Electrode differential capacity

According to this model, the experimental electrode differential capacity of the interface, which is potential-dependent, can be described in terms of the capacity of the inner layer CH and the capacity of the diffuse layer Cd. 

It should be noted that the capacity as given by C, = a/E, where a is obtained from the current flow at the dropping electrode or from Eq. V-49, is an integral capacity (E is the potential relative to the electrocapillary maximum (ecm), and an assumption is involved here in identifying this with the potential difference across the interface). The differential capacity C given by Eq. V-50 is also then given by... 

These electrodes have been evaluated in lithium-polymer cells that operate at 85 °C [35]. Although the electrochemical discharge is not yet fully understood, differential capacity plots have shown evidence of two reversible ordering transitions and a kinetically slow phase transformation. 

The electrical double layer at Hg, Tl(Ga), In(Ga), and Ga/aliphatic alcohol (MeOH, EtOH) interfaces has been studied by impedance and streaming electrode methods.360,361 In both solvents the value ofis, was independent of cei (0.01 < cucio4 <0.25 M)and v. The Parsons-Zobel plots were linear, with /pz very close to unity. The differential capacity at metal nature, but at a = 0,C,-rises in the order Tl(Ga) < In(Ga) < Ga. Thus, as for other solvents,120 343 the interaction energy of MeOH and EtOH molecules with the surface increases in the given order of metals. The distance of closest approach of solvent molecules and other fundamental characteristics of Ga, In(Ga), Tl(Ga)/MeOH interfaces have been obtained by Emets etal.m... 

Measurement of the differential capacitance C = d /dE of the electrode/solution interface as a function of the electrode potential E results in a curve representing the influence of E on the value of C. The curves show an absolute minimum at E indicating a maximum in the effective thickness of the double layer as assumed in the simple model of a condenser [39Fru]. C is related to the electrocapillary curve and the surface tension according to C = d y/dE. Certain conditions have to be met in order to allow the measured capacity of the electrochemical double to be identified with the differential capacity (see [69Per]). In dilute electrolyte solutions this is generally the case. 

The second differential of the electrocapillary curve yields the differential capacity of the electrode, C ... 

The differential capacity is given by the slope of the tangent to the curve of the dependence of the electrode charge on the potential, while the integral capacity at a certain point on this dependence is given by the slope of the radius vector of this point drawn from the point Ep = pzc. 

The charge density on the electrode a(m) is mostly found from Eq. (4.2.24) or (4.2.26) or measured directly (see Section 4.4). The differential capacity of the compact layer Cc can be calculated from Eq. (4.3.1) for known values of C and Cd. It follows from experiments that the quantity Cc for surface inactive electrolytes is a function of the potential applied to the electrode, but is not a function of the concentration of the electrolyte. Thus, if the value of Cc is known for a single concentration, it can be used to calculate the total differential capacity C at an arbitrary concentration of the surface-inactive electrolyte and the calculated values can be compared with experiment. This comparison is a test of the validity of the diffuse layer theory. Figure 4.5 provides examples of theoretical and experimental capacity curves for the non-adsorbing electrolyte NaF. Even at a concentration of 0.916 mol dm-3, the Cd value is not sufficient to permit us to set C Cc. 

Opinions differ on the nature of the metal-adsorbed anion bond for specific adsorption. In all probability, a covalent bond similar to that formed in salts of the given ion with the cation of the electrode metal is not formed. The behaviour of sulphide ions on an ideal polarized mercury electrode provides evidence for this conclusion. Sulphide ions are adsorbed far more strongly than halide ions. The electrocapillary quantities (interfacial tension, differential capacity) change discontinuously at the potential at which HgS is formed. Thus, the bond of specifically adsorbed sulphide to mercury is different in nature from that in the HgS salt. Some authors have suggested that specific adsorption is a result of partial charge transfer between the adsorbed ions and the electrode. 

