Site energy distribution integral

FIGURE 13.5 Calorimetric and volumetric data obtained from adsorption calorimetry measurements Raw pressure and heat flow data obtained for each dose of probe molecule and Thermokinetic parameter (a), Volumetric isotherms (b), Calorimetric isotherms (c), Integral heats (d), Differential heats (e), Site Energy Distribution Spectrum (f). (From Damjanovic, Lj. and Auroux, A., Handbook of Thermal Analysis and Calorimetry, Further Advances, Techniques and Applications, Elsevier, Amsterdam, 387-438, 2007. With permission.)... 

The second approximation to the F vs. b plot is shown in Figure 2,a as well as F3 vs. 6, obtained by repeating the above procedure. In the present example F i vs. b was taken to be in the terminal approximation (also shown in Figure 1,6) and, by means of Equation 4, the integral site energy distribution F(Q) was obtained. The corresponding differential site energy distribution is shown in... 

The site energy distribution function f Q) can be calculated by using the experimentally observed overall isotherm (p,T) and a theoretical local isotherm function d(p,T,Q). Here a Langmuir type model equation 9(p,T,Q) with corrections for multilayer adsorption and lateral interactions between the adsorbed molecules is chosen [54—56]. Then the integral equation can be solved by an analytical iterative method based on numerical integration [57]. More details about this procedure are found in [22,53]. 

Both the molecular ion energies (i.e., site energies, e ) and the hopping integrals, V, form distributions because of tRe local variations in composition and structure. While a proper analysis of the resulting model is complicated (25, 26), the qualitative features of interest to us can be defined in terms of a mean site energy g, the rms deviation from this mean... 

The integral kernel K(x,y) represents the local isotherm in equation (1), i.e., the physicochemical model of adsorption on sites of the same energy, g(y) is the experimentally measurable adsorption isotherm 0t(p), and f(x) = F(e) denotes the energy distribution function. 

In order to obtain the energy distribution functions of excitons, occupying the intrinsic sites, f(fc, t), one has to account for contributions from both excitons that still occupy molecules in which they have been initially generated and excitons that made one or more jumps within the manifold of intrinsic sites. The former contribution, p0(t), can be calculated by multiplying Eq. (3.12) by the intrinsic EDOS distribution and integrating the product over energy. The result reads ... 

Integration of the simple Langmuir expression assuming a uniform distribution of site energies yields the three-parameter Unilan expression [5] ... 

To obtain the adsorption energy distribution from experimental adsorption data, one can use a formalism of the integral equation for the overall adsorption [75,90]. This equation simply states that the overall adsorption is a sum of the contributions from adsorption on all of the adsorption sites present on the surface ... 

Initially the first two possibilities of integral adsorption equation were intensively expolored by investigators who used almost exclusively the Langmuir adsorption isotherm [223-231]. Then, the type of the topography of adsorption sites is of free choice. The mathematical forms of the overall adsorption isotherms depend only on the shape of the energy distribution functions, which characterize... 

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