Adsorption models for

Ruch and Bartell [84], studying the aqueous decylamine-platinum system, combined direct estimates of the adsorption at the platinum-solution interface with contact angle data and the Young equation to determine a solid-vapor interfacial energy change of up to 40 ergs/cm due to decylamine adsorption. Healy (85) discusses an adsorption model for the contact angle in surfactant solutions and these aspects are discussed further in Ref. 86. 

The acid monolayers adsorb via physical forces [30] however, the interactions between the head group and the surface are very strong [29]. While chemisorption controls the SAMs created from alkylthiols or silanes, it is often preceded by a physical adsorption step [42]. This has been shown quantitatively by FTIR for siloxane polymers chemisorbing to alumina illustrated in Fig. XI-2. The fact that irreversible chemisorption is preceded by physical adsorption explains the utility of equilibrium adsorption models for these processes. 

As noted above, adsorption isotherms are largely derived empirically and give no information on the types of adsorption that may be involved. Scrivner and colleagues39 have developed an adsorption model for montmorillonite clay that can predict the exchange of binary and ternary ions in solution (two and three ions in the chemical system). This model would be more relevant for modeling the behavior of heavy metals that actively participate in ion-exchange reactions than for organics, in which physical adsorption is more important. 

Adsorption and Film Formation. Inhibition of HC1 corrosion by organic compounds is a complicated multi-step process. Nevertheless, the effect of an inhibitor on corrosion of a metal is often treated mathematically with an equilibrium adsorption model for displacement of water (19,20) ... 

The deviations from the Szyszkowski-Langmuir adsorption theory have led to the proposal of a munber of models for the equihbrium adsorption of surfactants at the gas-Uquid interface. The aim of this paper is to critically analyze the theories and assess their applicabihty to the adsorption of both ionic and nonionic surfactants at the gas-hquid interface. The thermodynamic approach of Butler [14] and the Lucassen-Reynders dividing surface [15] will be used to describe the adsorption layer state and adsorption isotherm as a function of partial molecular area for adsorbed nonionic surfactants. The traditional approach with the Gibbs dividing surface and Gibbs adsorption isotherm, and the Gouy-Chapman electrical double layer electrostatics will be used to describe the adsorption of ionic surfactants and ionic-nonionic surfactant mixtures. The fimdamental modeling of the adsorption processes and the molecular interactions in the adsorption layers will be developed to predict the parameters of the proposed models and improve the adsorption models for ionic surfactants. Finally, experimental data for surface tension will be used to validate the proposed adsorption models. 

In the following analysis, adsorption models for solid diffusion control are applicable for isotopic exchange, i.e. exchange of isotopes, while in the case of liquid diffusion control and the intermediate case, only adsorption models for linear equilibrium can be used for isotopic exchange. 

Fig. 6.112. Comparison of coverage vs. potential curves for (o) experimental and ( ) theoretical [Eq. (6.270)] results predicted by the adsorption model for the adsorption of (a) 10-5 M phenol and (b) 10""4 M n-valeric acid on platinum electrodes. Under these experimental conditions, the pzc was found to be at about 0.35 V. (Reprinted from J. O M. Bockris and K. T. Jeng, J. Electroanal. Chem. 330 541, Copyright 1992, Figs. 18,19, and 20, with permission of Elsevier Science.)...

There are three adsorption models for molecular oxygen adsorption (Fig. 9) ... 

Now let us overview the theoretical adsorption models for characterization of the pore structures according to the pore size range. For physical adsorption of the gas molecules on such microporous solids as activated carbons and zeolites, Dubinin and Radushkevich95 developed an empirical equation, which describes the volume filling process in the micropores. Their theory incorporates earlier work by Polanyi96 in regard to the adsorption potential Ad defined as... 

Figure 3.2 Adsorption models for surfactants [6] (a) model of Fuerstenau, (b) model of Scame-horn, Chandar, Dobias and (c) model of Harwell etal.

As a first step toward overcoming the above problems, a hybrid diffusion-adsorption model for the terrace linked with a KMC model near the steps was developed (Schulze, 2004 Schulze et al., 2003). This domain decomposition stems from a natural separation of scales. The continuum terrace model between steps is... 

