Fase de liquidación

The previous section mainly focussed on adsorption at the gas-solid interface. Here, the structure of the solid electrode/liquid (aqueous) electrolyte interface shall be discussed. When a metal electrode is placed in contact with an electrolyte a potential difference is set up across the interface. The electrode will therefore be either positively or negatively charged with respect to the electrolyte. The electrolyte, interrupted by the electrode, will respond in various ways to the presence of this charged surface. Mainly, electrostatic interactions occur between the electrode and electrolyte. Ions of opposite charge are concentrated at the interface and dipole moments of the solvent molecules may be orientated towards the electrode. Therefore a structure, distinct to the bulk electrolyte, exists at the electrode electrolyte interface. Due to the charge at the electrode along with the opposite charge in solution, this interfacial structure is known as the electrical double layer. Many models have been developed and refined over the years to describe the electrical double layer. [64]

The first model of the electrical double layer was proposed in 1853 by German scientist Hermann von Helmholtz [65]. In the Helmholtz model the double layer is considered as two layers of charge separated by a fixed distance, analogous to a capacitor [64]. The, let’s say, negative charge at the electrode is exactly cancelled out by the layer of positive ions from the electrolyte and the potential drop at the interface is abrupt and linear. The composition of the electrolyte is the same as the bulk at a short distance from the electrode. In this model it is assumed that that the ions approach the electrode up to a distance, known as the Outer

Helmholtz Plane (OHP), which is limited by the ion’s solvation shell. Also it is assumed that a layer of solvation lies between the electrode and the ions. [50]

Figure 9. Schematic representation of the (a) Helmholtz, (b) Guoy-Chapman and (c) Stern models for the electrical double layer at an electrode/electrolyte interface. Below each model are the resulting distributions in

the potential perpendicular to the surface. [50]

The capacitance of the double layer from the Helmholtz model is the same as a parallel plate capacitor and therefore has the equation:

𝐶 =

𝑉

=

𝜀𝜀₀

𝑑 (1)

where ε is the dielectric constant between the plates, ε0 is the electric constant, V is the potential

difference between the plates in volts, σ is the charge held on the plates and d is the distance between the plates. The differential capacitance, the change in charge with voltage, for a parallel plate capacitor is constant, as seen through the following equation

𝜎 =

𝑉

=

Therefore the Helmholtz model for the electrical double layer predicted the same (𝜀𝜀0

𝑑 ) value

for the differential capacitance and capacitance. However, it was later observed that the differential capacitance of the double layer is not constant, as it varies with potential. This factor was then accounted for in the Guoy-Chapmann model [66] by the inclusion of a diffuse layer. In this model, the ions at the electrode surface are dispersed by Brownian motion. The

electrode charge is not cancelled by a single layer of opposite charge at the electrode surface, but by a diffuse layer of ions that are highest in concentration close to the electrode and decrease in concentration with distance. The Guoy-Chapmann model correctly simulates the capacitance observed at potentials close to the point of zero charge (PZC) and also in solutions with low ionic concentration. However, at potentials further from the PZC and at high ionic concentration this model does match observed behaviour. [64]

The next development in modelling of the electrical double layer came from Otto Stern in 1924 [67]. In the Stern model the Helmholtz and the Gouy-Chapman model are combined. Ions are considered to approach up to the point of the OHP as in the Helmholtz model and this can account for some of the potential drop at the electrode-electrolyte interface. The rest of the potential drop occurs throughout a diffuse layer, per the Gouy-Chapman model. In this hybrid model the potential drop is linear between the electrode and the OHP, where a certain amount of ions are immobilised, and is non-linear in the diffusion layer, where ions are spread diffusely through Brownian motion (see figure 9(c)). It must be noted here that the diffusion layer described in this section is different to the diffusion layer discussed later, which is to do with the flow of reactant to the electrode surface. [64]

The capacitance in the Stern model is the total of the capacitance in both the Helmholtz and Gouy-Chapman, diffuse, layers. Considering that these are capacitors in series, the capacitance is then 1 𝐶

=

+

This model is applicable to a greater variety of situations than the Helmholtz and Gouy- Chapman models alone. At high electrolyte concentrations equation 3 simplifies to the Helmholtz model and at low concentrations it simplifies to the Gouy-Chapman model. The Stern model, however, does not simulate the differential capacitance of solutions containing ions which may “specifically” adsorb (discussed below), as it does not account for such a phenomenon.

The next model of the double layer was proposed by Grahame in 1947 [68]. The Grahame model is distinct from those discussed thus far in that some ions are considered able to approach closer to the electrode surface than the OHP, the previous point of closest approach. This was postulated to occur by an ion losing its solvation shell and making direct contact with the

electrode surface. This closer plane of approach was called the inner Helmholtz plane (IHP). Ions that adsorb to the IHP are known as “specifically adsorbed” since this action is particular to certain chemical species. Through specific adsorption, negatively charged solution species, such as Cl- or I-, may specifically adsorb on a negative electrode surface. This is due to the weakly bound hydration shell that surrounds them. Small positively charged ions common to electrolyte solutions, such as Na+, often exhibit a strongly bound hydration layer and rarely specifically adsorb. These aspects mean that, in a solution containing negatively charged ions in contact with a negatively charged electrode, the potential between the electrode and the IHP may actually drop to more negative values, before increasing linearly between the IHP and the OHP. [64]

Figure 10. Grahame model of the double layer at the electrode/electrolyte interface. Charge distribution vs. distance, left, and potential variation vs. distance, right. MS = metal surface, IHP = inner Helmholtz plane, OHP

= outer Helmholtz plane. Reprinted from [64]

The final major contribution to our current understanding (except modern, statistical mechanics based models) of the electrical double layer came from the Bockris-Devanathan-Muller (BDM) model [69]. This model modifies that of the Stern model by considering that solvent molecules are orientated by the electric field of the electrode. The IHP in this model consists of specifically adsorbed species along with a layer of orientated solvent molecules. The second, third, etc. layers of solvent molecules are orientated to a progressively less degree by the charged electrode. Due to this orientation, this model predicts a dielectric constant for the solution which varies throughout the electrical double layer. For water as the solvent the dielectric constant varies from approximately 6 for in the first layer, to approximately 30 in the second, approaching the bulk value in successive layers [64].