Langmuir adsorption isotherm, modified

For nonlinear systems, however, the evaluation of the flow rates is not straightforward. Morbidelli and co-workers developed a complete design of the binary separation by SMB chromatography in the frame of Equilibrium Theory for various adsorption equilibrium isotherms the constant selectivity stoichiometric model [21, 22], the constant selectivity Langmuir adsorption isotherm [23], the variable selectivity modified Langmuir isotherm [24], and the bi-Langmuir isotherm [25]. The region for complete separation was defined in terms of the flow rate ratios in the four sections of the equivalent TMB unit ... 

Correlation between experimental and calculated concentrations is obtained using a modified Langmuir adsorption isotherm with the following parameters ... 

There are two factors that infiuence the particle formation conditions the adsorption of emulsifier on the droplets, which baves less emulsifier in the aqueous phase to facilitate particle formation-there, and the rate of radical absorption in monomer droplets. The former factor may be evaluated by talcing into account the adsorption isotherm of emulsifier on monomer droplets. Using a modified Langmuir adsorption isotherm in combination with a mass balance gives an expression for the aqueous phase concentration of emulsifier C... 

A. The modified Langmuir adsorption isotherm for species A is obtained when net, adsorption O Hence,... 

In this study, ephedra waste was modified by epichlorohydrin and diethylenetriamine to obtain aminated ephedra waste biosorbent and absorbed for Cu +. By dint of static absorption test, the effects of pH and contact time on absorption were investigated. Biosorbent characterization was determined with FTIR analysis. Langmuir adsorption isotherm was applied to the experimental data. The pseudo second-order model was used for determining of the adsorption kinetics. 

A final observation is that the mean field result can also be cast in the form of a modified Langmuir adsorption isotherm ... 

Almost all chiral stationary phases (see Section 2.6.3) have a heterogeneous surface. Besides the chiral selector molecule, the support (often based on silica) can also interact with the analyte and contribute to retention. In order to describe the adsorption, one often uses a modified Langmuir adsorption isotherm (Eq. 8)... 

Show that the Langmuir adsorption isotherm is modified to... 

The knowledge of these adsorption isotherms allows quantification of the respective affinity for the stationary phase with respect to the different solutes. Many different isotherm equations have been described in the literature, and experimental methods allowing their determination are reviewed by [58]. As a first approximation, modified competitive Langmuir isotherms can often he used ... 

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. 

Figure 24. Neutralization isotherms (adsorption isotherm of OH") for acidic surface groups on a carbon black The lower plot represents the linearized isotherms according to a modified Langmuir adsorption model.

Tang, P. Chew, N.Y.K. Chan, H.-K. Raper, J. Limitation of determination of surface fractal dimension using N2 adsorption isotherms and modified Frenkel-Halsey-Hill theory. Langmuir 2003, 7, 2632-2638. 

Experimental data are often fitted more precisely to the adsorption isotherm when an additional term is introduced that covers the non-specific adsorption of the solute to the adsorbent. This modifies the equation to the single-component, modified Langmuir isotherm (Eq. 2.40) ... 

For both the Langmuir and Jovanovic isotherms several exact methods exist for the determination of the energy distribution function adsorption isotherm is precisely known. Rather than trying to modify these exact methods for desorption kinetics, this work will use two approximate methods which give simple analytical expressions for the distribution function in terms of derivatives of the overall isotherm, and which allow a better and more friendly analysis of results. 

Adsorption isotherms are generally presented for a single component, but many applications involve multicomponent mixtures. The Langmuir isotherm is easily modified for multiple adsorbates by adding terms to the denominator ... 

The original adsorption isotherm of Langmuir has been modified to include neighbor interaction, mobility with one or two degrees of freedom, and other possible variants and expressions for the entropy changes involved in each case evaluated. 

Langmuir derived a different adsorption isotherm by assuming that adsorption is terminated upon completion of a monomolecular adsorbed gas layer [43]. He did this by asserting that any gas molecule that strikes an adsorbed atom must reflect from the surface. All the other assumptions (i.e., homogeneous surface and noninteracting adsorbed species) used to obtain Eq. 3.85 were also maintained. If oq is the surface coverage of a completely covered surface, the concentration of surface sites available for adsorption, after adsorbing a molecules, is ao — a. Of the total flux F incident on the surface, a fraction [(a/incident flux will be available for adsorption. Equation 2.84 should thus be modified as... 

The adsorption isotherms were fitted with the Langmuir model, from which the adsorption equilibrium constant K, as well as the maximum concentration of the solute uptake are established. The substrates can be easily recycled permanently by washing with ethanol or acetone without losing their adsorption capacity. This finding is one of the greatest advantages of such modified cellulose fibres compared to other much more conventional adsorbents such... 

Table 17.7 (cont.) Langmuir and Freudlich constants of of the adsorption isotherms of different organic solutes on modified cellulose fibres. ... 

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