Adsorption coverage

Zero-order desorption occurs if the rate of desorption does not depend on the adsorption coverage, as seen with relatively large silver islands on a ruthenium surface (Fig. 7.7), where the Ag atoms desorb from the edges of the island. As the 0" term in Eq. (12) vanishes, the curves exhibit a clearly recognizable exponential shape on the leading side. Such situations are rare. 

The equilibrium adsorption coverage is attained rapidly and reversibly. 

The other molecular probe method is the single-probe method (SP method), which is separately proposed by Avnir and Jaroniec,93 and Pfeifer et al.108-112 In the SP method, a single adsorption isotherm is analyzed using a modified FHH theory. The FHH model was developed independently by Frenkel,113 Halsey,114 and Hill,115 and describes the multilayer adsorption coverage. Since the SP method uses only one probe molecule, this method is more convenient than the MP method. However, there are many theoretical limitations in applying the SP method to determination of the surface fractal dimension. Therefore, it is really necessary to discuss whether the SP method is an adequate tool to investigate the surface fractal dimension or not before applying the SP method to certain system. 

The Kurbatov plot is a convenient tool to display in a simple way adsorption (surface complex formation) data. But care must be exercised in the interpretation of the data, because n varies with pH and may vary with the adsorption coverage. For an exact analysis of the proton release stoichiometry, see Hohl and Stumm (1976) or Honeyman and Leckie (1986). 

Fig. S-2. Activation energy both ibr reconstruction of the surface (100) plane of platinum crystals in vacuum and for im-reconstruction of the reconstructed surface due to adsorption of C 0 (1x1) (5x20) is surface lattice transformation (reconstruction and un-reconstruc-tion). 6 = adsorption coverage. [From Ertl, 1985.]...

The relationship between the activity of adsorbed ions fiQO in Eqn. 5-21 and the adsorption coverage 6i is known as an adsorption isotherm. Equations 5-23 and 5-24 show simple adsorption isotherms ... 

Fig. 6-25. Relative change in work function, d4>, of a (100) surface of single crystal of silver as a function of adsorption coverage 6 of bromine atoms and water molecules on the clean surface, and of bromine atoms on the surface with pre-adsorbed water molecules. [From Bange-Straehler-Sass-Parsons, 1987.]...

Fig. 6-34. Adsorption coverage of hydroxyl radicals on, and work function of, a platinum (111) surface plane observed as functions of coverage of potassium atoms coadsorbed with water molecules adsorption of water vapor takes place on a potassium-adsorbed surface of platimun at 305 K. 6k = coverage of adsorbed potassium atoms 6oh = coverage of hydroxyl radicals adsorbed by partial dissociation of water molecules A

Fig. S-S8. Electron levels of dehydrated redox particles, H ld + bh /h = H,d, adsorbed on an interface of metal electrodes D = state density (electron level density) 6 = adsorption coverage shVi - most probable vacant electron level of adsorbed protons (oxidants) eH(d = most probable occupied electron level of adsorbed hydrogen atoms (reductants) RO.d = adsorbed redox particles.

In adsorption equUibrimn, the Fermi level c m) of electrons in the metal electrode equals the Fermi level ep(HyH ) oi redox electrons in the adsorbed redox particles the state density of the occupied electron level equals the state density of the vacant electron level at the Fermi level ( >b = Da). Assuming the Langmuir adsorption isotherm at low adsorption coverages and the Gaussian distribution for the state density, we obtain Eqn. 5-55 for the Fermi level ... 

Since the electron transfer of the interfacial redox reaction, + cm = H.a> on electrodes takes place between the iimer Helmholtz plane (adsorption plane at distance d ) and the electrode metal, the ratio of adsorption coverages 0h,j/ in electron transfer equilibrium (hence, the charge transfer coefficient, 6z) is given in Eqn. 5-58 as a function of the potential vid /diOMn across the inner Helmholtz layer ... 

The electrochemical standard free enthalpy, of dissociation of the surface acid or base sites consists of the chemical standard free enthalpy, AG°, an electrostatic energy, eA, and an interaction energy, m0, for the adsorption coverage in the Frumkin adsorption model is the potential across the compact layer, 0 is the adsorption coverage, and m is the Frumkin parameter [Frumkin, 1925] ... 

