate a random distribution from a phase segregation of redox centers on (mixed) SAMs. This approach is compared to Laviron’s interactions model and voltammetric data of nitroxylalkanethiolate SAMs.

Introduction

Since the pioneering work by Nuzzo and Allara in 1983,¹self- assembled monolayers (SAMs) of alkanethiols have gained much attention in interfacial electrochemistry and other research ﬁelds.^2,3Nevertheless, as mentioned by Loveet al.,³ experimental data are missing to establish detailed structure–property relationships for interfacial reactions on SAM, especially in case of mixed SAMs.

The molecular homogeneity of alkanethiol SAMs allowed the characterization of the 2D orientation, the compactness of the network and the orientation of alkyl chains on the surface through diﬀerent advanced technologies.^4–8 In most cases, these characterizations are possible only if the substrate is Au(111).⁹ The molecular heterogeneity of mixed SAMs has required the use of STM to obtain direct information about the molecular distribution on the surface.^10–13XPS spectroscopy,^14,15 NEXAFS spectroscopy,^16,17 ellipsometry,¹⁸ IRRAS spectroscopy^19,20 and contact angle techniques^18,21–23 can also provide interesting relative information when the experimental conditions are well controlled.

Works focused on the study of mixed alkanethiol SAMs involving binary strings of different chain lengths show that several factors contribute to different distributions. The first factor is inherent to the binary used; several studies agree in showing that the greater the difference in chain length, the more the phase segregation is favored.^10,11,24When the difference in length of alkyl chain is more than four methylene groups, phase separation is observed. The temperature is the second factor influencing significantly the molecular distribution. In most cases, adsorption at lower temperature favors the coalescence of adsorbates.^11,25It has also been demonstrated that surface topography plays an important role in the molecular distribution, especially structures defects, which are points of preferential adsorption.^11,13,26Finally, studies show that the elaboration protocol of the monolayer strongly affects the distribution of species on the surface.^22,27–29 The X-ray

photoelectron spectroscopy has, in the case of alkanethiol/

ferrocene alkanethiol mixed SAMs, allowed the diﬀerentiation of the binding energies of iron and sulfur, depending on whether the SAMs are prepared by coadsorption or successive adsorptions.^17,30 Coadsorption preferentially leads to the establishment of segregated areas whereas successive adsorptions seem to generate a random distribution of device molecules in a passive matrix.

The control of surface distribution is important in most applications of SAMs but the techniques required to highlight organizational diﬀerences are complex and expensive, and most of macroscopic characterizations are insensitive to variations of surface structure. In the case of electroactive SAMs, electrochemical techniques can provide a simple way to estimate the lateral interactions between redox centers and predict the random- ness of the distribution of electroactive sites on SAMs. Indeed, Laviron’s model^31,32represents a powerful approach to establish relationships between classical electrochemical parameters of the cyclic voltammetry (apparent potential (Eapp), full width at half- maximum (FWHM) and peak intensity (ip)) and the amount of lateral surface interactions between redox entities.^33,34

Here, we develop a numerical model to diﬀerentiate a random distribution from a non-random distribution of redox centers on (mixed) SAMs. This approach is then compared to the Laviron’s interactions model and electrochemical data obtained from electroactive SAMs containing TEMPO nitroxyl radical derivative (C15T) (Scheme 1) and dodecanethiol (C12).

Methods

Electrochemical experiments

Electrochemical experiments were carried out with a Biologic SP-150 potentiostat in a glove box containing dry, oxygen-free

Scheme 1 Derivative of TEMPO radical aminoxyl C15T (see ref. 34 for the synthesis).

Laboratoire MOLTECH Anjou, Universite´ d’Angers – CNRS, UMR 6200 du CNRS, 2 Boulevard Lavoisier 49045, Angers cedex, France. E-mail: eric.levillain@univ-angers.fr,

tony.breton@univ-angers.fr; Fax: +33241735405;

Tel: +33241735095 Downloaded by BIBLIOTHEQUE UNIVERSITAIRE ANGERS on 30 September 2010 Published on 20 August 2010 on http://pubs.rsc.org | doi:10.1039/C0CP00085J

(2)

(o1 ppm) argon, at 293 K. Cyclic voltammetry (CV) was performed in a three-electrode cell equipped with a platinum- plate counter electrode. Reference electrodes were Ag/AgNO3

(0.01 M CH3CN). CVs were recorded in dry HPLC-grade dichloromethane (CH2Cl2) or acetonitrile (CH3CN). The supporting electrolyte was tetrabutylammonium hexaﬂuoro- phosphate (Bu₄NPF₆). Based on repeat measurements, absolute errors on potentials were found to be approximatelyB5 mV.

