Surface tension, potential-dependent

Surface tension-potential difference curves for each electrolyte against mercury are plotted in the capillary electrometer, the result being shown in Fig. 16. At P there is, according to Helmholtz, no potential difference between Hg — KC1, and at R none between Hg — KI. If the effects at the interface were purely electrostatic, i.e., dependent only on the lines of force, and if the anions had no specific influence, then QS should be zero. Actually, however, it represents a potential difference of 0 2 volt. 

The decrease in the surface tension at constant adsorption, occurring in agreement with the Gibbs equation, is solely due to the increase in chemical potential of the adsorbed substance caused by the increased concentration of the latter in solution. As is commonly known, the increase in the chemical potential in a stable two-component system always corresponds to the concentration increase. For the present case it translates into the increase of surface concentration, and consequently, of the adsorption. Therefore, in the concentration region where the surface tension linearly depends on the log of concentration, a slow but finite, increase in adsorption not detected experimentally should occur. At the same time a sharp increase in the chemical potential of the surfactant molecules in the adsorption layer... 

The Marcus theory is difficult to apply directly in a practical situation, owing to lack of knowledge of the probability of the formation of protrusions. One way to overcome this problem could be to employ capillary wave theory for the interface between two immiscible electrolyte solutions. Recently, theoretical efforts have been made to describe capillary waves at soft electrified interfaces [83]. It may be possible to use such theories to quantify the value of P(h)Ah. One of the major complications is related to the fact that the surface tension is dependent on the Gal-vani potential difference between the two... 

This potential depends on the interfacial tension am of a passivated metal/electrolyte interface shifting to the lower potential side with decreasing am. The lowest film breakdown potential AEj depends on the surface tension of the breakdown site at which the film-free metal surface comes into contact with the electrolyte. A decrease in the surface tension from am = 0.41 J m"2 to nonmetallic inclusions on the metal surface, will cause a shift of the lowest breakdown potential by about 0.3 V in the less noble direction. 

Figure 18 shows the dependence of the activation barrier for film nucleation on the electrode potential. The activation barrier, which at the equilibrium film-formation potential E, depends only on the surface tension and electric field, is seen to decrease with increasing anodic potential, and an overpotential of a few tenths of a volt is required for the activation energy to decrease to the order of kBT. However, for some metals such as iron,30,31 in the passivation process metal dissolution takes place simultaneously with film formation, and kinetic factors such as the rate of metal dissolution and the accumulation of ions in the diffusion layer of the electrolyte on the metal surface have to be taken into account, requiring a more refined treatment. 

In 1873, Gabriel Lippmann (1845-1921 Nobel prize, 1908) performed extensive experiments of the electrocapiUary behavior of mercury and established his equation describing the potential dependence of the surface tension of mercury in solutions. In 1853, H. Helmholtz, analyzing electrokinetic phenomena, introduced the notion of a capacitor-like electric double layer on the surface of electrodes. These publications... 

FIG. 2 Potential dependence of the surface tension of the interface between 0.1 M LiCl in water and 0.05 M tetrabutylammonium tetraphenylborate in nitrobenzene, taken from Ref. 38 ( ) and Ref. 36 ( ). The dotted line represents the data from Ref. 38 multiplied by a factor of 0.97. The potential scale from Ref. 36 was shifted so that the positions of the electrocapillary maxima coincide. 

Thus, we now have a reasonable model of the interface in terms of the classical Helmholtz model that can explain the parabolic dependence of y on the applied potential. The various plots predicted by equation (2.18) are shown in Figures 2.5(a) to (c). The variation in the surface tension of the mercury electrode with the applied potential should obey equation (2.18). Obtaining the slope of this curve at each potential V (i.e. differentiating equation (2.18)), gives the charge on the electrode, [Pg.49]

The quantities defined by Eqs. (2)—(7) plus Vs max, Vs min, and the positive and negative areas, A and, enable detailed characterization of the electrostatic potential on a molecular surface. Over the past ten years, we have shown that subsets of these quantities can be used to represent analytically a variety of liquid-, solid-, and solution-phase properties that depend on noncovalent interactions [14-17, 84] these include boiling points and critical constants, heats of vaporization, sublimation and fusion, solubilities and solvation energies, partition coefficients, diffusion constants, viscosities, surface tensions, and liquid and crystal densities. 

The potential model used in these simulations was truncated at 2.5 atomic diameters, while in our calculations the potential was truncated at 8.0 diameters. The effect of this difference in the model may be significant, particularly for small droplets. However, given the considerable difficulties in the evaluation of the surface tension by either Equation 24 or 25, the qualitative agreement with simulation reinforces the observation which is essential to an analysis of nucleation theoiy the radial dependence of the surface tension is much stronger than previously thought. 

Thus, in principle, we could determine the adsorption excess of one of the components from surface tension measurements, if we could vary ii independently of l2. But the latter appears not to be possible, because the chemical potentials are dependent on the concentration of each component. However, for dilute solutions the change in p for the solvent is negligible compared with that of the solute. Hence, the change for the solvent can be ignored and we obtain the simple result that... 

The interfacial tension depends on the forces arising from the particles present in the interphase region. If the arrangement of these particles (Le., the composition of the interface) is altered by varying, for example, the potential difference across the interface, then the forces at the interface should change and thus cause a change in the interfacial tension. One would expect therefore that the surface tension y of the metal/solution interface will vary with the potential difference V supplied by the external source. 

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