Adsorption isotherms heterogeneous surfaces

Fig. 6. A Frumkin-Fowler s adsorption isotherm for uniform surfaces. B, C Adsorption isotherm for heterogeneous surfaces with condensation [after Ref. 89]...

Katsanos, N.A. Arvanitopoulou, E. Roubani-Kalantzopoulou, E. Kalantzopoulos, A. Time distribution of adsorption energies, local monolayer capacities, and local isotherms on heterogeneous surfaces by inverse gas chrom atography. J. Phys. Chem. B. 1999,103,1152-1157. Katsanos, N.A. Gavril, D. Karaiskakis, G. Time-resolved determination of surface diffusion coefficients for physically adsorbed or chemisorbed species on heterogeneous surfaces by inverse gas chromatography. J. Chromatogr. A, 2003, 983,177-193. 

A New Approach to the Theory for Adsorption Isotherms on Heterogeneous Surfaces,... 

The BET model has been generalized by using of various monolayer isotherms for heterogeneous surfaces Langmuir-Freundlich [94], Toth [95], generalized Freundheh (GF) [94], Dubinin-Radushkevich [67,95,96], and others [5]. These equations have been apphed to the interpretation of experimental data [5,6]. The above-discussed procedure has also extended to the adsorption with lateral interactions on randomly heterogeneous surfaces also [5]. 

A somewhat subtle point of difficulty is the following. Adsorption isotherms are quite often entirely reversible in that adsorption and desorption curves are identical. On the other hand, the solid will not generally be an equilibrium crystal and, in fact, will often have quite a heterogeneous surface. The quantities ys and ysv are therefore not very well defined as separate quantities. It seems preferable to regard t, which is well defined in the case of reversible adsorption, as simply the change in interfacial free energy and to leave its further identification to treatments accepted as modelistic. 

Most calculations of f(Q) for a heterogeneous surface, using an adsorption isotherm assume a patchwise distribution of sites. Explain for what kind of local isotherm functions,/((2,P, T) this assumption is not necessary, and for which it is necessary. Give examples. 

Discuss physical situations in which it might be possible to observe a vertical step in the adsorption isotherm of a gas on a heterogeneous surface. 

A typical adsorption process in electrocatalysis is chemisorption, characteristic primarily for solid metal electrodes. The chemisorbed substance is often chemically modified during the adsorption process. Then either the substance itself or some fragment of it is bonded chemically to the electrode. As electrodes mostly have physically heterogeneous surfaces (see Sections 4.3.3 and 5.5.5), the Temkin adsorption isotherm (Eq. 4.3.46) is suitable for characterizing the adsorption. 

Adsorption Isotherm Measurements and Site-Selective Thermodynamics. For heterogeneous surfaces like CSPs, the adsorption isotherms are usually composite isotherms and often a Bi-Langmuir model (Equation 1.15) describes reasonably well the adsorption behavior [54]. 

Quantifying adsorption of contaminants from gaseous or liquid phases onto the solid phase should be considered valid only when an equilibrium state has been achieved, under controlled environmental conditions. Determination of contaminant adsorption on surfaces, that is, interpretation of adsorption isotherms and the resulting coefficients, help in quantifying and predicting the extent of adsorption. The accuracy of the measurements is important in relation to the heterogeneity of geosorbents in a particular site. The spatial variability of the solid phase is not confined only to field conditions variability is present at all scales, and its effects are apparent even in well-controlled laboratory-scale experiments. 

Freundlich Adsorbents that follow the Freundlich isotherm equation are assumed to have a heterogeneous surface consisting of sites with different adsorption potentials, and each type of site is assumed to adsorb molecules, as in the Langmuir equation (Perry and Green, 1999) ... 

Temkin (1941) approached the development of an adsorption isotherm by considering a heterogeneous surface (Section 6.8.3) where no molecular interactions exist. He divided the surface into different patches, and since there are no interactions between molecules, in each patch the Langmuir isotherm can be applied [see Eq. (6.196)] (Fig. 6.98). Thus, for the ith patch,... 

This is the equation, the isotherm, we were seeking. It is a generalized isotherm for the adsorption of ionic species on a heterogeneous surface. It considers the adsorption reaction as a substitution process, with the possibility of transfer of charge between the ion and the electrode and also lateral interactions among adsorbed species. 

As already discussed, DFT can be used to predict the capillary condensation and capillary evaporation pressures for pores with homogeneous surface and well-defined geometry. To generate model adsorption isotherms for heterogeneous pores, it is convenient to employ hybrid models based on both DFT data for homogeneous pores and experimental data for flat heterogeneous surfaces [6-9]. Such model adsorption isotherms can be used to calculate PSDs in mesopore [6-9] and micropore [9] ranges. This approach is particularly useful for pores of diameter below 2-3 nm (micropores and narrow mesopores), where an assumption about the common t-curve for pores of different sizes is less accurate, which in turn makes the methods based on such an assumption (even properly calibrated ones) less reliable [18],... 

The differences observed in the adsorption isotherm are also qualitatively and quantitatively significant for the entropy. It has been recently shown that the isotherm of adsorption of an ideal adsorbate on a heterogeneous surface can be appreciably improved by taking into account the exact form of S from Eq. (7) instead of the approximate one arising from F-H theory [22], Results for the coverage dependence of the chemical potential (adsorption isotherm) and entropy per site are shown in figs. 1-2 for various fc-mer s sizes and interaction energies [attractive (w<0) as well as repulsive (w>0)]. 

Two-dimensional condensation—on homogeneous surfaces—leads to sudden jumps in the adsorption isotherm. These jumps may already be found at very low pressures of the gas which is in equilibrium with the adsorbed layer (242). Heterogeneous surfaces do not give rise to sudden jumps but to gradual slopes (Sec. V,12). There is sometimes a tendency to consider such jumps as indications of multimoleeular adsorption this is not correct. It is of course true that stepwise adsorption can also occur together with multimoleeular adsorption. (See also Sec. V,12.)... 

For an energetically heterogeneous surface, where centers of different adsorption intensity are scattered, a superposition of the Langmuir isotherm results in... 

Fig. 7. Adsorption isotherm of a surfactant with patches and phase transition on heterogeneous surfaces [after Ref. 96]...

Surfaces, Academic Press, San Diego, CA, 1992. An exhaustive review of the site probability approach to describe adsorption isotherms for heterogeneous adsorbents, analogous to the rate coefficient probability approach discussed in Section 4.2. 

A previous paper of this series (13) describes the analysis of adsorption iso- therms for heterogeneous surfaces in terms of a Gaussian distribution of adsorptive potentials. The distribution of adsorptive potential energies may not, however, have a form that is symmetrical about a mean it could possess enough asymmetry so that the adsorption isotherm could not be described by a model that assumed a Gaussian distribution. 

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