Differential capacity determination

The variation of the integral capacity with E is illustrated in Fig. V-12, as determined both by surface tension and by direct capacitance measurements the agreement confrrms the general correctness of the thermodynamic relationships. The differential capacity C shows a general decrease as E is made more negative but may include maxima and minima the case of nonelectrolytes is mentioned in the next subsection. 

The zero-charge potential is determined by a number of methods (see Section 4.4). A general procedure is the determination of the differential capacity minimum which, at low electrolyte concentration, coincides with Epzc (Section 4.3.1). With liquid metals (Hg, Ga, amalgams, metals in melts) Epzc is directly found from the electrocapillary curve. 

In this manner, the surface excess of ions can be found from the experimental values of the interfacial tension determined for a number of electrolyte concentrations. These measurements require high precision and are often experimentally difficult. Thus, it is preferable to determine the surface excess from the dependence of the differential capacity on the concentration. By differentiating Eq. (4.2.30) with respect to EA and using Eqs (4.2.24) and (4.2.25) in turn we obtain the Gibbs-Lippmann equation... 

According to Eq. (4.3.13) the differential capacity of the diffuse layer Cd has a minimum at 2 = 0, i.e. at E = Epzc. It follows from Eq. (4.3.1) and Fig. 4.5 that the differential capacity of the diffuse layer Cd has a significant effect on the value of the total differential capacity C at low electrolyte concentrations. Under these conditions, a capacity minimum appears on the experimentally measured C-E curve at E — Epzc. The value of Epzc can thus be determined from the minimum of C at low electrolyte concentrations (millimolar or lower). 

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. 

Experimentally either the electrocapillary curve or the differential capacity (as a function of y) is determined. From either set of data, the interfacial properties (adsorption and/or charge) as a function of y and a quantitative description of the structure of the interface can be obtained. 

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... 

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). 

Naneva and Popov et al. [4, 5] have studied Cd(OOOl) grown electrolytically in a Teflon capillary in NaF aqueous solution. A value of fpzc equal to —0.99 V (versus saturated calomel electrode (SCE)) was evaluated from minimum potential (Amin) on the differential capacity C-E curves obtained in dilute electrolyte. The zero charge potential was found to be practically independent of the crystallographic orientation. The Apzc and the irmer layer capacity of Cd(OOOl) single crystals were determined in KF solution as a function of temperature [5]. The positive values of AApzc/AT indicated that the water dipoles in the inner part of the double layer were orientated with their negative part to the electrode surface. It was found that the hydrophilicity of the electrodes was increasing in the order Cd(OOOl) < Ag(100)[Pg.768]

Some conclusions pertaining to adsorption of 1-pentanol riboflavin and thioctic acid on Au electrode have been drawn from differential capacity-potential curves [274]. It has been found, for instance, that adsorption of these compounds obeys the Langmuir isotherm. Moreover, the free energies of adsorption have been determined. 

Turowska etal. [166] have studied adsorption of m-hydroxybenzoic acid in aqueous solutions on the dropping mercury electrode and determined the surface tension, differential capacity, and the potential of zero charge for this system. 

Recently, Japaridze etal. [170] have investigated adsorption of some aromatic compounds, including naphthalene, naphthonitrile, naphthylamine, anthracene, and phenathrene at the mercury electrode I ethylene glycol solution interface. The analysis of the differential capacity data obtained at the HMDE has revealed that adsorption of the above-mentioned compounds obeys the Frumkin model, with attractive interactions of the particles in the adsorption layer. The results for ethylene glycol were compared with those for other nonaqueous solvents and their role in determining the adsorption mode was discussed. 

Chronopotentiometry, galvanostatic transients, 1411 as analytical technique, 1411 activation overpotential, 1411 Clavilier, and single crystals, 1095 Cluster formation energy of, 1304 and Frumkin isotherm, 1197 Cobalt-nickel plating, 1375 Cold combustion, definition, 1041 Cole-Cole plot, impedance, 1129, 1135 Colloidal particles, 880, 882 and differential capacity, 880 Complex impedance, 1135 Computer simulation, 1160 of adsorption processes, 965 and overall reaction, 1259 and rate determining step, 1260... 

