Surface adsorption layer model

Figure 6.20 Surface adsorption layer model to account for experimental observations. The dotted, black, and white spheres represent carbon, oxygen, and hydrogen atoms, respectively. The atoms are scaled referring to the Ag-Ag distance (2.88 A) for the Ag(l 11)...

From a thermodynamic point of view (W. Schottky, M. Planck and others [1.63-1.65]) all the mass of gas included in the sorbent surface-near-layer of thickness (d) is adsorbed on the surface (Adsorption layer model [1.3], Fig. 1.20). Hence the volume (V ) of the sorptive gas phase is the volume of the Gibbs excess sorptive gas phase (Vqe) reduced by the volume of the adsorbed phase (V ), i. e. we have... 

To this point, it has been assumed that only the outermost layer of the coating, be it perfectly smooth or highly porous, is involved in the adsorption process. When this is not the case, the simple surface adsorption-based models discussed above are inadequate. 

Fig. 3. Layer-by-layer crystal growth (a) adsorption layer model, showing (i) addition of growth unit with migration to high-energy kink site, (ii) completion of a layer, (iii) further growth through surface nucleation (b) AFM image of growth terraces on a zeolite A surface (image area 2.5 x 2.5 pm2).

The surface adsorption layer thickness is calculated as follows. It is assumed that the extent of physical adsorption on the pore surfaces is given by the following Langmuir-like model... 

According to Everett s adsorption layer model [5,34,35], the heat of immersional wetting (A /f ), a thermodynamic parameter characteristic of the sohd-liquid interaction, can be easily calculated when the molar enthalpies of the components h- and h2 of the system are known. When a solid adsorbent is immersed in a liquid mixture, the amoimt of which is n + n . the interfacial forces of adsorption cause the formation of an adsorption layer on the surface of the adsorbent, the material content of which is = n] + 2-... 

In Sec. II we briefly review the experimental situation in surface adsorption phenomena with particular emphasis on quantum effects. In Section III models for the computation of interaction potentials and examples are considered. In Section IV we summarize the basic formulae for path integral Monte Carlo and finite size scahng for critical phenomena. In Section V we consider in detail examples for phase transitions and quantum effects in adsorbed layers. In Section VI we summarize. 

Snyder and Soczewinski created and published, at the same time, another model called the S-S model describing the adsorption chromatographic process [19,61]. This model takes into account the role of the mobile phase in the chromatographic separation of the mixture. It assumes that in the chromatographic system the whole surface of the adsorbent is covered by a monolayer of adsorbed molecules of the mobile phase and of the solute and that the molecules of the mobile phase components occupy sites of identical size. It is supposed that under chromatographic process conditions the solute concentrations are very low, and the adsorption layer consists mainly of molecules of the mobile phase solvents. According to the S-S model, intermolecular interactions are reduced in the mobile phase but only for the... 

The percolation model of adsorption response outlined in this section is based on assumption of existence of a broad spread between heights of inter-crystalline energy barriers in polycrystals. This assumption is valid for numerous polycrystalline semiconductors [145, 146] and for oxides of various metals in particular. The latter are characterized by practically stoichiometric content of surface-adjacent layers. It will be shown in the next chapter that these are these oxides that are characterized by chemisorption-caused response in their electrophysical parameters mainly generated by adsorption charging of adsorbent surface [32, 52, 155]. The availability of broad spread in heights of inter-crystalline barriers in above polycrystallites was experimentally proved by various techniques. These are direct measurements of the drop of potentials on probe contacts during mapping microcrystal pattern [145] and the studies of the value of exponential factor of ohmic electric conductivity of the material which was L/l times lower than the expected one in case of identical... 

We should point out that up to now we have considered only polycrystals characterized by an a priori surface area depleted in principal charge carriers. For instance, chemisorption of acceptor particles which is accompanied by transition-free electrons from conductivity band to adsorption induced SS is described in this case in terms of the theory of depleted layer [31]. This model is applicable fairly well to describe properties of zinc oxide which is oxidized in air and is characterized by the content of surface adjacent layers which is close to the stoichiometric one [30]. 

The competition model and solvent interaction model were at one time heatedly debated but current thinking maintains that under defined r iitions the two theories are equivalent, however, it is impossible to distinguish between then on the basis of experimental retention data alone [231,249]. Based on the measurement of solute and solvent activity coefficients it was concluded that both models operate alternately. At higher solvent B concentrations, the competition effect diminishes, since under these conditions the solute molecule can enter the Interfacial layer without displacing solvent molecules. The competition model, in its expanded form, is more general, and can be used to derive the principal results of the solvent interaction model as a special case. In essence, it seems that the end result is the same, only the tenet that surface adsorption or solvent association are the dominant retention interactions remain at variance. 

