Langmuir model of adsorption

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 first term on the right-hand side of Eq. (20) is just the result obtained by applying the condensation approximation, i.e., assuming the hypothetical limit r 0. Because of the symmetry of the function 90/9s, the second term on the right disappears, and the first nonvanishing correction to —X(Zc) is the second correction term. For the Langmuir model of adsorption, to a good approximation [371,... 

For the Langmuir model of adsorption on a homogeneous solid surface, the surface chemical potential of the adsorbed molecules, p is given by... 

First, we note that the line shape of the plot of surface tension for UI in Fig. 2C differs from that of I" and II The surface tension of aqueous solutions of III decreases abruptly at a concentration of 0.003 mM whereas the surface tensions of solutions of I" " and IIdecrease gradually with increasing concentration. The adsorption isotherm of III cannot be described by the Langmuir model of adsorption. The limiting area occupied by III" ( < 28 A /molec) is also substantially less than either I (55 A /molec) or II (85 A /molec). 

The Langmuir model of adsorption easily can be extended to multi-component adsorption processes [7.2 Chap. 4.6, 7.3 Chap. 5, 7.29, 7.75, 7.76]. The resulting adsorption isotherm is... 

Sarkisov, L., and Monson, P. A. 2001. Langmuir. Modeling of adsorption and desorption in pores of simple geometry nsing molecular dynamics. 17 7600. 

Retention of oxygen takes place at specific sites (Fe in the hemoglobin molecule). When all sites are occupied, the blood is saturated and no further uptake occurs. This is in line with the Langmuir model of adsorption. 

Problem 2.8. The flux of sodium atoms to the glass surface having a temperature T = 300 K is equal to / = 5 10 cm s. Estimate the steady-state surface coverage with Na adatoms assuming the Langmuir model of adsorption. Take for the estimate the pre-exponential factor for the rate of desorption V = 2 -10 s, the binding energy of adatoms Ej, = 0.8 eV, the surface density of adsorption centers No = 10 free adsorption center, cr = 1. 

This equation is valid also for the case of total internal reflection provided that 6i exceeds the critical angle. It relates the EW amplitude to the surface coverage, 6, defined in terms of Ng. In the framework of the Langmuir model of adsorption the quantity is related to the surface temperature by Eqs (2.146), (2.144) and (2.145). Therefore, measuring the EW fluorescence spectra from the gas as a function of surface temperature allows one to obtain information on the adsorbate. 

Langmuir Isotherm The adsorption isotherm which is obtained in the Langmuir model of adsorption. 

Langmuir model of adsorption A model of adsorption in which one assumes that adsorption can occur only at free adsorption sites. 

The most widely used model of adsorption is Langmuir s equation for reversible molecular adsorption [163]. However, this is inappropriate for charged latex particles, because... 

The model based on formal kinetics was used to model the TPD curves of adsorbed CO molecules, based on the model previously reported [4], The desorption is strongly affected by the fast readsorption of CO on unoccupied Cu+ ions, thus, a quasiequilibrium state is a suitable approximation for the description of adsorption. A Langmuir type of adsorption isotherm was assumed for the CO adsorption on the Cu+ sites in zeolite, without considering lateral interactions among adsorbed molecules. 

Na -loess clay, where batch experiments were analyzed by X-ray diffraction and infrared and far-infrared measurements. The adsorption isotherm (Fig. 8.36) shows that loess clay is selective for cesium cations. The raw material contained a large amount of quartz, and the clay material was a mixture of kaolinite and an interstrati-fied iUite-smectite mineral as a result, equilibrium Cs" adsorption data are not consistent with a single site Langmuir model. Cesium adsorption on this particular soil clay occurs by cation exchange on sites with various cesium affinities. At low concentration, far-infrared spechoscopy shows the presence of very selective adsorption sites that correspond to internal collapsed layers. At high concentration, Cs MAS-NMR shows that cesium essentially is adsorbed to external sites that are not very selective. 

This model of adsorption was suggested by Irving Langmuir and is referred to as the Langmuir adsorption isotherm . The aim of this experiment is to test the validity of this isotherm equation and to measure the surface area per gram of charcoal, which can easily be obtained from the measured value, if the area per solute molecule is known. 

