Electrocapillary curves

Fig. V-11. Electrocapillary curves (a) adsorption of anions (from Ref. 113) (b) absorption of cations (from Ref. 6) (c) electrocapillary curves for -pentanoic acid in QAN HCIO4. Solute activities from top to bottom are 0, 0.04761, 0.09096, 0.1666, and 0.500 (from Ref. 112).

The shape of the electrocapillary curve is easily calculated if it is assumed that the double layer acts as a condenser of constant capacity C. In this case, double integration of Eq. V-50 gives... 

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. 

Fig. V-12. Variation of the integral capacity of the double layer with potential for 1 N sodium sulfate , from differential capacity measurements 0, from the electrocapillary curves O, from direct measurements. (From Ref. 113.)...

The location and shape of the entire electrocapillary curve are affected if the general nature of the medium is changed. Fawcett and co-workers (see Ref. 126) have used nonaqueous media such as methanol, V-methylformamide, and propylene carbonate. In earlier studies, electrocapillaiy curves were obtained for O.OIA/ hydrochloric acid in mixed water-ethanol media of various compositions [117, 118]. The surface adsorption of methanol, obtained from... 

Rehbinder and co-workers were pioneers in the study of environmental effects on the strength of solids [144], As discussed by Frumkin and others [143-145], the measured hardness of a metal immersed in an electrolyte solution varies with applied potential in the manner of an electrocapillary curve (see Section V-7). A dramatic demonstration of this so-called Rehbinder effect is the easy deformation of single crystals of tin and of zinc if the surface is coated with an oleic acid monolayer [144]. 

A typical example of an ideal polarizable interface is the mercury-solution interface [1,2]. From an experimental point of view it is characterized by its electrocapillary curve describing the variation of the interfacial tension 7 with the potential drop across the interface, 0. Using the thermodynamic relation due to Lippmann, we get the charge of the wall a (-a is the charge on the solution side) from the derivative of the electrocapillary curve ... 

Fig. 20.5 Electrocapillary curves for KNO3, and different potassium halides showing how the former approximates to a parabola...

Fig. 20.6 Electrocapillary curves for HCI at various concentrations determined using a reversible hydrogen electrode (R.H.E.) immersed in the same concentration of HCI as that used for the determination (after Bockris and Reddy )...

It follows that the surface excess F of an anion / (e.g. the Cl ion) can be evaluated from the electrocapillary curves of a given electrolyte (e.g. HCl) by plotting surface tension against the logarithm of the activity of the electrolyte (evaluated at various constant potentials) and determining the slope of the curve dy/d log and introducing it into equation 20.7. 

The above provides a means of showing how the total excess charge on the solution side of the interface q the excess charge due to cations F+ and the excess charge due to anions F, vary with potential in a solution of fixed concentration of electrolyte. On the basis of this approach to the electrocapillary curves it has been shown that the Gibbs surface excess for cations is due solely to electrostatic forces (long-range coulombic), and this is reflected in the fact that the electrocapillary curves for different cations and... 

The simple Helmholz model, in which the charge on the model is regarded as the plate of a capacitor that attracts a counter layer of ions of opposite charge and results in two parallel plates of the same charge density, is inconsistent with the shapes of the electrocapillary curves obtained in practice. It can be shownthat if the Helmholz model applied, the electrocapillary curve would conform to the relationship... 

The excess charge on the electrode can be obtained from the slope of the electrocapillary curve (at any potential), by the Lippman equation ... 

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... 

FIGURE 1-14 Electrocapillary curve (surface tension y vs. potential). 

FIGURE 1-15 Electrocapillary curves for different electrolytes showing the relative strength of specific adsorption. (Reproduced with permission from reference 5.)... 

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. 

FIGURE 10.8 Influence of the adsorption of organic substances (a) on the electrocapillary curve, (b) on the capacitance curve, and (c) on the plot of surface charge against potential (1) 0.1 M H2SO4 solution (2) the same, with 0.1 MC4H9OH. 

Electrocapillary curves, i.e., the interfacial tension vs. the applied potential curves are well known for the mercury-solution interface and have been utilized also for interpreting the... 

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