Au substrates

Au substrates were prepared by deposition of ca. 5 nm of chromium followed byca.50 nm of gold onto a glass substrate using physical vapor deposition technique and were made immediately before use.^33,34

SAMs elaboration

SAMs were prepared on Au substrates according two routes:

Route 1: Successive adsorptions of C15T and dodecanethiol (C12) were performed by immersing the Au/glass substrate for 15 min in a millimolar solution of C15T in dichloromethane and then in a millimolar solution of C12 in dichloromethane.

The immersion time in the C12 solution varied from 1 min to 48 h to obtain the expected C15T surface coverage. We chose a 12-carbon chain for this study for two reasons. First, because 12 carbons is about the shortest chain length for which the high-quality packing is found in then-alkanethiol; we expect it to be the chain length at which the disruptive eﬀects of surface functional groups are most prominent.³⁵ Second, because a 12 carbon chain allows to obtain a complete surface covering range in our experimental conditions.

Route 2: Partial desorption of a densely packed C15T SAM was performed by immersing the Au/glass substrate for 15 min in a millimolar solution of C15T in dichloromethane and then in pure dichloromethane under ultrasonication (Bransonic^sModel 2510 – Frequency 40 kHz). The ultrasonic treatment time varied from 5 to 120 min to obtain the desired C15T surface coverage.^36,37

The normalized surface coverageyis deﬁned by the ratio of the experimental surface coverage (G) to the maximum surface coverage (G_max) according to: y = G/G_max. Experimental surface coverages (G) were deduced by integration of the voltammetric signal of SAMs. At 293 K, the maximum steady-state surface coverage (Gmax) was estimated to 5.00.110¹⁰mol cm²in CH₂Cl₂and CH₃CN.^33,34

Numerical calculations

All calculations were accomplished using home self-made programs written in C++ and run on an Intel Dual-Core 1.8 GHz computer. Details of calculations are given in the main text. The computing time depends on the size of the matrix and the normalized surface coverage, but is typically about 30 s.

Results and discussion

Numerical models

Many articles tried to explain phase-separated self-assembled ﬁlms by several methods using Monte Carlo dynamic simulations.

They include the lattice gas model,³⁸ the aggregation by surface diﬀusion and by adsorption from solution³⁹and were also performed in both semi-grand canonical and canonical ensembles.⁴⁰ Monte Carlo dynamic simulations produce a preferential adsorption and phase segregation for speciﬁc conditions but they require intricate mathematical treatments, preventing a general model. Here, we focused on a straight- forward and intuitive numerical approach.

Our numerical modeling determines the number of lateral interactions of each electroactive center of the SAM by simulating the process of phase segregation during the adsorption of thiols on the gold surface. During SAM structuring, the step-by-step self-assembly is governed by intermolecular attractive interactions (van der Waals forces). In the case of mixed SAMs, eﬃcient mixing or phase segregation can be obtained depending on the structural diﬀerences between the constituents. Then, it is assumed that the phase segregation mechanism is dependent on the binary heterogeneity.

Therefore, the model is based on preferential adsorption (or desorption) of molecules when they are (or not) in short distance interaction with similar molecules.

The SAMs were modeled by a square matrix M (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 toy[0,1]. A matrix exclusively composed of ‘‘1’’

corresponds to a SAM whose number of electroactive sites is maximum with y = 1. A mixed SAM is represented by a matrix whose yis included in the interval [0,1]. These non- unitary matrices (mixed SAM) are generated from the unitary matrix to be in agreement with the experimental conditions (generation of a SAM C15T then immersion in dodecanethiol or partial desorption by ultrasonic treatment). We made two hypotheses: (1) a SAM, with a full surface coverage, is perfectly self-assembled and (2) all sites are equivalent: the concept of size, length or geometric obstruction is not taken into account. We tested three types of possible mathematical 2D arrangements: face-centered cubic (4 neighbours), face- centered hexagonal (6 neighbours – the grid expected for a SAM) and octogonal (8 neighbours) to test the inﬂuence of the mesh, and we chose to work on matrices composed from 3600 to 10⁹elements to test the convergence and the precision of the calculations.

