Electrochemical behavior of a typical redox mediator on a modified electrode surface: Experiment and computer simulations

Author’s Accepted Manuscript Electrochemical behavior of a typical redox mediator on a modified electrode surface: Experiment and Computer Simulations E.M. Gavilán Arriazu, Verónica I. Paz Zanini, Florencia A. Gulotta, Virginia M. Araujo, O.A. Pinto www.elsevier.com

PII: DOI: Reference:

S0039-6028(16)30320-X http://dx.doi.org/10.1016/j.susc.2016.12.005 SUSC20973

To appear in: Surface Science Received date: 14 July 2016 Revised date: 26 December 2016 Accepted date: 27 December 2016 Cite this article as: E.M. Gavilán Arriazu, Verónica I. Paz Zanini, Florencia A. Gulotta, Virginia M. Araujo and O.A. Pinto, Electrochemical behavior of a typical redox mediator on a modified electrode surface: Experiment and Computer Simulations, Surface Science, http://dx.doi.org/10.1016/j.susc.2016.12.005 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Electrochemical behavior of a typical redox mediator on a modified electrode surface: Experiment and Computer Simulations

E.M. Gavilán Arriazu, Verónica I. Paz Zanini, Florencia A. Gulotta, Virginia M. Araujo, O. A. Pinto* Instituto de Bionanotecnología del NOA(INBIONATEC-CONICET), Universidad Nacional de Santiago de Estero, RN 9 Km 1125 Villa el Zanjón, Santiago del Estero, G4206XCP, Argentina * Corresponding author. [email protected]

Abstract This paper describes the study of a redox species electrosorption on a modified electrode by experimental measurements and computer simulation. The propose model is based on the fact that charges are transferred to the electrode when an electroactive species is adsorbed on its surface. The electrode surface is modified by the irreversible adsorption of a non-electroactive species, which blocks a percentage of the adsorption sites. Hence, the electroactive species can only be adsorbed on the surface vacancies, and, when this phenomenon occurs, interact laterally with the non-electroactive one. Lattice-gas models and Monte Carlo simulations in the Gran Canonical Ensemble are used. The analysis conducted is based on the study of adsorption isotherms and voltammograms, for several values of energies and adsorption degrees of the nonelectroactive species. In the case of experimental measurements, an artificial clay (Laponite®) represents the non-electroactive species while the redox probe Fe(CN)64- is the electroactive one. The results obtained by the proposed model are compared with experimental voltammograms.

Keyword: Monte Carlo simulation; lattice-gas model; modified electrode surface; redox species; experimental voltammograms, electrosorption.

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1.

Introduction In the last decades, electrochemistry has been fundamental to understand ionic

adsorption on metal electrodes [1-4]. Voltammetry is one of the most commonly used electrochemical techniques, which enables the study of mechanisms associated with electrochemical processes, charge transfer and adsorption on modified surfaces[5,6]. The electroactive species may be adsorbed on the electrode surface and lateral interactions between them can induce the formation of ordered structures. In this regard, Wandlowski and col. have reported an order-disorder phase transition for the adsorption of Bromide on Ag(001) [7]. Many thermodynamics and statistical mechanics concepts have been applied in recent years to electrochemical processes; and various methodologies, involving solutions of mathematical equations and stochastic simulations, have been developed to interpret and solve the specific issue of voltammetry [8-12]. In particular, the development of methodologies including digital simulations has been widely developed in this field [13-15]. In regard to the model, the metal–electrolyte interface can be interpreted by a two-dimensional system, where anionic species, ions or molecules interact with a metallic solid. This area has been one of the most studied by experimental measurements, and theoretical and computational methods. Several electrochemical systems have been analyzed from first principle techniques, such as the adsorption of H on Pt(111) and Pt(100), [16]. In particular, cyclic voltammetry and electrosorption isotherms, based on density functional theory calculations, show excellent agreement with experimental results.

