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Introduction to Atomic Scale Electrochemistry

Marko M. Melander, Tomi T. Laurila, and Kari Laasonen

1.1 Background

Electrochemistry and electrocatalysis are at the forefront of many technological fields related to solving the grand challenges encountered in advanced energy solutions, personalized medicine, and environmental issues. Electrochemical technologies of interest include, among others, batteries, C mitigation, various sensor technologies, water purification, molecular electronics, fuel-cells, hydrogen powered energies, and solar-powered renewable technologies.

To improve upon existing electrochemical technologies in a rational way, understanding and controlling the atomic scale properties of the electrochemical interface is vital. In particular, the connection between atomic scale surface chemistry and the electrocatalytical performance needs to be established. Rational design of better electrocatalysts working in complex electrochemical environments needs insight from experiments, computational methods, as well as theoretical approaches. While experimental electrochemical and spectroelectrochemical methods are well-established and can often be routinely applied, theoretical and computational methods have not yet reached the same level of maturity. The lack of generally accepted and applicable computational and theoretical tools is due to the high complexity of the electrochemical interface which provides a number of challenges for atomic scale theory and modelling. Specific challenges include; (i) inclusion of the electrode potential, (ii) the need for several time and length scales to assess both thermodynamic and kinetic properties of the solid-liquid interface, and (iii) a quantum mechanical treatment to describe chemical bond making and breaking.

The field of atomistic modelling in electrochemistry has made impressive progress during the last 15 years. In this book, we will the review state-of-the-art computational and theoretical methods for modelling, understanding, and predicting the properties of electrochemical interfaces. Specifically, we discuss different ways of (i) including the electrode potential in the computational setup and fixed potential calculations within the framework of grand canonical density functional theory, (ii) quantum mechanical models for the solid-liquid interface and the formation of an electrochemical double-layer using molecular dynamics and/or continuum descriptions, (iii) thermodynamic description of the interface and reactions taking place at the interface as a function of the electrode potential, (iv) novel ways of describing rates for heterogeneous electron transfer (both with the outer and inner sphere redox couples), proton-coupled electron transfer, and other electrocatalytic reactions as a function of the electrode potential, and (v) multiscale modelling where atomic level information is used for predicting experimental observables to enable direct comparison with experiments, to rationalize experimental results and to predict the electrochemical performance. We will also highlight several applications in electrocatalysis and electrochemistry using state-of-the-art methods.

This book will provide a comprehensive view on the current theoretical and computational methods and their application for understanding, predicting, and optimizing the properties of electrochemical interfaces starting from the atomic scale. While several books have been devoted to either experimental electrochemistry or computational chemistry, there are no books on atomistic computational electrochemistry! Hence, we hope that this volume contributes to fill this gap in the literature.

1.2 The thermodynamics of electrified interface

In Fig. 1.1, a simplified view of a typical electrochemical interface in aqueous electrolyte is shown. On the far left is the electrode, which provides the source/sink of electrons at a constant electrochemical potential as well as a substrate for any chemical reactions accompanying redox reactions. The surface of the electrode typically contains specifically adsorbed ions in addition to solvent molecules and reaction intermediates and products. In addition, the surface chemistry of the electrode is heavily dependent on the value of the applied potential.

Figure 1.1 Schematic presentation of the electrochemical double layer showing the IHP, OHP, and diffuse layer as well as how the potential changes as a function of distance from the electrode surface. See text for further details. Source: Courtesy of Nico Holmberg.

The structure of the solvent adjacent to the electrode is significantly affected by the charge on the electrode. On the solvent side we have one compact layer where the change in the potential is approximately linear and a more spread out region where the change is more or less exponential (diffuse layer). These layers together constitute the so-called electrical double layer (EDL). Note that the EDL is formed at the interface of any type of different phases owing to the electrostatic interactions and is by no means restricted to solid/liquid interfaces. However, the structure of this interphasial region can be quite different at different type of interfaces. For example, if one is working with ionic liquids the double layer region differs significantly from the one shown in Fig. 1.1 [1]. The compact layer is further composed of two sublayers as shown in Figure 1.1. The one closest to the electrode is called the inner Helmholtz layer (IHL) and it contains, in addition to the solvent molecules, specifically adsorbed ions (typically anions or large cations). These ions have lost at least partially their solvation sheet and have direct contact to (also partly desolvated) electrode. The so-called inner Helmholtz plane (IHP) is typically defined to go through the centers of these specifically adsorbed ions. In the other part of the compact layer further away from the electrode surface, in the outer Helmholtz layer (OHL), in addition to solvent, ions that have retained their solvation sheets are located. Thus, within OHL there are no specific chemical interactions between the electrode and the redox species and the interaction is thus purely electrostatic. The so-called outer Helmholtz plane (OHP) is typically defined as the plane going through the centers of the these non-specifically adsorbed ions. Thus, the OHP can be thought of as the distance of closest approach of surface inactive ions. After the compact layer, before the bulk of the solution, comes the diffuse layer, where there is a dynamic equilibrium between the ordering tendency caused by the electric field from the electrode and the disordering thermal motion. At this point, it is helpful to mention something about the dimensions of these layers. The thickness of the compact layer (consisting of inner and outer Helmholtz layers) is typically in the order of 0.5?nm or less. The thickness of the diffuse layer depends heavily on the total ionic concentration and is less than  10?nm for concentrations greater than 0.01?M. Note also that the inner layer and diffuse layer together have a net electrical charge equal in magnitude to that of the electrode surface but of opposite polarity. As a result, the complete structure is electrically neutral.

In addition to the ion distribution and potential profile, important properties of the double layer include its capacitance. The double layer capacitance is an important factor in electroanalytical measurements as well as in sensor technologies and electrocatalytical applications. The double layer capacitance defines the electric field experienced by the species at the surface and within the EDL. The surface capacitance also directly influences how the charge state of the electrode surface depends on the applied potential. In addition, when one drives reactions on the electrode surface by changing the potential, there will always be a contribution from the charging current of the double layer (so-called non-faradic current) to the total current that has to be somehow subtracted from it to obtain the faradic current corresponding to the actual redox reaction under investigation. The charging current arises from the rearrangement of the species constituting the double layer as the potential changes. In fact, there are several electroanalytical techniques, such as differential pulse voltammetry (DPV) and square wave voltammetry (SWV), that have been developed in order to minimize the contributions arising from this background current. This double layer capacitance can be measured with various different ways the simplest being cyclic voltammetry (CV) - if there is a suitable double layer region in the voltammogram. It is to be noted that when measured with CV the double layer capacitance usually contains some fraction of pseudocapacitance from the parasitic faradic reactions occurring during the potential cycling. Another feasible way is to use Electrochemical Impedance Spectroscopy (EIS) where the pseudocapacitance is typically neglible and one obtains smaller (perhaps more correct) values for the capacitance than in the case of CV.

Well-established classical models for the double layer capacitance exist and are reviewed for example in [2] and we will therefore not discuss those here. We just want to emphasize two things of importance: (i) the effect of the electrode on the magnitude of the double layer capacitance and (ii) variation of the...