Ab initio computational modeling of the electrochemical reactivity of quinones on gold and glassy carbon electrodes

Accepted Manuscript Ab initio computational modeling of the electrochemical reactivity of quinones on gold and glassy carbon electrodes R. Jaimes, R. Cervantes-Alcalá, W. García-García, M. Miranda-Hernández PII:

S0013-4686(18)31611-6

DOI:

10.1016/j.electacta.2018.07.110

Reference:

EA 32307

To appear in:

Electrochimica Acta

Received Date: 4 April 2018 Revised Date:

12 June 2018

Accepted Date: 16 July 2018

Please cite this article as: R. Jaimes, R. Cervantes-Alcalá, W. García-García, M. Miranda-Hernández, Ab initio computational modeling of the electrochemical reactivity of quinones on gold and glassy carbon electrodes, Electrochimica Acta (2018), doi: 10.1016/j.electacta.2018.07.110. 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 proof before it is published in its final 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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Graphical Abstract

R. Jaimes, et al Electrochimica Acta

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Revised Version (Ms. Ref. No.: EA18-2110)

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R. Jaimes, R. Cervantes-Alcalá, W. García-García, M. Miranda-Hernández* Instituto de Energías Renovables Universidad Nacional Autónoma de México Priv. Xochicalco S/N Temixco, Morelos 62580 México. *Corresponding author email: [email protected]*

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Ab initio computational modeling of the electrochemical reactivity of quinones on gold and glassy carbon electrodes

Abstract

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We propose electronic structure modeling, in accordance with the Gerischer conceptualization, to explain the electrochemical response of the benzoquinone/hydroquinone (BQ/HQ) redox couple on 15

gold and glassy carbon (GC) electrodes. Specifically, coupling differed to gold compared to GC; this is of interest because BQ/HQ are representative of a promising class of molecules used in redox flow

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batteries (RFBs). We calculated the energy difference between the highest occupied molecular orbital– lowest unoccupied molecular orbital (HOMO–LUMO), Fermi levels (EF), and density of states (DOS) of the electrode materials via density functional theory in periodic systems. The Au (111) surface was considered for gold modeling, whereas graphite and graphene were used for GC. We compared these

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results with experimental data to explain the differences in the reversible behavior of the BQ/HQ

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couple in both electrode materials, setting the pH, electrolyte composition, and electrode geometry equal in both electrodes. The loss of reversibility in GC can be attributed to the anodic branch of the cyclic voltammetry response, which is consistent with the larger energetic distance found for the HQ– 25

HOMO from the EF of the electrode compared to BQ–LUMO. In contrast, the energetic distances in gold are similar in both cases and agree with the symmetry of the experimental current–potential response for both the anodic and cathodic branch. To validate the model, we calculated the total DOS

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ACCEPTED MANUSCRIPT and projected DOS for different quinone molecules—such as 2,5-dichloro-1,4-benzoquinone, 2hydroxy-1,4-naphthoquinone, and 1,2,4-trihydroxynaphtalene—adsorbed on gold and GC. The 30

experimental findings support our hypothesis. Additionally, graphite and graphene models equivalently

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described GC electrodes; both models showed a similar trend in adsorption energy for quinone molecules [due to van der Waals (VDW) interactions], DOS, and partial charge density. For the gold electrode, we found a similar trend in adsorption energy to the graphite and graphene, also attributable

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to VDW interactions. Our results indicate that theoretical modeling can explain electrochemical principles which underpin quinone-based energy storage systems and RFBs.

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Keywords Quinone, glassy carbon, gold electrode, computational modeling, density of states.

1. Introduction 40

Quinones are naturally occurring molecules associated with electron transfer processes in biological systems. These molecules are the most heavily studied organic redox compounds [1]. Recently,

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quinones have raised great interest in the context of energy storage systems as electroactive couples in redox flow batteries (RFBs). The main advantages provided by quinones are good redox reaction reversibility, high availability compared to inorganic redox couples, and amenability to modifying the reversible potential as a function of the benzene ring substituents [2,3]. In RFBs, the maximum power

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is determined by the potential difference of the electroactive couples used in the anodic and cathodic containers, whereas the maximum current is associated with the redox reaction kinetics. The kinetics and potentials of the redox reactions are related to the nature of the molecule and its interactions with the electrode material. Therefore, studying such interactions is crucial to identifying a maximally 50

suitable electrode material for quinone molecules. In the RFB research field, carbon-based electrodes are preferred (including graphite, carbon paper, carbon felt, reticulated vitreous carbon, and carbon–polymer composites) [4]. Typically, researchers 2

ACCEPTED MANUSCRIPT use glassy carbon (GC) electrodes to evaluate the electrochemical behavior of active redox couples. However, the electrochemical response of the electroactive species is a function of electrode 55

pretreatment, rendering the redox couple sensitive to the surface modifications. In general, researchers

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have found that oxygenated groups on the electrode surface enhance RFB performance, increasing the efficiency and power [5]. Although there seems to be a consensus as to the effect of electrode pretreatment, the explanations for the enhanced behavior vary. Some researchers argue that the effect is

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related to the hydrophilicity increase whereas others attribute the behavior to enhanced kinetics. In this context, one must first clarify the interactions between the redox couples and electrode materials as a

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function of electrode properties.