To generate a non-unitary matrix with a ﬁxedyvalue from a unitary matrix, we used a pseudorandom number generator (PRNG) coupled to two methods:

A ‘‘random’’ method (RND) which simulates the absence of interaction during the phase of adsorption (or desorption): the PRNG generates an (X,Y) coordinate. If this coordinate corresponds to a site ‘‘1’’, we replace it by a site ‘‘0’’, or else we generate a new (X,Y) coordinate. Then we repeat.

A ‘‘constraint’’ method (CNT) which simulates preferential adsorption (or desorption) depending if a molecule is (or is not) in interaction with a similar molecule: the PRNG generates an (X,Y) coordinate. Then we calculate for each ‘‘1’’ element of the mesh centered on the (X,Y) position the number of primary neighbours (site ‘‘1’’). The element of the mesh, which has the fewest number of neighbours, Downloaded by BIBLIOTHEQUE UNIVERSITAIRE ANGERS on 30 September 2010 Published on 20 August 2010 on http://pubs.rsc.org | doi:10.1039/C0CP00085J

(3)

is replaced by a site ‘‘0’’ (if several elements have the same minimum number of neighbours, we randomly select one of these elements (PRNG)). If all the elements of the mesh are motives ‘‘0’’, we generate a new coordinate XY. Then we repeat.

The binary images from calculated matrix (Fig. 1) show that, as we expected, the RND method favors a completely random distribution of sites whereas the CNT method seems to favor the phase segregation.

This way we can draw parallels between the amount of short-distance interactions that permit monolayer to self- organize and the sum of lateral interactions exercised between redox sites. To compare simulations with experimental results, we have assumed that the interactions between two redox sites (site ‘‘1’’) exist only if these two sites are direct neighbours.

Then we can deﬁne a dimensionless quantityf, representative of the average number of lateral interactions per electroactive site in a formed SAM. Its calculation is made by counting, for

each occupied site, the non-null primary neighbours (site ‘‘1’’), according to the following equation:

FðyÞ ¼ 1 P^X

i

P^Y

j

M_y¼1ði;jÞ N_i;j

!: P^X

i

P^Y

j

M_yði;jÞ N_i;j P^X

i

P^Y

j

M_yði;jÞ

¼ 1

N_max;y¼1: P^X

i

P^Y

j

M_yði;jÞ N_i;j P^X

i

P^Y

j

M_yði;jÞ

ð1Þ

with

M_y½i;j ¼Binary Matrix for a given surface coverage Ni;j¼number of direct neighbours close toMði;jÞ Nmax;y¼1¼4;6 or 8

8>

><

>>

:

Simulations indicate that calculations onfare convergent, the precision onfis even larger than the size of the matrix is high (negligible border eﬀects) and that a relative standard deviation of 0.3% onfis obtained only from a size of 100100. As expected,⁴¹fis independent of ‘‘PRNG’’ and of chosen mesh (4, 6 and 8 neighbours).

Fig. 2 represents variations of fdepending of y. For the RND method, f is equal to y (f proportional to y of slope unit):

f^RND(y) =y (2)

For the CNT method,fis greater than or equal toy(equality is only obtained at boundary conditionsy= 0 andy= 1), conﬁrming the phase segregation observed. We can also notice that (i) curves are not intersecting, (ii) that tangent ofy= 1 (i.e.f= 1) is independent from the model used, and (iii) that tangents fory= 0 are very diﬀerent (i.e.f= 1 andf= +N respectively for RND and CNT methods). Note that an Fig. 1 Binary images obtained from calculated matrix with the

random numerical model (RND) (left) and with the constraint numerical model (CNT) (right) as a function of the normalized surface coverage of C15T. The size of the matrix is (100 100). For each matrix, a C15T occupied site is represented in black and a C15T free site is represented in white.

Fig. 2 Dimensionless quantity fas a function of the normalized surface coverage of C15T, calculated with the CNT method (’) and the RND method (K). The matrix used for the calculation contains 10⁺⁹elements.

