Adsorption basic model

Differences in the structure of monocrystalline, threshold or bridge type polycrystalline adsorbents are to be manifested in the shape of adsorption - caused response of electrophysical characteristics [25]. The basic models of adsorption - induced response of monocrystalline and barrier poly crystal line adsorbents have been considered in Chapter 1. Here we describe various theoretical models of adsorption-induced response of polycrystalline adsorbents having intercrystalline contacts of the bridge type and their comparison with experimental results. 

Equation (89) shows that the allowance for the variation of the charge of the adsorbed atom in the activation-deactivation process in the Anderson model leads to the appearance of a new parameter 2EJ U in the theory. If U — 2Er, the dependence of amn on AFnm becomes very weak as compared to that for the basic model [see Eq. (79)]. In the first papers on chemisorption theory, a U value of 13eV was usually accepted for the process of hydrogen adsorption on tungsten. However, a more refined theory gave values of 6 eV.57 For the adsorption of hydrogen from solution we may expect even smaller values for this quantity due to screening by the dielectric medium. 

In this section we shall discuss the development of a global kinetic model for DOC. The basic model reactions considered in the DOC model are summarized in Table II. Here the real HC mixture is modeled by two characteristic hydrocarbons—propene and decane. Propene represents more reactive, light hydrocarbons, which practically do not adsorb during cold start, while decane is a representative of heavier hydrocarbons with significant adsorption on... 

Retention on these supports is adaquetely described by the adsorption displacement model. Nevertheless, the adsorption sites are delocalized due to the flexible moiety of the ligand, and secondary solvent effects play a significant role. The cyano phase behaves much like a deactivated silica toward nonpolar and moderately polar solutes and solvents. Cyano propyl columns appear to have basic tendencies in chloroform and acidic tendencies in methyl tertiobutyl ether (MTBE)... 

A final area of difficulty is in the application of data analysis to specific models of adsorption isotherms. This difficulty results from the fact that different models for adsorption isotherms generate plots of surface versus dissolved concentration that have characteristic shapes. If a plot of observational data results in a curve with a shape similar to that generated by a model, this result is often taken as proof that the particular model applies. Unfortunately, this assumption has been made for situations where many of the basic requirements of the model are violated in the system under study. The Langmuir adsorption isotherm model has suffered considerable abuse by geochemists in this regard. It should be remembered that "shapes" of adsorption isotherms are far from proof that a specific model applies. 

The basic model for the separation of peptidic solutes on nonpolar stationary phases assumes that reversible interactions of the solute molecules S, S2,. . . , S occur with the hydrocarbonaceous ligand L and that the interactions are due to hydrophobic associations and not to electrostatic or hydrogen bonding effects. Conceptually, the sorption of peptides to alkyl-bonded reversed phases under these conditions can be based either on partition or on adsorption processes. In a partition pro-... 

The adsorption of acetone on the surface of group 10 hydrogenation catalysts provides a basic model system to study the adsorption and reaction of ketones. The insight provided... 

Eley-Rideal (ER), and stepwise (SW) mechanisms. The LH model was tested by Mark et al. in the C02 reforming of methane.50 It assumed that both reactant species of CH4 and C02 are adsorbed onto the catalyst active sites separately. Adsorbed reactants then associatively react on the active sites and lead to H2 and CO product formation. The basic model is established on the basis that the reactant species of CH4 and C02 follow the first-order behavior. In the ER mechanism, one of the two reactants (either CH4 or C02) is adsorbed onto the catalyst surface in adsorption equilibrium. The adsorbed species then react with the other reactant from the gas phase, and H2 and CO are formed subsequently.51 The SW mechanism assumes that CH4 dissociatively adsorbed (active carbon and hydrogen species) on the catalytic surface. The active carbon reacts with C02 in the gas phase and produces two equivalents of CO. 

To evaluate the adsorption of chelates and organic ligands, such as surfactants, a simple adsorption isotherm model may be used. The perhaps most straightforward model has been developed by Langmuir. Assuming that the surface is basic and the adsorbate is acidic in the Bronsted or the Lewis sense, we obtain for the displacement of the solvent liquid (L) molecules by the adsorbate (A) ... 

The basic model for the calculation of the adsorption flux of amphiphiles to an interface is shown in Fig. 2.13. This model consists of a so-called "sublayer", the coordinate x is oriented normal to the interface. The second assumption is an equilibrium between the sublayer and the interface at any time. The weakest point in this physical model is the problem of the validity of an equilibrium adsorption isotherm in a non-equilibrium state. In any case close to the equilibrium state the adsorption isotherms provides a good approximation. 

The modelling of the multiple scattering requires input of all atomic positions, so that the trial-and-error approach must be followed one guesses reasonable models for the surface stmcture, and tests them one by one until satisfactory agreement with experiment is obtained. For simple stmctures and in cases where stmctural information is already known from other sources, this process is usually quite quick only a few basic models may have to be checked, e.g. adsorption of an atomic layer in hollow, bridge or top sites at positions consistent with reasonable bond lengths. It is then relatively easy to refine the atomic positions within the best-fit model, resulting in a complete stmctural determination. The refinement is normally performed by some form of automated steepest-descent optimization, which allows many atomic positions to be adjusted simultaneously [21] Computer codes are also available to accomplish this part of the analysis [25]. The trial-and-error search with refinement may take minutes to hours on current workstations or personal computers. 