Theoretical/computational modeling offers an exciting route to obtain more insight into pertinent molecule–electrode interactions. Researchers have used first-principles theoretical modeling, applied to RFBs, to predict the reversible potential of active couples in the homogeneous phase [3,6], and the 65

effect of the solvent [7]. Several researchers have calculated the reversible potential of many quinone

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molecules by determining the energy differences in vacuum and continuous solvents (applicable in the limit of outer sphere charge transfer) [2,3,6]. The calculated potentials have been compared with experimental results, and showed a good correlation in many cases; this is an example of the clarity in

electroactivity modeling seems to lack such clarity, which has been a controversial topic since the early

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conceptualization and calculation methods applied to thermodynamics. In contrast, intrinsic

twentieth century. In the field of classical electrochemistry, the theory proposed by J. Butler and M. Volmer has been widely accepted. They proposed a theoretical explanation for the Tafel potential– current response due to two contributions: a pre-exponential factor (exchange current) related to the standard rate constant, which depends on the overpotential required to carry out the electrochemical 75

reaction at useful velocities; and the charge transfer coefficient, which is related to the slope of the potential–current curve when one reaches the overpotential required to carry out the reaction. The latter 3

ACCEPTED MANUSCRIPT parameter has been interpreted as the fraction of the energy supplied by the overpotential that is effectively used to lower the activation energy of the reaction. According to R. A. Marcus [8], the charge transfer coefficient depends on the shape of the potential energy surface in the trajectory of the oxidized and reduced species. Researchers redefined this concept

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empirically (regardless of the underlying mechanism) as –(RT/F)(dln|Jc|/dU), where U is the applied potential, R is the gas constant, T is the absolute temperature, F is the Faraday constant, Jc is the

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cathodic current density [9]. The main disadvantage of the classical theory is that the influence of the nature of the electrode material on the reaction rate is not considered. At the end of the twentieth century, Gerischer, Trassati and other researchers proposed a model that seeks to correct this deficiency

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[10,11]. In their model, they proposed that the density of states (DOS) of the electrode material, the electrochemical potential of the oxidized and reduced species, and the alignment of the Fermi level (EF) of the electrons in the electronic and ionic conductors should be considered. Fig. 1 shows a schematic representation of these concepts.

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< Figure 1 >

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According to this theory, the overpotential required to carry out the oxidation reaction is related to the

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energy difference between the Fermi level of the electrode material and the highest occupied molecular

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orbital (HOMO) of the reduced species. For the reduction reaction, the overpotential is related to the Fermi level of the electrode material and the lowest unoccupied molecular orbital (LUMO) of the oxidized species. The contribution to the kinetics of the charge transfer coefficient is a consequence of the electrode states population near the EF. Gerischer proposed that the current which flows through the cell is proportional to the integral of the DOS overlapped with the states of the redox couple. This conception has been used in different applications such as the adsorption of reaction intermediates 100

[12,13] and a solar cell sensitized with pigments [14]. 4

ACCEPTED MANUSCRIPT Although the Gerischer model has been widely applied it has not, to our best knowledge, been used to carry out computational calculations of electronic parameters in electrochemical processes, which could help validate its applicability for such purposes. The current in an electrochemical cell is a

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consequence of phenomena such as mass transport, geometric current distribution, and electronic factors. However, experimentally studying the electronic factors is difficult and requires special setups. Thus, comparing experimental data and electronic structure calculations is difficult; the most suitable

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method to validate the model is through correlations between different electrode materials for the same reaction.

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The electrode material as a catalyst can change the reaction mechanism from outer to inner sphere mechanisms. The latter involves breakup and formation of intra- and intermolecular bonds of the adsorbed species; such phenomena impact the exchange current and global transfer coefficient of the redox reaction. Because of this, the Gerischer model should be applied to outer sphere reactions, where the interactions between the redox species and surface are minimal. In such a case, the surface only

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plays the role of an electron sink, and charge transfer occurs via the tunnel effect. Under these conditions, the electrode material will impact the potential–current behavior since it depends on the intrinsic nature (i.e., DOS) of the electrode.

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Reduction–oxidation of the benzoquinone/hydroquinone (BQ/HQ) couple is an example of outer

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sphere reactions. Several researchers have studied this half-reaction [15–19], showing that it is a proton–electron coupled transfer reaction. Consequently, the reversible potential and reversibility are a 120

function of solution pH [1]. Furthermore, the presence or absence of a pH buffer and hydrogen bonds considerably affects the reversibility of the reaction, affecting the activation barriers of proton transfers. Nevertheless, experimental reports carried out under similar experimental conditions suggest that the reversibility of the reaction (calculated as the peak potential difference) changes when gold electrodes [20] are used instead of GC electrodes [1], which cannot be explained by the aforementioned 5

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homogeneous phase effect. Herein, we propose that the differences in the electrochemical response of the BQ/HQ couple on gold compared to GC electrodes can be explained by the electronic structure of the electrode. To corroborate this hypothesis, we evaluated the reversibility of the BQ/HQ couple on

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gold and GC electrodes via cyclic voltammetry under the same experimental conditions in buffered aqueous solutions, to determine the peak potential differences, attributable only to the electrode 130

chemical nature. These results were compared to the energy difference between the EF of the electrode

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material and the frontier orbitals of the redox couple at equilibrium conditions, determined by ab-initio computational calculations.