In the rate equations, Eqn. 9-14 through Eqn. 9-18, we have assumed that Langmiiir s adsorption isotherm holds this assumption applies to the range of low adsorption coverages. 

In the mechanism of the anodic iron dissolution, described in this section, the formation process of the intermediate of ferrous hydroxocomplexes, Eqn. 9-21a, is in the quasi-equilibrium state so that the Nemst equation applies between the adsorption coverage, 6p oa-, of the intermediate FeOH [d and the overvoltage, t). Accordingly, for the range of relatively low coverages of adsorption to which Langmuir s adsorption isotherm applies, we obtain Eqn. 9-22 ... 

Fig. 9-6. Adaorption coverage of a reaction intermediate of hydroxo-complezes in anodic dissolution of a metallic iron electrode as a function of electrode potential in acidic sulfate solutions at pH 1.0, 2.0 and 3.0 solution is 0.5 M (Ns2S04 + H2SO4) at room temperature. Oqh adsorption coverage of reaction intermediates FeOH,4 and PeOH Vss = volt referred to the saturated silver-silver chloride electrode. [Prom Tsuru, 1991.]...

In adsorptioDr-desorption equilibrium, the adsorption coverage of protons, 6h-(= is derived from the Nemst equation of electrochemical equilibria to... 

It follows that the ratio of concentrations Ch /ch , in adsorption equilibrium on semiconductor electrodes, in the state of band edge level pinning, changes with changing electrode potential as shown in Fig. 9-20. This differs from the case of metal electrodes where the ratio of concentrations remains constant irrespective of the electrode potential (Refer to Sec. 9.3.). Combining Eqns. 9-60 and 9-67 to produce Eqn. 9-68 describes the concentration of adsorbed hydrogen atoms as an exponential function of the electrode potential ( 4>sc) for low adsorption coverages ... 

Two models of oxygen adsorption are considered, vertical form and parallel form, which are illustrated in Fig. 9.1 and Fig. 9.2. For all the cases, the adsorbate/substrate system is optimized by GGA. In optimization, all atoms on the pyrite substrate are fixed only the O atoms are allowed to move. The initial 0—0 double bond length and the distance between Fe atom and O atom are 0.121 nm and 0.196 run, respectively. To simplify the calculation, the adsorption coverage will not be considered. 

A further question regarding the adsorption registry is whether it depends on adsorption coverage, i.e., on density of adatoms this is relevant to the effects of adatom-adatom interactions. The situation is illustrated by a limited set of results, namely those for quarter-monolayer and half-monolayer adsorption of 0, S, Se and Te on Ni(lOO) in p(2 X 2) and c(2 X 2) periodicities the adsorption site is found not to depend on coverage in these cases (the nearest adatom-adatom distances are 4.90 and 3.46 A for the two coverages, respectively, compared with the largest adatom diameter of about 2.7 A for Te). 

The intensity of the decrease of the equilibrium degree of adsorption (coverage) with rising temperature as well as the point of approximate saturation, however, are unknown for the problem at hand. But since, as discussed before, all reactions under consideration require aqueous solutions anyway, adsorptions on solid, i.e., dry surfaces are... 

Impedance spectra can also be used to obtain the adsorption coverage of CO, the reaction rates for CO formation and oxidation, and the effect of CO adsorption on hydrogen oxidation. In the presence of CO adsorption, H adsorption and oxidation rate can be deduced ... 

The integrated peak areas between 1650-1700 cm, at several bias potentials, are shown in Fig. 11. The adsorption of the anion, CO, increases in the cathodic direction. If the adsorbed CO radial were in equilibrium with C0 in solution a decrease in adsorption coverage would be expected when the potential is moved in the cathodic direction. However, increase in anion concentration at cathodic potentials is consistent with CO2 as an intermediate radical in the electrochemical reduction of CO. Thus, from (l)-(3). 

Differences in dispersion rheology associated with the surface energies (i.e., adsorption coverage) of the different latex types (e.g., vinyl acetate, 18 mN/m methyl methacrylate, 26 mN/m and styrene, 40 mN/m) are not realized (34). 

---