Theories of Adsorption

Langmuir (1918) derived a general equation for monomolecular adsorption. Under equilibrium conditions the rate of adsorption of a gas onto a surface must be equal to the rate of evaporation from the surfaee. If the fraction of the surface covered is x then the rate of evaporation is proportional to that fraction and equals to k]X, where 

Adsorption is more complicated than the Langmuir equation suggests and some implieit assumptions should be examined eritieally, namely that  

Real surfaces are heterogeneous and the affinity of the surface for the adsorbate (the gas) will depend on local structure. Heterogeneity leads to a decrease in binding energy (energy of adsorption) with increasing surface coverage as the most favoured sites are occupied first. 

In practice lateral attraction between adsorbed molecules on a well-covered surface increases the heat of adsorption since the adsorbed molecules are not only bonded to the surface but also to other adjacent adsorbed molecules. 

These two effects counterbalance one another. A further assumption is that  

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Clarke A 1970 The Theory of Adsorption and Catalysis (London Academic)... 

Mean-field Theory of Adsorption in Mesoporous Media... 

Computer Simulations and Theory of Adsorption on Energetically and Geometrically Heterogeneous Surfaces... 

Kinetic theories of adsorption, desorption, surface diffusion, and surface reactions can be grouped into three categories. (/) At the macroscopic level one proceeds to write down kinetic equations for macroscopic variables, in particular rate equations for the (local) coverage or for partial coverages. This can be done in a heuristic manner, much akin to procedures in gas-phase kinetics or, in a rigorous approach, using the framework of nonequihbrium thermodynamics. Such an approach can be used as long as... 

Most microscopic theories of adsorption and desorption are based on the lattice gas model. One assumes that the surface of a sohd can be divided into two-dimensional cells, labelled i, for which one introduces microscopic variables Hi = 1 or 0, depending on whether cell i is occupied by an adsorbed gas particle or not. (The connection with magnetic systems is made by a transformation to spin variables cr, = 2n, — 1.) In its simplest form a lattice gas model is restricted to the submonolayer regime and to gas-solid systems in which the surface structure and the adsorption sites do not change as a function of coverage. To introduce the dynamics of the system one writes down a model Hamiltonian which, for the simplest system of a one-component adsorbate with one adsorption site per unit cell, is... 

D. E. Martue, Unified theory of adsorption clrromatography gas, liquid and supercritical fluid mobile phases , 7. Chmmatogr. 451 17-30(1988). 

Typical adsorption isotherms are shown in Figs. 16 and 17. Despite the large experimental scatter, a steep increase in adsorption can be seen at low concentrations, followed by a plateau at concentrations exceeding the CMC. Similar behavior has been observed before with model surfactants [49-54] and has also been predicted by modem theories of adsorption [54]. According to Fig. 16, adsorption increases modestly with salinity provided that the calcium ion concentration remains low. The calcium influence, shown in Fig. 17, cannot be explained by ionic strength effects alone but may be due to calcium-kaolinite interactions. 

Langmuir s research on how oxygen gas deteriorated the tungsten filaments of light bulbs led to a theory of adsorption that relates the surface concentration of a gas to its pressure above the surface (1915). This, together with Taylor s concept of active sites on the surface of a catalyst, enabled Hinshelwood in around 1927 to formulate the Langmuir-Hinshelwood kinetics that we still use today to describe catalytic reactions. Indeed, research in catalysis was synonymous with kinetic analysis... 

Langmuir Quantitative theory of adsorption of gases on surfaces... 

Clearly, then, the chemical and physical properties of liquid interfaces represent a significant interdisciplinary research area for a broad range of investigators, such as those who have contributed to this book. The chapters are organized into three parts. The first deals with the chemical and physical structure of oil-water interfaces and membrane surfaces. Eighteen chapters present discussion of interfacial potentials, ion solvation, electrostatic instabilities in double layers, theory of adsorption, nonlinear optics, interfacial kinetics, microstructure effects, ultramicroelectrode techniques, catalysis, and extraction. 

The GvdW Theory A Density Functional Theory of Adsorption, Surface Tension, and Screening... 