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One of the strategies used to mimic the electrochemical processes involves Monte Carlo (MC) simulations [17,18], in which the electrode surface is approximated by a lattice-gas model. This model is characterized by a substrate having specific sites where the adsorbate can be deposited [19]. An interesting example of application is represented by the study of the adsorption of bromide on Ag(100), in which MC and Mean Field Approximation have been used to fit the experimental isotherm, taking into account long and short-range interactions [20,21]. Other experimental techniques, like choronocoulometry, have been simulated by MC, for example the electrodeposition study of Br on Ag(100) [22,23]. MC has been also applied in the case of small dimensions systems such as nanoparticles. For example, surface decorations on several nanoparticles geometries have been analyzed using the compressibility of monolayer or the derivative of the adsorption isotherms that is related with current in voltammetric studies [24]. Several energetic approaches, such as truncated-sum and mean-field-enhanced were used in order to fit experimental isotherms based on chronocoulometric data for the electrosorption of Br and Cl on Ag(100) [25]. In these systems theoretical approximations such as Mean-Field and Quasi-Chemical have been developed to obtain cyclic voltammograms [26]. Another numerical tool widely used to study the electrosorption process is MC dynamic. This method is characterized by considering time as a parameter; therefore it is possible to analyze the kinetics of the process under study. Vetter et. al. [27] have used a dynamic lattice model for Br on Ag(100), and the strategy involved the adjustment of the MC attempt frequency. They found good agreement between simulated and experimental peak separations. Otherwise, the electro-oxidation of CO on stepped electrodes [28] and the kinetics of CO oxidation on Pt(100) and Pt(111)

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surfaces, assuming a Langmuir–Hinshelwood mechanism, were studied with this methodology by Koper and col. [29]. In this work, we propose a simple model to emulate qualitatively the main characteristics of the electrosorption phenomenon in a real modified surface. Although all physicochemical process involved in the oxidation of Fe[CN6]4- are not included in this model, the results show that it is able to reproduce the electrochemical parameters behavior. In particular we are interested in consider the effect on the charge transfer of a redox species, when a second non-electroactive species, which interacts with the redox one, is previously deposited on the electrode surface.

This phenomenon will be

analyzed by two methods: Standard Monte Carlo simulation and linear sweep voltammetry. The experimental voltammograms were performed on a glassy carbon electrode (GCE) modified with Laponite particles. Laponite is synthetic clay with composition and structure similar to those of natural, trioctahedral smectite clay minerals [30]. In particular, laponite crystals have a negative surface charge of 50-55 mmol.100 g-1. Crystal edges have small localized positive charges (4-5 mmol.100 g-1) as a result of the absorption of cations. A surface which is modified with this clay acquires a net negative charge density. [Fe(CN)6]4- is a commonly redox mediator used in electrochemical characterization of electrode surfaces due to its electron transfer kinetics has been extensively studied [31]. In the present work, this redox species was used to assess the effect of electrostatic interactions in the electronic transfer and thus obtained voltammetric response. In previous work, we found that negative electrostatic interactions between the clay and the [Fe(CN)6]4- are observed. These interactions were tested both by cyclic

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voltammetry (CV) and electrochemical impedance spectroscopy (EIS) [32,33] and they have reflected in an increase in the charge transfer resistance (EIS), a decrease in the peak current (CV) and a shift of the peak potential towards higher ones (CV).

The paper is organized as follows: In Section 2, the lattice-gas model and details of Monte Carlo Simulations are presented. Section 3 describes the solutions and reagents, while section 4 details the characteristics of the electrochemical measurements.

Results and discussion are presented in Section 5.

Finally, the

conclusions are drawn in Section 6.