The stop-effect, a drastic increase of the reaction rate when the feed concentration of a reactant is switched to zero, was studied for the dehydration of ethanol to ethylene on 7-alumina at 180 and 200°C. Two basic models exist in the literature to describe this phenomenon. They were discriminated on the basis of transient and periodic experiments, coupled with FTIR data of the adsorbed species. The model that best describes these measurements postulates the adsorption of ethanol on two different sites, S and S2, with a free S2 site being necessary for ethylene formation. 

The adsorption of surfactants at interfaces is a time process. After the creation of a new surface the adsorption is zero and increases with time until reaching the equilibrium state. The main mechanism controlling this process is the diffusion of surfactants in the solution bulk. In this lesson the basic models will be discussed and the main physical parameters analysed. In particular, the type of adsorption isotherm plays an important role. On the basis of dynamic surface tensions the application of the theoretical models will be demonstrated in the subsequent paragraph. Besides complete solutions of the diffusion model, also approximate solutions exist. These models... 

The studies on the adsorption of model compounds, synthetic polynucleotides and degradation products of nucleic acids with the aid of a.c. polarography [98-101] indicate that all three basic constituents of nucleic acids, i.e., bases, sugars and phoshoric acid participate in the adsorption of nucleic acids at mercury electrodes. The extent of their participation in the adsorption of nucleic acids depends on their secondary structure in the bulk of solution, ionic strength and pH of the medium and the magnitude and sign of the surface charge [99, 102]. 

In this chapter, the key findings of such studies are briefly summarized and an outlook of promising trends in the treated fields is provided. In Seetion II, an introduetion to the theory of adsorption on soUds and a summary of basic models of heterogeneous surfaees will be given. The next sections are devoted to diflerent theoretical methods used in this field. 

In between these limiting cases, compromises are possible, but they should be explained. As examples, one might wish to apply a mechanistic model to a sorbent, for which the acid-base properties can for some reason (e.g., the dominating crystal planes are not known) not be described in such detail as is, for example, possible for well-crystaUized goethite. In such cases, the features, which are known to be relevant, should be included to such an extent that adjustable parameters are limited to the number, which is actually necessary to accurately describe the experimental data. In particular, the acid-base properties are important in deciding on the basic model concept. Therefore, the simplest model for the accurate description of acid-base properties accounting for electrolyte specific behavior (e.g. 1-pK, single site. Stem model) would be appropriate, which can be extended with many options to the description of solute adsorption. 

The solid-gas interface and the important topics of physical adsorption, chemisorption, and catalysis are addressed in Chapters XVI-XVIII. These subjects marry fundamental molecular studies with problems of great practical importance. Again the emphasis is on the basic aspects of the problems and those areas where modeling complements experiment. 

Because of the relatively strong adsorption bond supposed to be present in chemisorption, the fundamental adsorption model has been that of Langmuir (as opposed to that of a two-dimensional nonideal gas). The Langmuir model is therefore basic to the present discussion, but for economy in presentation, the reader is referred to Section XVII-3 as prerequisite material. However, the Langmuir equation (Eq. XVlI-5) as such,... 

Taking into account the hydration shell of the NA and the possibility of the water content changing we are forced to consider the water -I- nucleic acid as an open system. In the present study a phenomenological model taking into account the interdependence of hydration and the NA conformation transition processes is offered. In accordance with the algorithm described above we consider two types of the basic processes in the system and thus two time intervals the water adsorption and the conformational transitions of the NA, times of the conformational transitions being much more greater... 

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. 

The model is intrinsically irreversible. It is assumed that both dissociation of the dimer and reaction between a pair of adjacent species of different type are instantaneous. The ZGB model basically retains the adsorption-desorption selectivity rules of the Langmuir-Hinshelwood mechanism, it has no energy parameters, and the only independent parameter is Fa. Obviously, these crude assumptions imply that, for example, diffusion of adsorbed species is neglected, desorption of the reactants is not considered, lateral interactions are ignored, adsorbate-induced reconstructions of the surface are not considered, etc. Efforts to overcome these shortcomings will be briefly discussed below. 

In this review we put less emphasis on the physics and chemistry of surface processes, for which we refer the reader to recent reviews of adsorption-desorption kinetics which are contained in two books [2,3] with chapters by the present authors where further references to earher work can be found. These articles also discuss relevant experimental techniques employed in the study of surface kinetics and appropriate methods of data analysis. Here we give details of how to set up models under basically two different kinetic conditions, namely (/) when the adsorbate remains in quasi-equihbrium during the relevant processes, in which case nonequilibrium thermodynamics provides the needed framework, and (n) when surface nonequilibrium effects become important and nonequilibrium statistical mechanics becomes the appropriate vehicle. For both approaches we will restrict ourselves to systems for which appropriate lattice gas models can be set up. Further associated theoretical reviews are by Lombardo and Bell [4] with emphasis on Monte Carlo simulations, by Brivio and Grimley [5] on dynamics, and by Persson [6] on the lattice gas model. 

Figure 11.15 Cation-exchange mia O-LC analysis of a mixture of model proteins (a) the original sample consisting of myoglobin (M), cytochrome C (C) and lysozyme (L) (b) and (c) proteins adsorbed on to and then released from the polyaaylic acid coated fibre with exti ac-tion times of 5 and 240 s, respectively. Reprinted from Journal of Microcolumn Separations, 8, J.-L. Liao et al., Solid phase mia O exti action of biopolymers, exemplified with adsorption of basic proteins onto a fiber coated with polyaaylic acid, pp. 1-4, 1996, with permission from Jolm Wiley Sons, New York.

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