Physisorption equilibria

A general mathematical description of physisorption equilibria is given by Gibbs law, which relates the adsorbed amoimt r to the decrease in surface tension o if the concentration c of an adsorbable substance in solution increases. In its complete form Eq. (2.45), Gibbs law displays ct as a function of the chemical... 

Adsorbates can physisorb onto a surface into a shallow potential well, typically 0.25 eV or less [25]. In physisorption, or physical adsorption, the electronic structure of the system is barely perturbed by the interaction, and the physisorbed species are held onto a surface by weak van der Waals forces. This attractive force is due to charge fiuctuations in the surface and adsorbed molecules, such as mutually induced dipole moments. Because of the weak nature of this interaction, the equilibrium distance at which physisorbed molecules reside above a surface is relatively large, of the order of 3 A or so. Physisorbed species can be induced to remain adsorbed for a long period of time if the sample temperature is held sufficiently low. Thus, most studies of physisorption are carried out with the sample cooled by liquid nitrogen or helium. 

Chemical Potential. Equilibrium calculations are based on the equaHty of individual chemical potentials (and fiigacities) between phases in contact (10). In gas—soHd adsorption, the equiHbrium state can be defined in terms of an adsorption potential, which is an extension of the chemical potential concept to pore-filling (physisorption) onto microporous soHds (11—16). 

The chemistry of superheavy elements has made some considerable progress in the last decade [457]. As the recently synthesized elements with nuclear charge 112 (eka-Hg), 114 (eka-Pb) and 118 (eka-Rn) are predicted to be chemically quite inert [458], experiments on these elements focus on adsorption studies on metal surfaces like gold [459]. DFT calculations predict that the equilibrium adsorption temperature for element 112 is predicted 100 °C below that of Hg, and the reactivity of element 112 is expected to be somewhere between those of Hg and Rn [460, 461]. This is somewhat in contradiction to recent experiments [459], and DFT may not be able to simulate accurately the physisorption of element 112 on gold. More accurate wavefunction based methods are needed to clarify this situation. Similar experiments are planned for element 114. 

Table V collects the dimer yields that represent the essential quantity of the preparative data of anodic styrene oxidation. The table also contains the adsorption equilibrium coefficients AT" for styrene obtained by evaluating current voltage curves. Again, the particular physisorptive properties of graphitic carbon for unsaturated molecules are stressed by the data of Table V.

Because of its intrinsically specific nature, chemisorption has an irreplaceable role. It should be recognized, however, that well defined thermodynamic equilibrium physisorption is much more difficult to achieve by chemisorption than with physisorption. Moreover, it docs not obey simple kinetics. Empiricism permits... 

With the assumption of an inert adsorbent, we may consider the physisorption process as a simple phase change of the adsorptive from the gaseous state to an adsorbed state on the surface A of the adsorbent. Since for a closed adsorption system at equilibrium dn = dnCT + dn = 0, we may express the condition of equilibrium in the form... 

As explained in Chapter 1, the shape of an adsorption isotherm provides useful preliminary information concerning the mechanisms of physisorption, and hence the nature of the adsorbent. For example, a reversible Type II adsorption-desorption isotherm is generally associated with the formation of an adsorbed layer which progressively thickens as the equilibrium pressure is increased up to the saturation pressure this form of monolayer-multilayer physisorption is observed on an open and stable surface of a non-porous adsorbent. 

On the basis of the Saam-Cole-Findenegg approach, we are now able to revise the ideal isotherm for capillary condensation. A more realistic isotherm for the physisorption of a vapour in an assemblage of uniform cylindrical mesopores is shown in Figure 7.5. Here, C represents the limit of metastability of the multilayer (of thickness fc) and M the point at which the three phases (multilayer, condensate and gas) all coexist. Along MC the multilayer and gas are in metastable equilibrium. 

For physisorption on/in porous solids, transport into mesopores and micropores often limits the rate of adsorption. Two-stage equilibria are frequently observed the more accessible outer surfaces equilibrate rapidly and remain in equilibrium with the ambient phase, acting as a source for slower transport of the adsorbate into the interior of the solid. Establishment of cmnplete equilibrium can be a slow process. 

For physisorption the majority of the isotherms may be grouped into the six types shown in fig. 1.13. The quantity adsorbed may be presented in any suitable unit moles, grams, volumes s.t.p. (for "standard temperature and pressure"), per gram or per unit area of the adsorbent. The relative pressure is usually written as p/p(sat) where p(sat) is the saturated vapour pressure at that temperature the equilibrium pressure of the pure adsorbate if it were present as bulk liqiiid. Types I-V have already been distinguished by Brunauer ) and are sometimes referred to as BDDT types ). 

High-resolution isotherms of the equilibrium catalyst are represented in Figure 2. The observed sigmoid curves demonstrate the microporous character of the catalyst, but the relative pressure corresponding to the inflexion point depends on both the adsorbate and the adsorption temperature (Ar at 77 K or 87 K). Thus, mesopores and micropores are qualitatively evidenced from each physisorption isotherm but quantitative differences exist. 

When the van der Waal s attraction brings a particle (molecule) closer to the surface, a repulsive force develops between the core electrons of the particle (molecule) surface and those of the atoms in the surface. The equilibrium separation is determined by a balance between repulsive and the attractive forces and decreases with increasing radius of the particle. Note also that the dielectric constant of the medium separating the particle (molecule) and the surface also affects the magnitude of E in Equations (9.1)-(9.3), as the constant C is inversely proportional to the dielectric constant. The van der Waal s attractive interaction energy is small, and thus the physisorption bands are weak and can be easily broken, especially when cleaning in high dielectric constant liquids. 

The heats of adsorption of the probe molecules were measured in a heat-flow microcalorimeter of the Tian-Calvet type from Setaram, linked to a glass volumetric line to permit the introduction of successive small doses of gases [6]. The equilibrium pressure relative to each adsorbed amount was measured by means of a differential pressure gauge (Datametrics). Successive doses were sent onto the sample until a final equilibrium pressure of 133 Pa was obtained. The adsorption temperature was maintained at 353 K in order to limit physisorption interactions between the probe molecules and the zeolites. All the samples were pretreated at 773 K under vacuum overnight prior to any calorimetric measurement. 

This fact is especially disappointing because heterogeneity is expected to play in kinetics a role as important as, or even more important than, in equilibrium. Moreover the theory of equilibrium adsorption on heterogeneous surfaces is limited to physisorp-tion, while the theory of adsorption-desorption kinetics on heterogeneous surfaces includes physisorption and chemisorption and extends up to heterogeneous catalysis. 

Adsorption of atoms and molecules on surfaces plays a fundamental role in catalysis a distinction can be made between physisorption, in which weak Van der Waals forces bind the atom/molecule to the surface, and chemisorption in which chemical bonds dominate. Much experimental and theoretical work is devoted to studying energy changes as a molecule approaches the surface and dissociates (or doesn t) into separate atoms on the surface. Here we concentrate on the relation between structure and bonding for chemisorbed atoms in their equilibrium sites on the surface (ch. 1, sect. 2.4). 

Assumption 4. The possible steps of physisorption, hydrogenation/dehydrogen-ation, shift between the metallic and acid sites, and protonation/deprotonation, are in equilibrium. 

---