Surface excess density

Surface excesses are usually referred to the unit surface area of the dividing plane S (surface excess densities). 

Bromide adsorption on Au(lll) has also been studied, applying in situ surface X-ray scattering (SXS) and STM [56]. The potential-dependent adlayer density agreed well with the earlier pubKshed bromide surface excess densities, obtained in electrochemical measurements. At very positive potentials, a bromide-induced step-flow etching of Au occurred. 

Fig. 53. Schematic isotherms (density p versus chemical potential pi) corresponding to the gas-liquid condensation in capillaries of thickness D, for the case without (a) and with (b) prewetting, and adsorption isotherm (c) for a semi-infinite system, where the surface excess density pjs is plotted vs. pi. Full curves in (a) and (b) plot the density p vs. pi for a bulk system, phase coexistence occurs there between p,p, (bulk gas) and pn, (bulk liquid), while in the capillary due to the adsorption of fluid at the walls the transition is shifted from paKX to a smaller value rc(D, 7) (with pic(7>, T) 1 /D, the Kelvin equation ), and the density jump (from ps D) to pt D)) is reduced. Note also that in the ease where a semi-infinite system exhibits a first-order wetting transition 7W, for 7 > 7W one may cross a line of (first-order) prewetting transitions (fig. 54) where the density in the capillary jumps from p to p>+ or in the semi-infinite geometry, the surface excess density jumps from p to p +, cf. (c), which means that a transition occurs from a thin adsorbed liquid film to a thick adsorbed film. As pi the thickness of the adsorhed liquid film in the semi-infinite...

The surface excess density F can be measured easily. It is typically done as a function of the bulk solute concentration pi, to obtain the so-called adsorption isotherm If F > 0, the solute is considered surface-active, and according to Eq. [30] this is associated with a decrease in the surface tension relative to pure solvent(s). 

A quite different means for the experimental determination of surface excess quantities is ellipsometry. The technique is discussed in Section IV-3D, and it is sufficient to note here that the method allows the calculation of the thickness of an adsorbed film from the ellipticity produced in light reflected from the film covered surface. If this thickness, t, is known, F may be calculated from the relationship F = t/V, where V is the molecular volume. This last may be estimated either from molecular models or from the bulk liquid density. 

It was noted in connection with Eq. III-56 that molecular dynamics calculations can be made for a liquid mixture of rare gas-like atoms to obtain surface tension versus composition. The same calculation also gives the variation of density for each species across the interface [88], as illustrated in Fig. Ill-13b. The density profiles allow a calculation, of course, of the surface excess quantities. 

The integral of p over all space gives the total excess charge in the solution, per unit area, and is equal in magnitude but opposite in sign to the surface charge density a ... 

FIG. 20 (a) Density profiles p(z) vs z for e = —2 and four average bulk densities (f> as indicated, (b) Surface excess vs density in the bulk for four choices of e. (c) Profiles for the diagonal components of the pressure tensor and of the total pressure for (p = l.O and e = —2. Insert in (c) shows the difference between P, and Px to show that isotropic behavior in the bulk of the film is nicely obtained, (d) Interfacial tension between the polymer film and the repulsive wall vs bulk density for all four choices of e. Curve is only a guide for the eye [18]. 

In situ Fourier transform infrared and in situ infrared reflection spectroscopies have been used to study the electrical double layer structure and adsorption of various species at low-index single-crystal faces of Au, Pt, and other electrodes.206"210 It has been shown that if the ions in the solution have vibrational bands, it is possible to relate their excess density to the experimentally observed surface. 

In the case of the adsorption of ions, the adsorption free energy is proportional to the excess surface charge density [37],... 

The extensive variable Q associated with the electrical potential + in Eqs. (15), (17), and (21) is the thermodynamic surface excess charge density, which is defined by... 

Provided that Ag

P2 are constant, and Tjjx is proportional to (c "). The observed nonlinearity at higher electrolyte concentrations [2] is probably due to a change in the inner-layer potential difference A"y>, with the surface excess charge density. The inner-layer potential difference (< 50 mV) was evaluated from the linear part of the Tjj vs. plot, and was found to depend on the nature of the... 

Kakiuchi and Senda [36] measured the electrocapillary curves of the ideally polarized water nitrobenzene interface by the drop time method using the electrolyte dropping electrode [37] at various concentrations of the aqueous (LiCl) and the organic solvent (tetrabutylammonium tetraphenylborate) electrolytes. An example of the electrocapillary curve for this system is shown in Fig. 2. The surface excess charge density Q, and the relative surface excess concentrations T " and rppg of the Li cation and the tetraphenylborate anion respectively, were evaluated from the surface tension data by using Eq. (21). The relative surface excess concentrations and of the d anion and the... 

Figure 2.10 Schematic representation of the variation of the excess, or nett, surface charge density as a function of the distance away from the electrode surface, according to the Gouy-Chapman theory. The distance of nearest approach of the ions, with their associated solvation...

Consider a plane metal electrode situated at z = 0, with the metal occupying the half-space z < 0, the solution the region z > 0. In a simple model the excess surface charge density a in the metal is balanced by a space charge density p(z) in the solution, which takes the form p(z) = Aexp(—kz), where k depends on the properties of the solution. Determine the constant A from the charge balance condition. Calculate the interfacial capacity assuming that k is independent of a. 

Figure 16.5 Data required for the determination of the surface excess of pyridine on Au(110). Top surface charge density obtained by integrating the capacity curves in Fig. 16.4. Middle relative surface tension A7. Bottom Surface excess of pyridine. Supporting electrolyte 0.1 M KCIO4. (1) 6 x 10 4 M (2) 3 x 10 5 M (3) 2 x 10 6 M pyridine (4) no pyridine. Data taken from Ref. 2.

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