Adsorption isotherm individual

Equation XI-27 shows that F can be viewed as related to the difference between the individual adsorption isotherms of components 1 and 2. Figure XI-9 [140] shows the composite isotherms resulting from various combinations of individual ones. Note in particular Fig. XI-9a, which shows that even in the absence of adsorption of component 1, that of component 2 must go through a maximum (due to the N[ factor in Eq. XI-27), and that in all other cases the apparent adsorption of component 2 will be negative in concentrated solution. 

Until relatively recently, the fact that an experimental isotherm necessarily contained composite information concerning the adsorption of the two components of a binary solution was considered to be a major problem. For a rigorous interpretation it was felt necessary to process the data to obtain the so-called individual adsorption isotherm or separate adsorption isotherm of each component. However, this is not at all straightforward and requires the introduction of a number of assumptions relating to the structure of the adsorbed layer. The main problem is of course to know the composition of the adsorbed layer. One assumption often used in the case of volatile components is that introduced by Williams (1913) the solid will adsorb the same amount of each component from the vapour in equilibrium with the solution as from the solution itself. This of course implies that the adsorbed layer has the same composition at the liquid-solid and gas-solid interfaces and it requires numerous gravimetric measurements from the vapour... 

Nonlinearity of the Langmuir adsorption isotherms is observed even in noncompetitive chromatographic processes. Individual adsorption isotherms can be found experimentally using frontal analysis at overload conditions however, the adsorption isotherms in the separation of mixtures are different because of the interference of other compounds in the mixture. In PHPLC method development, it is necessary to optimize separation conditions and column loading experimentally. 

In Figures 4 and 5 the individual adsorption isotherms x = /(x, ) are presented. For both mixtures the mole fractions of benzene in surface phase are higher for the carbon AC-2. It means that the adsorption phase is richer in preferentially adsorbed component, i.e. benzene. Thus, the selectivity of adsorption is higher in the case of carbon with narrower micropore system. 

Figure 4. Individual adsorption isotherms for Figure 5. Individual adsorption isotherms benzene (1) + n-heptane (2) on the carbons for benzene (1) + 2-propanol (2) on the...

A successful theory should, for a certain set of parameters, fit simultaneously experimental titration curves, electrokinetic curves, and the individual adsorption isotherms of K+ and Cl measured radiometrically. Thus, to follow this investigation strategy, we took into consideration only the experimental data, measured at the salt concentration 0.01 M. For this electrolyte concentration the calculated activity coefficients of the cation and anion are equal to 0.902. 

The philosophy lying behind that best-fit exercise arose from our earlier observation that surface heterogeneity does not affect much titration curves and the estimated surface complexation parameters [22]. As we have already argued, there must exist some compensation effects in these composite adsorption isotherms. On the contrary, we found that surface heterogeneity affects strongly the individual adsorption isotherms of the surface complexes, measured radiometrically or in another way. This, of course, is also true in the case of the individually measured isotherms of adsorption of the bivalent ions. 

Individual adsorption isotherms from dilute solutions... 

DETERMINATION OF INDIVIDUAL ADSORPTION ISOTHERMS FROM COMPOSITE ISOTHERMS... 

The isotherm of concentration change or the composite isotherm represents the combined adsorption of the two components of the binary solution. It would be of interest to calculate the individual adsorption isotherms of the two components of the solution from the composite isotherm. The composite isotherm equation... 

This equation has four unknowns. But the two unknowns( i), and( 2)mCan be determined by direct measurement of adsorption that occurs when the solid is separately exposed to the saturated vapors of each of the two pure component as it has been assumed that the adsorption from the vapor phase over the pure components is the same as from the liquid phase. Thus, combining Equation 3.34 and Equation 3.17, two unknowns n[ and 2 for a given value of x can be calculated. Kipling and Tester used this treatment to their composite isotherms from benzene-ethanol, benzene-acetic acid, and benzene-ethylene dichloride solutions on charcoal, and obtained the individual adsorption isotherms (Figure 3.24(a) and Figure 3.24(b))... 

FIGURE 3.25 Individual adsorption isotherms of methanol and benzene from their mixtures on Mogul before and after various treatments. (Puri, B.R., Singh, D.D., and Kaistha, B.C., Carbon, 10, 481, 1972. With permission.)... 

Puri et al. " also calculated individual adsorption isotherms (Figure 3.25) from the composite isotherms for methanol-benzene binary solutions assuming adsorption to be monolayer and combining Equation 3.17 and Equation 3.34 as was done by Gasser and Kipling and using 16.7 A as the molecular areas of methanol and benzene respectively. These individual isotherms correspond to the composite isotherm shown in Figure 3.14. 

The adsorption from binary solutions on sohd adsorbents in general and on activated carbons in particular is discussed in Chapter 3. The nature and types of adsorption and adsorption isotherms from dilute solutions and from completely miscible binary solutions are described. The composite isotherm equation is derived. The shapes and classification of composite isotherms and the influence of adsorbate-adsorbent interactions, the heterogeneity of the carbon surface, and the size and orientation of the adsorbed molecules on the shapes are examined. The thickness of the adsorbed layer and the determination of individual adsorption isotherms from a composite isotherm are also described. 

The inversion of the integral adsorption isotherm to obtain the PSD is the well-known so-called ill-posed problem. Several qrproaches have been proposed to address this problem [3,7,8]. The DFT PLUS micromeritics software was used to determine the PSD using individual adsorption isotherms calculated by DFT. Details of this software are found elsewhere [9]. The use of this software requires the selection of the renormalization parameter, which in many cases is selected using the judgment of the researcher [4]. We used a low renormalization parameter for this work, which is comparable to lat was u for the determination of the PSD fiom isotherms obtained using Monte Carlo simulations. Smoother curves can be obtained if a larger renormalization parameter is used. 

Inspection of the PSDs obtaind from GCMC adsorption isotherms, it is evident that they show that there are no pores present with approximately 0.85 nm of pore width. Inspection of the structures obtained from simulations for systems of pore width, w, slightly smaller than 1 nm indicate that the transition from two adsorbed layers to three adsorbed layers occurs at approximately this pore width. Figure 7 shows a collection of snapshots of adsorbed systems at PIPo=0.S. The fact that no pores of these sizes appear in most porous carbons, is probably closely related to the particular shape of the individual adsorption isotherms when the pore is too large to accommodate only 2 layers of adsorbed molecules, but too small to have a third layer. Probably models that include pore-connectivity or that take into account smooth variations in size of a given pore, will not show this effect... 

In this work we report adsorption data of CO2 at 253 and 298 K as well as H2 at 77 K on the high surface area AX-21 activated carbon. The individual adsorption isotherms are used in order to calculate PSDs based on the GCMC approach. In a further step the individual isotherms are combined and new PSDs that respect combinations of the experimental... 

Fig. 25 shows adsorption curves for five binary mixtures of the four components above. The characteristic adsorption energies are taken from the correlation of individual adsorption isotherms with a common value of xg. A good quantitative agreement between experimental data and calculated curves is observed, except for the methane-ethane mixture, for which the agreement is slightly worse. The qualitative agreement is also excellent. For example, the ethane-propylene and methane-ethylene curves almost coincide and intersect at low molar... 

Explain the difference between apparent and individual adsorption isotherms. 

For a given adsorption system, the amount of solute adsorbed at equilibrium depends on the temperature T, the pressure P, and the composition of the equilibrium solution phase p. The experimental results of adsorption measurements are usually reported in the form of individual adsorption isotherms showing the quantity or... 

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