Charging of double layers

Charge density of electrode, determination, 858 Charge of double layer, 1217 Charge transfer, 1213 mechanism, 1294 overpotential and, 1172 rate determining step and, 1179 steady state and. 1213 transport in electrolyte, 1211 Charge transfer, equilibrium at interface kinetic treatment. 1058 Nemst s equilibrium treatment, 1058 polarography, 1240 thermodynamics, 1057... 

However, at least one additional current component has to be taken into account, because of the charging of -> double layer while stepping the potential from 1 to 2- The equation for the time dependence of the - capacitive current is given under the entry -> charging current. 

Correct experimental conditions and preliminary evaluations of the data are of vital importance. The effects of non-kinetic factors—charging of double layer, non-planarity and finiteness of diffusion—have to be eliminated. 

However, at least one additional current component has to be taken into account, because of the charging of double layer while stepping the potential from F to F2. After the application of a potential step of magnitude F = F2—E1, the exponential decay of the current with time depends on the double-layer capacitance (Ca) and the solution resistance (RJ, i.e., on the time constant x = Cj. Consequently, if we assume that Cd is constant and the capacitor is initially uncharged (g = 0 at < = 0), for the capacitive charge (gc)> we obtain ... 

Stem layer adsorption was involved in the discussion of the effect of ions on f potentials (Section V-6), electrocapillary behavior (Section V-7), and electrode potentials (Section V-8) and enters into the effect of electrolytes on charged monolayers (Section XV-6). More speciflcally, this type of behavior occurs in the adsorption of electrolytes by ionic crystals. A large amount of wotk of this type has been done, partly because of the importance of such effects on the purity of precipitates of analytical interest and partly because of the role of such adsorption in coagulation and other colloid chemical processes. Early studies include those by Weiser [157], by Paneth, Hahn, and Fajans [158], and by Kolthoff and co-workers [159], A recent calorimetric study of proton adsorption by Lyklema and co-workers [160] supports a new thermodynamic analysis of double-layer formation. A recent example of this is found in a study... 

Even in the absence of Faradaic current, ie, in the case of an ideally polarizable electrode, changing the potential of the electrode causes a transient current to flow, charging the double layer. The metal may have an excess charge near its surface to balance the charge of the specifically adsorbed ions. These two planes of charge separated by a small distance are analogous to a capacitor. Thus the electrode is analogous to a double-layer capacitance in parallel with a kinetic resistance. 

The simplest, and by far the most common, detection scheme is the measurement of the current at a constant potential. Such fixed-potential amperometric measurements have the advantage of being free of double-layer charging and surface-transient effects. As a result, extremely low detection limits—on the order of 1-100 pg (about 10 14 moles of analyte)—can be achieved, hi various situations, however, it may be desirable to change the potential during the detection (scan, pulse, etc.). 

Hence, for two similarly charged surfaces in electrolyte, interactions are determined by both electrostatic doublelayer and van der Waals forces. The consequent phenomena have been described quantitatively by the DLVO theory [6], named after Derjaguin and Landau, and Verwey and Over-beek. The interaction energy, due to combined actions of double-layer and van der Waals forces are schematically given in Fig. 3 as a function of distance D, from which one can see that the interplay of double-layer and van der Waals forces may affect the stability of a particle suspension system. 

Overbeek and Booth [284] have extended the Henry model to include the effects of double-layer distortion by the relaxation effect. Since the double-layer charge is opposite to the particle charge, the fluid in the layer tends to move in the direction opposite to the particle. This distorts the symmetry of the flow and concentration profiles around the particle. Diffusion and electrical conductance tend to restore this symmetry however, it takes time for this to occur. This is known as the relaxation effect. The relaxation effect is not significant for zeta-potentials of less than 25 mV i.e., the Overbeek and Booth equations reduce to the Henry equation for zeta-potentials less than 25 mV [284]. For an electrophoretic mobility of approximately 10 X 10 " cm A -sec, the corresponding zeta potential is 20 mV at 25°C. Mobilities of up to 20 X 10 " cmW-s, i.e., zeta-potentials of 40 mV, are not uncommon for proteins at temperatures of 20-30°C, and thus relaxation may be important for some proteins. 

ScheUman, JA Stigter, D, Electrical Double Layer, Zeta Potential, and Electrophoretic Charge of Double-Stranded DNA, Biopolymers 16, 1415, 1977. 

Many studies at single-crystal electrodes of xp-metals were directed at the special features of double-layer stracture and the potential of zero charge at the various single-crystal faces. It was shown that rather large differences could exist between the potentials of zero charge of different faces (see Table 10.1). 

This chapter is devoted to the behavior of double layers and inclusion-free membranes. Section II treats two simple models, the elastic dimer and the elastic capacitor. They help to demonstrate the origin of electroelastic instabilities. Section III considers electrochemical interfaces. We discuss theoretical predictions of negative capacitance and how they may be related to reality. For this purpose we introduce three sorts of electrical control and show that this anomaly is most likely to arise in models which assume that the charge density on the electrode is uniform and can be controlled. This real applications only the total charge or the applied voltage can be fixed. We then show that predictions of C < 0 under a-control may indicate that in reality the symmetry breaks. Such interfaces undergo a transition to a nonuniform state the initial uniformity assumption is erroneous. Most... 

FIG. 7 Simplified equivalent circuit for charge-transfer processes at externally biased ITIES. The parallel arrangement of double layer capacitance (Cdi), impedance of base electrolyte transfer (Zj,) and electron-transfer impedance (Zf) is coupled in series with the uncompensated resistance (R ) between the reference electrodes. (Reprinted from Ref. 74 with permission from Elsevier Science.)... 

Since the sorbing surface holds a charge, its electrical potential differs from that of the solution. The potential difference between surface and fluid is known as the surface potential T and can be expressed in volts. The product e 4 is the work required to bring an elementary charge e from the bulk solution to the sorbing surface. According to one of the main results of double layer theory, the surface potential is related to the surface charge density by,... 

If the reaction is too fast for this procedure, a double-pulse method can be used The current pulse is preceded by a short but high pulse which is designed to charge the double layer. The height of the pulse is adjusted in such a way that the transient 77(f) is horizontal at the... 

This proportionality to the scan rate is reminiscent of double-layer charging, leading to the appellation pseudo-capacitance, reflecting the fact that a Faradaic type of current is exchanged between the electrode and the molecules attached to the surface. 

Overlapping of Double-Layer Charging and Faradaic Currents in Potential Step and Double Potential Step Chronoamperometry. Oscillating and Nonoscillating Behavior... 

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