Polarizable interphase

Fig. 1.5 Current-potential plot for polarizable and non-polarizable interphases...

Charged components may or may not be able to cross the interface between the two phases. In this respect, interphases may be divided into limiting types, unpolariz-able and polarizable, respectively. Ideally, unpolarizable interphases are those in which the exchange of common-charged components between the phases proceed unhindered. Ideally, polarizable interphases are those in which there are no common components between the phases, or their exchange is hampered. Real interphases may approach, more or less well, one of the above two idealized cases. 

Fig. 13G Current response to a triangular potential sweep, plotted on an X-Y recorder, (a) ideally polarizable interphase (b) real interphase, with finite faradaic current.

What are the differences between this equation and the corresponding equation (Eq. 29H), for the ideally polarizable interphase ... 

The concept of the potential of zero charge (PZC or E, has already been discussed in the context of electrocapillary thermodynamics, where we showed that, for an ideally polarizable interphase, the PZC coincides with the electrocapillary maximum. In view of the very high accuracy attainable with the electrocapillary electrometer, it is possible to measure E for liquid metals near room temperature to within about 1 mV. This accuracy is limited, however, to mercury, some dilute amalgams, and gallium. 

Fig. 3A HE plots for polarizable nonpolarizable inter-phases. It is hard to pass a current across a polarizable interphase, while it is hard to change the potential of a nonpolarizable interphase.

If one studies an (almost) ideally polarizable interphase, such as the mercury electrode in pure acids, there is no need to measure at high frequency. In this case the equivalent circuit is a resistor and a capacitor in series. The accuracy of measurement is actually enhanced by making measurements at lower frequencies, since the impedance of the capacitor is higher. The high accuracy and resolution offered by modem instmmentation allows measurement in such cases in very dilute solutions or in poorly conducting nonaqueous media, which could not have been performed until about a decade ago. 

For the ideally polarizable interphase, they are all independent. For the ideally nonpolarizable interphase, only two can be controlled independently. We recall that an ideally nonpolarizable electrode is a reversible electrode. By setting the concentrations (more accurately, the activities) of ions in the two phases, we determine the potential. Alternatively, by selling the potential, we determine the ratio of concentrations of this ion in the two phases. We conclude that the electrocapillary equation for the nonpolarizable interphase must have one less degree of freedom. 

This equation makes all the difference between a nonpolarizable and a polarizable interphase. The rest of the derivation follows the lines given in Section 17.3. We write... 

If double-layer charging is the only process taking place in a given potential region (this would be the case for an ideally polarizable interphase) and one cycles the potential between two fixed values, the results should be such as shown in Fig. 2L(a). Plotting Ai = i - i = 2 i as a function of v, as shown by line 1 in Fig. 2L(b), one can obtain the value of the double-layer capacitance from the slope. If a faradaic reaction is taking place, a result such as shown by line 2, from which C can still be obtained (cf. Fig. 14G), might be observed. 

The thermodynamic treatment of ideally polarizable interphase (the term used when no charged component is common in two adjoining phases) leading to the Gibbs adsorption equation owing to the nature of the thermodynamic approach conveys no information about the structure of the interphase and has nothing to do with the forces playing role in the formation of this structure. 

The strict thermodynamic analysis of the interphase is based on data available from the bulk phases (concentration variables) and the total amount of material involved in the whole system figuring in the relations expressing the relative surface excess of suitably chosen (charged or not charged) components of the system. In addition, the Gibbs equation for a polarizable interphase contains a member related to the potential difference between one of the phases (metal) and a suitably chosen reference electrode immersed in the other phase (solution) (and attached to a piece of the same metal that forms one of the phases). 

The degree of polarizability of system can be found from the data calculated by Le Hung [25] with the use of Eqs. (16) and (17). In the equilibrium state of the interphase between the solutions of 0.05 M LiCl in water and 0.05 M TBATPhB in nitrobenzene, the concentrations of Li and CL in the organic phase lower than 10 M, and the concentrations of TBA and TPhB in the aqueous phase are about 3 x 10 M each [3]. These concentrations are too low to establish permanent reversible equilibria. They are, however, significantly higher compared to those of the components present in the mercury-aqueous KF solution system [20]. 

What are the capabilities of this system Since the system consists of a polarizable interface coupled to a nonpolarizable interface, changes in the potential of the external source are almost equal to the changes of potential only at the polarizable interface, i.e., the changes in zl< ) across the mercuiy/solution interface are almost equal to changes in potential difference Vacross the terminals of the source. Hence, the system can be used to produce predetermined zl< ) changes at the mercuiy/solution interface (Section 6.3.11). Further, measurement of the surface tension of the mercuiy/solution interface is possible, and since this has been stated /Section 6.4.5) to be related to the surface excess, it becomes possible to measure this quantity for a given species in the interphase. In short, the system permits what are called electrocapillary measurements, i.e., the measurement of the surface tension of the... 

Indeed, a small current does flow, though not across the interphase. It is called a charging current, i.e., a current observed because there is an electron flow either out of the electrode or into it. But this latter current does not result in any electrons crossing the interphase it s like charging the plates of a condenser. A perfectly polarizable electrode is the analogue of an absolutely leakproof condenser. 

As implied, no real electrode is exactly like a polarizable or a nonpolarizable electrode. But the idealizations of completely polarizable (potential changes, but no current flows across the interphase), or completely nonpolarizable (current passes, but there is no potential change) electrodes are useful. Real electrodes tend to be more like the one or the other of the two ideals. 

