Adsorption Langmuir’s isotherm

In the mechanism of the anodic iron dissolution, described in this section, the formation process of the intermediate of ferrous hydroxocomplexes, Eqn. 9-21a, is in the quasi-equilibrium state so that the Nemst equation applies between the adsorption coverage, 6p oa-, of the intermediate FeOH [d and the overvoltage, t). Accordingly, for the range of relatively low coverages of adsorption to which Langmuir s adsorption isotherm applies, we obtain Eqn. 9-22 ... 

F. Fowler. A Statistical Derivation of Langmuir s Adsorption Isotherm. Proc. Camb. Phil. Soc., 31 260-280,1935. 

The fractional factor with p of Equation (1) according to the accepted view corresponds to Langmuir s adsorption isotherm for mixtures on an almost covered homogeneous surface or on like active centers and the z are the relative adsorption coefficients. This fraction was so interpreted for other cases by Hinshelwood 13), Schwab 9), the author 1, 14), Frost 15), Hougen 16), and others. Two questions now arise ... 

Catalysis offers numerous examples of the simultaneous chemisorption of different molecules or atoms. The extremely important problems of poisoning, of promoting and of selective catalysis depend on this phenomenon. In the past numerical estimations of the relative amounts that will be bound by chemisorption in equilibrium were mostly based on the assumption that Langmuir s adsorption isotherm would be valid. In such a case the following equation is easily derived ... 

In the conceptions underlying Langmuir s adsorption isotherm the heats of adsorption are constant and independent of the amount that is adsorbed. We learned, in Sec. IX, that this does not hold for chemisorption and we shall, therefore, derive an expression based on the logarithmic adsorption isotherm [Eq. (71) or (74)]. 

The second question cannot be answered unequivocally because the kinetics of the Fischer-Tropsch reaction is not well enough understood to permit reliable extrapolations to very low pressures. Still, a tentative analysis based on Langmuir s adsorption isotherm suggests that the rate may be adequate even at 10 atm (Lancet, 1972). 

Two functions, Freundlich s and Langmuir s adsorption isotherms, are used to describe adsorption (see Figure 8.7). The former is more often used ... 

Langmuir s adsorption isotherm may sometimes be more appropriate. It was developed to describe the adsorption of gases to solid phases and has a better theoretical foundation. 

Many adsorption experiments on long chain fatty acids and other amphiphiles at the liquid/air interface and the close agreement with the von Szyszkowski equation is logically one proof of the validity of Langmuir s adsorption isotherm for the interpretation of y - log c -plots of typical surfactants in aqueous solutions (cf. Appendix 5D). This evidence is also justification for use of the kinetic adsorption/desorption mechanism based on the Langmuir model for interpreting the kinetics and dynamics of surface active molecules. 

Transformation of Eq. (15.19) finally results in the familiar equation for Langmuir s adsorption isotherm... 

The classical work of Clark (1937), based on the application of Langmuir s adsorption isotherm (see Section 8.1), assumed that the effect of a drug is proportional to the fraction of receptors occupied by drug molecules, and that a maximal effect is obtainable only when all receptors are occupied by the drug. As a statement of the action of inhibitors (so important for work in chemotherapy and agriculture) this simple occupation theory can hardly be bettered. However, it is inadequate to explain the kinetics of agents which elicit a positive response substances like the synaptic transmitter acetylcholine and innumerable artificial agonists. 

Equations (4) and (5) are written in a form corresponding to Langmuir s adsorption isotherm. Formally, they apply to any other isotherm however, in such a case, the rate constants depend not only on 0, but also on 6. 

According to Equation 14.25, the Langmuir s adsorption isotherm assumes a curved shape as shown in Figure 14.3a. Equation 14.25 may be linearized into... 

FIGURE 14.3 (a) Langmuir s adsorption isotherm and (b) linearized Langmuir s adsorption... 

A Naegeli-type amylodextrin of DP 21 and containing one branch-point in each molecule has been prepared from waxy corn starch. The adsorption of monobasic fatty acids from n-hexane on to dry amylose has been found to follow Langmuir s adsorption isotherm. Changes in the physical properties of a potato starch with a high content of phosphate in the presence of cations have been described. Alkali-metal cations produced an increase in the viscosity of solutions of this potato starch, whereas alkaline-earth-metal cations initiated a two-step swelling process and lowered the viscosity. 

MOISTURE EXPANSION (see alsO GAS ADSORPTION method). Langmuir s adsorption isotherm, with the equation f= ap/(l - ap), is based on the assumption that adsorption is limited to a monomolecular layer (f is the fraction of the surface covered p is the gas pressure a is a constant). 

An adsorption isotherm relates the surface concentration of an adsorbed species to the variables which determine it. Langmuir s adsorption isotherm has its roots in the chemical adsorption of gases according to the expression ... 

A Generalization of Langmuir s Adsorption Isotherm to Admolecules with Interaction,... 

The resummed series is just Langmuir s adsorption isotherm, which is indeed the correct physical limit of 6 given by Eq. (1.166) when the lateral interactions are turned off. TMs immediately suggests the form of the Fade approximant for general z and = l/u. For low fugacities... 

We have to realize that only the concentration in the bulk phase is measurable. Therefore, the relation between the unknown concentration at the surface and the measurable concentration in the fluid is needed to describe the surface reaction rate. These relations were surveyed in Section 3.3.5. In the following, we only recall Langmuir s adsorption isotherm as an important example of such a relationship. This isotherm describes the dimensionless coverage 0a of the surface with species A relative to the coverage with a monolayer for a given partial pressure. If only reactant A is adsorbed we have ... 

The Henry s law/Fick s law model previously described is a simplification of the actual permeation mechanism, and more complex models have been proposed. The dual system model, for example, is a more precise representation for many cases. It assumes that gas molecules which dissolve in the dense regions of the membrane surface follow Henry s law while molecules that adsorb on the walls of microscopic cavities in the membrane surface follow Langmuir s adsorption isotherms. Equations based on the dual system model have been developed and presented by Lee et al. (1988). Additional discussions of transport mechanisms are provided by Lacey and Loeb (1972) and Stem (1986). 

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