Potential Energies for Adsorption

Kirkwood-Muller formula, potential energies for adsorption, 83... 

Four general types of molecular interaction lead to a potential energy for adsorption ... 

We have developed general expressions in the preceding sections for the calculation of the dispersion potential contribution to the potential energy for adsorption and for the vibrational frequency of the adsorbed molecule, using various expressions for the lattice sums. We now propose to apply these equations, for the purpose of comparison with experiment, to the adsorption of the inert gases by graphite. 

The concept of adsorption potential comes from work with high-purity, synthetic microporous carbon, which relies solely on van der Waals dispersive and electrostatic forces to provide the energy for adsorption. The polymeric microporous adsorbents that operate solely through van der Waals dispersive and electrostatic forces often cannot provide the surface potential energy needed to trap compounds that are gases under ambient conditions, and for very volatile compounds the trapping efficiency can be low for similar reasons. 

Subsequently, it is possible to consider that the adsorbate-adsorbent interaction field inside these structures is characterized by the presence of sites of minimum potential energy for the interaction of adsorbed molecules with the zeolite framework and charge-compensating cations. A simple model of the zeolite-adsorbate system is that of the periodic array of interconnected adsorption sites, where molecular migration at adsorbed molecules through the array is assumed to proceed by thermally activated jumps from one site to an adjacent site, and can be envisaged as a sort of lattice-gas. 

Since the free energy for adsorption is expressed as the sum of the adsorbate-adsorbate and adsorbate-adsorbate-adsorbent interactions, the potential energy minimum, e, corresponding to these two interactions can be expressed in terms of two dispersion constants, Aa a and respectively, the number density of the adsorbate molecules (N ) and adsorbent atoms (Ng) per unit area [32]. Thus, the potential function becomes... 

Intercalated or surface adsorbed species in the electron conductor. Protons and li ions, if present in the hole conductor, may be capable of intercalating into the oxide film, affecting both the potential energy for electron stabilization and the ease of electronic conduction. Surface absorbed cations influence electronic states near the surface. Adsorption of OH groups influences electronic states and proton transport. Water molecules, which are expected to be present around the oxide surface even in dry solvent, may be dissociatively adsorbed leaving adsorbed OH species and mobile protons, which influence electronic states and conductivity. 

We have addressed the potential energy for a number of cases in the last sections (Sections 6.10-1 to 6.10-5). The analysis of the last two cases (i) a molecule and two parallel lattice planes and (ii) a molecule and two parallel slabs, are particularly useful for the study of adsorption of nonpolar molecules in slitshaped micropore solids, such as activated carbon. 

If the additional energy for adsorption of surfactant molecules is required due to the potential barriers in the adsorption system, then, similarly with (8.A.3), the exponential factor is introduced into Equation 8.A.10, that is. 

Fig. 3. a) Excess amount adsorbed as function of the isostoic heat of adsorption at 10 kPa. b) Corresponding distribution of methane / fiamewoik potential energies for individual methane molecules ( IRMOF-1, A IRMOF-9, X IRMOF-10). The lines were added to guide the eye. 

Atoms equilibrate efficiently with the temperature of a surface when their kinetic energy is small compared to the heat of adsorption. The thermal accommodation decreases, however, with increasing energy of the atoms. The minimum occurs when the kinetic energy is on the order of the depth of the potential well for adsorption. For higher kinetic energies thermal accommodation increases again to the value for collision with a free atom of the surface material. 

Hggg for water vapour, free water and adsorbed water in hardened fibre reinforced concrete. When free water is adsorbed on the cement gel, its enthalpy content is reduced physically, this means that the water molecules are transferred to a state with lower potential energy. For the adsorption process considered, AH —5 kJ/mol. This is of the same magnitude as AH for freezing of free water. 

Figure A3.10.17 Potential energy diagram for the dissociative adsorption of N2 [46].

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