Electric double layer capacities

The subsequent three chapters are devoted to the electric double-layer structure at the interface between immiscible electrolytes examined by the electrocapillary curves method (Prof. Senda and coauthors) and by measurement of the electric double-layer capacity (Dr. Samec and Dr. Mare ek) as well as to the investigation of the Galvani and Volta potentials in the above-mentioned systems (Prof. Koczorowski). These chapters will be of interest to many electrochemists since the results obtained here are comparable with the thoroughly studied metal/electrolyte solution interface. An insignificant potential shift in the compact layer at the interface between immiscible electrolytes in the absence of specific ion adsorption - this is the main conclusion arrived at by the authors of Chaps. 4 and 5. Chapter 6 deals with the scale of potentials in a system of immiscible electrolytes and the thermodynamic relation between the distribution coefficients and the Volta potentials. 

ELECTRICAL DOUBLE-LAYER CAPACITY AND IONIC ADSORPTION... 

WE, acting electrode RE, reference electrode CE, counter electrode Rg, Rg, resistance of solution (gel) Rp charge transfer resistance and electrical double layer capacity... 

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... 

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. 

In an analysis of an electrode process, it is useful to obtain the impedance spectrum —the dependence of the impedance on the frequency in the complex plane, or the dependence of Z" on Z, and to analyse it by using suitable equivalent circuits for the given electrode system and electrode process. Figure 5.21 depicts four basic types of impedance spectra and the corresponding equivalent circuits for the capacity of the electrical double layer alone (A), for the capacity of the electrical double layer when the electrolytic cell has an ohmic resistance RB (B), for an electrode with a double-layer capacity CD and simultaneous electrode reaction with polarization resistance Rp(C) and for the same case as C where the ohmic resistance of the cell RB is also included (D). It is obvious from the diagram that the impedance for case A is... 

The lipid bilayer has a very low water content and its core behaves quite hydrophobically, while the cell wall is rather hydrophilic, containing some 80% of water. Physicochemically, the cell wall is particularly relevant because of its high ion binding capacity, and the ensuing impact on the biointerphasial electric double layer. The presence of such an electric double layer ensures that the cell... 

In the three layer model shown in Fig. 5-8, the electric capacity C of an interfacial electric double layer is represented by a series connection of three... 

The interfacial electric double layer is represented by a combination of the improved jeUium model on the metal side and the hard sphere model of ions and dipoles on the aqueous solution side. Then, the electric capacity, Ch, of the compact layer is given by Eqn. 5-34 ... 

As described in this section, the distance Xta, to the image plane increases with increasing electron density in the electrode metal. Correspondingly, as shown in Fig. 5-24, the capacity of fbo compact layer, Ch, of sp metal electrodes in aqueous solution increases with increasing electron density in the metal. It thus appears that the interfadal electric double layer is affected significantly by the nature (electron density) of the electrode metal. 

Fig. 5-60. Equivalent circuit for an interfacial electric double layer comprising a space charge layer, a surface state and a compact la3 er at semiconductor electrodes Csc = capacity of a space charge layer C = capacity of a surface state Ch = capacity of a compact layer An = resistance of charging and discharging the surface state.

The current density, will be the sum of the faradaic current density, jF, and the charging current density, c, cf. eqn. (8). The latter is related to the interfacial potential indicated in an implicit way by eqn. (20). The theory of the electrical double layer provides no analytical expression for the relation between E and qM and so, rigorously, this part of the problem would have to be solved numerically using the empirical relationship, which is known for many commonly used indifferent electrolytes. If Cd = dqM/dE is the differential double-layer capacity, we have... 

The characteristics of the diffuse electric double layer at a completely polarized interface, such as at a mercury/aqueous electrolyte solution interface are essentially identical with those found at the reversible interface. With the polarizable interface the potential difference is applied by the experimenter, and, together with the electrolyte, specifically adsorbed as well as located in the diffuse double layer, results in a measurable change in interfacial tension and a measurable capacity. 

The differential capacitance between two regions of separated charges is, in general, defined as dQ/dU. Here, Q is the charge on each electrode and U is the voltage. The capacity of an electric double layer per unit area is thus... 

It is instructive to compare this to the capacitance of a plate capacitor o A/d. Here, A is the cross-sectional area and d is the separation between the two plates. We see that the electric double layer behaves like a plate capacitor, in which the distance between the plates is given by the Debye length The capacity of a double layer — that is the ability to store charge — rises with increasing salt concentration because the Debye length decreases. 

An important quantity with respect to experimental verification is the differential capacitance of the total electric double layer. In the Stern picture it is composed of two capacitors in series the capacity of the Stem layer, Cgt, and the capacitance of the diffuse Gouy-Chapman layer. The total capacitance per unit area is given by... 

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