Isotherm Fowler

Besides the heterogeneity of the adsorbent surface, the second major reason for the adsorption of a compound to deviate from Langmuir isotherm behavior is that the adsorbed molecules interact. In this category, we find the Fowler isotherm, the anti-Langmuirian isotherm, and several S-shaped isotherm models, including the quadratic isotherm, the extended BET isotherm models, and the Moreau model. 

Figure 3.22 Illustration of the Fowler isotherm. x = 0,l, and 2 fe = 1.61 mL/mg qs = 300 mg/mL. (a) Fowler adsorption isotherm, (b) First derivative of the Fowler isotherm.

For liquid-solid equilibria, the Fowler isotherm is extended empirically and written ... 

Figrue 3.22 illustrates the Fowler isotherm. For x = 0, we obtain the Langmuir isotherm (Eq. 3.48). For = 1, there is an inflection located at the origin, hence the isotherm appears to be linear in an rmusually wide concentration range (Figure 3.22a). For x between 1 and 4, the isotherm has an inflection point at a finite concentration. The inflection tangent becomes vertical for X for higher... 

Figure 3.23 Use of the Fowler isotherm to account for experimental data. The adsorption isotherms of 2-phenylethanol and 3-phenylpropanol between spherical ODS silica (Vydac, Hesperia, CA), 10 fim, and a methanol/water 50 50 solution. Column dimensions, 2.1 x 250 mm. Data from J. Zhu, AM. Katti and G. Guiochon, J. Ghromatogr., 552 (1991) 71.

This model applies to two compounds that both exhibit single-component Fowler isotherm behavior. Depending on the assumptions one can make regarding the interaction between the two competing components, several equations can be written. The simplest equation for a competitive Fowler isotherm is written ... 

Figure 4.14 Comparison between the experimental adsorption data of 2-phenylethanol (a, c) and 3-phenylpropanol (b, d) and the best competitive Fowler isotherms derived from the best single-component parameters. For mixtures, the mobile phase concentration is expressed via the relative composition of PE and PR All concentrations in mg/ml. Symbols data for single component, o data for 3 1 mixtures (3/1 PE and PP), x data for 1 1 mixtures (1/1 PE and PP), + and data for 1 3 mixtures (1/3 PE and PP),. The RSS are the residual sum of squares calculated for each set of experiments performed with a constant relation of the mobile phase concentrations of the phenylalcohols. ODS silica from Vydac and water-methanol mixture (50 50) at room temperature. I. Quinones, G. Guiochon, Langmuir, 12 (1996) 5433 (Figs 1 and 2) and J. Zhu, A. Katti and G. Guiochon,. Chromatogr. 552 (1991) (Figs 7 and 8)71.

X empirical interaction energy parameter in the Fowler isotherm, 3... 

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