Downloaded by BIBLIOTHEQUE UNIVERSITAIRE ANGERS on 30 September 2010 Published on 20 August 2010 on http://pubs.rsc.org | doi:10.1039/C0CP00085J

(4)

empirical approach led to approximate f = f(y) for CNT method by the following equation:

F^CNTðyÞ ¼ y 1þy

0:4

exp 1:44 y 1þy

4!

ð3Þ

Now the challenge is to compare the numerical approach to theoretical model and experimental data.

Numerical modelvs.Laviron’s interaction model

The RND model can be in agreement with the Laviron’s model because the main hypothesis of Laviron’s model is that the electroactive centers are randomly distributed on substrate, despite interactions.

According to the hypothesis developed by Laviron (Frumkin model),

The electroactive centers are randomly distributed on substrate, despite interactions,

The superﬁcial concentration GO and GR of O and R is constant and equal toGT, and designates byGmaxthe common value of the maximal surface coverage of O and R.

The coverage y_O and y_R being deﬁned by:y_O = G_O/G_max, yR=GR/GmaxandyT=GT/Gmax,

The activation energies of the cathodic and anodic processes are proportional to the coveragesyOandyR,

The surface occupied by one molecule of O is equal to the surface occupied by one molecule of R,

The adsorption coeﬃcients of O (b_O) and R (b_R) are assumed to be potential independent,

The rate constantksis independent of the coverage, aOO, aRR and aOR are the interaction constants between molecules of O, molecules of R and molecules of O and R, respectively (a_iis positive for an attraction and negative for a repulsion; the a values are assumed to be independent of the potential),

the i-E characteristic (IUPAC convention) can then be written:^31,32

iðtÞ ¼nFAk_sG_M

y_OðtÞZ^aexpð2aOOy_OðtÞ 2a_ORy_RðtÞÞ yRðtÞZ^1aexpð2aRRy_RðtÞ 2a_ROy_OðtÞÞ

" #

iðtÞ ¼ nFAGmax

dy_RðtÞ dt

¼nFAGmax

dy_OðtÞ dt

8>

>>

<

>>

>:

with

n;F;A;k_s;R;T;E₀andthave their usual meanings Z¼exp nFðEE⁰

0Þ RT

! andE⁰

0¼E₀RT nFln b_O

b_R 8>

><

>>

:

ð4Þ For a full reversible reaction (k_s- +N), two parameters, GandS, play a primary role.

G¼a_RRa_ROþa_OOa_OR S¼aRRaROaOOþaOR

(

ð5Þ

GandScan be deﬁned as ‘‘interaction’’ parameters ofOand R, respectively.⁴²

The parameter Gdeﬁnes the shape of the peak (FWHM) and the peak intensity (i_p) and the parameterS, the apparent

formal peak (E_p) as a function ofy_T. Final equations, derived from Laviron^31–33are:

E_pðyÞ ¼ E_O=R⁰ þRT

nFSy ð6Þ

i_pðyÞ ¼ n²F²vAG_max 2RT

y

ð2GyÞ ð7Þ

FWHMðyÞ ¼ RT

nF 2 lnð2 ffiffiffi 2

p þ3Þ 3 ffiffiffi p2

2 Gy

" #

ð8Þ

To validate the numerical approach, a relationship can be established between the dimensionless quantity f and the interaction parametersGandS.

First, the interactions among adsorbed molecules,^43,44 are included in the interaction constants

a_ik¼ N_max;y¼1e_ik

2RT ð9Þ

with eik = the interaction energy of one molecular pair between two species i and k, Nmax,y = 1 = the maximum number of nearest neighbours on a full surface coverage (y_T=y_max= 1), thata_ikare surface coverage independent.

Second, the number of electroactive nearest neighbours (N) depends on surface coverage (y) according to the regular solution theory:⁴⁵

N=N_max,y_{= 1}y (10)

Finally,Nis proportional tof^RND(eqn (2)) at a given surface coverage (y) for a random distribution.