2. Lattice- gas Model and Monte Carlo simulation The electrode surface can be modeled by a two-dimensional substrate, in the scheme of a lattice-gas which is characterized by a square lattice of M=L2 adsorption sites, where L is the lateral size. Since only first neighbor interactions are considered, the lateral coordination z is 4 and, to simulate a bulk surface, periodic boundary conditions are used. Electrosorption process occurs when the electroactive species (A) adsorbs and transfers a charge to the electrode, as long as that site is empty; conversely, when the species A is desorbed, an electron is transferred from the electrode to the electroactive compound. However, two electrons cannot be transferred in the same direction consecutively, by the same particle. The number of species A on the surface is defined as NA. Otherwise, the substrate may be modified by the random irreversible deposition of the nonelectroactive species B. The number of species B on the electrode surface is defined as N B.

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Hence, the surface density of blocked sites is monitored as   N B / M . If

  0[1] the substrate is empty[full]. Both species (A and B) can interact only if they are in adjacent sites, with an energy contribution defined as wAB . If wAB  0[wAB  0] , the A-B interaction is repulsive [attractive] but if wAB  0 the particles do not interact. The Hamiltonian is expressed by the mathematical equation:

H (N A , NB ) 





M 1 w         AB ci ,1 c j ,2 ci ,2 c j ,1 i ci ci 1 2 i , j 

(1)

where ci is the occupation variable, which takes the value 1[2], if the site is occupied for A[B] or 0 if the site is empty. Here δ is the Kronecker delta and



is the chemical

potential. The first sums on the eq. (1) runs over all nearest-neighbors (NNs) pairs and the second is for all available sites. The chemical potential can be connect to the electrochemical potential (E) in the dilute-solution approximation as[13],

C   e E  Co 

  0  k BT ln 

(2)

where 0 is a chemical reference potential, kBT is temperature expressed as relative units of the Boltzmann constant, k B . C and C0 are the bulk ionic concentration and a reference concentration, respectively.  is the electrosorption valence[30,31], e  is the elementary charge unit,  e is the charge transferred through the external circuit. This 

study assumes that  is constant [21,23]. The surface coverage of the species A can be obtained by:

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

1 M

M

c 

i ci 1



i

NA M

(3)

Where ... denote simple averages of the simulations. The current can be obtained as:

I   e 

 , E

(4)

here  is the number of adsorption sites per unit surface area and v is the sweep rate. Finally in a dimensionless scheme the current can be expressed by [32]:

i

I

 e v 



 E

(5)

As shown in eq. 5, the current (in arbitrary units) is proportional to the compressibility of the monolayer [13,16, 33]. The derivative  / E can be computed in the Grand Canonical ensemble via the normalized mean square fluctuations,

 / E  N A2  N A

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(6)

Eq. 6 results from the thermodynamics fluctuation theory [20,34,35]. The adsorption-desorption equilibrium process is simulated by a Monte Carlo technique in the Grand Canonical Ensemble, using the Glauber algorithm [36,37]. The Metropolis scheme [38] is also used in order to satisfy the principle of detailed balance.

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In resume, the simulation process follows the next sequence: initially the empty lattice is randomly occupied by NB particles of the species B. The modified surface is considered in contact with a particle A reservoir, at temperature T and potential E. The species A will adsorb [desorb] only if any of M  N B sites are empty [filled]. A Monte Carlo step (MCS) is achieved when each of the M sites has been tested to transfer its charge. Typically, the equilibrium state can be well reproduced after discarding the first 5 × 106 MCSs. Then, the next 2 × 106 MCSs are used to compute averages.

3. Solutions and Reagents Laponite R. D., a synthetic hectorite was obtained from Laportes industries. K4[Fe(CN)6] and KCl were from Cicarrelli (Argentina), and were used as received. The laponite colloidal suspensions were prepared by dispersing 2 g L-1 in water overnight, with continuous stirring. The background electrolyte solution was 0.1 M KCl and 5 mM K4[Fe(CN)6] was used as electroactive species.

