Outer potential difference

The inner and outer potential differ by the surface potential Xa — (fa — ipa- This is caused by an inhomogeneous charge distribution at the surface. At a metal surface the positive charge resides on the ions which sit at particular lattice sites, while the electronic density decays over a distance of about 1 A from its bulk value to zero (see Fig. 2.1). The resulting dipole potential is of the order of a few volts and is thus by no means negligible. Smaller surface potentials exist at the surfaces of polar liquids such as water, whose molecules have a dipole moment. Intermolecular interactions often lead to a small net orientation of the dipoles at the liquid surface, which gives rise to a corresponding dipole potential. 

The standard electrode potential [1] of an electrochemical reaction is commonly measured with respect to the standard hydrogen electrode (SHE) [2], and the corresponding values have been compiled in tables. The choice of this reference is completely arbitrary, and it is natural to look for an absolute standard such as the vacuum level, which is commonly used in other branches of physics and chemistry. To see how this can be done, let us first consider two metals, I and II, of different chemical composition and different work functions 4>i and 4>ii-When the two metals are brought into contact, their Fermi levels must become equal. Hence electrons flow from the metal with the lower work function to that with the higher one, so that a small dipole layer is established at the contact, which gives rise to a difference in the outer potentials of the two phases (see Fig. 2.2). No work is required to transfer an electron from metal I to metal II, since the two systems are in equilibrium. This enables us calculate the outer potential difference between the two metals in the following way. We first take an electron from the Fermi level Ep of metal I to a point in the vacuum just outside metal I. The work required for this is the work function i of metal I. 

We should like to define a work function of an electrochemical reaction which enables us to calculate outer potential differences in the same way for a metal-solution interface, and this work function should also refer to the vacuum. For this purpose we consider a solution containing equal amounts of Fe3+ and Fe2+ ions in contact with a metal M, and suppose that the reaction is at equilibrium. We now transfer an electron from the solution via the vacuum to the metal in the following way ... 

The scale of electrochemical work functions makes it possible to calculate the outer potential difference between a solution and any electrode provided the respective reaction is in equilibrium. A knowledge of this difference is often important in the design of electrochemical systems, for example, for electrochemical solar cells. However, in most situations one needs only relative energies and potentials, and the conventional hydrogen scale suffices. 

The difference in the work functions causes the flow of electrons from the metal with the lower work function to that with the higher one, so that a surface dipole moment is created. This effect is similar to the establishment of an outer potential difference at the contact between two different metals (see Chapter 2). An adsorbate layer does not have a work function in the same... 

Fig. 4-6. llie inner potential, 4, and the outer potential, tf, of two condensed phases A and B before and after their contact d4 )= inner (outer) potential difference between two contacting phases o = surface or interface charge dip = surface or interface dipole. 

Obviously, the interfacial charge differs from the initial (before contact) surface charges oa and ob (oa/b " Oa + ob) and the interfacial dipole dipA/s is not the same as the arithmetic sum of the initial surface dipoles igtjaibt) XA(dip)-Xadip)) Thus, it follows that both the inner and the outer potential differences, A( >a/b and Ai a , between the two contacting phases are not the same as those and Atp A/B before the contact. As a result, Eqn. 4-2 yields Eqn. 4-4 ... 

The inner potential difference between two contacting phases is cafied in electrochemistry the Galvani potential difference, and the outer potential difference is called the Volta potential difference. The outer potential difference corresponds to what is called the contact potential between the two phases. We call, in this test, the inner potential difference across an interface the interfacial potential. 

The outer potential difference between two contacting phases can be measured because it is a potential difference between two points in the same vacuum or gas phase outside the free surfaces of the two phases. On the other hand, the inner potential difference can not be measured, because the potential measuring probe introduces its interfacial potential that differs with the two phases and thus can not be canceled out this gives rise to an unknown potential in the potential measurement. 

Fig. 4-7. Ihe inner potential difference, d n/s, and the outer potential difference, dtpu/s, between a solid metal M and an aqueous solution S (a) charged interface where = gwauip) gwsio), (b) zero charge interface where - gM/scsp).

In the case of nonpolaiizable interfaces, the inner and the outer potential differences, 4>a/b and v a/b, are determined by the equilibrium of chai transfer that occurs across the interface. Figure 4—8 shows the electron energy levels in two sohd metals A and B before and after they are brought into contact with each other. As a result of contact, electrons in a metal B of the hi er electron level (the lower work function ) move into a metal A of the lower electron level (the higher work fiuiction), and the Fermi levels of the two metals finally become equal to each other in the state of electron transfer equilibrium. The electrochemical... 

Fig. 4- Electron energy levels of two different metals A and B in (a) isolated state and in (b) contact state e s electron energy a,= real potential of electrons in metal ty = Fermi level of electrons in metal MtJB = inner potential difference AtpA/B = outer potential difference.

Next, we consider the interface M/S of a nonpolarizable electrode where electron or ion transfer is in equilibrium between a solid metal M and an aqueous solution S. Here, the interfadal potential is determined by the charge transfer equilibrium. As shown in Fig. 4-9, the electron transfer equilibrium equates the Fermi level, Enn) (= P (M)), of electrons in the metal with the Fermi level, erredox) (= P s)), of redox electrons in hydrated redox particles in the solution this gives rise to the inner and the outer potential differences, and respectively, as shown in Eqn. 4-10 ... 

For partially immersed electrodes, as shown in Fig. 4-13, an outer potential difference di )n/s arises between the free surface of the electrode and the free surface of the electrol3de solution Anpius equals the difference in the real potential of electron (aeelectrode isolated fix>m the electrolyte solution as in Eqn. 4-15 ... 

Fi p 6-14. Inner and outer potential differences, AApk and at the zero charge interface between metal M and aqueous solution S. 

The Outer Potential Difference, MAsy, between the Metal and the Solution... 

At this stage, let the two conceptually separated pails of the double layer be brought together again. The interface has been reassembled. One can now refer to the outer potential difference, sometimes called the Volta potential difference, between the metal and solution. This outer potential difference is written... 

Hence, the Y / potentials of the metal and solution phases correspond to the charges that these phases actually have in the presence of the double layer at a metal/solution interface. The outer potential difference MAS / is, therefore, the contribution to the potential difference across an electrified interface arising from the charges on the two phases. 

The argument just presented can be extended to the differences of the various potentials. The outer potential difference A f can be measured (Klein and Lange Appendix 6.1) the surface potential difference A% cannot and therefore the inner potential differences d< ) = d y + Ax also cannot be experimentally obtained. 

Second, the inner potential difference across a double layer, d(J), was defined. It was determined that this inner potential can be resolved into two contributions. One of them, the outer potential difference or A jJ, emerged from the chaiges in the electrode and/or in the solution, and was found to be a measurable quantity. The other potential, the surface potential difference or A%, was due to the oriented dipoles existing on one... 

This outer potential difference is also called the Volta potential (also Volta potential difference, contact potential difference, or outer potential difference). It represents the potential difference between one point close to the electrode outer surface and the end point of the diffuse layer in the solution. The relationship between the outer and inner potentials can be expressed as ... 

Comparing Equations (2.22) and (2.25), it can be seen that the sum difference in the inner potential differences of the two electrodes is equal to that of the outer potential differences. 

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