Adsorption surface excess

In this chapter we have limited our discussion to certain aspects of the field, related particularly to submonolayer phenomena, such as the measurement of adsorption (surface excess), double-layer structure, and the underpotential deposition of metals, with an extension to the study of deposition of very thin metal films. 

Analogously, in an interface we may have distinct surface phases with first-order transitions between them. Ihat occurs when, for a given set of values of the themrodynamic fields, an interface has two alternative structures of equal tension. Hie two structures differ in their microscopic composition profiles, and therefore also (except for occasional azeotropies) in their macroscopic adsorptions (surface excesses). We may take... 

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). 

An adsorption isotherm known as the Temkin equation [149] has the form tt = ofF /F where a is a constant and F" is the limiting surface excess for a close-packed... 

Fig. XI-10. Isotherm of composition change or surface excess isotherm for the adsorption of (1) benzene and (2) n-heptane on Graphon. (From Ref. 141.)...

Surface heterogeneity may merely be a reflection of different types of chemisorption and chemisorption sites, as in the examples of Figs. XVIII-9 and XVIII-10. The presence of various crystal planes, as in powders, leads to heterogeneous adsorption behavior the effect may vary with particle size, as in the case of O2 on Pd [107]. Heterogeneity may be deliberate many catalysts consist of combinations of active surfaces, such as bimetallic alloys. In this last case, the surface properties may be intermediate between those of the pure metals (but one component may be in surface excess as with any solution) or they may be distinctly different. In this last case, one speaks of various effects ensemble, dilution, ligand, and kinetic (see Ref. 108 for details). 

Example of copredpitation (a) schematic of a chemically adsorbed inclusion or a physically adsorbed occlusion in a crystal lattice, where C and A represent the cation-anion pair comprising the analyte and the precipitant, and 0 is the impurity (b) schematic of an occlusion by entrapment of supernatant solution (c) surface adsorption of excess C. 

An additional method for increasing particle size deserves mention. When a precipitate s particles are electrically neutral, they tend to coagulate into larger particles. Surface adsorption of excess lattice ions, however, provides the precipitate s particles with a net positive or negative surface charge. Electrostatic repulsion between the particles prevents them from coagulating into larger particles. 

Equation 9 states that the surface excess of solute, F, is proportional to the concentration of solute, C, multipHed by the rate of change of surface tension, with respect to solute concentration, d /dC. The concentration of a surfactant ia a G—L iaterface can be calculated from the linear segment of a plot of surface tension versus concentration and similarly for the concentration ia an L—L iaterface from a plot of iaterfacial teasioa. la typical appHcatioas, the approximate form of the Gibbs equatioa was employed to calculate the area occupied by a series of sulfosucciaic ester molecules at the air—water iaterface (8) and the energies of adsorption at the air-water iaterface for a series of commercial aonionic surfactants (9). 

D. K. Chattoray and K. S. Birdi, Adsorption and Gibbs Surface Excess, Plenum Press, New York, 1984, Chaps. 5 and 6. 

The parameter nf always has positive values, whereas the parameters and Fj can have positive or negative values. Parameter Fj is called the Gibbs adsorption or Gibbs surface excess. 

However, the value of T depends on the position of the Gibbs surface. By common convention, this position is selected so that for one of the components (with the index j = 0), the value of T defined by Eq. (10.21) will become zero. The solvent is chosen in this capacity when one of the phases in contact is a solution. Once the position of the Gibbs surface has been fixed, one can unambiguously determine the Gibbs surface excesses of the other components. The adsorption of a component j is thus defined relative to the component y = 0 (relative Gibbs surface excess... 

We have also discussed two applications of the extended ab initio atomistic thermodynamics approach. The first example is the potential-induced lifting of Au(lOO) surface reconstmction, where we have focused on the electronic effects arising from the potential-dependent surface excess charge. We have found that these are already sufficient to cause lifting of the Au(lOO) surface reconstruction, but contributions from specific electrolyte ion adsorption might also play a role. With the second example, the electro-oxidation of a platinum electrode, we have discussed a system where specific adsorption on the surface changes the surface structure and composition as the electrode potential is varied. 