4. Electrochemical Measurements Experiments were carried out with Autolab (Eco-Chemie, Utrecht, Netherlands) equipped with a PGSTAT 30 potentiostat, and analyzed with the software package GPES. The measured were done in a three-compartment electrochemical cell with a Pt wire as counter electrode, and Ag│AgCl│Cl- (3M) as reference electrode. The working electrode was prepared on a 3 mm diameter glassy carbon disc (GCE). Prior to each experiment, the glassy carbon electrode (GCE) was polished sequentially with alumina powder of decreasing particle size, e.g. 1.0, 0.3, and 0.05 μm (Buehler, USA), copiously rinsed with ultra-pure water and sonicated for 1 min between polishing steps. Then, aliquots of a mixture containing 5, 10, 15, 20 and 25 µg of laponite were deposited on the GCE surface and air-dried at 277 K. Voltammograms were conducted at 50 mV/s,

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which is an appropriate value to check changes associated with surface modifications of electrodes, and at 298 K. The surface density of blocked sites, σ was calculated in relation to the oxidation current of 5 mM [Fe(CN)6]4-, obtained for the clean electrode. As the clay is incorporated, current decreases because of an increase in the coating. The latter is estimated from the ratio of the current obtained between an electrode modified with a certain amount of clay and the clean one. 5. Results and discussions In order to simulate the process, a square lattice of L=256 was considered. For this L value, no sizes effects were observed. For simplicity, the chemical potential and the lateral energies are expressed in units of kBT. The temperature is fixed at kBT=1.0 and the electrosorption valence at   1 . For sake of clarity three cases are considered:

Case I: wAB / kBT  0.0 Case II: wAB / kBT  0.0 Case III: wAB / kBT  0.0

At first, we analyze the case I, for which there are no interactions between species A and B. Figure 1(a) shows the adsorption isotherms ( E / k BT versus values of  . For

 ) for several

  0.0 , all the sites are empty and therefore the surface is clean.

When species A adsorbs, the resulting isotherm shows a sigmoid shape. The inflection point, which is indicated by the vertical dashed line, occurs at half coverage (  = 0.5), and matches with the positive peak current ( i p ) in the voltammogram; being the i p the maximum current transferred in the system (figure 1(b)). As the species A are oxidized,

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they block the surface for subsequent adsorption and the current decreases as consequence; when all the sites are occupied, i  0 . As  increases, the isotherms saturate at  sat  1   and the peak current decreases. Since there are no interactions, the sites occupied by species B are responsible of the charge transfer diminution. For all  values, the voltammograms are centered at E / kBT  0.0 . i p is a useful parameter to characterize the net charge transferred on the surface when fluctuation are maximal. The inset in figure 1 (b) describes the dependence of i p with  , which shows a lineal relationship. So as to introduce the repulsive interactions in the model, the case II is considered. In this case the interaction is set at wAB / kBT  2.0 , thus particles B try to reject the deposition of particles A in its neighborhood. Isotherms presented in figure 2(a) show a shift at high values of E / kBT as

  1 , and they all have different

saturation regimes as described previously. The respective voltammograms are presented in figure 2(b). An interesting effect is observed: the peak potential is shifted towards higher values of E / kBT as  increase. Inset in figure 2(a) shows the relation between ip and  , indicating a non-linear behavior. This fact suggests that interactions are partly responsive to the shift of ip. In order to understand better the influence of the repulsive interaction the voltammograms for wAB / kBT  0.0,0.5,1.0,1.5 and 2.0 at

  0.4 are shown in

figure 3(a). At first sight, two features that result from wAB/kBT increase can be observed:

a decrease in the peak current and a shift in the potential associated.

Therefore, as the wAB / kBT increases, the fluctuations are suppressed. The peak current decreases linearly as wAB / kBT increases as is shown in the inset of figure 3(b).

