Basics notions about electrolyte solutions

In order to understand the electrochemistry of semiconductors some
basics notions about electrolyte solutions are nevessary.

2.1.2 Basics notions about electrolyte solutions

The main component of most electrolytes is water. Therefore it is of importance to know the structure and behaviour of water molecules. Let us consider first a water molecule in its gaseous phase.

When the oxygen atom reacts with the two hydrogen atoms, six valence electrons of oxygen interact with the two electrons from the hydrogen atoms, forming a tetrahedral-like structure with four orbitals oriented in space in four different directions around the oxygen atom. Two orbitals, from four, are used for covalent O-H bonds, whereas the other two remain free. The angle formed by the H-O-H structure is approximately 105o and is slightly smaller than the tetrahedron angle of 109.3o (Figure 2.4a). Due to this distribution of the orbitals the molecules of water have a polarized structure, i.e. the center of negative charge does not coincide with the center of positive one. Thus, a water molecule looks like a dipole.

The structure of water

Figure 2.4: The structure of water

The two remaining free orbitals can also be used to form covalent bonds with other hydrogen ions. This way can be explained the structure of water in its crystalline form, i.e. ice. On the other hand, the structure of the water in the liquid state exhibits a short range order (Figure 2.4b).

However, the electrolytes do not contain only water molecules, but also ions of different elements. Due to the electrical field surrounding each ion, a certain number of water dipoles tend to reorient their directions along the electric field lines. These molecules are forming the so called first solvation level and follow the ion during its movement through solution (Figure 2.5). Outside the first solvation level the interaction between the ion and water molecules is weaker, therefore the dipoles are not strictly oriented along the electrical field lines anymore. The less perfectly oriented water dipoles will form a second solvation level. Finally, at even larger distances from the ion, the water is not desturbed. Thus, an electrolyte has the same structure as pure water, except the disturbances around the ions contained in it.

Solvation layers of ions in water

Figure 2.5: Solvation layers of ions in water

The presence of ions in electrolytes makes them to be ionic rather than electronic conductors as the usual solids are. A theory based on "chemical potentials" can be used in order to describe charge movement in electrolytes. However, when discussing electrolyte solutions in contact with solids it is important to describe the behaviour of ions in solution in the same terms as in the solids (semiconductors, metals etc.), i.e. in terms of energy levels rather than of "chemical potentials" [17].

The electronic energy levels of an ion or molecule in solution reflect the tendency of that species to release (occupied level) or to accept (free level) electrons when the ion/molecule approaches an electrode or another ion. Usually the species in solution have two or more oxidation states, for example K and K+ or Fe2+ and Fe3+. One of the oxidation states (e.g., K) can donate and the other (i.e., K+) can accept an electron.

Unfortunately, the energy level model for solutions is by far more complicated as it is usually encountered in semiconductor physics. This is because the polar solvent which is surrounding the ions (for example water, Figure 2.5) has a great impact on their energy levels, i.e. the solvent affects the potential distribution at the location of the ion. More than that, the solvent obeys thermal fluctuations, therefore the potential at the location of the ion is also fluctuating and consequently the energy levels of the ions will fluctuate as well [18]. Although the energy of thermal fluctuations is small (~kT), the resulting changes in the levels energy are large, typically of about of one electron volt. Thus, the ionic energy levels in solutions must be described in terms of probability distributions, because as a result of thermal fluctuations it is not possible to know exactly the energy of the ionic level at a certain time.

The oxidation states of the ions in solution can be represented schematically as strongly fluctuating energy levels. In Figure 2.6 two oxidation states are shown. The species which prefer to donate an electron are called reducing species (Ered), those which prefer to accept an electron are called oxidizing species (Eox). Pairs of reducing and oxidizing species are called redox couples. In Figure 2.6 two gaussian functions centered at Eox and Ered are sketched, which represent the probability distribution of the fluctuating energy levels in the electrolyte solution. Eox and Ered are the ionic energy levels for the ideal case of a non oscillating solvent.

Fluctuating energy levels in a polar solution.

Figure 2.6: Fluctuating energy levels in a polar solution.

As can be observed from Figure 2.13, the energy of the oxidizing and reducing species in solution are different. The electron transfer is subjected to the Frank-Condon principle. This means that the solvent molecules remain frozen during the transfer, however, after the electron was transferred e.g. from an electrode to Fe3+, the resulted ion Fe2+ has a lower positive charge and the ion-solvent interaction is correspondingly weaker. The solvation shell will therefore relax to a new equilibrium distribution. Thus, the polarization energy arising from the interaction with the solvent effectively splits the electron energy levels of the oxidized and reduced species.

For a solution containing one dominant redox couple it is convenient to define an "effective Fermi level" Eredox similar to the solid. Eredox is defined in such a way that at equilibrium the following relation is satisfied:

Equation 3 (3)

where EF is the Fermi energy of the electrode.

Of particular interest is the redox energy level, Eoredox, of a redox couple when an equal number of reducing and oxidizing species are present in solution. The two redox levels, at different and equal concentrations of oxidizing and reducing species, are related by the following formula

Equation 4 (4)

where [Eox] and [Ered] are the concentrations (activities) of the oxidizing and reducing species respectively. Equation 4 is also known as Nernst equation. More than that, it is possible to demonstrate [19] that Eoredox satisfies the following relation

Equation 5 (5)

Equation 5 is the fundamental definition of Eoredox and is always valid, whereas the Equation 3 is valid only at equilibrium. Thus, for a single redox system with equal concentrations of oxidizing and reducing species, the redox energy level Eoredox in solution is at half-way between the energy level of the oxidizing agent and the energy level of the reducing agent.

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