Binary Adsorbed Phase

The analysis of macropore diffusion in binary or multicomponent systenis presents no particular problems since the transport properties of one compos nent are not directly affected by changes ini the concentration of the bther components. In an adsorbed phase the situation is more complex since ih addition to any possible direct effect on thei mobility, the driving force for each component (chemical potential gradient is modified, through the multi-component equilibrium isotherm, by the coiicentration levels of all components in the system. The diffusion equations for each component are therefore directly coupled through the equilibrium relationship. Because of the complexity of the problem, diffusion in a mixed adscjrbed phase has been studied tjs only a limited extent. 

A theoretical study of diffusion in a binary adsorbed phase was presented by Round, Newton, and Habgood and an essentially similar analysis was reported independently by Karger and Bulow. Starting from the irreversible thermodynamic formulation and neglecting the cross coefficients, the fluxes of the two components are given by 

A differential mass balance for a spherical shell element yields for the relevant form of the diffusion equation  

Representation of the exchange process as a simple diffusive process is possible in the special case of equimolar counterdiffusion which requires Doa = BO and 0.4. 0.4O (0a bo)- Under these condi- 

FIGURE 6.21. Theoretical uptake curves for counterdiffusion. A is adsorbing, S is desorbing, and D q Dg0 - Dq. Theoretical adsorption and deiorption curves for both and R, calculated from q. (6.83) are shown by continuous lines. In (n) the uptake curve for A is similar to curve calculated from Eq. (6.4) with Z - Z o —). (The curve for D - DJ 6) is sho ——In (b) the uptake curves for A and B are both dose to the dmpte diffusion curve (. (6.4)1 afld rouch slower than the curves for 2) - Dq/( - 8). 

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To establish the relationship between self- and transport diffusion it is necessary first to consider diffusion in a binary adsorbed phase within a micropore. This can be conveniently modeled using the generalized Maxwell-Stefan approach [45,46], in which the driving force is assumed to be the gradient of chemical potential with transport resistance arising from the combined effects of molecular friction with the pore walls and collisions between the diffusing molecules. Starting from the basic form of the Maxwell-Stefan equation ... 

Haeany Solution Model The initial model (37) considered the adsorbed phase to be a mixture of adsorbed molecules and vacancies (a vacancy solution) and assumed that nonideaUties of the solution can be described by the two-parameter Wilson activity coefficient equation. Subsequendy, it was found that the use of the three-parameter Flory-Huggins activity coefficient equation provided improved prediction of binary isotherms (38). 

Taking Simultaneous Micellizadon and Adsorption Phenomena into Consideration In the presence of an adsorbent in contact with the surfactant solution, monomers of each species will be adsorbed at the solid/ liquid interface until the dual monomer/micelle, monomer/adsorbed-phase equilibrium is reached. A simplified model for calculating these equilibria has been built for the pseudo-binary systems investigated, based on the RST theory and the following assumptions ... 

The grand canonical ensemble is appropriate for adsorption systems, in which the adsorbed phase is in equilibrium with the gas at some specified temperature. The use of a computer simulation allows us to calculate average macroscopic properties directly without having to explicitly calculate the partition function. The grand canonical Monte Carlo (GCMC) method as applied in this work has been described in detail earlier (55). The aspects involving binary fluid mixtures have been described previously in our Xe-Ar work (30). 

In this chapter, we have so far discussed the adsorption of gases in solids. This section gives a brief description of the adsorption process from liquid solutions. This adsorption process has its own peculiarities compared with gas-solid adsorption, since the fundamental principles and methodology are different in almost all aspects [2,4,5], In the simplest situation, that is, a binary solution, the composition of the adsorbed phase is generally unknown. Additionally, adsorption in the liquid phase is affected by numerous factors, such as pH, type of adsorbent, solubility of adsorbate in the solvent, temperature, as well as adsorptive concentration [2,4,5,84], This is why, independently of the industrial importance of adsorption from liquid phase, it is less studied than adsorption from the gas phase [2],... 

Adsorbent nonpermeability is an important condition, since it essentially states that all processes occurs in the liquid phase. Since adsorption is related to the adsorbent surface, it is possible to consider the analyte distribution between the whole liquid phase and the surface. Using surface concentrations and the Gibbs concept of excess adsorption [20], it is possible to describe the adsorption from binary mixtures without the definition of adsorbed phase volume. 

Applying this function into the mass-balance equation (2-33) and performing the same conversions [Eqs. (2-34)-(2-39)], the final equation for the analyte retention in binary eluent is obtained. In expression (2-67) the analyte distribution coefficient (Kp) is dependent on the eluent composition. The volume of the acetonitrile adsorbed phase is dependent on the acetonitrile adsorption isotherm, which could be measured separately. The actual volume of the acetonitrile adsorbed layer at any concentration of acetonitrile in the mobile phase could be calculated from equation (2-52) by multiplication of the total adsorbed amount of acetonitrile on its molar volume. Thus, the volume of the adsorbed acetonitrile phase (Vj) can be expressed as a function of the acetonitrile concentration in the mobile phase (V, (Cei)). Substituting these in equation (2-67) and using it as an analyte distribution function for the solution of mass balance equation, we obtain... 

In Fig 3a, the binary adsorption isotherms of a C8/C12 mixture is shown. C12 is adsorbed in a very selective way from the mixture, as can be seen in the selectivity diagram (Fig 3b), in which x and y represent the molar fractions in the liquid and adsorbed phases respectively. This selectivity for the longer chain can be explained by its higher interaction with the zeolite. 

This study firstly aims at understanding adsorption properties of two HSZ towards three VOC (methyl ethyl ketone, toluene, and 1,4-dioxane), through single and binary adsorption equilibrium experiments. Secondly, the Ideal Adsorbed Solution Theory (IAST) established by Myers and Prausnitz [10], is applied to predict adsorption behaviour of binary systems on quasi homogeneous adsorbents, regarding the pure component isotherms fitting models [S]. Finally, extension of adsorbed phase to real behaviour is investigated [4]. 

In NP gradient LC on polar adsorbents, the concentration of one (or more) polar solvent(s) in a nonpolar solvent increases. A simple equation (Eq. 5) can often adequately describe the experimental dependencies of the retention factors k of sample compounds on the volume fraction q> of a polar solvent B in a binary mobile phase comprised of two organic solvents with different polarities, if the sample solute is very strongly retained in the pure, less polar solvent ... 

Assuming that the adsorbent surface occupied by an adsorbed solute molecule (A ) and that occupied by a stronger solvent (n ) are equal, the eluent strength of a binary mobile phase, eab, has the following dependence on its quantitative composition ... 

These equations form a system of partial differential equations of the second order. Examples of two complete systems are given in Table 2.1 (a binary mixture and a pure mobile phase or a mobile phase containing only weakly adsorbed additives, a two-component system) and Table 2.2 (a binary mixture and a binary mobile phase with a strongly adsorbed additive, a three-component system). For the sake of simplicity, the equilibrium-dispersive model (see Section 2.2.2) has been used in both cases. The problem of the choice of the isotherm model will be discussed in the next two chapters. 

Numerous analytical models have also been developed for binary liquid phase surface excess isotherms. A model equation that accounts for adsorbate size differences, bulk liquid phase nonideality, as well as a simplified description of adsorbent heterogeneity is given below ... 

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