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2. Methodology 2.1 Experimental 135

The electrolyte solutions consisted of 10 mM K3[Fe(CN)6]/1 M KCl and a buffered aqueous solution of 1 mM benzoquinone/100 mM KH2PO4 + K2HPO4 at pH 6.6. All of the solutions were prepared with analytical grade reagents and deionized water (18 MΩ cm). We characterized the redox reactions via

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cyclic voltammetry in a three-electrode cell in phosphate buffer solution using a platinum mesh as a counter electrode and an Ag/AgCl reference electrode. All experiments were conducted under an inert 140

nitrogen atmosphere.

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We used disk GC and gold electrodes with a geometric area of 0.071 and 0.031 cm2, respectively. Prior

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to electrochemical evaluation, both of the electrodes surfaces were polished to a mirror shine with alumina powder (3-µm diameter). After polishing, we immersed the electrodes in an ultrasonic bath to eliminate alumina residues. In addition, the gold electrode was put through an electrochemical 145

polishing in 0.5 M H2SO4, performing 30 consecutive cycles from 0 to 1.8 V vs. standard hydrogen electrode (SHE), and rinsed with abundant deionized water. We evaluated the reproducibility of the surface via cyclic voltammetry until reaching a peak potential difference of ~80 mV in a solution of 10 mM K3[Fe(CN)6]/1 M KCl, using a platinum mesh as the counter electrode. Ag/AgCl (0.197 vs. SHE) 6

ACCEPTED MANUSCRIPT or Hg/Hg2SO4(s)/K2SO4 (saturated sulfate electrode, 0.640 V vs. SHE) reference electrodes were used 150

depending on the electrolyte composition. Nevertheless, all of the potentials reported herein are versus SHE. Throughout this paper, we will use U instead of E to refer to the electrode potentials, to avoid

302N) was used to perform all of the measurements. 2.2 Computational model

In the computational modeling of surface reactions, one of the most critical challenges is to generate

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confusion with the theoretically calculated energies. A potentiostat/galvanostat (Autolab PGSTAT-

surface models to describe real conditions. For this reason, experimental characterization is

2.2.1 Modeling the GC surface

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indispensable for model validation.

Carbon-based electrode materials are widely used in RFBs. Consequently, we considered GC for our 160

research. The GC structure is very complex and has not been completely elucidated [21]. However, Jenkins and Kawamura proposed the structure as a network of long ribbons of aromatic molecules

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tangled and articulated by carbon–carbon covalent bonds with a wide energy spectrum of weak bonds [22], based on X-ray diffraction analysis and high-resolution electron micrographs at different temperatures during GC fabrication. The electrochemical field has largely accepted this model. The Jenkins and Kawamura model of the GC surface has been modeled as its graphite from its most stable

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crystalline face, (111) [23,24], showing results that are in agreement with experimental data. Typically, defects in zones adjacent to the basal plane create strong interactions between the graphite and adsorbed species, affecting the electrochemical response. However, most of these zones are removed during the GC activation procedure. Therefore, in our work, we carried out the calculations in 170

the graphite basal plane without considering defects, due to the basal plane representing a greater proportion of the GC surface. In a more recent study, Harris proposed a model similar to the structure of fullerenes based on high-resolution transmission electron microscopy [25]. This model is more 7

ACCEPTED MANUSCRIPT suitable to describe the inert behavior and porosity of commercial GC. Therefore, we also modeled the GC surface as graphene. 175

The surface models were built as follows: first, the bulk cell parameters were optimized for the

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graphite, verifying the convergence in k-points and cutoff energy. Then, we carried out the geometry optimization and adsorption energy calculations considering two layers of graphene in a supercell of 7×7 unit cells, a vacuum of 25 Å (Fig. 2a and 2b), and a kinetic energy cutoff of 150 Ry for

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wavefunctions. The number of sampled k-points in the first Brillouin zone were 4×4×1 generated under the Monkhorst–Pack scheme. For geometric optimization of the graphite surface, we kept the lower

2.2.2 Modeling the gold surface

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carbon layer fixed in the bulk geometry.

The cutoff energy and the k-point grid were optimized first for bulk gold (48 eV and 8×8×8, respectively). We achieved a representative gold surface model considering the most stable crystalline 185

plane (111) with six layers of gold atoms (Fig. 2c) and a 10 Å vacuum, which are adequate to reach

and 90 Ry of cutoff energy).

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convergence in the mean electrostatic potential in the perpendicular axis to the surface (5×5×1 k-points

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2.2.3 Model considerations for adsorbed species on GC and Au electrodes We initiated our molecular adsorption study based on the graphite model, from the optimized geometry of the substrate and different orientations of the adsorbates. Different positions were explored in the

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potential surface, considering the most favorable position to be that with the lower energy, until the resultant forces were less than 0.002 Ry/Bohr. We used the most stable geometries obtained for the graphite for graphene with complete re-optimization. For the gold surface (111), we considered the most stable geometry calculated for benzene by Bilic et al. [26–28]. The aforementioned methodology 195

was used to obtain the surface/quinoneads reference system for the adsorption energy calculations in

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ACCEPTED MANUSCRIPT both systems. Correction of the dipolar moment in the perpendicular direction to the surface showed no effect in these systems. All of our calculations were carried out in the framework of density functional theory (DFT) with the