Accordingly, FWHM and Ep vs.ymust be normalized to 0 and 1, fory= 0 andy= 1 respectively in order to ﬁt with the dimensionless quantityf:

E^Norm:

P ðyÞ ¼ E_PðyÞ E_Pðy¼0Þ

E_Pðy¼1Þ E_Pðy¼0Þ ð11Þ

FWHM^Norm:ðyÞ ¼ FWHMðyÞ FWHMðy¼0Þ

FWHMðy¼1Þ FWHMðy¼0Þ ð12Þ leading to:

E^Norm:

P ðyÞ ¼ nF

SRTðE_pðyÞ E_O=R⁰ Þ

¼y ð13Þ

FWHM^Norm:ðyÞ¼ 2

3 ffiffiffi p2

G 2lnð2 ffiffiffi p2

þ3ÞnF

RTFWHMðyÞ

¼y

ð14Þ As a result, normalized apparent formal peak and full width at half-maximum are equal to the dimensionless quantityf^RND (eqn (2)).

The agreement with the RND method and the Laviron’s model was expected but what about the CNT model? To the best of our knowledge, no theory has been established to take into account a non-random distribution.

Numerical modelvs.experimental data

C15T compound presents a fully reversible one- electron oxidation in usual non-aqueous solvents.^34,46 In Downloaded by BIBLIOTHEQUE UNIVERSITAIRE ANGERS on 30 September 2010 Published on 20 August 2010 on http://pubs.rsc.org | doi:10.1039/C0CP00085J

(5)

0.1 M Bu₄NPF₆/CH₂Cl₂, the electrochemical properties of SAMs, prepared from route 1 and 2, were very similar (see ref. 33 and 34). The shape of voltammetric waves (CVs) and the linear dependency between peak intensities and scan rates were characteristic of surface-conﬁned redox species (Fig. 3).

Experimentally, FWHM is the most sensitive parameter of lateral interactions and also easier to estimate than E_p.³⁴ All full widths at half maximum (FWHM) deviate from the expected value (B89/n mV at 293 K) of an ‘‘ideal system’’, based on a Langmuir isotherm (i.e. all adsorption sites are equivalent and there are no interactions between immobilized electroactive centers). These atypical characteristics have been already presented and discussed in our previous works.^33,34

Two routes were used to produce gradients of surface concentration of C15T to confront the numerical model and experimental data:

Route 1: Synthesis of C15T/C12 mixed SAMs by successive adsorptions;

Route 2: Partial desorption of a compact C15T SAM by ultrasonic treatment.

Our previous works have shown that Route 1 matches with the Laviron’s model (random distribution). FWHM vs. yis quasi linear, according to C15T coverage, with a minimum value of 34 mV for a maximum surface concentration of 4.610¹⁰mol cm²and a limit value of 95 mV for a quasi null surface coverage (Fig. 3 and 4). This behavior is close to the one observed in the case of a binary C15T/C10,³³ and consistent with predictions of Laviron’s model.

Previous works reported the poor organization of SAMs with a low surface coverage.⁴⁷ Based on those results, we assumed that phase segregation could be easily obtained with diluted monolayers.

Accordingly, Route 2 was used to know if it was possible to observe a diﬀerence from Laviron’s model on the representation FWHM =f(y), in assuming that a low surface coverage would lead to cluster formation, caused by attractive intermolecular unmatched interactions.

Experimental CVs from Routes 1 and 2 seem,prima facie, comparable (Fig. 3). However, FWHM vs. y is route dependent. From Route 2, FWHMvs.yis clearly below the expectations of Laviron’s model (Fig. 4), which tends to mean that the number of lateral interactions between electro-active heads is higher, compared to that observed for the case of a stochastic distribution. This fact is,a priori, interpretable only if we consider more or less segregated phases, resulting in the formation of compact C15T areas.

To confront numerical model with experimental data, experimental FWHMvs.ywere normalized according to the eqn (12) (Fig. 5). As anticipated, experimental data obtained from route 1 match with the RND method. An agreement between CNT model and ultrasonic experiences could be also expected because the desorption process by ultrasonication favours desorption of molecules with the fewest number of neighbours with attractive interactions.

Fig. 3 (A) Experimental CVs of SAMs of C15T in 0.1 M nBu4NPF6/ CH2Cl2, prepared from route 1, leading to 4.6, 3.7, 2.8, 2.1, 1.4 and 0.810¹⁰mol cm².³³(B) Experimental CVs of SAMs of C15T in 0.1 M nBu4NPF6/CH2Cl2, prepared from route 2, leading to 4.6, 3.8, 3.3, 2.7, 1.8, 1.5 and 0.610¹⁰mol cm².

