Langmuir-kinetics

The tendency to form organized monolayers improves with chain length. This is illustrated in a study of adsorption kinetics in alkanoic acid monolayers on alumina by Chen and Frank [36]. They find that the Langmuir kinetic equation, discussed in Section XVII-3, (see Problem XI-6)... 

They varied only the values of the adsorption and desorption rate constants of the reaction intermediate B, and by using the simplest Langmuir kinetics, they calculated time-concentration curves of compounds A, B, and C shown in Fig. 5. Also from this example, which does not consider any step as clearly rate determining, it is evident how very different concentration versus time plots can be obtained for the same sequence of surface reactions if adsorption and desorption of the intermediate B proceed by different rates, which are, however, comparable with the rate of surface reactions. In particular, the curves in the first and second columns of Fig. 5 simulate the parallel formation of substances B and C, at least... 

We should point out that the Langmuir kinetics given by expressions (1.11) and (1.12) which is often observed in experiment is as often violated. In numerous cases the data on adsorption kinetics follows the well-known Roginsky-Zeldovich-Elovich kinetics isotherm [47, 48]... 

Langmuir kinetics have usually been considered for ammonia adsorption-desorption kinetics [48, 51, 52]. On the other hand, Andersson et al. ruled out that... 

Figure 13.6 Step feed and shut-off of 700 ppm NH3 in He -I- 700 ppm NO -I- l%v/v Oj over VjO., WO,/liO, model catalyst at 220 C. Dashed lines, inlet NH, concentration solid lines, model fit with Temkin-type coverage dependence and modified Langmuir kinetics, Equation (13.10). (Adapted from ref. [52]).

The solution of the simplest kinetic model for nonlinear chromatography the Thomas model [9] can be calculated analytically. The Thomas model entirely ignores the axial dispersion, i.e., 0 =0 in the mass balance equation (Equation 10.8). For the finite rate of adsorption/desorption, the following second-order Langmuir kinetics is assumed... 

A good example is afforded by Langmuir kinetics of a continuous mixture,... 

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.

Figure 7. Langmuir kinetic model fitting of C18 adsorption on aluminum ...

The qualitative features pertinent to the present topic can even satisfactorily be modeled by an ansatz based on modified Langmuir kinetics for the above reaction scheme ... 

Defects which arise as the result of a monomolecular reaction will yield the characteristic Langmuir kinetics if p 1 however if <5C I kinetics will be observed which are typical of activated adsorption, that is,... 

By introducing a number of simplifying assumptions, Brunauer, Emmett and Teller (1938) were able to extend the Langmuir mechanism to multilayer adsorption and obtain an isotherm equation (the BET equation), which has Type II character. The original BET treatment involved an extension of the Langmuir kinetic theory of monomolecular adsorption to the formation of an infinite number of adsorbed layers. 

The system analyzed above is easily extended to arbitrary kinetics. Langmuir kinetics are discussed here as an example, in which case... 

Adsorption of fluorine on the surface is supposed to obey Langmuir kinetics 0 the fraction of the surface covered with fluorine is smaller than one, with Ka (m3 s-1) being the adsorption rate constant per fluorine, and t] F the fluorine concentration in the gas phase near the surface. 

Since 1916 when Langmuir published his fundamental paper on adsorption, the Theory of Activated Adsorption/Desorption Kinetics (TAAD) has, almost exclusively, been used for the interpretation of adsorption/desorption kinetics. However, contraiy to the success of Langmuir equation to represent the adsorption equilibria, a dramatic failure of TAAD was observed to represent by the Langmuir kinetic equation and its further modifications, [1-3] the monitored adsorption/desorption kinetics. 

For the kinetics of adsorption the bimolecular production of sites can be shown to 3deld either a rapid Langmuir kinetics determined by the rate at which molecules strike the surface or an adsorption proportional to the square root of the time. For a unimolecular production of sites the kinetic expression for adsorption is that typical of the so-called activated adsorption, k = exp (— Et,ct/RT). In the theory of activated adsorption a potential brrrier between adsorption sites and impinging molecule is assumed. In Volkenstein s treatment it is the number of sites which increases with temperature and proportionally to exp — ufRT). No potential barrier is assumed. An alternative method of stating the same is to say that the number of sites remains constant but the number of excited centres which are able to absorb increases as observed. 

L. V. Lutsevich, V. I. Elokhin, A. V. Myshlyavtsev, A. G. Usov, and G. S. Yablonskii, Monte Carlo modeling of a simple catalytic reaction mechanism comparison with langmuir kinetics, J. Catal., 132 (1991) 302. 

In an electrolyte containing a dilute SPS concentration, disulfide adsorption occurs coincident with displacement of the less strongly bound PEG-based inhibitor. The adsorption or exchange process can be described by irreversible Langmuir kinetics [112,135, 281], The effective rate constant, fcads, is potential dependent, the rate increasing exponentially with overpotential T) according to... 

Equation 5.63 can also be derived assuming Langmuir kinetics for adsorption processes [59]. This equation shows that the effective surface diffusivities depend strongly both on the surface concentration and on the surface concentration gradient. In addition the effective surface diffusivity of each component is affected by the surface concentration gradient of the other component. 

Note that the definition of Nrea is different here and in Chapter 6 (Eq. 6.93). In the former case, Nrea corresponds to a first-order kinetics (Eq. 6.65). In the present case, Nrea corresponds to a Langmuir kinetics (Eq. 14.50). With these new parameters, Eqs. 14.2 and 14.36 become... 

Wade et al. [46] have compared the experimental band profiles of p-nitrophenyl-ff-D-mannopyranoside on silica-bonded Concanavalin A, obtained in affinity chromatography, and the best fit parameters to their model. This model i.e., Thomas model) uses a Langmuir kinetic and neglects the axial dispersion. The best values of the parameters are calculated using a Simplex program to minimize the sum of the residuals of the predided and experimental band profiles. Figure 14.10 illustrates the results obtained and shows excellent agreement. 

The reaction-dispersive model is an extension of the Thomas model with a Langmuir kinetics... 

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