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Tkatchenko–Schefler (DFT-TS) method [29,30] to account for van der Waals (VDW) interactions. The Perdew–Burke–Ernsherhof (PBE) approximation was used for the calculation of the exchange and correlation contributions [31], and a plane wave basis set with Martins–Troullier norm-conserving pseudopotentials, as implemented in the Quantum Espresso package [32]. We conducted a DOS

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analysis using the local density approximation (LDA) and a 20×20×1 k-points grid for clean graphene

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and graphite surfaces. On the other hand, 12×12×1 k-points with a PBE functional were used for gold and graphene in the presence of molecules, in adsorption and non-adsorption conditions. We initially modeled quinones in vacuum using the Gaussian-09 code [33], with the PBE functional and a density Gauss double-zeta with polarization functions (DGDZVP) basis set, followed by a plane wave

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optimization with Quantum Espresso code calculated in a cubic cell of 25×25×25 Å, with a VDW correction. The calculations were performed using the unpolarized spin method, due to the fact that all 210

species and surfaces are closed-shell neutral systems.

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< Figure 2 >

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3. Results and discussion

3.1 Electrochemical characterization of GC and gold electrodes by cyclic voltammetry 215

We initiated our experiments by characterizing the electrode surfaces after the cleaning procedure. Fig. 3a shows the voltammetric response of the GC electrode in a 10 mM K3[Fe(CN)6]/1 M KCl solution. The ∆Up value was 73 mV, a very common response for this electrode in the aforementioned system, which indicates a reproducible surface response [34]. Fig. 3b shows the response of the gold electrode

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ACCEPTED MANUSCRIPT in a sulfuric acid solution, which exhibits a distinctive oxidation peak at potentials greater than 1.3 V, 220

and reduction at 1.1 V vs SHE, which is accompanied by a small process related to the presence of

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surface impurities at potentials less than 0.9 V [20].

< Figure 3 >

Fig. 3c shows a comparison of the voltammetric response of benzoquinone in phosphate buffer solution

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(pH = 6.6) in GC and gold electrodes. Curve (i) corresponds to the system with a GC electrode, which

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presents a peak potential difference of 229 mV. The ∆Up value is less than the value of 334 mV solutions

at

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in

both

phosphates

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tris(hydroxymethyl)aminomethane + HCl [1]. This change in the peak potential difference is associated 230

with differences in GC pretreatment, and possibly with the slight difference in pH (a higher pH

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corresponds to a larger ∆Up value). Quan et al. agree with previous reports that the large ∆Up value is characteristic of the intrinsic reactivity of the redox couple, in which the charge-transfer process is coupled to proton transfer, and strongly related to the solution acidity. At the chosen conditions the

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redox reaction of benzoquinone follows two-electron two-proton transfer, having hydroquinone as a final product (Scheme 1). In both cases, the reduction of BQ and the oxidation of HQ, electron transfer

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is expected as the first step. In this sense, there seems to be a consensus regarding the fundamental role that hydronium ions (in solution) play in the electrochemical reversibility of the system, due to its concentration and the formation of hydrogen bonds that stabilize them. Nevertheless, such homogeneous phase effects do not explain the different behavior of the same redox couple under the 240

same experimental conditions (i.e., the composition of the electrolytic solution, pH, and geometric arrangement), where the only variable is the working electrode, from gold to GC. Curve (ii) of Fig. 3c

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ACCEPTED MANUSCRIPT shows the response of the BQ/HQ system in the presence of a gold electrode. The ∆Up value is 59 mV, which considerably differs from that obtained in GC, and slightly larger than the value of 52 mV reported on gold by Walczak et al. [20] at pH 6.3. Although Walczak et al. performed their tests at 100 mVs−1, the reversibility of the reaction is not modified in the voltammetric response [35], whenever k°

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is greater (in cm/s) than 0.3 v 1/2 (v in V/s), such as in this case for the BQ/HQ couple [18].

The loss of reversibility in GC compared to gold can be explained if one of the processes (reduction or

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< Scheme 1 >

oxidation) is slower or both reactions are equally slow. A simple method of answering this question is to estimate the value of the reversible potential of the system (Eq. 1) since it is well-known that this potential does not depend on the electrode nature [11,36]

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∗ ݈‫ ݃݋‬ቀሾ஻ொሿ ቁ − 0.0592‫ܪ݌‬

(1)

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where U° (0.697 V vs. SHE) is the formal potential of the BQ/HQ couple [20,37]; and [HQ] and [BQ] represent hydroquinone and benzoquinone concentration, respectively, at the interface. Considering

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that at the half-wave potential, the concentration of the oxidized species is approximately equal to the reduced species at the interface, we can assume that the [HQ]/[BQ] ratio is equal to 1 in Eq. (1). This assumption allows calculating a Urev = 0.306 V vs. SHE, at pH 6.6. Thus, the potential difference between the cathodic peak and the reversible potential for GC would be 93 mV, and 136 mV for the anodic peak. This means that the slower process would be in the anodic branch. A similar effect can be inferred from the results reported by Quan et al. for the BQ voltammetry response in GC electrodes [1]

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(Table 1). Under the same assumptions presented herein, for their results at pH 7.2, the difference between the cathodic peak potential and the reversible potential is 140 and 210 mV for the anodic peak. In both cases, the ratio |Uap − Urev|/|Ucp − Urev| is 1.5, indicating analogous behavior. On the other hand,

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for the gold electrode, our experiments at pH 6.6 provide a ratio of approximately 1.1, which resembles the data of 0.9 at pH 6.3, inferred from Walczak et al. for BQ in gold [20]. Therefore, one can say that the oxidation–reduction kinetics of the BQ/HQ couple in gold is similar for both processes, whereas in GC the HQ oxidation is slower.

