Adsorption single-component adsorbates

Eqs. (1,4,5) show that to determine the equilibrium properties of an adsorbate and also the adsorption-desorption and dissociation kinetics under quasi-equilibrium conditions we need to calculate the chemical potential as a function of coverage and temperature. We illustrate this by considering a single-component adsorbate. The case of dissociative equilibrium with both atoms and molecules present on the surface has recently been given elsewhere [11]. 

Adsorption and Desorption Kinetics of Single-Component Adsorbates. . 156... 

Adsorption and Desorption of Single-Component Adsorbates by "Macro"-FTIR... 

Ideal Adsorbed Solution Theory. Perhaps the most successful approach to the prediction of multicomponent equiUbria from single-component isotherm data is ideal adsorbed solution theory (14). In essence, the theory is based on the assumption that the adsorbed phase is thermodynamically ideal in the sense that the equiUbrium pressure for each component is simply the product of its mole fraction in the adsorbed phase and the equihbrium pressure for the pure component at the same spreadingpressure. The theoretical basis for this assumption and the details of the calculations required to predict the mixture isotherm are given in standard texts on adsorption (7) as well as in the original paper (14). Whereas the theory has been shown to work well for several systems, notably for mixtures of hydrocarbons on carbon adsorbents, there are a number of systems which do not obey this model. Azeotrope formation and selectivity reversal, which are observed quite commonly in real systems, ate not consistent with an ideal adsorbed... 

AH practical adsorbents have surfaces that are heterogeneous, both energetically and geometrically (not all pores are of uniform and constant dimensions). The degree of heterogeneity differs substantially from one adsorbent type to another. These heterogeneities are responsible for many nonlinearities, both in single component isotherms and in multicomponent adsorption selectivities. 

Selectivity for C02 it represents the C02 uptake ratio to the adsorption of any other gas (typically nitrogen for post-combustion capture, and methane for natural gas). It is an essential evaluation criterion, and affects the purity of the adsorbed gas, which will significantly influence the sequestration of C02. The simplest method to estimate the selectivity factor is to use single-component adsorption isotherms of C02 and nitrogen. 

The Langmuir adsorption isotherm describes the equilibrium between a single-component gas A and adsorbed species A(s) at a surface [237]. The expression relates the fraction of the surface 6a covered by adsorbed species as a function of the partial pressure pa exposed to the surface. The usual form of the Langmuir adsorption isotherm is... 

It is rather desirable that investigations should be made of promoter action in reactions which only involve the decomposition or transformation of a single substance. When two substances interact, it is always possible that one component of the surface adsorbs one reactant and the other component adsorbs the other reactant. From what has been said about the localization of catalytic activity in special regions of the surface it will be seen that measurements of the total adsorption of the reactants by the separate constituents of the composite catalyst would throw no light on whether or not this actually occurred. 

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 ... 

When the relative volumes are known and the diffusion coefficients in the capsule core and capsule membrane can be estimated a priori in single component adsorption, the parameter to work with is the effective diffusivity in the adsorbent pore (Dn). Then, with the above estimated parameter values, the parameters of competitive adsorption are the maximum concentration at the solid phase of the adsorbent (CsmT), and the equilibrium constants of the target product (KS1) and byproduct (KS2)-... 

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],... 

The Langmuir isotherm equation for the correlation of the liquid-phase adsorption equilibrium of a single component, can, in principle, as was previously stated, be extended to liquid-phase adsorption by the simple replacement of adsorbate pressure by concentration [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. 

As a molecule approaches the solid surface, a balance is established between the intermolecular attractive and repulsive forces. If other molecules are already adsorbed, both adsorbent-adsorbate and adsorbate-adsorbate interactions come into play. It is at once evident that assessment of the adsorption energy is likely to become exceedingly complicated in the case of a multicomponent system - especially if the adsorption is taking place from solution at a liquid-solid interface. For this reason, in the numerous attempts made to calculate energies of adsorption, most attention has been given to the adsorption of a single component at the gas-solid interface. 

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