Electroneutral substances that are less polar than the solvent and also those that exhibit a tendency to interact chemically with the electrode surface, e.g. substances containing sulphur (thiourea, etc.), are adsorbed on the electrode. During adsorption, solvent molecules in the compact layer are replaced by molecules of the adsorbed substance, called surface-active substance (surfactant).t The effect of adsorption on the individual electrocapillary terms can best be expressed in terms of the difference of these quantities for the original (base) electrolyte and for the same electrolyte in the presence of surfactants. Figure 4.7 schematically depicts this dependence for the interfacial tension, surface electrode charge and differential capacity and also the dependence of the surface excess on the potential. It can be seen that, at sufficiently positive or negative potentials, the surfactant is completely desorbed from the electrode. The strong electric field leads to replacement of the less polar particles of the surface-active substance by polar solvent molecules. The desorption potentials are characterized by sharp peaks on the differential capacity curves. 

Of the quantities connected with the electrical double layer, the interfacial tension y, the potential of the electrocapillary maximum Epzc, the differential capacity C of the double layer and the surface charge density q(m) can be measured directly. The latter quantity can be measured only in extremely pure solutions. The great majority of measurements has been carried out at mercury electrodes. 

The differential capacity can be measured primarily with a capacity bridge, as originally proposed by W. Wien (see Section 5.5.3). The first precise experiments with this method were carried out by M. Proskurnin and A. N. Frumkin. D. C. Grahame perfected the apparatus, which employed a dropping mercury electrode located inside a spherical screen of platinized platinum. This platinum electrode has a high capacitance compared to a mercury drop and thus does not affect the meaurement, as the two capacitances are in series. The capacity component is measured for this system. As the flow rate of mercury is known, then the surface of the electrode A (square centimetres) is known at each instant ... 

The resulting dependence of Z" on Z (Nyquist diagram) is involved but for values of Rp that are not too small it has the form of a semicircle with diameter Rp which continues as a straight line with a slope of unity at lower frequencies (higher values of Z and Z"). Analysis of the impedance diagram then yields the polarization resistance (and thus also the exchange current), the differential capacity of the electrode and the resistance of the electrolyte. 

The impedance can be measured in two ways. Figure 5.23 shows an impedance bridge adapted for measuring the electrode impedance in a potentiostatic circuit. This device yields results that can be evaluated up to a frequency of 30 kHz. It is also useful for measuring the differential capacity of the electrode (Section 4.4). A phase-sensitive detector provides better results and yields (mostly automatically) the current amplitude and the phase angle directly without compensation. 

In order to determine the electrochemical properties of the solvent, the electrode process in molten carbamide and in carbamide-MeCl (where Me - NH4, K) mixtures on inert electrodes (platinum, glassy carbon) were investigated using cyclic voltammetry. The electrode reaction products were analysed by spectroscopic methods. The adsorbtion of carbamide- NH4CI anodic product was investigated by differential capacity method. 

Figure 4. Differential capacity of Pt electrode in carbamide-NH4Cl melt (curve 1) and after 0.5 (curve 2), 1 (curve 3), 1.5 (curve 4), 2 (curve 5) hours of electrolysis.

Electrocapiilary phenomena on Hg-electrode in presence and absence of an adsorbate (camphor). From a measurement of interfacial tension (a) (e.g., from droptime of a Hg-electrode) or of differential capacity (d) (e.g., by an a.c-method) as a function of the electrode potential (established by applying a fixed potential across tine Hg-electrolyte interface) one can calculate the extent of adsorption (b) (from (a) by the Gibbs Equation) and of the structure of the interface as a function of the surface potential. Figs, a, c and d are interconnected through the Lippmann Equations. 

A comparison with the reversible interface can be made. The reversible solid electrolyte interface can be used in a similar way to explore the distribution of charge components at solid-water interfaces. As we have seen, the surface charge density, o, (Eqs. (3.1) and (iii) in Example 2.1) can be readily determined experimentally (e.g., from an alkalimetric titration curve). The Lippmann equations can be used as with the polarized electrodes to obtain the differential capacity from... 

