Adsorption simple Langmuir model

A more searching test of conformity to the Langmuir equation is obtained by plotting the adsorption data as a function of 0 rather than p (Barrer, 1978, p. 407). Some pronounced deviations then appear, which are consistent with the inadequacy of the simple Langmuir model. 

Surface SHG is a viable method to monitor adsorption and desorption of molecules on well-defined metal and semiconductor surfaces in ultra-high vacuum UHV).2.5,9 Figure 3 is an example, showing how the SHG responds to the adsorption of CO on Cu 100). 0 The sample properly cleaned and kept at 1i 0 K in UHV was allowed to be exposed to CO, and SHG with a Nd YAG laser becim was used to monitor the adsorption of CO. It is known that at T - 140°K, CO adsorbs on Cu(IOO) only at the top sites. The adsorption kinetics is then likely to obey the simple Langmuir model. 

Many modifications to the simple Langmuir model are amenable to analysis in this way. For example, consider adsorption on a set of M independent pairs of identical sites such that there is an interaction energy (2w) when both sites of a given pair are occupied. The expression for the grand partition function for such a system is... 

The data of Barrer and Wasilewski " for the sorption of I2 on 5A and 13X zeolites (Figure 4.2) are remarkable since they show conformity with the simple Langmuir model over very wide concentration ranges. More detailed analysis reveals that the heat of sorption varies strongly with sorbate concentration, as may be seen from Figure 4.2c. A constant heat of sorption is one of the requirements of the Langmuir model so the variation of heat of adsorption... 

Thus the generalization of the simple Langmuir model applies to the two assumptions made in the introduction to section 2.8. First, there are two adsorption parameters Ul and Uh instead of one. Second, the process of adsorption might perturb the sites, in the sense that the equilibrium composition of L and H is in general affected by the adsorption of G. 

We generalize the adsorption model of section 2.8. Most of the assumptions of the simple Langmuir model are still retained, except for two the sites are not localized, and they are solvated by the solvent (the solvent may be any mixture of liquids, but for simplicity we assume that it is a one-component liquid, denoted by w). The simplest way to obtain the modified binding isotherm is to use the thermodynamic approach of section 2.9.1 with the appropriate modification introduced into the chemical equilibrium condition in solution, as in section 8.3. 

As noted in Chapter 1, the most simple and theoretically sound model for drug-receptor interaction is the Langmuir adsorption isotherm. Other models, based on receptor behavior (see Chapter 3), are available. One feature of all of these models (with the exception of some instances of the... 

Non-compliance with the simple Langmuir adsorption model is indicative of violation under experimental conditions of certain assumptions used to derive the model. Therefore, while developing the theoretical models adequately describing experimental data one usually resorts to one of two approaches either introduces the notion of a inhomogeneous surface [36, 37] or accounts for various types of interaction developing between the particles absorbed [4, 38]. 

Simple evidence about the information content of the dynamic properties can be obtained by considering the Langmuir model of adsorption of molecules from gas phase to a limited number of interacting sites on a sensor surface [3]. 

The estimation of the surface area of finely divided solid particles from solution adsorption studies is subject to many of the same considerations as in the case of gas adsorption, but with the added complication that larger molecules are involved whose surface orientation and pore penetrability may be uncertain. A first condition is that a definite adsorption model is obeyed, which in practice means that area determination data are valid within the simple Langmuir Equation 5.23 relation. The constant rate is found, for example, from a plot of the data, according to Equation 5.23, and the specific surface area then follows from Equations 5.21 and 5.22. The surface area of the adsorbent is generally found easily in the literature. 

Kinetic models referred to as adsorption models have been proposed, especially for olefin polymerisation with highly active supported Ziegler-Natta catalysts, e.g. MgCl2/ethyl benzoate/TiCU AIR3. These models include reversible processes of adsorption of the monomer (olefin coordination at the transition metal) and adsorption of the activator (complexation via briding bonds formation). There are a variety of kinetic models of this type, most of them considering the actual monomer and activator concentrations at the catalyst surface, m and a respectively, described by Langmuir-Hinshelwood isotherms. It is to be emphasised that M and a must not be the same as the respective bulk concentrations [M] and [A] in solution. Therefore, fractions of surface centres complexed by the monomer and the activator, but not bulk concentrations in solution, are assumed to represent the actual monomer and activator concentrations respectively. This means that the polymerisation rate equation based on the simple polymerisation model should take into account the... 

In a recent review of this topic [B.C. Gaietl, Science 303 (2004) 1146] the emphasis was on some recent experiments, in which it was found that some anions accumulate at the air/water interface and not in the bulk, as usually happens to the cations, and on some simulations which explained those positive surface adsorption excesses. Because a large number of these experiments could be explained on the basis of some simple physical models proposed by the authors for the interaction between the ions and the air/water interface [M. Mandu, E. Ruckenstein, Adv. Colloid Interface Sci. 105 (2003) 63 Adv. Colloid Interface Sci. 112 (2004) 109 Langmuir 21 (2005) 11312], those models ate reviewed in the present note, the goal being to draw attention to them. 

The fact that many Type I isotherms appear to obey a simple form of Langmuir equation - Equation (4.13) - over a wide range of pressure was for many years accepted as confirmatory evidence for the Langmuir model. According to this view (Brunauer, 1945), the limiting plateau would be the result of monolayer adsorption on the pore walls. 

The Brunauer-Emmett-Teller (BET) adsorption model was developed to account for multilayer adsorption. The BET model can be thought of as the sum of two terms the Langmuir model is used to account for coverage from zero to the completion of the first monolayer, while the second and all subsequent layers (not treated by the Langmuir model) are assumed to have a heat of adsorption equal to the heat of vaporization of the bulk liquid phase of the adsorbing species. The heat of adsorption of the first monolayer usually exceeds the liquid s heat of vaporization. Although it might seem a erode oversimplification, the BET model works well for many systems that involve physisorption of simple molecules,... 

The transient response experiments were analyzed by a dynamic isothermal PFR model, and estimates of the relevant kinetic parameters were obtained by global nonlinear regression over all runs. It was found that a simple Langmuir approach could not represent the data accurately, and surface heterogeneity had to be invoked. The best fit was obtained using a Temkin-type adsorption isotherm with coverage-dependent desorption energy ... 

The heterogeneity of the surface of the adsorbents used in chromatography has two important consequences. First, adsorption isotherm data do not fit well to the simple isotherm models designed for homogeneous srufaces, i.e., the Langmuir... 

The conditions of validity of this isotherm model are the same as those of the competitive Langmuir isotherm, ideal behavior of the mobile phase and the adsorbed layer, localized adsorption, and equal column saturation capacities of both t3q>es of sites for the two components. The excellent results obtained with a simple isotherm model in the case of enantiomers can be explained by the conjunction of several favorable circumstances [26]. The interaction energy between two enantiomeric molecules in solutions is probably very close to the interaction energy between two R or two S molecules and their interactions with achiral solvents are... 

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