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< Table 1 >

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Herein, we propose an explanation for the aforementioned behavior, based on the electronic structure 275

of the electrodes through ab-initio computational modeling of the redox species adsorbed on both surfaces, calculating the DOS of the material and the relative position of the frontier orbitals of the

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molecules, with respect to the EF of the electrode.

3.2 Surface models and quinones in vacuum 280

Before generating the surface models, we optimized the bulk cell parameters of the material. In the case

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of graphite, due to the cell size, convergence in energy was obtained at 18×18×18 k-points, where the

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energy difference is less than 0.005 eV, with respect to a denser set of k-points. On the other hand, the total energy presents a convergence value of 0.005 eV at 66 Ry of plane–wave cutoff energy. Therefore, we carried out cell parameter optimization for bulk graphite in those conditions (18×18×18 285

k-points and cutoff of 66 Ry). The optimized cell parameters are a = b = 2.459 Å, and d002 = 3.339 Å, very close to the experimental value d002 = 3.354 Å reported by McCreery [38]. For the graphite surface, the cutoff energy convergence was achieved at E > 150 Ry, where the precision in total energy

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ACCEPTED MANUSCRIPT is 0.01 eV with respect to that at 300 Ry. Due to the high computational cost of using a cutoff energy above 150 Ry, we selected this value for optimizing the substrate–adsorbate models. The optimized 290

surface is not distorted with respect to the bulk geometry, d002 = 3.339 Å, and a carbon–carbon bond

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length of 1.419 Å, which are in agreement with the literature [23]. Since the graphene surface model has the same geometric parameters as graphite, we utilized a cutoff energy of 150 Ry and a 4×4×1 k-points grid. A cutoff energy of 48 Ry and an 8×8×8 k-point grid gave

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a cutoff energy of 90 Ry and 5×5×1 k-points for the surface.

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a convergence of 9 and 7 meV for the total energy of bulk gold, whereas 2 and 5 mV were obtained for

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We first optimized molecules in vacuum in Gaussian-09 since this code uses a basis set of atomiccentered functions and is efficient for our purposes. Once the initial structures were obtained, a reoptimization employing plane–wave basis sets in Quantum Espresso was performed to calculate the reference values for the adsorption energy. Fig. S1 compares the calculated bond lengths with literature values and crystallographic data. The bond lengths for the hydroquinone molecule (Fig. S1a: 1.381,

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1.400, and 1.089 Å) are similar to that obtained from crystallography (1.392, 1.38, and 1.09 Å) [39]. We also observed this trend for other quinone molecules [1,4-benzoquinone (14BQ), 2-hydroxy-1,4-

3.3 DOS and adsorption energy in graphite vs graphene

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naphthoquinone (2HNQ), and 2,5-dichloro-1,4-benzoquinone(DCBQ)].

Fig. 4 shows the total density of states (TDOS) determined with 20×20×1 k-points, for graphite and graphene supercells. The TDOS of graphite is very similar to that in the literature [40], and the TDOS for the graphene is almost equal to that of graphite (differences in peak heights, not in peak shape). Both models present the corresponding s-band at more negative energies. The px and py bands conform 310

to states far from the EF, both above and under it, and the pz conforms to the band around the Fermi

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ACCEPTED MANUSCRIPT level, indicating the semimetallic behavior of the material [41,42]. Fig. 4, insets, show the partial charge density evaluated at 2 eV above and below the Fermi level for both surface models. These isosurfaces provide evidence that the spatial electronic features are similar for both materials; however,

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the electronic population in the graphite is larger than in graphene, as can be inferred from the DOS. The interactions between atomic layers of carbon in the graphite have been modeled in the literature using LDA and generalized gradient approximation (GGA). According to Ooi et al. [41], the LDA

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offers systematically superior results for graphite modeling. They show that the interaction between graphite planes corresponds to the attraction energy, generated by the decrease of the kinetic energy

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(due to the delocalization of pz electrons between planes), and to the interaction between fluctuating dipoles (VDW) of carbon atoms of adjacent layers. Additionally, repulsion energy originates from the electron overlap of those layers.

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< Figure 4 >

From the aforementioned calculations, one can infer that the chemical behavior of graphite and graphene surfaces may be very similar. Therefore, we carried out geometric optimization for different

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quinones only in the presence of graphite. Owing to the possible multiple spatial dispositions for the

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quinones in graphite, the potential surface was explored systematically to obtain the most stable surface–quinone system in accordance with the following steps: 330

(1) Relaxation of the separation distance between the quinones and graphite surface. To reach this goal we performed a restricted optimization in the z-axis (perpendicular to the graphite plane), keeping the other two axes constant (completely rigid). This was carried out by starting with a molecular orientation in the horizontal (in two type of registers) and vertical (approaching initially different quinone atoms to the surface) positions. Fig. S2 shows some examples of these structures. 14

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(2) From the aforementioned relaxation process, we selected relaxation with the minimum energy to carry out complete relaxation (three axes) for all of the atoms in the supercell, except for the lower

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carbon atom layer of graphite. Fig. S3 shows the final structures.