Fig. 4 Anodic FWHM as a function of the normalized surface coverage of C15T. Monolayers elaborated by route 1 (K) follow the Laviron’s interaction model, while monolayers elaborated by route 2 (.) do not ﬁt the model.

Fig. 5 Normalized FWHM (rightY-axis) for route 1 (K) and route 2 (.) as a function of the normalized surface coverage of C15T. The dimensionless quantityf(leftY-axis) is represented to highlight the agreement between the models (CNT in dashed line, RND in solid line) and the experimental data.

(6)

As noted in our previous works,^33,34,37 the interactions between adjacent TEMPO molecules in one or both oxidation states are solvent dependent; attractive and repulsive interactions in dichloromethane and acetonitrile, respectively.

To evaluate the inﬂuence of solvent on ultrasonic desorption, we performed same experiments in acetonitrile (Fig. 6).

As shown in Fig. 5 and 6, the preferential desorption is solvent independent. Therefore, attractive or repulsive interactions between adjacent molecules occurring during the electron transfer, in the one hand, and the preferential desorption of molecules, in the other hand, are independent processes. We can assume that the SAM structuring (the step by step self-assembly) is mainly governed by intermolecular attractive interactions (van der Waals forces).

Aminoxylalkanethiolate and ferrocenylalkanethiolate SAMs This last part tries to rationalize why the TEMPO SAMs exhibit only one well deﬁned current peak instead of the two or more seen with ferrocene SAMs when there are both isolated and clustered redox centers present.

Herein, and as previously mentioned,33,34,46,48,49 CVs of aminoxylalkanethiolate SAMs in aqueous or non aqueous solvents only present a single peak regardless of the surface coverage of TEMPO or molecular distribution. This electrochemical behavior disagrees with the ones observed for ferrocene SAMs. Indeed, in the mixed ferrocenylalkanethiolate SAMs formed by co-adsorption, two peaks are observed for the ferrocenes, one for the ferrocenes that are isolated from one other and one for those that are aggregated or clustered together.^50–52 The peak for the clustered ferrocenes appears at a higher potential (100 mV more positive) due to electrostatic repulsion between the neighbouring ferrocenium cations.

As a result, the structure of SAMs depends on the nature of the electroactive sites. The coexistence of isolated and clustered phases, observed for ferrocenalkanethiolate SAMs in HClO₄,

induces a peak multiplicity. For aminoxylalkanethiolate SAMs in aqueous and non-aqueous solvents, phase segregation leads to a unique peak.

From RND and CNT models, we extracted the probability to locaten neighbours (n is between 0 andNmax,y = 1) per

‘‘redox’’ sites in order to obtain an estimation of the ‘‘redox’’

site distributionvs.surface coverage (y). As shown in Fig. 7, the neighbour proportions, at a given surface coverage, form a continuum in both methods, ruling out the presence of a splitting of the voltammetric peak.

Based on Laviron’s approach, RND and CNT models do not include a formal potential distribution.⁵³For the ferrocenylalkanethiolate SAMs, we can suggest that the peak splitting between isolated and aggregated redox centers is due to the existence of a large discrete potential distribution.

Conclusion

The results presented here show that it is possible to simulate non-stochastic distributions of mixed SAMs with a simple model based on the aggregation of the molecules. Associated with electrochemical measurements, this approach gives access to a quite ﬁne description of the average distribution of redox sites on SAMs.

In our opinion, this numerical model can be used in the case of electroactive monolayers presenting lateral interactions, Fig. 6 Normalized FWHM (rightY-axis) for route 1 (K) and route 2

(.) in 0.1 M nBu4NPF6/CH3CN, as a function of the normalized surface coverage of C15T. The dimensionless quantityf(leftY-axis) is represented to highlight the agreement between the models (CNT in dashed line, RND in solid line) and the experimental data in acetonitrile. Insert: Experimental CVs of SAMs of C15T in 0.1 M nBu4NPF6/ CH3CN, prepared from route 2 (see ref. 33 for Route 1), leading to 3.8, 2.0, 1.3, 1.0, 0.6, 0.4, 0.2 and 0.0610¹⁰mol cm².

