Energy, adsorption

Using guest fluorophores, they show that the adsorption energy increases linearly with the alkyl chain length as... 

The following derivation is modified from that of Fowler and Guggenheim [10,11]. The adsorbed molecules are considered to differ from gaseous ones in that their potential energy and local partition function (see Section XVI-4A) have been modified and that, instead of possessing normal translational motion, they are confined to localized sites without any interactions between adjacent molecules but with an adsorption energy Q. 

Fig. XVII-18. Contours of constant adsorption energy for a krypton atom over the basal plane of graphite. The carbon atoms are at the centers of the dotted triangular regions. The rhombuses show the unit cells for the graphite lattice and for the commensurate adatom lattice. (From Ref. 8. Reprinted with permission from American Chemical Society, copyright 1993.)...

Alternatively, an integral distribution function F may be defined as giving the fraction of surface for which the adsorption energy is greater than or equal to a given Q,... 

The fact that more than one molecule of water may be displaced for each anion adsorbed, and that the adsorption energy of these water molecules will show a complex dependence on the electrode potential. 

With the aid of (B1.25.4), it is possible to detennine the activation energy of desorption (usually equal to the adsorption energy) and the preexponential factor of desorption [21, 24]. Attractive or repulsive interactions between the adsorbate molecules make the desorption parameters and v dependent on coverage [22]- hr the case of TPRS one obtains infonnation on surface reactions if the latter is rate detennming for the desorption. 

Application of Snyder s theory of linear chromatographic adsorption (171) gives the variation in adsorption energy of the thiazole nitrogen atom as a function of this steric hindrance for silica and alumina (see Table III-22). These results show that alumina is more sensitive toward steric effects while silica shows a higher selectivity in the case of polar effects. 

TABLE m-22. VARIATION OF THE ADSORPTION ENERGY OF THE THIAZOLE NITROGEN ATOM WITH SUBSTITUENTS [A0°(-N=)] (171)... 

The potential energy 0(z) depends not only on the distance z hut also on the position of the gas molecule in the xy plane parallel to the surface of the solid and distant z from it. For any given position, the adsorption energy will be equal to the value of 0 = 0o minimum of the potential curve (cf. Fig. 1.2), which of course represents the equilibrium position. 

From these various examples, it is clear that the adsorption energy for a given kind of site can vary quite markedly from one crystal face of the adsorbent to another. For argon on solid xenon (Table 1.1), for example, the most favourable site has a o value of —1251 x 10" J on the (100) face but only -1072 on the (111) face. Such differences are in no way surprising, and they have been found also with ionic crystals. 

The lower pressure sub-region is characterized by a considerable enhancement of the interaction potential (Chapter 1) and therefore of the enthalpy of adsorption consequently the pore becomes completely full at very low relative pressure (sometimes 0 01 or less), so that the isotherm rises steeply from the origin. This behaviour is observed with molecular sieve zeolites, the enhancement of the adsorption energy and the steepness of the isotherm being dependent on the nature of the adsorbent-adsorbate interaction and the polarizability of the adsorbate. -... 

Fig. 10. Calculations of the adsorption of a polymer at an interface show pronounced sensitivity to the total adsorption energy, leaving only a limited range...

Several numerical procedures for EADF evaluation have also been proposed. Morrison and Ross [19] developed the so-called CAEDMON (Computed Adsorption Energy Distribution in the Monolayer) method. Adamson and Ling [20] proposed an iterative approximation that needs no a priori assumptions. Later, House and Jaycock [21] improved that method and proposed the so-called HILDA (Heterogeneity Investigation at Loughborough by a Distribution Analysis) algorithm. Stanley et al. [22,23] presented two regularization methods as well as the method of expectation maximalization. 

In the ease of a lattiee model the procedure to generate a pseudo-random distribution of adsorption energies over sites, with the preassumed form of the EADF, ean be summarized in just a few steps ... 

Choose a site on the lattiee. That ean be done either in a systematie or a random way, but the latter method requires more eomputing time. Draw the value of the adsorption energy, from the speeified interval, aeeording to the assumed form of x( ) and assign this value to the ehosen site. (The proeedures to generate random sequenees of numbers aeeording to a given probability distribution ean be found in many textbooks on probability theory [67] and eomputer simulation methods [52].)... 

In the ease of intermediate topography, they assume that there is a eertain eharaeteristie (for a given surfaee) length, r or, whieh defines the size of small domains eharaeterized by the same value of adsorption energy, and write the pair density distribution as... 

FIG. 2 Distribution of the adsorption energy (a) and of the adsorbate-adsorbate interaction energy (b) for the adsorbed Ar atoms obtained from computer simulations at r = 90 K. (Reprinted with permission from Langmuir 5 148-154, August 1992. 1992, American Chemical Society.)... 

In the above, U] ] is the nearest neighbor interaction energy, V is the adsorption energy and Fb is the boundary field acting on the particles located at the patch boundary... 

The main controlling parameters of that model are the size of homogeneous clusters M, and the difference between the adsorption energies AF= - V2. 

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