Fractional coverage, adsorption

Fig. 2.22 Adsorption isotherms of argon on graphitized carbon black at a number of temperatures," plotted as fractional coverage 0 against relative pressure p/p°. (Courtesy Prenzlow and Halsey.)...

Fig. 5.2 Type III isotherms, (a) n-hexane on PTFE at 25°C (b) n-octane on PTFE at 20 C (c) water on polymethylmethacrylate at 20°C (d) water on bis(A-polycarbonate) (Lexan) at 20°C. The insets in (c) and (d) give the curves of heat of adsorption against fractional coverage the horizontal line marks the molar heat of liquefaction. (Redrawn from diagrams in the original papers, with omission of experimental points.)...

The flux of flie adsorbed species to die catalyst from flie gaseous phase affects die catalytic activity because die fractional coverage by die reactants on die surface of die catalyst, which is determined by die heat of adsorption, also determines die amount of uncovered surface and hence die reactive area of die catalyst. Strong adsorption of a reactant usually leads to high coverage, accompanied by a low mobility of die adsorbed species on die surface, which... 

Category II. The rate of chemical reaction on the surface is so rapid that adsorption equilibrium is not achieved, but a steady-state condition is reached in which the amount of adsorbed material remains constant at some value less than the equilibrium value. This value is presumed to be that corresponding to equilibrium for the surface reaction at the appropriate fractional coverages of the other species involved in the surface reaction. The rate of adsorption or desorption of one species is presumed to be much slower than that of any other species. This step is then the rate limiting step in the overall reaction. 

So the fractional coverage of the total adsorption sites 0 becomes... 

The frequent occurrence of ordered fractional-coverage adsorption indicates that adsorbate-adsorbate interactions at close range (S 5 A) are often repulsive. Island formation can occur simultaneously, showing that at larger separations these interactions can become attractive. 

Fig. 12.1. The Langmuir-Hinshelwood adsorption isotherm, showing the fractional coverage of the catalyst surface as a function of the partial pressure of p in the gas phase.

Fig. 12.2. The stationary-state fractional coverage of the surface for adsorption with cover-age-dependent parameters and no reaction (a) a = 2, showing unique solution for all partial pressures (b) a = 4.5, typical of all a > 4, showing multiplicity at low pressures,...

Fig. 12.3. Stationary-state fractional coverage for adsorption and reaction involving two vacant sites (a) k2/K = 36 showing multiplicity, (b) multiplicity in absence of desorption now one solution corresponding to a fully covered surface exists for all reactant pressures.

The surface is uniform and all adsorption sites are equivalent for all values of the fractional coverage, 0, of the surface by A. 

Theory of Vapor-Particle Partitioning of PAH Compounds in the Atmosphere. Yamasaki et al. (64) treated semivolatile PAHs as inherently vapor-phase materials, existing in the particle phase only because of their tendency to sorb on nonvolatile materials. Under this assumption, the proportion in each phase should vary with the available surface area for sorption and with the ambient temperature. They assumed that sorption followed a Langmuir adsorption isotherm, requiring that there be only a low fractional coverage of the particulate matter with semivolatile material. In this case, competition for sorption sites can be ignored. At equilibrium, the rate of sorption equals the rate of evaporation. They derived this relationship ... 

Figure 6. Langmuir kinetic model fitting of Cl adsorption on glass (a) fractional coverage as a function of time and solution concentration, (b) equilibrium coverage as a function of concentration, and (c) check of fitting of equation 2 by the correlation of the fitted exponential constant and concentration.

Relative Adsorption Kinetic Constants From Fluorescence Data. Using a two-component, competitive adsorption Langmuir isotherm, 0g, the fractional coverage of the guest molecule can be expressed as... 

Although the same model was applicable for each of the different substrates, the adsorbed amount or fractional coverage varied between 40 and 75%. There was an implication in the data that this correlated with the surface roughness of the substrates, but the evidence is not conclusive. Subsequently, Penfold et al. [25] have considered the consequences of the different surface treatments on the adsorption of nonionic surfactants at the hydrophilic silicon-solution interface. The delicate nature of the cooperativity of the adsorption results in variations in the adsorbed amount, which depend strongly upon... 

The degree of adsorption is expressed either by T, the surface concentration, in units of moles per unit area, or in terms of the fractional coverage 6 ... 

Results of previous investigations 23,110, 111, 113, 141, 157-165) show that hydrogen adsorption on nickel at room temperature is lowered by preadsorbed sulfur. Moreover, the fraction by which hydrogen adsorption is reduced in polycrystalline and supported nickel catalysts is generally proportional to the mean fractional coverage of sulfur. This is illustrated by data in Fig. 16 from Bartholomew and co-workers 112, 113, 141, 157-162). 

From the foregoing one can easily derive that for the fractional coverage of A in case of a one-component adsorption, Eqn. (3.18) is valid. Figure 3.3 gives a graphical representation for several values of Ka (= K ), the adsorption equilibrium constant of A. 

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