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Finally, the case III for attractive interactions is considered. According to the model these interactions enable the particles A to adsorb next to particles B. The interactions were settled at

wAB / kBT  2.0 and induce a shift of E / kBT , in the

sigmoid isotherms, to more negative values

(not show here by simplicity); the

saturation of each is as described above. Figure 4(a) shows the voltammograms as a function of  . The peak potential of the voltammograms shifts to more negative potentials as  tends to unity and the peak current decreases as shown in the inset. The charge transferred depends on the availability of empty sites, and the value of  . Figure 4(b) describes the voltammograms for the different interaction values for   0.4 .The current decreases as the interaction becomes more negative. This effect is

more intense as wAB / kBT becomes more negative, and then fluctuations and current are reduced. According to the experimental conditions described in section 4, lineal voltammograms were performed for several values of  . Figure 5 (a) shows the original voltammograms, while figure 5b presents the same data without capacitive current. The baseline subtraction was performed with the software included in the equipment. For experimental measurements, an artificial clay (laponite®) represents the non-electroactive species while the redox probe Fe(CN)64- is the electroactive one. The general behavior is similar to that described by case II, for repulsive interactions. This is because both, the clay and the redox probe, have negative charge density and therefore their interactions are repulsive. According to this model, charge transfer depends on two factors: the availability of empty sites and the interactions wAB / kBT . In turn, the effect can be quantified by the mean transferred charge cm, which can be obtained by:

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Ef

cm 

 i( E )dE

(7)

Ei

Qualitative differences between simulation and experimental data can be computed for cm , ip and  E .  E  Ei p (  0)  Ei p ( ) is defined as the shift of the potential associated to ip , in relation to the clean electrode (   0.0 ). In order to reproduce qualitatively the experimental condition, MC simulation was compute for T  298K , wAB  0.05eV and   0.0,0.18,0.23 , 0.53, 0.65 and 0.73. Figure 6 (a-c) shows cm ,

ip and  E versus  for experimental and MC data (Note that two scales are used). Green lines indicate the tendencies. In cm a linear tendency is shown with  . However, ip and  E shows a nonlinear trend. All parameters show that the model is able to describe the experimental situation. Although several qualitative characteristic of experimental voltammograms are reproduced by the simulation, some considerations are necessary to understand the model. Current generated from the electrochemical reaction depends on several properties such as chemical nature of the species, electrosorption valence, interactions, etc. In the experimental situation, the current is a function of the concentration gradient in the vicinity of the electrode surface. Once the concentration on the electrode surface approaches to zero, the concentration gradient starts to decrease due to the relaxation effect. This effect results from the fact that it is not kept constant but decreases because the electroactive species must diffuse from the bulk of the solution to the electrode surface, and hence the current flowing must also decrease. In other words, the diffusion layer has grown sufficiently above the electrode so that the flux of reactant to the electrode is not fast enough to satisfy that required by the Nernst equation.

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This behavior gives rise to a peak shaped current-potential response. From the point of view of simulations, both processes (concentration gradient and diffusion) are equivalent to the fluctuations of the number of adsorbed particles (see equation 6). Fluctuations can be interpreted as the effective rate of adsorption-desorption and depend on the intensity of lateral interactions and the amount of empty sites. The current increases when the fluctuations increase, but when fluctuations are maximal and constant, a peak is observed. In the proposed model, the fluctuations are reduced due to repulsions avoiding adsorption of the species A in the empty sites next to the species B, and consequently the current is reduced. In other words,  and θ, controls the charge transfer similarly to the concentration gradient previously described.

6. Conclusions In this work, the electrosorption of a redox species on a modified electrode was studied. The electrode surface was modified with the irreversible adsorption of nonelectroactive species (species B). The amount of sites blocked by this species is controlled by surface density  . A second electroactive species (species A) is able to transfer charge which results in a current, which is determined by voltammetry. This phenomenon was analyzed by two methods: Standard Monte Carlo simulation in the Grand Canonical Ensemble and linear sweep voltammetry. In regards to the simulation, the electrode surface is described by a lattice-gas model. Three cases were analyzed according to the type of lateral energy between species: repulsive, attractive or without interaction. Several conclusions can be drawn:

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

Case I : the voltammograms simulated in all cases are centered in zero, because there are no interactions between species. The peak current of the voltammogram decreases linearly as





tends to the unit.

