Solutions, electrochemical potential electrons

Figure Bl.28.9. Energetic sitiration for an n-type semiconductor (a) before and (b) after contact with an electrolyte solution. The electrochemical potentials of the two systems reach equilibrium by electron exchange at the interface. Transfer of electrons from the semiconductor to the electrolyte leads to a positive space charge layer, W. is the potential drop in the space-charge layer.

The huge literature on the electronic conductivity of dry conducting polymer samples will not be considered here because it has limited relevance to their electrochemistry. On the other hand, in situ methods, in which the polymer is immersed in an electrolyte solution under potential control, provide valuable insights into electron transport during electrochemical processes. It should be noted that in situ and dry conductivities of conducting polymers are not directly comparable, since concentration polarization can reduce the conductivity of electrolyte-wetted films considerably.139 Thus in situ conductivities reported for polypyrrole,140,141 poly thiophene,37 and poly aniline37 are orders of magnitude lower than dry conductivities.15... 

Electrolyte solutions ordinarily do not contain free electrons. The concept of electrochemical potential of the electrons in solution, ft , can stiU be used for those among the bound electrons that will participate in redox reactions in the solution. Consider the equilibrium Ox + ne Red in the solution. In equilibrium, the total change in Gibbs energy in the reaction is zero hence the condition for equilibrium can be formulated as... 

When the solution in this redox system is in contact with a nonconsumable metal electrode (e.g., a platinum electrode), the equilibrium set up also implies equal electrochemical potentials, and pp, of the electrons in the metal and electrolyte. 

It follows from the Franck-Condon principle that in electrochemical redox reactions at metal electrodes, practically only the electrons residing at the highest occupied level of the metal s valence band are involved (i.e., the electrons at the Fermi level). At semiconductor electrodes, the electrons from the bottom of the condnc-tion band or holes from the top of the valence band are involved in the reactions. Under equilibrium conditions, the electrochemical potential of these carriers is eqnal to the electrochemical potential of the electrons in the solution. Hence, mntnal exchange of electrons (an exchange cnrrent) is realized between levels having the same energies. 

At electrode potentials more negative than approximately - 2.8 V (SHE), free solvated electrons appear in the solution as a result of (dark) emission from the metal. At this potential the electrochemical potential of the electrons according to Eq. (29.6) is about —1.6 eV, which is at once the energy of electron hydration in electron transfer from vacuum into an aqueous phase. 

Because of the excess holes with an energy lower than the Fermi level that are present at the n-type semiconductor surface in contact with the solution, electron ttansitions from the solution to the semiconductor electrode are facilitated ( egress of holes from the electrode to the reacting species ), and anodic photocurrents arise. Such currents do not arise merely from an acceleration of reactions which, at the particular potential, will also occur in the dark. According to Eq. (29.6), the electrochemical potential, corresponds to a more positive value of electrode potential (E ) than that which actually exists (E). Hence, anodic reactions can occur at the electrode even with redox systems having an equilibrium potential more positive than E (between E and E ) (i.e., reactions that are prohibited in the dark). 

Figure 29.4 shows an example, the energy diagram of a cell where n-type cadmium sulfide CdS is used as a photoanode, a metal that is corrosion resistant and catalytically active is used as the (dark) cathode, and an alkaline solution with S and S2 ions between which the redox equilibrium S + 2e 2S exists is used as the electrolyte. In this system, equilibrium is practically established, not only at the metal-solution interface but also at the semiconductor-solution interface. Hence, in the dark, the electrochemical potentials of the electrons in all three phases are identical. 

Fig. 3.4 A metal in contact with a solution of an oxidation-reduction system. (A) Situation before the contact when the electrochemical potential of electrons in the electronic conductor (fiXa) = f(< )) has a different value from the electrochemical potential of electrons in the oxidation-reduction system. (B) When the phases are in contact the electrochemical potential of electrons becomes identical in both a and by charge transfer between them...