Fig. 7. The relationships between the different models of adsorption. The various assumptions involved in the classical Langmuir treatment can be considered explicitly in other, more complex models (see Ref. 451 for further details)...

It is a molar quantity but since the name is so long the molar is not explicitly stated. The problem with AadGQm is that we cannot measure it directly but its value depends on the specific model of adsorption used. We return to it when introducing the Langmuir model. 

A final area of difficulty is in the application of data analysis to specific models of adsorption isotherms. This difficulty results from the fact that different models for adsorption isotherms generate plots of surface versus dissolved concentration that have characteristic shapes. If a plot of observational data results in a curve with a shape similar to that generated by a model, this result is often taken as proof that the particular model applies. Unfortunately, this assumption has been made for situations where many of the basic requirements of the model are violated in the system under study. The Langmuir adsorption isotherm model has suffered considerable abuse by geochemists in this regard. It should be remembered that "shapes" of adsorption isotherms are far from proof that a specific model applies. 

The BET theory, developed by Brunauer, Emmett, and Teller [26], is based on the kinetic model of adsorption proposed by Langmuir [24,25] and was extended to describe the multilayer adsorption by the introduction of some assumptions listed below ... 

Type II and III Shows large deviation from Langmuir model. The model of adsorption keeps on rising in each case with increase in pressure. 

A number of different types of adsorption relationships prevail under different circumstances. The most common relationship between the amount of solute adsorbed per unit of adsorbent and the equilibrium concentration in solution is obtained for systems in which it appears that adsorption from solution leads to the deposition of only a single layer of solute molecules on the surface of the solid. This type of adsorption equilibrium is best represented by the Langmuir model for adsorption, which assumes that maximum adsorption corresponds to a saturated monolayer of solute molecules on the adsorbent surface, that the energy of adsorption is constant, and that there is no movement of adsorbate molecules in the plane of the surface after initial adsorption (5). 

Figure 8. Langmuir plot for 2,4,5-T In accord with the Langmuir model for adsorption equilibrium, a linear trace is obtained for the isotherm for 2,4,5-T when (X) 1 is vlotted vs. (Ceq) 1. Intercept of plot is (Xm) 1, and the slope is (bXm) K...

While assuming the Langmuir model for adsorption of atoms, and the ideal gas expression for p fiom eq. (2), we obtain. 

As has become clear adsorption phenomena play an important, if not, decisive role in this behaviour, and good data and modelling of adsorption are mandatory, too, to serve as the input parameters for the permeation description. This should not be l ted to the T.angmnir model, but other theories like the IAS (ideal adsorbed solution) and NIAS (non-ideal) should be considered, since they sometines work well for binary systems where the Langmuir model fails. 

Metals and compete for the available surface sites, the number of which depends on the manner of surface preparation. The surface concentration of the metals, a, can be described by the Langmuir model for adsorption ... 

With such a surface, covered with two different kinds of sites that behave independently (and on each of which the two basic principles of the Langmuir model, local adsorption and lack of adsorbate-adsorbate interactions, apply), the equilibrium isotherm results from the addition of the two independent contributions of the two types of sites [35]. Since in most cases the Langmuir isotherm is appropriate to account for single-component adsorption on a homogeneous surface (in practice if not in principle, see earlier), we have the following isotherm (see example in Figure 3.12.)... 

Figure 4.33 Top. Simultaneous fitting to a competitive bi-Langmuir model of the chromatograms obtained with a large (50.7 mg) and a moderate (10.14 mg) sample of the racemic mixture of 1-indanol. Bottom. Comparison of the FA adsorption data points (s)rmboIs) and the best competitive bi-Langmuir isotherms obtained by the inverse method (lines) for the racemic mixture. Reproduced with permission from A. Felinger, D. Zhou, G. Guiochon, f. Chromatogr. A, 1005 (2003) 35 (Figures 7 and 8).

Langmuir kinetics A simple competitive kinetic model of adsorption-desorption. The rate of adsorption is proportional to the free surface area, the rate of desorption proportional to the surface area occupied by the adsorbate. 

The frequently used Langmuir model describes adsorption of equal-sized adsorbates (m, = m/) on an energetically homogenous adsorbent. The multisite Langmuir model is an extension to include the effects of dissimilar adsorbate sizes (m/ m/). The... 

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