Case II, for repulsive interactions: the peak current of the voltammogram decreases as  tends to the unit and shifts to higher values of E. This effect is reinforced when the interactions are stronger, because fluctuations are reduced. In other words, as the repulsive interactions become stronger it is necessary to increase the potential (E) to favor adsorption. This means that the repulsion decreases fluctuations, resulting in a reduction in the current of the system.



Case III: Contrary to case II, the peak potentials of the voltammograms are shifted toward lower potentials as  tends to the unit. In the same way as in the previous case, the current decreases as interactions become more negative. This is because attractive interactions try to form A-B pairs so as to reduce the energy of the system.



To support the case II, the simulations was compared with the Fe(CN)64reaction on a modified glassy carbon electrode surface. In this case cm , ip and

 E obtained by both simulation and experimental measurements shows a very similar phenomenology behavior. Therefore, this is the first step in designing of a promising model to be applied in many electrochemical systems, following two facts: the availability of empty sites and the interaction between species.

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Acknowledgements The authors acknowledge financial support from Universidad Nacional de Santiago del Estero, under project CICyT-UNSE 23 A 212 .This work was supported in part by CONICET (Argentina) under project number PIO 112-201101-00615. The numerical work were done using the Huauke parallel cluster (located in Instituto de Bionanotecnología del NOA (INBIONATEC-CONICET), Universidad Nacional de Santiago de Estero, Argentina.

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interactions and adsorption geometry on the voltammetry at (111) and (100) electrodes, Surf. Sci. 498 (2002) 105–115. [38] M.E.J. Newman, G.T. Barkema, Monte Carlo Method

in statistical physics,

Clarenton –Press Oxford, 1999. [39] H. B. Callen, Thermodynamics and an introduction to thermostatistics, John Wiley and Sons, 1985. [40]K. Binder , D. Stauffer, in K. Binder (ed.) Applications of the Monte Carlo, Method in Statistical Physics, Vol. 36, Springer, Berlin, 1984. [41] K. Kehr, K. Binder, Simulation of Diffusion in Lattice Gases and Related Kinetic Phenomena, in: K. Binder (ed.) Applications of the Monte Carlo Method in Statistical Physics, Topics in Current Physics Vol. 36 , Springer, Berlin, 1987, pag. 181. [42] N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller , E. Teller, Equation of state calculations by fast computing machines, J. Chem. Phys. 21 (1953) 1087-1092.

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Figure 1 : case I. a) Adsorption isotherms for several values of  . B) Voltammogram simulated in correspondence with a).The inset shows

i p versus  , where a lineal

relationship is observed. Figure 2: Case II. Idem to figure 1. Figure 3: Voltammograms simulated for

  0.4 and several values of wAB / kBT as

are shown. Figure 4: Voltammograms simulated for the case III a) wAB / kBT  2.0 and several values of  . The inset shows i p versus  for this case. b)

  0.4 and several

values of wAB / kBT . The inset shows i p versus wAB / kBT  for this case. Figure 5 : Experimental voltammograms for several values of  . a) Original data. b) voltammograms without the capacitive current. Figure 6: Experimental and MC data for a) cm , b) ip and c)  E for several values of

 . Two scales are shown. Green lines indicate the linearity. The bar errors of experimental data are included and in the case of MC simulation the error is less of the point size.

Highlights 

Monte Carlo simulation and experimental data were used to study the electrosorption of a redox species on the surface of a modified electrode.



This model is able to reproduce the main electrochemical behavior of a redox species on a modified electrode surface in the presence of a non electroactive species.



The experimental measurements were properly describes by the developed model.

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Graphical Abstract