Comparison between the polarized electrode-electrolyte interface and the reversible (Al203) oxide-electrolyte interface. Surface tension (interfacial) tension, charge density and differential capacity, respectively, are plotted as a function of the rational potential vy (at pzc vy is set = 0) in the case of Hg and as a function of ApH (pH-pH ) in the case of Al203 (pH = pHpzc when a = 0). 

The role of supporting electrolyte in adsorption processes is sometimes unclear. The adsorption of mannitol and sucrose on the Hg electrode from NaF and NaCl solutions shows that CT ions exert small, though observable, effects on the differential capacity curves (the saturation coverage and surface excess are slightly different in both solutions). Unexpectedly, at low surface excess of sucrose, the adsorption of sucrose is greater in the NaCl than in the NaF solution. At high surface excesses, the opposite situation is observed. 

Amokrane and Badiali proposed a semiempirical approach to the determination of the solvent contribution C, to the capacitance of the double layer in aqueous and nonaqueous " solutions. They used the relation C = Cf - C m, where Q is the experimentally determined capacity of the inner layer and Cm is the contribution of the metal. The plots ofC, vs. (Tm were presented for various solvents and correlated with their properties.However, the problem of the supporting electrolyte was entirely neglected in the quoted papers. It was shown recently that the height and position of the maximum on the C, vs. Gm plots depend on the type of the supporting electrolyte. Experimental differential capacity data obtained on the Hg electrode in methanol and ethanol containing various electrolytes with nonadsorbing anions (F , PFg, ClOi) indicate that the type as well as concentration of the electrolyte influences the position and the height of the maximum on the C, vs. plots (Fig. 13). 

Fig. 6-24. Inverse differential capacity 1/Ch of a compact layer as a function of electron density n, of polycrystalline sp-metal electrodes in aqueous solution open drdes = observed solid line = calculated au s atomic unit. [From Schmidder, 1993.]...

Fig. 6-96. Change in differential capacity of an interfadal double layer leading or not leading to interfadal lattice transformation in anodic and cathodic potential sweeps for a gold electrode surface (100) in perchloric add solution Ey = critical potential beyond which the interfadal lattice transforms from (5 x 20) to (1 x 1) E = critical potential below which the interfadal lattice transforms from (1 x 1) to (5 x 20) Ejm = potential of zero charge VacE = volt referred to the saturated calomel electrode. [From Kolb-Schneider, 1985.]...

Figure 5-45 shows the differential capacity for an intrinsic semiconductor electrode of germanium estimated by calculation as a function of electrode potential. Here, the capacity is minimum at the flat band potential, Ea, where is zero. As the electrode potential shifts so far away from that the Fermi level at the interface may be dose to the band edge levels, Fermi level pinning is reaUzed both with A sc remaining constant and with Csc being constant and independent of the electrode potential. 

Fig. 5-46. Differential capacity estimated for an electrode of intrinsic semiconductor of germanium by calculation as a function of electrode potential C = electrode capacity solid curve = capacity of a space charge broken curve = capacity of a series connection of a space charge layer and a compact layer. [From Goischer, 1961.)...

Fig. 6-46. Differential capacity observed and computed for an n-type semiconductor electrode of zinc oxide (conductivity 0. 59 S cm in an aqueous solution of 1 M KCl at pH 8.5 as a function of electrode potential solid curve s calculated capacity on Fermi distribution fimction dashed curve = calculated capacity on Boltzmann distribution function. [From Dewald, I960.]...

Fig. 6-48. Differential capacity of a space charge layer of an n-type semiconductor electrode as a function of electrode potential solid cunre = electronic equilibrium established in the semiconductor electrode dashed curve = electronic equilibrium prevented to be established in the semiconductor electrode AL = accumulation layer DL = depletion layer IL = inversion layer, DDL - deep depletion layer.

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