Electrocapillary curves maximum

Equation V-64 is that of a parabola, and electrocapillary curves are indeed approximately parabolic in shape. Because E ax tmd 7 max very nearly the same for certain electrolytes, such as sodium sulfate and sodium carbonate, it is generally assumed that specific adsorption effects are absent, and Emax is taken as a constant (-0.480 V) characteristic of the mercury-water interface. For most other electrolytes there is a shift in the maximum voltage, and is then taken to be Emax 0.480. Some values for the quantities are given in Table V-5 [113]. Much information of this type is due to Gouy [125], although additional results are to be found in most of the other references cited in this section. 

An important point of the electrocapillary curve is its maximum. Such maximum value of y, obtained when q = 0, corresponds to the potential of zero charge (E ). The surface tension is a maximum because on the uncharged surface there is no repulsion between like charges. The charge on the electrode changes its sign after the... 

Thus an electrocapillary curve can be obtained. The assumption of being independent from the electrode potential has been questioned by Fmmkin et al. [32Fru]. Although closer inspection of the influence of the potential resulted in the conclusion, that the maximum of 0 occurs at (for further disscussions see [69Per]), the method has been used infrequently. 

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. 

Girault and Schiffrin [6] and Samec et al. [39] used the pendant drop video-image method to measure the surface tension of the ideally polarized water-1,2-dichloroethane interface in the presence of KCl [6] or LiCl [39] in water and tetrabutylammonium tetraphenylborate in 1,2-dichloroethane. Electrocapillary curves of a shape resembling that for the water-nitrobenzene interface were obtained, but a detailed analysis of the surface tension data was not undertaken. An independent measurement of the zero-charge potential difference by the streaming-jet electrode technique [40] in the same system provided the value identical with the potential of the electrocapillary maximum. On the basis of the standard potential difference of —0.225 V for the tetrabutylammonium ion transfer, the zero-charge potential difference was estimated as equal to 8 10 mV [41]. 

In situation (b) the anion adsorption is compensated by the negative overall potential of the dme. In situation (c), with a further increase in the negative potential, an electric double layer will now be formed with cations from the solution, so that the apparent <7Hg is lowered again. Hence crHg as a function of the negative dme potential, yielding the so-called electrocapillary curve, shows a maximum at about -0.52 V (see Fig. 3.18). 

The quantity dyl3 In a2 at the potential of the electrocapillary maximum is of basic importance. As the surface charge of the electrode is here equal to zero, the electrostatic effect of the electrode on the ions ceases. Thus, if no specific ion adsorption occurs, this differential quotient is equal to zero and no surface excess of ions is formed at the electrode. This is especially true for ions of the alkali metals and alkaline earths and, of the anions, fluoride at low concentrations and hydroxide. Sulphate, nitrate and perchlorate ions are very weakly surface active. The remaining ions decrease the surface tension at the maximum on the electrocapillary curve to a greater or lesser degree. 

Specific adsorption occurs, i.e. ions enter the compact layer, in a considerable majority of cases. The most obvious result of specific adsorption is a decrease and shift in the maximum of the electrocapillary curve to negative values because of adsorption of anions (see Fig. 4.2) and to positive values for the adsorption of cations. A layer of ions is formed at the interface only when specific adsorption occurs. 

The potential of the electrocapillary maximum can be found from the electrocapillary curve while the Paschen method is an alternative. In this... 

The potential of zero charge, ac, can be obtained from the condition at which Om = - (dy/d.E)=O.This is the potential at which the interfacial tension is maximum in an electrocapillary curve (yvs.E) and is called the electrocapillary maximum. Figure 5-17 illustrates the electrocapillary curves observed for a liquid mercury electrode in aqueous solutions of varioxis anions. It is found that the greater the adsorption affinity of the anions (Cl" < Br" < I") on mercury, the more negative is the potential of zero charge (the potential of electrocapillary maximum). 

A relation between the surface stress and the structural change within the Pb UPD layer on Au film electrode has been studied, applying a bending beam method [487]. A maximum in the surface stress versus potential dependence emerged at the onset of UPD, similarly as in electrocapillary curve. 

The general shape of the curves is roughly parabolic. The coordinates of the maximum in the electrocapillary curve depend on the electrolyte content of the system. Since 7 decreases on both sides of the electrocapillary maximum and since reductions in 7 are associated with adsorption, we conclude that adsorption increases as we move in either direction from the maximum that is, the electrocapillary maximum seems to be a point of minimum adsorption. 

This result shows that the vertical displacements (at fixed potential) of the electrocapillary curve with changes in electrolyte concentration measure the sum of the surface excesses at the solution surface. Curves such as those in Figure 7.23b may be interpreted by this result. We have already seen that T+ = T at the electrocapillary maximum (where E = Emax) therefore... 

If we measure electrocapillary curves of mercury in an aqueous medium which contains KF, NaF, or CsF, then we observe that the typical parabolas become narrower with increasing concentration. Explanation With increasing salt concentration the Debye-length becomes shorter, the capacity of the double layer increases. The maximum of the electrocapillarity curve, and thus the point of zero charge (pzc), remains constant, i.e., neither the cations nor fluoride adsorb strongly to mercury. 

Figure 5.4 ElectrocapiUary curves of mercury measured in different aqueous electrolytes at 18°C. The zero of the applied electric potential was chosen to be at the maximum of the electrocapillary curve for electrolytes such as NaF, Na2S04, and KNO3, which do not strongly adsorb to mercury. Redrawn after Ref. [59].

The fact that the Lippmann equation is the derivative of the electrocapillary equation shows that the charge aM is zero when the slope of the electrocapillary curve is zero. The potential where this occurs is called the point of zero charge, Ez, and occurs at the maximum in the electrocapillary curve, see Fig. 3.3. 

At the maximum of the electrocapillary curve, q = 0, and the ions of opposite sign are adsorbed in equal amounts on the water side of the interface, so that... 

The -> surface tension (y) of the mercury (see electrocapillary curves) is a function of the potential (i.e., the surface charge, a). When o - 0 y has a maximum value, consequently the mercury drop will take a spherical or round shape. When a > 0 y decreases, and the drop tends to flatten. 

Curves 1 (a = 1.0) and 2 (a = 2.0) in Figure 7.2a and those in Figure 7.2b were obtained by adding the curves 1 and 2 in Figure 7. lb to the curves in the absence of the specific adsorption (dashed lines in Figures 7.2a and 7.2b) for the special case when Aq< coincides with the electrocapillary maximum, Aopzc. Resultant electrocapillary curves exhibit dips and the curvature of the electrocapillary curves becomes positive in the middle of the dips both in Figures 7.2a and 7.2b. 

The Integration should start at a reference potential E (p.z.c.) where a° = 0, which coincides with the electrocapillary maximum, e.c.m. Small errors In the establishment of this value lead to an Integration constant In [3.10.61. Generally, the results of the two ways of obtaining a° agree with an accuracy that Is enviable for those working with disperse systems. Double differentiation of electrocapillary curves and comparison with directly measured differential capacitances is more critical but can be achieved within less than 0.2 pF cm", seel). 

The Wilhelmy plate technique has also been modified to measure surface or interfacial tensions under special conditions. By way of illustration we mention the application to the measurement of electrocapillanj curves for the mercuiy-aqueous electrolyte solution interface by Montgomery and Anson ), extending earlier work by Smith ). Electrocapillary curves are plots of y as a function of the potential applied across the interface, which should be polarizable. In fig. II.3.48 we already gave a few such curves. Montgomery and Anson found that their curve in 10 2 M NaF agreed within 0.005 mN m- with data obtained using the maximum bubble pressure. 

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