Besides the resuspension of particles, the perfect sink model also neglects the effect of deposited particles on incoming particles. To overcome these limitations, recent models [72, 97-99] assume that particles accumulate within a thin adsorption layer adjacent to the collector surface, and replace the perfect sink conditions with the boundary condition that particles cannot penetrate the collector. General continuity equations are formulated both for the mobile phase and for the immobilized particles in which the immobilization reaction term is decomposed in an accumulation and a removal term, respectively. Through such equations, one can keep track of the particles which arrive at the primary minimum distance and account for their normal and tangential motion. These equations were solved both approximately, and by numerical integration of the governing non-stationary transport equations. 

Let us now extend the long-period hydronium ice-like model for the IHP on Pt(lll) to explain the observations in electrolytes other than sulphate. In acid chloride, both the observations and the model carry-over directly from the case of sulphate. In fluoride, perchlorate, bicarbonate and hydroxide, in Which the anomalous features shift considerably in both potential and appearance (especially in the basic media) from sulphate, another model is needed. Both (bi)sulphate and chloride are large weakly hydrated anions, and in the double-layer model of Figures 4-5, they interact strongly with both the hydronium ions and the Pt surface. The contact adsorption... 

Some emphasis is given in the first two chapters to show that complex formation equilibria permit to predict quantitatively the extent of adsorption of H+, OH , of metal ions and ligands as a function of pH, solution variables and of surface characteristics. Although the surface chemistry of hydrous oxides is somewhat similar to that of reversible electrodes the charge development and sorption mechanism for oxides and other mineral surfaces are different. Charge development on hydrous oxides often results from coordinative interactions at the oxide surface. The surface coordinative model describes quantitatively how surface charge develops, and permits to incorporate the central features of the Electric Double Layer theory, above all the Gouy-Chapman diffuse double layer model. 

Fig. 4.8 compares data on the adsorption of lauric acid (C12) and caprylic acid (Cs) at a hydrophobic surface (mercury) as a function of the total bulk concentration for different pH-values. As is to be expected the molecular species becomes adsorbed at much lower concentrations than the carboxylate anions. The latter cannot penetrate into the adsorption layer without being accompanied by positively charged counterions (Na+). As was shown in Fig. 4.4, the adsorption data of pH = 4 can be plotted in the form of a Frumkin (FFG) equation. Fig. 4.9 compares the adsorption of fatty acids on a hydrophobic model surface (Hg) with that of the adsorption on Y-AI2O3. 

A specific example of the relationship between the microscopic subreactions required to model experimental observations of metal removal and the macroscopic proton coefficient is shown for the case of Cd(II) adsorption onto a-A f (Figure 3). One variation of the surface coordination concept is used to describe the system subreactions the Triple Layer Model of Davis et al., (1,20). The specific subreactions which are considered, the formation constants and compact layer capacitances, are shown in Table IV. Protons are assigned to the o-plane (the oxide surface) and Cd(II) surface species and electrolyte ions to the 8-plane located a distance, 8, from the o-plane. 

Figure 14. Triple-layer model (1) results for Cd(II) adsorption onto a-alumina at different site/adsorbate ratios. Top, Cd(II) surface reaction best fit constants middle, Cd(II) surface species mole fractions and bottom, slopes of fractional adsorption edges used as the criteria of fit.

Figure 5-11 shows a simple model of the compact double layer on metal electrodes. The electrode interface adsorbs water molecules to form the first mono-molecular adsorption layer about 0.2 nm thick next, the second adsorption layer is formed consisting of water molecules and hydrated ions these two layers constitute a compact electric double layer about 0.3 to 0.5 nm thick. Since adsorbed water molecules in the compact layer are partially bound with the electrode interface, the permittivity of the compact layer becomes smaller than that of free water molecules in aqueous solution, being in the range from 5 to 6 compared with 80 of bulk water in the relative scale of dielectric constant. In general, water molecules are adsorbed as monomers on the surface of metals on which the affinity for adsorption of water is great (e.g. d-metals) whereas, water molecules are adsorbed as clusters in addition to monomers on the surface of metals on which the affinity for adsorption of water is relatively small (e.g. sp-metals). 

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