Surface sites coefficient

It is not necessary to limit the model to idealized sites Everett [5] has extended the treatment by incorporating surface activity coefficients as corrections to N and N2. The adsorption enthalpy can be calculated from the temperature dependence of the adsorption isotherm [6]. If the solution is taken to be ideal, then... 

For a radionuclide to be an effective oceanic tracer, various criteria that link the tracer to a specihc process or element must be met. Foremost, the environmental behavior of the tracer must closely match that of the target constituent. Particle affinity, or the scavenging capability of a radionuclide to an organic or inorganic surface site i.e. distribution coefficient, Kf, is one such vital characteristic. The half-life of a tracer is another characteristic that must also coincide well with the timescale of interest. This section provides a brief review of the role of various surface sites in relation to chemical scavenging and tracer applications. 

The first terms in (99) and (100) say that adsorption can take place either on the remaining sites of the reconstructed surface or on those surface sites that are neither reconstructed nor occupied. The first term in (101) allows for reconstruction from the unreconstructed area, 1 — 9, but also says that this reconstruction may be hindered or helped if there is an adsorbate on the unreconstructed surface. A similar interpretation holds for the last term in (101) describing the lifting of the reconstruction. For the adsorption coefficients Wy, Ws, etc., one writes expressions analogous to (47). 

Frequently, adsorption proceeds via a mobile precursor, in which the adsorbate diffuses over the surface in a physisorbed state before finding a free site. In such cases the rate of adsorption and the sticking coefficient are constant until a relatively high coverage is reached, after which the sticking probability declines rapidly. If the precursor resides only on empty surface sites it is called an intrinsic precursor, while if it exits on already occupied sites it is called extrinsic. Here we simply note such effects, without further discussion. 

There are several factors through which anions can influence the pathway and O2 reduction kinetics. The main factors are competition with O2 for surface sites changes in the activity coefficients of the reactants, intermediates, and transition states and the acidity and dielectric properties of the electrolyte side of the interface [Adzic, 1998]. For example, perfluoro acids have higher O2 solubility and lower adsorbability than... 

A possible explanation for the difference in tendencies of the deposition rate between experiment and model is that in the model the surface reaction and sticking coefficients of the radicals are taken to be independent of the discharge characteristics. In fact, these surface reaction coefficients may be influenced by the ions impinging on the surface [251]. An impinging ion may create an active site (or dangling bond) at the surface, which enhances the sticking coefficient. Recent experiments by Hamers et al. [163] corroborate this the ion flux increases with the RF frequency. However, Sansonnens et al. [252] show that the increase of deposition rate cannot be explained by the influence of ions only. 

The concentration of surface sites was measured by the integral intensity of the CO absorbance band using the formula C [pmol/g] = A/Aq, where A is the integral intensity of the CO stretching band and Aq is the coefficient of the integral absorbance [6]. Concentrations are measured to within 20%. 

Here m>u and m>UCd++ are molal concentrations of the unoccupied and occupied sites, respectively, and aCd++ is the activity of the free ion. Activity coefficients for the surface sites are not carried in the equation they are assumed to cancel. Equilibrium constants reported in the literature are in many cases tabulated in terms of the concentrations of free species, rather than their activities, as assumed here, and hence may require adjustment. 

As described in Chapter 3, v ,/ and so on are the reaction coefficients by which species are made up from the current basis entries. Mass transfer coefficients are not needed for gases in the basis, because no accounting of mass balance is maintained on the external buffer, and the coefficients for the mole numbers Mp of the surface sites are invariably zero, since sites are neither created nor destroyed by a properly balanced reaction. 

In surface-complexation models, the relationship between the proton and metal/surface-site complexes is explicitly defined in the formulation of the proposed (but hypothetical) microscopic subreactions. In contrast, in macroscopic models, the relationship between solute adsorption and the overall proton activity is chemically less direct there is no information given about the source of the proton other than a generic relationship between adsorption and changes in proton activity. The macroscopic solute adsorption/pH relationships correspond to the net proton release or consumption from all chemical interactions involved in proton tranfer. Since it is not possible to account for all of these contributions directly for many heterogeneous systems of interest, the objective of the macroscopic models is to establish and calibrate overall partitioning coefficients with respect to observed system variables. 

