Desorption energy, heterogeneous surface

An important result is that the effective desorption energy for the heterogeneous surfaces depends on temperature Nevertheless, let us for a while abandon it and suppose that jjet does not depend on temperature. Another assumption will be that the entropy change is the same for all partial isotherms, independent of EA. Then we take into account Eq. 5.3 for the experimental constant of adsorption and move to the characteristics of desorption from heterogeneous surfaces. It follows that the measurements yield an equilibrium constant, which is to be interpreted as the entropy factor multiplied by the expectation value of the desorption energy factor ... 

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. 

CI2 evolution reaction, 38 56 electrochemical desorption, 38 53-54 electrode kinetics, 38 55-56 factors that determine, 38 55 ketone reduction, 38 56-57 Langmuir adsorption isotherm, 38 52 recombination desorption, 38 53 surface reaction-order factor, 38 52 Temkin and Frumkin isotherm, 38 53 real-area factor, 38 57-58 regular heterogeneous catalysis, 38 10-16 anodic oxidation of ammonia, 38 13 binding energy quantification, 38 15-16 Haber-Bosch atrunonia synthesis, 38 12-13... 

In a real system, the desorption energy (E is dependent on the coverage. Therefore, Gillis-D Hamers has evaluated the surface heterogeneity by the constant coverage, variable heating rate method, developed by Richards and Rees.30 This method estimates Ed as a function of coverage by the least-squares minimization of the experimental data. 

The transient response experiments were analyzed by a dynamic isothermal PFR model, and estimates of the relevant kinetic parameters were obtained by global nonlinear regression over all runs. It was found that a simple Langmuir approach could not represent the data accurately, and surface heterogeneity had to be invoked. The best fit was obtained using a Temkin-type adsorption isotherm with coverage-dependent desorption energy ... 

The surface energetic heterogeneity determination constitutes an additional aspect of the present study. This was performed by means of the methylene chloride adsorption energy distribution functions (AEDF) computation, relating the number of interactive surface sites to the desorption energy of each individual site. The latter are displayed in Fig. 1. 

Next, the qualitative and quantitative compositions of the carrier gas, especially as to the most chemically active components, have not been the same in different laboratories. As a result it is not known whether the surfaces were modified to a comparable degree in different studies. An even more important question is, how complete was the coverage of the surface by the grafted molecular fragments These factors critically affect the resulting surface heterogeneity and the spectrum of the desorption energies. 

In the Monte Carlo simulations of the chromatographic and related processes we should also account for the new knowledge about the deep heterogeneity of surfaces, about the role of localized adsorption and about the occurrence of surface diffusion. Evidently, now the molecular desorption energy accepted for a concrete simulation is to be understood as the effective value over the spectrum of possible energies in the sense of Eq. 5.71. As such, it is related to a concrete form of the p(E ). The... 

The asymptotically correct approximation (ACA) was first introduced by Hobson [44] for the description of adsorption equilibrium on heterogeneous surfaces it has however become of wide use in the analysis of adsorption isotherms only after Cerofolini s investigation of the involved errors (which are of the same order as in the CA) and demonstration of its usefulness in determining the maximum adsorption energy [28]. The ACA can be extended to desorption kinetics by replacing the supposedly true desorption isotherm kinetics A (t,E) with their asymptotic limits. Since... 

This section is devoted to the calculation of the desorption kinetics from a heterogeneous surface characterized by a desorption energy distribution function (peq(E) given by Eq. (9) with E = q, i.e. of the desorption kinetics from a surface which in equilibrium conditions obeys the Freundlich or Temkin isotherm. The local desorption kinetics will be assumed to be of the first order. 

The energetic heterogeneity of the solid surface is described by the energy distribution function distribution probability on the surface of the studied sample in relation to the quantity of desorption energy. 

Tables 3 and 4 present the ranges of Ei value changes for individual systems. The shape of the curves of the thermodesorption energy distribution functions presented in Figure 12 are similar to Gaussian curves with one distinct peak indicating the existence of one main active centre on the surface of the adsorbents. The increase of desorption energy dmax for polar liquids (in kJ/mol 32.29< dmax<84.59 for water and 24.44< dmax<60.06 for n-butanol) is evidence of an increase of the adsorbent-adsorbate interaction forces. Broadening of bands on the desorption energy distribution curves indicates the increase of energetic heterogeneity of the studied materials.

Unimolecular (desorption of intact molecules =MOH- OH2 =MOH -I- H2O) or associative (=M(OH)—0(H)— =M-0-M= + H2O or =M(OH)—O—(HO)M= -> =M(Oo)M= + H2O) desorption of water molecules can be described by the rate with Equation (37.12) of first or second order, respectively. The relationship between the ion current measured and the reaction rate constants was described elsewhere [29]. The fumed oxide surfaces are heterogeneous and every type of surface sites can influence the corresponding desorption peak and the corresponding center (E ) in a desorption energy distribution for this peak. If the TPD spectrum is convoluted into several peaks without any restriction that the activation energy calculated over the total temperature ranges for each of the peaks can be underestimated due to the overestimation of the peak width. Therefore, we used some modification of the calculations described in detail elsewhere [25,29]. 

The only gas chromatographic method used for the measurement of diffusion coefficients of gases on solid surfaces is the RF-GC technique validating a recent mathematical analysis, also permitting the estimation of adsorption and desorption rate constants, local adsorbed concentrations, local isotherms, local monolayer capacities, and energy distribution functions." The RF-GC technique has been successfully applied for the time-resolved determination of surface diffusion coefficients for physically adsorbed or chemisorbed species of O2, CO, and CO2 on heterogeneous surfaces of Pt/Rh catalysts supported on Si02." All calculations for the... 

Brun has extended the concept of LCCC to the cases of statistical copolymers as well as porous stationary phases with heterogeneous surfaces (viz., surfaces with both inert and active groups) [ 162]. The theory predicted that a statistical copolymer with narrow CCD always possesses a single adsorption-desorption transition point and behaves like a homopolymer with a single energy of interaction between the effective monomer units and the active groups at the surface. If copolymer has a broad CCD, each compositionally homogeneous fraction has its own adsorption-desorption threshold. 

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