Electroanalytical Chemistry. Gary A. Mabbott

between two different phases. In potentiometric experiments, interesting processes give rise to a separation of charge at the boundary between the sample and sensor; in voltammetric experiments an outside power source applies a voltage to the working electrode creating a separation of charge that drives interesting processes there. It is common for charges to appear at many different phase boundaries in nature, for example, at the surface of biological cell walls, on the surface of water droplets or solid aerosols, and at the surface of wet materials such as ceramics, clays, sediments, and soils. The same electrochemical principles that are involved in electrochemical analysis drive lots of natural phenomena as well. One of the most important concepts that is universal is the boundary between two phases where charges accumulate. It is called the electrified interface or the electrical double layer.

      1.4.1 Structure of the Double Layer

      There are numerous electrochemical sensors that selectively respond to a specific chemical species of interest. For example, fluoride is routinely monitored in municipal drinking water by fluoride selective electrodes. Lithium ion can be determined in the blood or urine of a patient being treated for depression by lithium‐containing medications using a lithium ion selective electrode. These devices are popular because of their simplicity of use and their reliability. The increasing interest in monitoring select chemical species in clinical, environmental, industrial settings and, more recently, in private homes and for personal health monitoring is likely to encourage the development and implementation of even more sensors of this type.

The heart of all electrochemical sensing devices is the boundary between the sensor and the test solution. It is there that a charge separation develops. Because of its importance, it is very useful to take a closer look at the structure of the boundary. Consider, for example, a metal wire dipping into a salt solution. Assume, for the sake of discussion, that an excess of negative charge (i.e. electrons) appears on the wire. Electromagnetic theory predicts that the excess charge will appear at the surface of the metal. The arrangement of charges on the solution side is a bit more complicated. The excess electrons will naturally attract cations from solution. In the mid‐nineteenth century, the German scientist Herman Helmholtz imagined that all of the cations necessary to balance the charge on the metal surface migrate into position at a small distance from the surface forming a plane of charge [5]. It is now known that the cations do not actually come into contact with the metal surface because a monolayer of water molecules cling directly to the surface and are not easily displaced. Furthermore, individual cations are surrounded by a sphere of water molecules, known as the hydration sphere, that are also tightly bound. As a consequence, the cations approach the electrode surface no closer than about a distance equal to the length of two water molecules (about 5–6 Å total). Figure 1.5 shows cations with their hydration spheres parked in a line outside a layer of water molecules attached to the electrode surface. The centers of these cations represent a layer now known as the OHP. In the Helmholtz model, the charge on the OHP is equivalent in magnitude to the charge on the metal. This model closely resembles a simple capacitor.

      (1.18)

Figure 1.5 The Helmholtz model of the electrified boundary between a metal surface (dark spheres) with a net negative charge and an aqueous salt solution. (a) Cations are attracted to the surface forming a net positive layer to balance the negative charge in the metal. Water molecules occupy the first layer on the metal surface. They also surround ions in solution aligning their dipoles according to the type of charge on the ion. (Arrows point toward the oxygen atoms.) The charges on the solution side define a layer called the outer Helmholtz plane (OHP) [5]. (b) The double layer of charge behaves like a capacitor producing an electrical potential energy difference between the two layers whose magnitude is proportional to the charge.

In cases where the solid surface has a net positive charge, it attracts an excess of anions to balance the charge and the OHP is occupied by an excess of anions. In some cases, individual anions are able to come into direct contact with the metal surface. This phenomenon is called contact adsorption. Whether or not contact adsorption occurs depends upon the net free energy for three separate steps in the overall adsorption process. Two of the steps are obviously endothermic. Removing water molecules from the electrode surface to make room for the anion and removing part of the hydration sphere around the ion both cost energy. Therefore, only interactions between the ion and the electrode surface that lead to strong bonds make the adsorption process favorable. The electrostatic attractions between oppositely charged ions and the electrode are not decisive by themselves. Contact adsorption relies on London dispersion forces, overlap of electron orbitals, and image forces. An image force is similar to the mechanism known as London dispersion forces where a momentary dipole resulting from the instantaneous arrangement of charge density around a molecule induces a rearrangement of electron density in a neighboring molecule creating a momentary dipole that results in dipole–dipole attraction. Unlike London dispersion forces, the image force is created by a permanent dipole or a charge on the ion inducing a dipole or local excess of charge in the electrode that leads to attraction at that location. The plane that includes the center of ions that are contact‐adsorbed to the electrode surface is often called the inner Helmholtz plane (IHP) (see Figure 1.6). An interesting consequence of these additional forces is that some anions can remain attached to the electrode surface even when the electrode is also negatively charged. To account for contact adsorption, the equation for the charge balance becomes

      (1.19)

Figure 1.6 The inner Helmholtz plane (IHP) is a plane parallel to the electrode drawn through the center of ions or neutral molecules adsorbed directly in contact with the electrode surface. London and image forces as well as electron overlap between the metal and ion are responsible for the net attraction. These forces can result in binding even when charge considerations oppose adsorption [5].

The model of Helmholtz suggests that all of the counter ions necessary to balance the charge on the electrode are held rigidly near the electrode surface. However, the experimental evidence suggests that thermal forces are great enough to dislocate counter ions to some degree. These observations inspired work by Louis Gouy [6] and by David Chapman [7] that led to a different model [5]. They proposed that the counter ions are distributed in a nonuniform manner with a high concentration of counter ions near the electrode that falls off exponentially with distance from the electrode surface (Figure 1.7).

Figure 1.7 (a) Gouy–Chapman model of electrical double layer showing a diffuse region of excess charge on the solution side. (Solvent molecules are not shown for clarity.) (b) The excess concentration drops off exponentially with distance from the electrode surface.

Unfortunately, this diffuse–charge model seemed to overcompensate. Experiments indicate that only a fraction of the charge appears to be disrupted by