Isotherms Fowler-Guggenheim

There are several isotherm models for which the isotherm shapes and peak prohles are very similar to that for the anti-Langmuir case. One of these models was devised by Fowler and Guggenheim [2], and it assumes ideal adsorption on a set of localized active sites with weak interactions among the molecules adsorbed on the neighboring active sites. It also assumes that the energy of interactions between the two adsorbed molecules is so small that the principle of random distribution of the adsorbed molecules on the adsorbent surface is not significandy affected. For the liquid-solid equilibria, the Fowler-Guggenheim isotherm has been empirically extended, and it is written as ... 

The most spectacular peak profiles, which suggest self-associative interactions, were obtained for 5-phenyl-1-pentanol on the Whatman No. 1 and No. 3 chromatographic papers (see Figure 2.15 and Figure 2.16). Very similar band profiles can be obtained using the mass-transfer model (Eqnation 2.21), coupled with the Fowler-Guggenheim isotherm of adsorption (Equation 2.4), or with the multilayer isotherm (Equation 2.7). 

In Figure 2.22, the exemplary peak profiles calculated using the Fowler-Guggenheim isotherm are presented. These calculations were performed for the parameter values given in Table 2.1. 

FIGURE 2.23 Peak profiles calculated for the Fowler-Guggenheim isotherm model for % = 3 and the concentrations of 2, 1.5, 1, and 0.5 mol L (peaks from the largest to the smallest, respectively). 

Bumble and Honig (I) have discussed the HB procedure as applied to gas adsorption and the approximations inherent in the model used below. Honig (6) gives additional background information, where the Fowler-Guggenheim isotherm equation is derived in an elementary fashion. 

Finally, it is necessary to introduce the Fowler-Guggenheim isotherm equation... 

Figure 3. Adsorption isotherms calculated as described in text forC = 4 and 5 ----------------Fowler-Guggenheim isotherm...

The second type of isotherm which commonly occurs arises when the lateral interactions between adsorbed molecules are taken into account or the Van der Waals type of equation is used to describe the state of the adsorbate (J7). The equations for these isotherms usually have the form u = f(v), for example, the Fowler-Guggenheim isotherm studied with some care in the earlier work (2. ... 

The simplest representation of adsorbate - adsorbate- adsorbent interactions is the Fowler -Guggenheim isotherm which is formally similar to the Bragg-Williams approximation. This isotherm differs from the Langmuir one in the exponential term, accounts for the interactions. 

Figure 2.3-2 Plot of y = bP versus the fractional loading for the Fowler-Guggenheim isotherm (c = 7)...

FIGURE 4.26 Plots of the Fowler-Guggenheim isotherm for different values of the interaction parameter BpQ in (a) linear and (b) logarithmic concentration scale. 

The thermodynamics of adsorption is particularly important for analyzing the catalytic reactions as weU as the surface characterization of the catalysts. In this section, first, we will derive the Gibbs adsorption isotherm, and then we will use the Gibbs adsorption isotherm to derive the more useful isotherms such as Langmuir s and Fowler Guggenheim isotherms. 

For the derivation of Volmer s and Fowler Guggenheim isotherms from the gas phase equations of state and Gibbs adsorption isotherms, we will refer the reader to Ruthven (1984). 

What is the difference between Langmuir and Fowler-Guggenheim isotherms ... 

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