Fig. 7 Probability to locate a redox site withnneighbours (nbetween 0 and 6 withNmax,y= 1= 6-face-centered hexagonal) for RND (up) and CNT (down) methods. The size of the matrix is (200200).

(7)

and more precisely, when electrochemical characteristics (E_peak, Ipeak, FWHM) deviate from the theoretical values.

This approach could be applied to monolayers of molecules for which intermolecular interactions are known. For example, Enoki et al.⁵⁴ have observed, in the case of tetra- thiafulvalene derivative SAMs, that the peak widths of the redox waves are strongly dependent on the oxidation states.

Conversely, this approach is not suitable for SAMs presenting a wide distribution of formal potentials (i.e. ferrocenylalkanethiolate SAMs in acidic medium).

Further work is aimed at establishing structure–reactivity relationships of aminoxylalkanethiolate SAMs designed for electrocatalytically active responsive materials.

Acknowledgements

This work was supported by the Centre National de la Recherche Scientiﬁque (CNRS-France), the ‘‘Agence Nationale de la Recherche’’ (ANR-France), and the ‘‘Re´gion des Pays de la Loire’’ (France). The authors thank Flavy Ale´veˆque for her critical reading of the manuscript.

Notes and references

1 R. G. Nuzzo and D. L. Allara,J. Am. Chem. Soc., 1983,105, 4481.

2 A. Ulman, An Introduction to Ultrathin Organic Films From Langmuir–Blodgett to Self-Assembly, Academic Press, Boston, MA, 1991.

3 J. C. Love, L. A. Estroﬀ, J. K. Kriebel, R. G. Nuzzo and G. M. Whitesides,Chem. Rev., 2005,105, 1103.

4 L. Strong and G. M. Whitesides,Langmuir, 1988,4, 546.

5 C. E. D. Chidsey, G. -Y. Liu, P. Rowntree and G. Scoles,J. Chem.

Phys., 1989,91, 4421.

6 N. Camillone, C. E. D. Chidsey, G.-Y. Liu and G. Scoles,J. Chem.

Phys., 1993,98, 4234.

7 K. Uosaki and R. Yamada,J. Am. Chem. Soc., 1999,121, 4090.

8 M. D. Porter, T. B. Bright, D. L. Allara and C. E. D. Chidsey, J. Am. Chem. Soc., 1987,109, 3559.

9 F. Schreiber,Prog. Surf. Sci., 2000,65, 151.

10 Y.-K. Kim, J. P. Koo, C.-J. Huh, J. S. Ha, U. H. Pi, S.-Y. Choi and J.-H. Kim,Appl. Surf. Sci., 2006,252, 4951.

11 S. Chen, L. Li, C. L. Boozer and S. Jiang,Langmuir, 2000,16, 9287.

12 E. Delamarche, B. Michel, H. A. Biebuyck and C. Gerber, Adv. Mater., 1996,8, 719.

13 B. Lu¨ssem, L. Mu¨ller-Meskamp, S. Kartha¨user, R. Waser, M. Homberger and U. Simon,Langmuir, 2006,22, 3021.

14 K. Heister, M. Zharnikov, M. Grunze and L. S. O. Johansson, J. Phys. Chem. B, 2001,105, 4058.

15 J. P. Folkers, P. E. Laibinis, G. M. Whitesides and J. Deutch, J. Phys. Chem., 1994,98, 563.

16 N. Ballav, A. Shaporenko, A. Terfort and M. Zharnikov, Adv. Mater., 2007,19, 998.

17 S. Watcharinyanon, E. Moons and L. S. O. Johansson,J. Phys.

Chem. C, 2009,113, 1972.

