Electrocapillary effect

Alternately, for potential-step experiments (e.g., chronoamperometry see Section 3.1), the charging current is the same as that obtained when a potential step is applied to a series RC circuit  

the current decreases exponentially with time. Here, E is the magnitude of the potential step, while Rs is the (uncompensated) solution resistance. 

Measurements of the double-layer capacitance provide valuable insights into adsorption and desorption processes, as well as into the structure of film-modified electrodes (6). 

Further discussion of the electrical double layer can be found in several reviews (5,7-11). 

Electrocapillary is the study of the interfacial tension as a function of the electrode potential. Such a study can shed useful light on the structure and properties of the electrical double layer. The influence of the electrode-solution potential difference on the surface tension (y) is particularly pronounced at nonrigid electrodes (such as the dropping mercury one, discussed in Section 4.5). A plot of the surface tension versus the potential (like the ones shown in Fig. 1.13) is called an electrocapillary curve. 

Electrocapillarity is the study of the mterfacial tension as a function of the electrode potential. Such a study can provide useflil msight into the sfraicture and properties of 

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

tire differential capacitance represents the slope of the plot of q vs. E. 

An unpoitant pomt of the electr ocapillaiy cruwe is its maximum. Such maximum value of 7, obtained when = 0, conesponds to the potential of zero charge (E. The surface tension is a maxumim 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 Electrocapillaiy ciuve (smface tension y vs. potential). 

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It has long been known that the form of a curved surface of mercury in contact with an electrolyte solution depends on its state of electrification [108, 109], and the earliest comprehensive investigation of the electrocapillary effect was made by Lippmann in 1875 [110]. A sketch of his apparatus is shown in Fig. V-10. 

It is necessary that the mercury or other metallic surface be polarized, that is, that there be essentially no current flow across the interface. In this way no chemical changes occur, and the electrocapillary effect is entirely associated with potential changes at the interface and corresponding changes in the adsorbed layer and diffuse layer. 

A. Thermodynamics of the Electrocapillary Effect The basic equations of electrocapillarity are the Lippmann equation [110]... 

FIG. 7.22 Schematic illustration of an apparatus to measure the electrocapillary effect. 

What is the electrocapillary effect How is it used to study adsorption of solutes under an applied potential ... 

We start this chapter with electrocapillarity because it provides detailed information of the electric double layer. In a classical electrocapillary experiment the change of interfacial tension at a metal-electrolyte interface is determined upon variation of an applied potential (Fig. 5.1). It was known for a long time that the shape of a mercury drop which is in contact with an electrolyte depends on the electric potential. Lippmann1 examined this electrocapillary effect in 1875 for the first time [68], He succeeded in calculating the interfacial tension as a function of applied potential and he measured it with mercury. 

Hydrodynamic Mode Selection Due to the Electrocapillary Effect The Mercury Beating Heart in Neutral and Basic Solutions. 

Fig. 2. Cyclic voltammogram/stress curves of electrocapillary effects on a gold(l 1 l)-coated cantilever in 0.1 MKCl. Scan rate lOmVs. ...

The basic EW theory elucidated here has been directly extended to analyze electrocapillary effects under AC electrical fields as well. For instance, if the AC frequency correspruids to a timescale that is less than the hydrodynamic response time of the droplet (typically O.Ol s for mm-sized droplets), the droplet shape and contact angle evolution can be described by employing instantaneous quasi-equilibrium considerations in accordance with Eq. 13. On the other hand, for higher fi-equencies, the droplet response depends only on the r.m.s value of the applied voltage, so long as the liquid can be... 

Electrocapillary effect Electrowetting on dielectric (EWOD) Electrowetting on insulator-coated electrodes (EICE) Electrowetting on line electrodes (ELE)... 

Figure 6 shows the effect of surfactant concentration on interfacial tension and electrophoretic mobility of oil droplets (14). It is evident that the minimum in interfacial tension corresponds to a maximum in electrophoretic mobility and hence in zeta potential at the oil/brine interface. Similar to the electrocapillary effect observed in mercury/water systems, we believe that the high surface charge density at the oil/brine interface also contributes to lowering of the interfacial tension. This correlation was also observed for the effect of caustic concentration on the interfacial tension of several crude oils (Figure 7). Here also, the minimum interfacial tension and the maximum electrophoretic mobility occurred in the same range of caustic concentration (17). Similar correlation for the effect of salt concentration on the interfacial tension and electrophoretic mobility of a crude oil was also observed (18). Thus, we believe that surface charge density at the oil/brine interface is an important component of the ultralow interfacial tension.

The basic EW theory elucidated here has been directly extended to analyze electrocapillary effects under AC electric fields as well. For instance, if the AC frequency corresponds to a time scale that is less than the hydrodynamic response time of the droplet (typically 0.01 s for mm-sized droplets), the droplet shape and contact angle evolution can be described by employing instantaneous quasiequilibrium considerations in accordance with Eq. (13). On the other hand, for higher frequencies, the droplet response depends only on the r.m.s value of the applied voltage, so long as the liquid can be treated as a perfect conductor. However, beyond a critical frequency (a>c), the dissolved ions cannot follow the applied field and therefore, cannot screen the electric field from the interior of the liquid [2]). Far beyond a>c, the droplet behaves like a dielectric, and is effectively actuated by dielectrophoresis mechanisms. For homogeneous bulk liquids, a>c (Ti/si, where <7 and are the conductivity and permittivity of the liquid, respectively. For a t)fpical aqueous solution (such as NaCl, with cr 0.1 Sm ), o)c 10 s However, for demineralised water (tr 10 Sm ), a>c can be as low as 10 s . ... 

E. K.Venstrem, P. A. Rebinder, The electrocapillary effect of the lowering of the hardness of metals, Doklady Akademii Nauk SSSR, 68 (1949) 329-332. 

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