One important advantage of the polarized interface is that one can determine the relative surface excess of an ionic species whose counterions are reversible to a reference electrode. The adsorption properties of an ionic component, e.g., ionic surfactant, can thus be studied independently, i.e., without being disturbed by the presence of counterionic species, unlike the case of ionic surfactant adsorption at nonpolar oil-water and air-water interfaces [25]. The merits of the polarized interface are not available at nonpolarized liquid-liquid interfaces, because of the dependency of the phase-boundary potential on the solution composition. 

Charge transfer reactions at ITIES include both ET reactions and ion transfer (IT) reactions. One question that may be addressed by nonlinear optics is the problem of the surface excess concentration during the IT reaction. Preliminary experiments have been reported for the IT reaction of sodium assisted by the crown ether ligand 4-nitro-benzo-15-crown-5 [104]. In the absence of sodium, the adsorption from the organic phase and the reorientation of the neutral crown ether at the interface has been observed. In the presence of the sodium ion, the problem is complicated by the complex formation between the crown ether and sodium. The SH response observed as a function of the applied potential clearly exhibited features related to the different steps in the mechanisms of the assisted ion transfer reaction although a clear relationship is difficult to establish as the ion transfer itself may be convoluted with monolayer rearrangements like reorientation. 

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). 

The quantity dyl3 In a2 at the potential of the electrocapillary maximum is of basic importance. As the surface charge of the electrode is here equal to zero, the electrostatic effect of the electrode on the ions ceases. Thus, if no specific ion adsorption occurs, this differential quotient is equal to zero and no surface excess of ions is formed at the electrode. This is especially true for ions of the alkali metals and alkaline earths and, of the anions, fluoride at low concentrations and hydroxide. Sulphate, nitrate and perchlorate ions are very weakly surface active. The remaining ions decrease the surface tension at the maximum on the electrocapillary curve to a greater or lesser degree. 

Electroneutral substances that are less polar than the solvent and also those that exhibit a tendency to interact chemically with the electrode surface, e.g. substances containing sulphur (thiourea, etc.), are adsorbed on the electrode. During adsorption, solvent molecules in the compact layer are replaced by molecules of the adsorbed substance, called surface-active substance (surfactant).t The effect of adsorption on the individual electrocapillary terms can best be expressed in terms of the difference of these quantities for the original (base) electrolyte and for the same electrolyte in the presence of surfactants. Figure 4.7 schematically depicts this dependence for the interfacial tension, surface electrode charge and differential capacity and also the dependence of the surface excess on the potential. It can be seen that, at sufficiently positive or negative potentials, the surfactant is completely desorbed from the electrode. The strong electric field leads to replacement of the less polar particles of the surface-active substance by polar solvent molecules. The desorption potentials are characterized by sharp peaks on the differential capacity curves. 

The basic quantity in the study of adsorption is the surface excess of the surface-active substance. In the formation of a monomolecular film of the... 

If the supply of surfactant to and from the interface is very fast compared to surface convection, then adsorption equilibrium is attained along the entire bubble. In this case the bubble achieves a constant surface tension, and the formal results of Bretherton apply, only now for a bubble with an equilibrium surface excess concentration of surfactant. The net mass-transfer rate of surfactant to the interface is controlled by the slower of the adsorption-desorption kinetics and the diffusion of surfactant from the bulk solution. The characteris-... 

An adsorption-desorption transition is illustrated schematically in Figure 1, where we plot a displacement isotherm, i.e. the adsorbed amount of a polymer as a function of the composition of a mixture of solvent and displacer. At the left in Figure 1, where the concentration of displacer is low, the polymer surface excess is positive. As we increase the proportion of displacer in the mixture, we observe a decrease in the adsorbed amount. At a certain composition the adsorbed amount of polymer becomes zero. The concentration at which the polymer surface excess just vanishes will be denoted as the critical displacer concentration cr. Beyond 4>cr, the surface excess of the polymer is negative (and very small if the polymer concentration is low). 

Another possible factor for the decrease of If is adsorption that is excess of G on a surface of H. According to Gibbs, the isotherm of adsorption (the specific surface excess of /th guest) has a form ... 

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