Adsorption Langmuir type

Such a model should be as simple as possible, without however missing any of the underlying thermodynamic and physicochemical factors which cause electrochemical promotion. In particular it will be shown that even the use of Langmuir-type adsorption isotherms, appropriately modified due to the application of potential (or equivalently by the presense of promoters) suffice to describe all the experimentally observed rules G1 to G7 as well as practically all other observations regarding electrochemical promotion including the effect of potential on heats of adsorption as well as on kinetics and reaction orders. 

We first assume Langmuir-type adsorption (E=0 or P,=0) which implies negligible lateral interactions between adsorbed molecules and negligible inherent or induced heterogeneity of the catalyst-electrode surface ... 

Plots of an amount of material adsorbed versus pressure at a fixed temperature are known as adsorption isotherms. They are generally classified in the five main categories described by Brunauer and his co-workers (4). In Figure 6.2 adsorbate partial pressures (P) are normalized by dividing by the saturation pressure at the temperature in question (P0). Type I is referred to as Langmuir-type adsorption and is characterized by a monotonic approach to a limiting amount of adsorption, which presumably corresponds to formation of a monolayer. This type of behavior is that expected for chemisorption. 

An assumed instantaneous distribution between the adsorbed and free solute is modelled by a Langmuir-type adsorption isotherm, where... 

The conditions for the validity of a Langmuir type adsorption equilibrium are i) thermal equilibrium up to the formation of a monolayer, 0 = 1 ii) the energy of adsorption is independent of 0, (i.e., equal activity of all surface sites). There is no difference between a surface complex formation constant and a Langmuir adsorption... 

A Langmuir type adsorption isotherm is given in Fig. 4.2a. As is shown in Fig. 4.2b the evaluation of the equilibrium adsorption constant and of rmax is readily obtained from experimental data by plotting Eq. (4.10a) in the reciprocal form... 

Instead of ion-exclusion, size exclusion has been used in the separation of NH4S04 from a protein [41]. In that case, the adsorption isotherms were found to be simply linear. A hydrophobic interaction separation has been used for desalting in the case of phenylalanine and NaCl [41]. NaCl shows almost no interaction with the packing and consequently has a linear adsorption isotherm. The phenylalanine, on the other hand, showed a classical Langmuir-type adsorption isotherm. 

Fig. 5 (a) shows the nitrogen adsorption isotherms of aluminum hydroxy pillared clays after heat-treatment at 300-500°C. These are of the typical Langmuir type isotherm for microporous crystals. Fig, 5 (b) shows the water adsorption isotherms on the same Al-hydroxy pillared clays [27]. Unlike the water adsorption isotherms for hydrophilic zeolites, such as zeolites X and A, apparently these isotherms cannot be explained by Langmuir nor BET adsorption equations the water adsorption in the early stages is greatly suppressed, and shows hydrophobicity. Water adsorption isotherms for several microporous crystals [20] are compared with that of the alumina pillared clay in Fig. 6. Zeolites NaX and 4A have very steep Langmuir type adsorption isotherms, while new microporous crystals such as silicalite and AlPO -S having no cations in the...

Co-adsorption and mutual interactions between the reactants on the surface form the basis for understanding the microscopic steps of the reaction. Since product formation takes place rather rapidly above room temperature, this information mainly became available from low-temperature studies. As a result, these processes are much more complicated than can be described by a Langmuir-type adsorption model (i.e., simple competition for free adsorption sites) and, moreover, an asymmetric behavior is found which means that pre-adsorbed CO inhibits the adsorption of oxygen, whereas the reverse is not the case. At very low surface concentrations of CO and Oad these will be randomly distributed over the surface as illustrated schematically by Fig. 32a (88). 

According to the Langmuir-type adsorption model, a differential equation for time dependence of the amount of FeCp-X adsorbed on the droplet (m) is given as... 

Sensitization of Ti02 nanosized particle films soaked in water was tried by dissolving a sensitizer and a sacrificial electron donor (EDTA) in the water phase (Fig. 19.7). Photocurrent was strongly dependent on the concentration of Ru(bpy)32+, reaching saturation at higher concentrations beyond 2 mM. By analysis of the photocurrent-vs.-concentration curve, a Langmuir-type adsorption of the dye was suggested. 

If one assumes that a Langmuir-type adsorption isotherm can be used to relate the concentration of adsorbed cellulase on the cellulose to the free cellulase in solution, i.e.,... 

The adsorption of the enzyme, Eq. (4.1), can be described by the Langmuir-type adsorption isotherm ... 

Stern assumed that a Langmuir-type adsorption isotherm could be used to describe the equilibrium between ions adsorbed in the Stern layer and those in the diffuse part of the double layer. Considering only the adsorption of counter-ions, the surface charge density cr, of the Stern layer is given by the expression... 

Mechanism f Langmuir Type Adsorption-Desorption Reaction. Consider the reaction... 

The dependence of the distribution coefficient of the protein on an ion-exchanger with regard to protein and salt concentration [K(Cm, /)] can be empirically described by the following equation assuming a Langmuir-type adsorption behavior for the protein ... 

One of the most significant points that we must consider in scientific studies, not limited to studies on photocatalysis, is distinction between evidence and consistency, as least as far as the author thinks. In other words, it is necessary to recognize every fact to be a necessary condition but not a sufficient condition in a strict scientific sense. For example, the fact that a reaction rate obeys the first-order rate law giving a linear relation in a plot of data as in Fig. 6 is only a necessary condition for a monomolecular reaction in homogeneous phase and also a necessary condition for heterogeneous photocatalytic reaction in diffusion-limited conditions or that in surface-reaction limited conditions with a Henry-type adsorption or a Langmuir-type adsorption in the lower-concentration region. 

In some reports on photocatalytic reaction, it has been stated that the time-course curve obeys the first-order rate law and that the rate of reaction changes following Langmuir-type adsorption behavior (so-called... 

In addition to the above technique, the heat of adsorption can also be determined from Langmuir-type adsorption isotherms. Langmuir s adsorption equation pro-... 

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