Thus, all above experimental examples indicate that additionally to effect of disordering of the surface of adsorbent on its adsorption characteristics it is necessary to account for the effect of the adsorption itself on degree of adsorbent disordering controlling both its own electrophysical characteristics and the adsorption-caused change while deriving the theory of adsorption response of polycrystalline semiconductor adsorbent. 

The theoretical models of effects of recharging of the surface on the band diagram in the surface-adjacent domain of semiconductor adsorbent accompanying adsorption have been developed. The effect of the surface band bending in semiconductor adsorbent on its electrophysical characteristics caused by transition phenomena have been studied. The theories of adsorption-caused response of above characteristics were derived for both ideal monocrystalline adsorbent [4] and monocrystal with... 

The theory of adsorption-induced response of electrophysical characteristics in semiconductor adsorbents... 

Our understanding of polymer adsorption has followed in the wake of developments in the theory of adsorption of small molecules and that of polymer solutions. It is useful, at the outset to introduce some of the ideas that have been developed in recent years, particularly with regard to the latter topic. 

The mathematical theory of adsorption was first developed by Willard Gibbs and later, independently, by Sir J. J. Thomson. We must confine ourselves to giving the result of their investigations. Let c be the concentration of the solute in the bulk of the solution and u the excess concentration, in grammes per square centimetre, in the surface layer u is, of course, taken as positive if the concentration... 

Although it is sometimes possible to view pores with an electron microscope and to obtain a measure of their diameter, it is difficult by this means to measure the distribution of sizes and impossible to measure the associated surface area. Adsorptive methods are used instead, employing some of the theories of adsorption explained previously. 

POLANYI, M. Trans. Farad. Soc 28 (1932) 316. Theory of adsorption of gases — introductory paper. 

The removal of an electron from an acceptor level or a hole from a donor level denotes, as we have seen, not the desorption of the chemisorbed particle but merely its transition from a state of strong to a state of weak bonding with the surface. The neglect of this weak form of chemisorption (i.e., electrically neutral form) which is characteristic of all papers on the boundary-layer theory of adsorption makes it quite impossible to depict the chemisorbed particle in terms of an energy level, i.e., to apply the energy band scheme depicted in Fig. 10 and used in these papers. ... 

Zaremba, E., and Kohn, W. (1977). Theory of adsorption on simple and noble-metal surfaces. Phys. Rev. B 15, 1769-1781. 

Polanyi s potential theory of adsorption views the area immediately above an adsorbent s surface as containing equipotential lines which follow the contour of the surface potential. When a molecule is adsorbed it is considered trapped between the surface and the limiting equipotential plane at which the adsorption potential has fallen to zero. Figure 9.1 illustrates these equipotential planes. In the diagram, Y represents a pore and X depicts some surface impurity. 

Adhesion is created by primary and secondary forces according to the theory of adsorption interaction. This theory is applied the most widely for the description of interaction in particulate filled or reinforced polymers [30]. The approach is based on the theory of contact wetting and focuses its attention mainly on the influence of secondary forces. Accordingly, the strength of the adhesive bond is assumed to be proportional to the reversible work of adhesion (W ), which is necessary to separate two phases with the creation of two new surfaces. 

B. Hammer and J.K. Nprskov. Theory of adsorption and surface reactions in NATO ASI Series E 331, Eds. R. Lambert and G. Pacchioni, Kluwer Academic Publishers, Dordrecht (1997). 

Many theories of adsorption, following Langmuir, have assumed that the rate of adsorption is proportional to (1 — 0), i.e., to the fraction of the surface which is bare or not yet covered. Langmuir first proved the (1 — 0) law by measuring experimentally how the thermionic work function

changed with time as thorium reached the surface of a tungsten filament at a constant rate (10). He then assumed that tp decreased linearly with 0 and thus deduced that dd/di was proportional to (1 — 0). But this assumption has been shown to be incorrect for such cases as Cs on W, Ba on W, SrO on W, and other systems. Hence it follows that the (1 — 0) law is not valid. The experiments described above for N2 on W not only show that dQ/dt is not proportional to (1 — 0), but they show by a direct experiment that dd/dt for a constant arrival rate is independent of 0 between 0 = 0 and 1.0. 

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