Adsorption of Single Component

As the adsorption process is an accumulation of gas at the solid surface, the gas concentration decreases progressively with increased distance z from the surface to the bulk phase (Fig. 7.2). 

The adsorbed amount, n , is defined as the amount of matter present in the layer of thickness t adsorbed at the surface [3]. This amount is given by the relation  

Adsorbed amount and surface excess amount are two different quantities, which are often used without clear distinction. We will see later in which conditions these two values can be considered as equal. 

The adsorption equilibrium of a single component i on a solid can be written  

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Adsorption of single components in zeolites can often be described by a simple Langmuir isotherm, Eq. (18), or the Langmuir-Freundlich isotherm, Eq. (26) [50-52] ... 

The isotherm that is most easily understood theoretically and widely applicable to experimental data is, known as the Langmuir isotherm. This is also the simplest model of a nonlinear isotherm. It accounts well for the adsorption of single components on homogenous surfaces at low to moderate concentrations, or for the adsorption to isolated type-I or type-II sites [103, 110, 111]. The Langmuir adsorption isotherm equation is written ... 

To complete the set of possible operating parameters for a four-section SMB unit, values for the dimensionless flow rate ratios mt and mw have to be determined as well. In sections I and IV things are a little less complicated, since only the adsorption of single components is involved. 

However, if the adsorbed phase can be considered as an ideal solution, in which the molecular interactions are the same as for the adsorption of single components, it is possible to calculate the molar differential coadsorption enthalpy by mean of the relation ... 

At this point, it is feasible to correlate the liquid-phase adsorption equilibrium single component data, with the help of isotherm equations developed for gas-phase adsorption, since, in principle, it is feasible to extend these isotherms to liquid-phase adsorption by the simple replacement of adsorbate pressure by concentration [92], These equations are the Langmuir, Freundlich, Sips, Toth, and Dubinin-Radushkevich equations [91-93], Nevertheless, the Langmuir and Freudlich equations are the most extensively applied to correlate liquid-phase adsorption data. [2,87],... 

Diffusion measurements under nonequilibrium conditions are more complicated due to the difficulties in ensuring well defined initial and boundary conditions. IR spectroscopy has proved to be a rather sensitive tool for studying simultaneously the intracrystalline concentration of different diffusants, including the occupation density of catalytic sites [28], By choosing appropriate initial conditions, in this way both co- and counterdiffusion phenomena may be followed. Information about molecular transport diffusion under the conditions of multicomponent adsorption may also be deduced from flow measurements [99], As in the case of single-component adsorption, the diffusivities arc determined by matching the experimental data (i.e. the time dependence of the concentration of the effluent or the adsorbent) to the corresponding theoretical expressions. 

Modeling in multicomponent adsorption systems is an extension to that of single component adsorption. Many models have been reported in the literature for the prediction of concentration versus time decay curves in single component batch adsorption stem. However, there are very few research papers on the topic of multicCHnponent mass transport studies for liquid phase adsorption, therefore, it is a valuable contribution and novel development to adsorption research. 

As far as simple modelling of self-assembly is concerned, the treatment of single component lipid molecules given here has probably been pushed as far as it can. The refinement of our theory of self-assembly requires a proper examination of Stern layers, consequences of deviations from liquid-like properties of hydrocarbon chains, head group steric elfects, specific ion adsorption and other effects. While such a more rigorous analysis would undoubtedly provide specific insights into the properties of particular molecules, it is doubtful if a more refined theory will provide a better overview. 

From Eqs. (20) and (21) it follows that if is independent of concentration, binary fluxes can be predicted on the basis of single-component permeation data once the multicomponent adsorption isotherm is known. 

As we have seen previously, the separation mechanism in pervaporation is explained by an adsorption-diffusion process. In this way, the selective adsorption of the components in the zeolite will be responsible for the selectivity in the separation. Adsorption is an exothermic nonactivated process. In general, the isotherm of adsorption on zeohtes follows a single site Langmuir-type isotherm [74]. 

Having obtained the adsorption equilibrium and mass transfer parameters of single component systems (Tables 1 to 2), we are ready to examine the predictability of the model in simulating the sorption kinetics of multicomponent systems on Norit activated carbon. 

Determination of Single Component Adsorption Isotherm Parameters - Characterization of a New CSP (Paper III)... 

The most dramatic difference between analytical and preparative chromatography is the extension of the working range of the adsorption isotherm into its nonlinear region. The behavior of single components as well as their mixtures over the complete range of the adsorption isotherm has, therefore, to be determined with great accuracy. 

Unfortunately, the study of phase equilibria in solution, e.g., liquid-solid adsorption, is not a highly popular area of research. Gas-solid adsorption and vapor-solution equilibria have been studied in far more detail, although most of the information available concerns the fate of single components in a diphasic system. Liquid-solid adsorption has benefited mainly from the extension of the concepts developed for gas phase properties to the case of dilute solutions. Multicomponent systems and the competition for interaction with the stationary phase are research areas that have barely been scratched. The problems are difficult. The development of preparative chromatography and its applications are changing this situation. 

The agreement that was observed between the experimental results and the prediction of a competitive Langmuir model based on the use of single-component Langmuir isotherms in the case of the adsorption of enantiomeric derivatives of amino acids on immobilized serum albumin [26] is imusual. It demonstrates the validity of the competitive Langmuir model based on the use of the parameters of the single-component Langmuir model. However, as explained before, the experimental conditions are exceptionally favorable since the column saturation capacities for the two enantiomers are equal. Nevertheless, Zhou et ah have shown that it is possible, in certain favorable cases, to derive the equilibrium isotherms of the pure enantiomers and to calculate isotherm equilibrium data for any mixture of... 

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