The measurement of the differential capacity is now the most widely used method of determining the flat band potential

semiconductor materials the values of [Pg.267]

Now we briefly touch upon certain practical applications concerning the measurement of photopotential. Its measurement is a convenient method to determine the flat band potential

limiting case of very intensive illumination the bands unbend completely, i.e., the flat band potential is attained. Tyagai and Kolbasov (1975) used this technique to measure (plb for several AnBVI semiconductors the values obtained are in good agreement with those measured by the differential capacity method. 

Another useful thermodynamic relationship that allows the potential dependence of l to be determined from the differential capacity Co, of the interphase at constant rs is readily obtained from the very definition of l. Choosing Ez as the reference potential and denoting by lz the electrosorption valency at Ez, the l value at any other applied potential E is given by ... 

This equation can be used to determine V if the differential capacity C is extrapolated to zero frequency, namely under the quasi-equilibrium conditions required to apply the electrocapillary equation for a thermodynamic estimate of dE/dE (see Eq. 12) ... 

Since l is a thermodynamic quantity, the most reliable procedures for its determination are based on a thermodynamic analysis of adsorption data, possibly at low coverages. Adsorption data to be analyzed by the Gibbs adsorption equation can be obtained by measuring the interfacial tension y, the charge density crM or the differential capacity C. Direct y measurements are equilibrium measurements that can only be carried out on mercury. Direct charge measurements are conveniently carried out by the potential-step chronocoulometric technique, which can be... 

The simplest model of solvent structure in the inner layer is that proposed by Watts-Tobin [36]. In this treatment, the inner layer is assumed to consist of a monolayer of solvent dipoles represented as hard spheres the dipoles may assume one of two orientations, that is, with the electrode field or against it (fig. 10.23). By estimating the relative concentrations of the two orientations, the potential drop across the monolayer, and its differential capacity may be found as a function of electrode charge density. In order to calculate the electrochemical potential of a dipolar molecule, one must determine the local field at the position of the molecule. In general, the local field is given by the sum of the field due to the charge... 

A certain relationship, which exists between the bulk and surface properties of semiconducting materials and their electrochemical behavior, enables, in principle, electrochemical measurements to be used to characterize these materials. Since 1960, when Dewald was the first to determine the donor concentration in a zinc oxide electrode using Mott-Schottky plots, differential capacity measurements have frequently been used for this purpose in several materials. If possible sources of errors that were discussed in Section III.3 are taken into account correctly, the capacity method enables one to determine the distribution of the doping impurity concentration over the surface" and, in combination with the layer-by-layer etching method, also into the specimen depth. The impurity concentration profile can be constructed by this method. It has recently been developed in greatest detail as applied to gallium arsenide crystals and multilayer structures. 

The macroscopic description of the adsorption on electrodes is characterised by the development of models based on classical thermodynamics and the electrostatic theory. Within the frames of these theories we can distinguish two approaches. The first approach, originated from Frumkin s work on the parallel condensers (PC) model,attempts to determine the dependence of upon the applied potential E based on the Gibbs adsorption equation. From the relationship = g( ), the surface tension y and the differential capacity C can be obtained as a function of E by simple mathematical transformations and they can be further compared with experimental data. The second approach denoted as STE (simple thermodynamic-electrostatic approach) has been developed in our laboratory, and it is based on the determination of analytical expressions for the chemical potentials of the constituents of the adsorbed layer. If these expressions are known, the equilibrium properties of the adsorbed layer are derived from the equilibrium equations among the chemical potentials. Note that the relationship = g( ), between and , is also needed for this approach to express the equilibrium properties in terms of either or E. Flere, this relationship is determined by means of the Gauss theorem of electrostatics. 

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