Note that in this specific model, desorption is neglected, and sites get regenerated upon adsorption, so the classic Langmuir blocking of sites is uncommon for MBE modeling. Furthermore, the diffusion-adsorption model for the terrace is only approximate since interactions between molecules are not accounted for. As a result, this hybrid model cannot handle nucleation between terraces, and applies only to small supersaturations or high temperatures [note that for high temperatures, one needs to include desorption in Eq. (2)] where the adatom concentration on terraces is relatively low. 

Ionization of the oxide/water interface and the resultant electrical double layer have been studied intensively by a variety of techniques within the last decade. Although many electrical double layer and adsorption models have been proposed, few are sufficiently general to consider surface equilibria in complex electrolyte solutions. Recently we proposed a comprehensive adsorption model for the oxide/water interface which can simultaneously estimate adsorption density, surface charge, and electro-kinetic potential in a self-consistent manner (jL, 2, 3). One advantage of the model was that it could be incorporated within the computer program, MINEQL ( ), by adding charge and mass-balance equations for the surface. 

A Two-Stage Horvath-Kawazoe Adsorption Model for Pore Size Distribution Analysis... 

A two-stage Horvath-Kawazoe adsorption model for pore size distribution analysis... 

Ward D., Bryan C., and Siegel M. D. (1994) Detailed characterization and preliminary adsorption model for materials for an intermediate-scale reactive transport experiment. In Proceedings of 1994 International Conference of High Level Radioactive Waste Management, pp. 2048-2062. 

FIG. 14 Schematic representation of the adsorption model for silver cyanide on activated carbons. (From Ref. 264.)... 

The objective of the work is to present an experiment-founded adsorption model for precipitate flotation. Batch precipitate flotation of CufOH) with dodecylbenzene sulphonate (DBS) as collector, was carried out both with dissolved (DAF) and dispersed (DIS) air. The processes were considered as a succession of the dynamic equilibria taking place at the gasliquid and solidliquid interfaces. Both flotation processes were expressed quantitatively in terms of surface concentrations of Cu(OH)2 and DBS per unit surface area of the air buble, as well as the ratio of the numbers of air bubbles and solid particles (B /P ). Also the maximal concentrations of both DBS and Cu(OH)2, recoverable under the given conditions were calculated. All these values were determined by following the Cu(OH)2 and DBS recovery. The 2 flotation techniques were compared in regard to their efficiency and mechanism. Finally, the results obtained were discussed in terms of the other models for the colloid particle adsorption at the air-water interface. 

Compare the application of the distribution coefficient (k",) concept and surface complexation adsorption models for predicting the adsorption behavior of radionuclides. Discuss potential advantages and pitfalls of assuming bounding A", values for a given radionuclide in groundwater. 

In the remainder of this paper, adsorption models for adsorbent characterization based upon both amorphous (disordered) and idealized (simple... 

A adsorption model for a templated porous material may be posed in terms of seven replica Ornstein-Zernicke (ROZ) integral equations [58-60] that relate the direct and total correlation functions, c, (r) and hij (r), respectively, of the matrix-adsorbate system... 

Fig. 12 Repulsion-adsorption model for the gel friction on a smooth solid substrate. P normal...

An alternative type of component additivity approach is to use different adsorption models for different adsorbents (Weng et al., 2001, 2002). These authors described Cd2+, Zn2+, and NP+ binding in soils by combining the diffuse layer model for hydrous ferric oxide, the CD-MUSIC model for goethite, the Donnan model for illite, and the nonideal competitive adsorption (NICA) Donnan model (Kmniburgh et al., 1999) for humic acid. 

Li, Q., Marinas, B.J., Snoeyink, V.L., and Campos, C. (2003). Three component competitive adsorption model for flow through PAC systems 1 Model development and verification with a PAC/membrane system. Environ. Sci. TechnoL, 37, 2997-3004. 

Figure 7-8. A proposed adsorption model for chemisorbed uracil and thymine. ...

FIGURE 18.3 Polarization curves comparing the one-step electrochemical reaction model with the adsorption model for the ORR in acidic media note that the adsorption model captures the change in the slope of the current-voltage curve as observed in experiments. 

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