Distribution function of adsorption energy

Distribution Function of Adsorption Energy. From chromatographic data it is possible to relate the amount of solute adsorbed on a solid to the equilibrium pressure and thus to plot its adsorption isotherm. For a heterogeneous surface, the experimentally measured adsorption isotherm can be described as a sum of local isotherms corresponding to different surface-active sites. The isotherm can then be represented by the following integral equation ... 

It is clear that on a uniform surface one would expect stepwise condensation. That this is not the case leads one to discard the assumption of uniformity, and assume that there is a distribution function of adsorption energies over the surface. If the surface is characterized by a distribution function. Vae, and the sites of equal energy are collected in patches, each patch will fill at a pressure p/po = erAE/RT. The total coverage will be... 

For this work, we [109] proposed an analytical method for the correlation between infinite dilution and finite dilution in adsorbate-adsorbent interaction system. And we reported the results of the experimental adsorption isotherm calculated by a distribution function of adsorption site energies on the basis of Fermi-Dirac s law. 

The study of adsorption isotherm starts from the chromatographic results obtained at the state of infinite dilution which can be taken as a first value of adsorption energy when evaluating the distribution function of adsorption site energies as increasing the amount adsorbed. Thereby, we obtain a new... 

Figure 17 obviously shows that the distribution function of adsorption site energies, /(e), is very similar to BET distribution transform, at low coverage (e > e/(g)=i/2), and behaves similarly to Langmuir s adsorption [178] towards surface monolayer at high coverage. 

FIG. 17 Distribution functions of adsorption site energies on the electrochemically treated carbon fibers (supplied by Soficar, T-300), measured at 30 °C. 

Figure 18 shows all experimental distribution functions of adsorption site energies studied. In Fig. 19, the [e/( )= 1/2] of the n-hexane and ethyl acetate adsorption are increased by electrochemical or anodic oxidation of the carbon fibers. In particular, the results of the ethyl acetate probe which is... 

In the absence of redistribution of molecules on the surface the velocity of the adsorption process is determined solely by the distribution function of activation energies. The velocity of adsorption on sections of the surface characterized by the activation energy E is expressed in terms of the change in the fractional surface coverage 8(E,t) with the time t by... 

S. J. Park and J. B. Donnet, Evaluation of the distribution function of adsorption site energies based on the Fermi-Dirac s law in a monolayer, J. Colloid Interface Sci. 200 (1998) pp. 46-51. 

The results obtained with the different silicas point to the importance of the mode of preparation on their surface characteristics and thus on their surface heterogeneity. Understanding of the surface heterogeneity can be attained by calculation of the distribution function of the energy of adsorption of alkane molecules on the surface of the solids. 

FIGURE 1.13 Isotherms of water adsorption at 293 K on silicas shown in Table 1.4 in (a, c) mmol/g and (b) mmol/m, (c) adsorption and desorption of water is shown, and (d) distribution functions of free energy of water adsorption onto silicas. (Adapted from J. Colloid Interface Sci., 242, Gun ko, V.M., Mironyuk, I.F., Zarko, V.I. et al.. Fumed silicas possessing different morphology and hydrophilicity, 90-103,2001d. Copyright 2001, with permission from Elsevier.)... 

AG) is the distribution function of free energy of adsorption AG Vl if the flow velocity L is the filter (bed) thickness Vp is pore volume... 

Figure 6. Distribution function of changes in Gibbs free energy of Cu(II) adsorption on APDMS silicas.

If the surface of an adsorbent is energetically homogeneous, three well-known statistics are fundamentally considered for evaluating the distribution functions of the adsorption site energy or probability of a state of energy, /(e), in the adsorbate-adsorbent system [109]. 

Fig. 15 Adsorption isotherms and evaluated energy distribution functions of ethylene on four different colloidal fillers at T=223 K (1) channel gas black (2) graphitic powder (3) N220 (4) graphitized N220g...

Inverse Gas Chromatography at finite concentration conditions (IGC-FC) offers another possibility to perform such determinations. Furthermore, IGC readily provides the data required for the calculation of adsorption energy distribution functions. The aim of the present study was to... 

The first domain is used to determine the specific surface area (5 bet(H20)) and the BET constant values. Moreover, the large number of available experimental points allows the calculation of the corresponding adsorption energy distribution function of water on silica. 

In the above, the heterogeneity parameters nt and m characterize the shape (width and asymmetry) of adsorption energy distribution function, and the equilibrium constant, ATi , describes the position of distribution function on energy axis... 

The use of the characteristic functions facilitated the extension of the stochastic theory to two-site [99] or to generic multiple-site heterogeneous surfaces [100] that are very complex to handle otherwise [5,101,102]. Thus, the stochastic theory is able to model the band profiles that are due to any unimodal or multimodal distribution of adsorption energies. The stochastic model was further extended to describe the effect of mobile phase dispersion and size exclusion effects as well [7,8,103]. 

Correlation of the parameters of heterogeneous surface active sites or its distribution functions on these parameters with activation parameters of organic compound chemisorption on the oxides surface is required for establishment of the reaction mechanism (for example, SeI or SnI)- An approach for calculation of distribution functions of heterogeneous surface active sites on the donor, acceptor and polarization components of organic compounds adsorption energy using the nonlinear inverse gas chromatography... 

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