Adsorption interaction energies

Inverse gas chromatography provides accurate thermodynamic data for solid surfaces [20]. It can be used to determine the DN and AN values of oxides and to establish adsorption isotherms [20, 21]. In this method, the solid is placed in a gas chromatographic column as the stationary phase, and probe gases are introduced into an inert carrier gas. The measured quantity is the retention time, which is related to the adsorption interaction energy and the equilibrium between adsorbed and non-adsorbed gas molecules. 

If a solid contains micropores—pores which are no more than a few molecular diameters in width—the potential fields from neighbouring walls will overlap and the interaction energy of the solid with a gas molecule will be correspondingly enhanced. This will result in a distortion of the isotherm, especially at low relative pressures, in the direction of increased adsorption there is indeed considerable evidence that the interaction may be strong enough to bring about a complete filling of the pores at a quite low relative pressure. 

In the higher pressure sub-region, which may be extended to relative pressure up to 01 to 0-2, the enhancement of the interaction energy and of the enthalpy of adsorption is relatively small, and the increased adsorption is now the result of a cooperative effect. The nature of this secondary process may be appreciated from the simplified model of a slit in Fig. 4.33. Once a monolayer has been formed on the walls, then if molecules (1) and (2) happen to condense opposite one another, the probability that (3) will condense is increased. The increased residence time of (1), (2) and (3) will promote the condensation of (4) and of still further molecules. Because of the cooperative nature of the mechanism, the separate stages occur in such rapid succession that in effect they constitute a single process. The model is necessarily very crude and the details for any particular pore will depend on the pore geometry. 

Adsorption on a nonpolar surface such as pure siUca or an unoxidized carbon is dominated by van der Waals forces. The affinity sequence on such a surface generally follows the sequence of molecular weights since the polarizabiUty, which is the main factor governing the magnitude of the van der Waals interaction energy, is itself roughly proportional to the molecular weight. 

The total potential energy of adsorption interaction may be subdivided into parts representing contributions of the different types of interactions between adsorbed molecules and adsorbents. Adopting the terminology of Barrer (3), the total energy of interaction is the sum of contributions... 

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 lateral interactions in the adsorbate can enhance or diminish the interaction energy in the surface. If the adsorption sites at the boundary between reconstructed and unreconstructed areas of surface are further distinguished from those inside these patches, we can introduce more interactions such as... 

In cases when the two surfaces are non-equivalent (e.g., an attractive substrate on one side, an air on the other side), similar to the problem of a semi-infinite system in contact with a wall, wetting can also occur (the term dewetting appHes if the homogeneous film breaks up upon cooHng into droplets). We consider adsorption of chains only in the case where all monomers experience the same interaction energy with the surface. An important alternative case occurs for chains that are end-grafted at the walls polymer brushes which may also undergo collapse transition when the solvent quality deteriorates. Simulation of polymer brushes has been reviewed recently [9,29] and will not be considered here. 

We did not extensively discuss the consequences of lateral interactions of surface species adsorbed in adsorption overlayers. They lead to changes in the effective activation energies mainly because of consequences to the interaction energies in coadsorbed pretransition states. At lower temperatures, it can also lead to surface overlayer pattern formation due to phase separation. Such effects cannot be captured by mean-field statistical methods such as the microkinetics approaches but require treatment by dynamic Monte Carlo techniques as discussed in [25]. 

Figure 7.9. Effect of lateral interactions on the distribution of a single adsorbate species A on the surface. The adsorption energy of each atom A is calculated using Eq. (20) and the interaction energies indicated underthe maps. Negative energies correspond to attraction,...

The interaction between the adsorbed molecules and a chemical species present in the opposite side of the interface is clearly seen in the effect of the counterion species on the HTMA adsorption. Electrocapillary curves in Fig. 6 show that the interfacial tension at a given potential in the presence of the HTMA ion adsorption depends on the anionic species in the aqueous side of the interface and decreases in the order, F, CP, and Br [40]. By changing the counterions from F to CP or Br, the adsorption free energy of HTMA increase by 1.2 or 4.6 kJmoP. This greater effect of Br ions is in harmony with the results obtained at the air-water interface [43]. We note that this effect of the counterion species from the opposite side of the interface does not necessarily mean the interfacial ion-pair formation, which seems to suppose the presence of salt formation at the boundary layer [44-46]. A thermodynamic criterion of the interfacial ion-pair formation has been discussed in detail [40]. 

Interaction energies, geometrical parameters and shifts in vibrational frequencies for various AN and CO adsorption complexes found in zeolites Na-A and Na-FER. 

The interaction energy, AIT, is the contribution (positive or negative) to AE, due to the (indirect) interaction between the two adatoms. In other words, AIT is the difference between the chemisorption energy AE for the doubleadsorption system and the sum of the chemisorption energies A (A = a or b) for the two individual single-adsorption systems, i.e.,... 

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