Multicomponent adsorption phase surfaces

However, in normal phase adsorption systems (or liquid-solid chromatography) the interaction of the mobile phase solvent with the solute is often less Important than the competing Interactions of the mobile phase solvent and the solute with the stationary phase adsorption sites. Solute retention is based upon a displacement mechanism. Multicomponent mobile phases and their combination to optimize separations in liquid-solid chromatography have been studied in detail (31-35). Here, solvents are classified as to their interaction with the adsorption surface (Reference 32, in particular) ... 

It can be seen that lAST predictions seriously deviate from the experimental data for this system even though the adsorbed phase is known to be very close to ideal under the experimental conditions. This deviation therefore points to the surface heterogeneity. T o address this heterogeneity, new models continue to emerge in the study of multicomponent adsorption equilibria. 

MSL models present the correct Henry s law limit and obey the requirement of thermodynamic consistency. This model is often used to account for the effect of the size difference in the study of multicomponent adsorption equilibria [29,30]. The MSL model can be extended to include effects such as lateral interactions in the adsorbed phase as well as surface heterogeneity [80]. 

This isotherm may be derived from kinetic considerations for intermediate surface coverages (0.2 < 0 < 0.8), but it does not lend itself to multicomponent adsorption and also fails to predict the limiting conditions of — 0 when Pa 0 and 9 — when 00. Even though it was used for correlating the kinetics of ammonia synthesis, the Temkin isotherm has not found much use in the kinetic analysis of solid-catalyzed gas-phase reactions. 

The most straightforward (and the most developed) approach to multicomponent adsorption is in further development of the thermodynamics of a surface phase, similar to the bulk-phase thermodynamics. In this way, the Gibbs surface thermodynamics should be completed by an equation of state or by an excess model for a proper thermodynamie potential. An extended review of the fundamentals and the history of the development of this approaeh may be found in Refs. 8, 9, and 78. The approach has become espeeially popular and widely used for praetieal modeling of multicomponent adsorption after the works of de Boer [79] and, especially, Myers and Prausnitz [80]. The latter authors made the natural step of introducing the activity coefficients y of the components in an adsorbed phase. In terms of these coefficients, the chemical potentials of the adsorbate may be expressed as... 

In many cases, the surface phase may be assumed to be ideal and its activity coefficients f set unity. The corresponding theory has been called lAST (Ideal Adsorbed Solution Theory) [80]. The main advantage of the lAST is its capabdity to predict multicomponent adsorption equilibria on the basis of the experimental data on the single-component adsorption. Relations (43) and (44) are greatly simplified in this case. 

The ideal adsorption solution theory described in Section IVA is the simplest approach to multicomponent adsorption from the point of view of the general thermodynamic theory of the surface phase. The lAST is comparable with potential adsorption theory by predictability. Both theories need the correlation of experimental data for pure components in order to estimate adsorption of mixtures. However, in general, the predictions of the two theories are different, as illustrated in Section IVD. Let us analyze assumptions on which the two theories may become similar. 

The interfacial layer is the inhomogeneous space region intermediate between two bulk phases in contact, and where properties are notably different from, but related to, the properties of the bulk phases (see Figure 6.1). Some of these properties are composition, molecular density, orientation or conformation, charge density, pressure tensor, and electron density [2], The interfacial properties change in the direction normal to the surface (see Figure 6.1). Complex profiles of interfacial properties take place in the case of multicomponent systems with coexisting bulk phases where attractive/repulsive molecular interactions involve adsorption or depletion of one or several components. 

When modeling phenomena within porous catalyst particles, one has to describe a number of simultaneous processes (i) multicomponent diffusion of reactants into and out of the pores of the catalyst support, (ii) adsorption of reactants on and desorption of products from catalytic/support surfaces, and (iii) catalytic reaction. A fundamental understanding of catalytic reactions, i.e., cleavage and formation of chemical bonds, can only be achieved with the aid of quantum mechanics and statistical physics. An important subproblem is the description of the porous structure of the support and its optimization with respect to minimum diffusion resistances leading to a higher catalyst performance. Another important subproblem is the nanoscale description of the nature of surfaces, surface phase transitions, and change of the bonds of adsorbed species. 

A multicomponent HSDM for acid cfye/carbon adsorption has been developed based on the ideal adsorbed solution theory (lAST) and the homogeneous surface diffusion model (H SDM) to predict the concentration versus time decay curves. The lAST with the Redlich-P eterson equation is used to determine the pair of liquid phase concentrations, Q and Qj, from the corresponding pair of solid phase concentrations, q j and q jy at fha surface of the carbon particle in the binary component. 

For non-porous catalyst pellets the reactants are chemisorbed on their external surface. However, for porous pellets the main surface area is distributed inside the pores of the catalyst pellets and the reactant molecules diffuse through these pores in order to reach the internal surface of these pellets. This process is usually called intraparticle diffusion of reactant molecules. The molecules are then chemisorbed on the internal surface of the catalyst pellets. The diffusion through the pores is usually described by Fickian diffusion models together with effective diffusivities that include porosity and tortuosity. Tortuosity accounts for the complex porous structure of the pellet. A more rigorous formulation for multicomponent systems is through the use of Stefan-Maxwell equations for multicomponent diffusion. Chemisorption is described through the net rate of adsorption (reaction with active sites) and desorption. Equilibrium adsorption isotherms are usually used to relate the gas phase concentrations to the solid surface concentrations. 

A curious example is that of the distribution of benzene in water benzene will initially spread on water, then as the water becomes saturated with benzene, it will round up into lenses. Virtually all of the thermodynamics of a system will be affected by the presence of the surface. A system containing a surface may be considered as being made up of three parts two bulk phases and the interface separating them. Any extensive thermodynamic property will be apportioned among these parts. For example, in a two-phase multicomponent system, the extra amount of an i component that can be accom-mondated in the system due to the presence of the interface ( ) may be expressed as Qi Qii where is the total number of molecules of i in the whole system, Vj and Vjj are the volumes of phases I and II, respectively, and Q and Qn are the concentrations of i in phases I and II, respectively. The surface (excess) concentration of i is defined as Fj = A, where A is the surface area. At equilibrium, the chemical potential of any component is the same in each bulk phase and at the surface. The Gibbs adsorption equation, which is one of the most widely used expression in surface and colloid science is shown in Eq. (2) ... 

The processes discussed in this chapter demonstrate the great variety of phase equilibrium that can arise beyond the basic vapor-liquid problems discussed in most of the previous chapters. Many other systems could be included The adsorption of gases onto solids (used in the removal of pollutants from air), the distribution of detergents in water/oil systems, the wetting of solid surface by a liquid, the formation of an electrochemical cell when two metals make contact are all examples of multiphase/multicomponent equilibrium. They all share one important common element their equilibrium state is determined by the requirement that the chemical potential of any species must be the same in any phase where the species can be found. These problems are beyond the scope of this book. The important point is this The mathematical development of equilibrium (Chapter 10) is extremely powerful and encompasses any system whose behavior is dominated by equilibrium. 

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