The Electrocapillary Electrometer

The measurement of surface tension is an old trade in science. There are consequently many methods of determining this quantity. In chemistry, the surface 

To be more exact, we should be talking about the inteifadal tension, which is the surface tension between two specified phases. In electrochemistry it is customary to use the term surface tension to refer to the interfacial tension at the metal/solution interface, or more generaUy, at the interface between an electronic and an ionic conductor. 

This equation shows the pressure difference Ap needed to keep two phases in mechanical equilibrium, if the interface has a radius of curvature r. One shoidd distinguish here between thermodynamic equilibrium and mechanical equilibrium. The former is defined by the condition of minimum Gibbs energy of the system. The latter represents the condition that the vector sum of all forces acting on the interface is zero. When the interface is flat, r goes to infinity and Ap 0. In the present example, the pressure in each capillary is related to the height of the liquid, since 

the capillary rise is determined by the surface tension and the density of the liquid on the one hand, and on the other hand by the radius of curvature, which in this case equals the radius of the capillary. 

The reader may object to the use of an artificial concept such as a negative radius, but this is not an uncommon practice in science. For instance, the capacitive impedance of the metal/solution interface is described as the imaginary part of the impedance, although it is a very real impedance indeed  

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Fig. 3H The electrocapillary electrometer. For each potential the pressure of nitrogen is adjusted to bring the mercury inside the capillary back to the same fixed position.

The concept of the potential of zero charge (PZC or E, has already been discussed in the context of electrocapillary thermodynamics, where we showed that, for an ideally polarizable interphase, the PZC coincides with the electrocapillary maximum. In view of the very high accuracy attainable with the electrocapillary electrometer, it is possible to measure E for liquid metals near room temperature to within about 1 mV. This accuracy is limited, however, to mercury, some dilute amalgams, and gallium. 

Fortunately, the normal manufacturing process of glass tubing produces slightly tapered capillaries, and the problem does not arise, unless one connects the capillary in the electrocapillary electrometer in the wrong direction. 

If the relation between the e.m.f. applied to the terminals of the capillary electrometer, and the interfacial tension between mercury and the electrolyte, is plotted with tension as ordinate and the (negative) potential applied to the small mercury meniscus increasing as abscissae, the curve is called the electrocapillary curve.5... 

In the classical electrocapillary electrometer the configuration is inverted. Mercury is placed in a glass tube that ends with a fine capillary, as shown in Fig. 3H. Since we need pressure to force mercury into a fine capillary, there will be a certain height of mercury column supported by the capillary in this configuration. This is the exact equivalent of the capillary depression shown in Fig. 2H(b), and the height of the column is also given by Eq. 53H. In this equation we note that h depends on y, and the surface tension depends on potential hence, the height of the mercury column above the capillary is a function of potential. 

Setting up an electrocapillary electrometer is a long and tedious process. If one can tolerate lower accuracy, enough to determine and its change with concentration of a certain component in solution, or to determine qualitatively whether adsorption occurs, the drop-time method may be used. ... 

Electrocapillary curves obtained with the Lippmann electrometer are not usually parabolic. For a few electrolytes, such as potassium nitrate (and even then within a limited concentration range) parabolic curves are found but more usually the curves show varying degrees of distortion. Such behaviour is always found with cations and anions which are specifically adsorbed. 

The position of the mercury in the capillary is observed either though a long-focal-length microscope, or by a video camera connected to a high-resolution monitor. We shall not dwell on technical details, except to note that building and operating an electrocapillary electrometer at the desired level of accuracy is a delicate matter requiring both skill and experience. 

Ring method — Method to determine the - interfacial tension in liquid-gas systems introduced by Lecomte du Noiiy [i]. It is based on measuring the force to detach a ring or loop of a wire from the surface of a liquid. The method is similar to the -> Wilhelmyplate method when used in the detachment mode [ii]. See also -> electrocapillarity, -r electrocapillary curve, -> Gibbs-Lippmann equation, - Wilhelmy plate (slide) method, - drop weight method, - Lippmann capillary electrometer. 

It is not obvious why (13.1.31) is called an electrocapillary equation. The name is a historic artifact derived from the early application of this equation to the interpretation of measurements of surface tension at mercury-electrolyte interfaces (1-4, 6-8). The earliest measurements of this sort were carried out by Lippmann, who invented a device called a capillary electrometer for the purpose (9). Its principle involves null balance. The downward pressure created by a mercury column is controlled so that the mercury-solution interface, which is confined to a capillary, does not move. In this balanced condition, the upward force exerted by the surface tension exactly equals the downward mechanical force. Because the method relies on null detection, it is capable of great precision. Elaborated approaches are still used. These instruments yield electrocapillary curves, which are simply plots of surface tension versus potential. 

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