With these modeled structures, we used Eq. (2) to calculate the adsorption energy: 340

(2)

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Eads = Esurface+quinone – Esurface – Equinone

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Table 2 shows the calculated adsorption energies. All of the molecules show favorable interactions with the surface. The largest adsorption energy (more negative ∆E) corresponds to 2HNQ, and ∆E 345

seems to diminish as the molecular complexity decreases (number and type of atoms). < Table 2 >

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By exploring the potential surface, one can infer that when the quinone molecule approaches the graphite surface, orientated in a manner that the oxygen atoms (of the quinone) are closer to the surface (it does not matter if the molecule is in a vertical or horizontal position), the quinone is repelled from

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the surface. In contrast, when the quinone molecule approaches the surface in a manner that is oriented

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to the hydrogen atoms, the molecule is attracted to the surface (affinity). Adsorption originates as per VDW interactions (dipole–dipole and induced dipoles), electrostatic forces, and covalent bonds. To evaluate if VDW interactions are the prevalent forces, we used Eq. (3): 355

EVDW = EVDW−surf+quin – EVDW−surf – EVDW−quin

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(3)

ACCEPTED MANUSCRIPT where EVDW, EVDW−surf+quin, EVDW−surf, and EVDW−quin are the energy contribution of VDW forces of the surface–quinone system, the clean surface, and quinone in vacuum, respectively. Table 2 shows 360

calculated energies. One can see that almost all of the molecule stabilization corresponds to VDW

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interactions that are nevertheless attenuated by unfavorable interactions. Perea–Ramirez et al. modeled the interaction of catechol and guaiacol molecules as well as the byproduct radicals produced by their oxidation, over a bilayer of graphene (to model graphite) [23].

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The adsorption energies (physisorption) and spin density distributions correspond to VDW-type interactions, as well as a reversible potential trend that reproduces experimental data obtained on GC

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electrodes. Zhao et al. found non-covalent interactions between 2,3-dichloro-5,6-dicyano-1,4benzoquinone and carbon nanotubes [43]. In contrast, some organic molecules are susceptible of chemisorption, such as anthraquinone in GC [38].

We found a similar trend in adsorption energies for the same quinones on graphene (Fig. 5). Therefore, since graphene is much easier for computational modeling, the DOS calculations in the presence of

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quinones were carried out with the graphene surface model.

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3.4. Electronic structure of benzoquinone and hydroquinone in graphene (surface model for GC). We calculated the DOS of the surface, in the presence of adsorbates, with the PBE functional (which has been successfully employed for these systems). Fig. 6 shows the TDOS and localized density of states (LDOS) of the graphene surface with adsorbed benzoquinone (Fig. 6a) and hydroquinone (Fig. 6b). BQ–LUMO was found immediately above the EF of graphene (GC), which facilitates reduction of the molecules. This indicates that by applying a more negative external potential, the entire set of bands

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are displaced towards more-positive energies. Since a negative external potential (more-negative Volta potential ψ) implies addition of charge to the electronic conductor, the electron repulsion increases. As a consequence, the Galvani potential becomes more negative (φ = χ + ψ, where χ = surface potential)

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and the electrochemical potential of the electrons becomes more positive (ߤ෤ = ߤ − ߶, where µ is the chemical potential), facilitating expulsion of the electrons of the electrode. 385

Nevertheless, the localized states of the adsorbate do not shift in accordance with the applied external

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potential to the surface. Consequently, the potential must only be moved to an extent such that the occupied states below the electrode EF (equivalently, the electrochemical potential) align with the

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benzoquinone LUMO, since the electrochemical charge transfer does not involve radiation. In this case, the BQ–LUMO is immediately above the EF of graphene; therefore, the required overpotential will be 390

determined primarily by the energetic distance between the more populated bands of the graphene below the EF. If a more positive potential is applied, the graphene bands will be displaced toward more-

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negative energy values, but given the symmetry of the density of states of graphene between −2 and +2 eV (against the EF), the empty states require a displacement of more than 1.5 eV to align with the BQ– HOMO. This indicates that the BQ is susceptible to reduction but not oxidation, as is well-known experimentally. In the case of HQ, the HOMO is the nearest orbital to the EF, whereas the LUMO is

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very distant in energy (Fig. 6b). Therefore, application of a more negative potential to move the bands

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toward a more positive value (where the graphene can transfer charge to that orbital) is not feasible, which indicates that the HQ is not electrochemically reducible. Probably because the interaction between the HQ and the surface is almost entirely of VDW forces, the relative position of the peaks 400

does not change appreciably when the quinone is adsorbed and when it is not, which can be observed comparing the TDOS in both situations (adsorption to non-adsorption conditions, not shown herein). According to the experimental results, a lower overpotential is necessary for the reduction of BQ than

17

ACCEPTED MANUSCRIPT that for the oxidation of HQ, leading to a minor |Up − Urev| for the reduction than that for the oxidation (Section 3.1). This agrees with the fact that the energetic difference between the EF of graphene to the 405

HQ–HOMO is larger than that to the BQ–LUMO.

