Inner layer potential difference

Provided that Ag

P2 are constant, and Tjjx is proportional to (c "). The observed nonlinearity at higher electrolyte concentrations [2] is probably due to a change in the inner-layer potential difference A"y>, with the surface excess charge density. The inner-layer potential difference (< 50 mV) was evaluated from the linear part of the Tjj vs. plot, and was found to depend on the nature of the... 

Recently, Samec et al. [38] have investigated the same system by the video-image pendant drop method. Surface tension data from the two studies are compared in Fig. 2, where the potential scale from the study [36] was shifted so that the positions of the electrocapillary maxima coincide. The systematic difference in the surface tension data of ca. 3%, cf. the dotted line in Fig. 2, was ascribed to the inaccurate determination of the drop volume, which was calculated from the shape of the drop image and used further in the evaluation of the surface tension [38]. A point of interest is the inner-layer potential difference A (pj, which can be evaluated relative to the zero-charge potential difference A cpp c by using Eq. 

FIG. 3 Inner-layer potential difference A"y), relative to the zero-charge potential difference... 

Fig. 14. Logarithm of the true forward rate constant vs. the inner layer potential difference relative to the potential of zero charge (corrected Tafel plots) for picrate ion transfer between nitrobenzene solution of 0.1 M Bu4NPh4B and an aqueous solution of (O) 0.05, ( ) 0.1, (V) 0.2, ( ) 0.5, and ( ) 1.0 M LiCl at 298 K. Vertical bars indicate the standard deviation the broken line corresponds to a = 0.5. (After [143]).

FIG. 3 Inner-layer potential difference A zero-charge potential difference Aoexcess surface charge Q for the interface between LiCl in water and tetrabutylammonium tetraphenylborate in nitrobenzene Ref. 38 (full line) and Ref. 36 (dotted line). 

Fig. 7. Inner layer potential difference across the two outer Helmholtz planes as a function of the surface charge density in aqueous phase for the interface between TBATPB(NB) and LiCl(W) at various electrolyte concentrations. The concentration of LiCl was 0.05 ( ), 0.1 (A), 0.2 (O), 0.5 (v), and 1.0 (o) mol dm" when the concentration of TBATPB was 0.1 mol dm and the concentration of TBATPB was 0.05 ( ), 0.1 ( ), and 0.17 (a) mol dm" when the concentration of LiCl was 0.1 mol dm ...

The dashed lines in Fig. 13 show the inner-layer potential difference A cpi as a function of the surface charge density. It is apparent that at a constant value of q, A cpi is not independent of the electrolyte concentration and the same is true for the inner-layer capacitance C - [21]. The second trend is obvious at higher surface charge densities, where the experimental capacitance tends to rise above the Gouy-Chapman value, which would correspond to the negative inner-layer capacitance C,... 

In elementary physics, a capacitor is usually depicted as comprising two layers (or plates ) which are separated by a distance and bear different amounts of charge (Figure 5.3), as seen in practice by the formation of a difference in potential between the two plates. The electric double-layer around the electrode will similarly behave as a capacitor since the inner layer is different from the outer layer in terms of the numbers of ions adsorbed, and hence the total amount of charge it comprises (Figure 5.4). 

Mishuk et a/.675,676 have applied the modified amplitude demodulation method to electrochemically polished pc-Bi in aqueous NaF solution. The curves of the real component of the nonlinear impedance Z" as a function of the electrode potential, unlike pc-Cd and pc-Pb, intersect for various cNaF at E - -0.62 V (SCE),674 i.e., at Ea=0 for pc-Bi, as obtained by impedance.666-672 The different behavior of pc-Bi from pc-Cd and pc-Pb at a > 0 has been explained by the semimetallic nature of pc-Bi electrodes. A comparison of inner-layer nonlinear parameter values for Hg, Cd, and Bi electrodes at a < 0 shows that the electrical double-layer structure at negative charges is independent of the metal.675,676... 

Figure 5.18. Schematic representation of the density of states N(E) in the conduction band and of the definitions of work function d>, chemical potential of electrons p, electrochemical potential of electrons or Fermi level p, surface potential x> Galvani (or inner) potential

Assuming that the two space-charge regions are separated by a layer of solvent molecules (inner layer or mixed solvent layer), the Galvani potential difference can be expressed as the sum of three contributions ... 

From a practical point of view, the potential drop across the inner layer A 02 must be determined by fitting the experimental data to the equations derived from this theoretical approach, which led to some controversy about its value [53,54,56,57]. For the sake of simplicity, and also because recent studies of the ITIES structure do not confirm the presence of an inner layer [51,58], we neglect the finite size of the transferring ion and take X2 = X2 = 0 and A 02 = 0. This is equivalent to accepting that the potential difference Afl02 — A 0 is not modified by the presence of the phospholipids. 

It should be recalled that the term surface potential is used quite often in membranology in rather a different sense, i.e. for the potential difference in a diffuse electric layer on the surface of a membrane, see page 443.) It holds that 0 = 0 + X (this equation is the definition of the inner electrical potential 0). Equation (3.1.2) can then be written in the form... 

The experimental data bearing on the question of the effect of different metals and different crystal orientations on the properties of the metal-electrolyte interface have been discussed by Hamelin et al.27 The results of capacitance measurements for seven sp metals (Ag, Au, Cu, Zn, Pb, Sn, and Bi) in aqueous electrolytes are reviewed. The potential of zero charge is derived from the maximum of the capacitance. Subtracting the diffuse-layer capacitance, one derives the inner-layer capacitance, which, when plotted against surface charge, shows a maximum close to qM = 0. This maximum, which is almost independent of crystal orientation, is explained in terms of the reorientation of water molecules adjacent to the metal surface. Interaction of different faces of metal with water, ions, and organic molecules inside the outer Helmholtz plane are discussed, as well as adsorption. 

There are other ways of estimating inner potential differences. Gi rault and Schiffrin [4] assume that the difference in the inner potential is negligible at the pzc, because the interface consists of an extended layer where both solvents mix, so that any dipole potentials will be small. The resulting scale of Gibbs energies of transfer agrees reasonably well with the TPAs+/TPB scale, if the small difference in the radii of these ions is accounted for. 

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