18 S. V. Atre, B. Liedberg and D. L. Allara,Langmuir, 1995,11, 3882.

19 L. Bertilsson and B. Liedberg,Langmuir, 1993,9, 141.

20 C. E. D. Chidsey and D. N. Loiacono,Langmuir, 1990,6, 682.

21 C. D. Bain, J. Evall and G. M. Whitesides,J. Am. Chem. Soc., 1989,111, 7155.

22 C. D. Bain and G. M. Whitesides,J. Am. Chem. Soc., 1989,111, 7164.

23 J. P. Folkers, P. E. Laibinis and G. M. Whitesides,Langmuir, 1992, 8, 1330.

24 H. Munakata, S. Kuwabata, Y. Ohko and H. Yneyama, J. Electroanal. Chem., 2001,496, 29.

25 R. Yamada, H. Wano and K. Uosaki, Langmuir, 2000, 16, 5523.

26 S. J. Stranick, A. N. Parikh, Y.-T. Tao, D. L. Allara and P. S. Weiss,J. Phys. Chem., 1994,98, 7636.

27 N. Ballav, T. Weidner, K. Ro¨ssler, H. Lang and M. Zharnikov, ChemPhysChem, 2007,8, 819.

28 C. D. Bain, E. B. Troughton, Y.-T. Tao, J. Evall, G. M. Whitesides and R. G. Nuzzo,J. Am. Chem. Soc., 1989,111, 321.

29 F. Tielens, V. Humblot, C.-M. Pradier, M. Calayayud and F. Illas, Langmuir, 2009,25, 9980.

30 A. Shaporenko, K. Ro¨ssler, H. Lang and M. Zharnikov,J. Phys.

Chem. B, 2006,110, 24621.

31 E. Laviron,J. Electroanal. Chem., 1979,100, 263.

32 E. Laviron and L. Roullier,J. Electroanal. Chem., 1980,115, 65.

33 O. Ale´veˆque, T. Breton, M. Dias, C. Gautier, E. Levillain and F. Seladji,Electrochem. Commun., 2009,11, 1776.

34 O. Ale´veˆque, F. Seladji, C. Gautier, M. Dias, T. Breton and E. Levillain,ChemPhysChem, 2009,10, 2401.

35 M. D. Porter, T. B. Bright, D. L. Allara and C. E. D. Chidsey, J. Am. Chem. Soc., 1987,109, 3559.

36 K. Shimazu, I. Yagi, Y. Sato and K. Uosaki,J. Electroanal. Chem., 1994,372, 117.

37 C. Gautier, O. Ale´veˆque, F. Seladji, M. Dias, T. Breton and E. Levillain,Electrochem. Commun., 2010,12, 79.

38 W. Mizutani, T. Ishida and H. Tokumoto,Appl. Surf. Sci., 1998, 130–132, 792.

39 D. K. Schwartz, S. Steinberg, J. Israelachvili and J. A. N.

Zasadzinski,Phys. Rev. Lett., 1992,69, 3354.

40 A. V. Shevade, J. Zhou, M. T. Zin and S. Jiang,Langmuir, 2001, 17, 7566–7572.

41 B. B. Mandelbrot, The Fractal Geometry of Nature, W. H.

Freeman Ed., New-York, 1982.

42 A. P. Brown and F. C. Anson,Anal. Chem., 1977,49, 1589.

43 P. A. Allen and A. Hickling,Trans. Faraday Soc., 1957,53, 1626.

44 Modern electrochemistry 2A: Fundamentals of Electrodics, ed. J. O’ M. Bockris, A. K. N. Reddy and M. Gamboa-Aldec, Kluwer Academic Publishers, New-York, 2nd edn, 2002.

45 W. L. Bragg and E. J. Williams,Proc. R. Soc. London, 1936,145, 699.

46 H. O. Finklea and N. Madhiri,J. Electroanal. Chem., 2008,621, 129.

47 S. Ye, T. Haba, Y. Sato, K. Shimazu and K. Uosaki,Phys. Chem.

Chem. Phys., 1999,1, 3653.

48 T. Fuchigami, T. Shintani, A. Konno and S. Higashiya, Denki Kagaku, 1997,65, 506.

49 Y. Kashiwagi, K. Uchiyama, F. Kurashima, J.-I. Anzai and T. Osa,Anal. Sci., 1999,15, 907.

50 L. Y. S. Lee, T. C. Sutherland, S. Rucareanu and R. B. Lennox, Langmuir, 2006,22, 4438.

51 G. K. Rowe and S. E. Creager,Langmuir, 1991,7, 2307.

52 L. Y. S. Lee and R. B. Lennox,Langmuir, 2007,23, 292.

53 M. J. Honeychurch and G. A. Rechnitz,Electroanalysis, 1998,10, 285.

54 R. Yuge, A. Miyazaki, T. Enoki, K. Tamada, F. Nakamura and M. Hara,J. Phys. Chem. B, 2002,106, 6894.