General Observations About x. its Relationship to the Overall Partitioning Coefficient and to the Concept of Surface-Site Heterogeneity. One approach to metal/particle surface interactions which has been developed, historically, in a variety of forms, is a conceptual model that assumes only two conditions for surface sites occupied by an adsorbate or unoccupied. In applying this approach to the solid/aqueous solution interface, the adsorption... 

In their description of metal ion adsorption, Benjamin and Leckie used an apparent adsorption reaction which included a generic relationship between the removal of a metal ion from solution and the release of protons. The macroscopic proton coefficient was given a constant value, suggesting that x was uniform for all site types and all intensities of metal ion/oxide surface site interaction. Because the numerical value of x is a fundamental part of the determination of K, discussions of surface site heterogeneity, which are formulated in terms similar to Equation 4, cannot be decoupled from observations of the response of x to pH and adsorption density. As will be discussed later, It is not the general concept of surface-site heterogeneity which is affected by what is known of x> instead, it is the specific details of the relationship between K, pH and T which is altered. 

Surface site densities used in the computation of the oxide site concentrations presented in this paper were determined by either rapid tritium exchange or acquired from published values (18). Reported total site densities for hydrous metal oxides show relatively little variation generally they range by less than a factor of 3. Since [M], [SOM], [H] and x are known or can be determined from experimental data, uncertainties in estimates of the total site concentration are directly translated into uncertainties in the calculated partitioning coefficient. 

Macroscopic Coefficients and Surface-Site Heterogeneity. Beniamin and heckles model (5) of heterogeneous metal oxide surface sites includes two observations of metal ion/surface site Interactions. 

To what extent is the macroscopic proton release the direct expression of the metal/surface site reactions Table V compares the macroscopic proton coefficients (Xp ) ) with the coefficient expected if only the Cd(II) surface reactions are considered is the proton coefficient determined by considering the mole fraction of Cd(II) surface species and their formation reactions (Figure 14b). For example, when pSOH is 2.84, y = 0.11 x 1 + 0.89 x 2 = 1.89. At high alumina concentrations pSOH 2.14-2.53) the single surface reaction required to fit the data sets a limiting proton release of 2.0. 

Equation 17.59 has been confirmed experimentally, suggesting that molecules move over a surface by hopping to adjacent adsorption sites. It may be assumed that this process involves a lower energy of activation than that required for complete desorption. The molecule will continue to hop until it finds a vacant adsorption site, thus explaining the increase of surface diffusion coefficient with coverage. 

Etchant species (for example, fluorine atoms) diffuse to the surface of the material and adsorb onto a surface site. It has been suggested (20) that free radicals have fairly large sticking coefficients compared with relatively inert molecules such as CF4, so adsorption occurs easily. In addition, it is generally assumed (20) that a free radical will chemisorb and react with a solid surface. Further, surface diffusion of the adsorbed species or of the product molecule can occur. 

There are a host of physical questions that cannot be easily answered just by knowing the rates listed in Fig. 6.13. For example, once an Ag atom is deposited on the surface, how long will it be (on average) before that Ag atom visits a site adjacent to a Pd surface atom How many different Pd surface sites will an Ag atom visit per unit time on the surface What is the net diffusion coefficient of Ag atoms on this surface To answer these questions, we need a tool to describe the evolution in time of a set of Ag atoms on the surface. 

Thus, the sorption of chemicals on the surface of the solid matrix may become important even for substances with medium or even small solid-fluid equilibrium distribution coefficients. For the case of strongly sorbing chemicals only a tiny fraction of the chemical actually remains in the fluid. As diffusion on solids is so small that it usually can be neglected, only the chemical in the fluid phase is available for diffusive transport. Thus, the diffusivity of the total (fluid and sorbed) chemical, the effective diffusivity DieS, may be several orders of magnitude smaller than diffusivity of a nonsorbing chemical. We expect that the fraction which is not directly available for diffusion increases with the chemical s affinity to the sorbed phase. Therefore, the effective diffusivity must be inversely related to the solid-fluid distribution coefficient of the chemical and to the concentration of surface sites per fluid volume. 

According to the assumption made, c is identical for all surface sites. Thus, adsorption coefficients of gases A and A are mutually proportional. Equilibrium surface coverage by gas A is... 

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