Langmuir adsorption isotherm multicomponent

The Langmuir Equation for the Case Where Two or More Species May Adsorb. Adsorption isotherms for cases where more than one species may adsorb are of considerable significance when one is dealing with heterogeneous catalytic reactions. Reactants, products, and inert species may all adsorb on the catalyst surface. Consequently, it is useful to develop generalized Langmuir adsorption isotherms for multicomponent adsorption. If 0t represents the fraction of the sites occupied by species i, the fraction of the sites that is vacant is just 1 — 0 where the summation is taken over all species that can be adsorbed. The pseudo rate constants for adsorption and desorption may be expected to differ for each species, so they will be denoted by kt and k h respectively. 

The multicomponent Langmuir adsorption isotherm given in Eq. (7) is the simplest model for the description of non-linear, multicomponent, adsorption equilibrium. At high concentration, the model predicts saturation of the stationary phase and overload of the chromatographic column. At low concentration (high dilution) the behavior can be correctly described by the non-competitive linear adsorption isotherm ... 

The preceding set of equation is valid only for Langmuir adsorption isotherms, and numerical simulation must be used to obtain the flow rates for other adsorption isotherm shapes or for multicomponent mixtures. 

In this chapter we are going to discuss the Langmuir adsorption isotherm (LAI) and several of its generalizations for single- and multicomponent systems in Sect. 2. This isotherm has proved to he most useful to describe adsorption in microporous materials. In Sect. 3 we will provide some information on a few empirical adsorption isotherms used to describe gas adsorption in micro- and mesoporous materials, i. e. showing pore condensation leading to an unlimited amount of mass in the adsorbed phase. 

In this section we have assumed that the adsorption isotherm of an adsorbate is unaffected by the presence of constituents other than the adsorbate in the fluid mixture. If such ideaiir> is assumed for the Langmuir isotherm developed in the previous example, you could use the derived expression for any gaseous system containing carbon tetrachloride and the same activated carbon. In reality, however, the presence of other solutes that have an affinity for the carbon surface alters the CCI4 equilibrium behavior. An accurate system representation would require data or models for the complete multicomponent mixture. 

For multicomponent systems, the local adsorption isotherm for a given micropore is assumed to follow the extended Langmuir equation. 

The Langmuir isotherm model can be extended to multi-component systems [109], When several components are simultaneously present in a solution, the amount of each component adsorbed at equilibrium is smaller than if that component were alone [13] because the different components compete to be adsorbed on the stationary phase. The adsorption isotherm for the / th component in a multicomponent system is written ... 

Extension of the Series Solution of the LeVan-Vermeulen Isotherm to multi-component systems Frey and Rodrigues [56] have extended the binary LeVan-Vermeulen isotherm to the case of multicomponent systems. They showed that, if we assume that the adsorption isotherm of each single component follows Langmuir isotherm behavior, the multicomponent isotherm is given by [56]... 

The selectivity of adsorption (S = niyj/njyi) of water vapour (component 1, mole fraction yi) on aluminas over component j (mole fraction yj) of a gas mixture can be complex functions of adsorbate loadings (ni,nj), system temperature and pressure. There is a scarcity of published data on water adsorption from multicomponent gas mixtures on alumina. Typically, it is assumed that water is exclusively adsorbed on aluminas (S — oo,nj —> 0) from non- polar gases such as air or natural gas. The assumption may not be valid when the gas mixture contains polar components. The mixed gas Langmuir or Toth models may be used to describe multicomponent Type I equilibria on aluminas [6,7]. No isotherm model is available to describe adsorption of water from gas mixtures when there is partial condensation of water in the mesopores of the alumina. 

Adsorption on solids is characterized by adsorption isotherms that show the concentration of the respective species on the adsorbent as a function of its concentration in the contacting fluid phase. Isotherms may have different shapes, depending on whether adsorption is competitive (adsorbed molecules discourage additional adsorption) or synergistic (they encourage it). The most commonly used isotherm is Langmuir s, applicable to multicomponent adsorption, but restricted to competitive behavior. 

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 prediction of multicomponent equilibria based on the information derived from the analysis of single component adsorption data is an important issue particularly in the domain of liquid chromatography. To solve the general adsorption isotherm, Equation (27.2), Quinones et al. [156] have proposed an extension of the Jovanovic-Freundlich isotherm for each component of the mixture as local adsorption isotherms. They tested the model with experimental data on the system 2-phenylethanol and 3-phenylpropanol mixtures adsorbed on silica. The experimental data was published elsewhere [157]. The local isotherm employed to solve Equation (27.2) includes lateral interactions, which means a step forward with respect to, that is, Langmuir equation. The results obtained account better for competitive data. One drawback of the model concerns the computational time needed to invert Equation (27.2) nevertheless the authors proposed a method to minimize it. The success of this model compared to other resides in that it takes into account the two main sources of nonideal behavior surface heterogeneity and adsorbate-adsorbate interactions. The authors pointed out that there is some degree of thermodynamic inconsistency in this and other models based on similar -assumptions. These inconsistencies could arise from the simplihcations included in their derivation and the main one is related to the monolayer capacity of each component [156]. 

The last three chapters deal with the fundamental and empirical approaches of adsorption isotherm for pure components. They provide the foundation for the investigation of adsorption systems. Most, if not all, adsorption systems usually involve more than one component, and therefore adsorption equilibria involving competition between molecules of different type is needed for the understanding of the system as well as for the design purposes. In this chapter, we will discuss adsorption equilibria for multicomponent system, and we start with the simplest theory for describing multicomponent equilibria, the extended Langmuir isotherm equation. This is then followed by a very popularly used IAS theory. Since this theory is based on the solution thermodynamics, it is independent of the actual model of adsorption. Various versions of the IAS theory are presented, starting with the Myers and Prausnitz theory, followed by the LeVan and Vermeulen approach for binary systems, and then other versions, such as the Fast IAS theory which is developed to speed up the computation. Other multicomponent equilibria theories, such as the Real Adsorption Solution Theory (RAST), the Nitta et al. s theory, the potential theory, etc. are also discussed in this chapter. 

We have shown in the last few sections the LAS theory as well as its computation implementation to obtain multicomponent adsorption isotherm. Since this theory is based on solution thermodynamics it can be applied to prove the thermodynamic consistency of the extended Langmuir equation. 

The approach of IAS of Myers and Prausnitz presented in Sections 5.3 and 5.4 is widely used to calculate the multicomponent adsorption isotherm for systems not deviated too far from ideality. For binary systems, the treatment of LeVan and Vermeulen presented below provides a useful solution for the adsorbed phase compositions when the pure component isotherms follow either Langmuir equation or Freundlich equation. These expressions are in the form of series, which converges rapidly. These arise as a result of the analytical expression of the spreading pressure in terms of the gaseous partial pressures and the application of the Gibbs isotherm equation. 

We shall illustrate the utility of the theory by applying to a multicomponent system in which the adsorption isotherm is described by the following extended Langmuir isotherm equation ... 

FIGURE 7.22 Adsorption isotherms of copper cyanide complexes at three different pH values. Symbols represent experimental data for the different pH conditions and solid lines represent the the modified multicomponent Langmuir Equation (7.13). (Reproduced from J. S. Lee, N. V. Deokar, and L. L. Tavlarides. Ind. Eng. Chem. Res. 37 2812-2820,1998. With permission.)... 

Table 14.1 Percentage absolute average deviations (%AAD) between predicted results and experimental data for the adsorption isotherms (x) and total amounts adsorbed (n) using the multicomponent Langmuir and lAST models. The first value is the % AAD in x and the second is the % AAD In n...

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