Energy distribution functions evaluations

The physicochemical interpretation of the energy distribution functions evaluated from adsorption isotherms the structural aspects such as the question of which functional groups on the surface are connected with the particular peaks on the energy distribution [39,140,162]... 

In order actually to evaluate eqs. (19)-(22), the energy distribution function must be known or calculable. This function depends upon the technique used to produce the excited species and its evaluation will be considered here for chemical and thermal activation direct photoactivation, if it occurs, requires a special case in each instance and a general form cannot be given. 

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...

The second term of Eq. (17-75) can be computed by QM/MM simulations directly. To evaluate Sjl, we consider the distribution function over the energy coordinate f. Indeed, it is possible to show that the correspondence is one-to-one from the solute-solvent interaction defined over the coordinate f to the resultant energy distribution function of f. An approximate expression for 8 ft can be given by a set of equations listed as... 

The methylene chloride adsorption isotherms were determined at 30 °C for each selected relative humidity. The BET surface area (5bet(CH2C12)), the corresponding BET constant (Cbet), and the adsorption energy distribution functions (AEDF) were then computed. The results obtained fix)m the evaluation of the adsorption isotherms are shown in Table 5. 

The numerical procedure as described above gives credible results with respect to the values of the surface phase capacity the systems studied. On the other hand, knowledge the heterogeneity parameters Bj and X° gives possibility for evaluating the energy distribution functions by means of the suitable equation corresponding with the expression (8) [1]. 

Any application of Equation (6.60) to experimental data requires knowledge of the surface fractal dimension of the adsorbent investigated so that the evaluation of the energy distribution function is reduced to an approximation of the experimental data using Equation (6.60). This calculation is most conveniently performed using a method quite similar to that described by Jaroniec and Madey [60] for geometrically uniform surfaces. 

As for the second parameters, the electric field strength Emax, we have found more sensible to employ the electron temperature instead. In fact it was simpler to express the electron rate constants, calculated from their cross-sections and evaluated assuming a Maxwellian energy distribution function for electrons, described by a single parameter, their temperature Te. 

Mizuochi, J. Sakamoto, T. Matsuura, H. Akatsuka, H. (2010). Evaluation of Electron Energy Distribution Function in Microwave Discharge Plasmas by Sp>ectroscopic Diagnostics with Collisional Radiative Model. Jpn. J. Appl Phys., Vol. 49, No. 3, (March 2010), pp. 036001-1-036001-14, ISSN 1347-4065... 

Recently, thermal-desorption [300,301] and adsorption kinetics measurements on heterogeneous surfaces [302-304] have been proposed for evaluating the energy distribution functions. These methods have been tested extensively during the last few years. 

One important line of study has been the use of experimental adsorption data to extract information about the energy distribution function. Extensive theoretical and numerical investigations were performed to answer the question of how the chosen local isotherm affects the evaluated energy distribution [5,37-39]. It follows from these studies that the functions calculated for localized and mobile adsorption are analogous [32]. On the other hand, the results obtained by Jaroniee and Brauer [37] suggest that lateral molecular interactions and the multilayer nature of the surfaee phase may play a more significant role. However, in practice, the choice of loeal isotherm has been usually treated quite casually in the majority studies, it is assumed that the loeal isotherm has a limited influence on the shape of the adsorption energy distribution funetion. 

The methods available for the evaluation of energy distribution functions can be divided into two main classes. In the procedures of the first type, a general form of the distribution funetion is assumed and the parameters are calculated from the experimental data. For other elasses, no a priori assumption is made about the shape of the energy distribution. 

One of the most effective methods of evaluation of the energy distribution function %(e) relating to the overall adsorption isotherm assumed a priori was proposed by Sips [21,22], He proved that the integral equation (10) with the Langmuir local isotherm [Eq. (11)] could be rewritten as the Stieltjes transform [105] ... 

The HILDA method developed by House and Jaycock [100] may be considered a modified, numerical version of the iterative procedure proposed by Adamson and Ling [126]. An excellent short presentations of the method can be found in the review by House [127] or in the monograph by Rudzinski and Everett [6]. This procedure can be outlined as follows The form of local isotherm is assumed and the distribution function is evaluated by using the iterative routine for each iterative step appropriate adjustments in distribution are made to bring the calculated and experimental isotherms into the best possible coincidence the condensation-approximation is used to determine the first approximation of the distribution. The Adamson-Ling method was widely applied to evaluate the energy distribution function from the measmed adsorption isotherm [97,122,128-135]. 

AH of the above-presented models of amorphous surfaces are of great importanee in theoretical studies directed toward the development of methods for the evaluation of the energy distribution function. 

The time-logarithm and time-power laws do not exhaust the kinetics observed in practical situations. If a certain behavior is observed and can reasonably be ascribed to adsorbent heterogeneity, the energy distribution function accounting for it can be evaluated as follows ... 

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