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The PBE functional has been implemented in the literature in similar systems for modeling the DOS and projected density of states (PDOS) of bare graphene and fluor-doped graphene [44]; modification of the DOS around the Fermi level by the presence of CO, N, and Al in graphene [45]; and

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determination of the DOS in graphene doped with boron and iron selenide [46]. According to Duan et al., although the PBE functional underestimates the experimental gap values, the difference between

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the experimental gap value of the bare material and the doped material is similar to the difference between the calculated gap value for the bare material and the calculated gap value for the doped material (relative values are consisted). Roy et al. report modeling the DOS and PDOS in gold nanostructures [47]. 415

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< Figure 6 >

3.5. Benzoquinone/hydroquinone in gold electrodes

smaller ∆Up than GC, with quasi-symmetric current maximums around Urev of the redox couple.

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From the cyclic voltammetry results (Fig. 3), under the same experimental conditions, gold presents a

Accordingly, both the BQ–LUMO and HQ–HOMO should be at almost the same energetic separation from the EF of gold. Fig. 7 shows the TDOS and LDOS of the benzoquinone–gold and hydroquinone– gold systems. The symmetry of the observed energy difference, and the fact that the surface states are highly populated (metallic behavior, with a DOS that varies little at energies higher than –1.5 eV vs EF 425

[48,49]), could explain the symmetry and lower ∆Up values of the voltammetric experimental result

18

ACCEPTED MANUSCRIPT (Fig. 3c). The same considerations mentioned for graphene are valid herein, regarding that the energy separation between the BQ–HOMO and EF renders BQ oxidation unviable according to the calculated LDOS (Fig. 7a), and the separation of HQ–LUMO with respect to EF renders the reduction of HQ

< Figure 7 >

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impossible.

Due to the limitations of theoretical/computational modeling regarding the ability to capture the huge

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variety of factors that influence the response in cyclic voltammetry experimental results, and the

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corresponding limitations of the approximations used in the model (i.e., the exchange–correlation functional utilized for saving computational cost), the aforementioned analysis is not quantitative. The purpose of our work is to make evident the possibility of correlating the electronic structure through DFT modeling with the reversibility of the experimental I–U response, when it depends primarily on the electrode nature compared to other factors (namely mass transport, chemical purity, rugosity,

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porosity, or electrolyte composition) which, to our best knowledge, has not been reported in the literature. As mentioned previously, the concept was developed by Gerischer almost 30 years ago and a qualitative application is presented herein. The difference between the calculations reported in the

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literature for molecules in vacuum or in a continuous solvent with respect to those we have shown

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herein is that in the former, the determination of whether oxidation or reduction is favored (verifying if the energy of the HOMO–LUMO molecular orbitals with respect to the vacuum increases or decreases) 445

enables one to estimate the redox potentials. The orbital energies of the redox couple herein are in reference to the EF of the electrode (once the molecules are in equilibrium with the electrode), which could lead to a quantitative estimation of the overpotentials. The overpotential is also modified by the magnitude and sign of the intermediary adsorption energies which should be added to the calculations [50–52]; nevertheless, since the adsorption energy of both species conforming to the redox couple is 19

ACCEPTED MANUSCRIPT 450

very similar (Table 2), its influence is not significant. To explore the consistency of this application, in the next section we present results with other quinone molecules of known experimental response.

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3.6. 2-hydroxy-1,4-naphtoquinone, 1,2,4-trihydroxy-naphtalene, and 2,5-dichloro-1,4-benzoquinone in GC and gold. 455

Fig. 8 shows the localized density of states on the quinone molecules adsorbed on graphene and gold.

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The 2HNQ–LUMO is very close to the EF of graphene, and the HOMO is situated at an energy level that is very far away (Fig. 8a); this agrees with the known-capacity of this molecule to be

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electrochemically reduced. The same situation occurs with 2HNQ on gold (Fig. 8c) and DCBQ on graphene (Fig. 8e). On the other hand, Fig. 8b and Fig. 8d show the 1,2,4-trihydroxy-naphtalene 460

(124THN)–HOMO in graphene and gold, respectively, which is closer to the EF in both cases, a result that agrees with the oxidizable nature of this compound.

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A more rigorous analysis of these effects on the reactivity of quinones on different materials should include possible displacement of the molecular state energies caused by the presence of the solvent or specific ions. In addition to the increase of ∆Up, the presence of hydronium ions in aqueous solution is

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important; when the concentration of hydronium ions goes down the peak current also decreases. Due

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to the difficulty of executing such computational modeling, we modeled our systems in the complete absence of hydronium ions, which experimentally resembles more-neutral pH values. Additionally, at pH 6.6, we assure a two–electron and two–proton transfer reaction and the presence of the modeled 470

molecules since the pKa of BQ is 9.9 [16]. In any event, in experiments, a high concentration of hydronium ions will probably mask the effects otherwise attributable to proton transfer, especially for those that involve activation barriers. There is also the possibility that the interactions of protons with

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ACCEPTED MANUSCRIPT the surface modify surface reactivity toward the quinone, which in turn will also modify the response in accordance with the electrode material. 475

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< Figure 8 >

4. Conclusions

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Herein, we proposed a unique approach to explain the difference in the intrinsic reactivity of quinones on GC and gold surfaces, based on the electronic structure of the material using Gerischer’s model. The

