1
Nanoelectrochemistry of Adsorption-Coupled Electron Transfer at Carbon Electrodes

Shigeru Amemiya

Department of Chemistry, University of Pittsburgh, USA

1.1 Introduction

This chapter is concerned with studies of heterogeneous electron transfer (ET) at carbon electrodes when redox-active molecules can be reversibly and specifically adsorbed on the electrode surfaces [1]. These studies of adsorption-coupled ET complement seminal studies of redox-active molecules irreversibly attached to the electrode surfaces [2,3]. Adsorption-coupled ET is ubiquitous in applied electrochemistry and plays crucial roles in electrocatalysis [4], photocatalysis [4], electrodeposition [5], electropolymerization [6], electrochemical remediation [7], and electroanalysis [8]. For these applications, carbon materials are highly attractive owing to their well-known propensity to adsorb molecules [9,10]. In fact, significant attention has been given not only to traditional carbon materials, but also to emerging carbon nanomaterials as important electrode materials [11] for diverse applications, especially in energy conversion and storage, e.g. fuel cells [12], batteries [13], solar cells [14], and supercapacitors [15]. This propensity, however, hampers a fundamental understanding of adsorption-coupled ET at carbon electrodes, which are readily contaminated [9,16,17]. The adventitious contamination of carbon surfaces has been well recognized [16,18], but has not been prevented effectively despite a huge body of work on carbon electrochemistry [11,19]. It has been difficult to reliably characterize the intrinsic electrochemical reactivity and adsorption properties of carbon electrodes [20].

In this chapter, we introduce recent progress in theory of adsorption-coupled ET and its experimental assessment at carbon electrodes. Theoretical progress was made recently by Amatore and coworkers [21,22], who refined a quantitative model of adsorption-coupled ET developed by Laviron [1,23] by considering outer- and inner-sphere ET and surface adsorption as elementary electrode steps [24]. Experimental progress were made by the development and nanoelectrochemical characterization of clean carbon electrodes as requisites to reliably examine theories for adsorption-coupled ET. In particular, nanoscale scanning electrochemical microscopy (SECM) [25,26] serves as an emerging powerful method to quantitatively investigate carbon electrochemistry [27] and beyond.

Figure 1.1 The reaction scheme of outer- and inner-sphere ET of non-adsorbed and adsorbed redox molecules, respectively. Dashed arrows indicate heterogeneous self-exchange ET.

1.2 Overview of Adsorption-Coupled ET

The specific and reversible adsorption of a redox molecule from the solution to the electrode surface couples heterogeneous outer- and inner-sphere ET as modeled by Laviron [23] and Amatore [24]. In their model (Figure 1.1), a redox molecule, O, is transported from the solution to the outer Helmholtz plane (OHP) [28] near the electrode surface to participate in outer-sphere ET, i.e.

where the transported molecule, Osol, and the product of outer-sphere ET, Rsol, can be adsorbed at the inner Helmholtz plane (IHP) [28] of the electrode surface, i.e.

When both forms of the redox couple are adsorbed, inner-sphere ET can be mediated, i.e.

In addition, a heterogeneous self-exchange ET reaction is possible as given by

A quantitative understanding of the Laviron-Amatore model requires the knowledge of time-dependent concentrations of four species including Oads, Rads, Osol, and Rsol in addition to time- and distance-dependent concentrations of O and R in a diffusion layer near the electrode surface, where the respective concentrations are given by GO, GR, CO(0, t), CR(0, t), CO(x, t), CR(x, t) (Figure 1.1). Mathematically, adsorption-coupled ET can be modeled by solving two Fickian diffusion equations with four independent equations at the electrode surface as boundary conditions. For instance, the equilibrium adsorption of oxidized and reduced forms of a redox couple is described by two isotherms for competitive adsorption. In addition, two Nernst equations are obtained to describe the equilibrium of outer- and inner-sphere ET. Adsorption isotherms and Nernst equations must be substituted by the corresponding kinetic expressions when equilibrium adsorption or reversible ET is not maintained, respectively.

Historically, the coupling between outer- and inner-sphere ET of a redox couple through specific adsorption and heterogeneous self-exchange ET was proposed by Anson in 1961 [29] to account for the anomalous non-linear concentration-dependence of exchange current based on the Fe3+/2+ couple at the Pt electrode [30]. Anson's work [29] is theoretically pioneering and insightful, but seems overshadowed by the erroneous assignment of a thin-layer effect to an adsorption effect [29], and is well known rather for the following development of thin-layer electrochemistry [31-33]. Prior to Anson, Laitinen and Randels proposed a model based on inner-sphere ET of tris(ethylenediamine) complexes of Co3+ and Co2+ adsorbed on the mercury electrode without considering an outer-sphere pathway [34]. Similarly, others also considered only the inner-sphere pathway [35,36]. Later, Anson attempted to kinetically distinguish between outer- and inner-sphere ET using the Marcus theory [37] and also experimentally identify the electrode reaction mechanism of a redox couple as either outer or inner sphere [38,39]. More recently, Laviron [23,40-42] and Amatore [21] theoretically demonstrated conditions where outer- and inner-sphere ET of a redox couple are not distinguishable electrochemically, which will be discussed through this chapter. A redox couple, however, is still considered either as an outer- or inner-sphere couple [4], even controversially [43,44], despite the possibility that both outer- and inner-sphere pathways can be mediated simultaneously and indistinguishably by the same redox couple.

A quantitative understanding of adsorption-coupled ET is highly challenging even under diffusion-controlled conditions owing to the requirement of adsorption isotherms with multiple parameters. For instance, four parameters are introduced when the adsorption of each form of a redox couple is represented by the simple Langmuir isotherm for competitive adsorption of both forms of the redox couple, to yield [45]

where Gi,s is the saturated surface concentration of species i and ßi is a parameter characterizing the magnitude of adsorbate-substrate interaction. In addition, two Nernst equations must be considered to describe diffusion-controlled outer- and inner-sphere ET. A conventional Nernst equation is given for outer-sphere ET by [46]

where n is the number of transferred electrons and is the formal potential of outer-sphere ET. Equation (1.8) can be combined with Langmuir isotherms, Eqs. (6) and (1.7), to yield a Nernst equation for inner-sphere ET as [47]

with

Equation (1.10) indicates that the equilibrium of inner-sphere ET is controlled by the equilibrium of outer-sphere ET and surface adsorption, thereby introducing no additional parameter. It should be noted that a formal potential is defined for non-adsorbed redox couples in the electrochemistry literature [48] to represent outer-sphere ET, i.e. . By contrast, interactions between redox molecules and electrodes were considered in a recent theoretical study to calculate formal potentials [49], which should be more directly relevant to inner-sphere ET, i.e. , rather than outer-sphere ET.

A comparison of Nernst equations for outer- and inner-sphere ET predicts that these two pathways are thermodynamically coupled or decoupled depending on the adsorptivities of a redox couple. Specifically, outer- and inner-sphere ET are coupled and driven simultaneously when both forms of a redox couple are adsorbed similarly, i.e. GO,sßO = GR,sßR, to yield in Eq. (1.10). In this case, reduction (or oxidation) is driven through both outer- and inner-sphere pathways simultaneously at (or ), thereby yielding an electrochemical response based on the convolution of both pathways....