Distribution function site energy

The state of the surface is now best considered in terms of distribution of site energies, each of the minima of the kind indicated in Fig. 1.7 being regarded as an adsorption site. The distribution function is defined as the number of sites for which the interaction potential lies between and (rpo + d o)> various forms of this function have been proposed from time to time. One might expect the form ofto fio derivable from measurements of the change in the heat of adsorption with the amount adsorbed. In practice the situation is complicated by the interaction of the adsorbed molecules with each other to an extent depending on their mean distance of separation, and also by the fact that the exact proportion of the different crystal faces exposed is usually unknown. It is rarely possible, therefore, to formulate the distribution function for a given solid except very approximately. 

The requirement that E is continuous function of q means that, in the limit, point heterogeneity (or one site per element ds) is assumed. Hence, at any time, there is a Maxwellian distribution of probabilities for adsorption on all sites with the maximum probability centered at Et. We now examine the effect of such a distribution on rates of desorption in view of the fact that thermal desorption techniques are frequently being employed to obtain information about the distribution of site energies and about the different adsorbed states on an adsorbent surface. 

It would seem better to transform chemisorption isotherms into corresponding site energy distributions in the manner reviewed in Section XVII-14 than to make choices of analytical convenience regarding the f(Q) function. The second procedure tends to give equations whose fit to data is empirical and deductions from which can be spurious. 

An analysis of the rate of release of adsorbed atoms from sites with a continuous energy spectrum for the case of an arbitrary distribution function of initial site populations was given by Carter (32). The rate equation for the t th desorption process with x = 1 and negligible readsorption is... 

To measure the site energy distribution or other surface properties of powders by measuring heats of immersion as a function of the amount of preadsorbed wetting liquid. Heats of immersion of the partly covered surfaces reveal the site energy distributions. For acid sites on cracking catalysts, for example, adsorbates of different basicity can be used to develop a topographical map of the surface activity. 

In order to solve this equation, it is necessary to have the distribution function, 4 1/. What is this distribution function It is a way to describe how the sites are distributed according to their energies, i.e., how many surface sites have energy Uv how many U2, etc. One of these functions is (Nikitas, 1988)... 

In considering the interaction energy at a given experimental temperature, it may lead to obtain very useful absolute value in the adsorbate-adsorbent system for determining the adsorption value of enthalpy in the infinite dilution region [70]. And it also leads to estimate the maximum adsorption value on the highest active site of a solid surface when evaluating the distribution function with the amount adsorbed in a monolayer [109]. 

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... 

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]. 

When evaluating the distribution function, the adsorption site energies, e, may be determined by the experimental adsorption isotherm, according to originally Zeldowitsch s expression [212]... 

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. 

---