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DOS of the surface models were calculated using periodic methods of DFT with plane waves in the presence of quinone molecules. We compared the alignment of the calculated frontier orbitals (HOMO–LUMO) with the EF of the electrode to cyclic voltammetry results, carried out under the same experimental conditions for the hydroquinone/1,4-benzoquinone couple, changing only the electrode 485

material from gold to GC. The loss of reversibility observed on GC with respect to gold corresponds to

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a larger energetic distance of the more populated bands of graphene (GC model), above and below the EF from the frontier orbitals. We proposed that the experimental quasi-reversible behavior in GC corresponds to the anodic branch of the cyclic voltammogram, and this is justified by a larger energetic

energetic distances in gold are similar and agree with the symmetry of the observed experimental

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distance of the HQ–HOMO than that to BQ–LUMO from the EF of the electrode. In contrast, the

current–potential response, for both the anodic and cathodic branch. The TDOS and PDOS of other quinone molecules adsorbed on gold and GC were also shown, supporting the consistency of our hypothesis. Modeling the GC surface, considering graphene and graphite, showed that both surface models describe similar chemical interactions. However, due to the computational cost, graphene is 495

more suitable for modeling GC. Our results indicate that theoretical modeling can explain electrochemical principles which underpin quinone-based energy storage systems and RFBs. 21

ACCEPTED MANUSCRIPT 5. Acknowledgments The authors acknowledge Fondo de Sustentabilidad SENER-CONACYT (Ref: 245754) for the economic support. The authors thank the supercomputing facilities offered by MIZTLI (DGTICUNAM) system. Raciel Jaimes acknowledges the support provided by “Fondo Sectorial Conacyt-

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Secretaría de Energía-Sustentabilidad Energética” through the assignment postdoctoral fellowship, Convocatory 2016-2017. R. Cervantes-Alcalá thanks CONACYT for the PhD scholarship.

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electrochemical

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Scheme 1. Benzoquinone redox reaction: a) in buffered aqueous solutions, and b) schematic of reaction

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mechanisms (indicating the pKa values of BQ).

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Figure 1. Gerischer conceptualization of electrochemical reaction. Left: DOS of the electrode material. Right: localized orbitals of the redox couple.

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Figure 2. Surface models: a) graphite, b) graphene, and c) gold. Gray and yellow spheres represent

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carbon and gold atoms, respectively.

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Figure 3. Cyclic voltammetry responses corresponding to the following electrodes: a) GC in 10 mM

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K3[Fe(CN)6]/1 M KCl, at 100 mVs–1; (b) gold electrode in 0.5 M H2SO4, at 100 mVs–1; and (c) response obtained in 1 mM BQ/ 100 mM KH2PO4 + K2HPO4 at pH 6.6, in glassy carbon (curve i) and gold (curve ii), at 20 mVs–1.

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Figure 4. Comparison of the DOS of graphite and graphene calculated with 20×20×1 k-points and the LDA functional. The black and brown lines correspond to the TDOS of graphite and graphene models,

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respectively. Curves s (blue line), px (green line), py (green line), and pz (red line) correspond to the bands projected on the carbon atoms of the graphene. Insets show the partial charge density evaluated

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at –2 and +2 eV from the EF for graphene and graphite.

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Figure 5. Calculated adsorption energy on graphite (blue) and graphene (red) of different quinones:

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hydroquinone (HQ), 1,4-benzoquinone (BQ), 2,5-dichloro-1,4-benzoquinone (DCBQ), and 2-hydroxy-

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1,4-naphthoquinone (2HNQ). Plot lines are only intended for visualization.

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Figure 6. TDOS (blue) and LDOS (green) of quinone: (a) BQ in graphene, (b) HQ in graphene.

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RI PT

840

M AN U

SC

845

TE D

850

Figure 7. TDOS (blue) and LDOS (green) of quinone: (a) BQ in gold, (b) HQ in gold.

AC C

EP

855

860

865

870 34

875

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

Figure 8. Location of the HOMO–LUMO orbitals of the LDOS of quinones with respect to the EF of graphene and gold. (a) 2-hydroxy-1,4-naphthoquinone (2HNQ) on graphene, (b) 1,2,4-trihydroxynaphthalene (124THN) on graphene, (c) 2HNQ on gold, (d)124THN on gold, and (e) 2,5-dichloro-1,4benzoquinone (DCBQ) on graphene.

880

35

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885

|Ucp − Urev|/mV

|Uap − Urev|/mV |Uap − Urev|/|Ucp − Urev|

93 140 28 27

136 210 31 25

1.4 1.5 1.1 0.9

Reference * [1] * [20]

SC

GC GC Gold Gold * This work.

RI PT

Table 1. Potential difference between the peak potential (Up) and reversible potential (Urev) in GC and gold electrodes, determined from the voltammetry test of Fig. 3 compared with the literature.

M AN U

890

895

TE D

Table 2. Adsorption energies (eV) and VDW contribution energies to the adsorption of the hydroquinone (HQ), 1,4-benzoquinone (BQ), 2,5-dichloro-1,4-benzoquinone (DCBQ), and 2-hydroxy1,4-naphthoquinone (2HNQ), relative to vacuum in the graphite surface. BQ HQ DCBQ 2HNQ Eads −0.64 −0.63 −0.83 −0.93 EVDW −0.76 −0.83 −0.95 −1.24

AC C

EP

900

36