In the mechanisms to be described in this section, one of the idealizations of electrochemistry is being portrayed. Thus, in perfectly polarizable metal electrodes, it is accepted that no charge passes when the potential is changed. However, in reality, a small current does pass across a perfectly polarizable electrode/solution interphase. In the same way, here the statement free from surface states (which has been assumed in the account given above) means in reality that the concentration of surface states in certain semiconductors is relatively small, say, less than 10 states cm. So when one refers to the low surface state case, as here, one means that the surface of the semiconductor, particularly in respect to sites energetically in the energy gap, is covered with less than the stated number per unit area. A surface absolutely free of electronic states in the surface is an idealization. (If 1012 sounds like a large number, it is in fact only about one surface site in a thousand.) A consequence of this is the location of the potential difference at the interphase of a semiconductor with a solution. As shown in Fig. 10.1(a), the potential difference is inside the semiconductor, and outside in the solution there is almost no potential difference at all. 

When a small current or potential is applied, the response is in many cases linear. The effective resistance can, however, vary over a wide range. When this resistance is high, we refer to it as a polarizable interface, since a small current generates a high potential across it (i.e., it polarizes the interphase to a large extent). 

It may be appropriate to ask here why the potential at a reversible electrode should change at all with current density. This does not occur because "no system is really ideally polarizable", and one is observing a small polarization. Indeed the relationship shown in Eq. 17D holds strictly only when the interphase is ideally nonpolariz-able. Each value of the potential given by Eq. 17D represents the reversible potential for the concentration of the species at the surface, C(s). These concentrations deviate, however, from the corresponding bulk concentrations C° as a result of mass-transport limitations, according to Eq. 13D. 

If we wish to measure the capacitance as a function of potential, it is possible to apply a relatively slow triangular potential waveform, and determine the current as a function of potential. If the interphase is highly polarizable, the result will be that shown in Fig. 13G(a). If there is a significant faradaic current, a plot such as shown in Fig. 13G(b) will be observed. Ideally the box representing the anodic and cathodic charging currents in Fig. 13G(a) should be symmetrical around zero. Unfortunately, this is rarely the case. The best way to calculate the capacitance from such experiments is to conduct measurements over a range of sweep rates, obtaining from the plot of Ai = i - i versus dE/dt, as shown in Fig. 14G. 

A third electrode is not needed in this case, since the mercury-solution interphase is assumed to be ideally polarizable. 

But the Mg/Il O inlerphase is not ideally polarizable in this case How is the notion of an ideally nonpolarizable interphase introduced into... 

Equations 49H and 50H explain why there has been little interest in obtaining the electrocapillary curve for ideally nonpolarizable interphases. On the other hand, this analysis can give us a feel for the type and magnitude of error that may arise when measurements are conducted with an electrode that is presumed to be ideally polarizable but in fact does allow some faradaic current to flow across the interphase. 

The difference between polarizable and nonpolarizable interphases can be easily understood in terms of this equivalent circuit. A high... 

If the interphase is ideally polarizable, the faradaic resistance approaches infinity, and the equivalent circuit shown in Fig. lG(a) can be simplified to that shown in Fig. 2G(b). If it is ideally nonpolari-zable, the faradaic resistance tends to zero, and the equivalent circuit shown in Fig. lG(c) results. Real systems never behave ideally, of course they may approach one extreme behavior or the other, or be... 

The formation of 2D Meads phases on a foreign substrate, S, in the underpotential range can be well described considering the substrate-electrolyte interface as an ideally polarizable electrode as shown in Section 8.2. In this case, only sorption processes of electrolyte constituents, but no Faradaic redox reactions or Me-S alloy formation processes are allowed to occur, The electrochemical double layer at the interface can be thermodynamically considered as a separate interphase [3.54, 3.212, 3.213]. This interphase comprises regions of the substrate and of the electrolyte with gradients of intensive system parameters such as chemical potentials of ions and electrons, electric potentials, etc., and contains all adsorbates and all surface energy. Furthermore, it is assumed that the chemical potential //Meads is a definite function of the Meads surface concentration, F, and the electrode potential, E, at constant temperature and pressure Meads (7", ). Such a model system can only be... 

The thermodynamics of 2D Meads overlayers on ideally polarizable foreign substrates can be relatively simply described following the interphase concept proposed by Guggenheim [3.212, 3.213] and later applied on Me UPD systems by Schmidt [3.54] as shown in Section 8.2. A phase scheme of the electrode-electrolyte interface is given in Fig. 8.1. Thermodynamically, the chemical potential of Meads is given by eq. (8.14) as a result of a formal equilibrium between Meads and its ionized form Me in the interphase (IP). The interphase equilibrium is quantitatively described by the Gibbs adsorption isotherm, eq. (8.18). In the presence of an excess of supporting electrolyte KX, i.e., c , the chemical potential is constant and... 

The thermodynamics of an Me UPD system forming a 2D Meads phase and a 2D Me-S surface alloy phase on top of unmodified S are the same as the thermodynamics of a 2D Meads phase on an ideally polarizable foreign substrate S (cf. Sections 3.3 and 8.2). However, both phases belong to the interphase and cannot be thermodynamically distinguished. Information on the different binding energies of Me in a 2D Meads phase and a 2D Me-S surface alloy phase can be obtained from kinetic measurements. 

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