Surface Excess Measurable

A range of fluorinated anionic surfactants, which are structural relatives of Aerosol-OT, were synthesized and characterized, with the aim of investigating the effects of chemistry on the structure and stability of water-in-carbon dioxide microemulsions. The dilute aqueous phase behavior was studied to check for chemical purity and fuUy characterize the compounds. Once appropriate measures were taken to achieve sufficient purity, the surface excesses measured by both tensiometry and neutron reflection measurements agreed well, and the surface tensions were consistent with a prefactor of 2 in the Gibbs equation. 

The most widely used experimental method for determining surface excess quantities at the liquid-vapor interface makes use of radioactive tracers. The solute to be studied is labeled with a radioisotope that emits weak beta radiation, such as H, C, or One places a detector close to the surface of the solution and measures the intensity of beta radiation. Since the penetration range of such beta emitters is small (a ut 30 mg/cm for C, with most of the adsorption occurring in the first two-tenths of the range), the measured radioactivity corresponds to the surface region plus only a thin layer of solution (about 0.06 mm for C and even less for H). 

McBain reports the following microtome data for a phenol solution. A solution of 5 g of phenol in 1000 g of water was skimmed the area skimmed was 310 cm and a 3.2-g sample was obtained. An interferometer measurement showed a difference of 1.2 divisions between the bulk and the scooped-up solution, where one division corresponded to 2.1 X 10 g phenol per gram of water concentration difference. Also, for 0.05, 0.127, and 0.268M solutions of phenol at 20°C, the respective surface tensions were 67.7, 60.1, and 51.6 dyn/cm. Calculate the surface excess Fj from (a) the microtome data, (b) for the same concentration but using the surface tension data, and (c) for a horizontally oriented monolayer of phenol (making a reasonable assumption as to its cross-sectional area). 

Finding F Either Eq. (22-45) or Eq. (22-46) can be used to find the surface excess indirectly from experimental measurements. To assure a close approach to operation as a single theoretical stage, coalescence in the rising foam should be minimized by maintaining a proper gas rate and a low foam height [Brunner and Lemhch, Ind. Eng. Chem. Fundam. 2, 297 (1963)]. These precautions apply particularly with Eq. (22-45). 

The surface concentration Cq Ajc in general depends on the electrode potential, and this can affect significantly the form of the i E) curves. In some situations this dependence can be eliminated and the potential dependence of the probability of the elementary reaction act can be studied (called corrected Tafel plots). This is, for example, in the presence of excess concentration of supporting electrolyte when the /i potential is very small and the surface concentration is practically independent of E. However, the current is then rather high and the measurements in a broad potential range are impossible due to diffusion limitations. One of the possibilities to overcome this difficulty consists of the attachment of the reactants to a spacer film adsorbed at the electrode surface. The measurements in a broad potential range give dependences of the type shown in Fig. 34.4. 

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... 

For solutions of simple electrolytes, the surface excess of ions can be determined by measuring the interfacial tension. Consider the valence-symmetrical electrolyte BA (z+ = —z = z). The Gibbs-Lippmann equation then has the form... 

In this manner, the surface excess of ions can be found from the experimental values of the interfacial tension determined for a number of electrolyte concentrations. These measurements require high precision and are often experimentally difficult. Thus, it is preferable to determine the surface excess from the dependence of the differential capacity on the concentration. By differentiating Eq. (4.2.30) with respect to EA and using Eqs (4.2.24) and (4.2.25) in turn we obtain the Gibbs-Lippmann equation... 

Double integration with respect to EA yields the surface excess rB+ however, the calculation requires that the value of this excess be known, along with the value of the first differential 3TB+/3EA for a definite potential. This value can be found, for example, by measuring the interfacial tension, especially at the potential of the electrocapillary maximum. The surface excess is often found for solutions of the alkali metals on the basis of the assumption that, at potentials sufficiently more negative than the zero-charge potential, the electrode double layer has a diffuse character without specific adsorption of any component of the electrolyte. The theory of diffuse electrical double layer is then used to determine TB+ and dTB+/3EA (see Section 4.3.1). 

Other methods, based on kinetic methods of measuring surface excesses, will be discussed in Section 5.7. 

Tauber et al. [23] following the same method as Hart et al. but using tert-butanol as the methyl radical source, obtained a temperature of 3,600 K in 10 3 M /(77-butanol and reported, similar to Hart et al. that this temperature decreased with increasing /( / /-butanol concentration. More recently, this method was adopted by Rae et al. [24] and Ciawi et al. [25, 26] in aqueous solutions. Rae et al. examined the effect of concentration of a series of aliphatic alcohols, extrapolating a maximum temperature of about 4,600 K at zero alcohol concentration [24]. They also observed a decrease in temperature with increasing alcohol concentration, which correlated well with the alcohol surface-excess and SL measurements obtained in the same system. Ciawi et al. investigated the effects of ultrasound frequency, solution temperature and dissolved gas on bubble temperature [26],... 

The electrocapillary equation (16.12) makes it possible to measure the surface excess of a species through ... 

It is practically impossible to measure 7 for solid electrodes. However, in some applications one needs only the change in 7 with certain parameters. For example, for the determination of the surface excess of a neutral organic species, one requires the change in the interfacial tension with the activity of the species. This can be measured if there is a reference potential 4>r at which the species is not adsorbed the change in the interfacial tension is then referred to this potential. One proceeds in the following way [2] ... 

In Eq. 30, Uioo and Fi are the activity in solution and the surface excess of the zth component, respectively. The activity is related to the concentration in solution Cioo and the activity coefficient / by Uioo =fCioo. The activity coefficient is a function of the solution ionic strength I [39]. The surface excess Fi includes the adsorption Fi in the Stern layer and the contribution, f lCiix) - Cioo] dx, from the diffuse part of the electrical double layer. The Boltzmann distribution gives Ci(x) = Cioo exp - Zj0(x), where z, is the ion valence and 0(x) is the dimensionless potential (measured from the Stern layer) obtained by dividing the actual potential, fix), by the thermal potential, k Tje = 25.7 mV at 25 °C). Similarly, the ionic activity in solution and at the Stern layer is inter-related as Uioo = af exp(z0s)> where tps is the scaled surface potential. Given that the sum of /jz, is equal to zero due to the electrical... 

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. 

Ocko etal. [57, 58] have studied adsorption of bromide on Au(lOO) using in situ surface X-ray diffraction (SXD) in combination with electrochemical measurements. Low surface excess of bromide ions at Au(100)-(hex) caused a lifting of the... 

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... 

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