Oxidation-reduction electrodes. An inert metal (usually Pt, Au, or Hg) is immersed in a solution of two soluble oxidation forms of a substance. Equilibrium is established through electrons, whose concentration in solution is only hypothetical and whose electrochemical potential in solution is expressed in terms of the appropriate combination of the electrochemical potentials of the reduced and oxidized forms, which then correspond to a given energy level of the electrons in solution (cf. page 151). This type of electrode differs from electrodes of the first kind only in that both oxidation states can be present in variable concentrations, while, in electrodes of the first kind, one of the oxidation states is the electrode material (cf. Eqs 3.1.19 and 3.1.21). 

Basic properties of semiconductors and phenomena occurring at the semiconductor/electrolyte interface in the dark have already been discussed in Sections 2.4.1 and 4.5.1. The crucial effect after immersing the semiconductor electrode into an electrolyte solution is the equilibration of electrochemical potentials of electrons in both phases. In order to quantify the dark- and photoeffects at the semiconductor/electrolyte interface, a common reference level of electron energies in both phases has to be defined. 

Emersion has been shown to result in the retention of the double layer structure i.e, the structure including the outer Helmholtz layer. Thus, the electric double layer is characterised by the electrode potential, the surface charge on the metal and the chemical composition of the double layer itself. Surface resistivity measurements have shown that the surface charge is retained on emersion. In addition, the potential of the emersed electrode, , can be determined in the form of its work function, , since and represent the same quantity the electrochemical potential of the electrons in the metal. Figure 2.116 is from the work of Kotz et al. (1986) and shows the work function of a gold electrode emersed at various potentials from a perchloric acid solution the work function was determined from UVPES measurements. The linear plot, and the unit slope, are clear evidence that the potential drop across the double layer is retained before and after emersion. The chemical composition of the double layer can also be determined, using AES, and is consistent with the expected solvent and electrolyte. In practice, the double layer collapses unless (i) potentiostatic control is maintained up to the instant of emersion and (ii) no faradaic processes, such as 02 reduction, are allowed to occur after emersion. 

Fig. 10 Electrochemical energy level model for orbital mediated tunneling. Ap and Ac are the gas-and crystalline-phase electron affinities, 1/2(SCE) is the electrochemical potential referenced to the saturated calomel electrode, and provides the solution-phase electron affinity. Ev, is the Fermi level of the substrate (Au here). The corresponding positions in the OMT spectrum are shown by Ar and A0 and correspond to the electron affinity and ionization potential of the adsorbate film modified by interaction with the supporting metal, At. The spectrum is that of nickel(II) tetraphenyl-porphyrin on Au (111). (Reprinted with permission from [26])...

For a metal, the negative of the work function gives the position of the Fermi level with respect to the vacuum outside the metal. Similarly, the negative of the work function of an electrochemical reaction is referred to as the Fermi level Ep (redox) of this reaction, measured with respect to the vacuum in this context Fermi level is used as a synonym for electrochemical potential. If the same reference point is used for the metal s,nd the redox couple, the equilibrium condition for the redox reaction is simply Ep (metal)= Ep(redox). So the notion of a Fermi level for a redox couple is a convenient concept however, this terminology does not imply that there are free electrons in the solution which obey Fermi-Dirac statistics, a misconception sometimes found in the literature. 

Thus, the electrochemical potential difference between an electron in the solution and in the electrode is related to the absolute electrode potential. If the solution composition is assumed to be constant with potential, the chemical potential and dipole potential of the solution are constant. Thus, the ability of an electron to transfer across the interface for a given solution composition is controlled exclusively by the electrode potential. 

Fig. 4-17. Electronic electrode in equilibrium of electron transfer OX = hydrated oxidant particles RED = hydrated reductant partides FWEDQx, s) = Fermi level of redox electrons in hydrated redox partides in solution S p. = electrochemical potential of electrons.

We now consider a transfer reaction of charged particles across the interface of electrodes. For a hydrated particle in aqueous solution, the electrochemical potential of the particle is independent of the electrode potential, though it depend on the activity of the partide (the concentration of the partide), regardless of whether the partide is charged (ion) or noncharged (neutral partide). In contrast, for a charged particle (electron or ion) in the electrode, the electrochemical potential of the particle depends on both the electrode potential E and the absolute activity Xk Pk = A7 lnXk-i-zeE. From Eqn. 7-34 we then obtain Eqn. 7-35 for the reaction order, Ck, with respect to a charged particle k in the electrode if the activity of k is constant ... 

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