Langmuir binary

Atre S V, Liedberg B and Allara D L 1995 Chain length dependenoe of the struoture and wetting properties in binary oomposition monolayers of OH and CHj-terminated alkanethiolates on gold Langmuir 3882-93... 

Consider a binary adsorbed mixture for which each pure component obeys the Langmuir equation, Eq. (16-13). Let n = 4 mol/kg, nl =. 3 mol/kg, Kipi = K2P2 = 1. Use the ideal adsorbed-solution theory to determine ni and n. Substituting the pure component Langmuir isotherm... 

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 ... 

It should be mentioned that the extension of the Langmuir theory to adsorption from binary adsorbate systems is thermodynamically consistent only in the special case where Q = Q2. However, that thermodynamic consistency is of secondary importance if Eq. (18) provides the correct analytical description of the adsorption phenomena. 

The Sips [38] model (Eq. 10) can easily be extended to binary or multicomponent systems [34, 74]. The resulting expression for the multicomponent Langmuir-Freundlich adsorption model is ... 

Xu, S., Damodaran, S. (1994). Kinetics of adsorption of proteins at the air-water interface from a binary mixture. Langmuir, 10, 472 480. 

One isotherm that is both easy to understand theoretically and widely applicable to experimental data is due to Langmuir and is known as the Langmuir isotherm. In Chapter 9, we see that the same function often describes the adsorption of gases at low pressures, with pressure substituted for concentration as the independent variable. We discuss the derivation of Langmuir s equation again in Chapter 9 specifically as it applies to gas adsorption. Now, however, adsorption from solution is our concern. In this section we consider only adsorption from dilute solutions. In Section 7.9c.4 adsorption over the full range of binary solution concentrations is also mentioned. 

EXAMPLE 9.4 Kinetic-Theory-Based Description of Binary Adsorption. Assume that two gases A and B individually follow the Langmuir isotherm in their adsorption on a particular solid. Use the logic that results in Equation (46) to derive an expression for the fraction of surface sites covered by one of the species when a mixture of the two gases is allowed to come to adsorption equilibrium with that solid. 

Furthermore, in 3.3 we turn to reactive binary ion-exchange. An equilibrium binding reaction (adsorption) with a Langmuir-type isotherm is considered. Formation of sharp propagating concentration fronts is studied via an unconventional asymptotic procedure [1]. 

The sorption and diffusion behaviour of gas mixtures is of particular interest from the point of view of membrane gas separation, which is steadily gaining in importance by virtue of its low energy requirements. On the basis of the dual mode sorption model, one may reasonably expect that sorption of a binary gas mixture A, B in the polymer matrix will exhibit little gas-gas interaction and hence will tend to occur essentially additively. In the Langmuir-like mode of sorption, on the other hand, there will be competition between A and B for the limited number of available sites. These considerations led 67) to the following reformulation of Eqs. (8) and (9)... 

Adsorption of Mixtures. The Langmuir model can be easily extended to binary or multicomponent systems ... 

FIGURE 7.10 Pseudo-binary phase diagram of the water, HNO3/DMDBTDMA, dodecane system to identify the third-phase limit. Experimental points (circles) and theory (lines) obtained from Baxter sticky hard-sphere approach. The theoretical line is obtained with the experimental determination of the linear variation of the stickiness parameter tt1 versus [HN03]/[DMDBTDMA]. The different lines illustrate the impact of the error in this T-1 experimental linear law. (From C. Erlinger, L. Belloni, T. Zemb, and C. Madic, Langmuir, 15 2290-2300, 1999. With permission). 

Langmuir isotherm or model Simple mathematical representation of a favorable (type I) isotherm defined by Eq. (2) for a single component and Eq. (4) for a binary mixture. The separation factor for a Langmuir system is independent of concentration. This makes the expression particularly useful for modeling adsorption column dynamics in multicomponent systems. 

The Langmuir equation can be easily extended to multi-component adsorption, for example, for a binary mixture of components 1 and 2 ... 

The problem of predicting multicomponent adsorption equilibria from single-component isotherm data has attracted considerable attention, and several more sophisticated approaches have been developed, including the ideal adsorbed solution theory and the vacancy solution theory. These theories provide useful quantitative correlations for a number of binary and ternary systems, although available experimental data are somewhat limited. A simpler but purely empirical approach is to use a modified form of isotherm expression based on Langmuir-Freundlich or loading ratio correlation equations ... 

New phenomena compared to nonreactive Langmuir systems are the same as in the binary case - that is, the existence of combined waves due to the occurrence of inflection points of the equilibrium functions y(x) or Y(X) and limitations on feasible product composition due to adsorptivity reversal similar to azeotropic distillation. Nonreactive examples for the latter were treated in Refs. [6 - 8], reactive examples will be discussed in the next section. 

D. Basmadjian and P. Coroyannakis, Equilibrium-theory revisited -Isothermal fixed-bed sorption of binary systems. 1. Solutes obeying the Langmuir isotherm. Chem. 

Wagner, R. andStrey, R. (1999) Phase behavior of binary water-trimethylsilane surfactant systems origin ofthe dilute lamellar phase. Langmuir, 15(4), 902-05. 

FIGURE 4.7 Adsoprtion isotherm with a binary site (a) Langmuir and (b) adsorption with two sites. 

An alternative approach which can be used to describe the adsorption phenomena of a multicomponent system is to assume that there is total competition between target polypeptides, proteins, and other components in the mixture for adsorption to all the accessible sites of the ligate. In this case, the Langmuir approach can be expanded to encompass binary (or more generalized examples) of adsorption isotherms8, A48-151,167175,227-236,365,369,372- for two or more... 

Imabayashi S, Hobara D, Kakiuchi T (2001) Voltammetric detection of the surface diffusion of adsorbed thiolate molecules in artificially phase-separated binary self-assembled monolayers on a Au(lll) surface. Langmuir 17 2560-2563... 

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